Finite Group Databasebeta

← #29888807

Subgroups — #29888807

Order 15616.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454109C211yesmaximal, characteristic, complemented
2#21454099C211yesmaximal, characteristic, complemented
3#21453760C211yesmaximal, characteristic, complemented
4#21453678C211yesmaximal, characteristic, complemented
5#21453570C211yesmaximal, characteristic, complemented
6#21453517C211yesmaximal, characteristic, complemented
7#21453471C211yesmaximal, characteristic, complemented
8#21453437C211yesmaximal, characteristic, complemented
9#21453078C211yesmaximal, characteristic, complemented
10#21453051C211yesmaximal, characteristic, complemented
11#21452994C211yesmaximal, characteristic, complemented
12#21452617C211yesmaximal, characteristic, complemented
13#21452563C211yesmaximal, characteristic, complemented
14#21452535C211yesmaximal, characteristic, complemented
15#21452532C211yesmaximal, characteristic, complemented
16#21452349C211yesmaximal, characteristic, complemented
17#21452223C211yesmaximal, characteristic, complemented
18#21452186C211yesmaximal, characteristic, complemented
19#21451774C211yesmaximal, characteristic, complemented
20#21451749C211yesmaximal, characteristic, complemented
21#21450079C211yesmaximal, characteristic, complemented
22#21449944C211yesmaximal, characteristic, complemented
23#21449560C211yesmaximal, characteristic, complemented
24#21449497C211yesmaximal, characteristic, complemented
25#21449423C211yesmaximal, characteristic, complemented
26#21449351C211yesmaximal, characteristic, complemented
27#21449204C211yesmaximal, characteristic, complemented
28#21448485C211yesmaximal, characteristic, complemented
29#21448411C211yesmaximal, characteristic, complemented
30C2×#16839637C211yesmaximal, characteristic, complemented
31C61×#2404C211yesmaximal, characteristic, complemented
32C24×Dic61C2211yescharacteristic
33C2×#14519770C2211yescharacteristic, complemented
34C2×#14519764C2211yescharacteristic
35C2×#14519760C2211yescharacteristic
36C2×#14519759C2211yescharacteristic, complemented
37C2×#14519758C2211yescharacteristic
38C2×#14519758C2211yescharacteristic
39C2×#14519754C2211yescharacteristic
40C2×#14519749C2211yescharacteristic
41C2×#14519749C2211yescharacteristic
42C2×#14519749C2211yescharacteristic
43C2×#14519749C2211yescharacteristic
44C2×#14519748C2211yescharacteristic
45C2×#14519746C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47C2×#14519736C2211yescharacteristic
48C22×C4⋊Dic61C2211yescharacteristic
49C22×C4⋊Dic61C2211yescharacteristic
50C22×C22⋊Dic61C2211yescharacteristic
51C61⋊#401C2211yescharacteristic, complemented
52#16839704C2211yescharacteristic, complemented
53#16839704C2211yescharacteristic, complemented
54#16839704C2211yescharacteristic, complemented
55#16839704C2211yescharacteristic, complemented
56#16839703C2211yescharacteristic, complemented
57#16839703C2211yescharacteristic, complemented
58#16839702C2211yescharacteristic, complemented
59#16839702C2211yescharacteristic, complemented
60#16839698C2211yescharacteristic, complemented
61#16839696C2211yescharacteristic, complemented
62#16839696C2211yescharacteristic, complemented
63#16839694C2211yescharacteristic, complemented
64#16839691C2211yescharacteristic, complemented
65#16839690C2211yescharacteristic, complemented
66#16839690C2211yescharacteristic, complemented
67#16839690C2211yescharacteristic, complemented
68#16839689C2211yescharacteristic, complemented
69#16839687C2211yescharacteristic
70#16839687C2211yescharacteristic, complemented
71#16839687C2211yescharacteristic, complemented
72#16839685C2211yescharacteristic
73#16839685C2211yescharacteristic
74#16839685C2211yescharacteristic
75#16839685C2211yescharacteristic, complemented
76#16839685C2211yescharacteristic, complemented
77#16839683C2211yescharacteristic, complemented
78#16839681C2211yescharacteristic, complemented
79#16839678C2211yescharacteristic
80#16839678C2211yescharacteristic
81#16839678C2211yescharacteristic
82#16839678C2211yescharacteristic, complemented
83#16839678C2211yescharacteristic, complemented
84#16839677C2211yescharacteristic, complemented
85#16839676C2211yescharacteristic
86#16839676C2211yescharacteristic
87#16839676C2211yescharacteristic
88#16839676C2211yescharacteristic, complemented
89#16839675C2211yescharacteristic, complemented
90#16839674C2211yescharacteristic
91#16839674C2211yescharacteristic, complemented
92#16839673C2211yescharacteristic, complemented
93#16839670C2211yescharacteristic
94#16839670C2211yescharacteristic, complemented
95#16839669C2211yescharacteristic, complemented
96#16839669C2211yescharacteristic, complemented
97#16839666C2211yescharacteristic, complemented
98#16839665C2211yescharacteristic
99#16839665C2211yescharacteristic
100#16839665C2211yescharacteristic, complemented
101#16839665C2211yescharacteristic, complemented
102#16839662C2211yescharacteristic
103#16839662C2211yescharacteristic
104#16839659C2211yescharacteristic, complemented
105#16839659C2211yescharacteristic, complemented
106#16839659C2211yescharacteristic, complemented
107#16839656C2211yescharacteristic
108#16839656C2211yescharacteristic
109#16839656C2211yescharacteristic
110#16839656C2211yescharacteristic
111#16839655C2211yescharacteristic, complemented
112#16839655C2211yescharacteristic, complemented
113#16839654C2211yescharacteristic, complemented
114#16839654C2211yescharacteristic, complemented
115#16839650C2211yescharacteristic
116#16839649C2211yescharacteristic, complemented
117#16839649C2211yescharacteristic, complemented
118#16839649C2211yescharacteristic, complemented
119#16839649C2211yescharacteristic, complemented
120#16839647C2211yescharacteristic, complemented
121#16839645C2211yescharacteristic, complemented
122#16839645C2211yescharacteristic, complemented
123#16839642C2211yescharacteristic
124#16839642C2211yescharacteristic
125#16839642C2211yescharacteristic
126#16839642C2211yescharacteristic
127#16839642C2211yescharacteristic
128#16839642C2211yescharacteristic
129#16839642C2211yescharacteristic
130#16839642C2211yescharacteristic
131#16839642C2211yescharacteristic
132#16839642C2211yescharacteristic
133#16839641C2211yescharacteristic
134#16839641C2211yescharacteristic, complemented
135#16839641C2211yescharacteristic, complemented
136#16839639C2211yescharacteristic
137#16839639C2211yescharacteristic
138#16839639C2211yescharacteristic
139#16839638C2211yescharacteristic
140#16839637C2211yescharacteristic
141#16839637C2211yescharacteristic
142#16839637C2211yescharacteristic
143#16839637C2211yescharacteristic
144#16839637C2211yescharacteristic
145#16839637C2211yescharacteristic
146#16839637C2211yescharacteristic
147#16839637C2211yescharacteristic
148#16839637C2211yescharacteristic
149#16839636C2211yescharacteristic, complemented
150#16839636C2211yescharacteristic, complemented
151#16839636C2211yescharacteristic, complemented
152#16839635C2211yescharacteristic
153#16839635C2211yescharacteristic, complemented
154#16839635C2211yescharacteristic, complemented
155#16839634C2211yescharacteristic
156#16839634C2211yescharacteristic
157#16839634C2211yescharacteristic
158#16839634C2211yescharacteristic
159#16839623C2211yescharacteristic
160#16839623C2211yescharacteristic
161#16839622C2211yescharacteristic, complemented
162#16839622C2211yescharacteristic, complemented
163#16839622C2211yescharacteristic, complemented
164#16839622C2211yescharacteristic, complemented
165#16839620C2211yescharacteristic
166#16839620C2211yescharacteristic
167#16839620C2211yescharacteristic
168#16839618C2211yescharacteristic
169C22⋊C4×Dic61C2211yescharacteristic
170C2×#14519684C2211yescharacteristic
171C2×#14519684C2211yescharacteristic
172C22×#41×C61C2211yescharacteristic
173C2×#120×C61C2211yescharacteristic
174C2×#120×C61C2211yescharacteristic
175C22×C22⋊C4×C61C2211yescharacteristic
176C61×#393C2211yescharacteristic
177C61×#393C2211yescharacteristic
178C61×#392C2211yescharacteristic
179C61×#392C2211yescharacteristic
180C61×#386C2211yescharacteristic
181C61×#386C2211yescharacteristic
182C61×#386C2211yescharacteristic
183C61×#386C2211yescharacteristic
184C61×#386C2211yescharacteristic
185C61×#386C2211yescharacteristic
186C61×#381C2211yescharacteristic
187C22×Dic122C2311yescharacteristic
188C22×C22⋊D61C2311yescharacteristic
189C22×C22⋊D61C2311yescharacteristic
190C22×C22⋊D61C2311yescharacteristic
191C22×C22⋊D61C2311yescharacteristic
192C22×C22⋊D61C2311yescharacteristic
193C23×Dic61—42no—
194C23×Dic61—42no—
195C23×Dic61—42no—
196C23×Dic61C2311yescharacteristic
197C23×Dic61C2311yescharacteristic
198C23×Dic61C2311yescharacteristic
199C23×Dic61C2311yescharacteristic
200C23×Dic61C2311yescharacteristic
201C23×Dic61C2311yescharacteristic
202C23×Dic61C2311yescharacteristic
203C23×Dic61C2311yescharacteristic
204C22×C4×D61C2311yescharacteristic
205#14519770—42no—
206#14519764—42no—
207#14519760—24no—
208#14519759—42no—
209#14519758—42no—
210#14519758—42no—
211#14519754—42no—
212#14519749—42no—
213#14519749—42no—
214#14519749—42no—
215#14519749—42no—
216#14519748—42no—
217#14519746—42no—
218#14519737—42no—
219#14519736—42no—
220C2×C4⋊Dic61—42no—
221C2×C4⋊Dic61—42no—
222C2×C4⋊Dic61C2311yescharacteristic
223C2×C4⋊Dic61C2311yescharacteristic
224C2×C4⋊Dic61C2311yescharacteristic
225C2×C4⋊Dic61C2311yescharacteristic
226C2×C4⋊Dic61C2311yescharacteristic
227C2×C4⋊Dic61C2311yescharacteristic
228C2×C4⋊Dic61C2311yescharacteristic
229C2×C4⋊Dic61C2311yescharacteristic
230C2×C4⋊Dic61C2311yescharacteristic
231C2×C4⋊Dic61C2311yescharacteristic
232C2×C4⋊Dic61C2311yescharacteristic
233C2×C4⋊Dic61C2311yescharacteristic
234C2×C4⋊Dic61C2311yescharacteristic
235C2×#11758196C2311yescharacteristic
236C2×#11758196C2311yescharacteristic
237C2×#11758196C2311yescharacteristic
238C2×#11758196C2311yescharacteristic
239C2×#11758196C2311yescharacteristic
240C2×#11758196C2311yescharacteristic
241C2×#11758196C2311yescharacteristic
242C2×#11758196C2311yescharacteristic
243C2×#11758196C2311yescharacteristic
244C2×#11758196C2311yescharacteristic
245C2×#11758196C2311yescharacteristic
246C2×#11758196C2311yescharacteristic
247C2×#11758196C2311yescharacteristic
248C2×#11758196C2311yescharacteristic
249C2×#11758196C2311yescharacteristic
250C2×C22⋊Dic61—42no—
251C2×C22⋊Dic61C2311yescharacteristic
252C2×C22⋊Dic61C2311yescharacteristic
253C2×C22⋊Dic61C2311yescharacteristic
254C2×C22⋊Dic61C2311yescharacteristic
255C2×C22⋊Dic61C2311yescharacteristic
256C2×C22⋊Dic61C2311yescharacteristic
257C2×C22⋊Dic61C2311yescharacteristic
258C2×C22⋊Dic61C2311yescharacteristic
259C2×C22⋊Dic61C2311yescharacteristic
260C2×C22⋊Dic61C2311yescharacteristic
261C2×C22⋊Dic61C2311yescharacteristic
262C2×C22⋊Dic61C2311yescharacteristic
263C2×C22⋊Dic61C2311yescharacteristic
264C2×C22⋊Dic61C2311yescharacteristic
265C2×C22⋊Dic61C2311yescharacteristic
266C2×C22⋊Dic61C2311yescharacteristic
267C2×C22⋊Dic61C2311yescharacteristic
268C2×C22⋊Dic61C2311yescharacteristic
269C2×C22⋊Dic61C2311yescharacteristic
270C2×C22⋊Dic61C2311yescharacteristic
271C2×C22⋊Dic61C2311yescharacteristic
272C2×C22⋊Dic61C2311yescharacteristic
273C2×C22⋊Dic61C2311yescharacteristic
274C2×C22⋊Dic61C2311yescharacteristic
275C2×C22⋊Dic61C2311yescharacteristic
276C2×C22⋊Dic61C2311yescharacteristic
277C2×C22⋊Dic61C2311yescharacteristic
278C2×#11758198C2311yescharacteristic
279C2×#11758198C2311yescharacteristic
280C2×#11758198C2311yescharacteristic
281C2×#11758198C2311yescharacteristic
282C2×#11758198C2311yescharacteristic
283C2×#11758198C2311yescharacteristic
284C2×#11758198C2311yescharacteristic
285C2×#11758198C2311yescharacteristic
286C2×#11758198C2311yescharacteristic
287C2×C4×Dic61C2311yescharacteristic
288C2×C4×Dic61C2311yescharacteristic
289C2×C4×Dic61C2311yescharacteristic
290C2×C4×Dic61C2311yescharacteristic
291C2×C4×Dic61C2311yescharacteristic
292#14519684C2311yescharacteristic
293#14519684C2311yescharacteristic
294#14519684C2311yescharacteristic
295#14519684C2311yescharacteristic
296#14519684C2311yescharacteristic
297#14519684C2311yescharacteristic
298#14519684C2311yescharacteristic
299#14519684C2311yescharacteristic
300#14519684C2311yescharacteristic
301#14519684C2311yescharacteristic
302#14519684C2311yescharacteristic
303#14519684C2311yescharacteristic
304#14519684C2311yescharacteristic
305#14519684C2311yescharacteristic
306#14519684C2311yescharacteristic
307#14519684C2311yescharacteristic
308#14519684C2311yescharacteristic
309#14519684C2311yescharacteristic
310#14519684C2311yescharacteristic
311#14519684C2311yescharacteristic
312#14519684C2311yescharacteristic
313#14519684C2311yescharacteristic
314#14519684C2311yescharacteristic
315#14519684C2311yescharacteristic
316#14519684C2311yescharacteristic
317#14519684C2311yescharacteristic
318#14519684C2311yescharacteristic
319#14519684C2311yescharacteristic
320#14519684C2311yescharacteristic
321#14519684C2311yescharacteristic
322#14519684C2311yescharacteristic
323#14519684C2311yescharacteristic
324#14519684C2311yescharacteristic
325#14519684C2311yescharacteristic
326#14519684C2311yescharacteristic
327#14519684C2311yescharacteristic
328C25×C61C2311yescharacteristic
329C2×#41×C61—24no—
330C2×#41×C61—42no—
331C2×#41×C61—42no—
332C22×Q8×C61C2311yescharacteristic
333C22×D4×C61C2311yescharacteristic
334C22×D4×C61C2311yescharacteristic
335C22×D4×C61C2311yescharacteristic
336C22×D4×C61C2311yescharacteristic
337C22×D4×C61C2311yescharacteristic
338C22×D4×C61C2311yescharacteristic
339C22×D4×C61C2311yescharacteristic
340C23×C4×C61C2311yescharacteristic
341C23×C4×C61C2311yescharacteristic
342C23×C4×C61C2311yescharacteristic
343C23×C4×C61C2311yescharacteristic
344#120×C61—42no—
345#120×C61—42no—
346C2×C22⋊C4×C61—24no—
347C2×C22⋊C4×C61C2311yescharacteristic
348C2×C22⋊C4×C61C2311yescharacteristic
349C2×C22⋊C4×C61C2311yescharacteristic
350C2×C22⋊C4×C61C2311yescharacteristic
351C2×C22⋊C4×C61C2311yescharacteristic
352C2×C22⋊C4×C61C2311yescharacteristic
353C2×C22⋊C4×C61C2311yescharacteristic
354C2×C22⋊C4×C61C2311yescharacteristic
355C2×C22⋊C4×C61C2311yescharacteristic
356C2×C22⋊C4×C61C2311yescharacteristic
357C2×C22⋊C4×C61C2311yescharacteristic
358C2×C22⋊C4×C61C2311yescharacteristic
359C2×C22⋊C4×C61C2311yescharacteristic
360C2×C22⋊C4×C61C2311yescharacteristic
361#95×C61C2311yescharacteristic
362#95×C61C2311yescharacteristic
363#95×C61C2311yescharacteristic
364#95×C61C2311yescharacteristic
365#95×C61C2311yescharacteristic
366#95×C61C2311yescharacteristic
367#95×C61C2311yescharacteristic
368#95×C61C2311yescharacteristic
369C24×C61—22no—
370C24×C61—22no—
371C24×C61—22no—
372C24×C61—22no—
373C24×C61—22no—
374C24×C61—41no—
375C24×C61—41no—
376C24×C61C2411yescharacteristic
377C24×C61C2411yescharacteristic
378C24×C61C2411yescharacteristic
379C24×C61C2411yescharacteristic
380C24×C61C2411yescharacteristic
381C23×D61C2411yescharacteristic
382#41×C61—416no—
383C2×Q8×C61—22no—
384C2×Q8×C61—41no—
385C2×Q8×C61—41no—
386C2×D4×C61—22no—
387C2×D4×C61—22no—
388C2×D4×C61—22no—
389C2×D4×C61—22no—
390C2×D4×C61—22no—
391C2×D4×C61—22no—
392C2×D4×C61—22no—
393C2×D4×C61—22no—
394C2×D4×C61—22no—
395C2×D4×C61—22no—
396C2×D4×C61—22no—
397C2×D4×C61—41no—
398C2×D4×C61—41no—
399C2×D4×C61—41no—
400C2×D4×C61—41no—
401C2×D4×C61—41no—
402C2×D4×C61—41no—
403C2×D4×C61—41no—
404C2×D4×C61—41no—
405C2×D4×C61—41no—
406C2×D4×C61—41no—
407C22×C4×C61—22no—
408C22×C4×C61—22no—
409C22×C4×C61—22no—
410C22×C4×C61—22no—
411C22×C4×C61—22no—
412C22×C4×C61—41no—
413C22×C4×C61—41no—
414C22×C4×C61—41no—
415C22×C4×C61—41no—
416C22×C4×C61—41no—
417C22×C4×C61—41no—
418C22×C4×C61#4114yes—
419C22×C4×C61C2411yescharacteristic
420C22×C4×C61C2411yescharacteristic
421C22×C4×C61C2411yescharacteristic
422C22×C4×C61C2411yescharacteristic
423C22×C4×C61C2411yescharacteristic
424C22×C4×C61C2411yescharacteristic
425C22×C4×C61C2411yescharacteristic
426C22×C4×C61C2411yescharacteristic
427C22×C4×C61C2411yescharacteristic
428C22×C4×C61C2411yescharacteristic
429C2×C22⋊D61—22no—
430C2×C22⋊D61—22no—
431C2×C22⋊D61—22no—
432C2×C22⋊D61—22no—
433C2×C22⋊D61—22no—
434C2×C22⋊D61—22no—
435C2×C22⋊D61—41no—
436C2×C22⋊D61—41no—
437C2×C22⋊D61—41no—
438C2×C22⋊D61—41no—
439C2×C22⋊D61—41no—
440C2×C22⋊D61—41no—
441C2×C22⋊D61—41no—
442C2×C22⋊D61—41no—
443C2×C22⋊D61—41no—
444C22×Dic61—22no—
445C22×Dic61—22no—
446C22×Dic61—22no—
447C22×Dic61—22no—
448C22×Dic61—22no—
449C22×Dic61—22no—
450C22×Dic61—22no—
451C22×Dic61—22no—
452C22×Dic61—22no—
453C22×Dic61—41no—
454C22×Dic61—41no—
455C22×Dic61—41no—
456C22×Dic61—41no—
457C22×Dic61—41no—
458C22×Dic61—41no—
459C22×Dic61—41no—
460C22×Dic61—41no—
461C22×Dic61—41no—
462C22×Dic61—41no—
463C22×Dic61—41no—
464C22×Dic61—41no—
465C22×Dic61—41no—
466C22×Dic61—41no—
467C22×Dic61—41no—
468C22×Dic61—416no—
469C22×Dic61C2411yescharacteristic
470C22×Dic61C2411yescharacteristic
471C22×Dic61C2411yescharacteristic
472C22×Dic61C2411yescharacteristic
473C22×Dic61C2411yescharacteristic
474C22×Dic61C2411yescharacteristic
475C22×Dic61C2411yescharacteristic
476C22×Dic61C2411yescharacteristic
477C22×Dic61C2411yescharacteristic
478C22×Dic61C2411yescharacteristic
479C22×Dic61C2411yescharacteristic
480C22×Dic61C2411yescharacteristic
481C22×Dic61C2411yescharacteristic
482C22×Dic61C2411yescharacteristic
483C22×Dic61C2411yescharacteristic
484C2×C4×D61—41no—
485C2×C4×D61—41no—
486C2×C4×D61—41no—
487C2×Dic122—41no—
488C2×Dic122—41no—
489C2×Dic122—41no—
490C22⋊C4×C61—22no—
491C22⋊C4×C61—22no—
492C22⋊C4×C61—22no—
493C22⋊C4×C61—22no—
494C22⋊C4×C61—22no—
495C22⋊C4×C61—22no—
496C22⋊C4×C61—41no—
497C22⋊C4×C61—41no—
498C22⋊C4×C61—41no—
499C22⋊C4×C61—41no—
500C22⋊C4×C61—41no—
501C22⋊C4×C61—41no—
502C22⋊C4×C61—41no—
503C22⋊C4×C61—41no—
504C22⋊Dic61—22no—
505C22⋊Dic61—22no—
506C22⋊Dic61—22no—
507C22⋊Dic61—22no—
508C22⋊Dic61—22no—
509C22⋊Dic61—22no—
510C22⋊Dic61—22no—
511C22⋊Dic61—22no—
512C22⋊Dic61—41no—
513C22⋊Dic61—41no—
514C22⋊Dic61—41no—
515C22⋊Dic61—41no—
516C22⋊Dic61—41no—
517C22⋊Dic61—41no—
518C22⋊Dic61—41no—
519C22⋊Dic61—41no—
520C22⋊Dic61—41no—
521C22⋊Dic61—41no—
522C22⋊Dic61—41no—
523C22⋊Dic61—41no—
524C22⋊Dic61—41no—
525C22⋊Dic61—41no—
526C22⋊Dic61—41no—
527C22⋊Dic61—41no—
528C22⋊Dic61—41no—
529C22⋊Dic61—41no—
530C22⋊Dic61—41no—
531#11758198—22no—
532#11758198—22no—
533#11758198—41no—
534#11758198—41no—
535#11758198—41no—
536#11758198—41no—
537#11758198—41no—
538#11758198—41no—
539#11758198—41no—
540C4⋊Dic61—22no—
541C4⋊Dic61—22no—
542C4⋊Dic61—41no—
543C4⋊Dic61—41no—
544C4⋊Dic61—41no—
545C4⋊Dic61—41no—
546C4⋊Dic61—41no—
547C4⋊Dic61—41no—
548C4⋊Dic61—41no—
549C4⋊Dic61—41no—
550C4⋊Dic61—41no—
551C4⋊Dic61—41no—
552C4⋊Dic61—41no—
553#11758196—22no—
554#11758196—22no—
555#11758196—22no—
556#11758196—22no—
557#11758196—41no—
558#11758196—41no—
559#11758196—41no—
560#11758196—41no—
561#11758196—41no—
562#11758196—41no—
563#11758196—41no—
564#11758196—41no—
565#11758196—41no—
566#11758196—41no—
567#11758196—41no—
568C4×Dic61—41no—
569C4×Dic61—41no—
570C4×Dic61—41no—
571C4×Dic61—41no—
572C4×Dic61—41no—
573C23×C61—21no—
574C23×C61—21no—
575C23×C61—21no—
576C23×C61—21no—
577C23×C61—28no—
578C23×C61—21no—
579C23×C61—21no—
580C23×C61—21no—
581C23×C61—21no—
582C23×C61—21no—
583C23×C61—21no—
584C23×C61—21no—
585C23×C61—21no—
586C23×C61—21no—
587C23×C61—21no—
588C23×C61—21no—
589C23×C61—21no—
590C23×C61—21no—
591C23×C61—21no—
592C23×C61—21no—
593C23×C61—21no—
594C23×C61—21no—
595C23×C61—21no—
596C23×C61—21no—
597C23×C61—21no—
598C23×C61—21no—
599C23×C61—21no—
600C23×C61—21no—
601C23×C61—21no—
602C23×C61—21no—
603C23×C61—21no—
604C23×C61—44no—
605C23×C61—44no—
606C23×C61—44no—
607C23×C61—44no—
608C23×C61—44no—
609C23×C61—44no—
610C23×C61C2×#4112yes—
611C23×C61H(5,𝔽2)12yes—
612C23×C61H(5,𝔽2)12yes—
613C23×C61H(5,𝔽2)12yes—
614C23×C612−1+412yes—
615C23×C61C2511yescharacteristic
616C22×D61—21no—
617C22×D61—21no—
618C22×D61—21no—
619C22×D61—21no—
620C22×D61—21no—
621C22×D61—21no—
622C22×D61—21no—
623Q8×C61—44no—
624D4×C61—44no—
625D4×C61—44no—
626D4×C61—44no—
627D4×C61—82no—
628D4×C61—82no—
629D4×C61—82no—
630D4×C61—82no—
631C2×C4×C61—28no—
632C2×C4×C61—21no—
633C2×C4×C61—21no—
634C2×C4×C61—21no—
635C2×C4×C61—21no—
636C2×C4×C61—21no—
637C2×C4×C61—21no—
638C2×C4×C61—21no—
639C2×C4×C61—21no—
640C2×C4×C61—21no—
641C2×C4×C61—21no—
642C2×C4×C61—21no—
643C2×C4×C61—21no—
644C2×C4×C61—21no—
645C2×C4×C61—21no—
646C2×C4×C61—21no—
647C2×C4×C61—21no—
648C2×C4×C61—21no—
649C2×C4×C61—21no—
650C2×C4×C61—21no—
651C2×C4×C61—21no—
652C2×C4×C61—21no—
653C2×C4×C61—21no—
654C2×C4×C61—21no—
655C2×C4×C61—21no—
656C2×C4×C61—21no—
657C2×C4×C61—21no—
658C2×C4×C61—21no—
659C2×C4×C61—21no—
660C2×C4×C61—44no—
661C2×C4×C61—44no—
662C2×C4×C61—44no—
663C2×C4×C61C2×#4112yes—
664C2×C4×C61C2×#4112yes—
665C22⋊D61—44no—
666C22⋊D61—82no—
667C22⋊D61—82no—
668C22⋊D61—82no—
669C22⋊D61—82no—
670C2×Dic61—21no—
671C2×Dic61—21no—
672C2×Dic61—21no—
673C2×Dic61—21no—
674C2×Dic61—21no—
675C2×Dic61—21no—
676C2×Dic61—21no—
677C2×Dic61—21no—
678C2×Dic61—21no—
679C2×Dic61—21no—
680C2×Dic61—21no—
681C2×Dic61—21no—
682C2×Dic61—21no—
683C2×Dic61—21no—
684C2×Dic61—21no—
685C2×Dic61—21no—
686C2×Dic61—21no—
687C2×Dic61—21no—
688C2×Dic61—21no—
689C2×Dic61—21no—
690C2×Dic61—21no—
691C2×Dic61—21no—
692C2×Dic61—21no—
693C2×Dic61—21no—
694C2×Dic61—21no—
695C2×Dic61—21no—
696C2×Dic61—21no—
697C2×Dic61—21no—
698C2×Dic61—21no—
699C2×Dic61—21no—
700C2×Dic61—21no—
701C2×Dic61—21no—
702C2×Dic61—21no—
703C2×Dic61—21no—
704C2×Dic61—21no—
705C2×Dic61—21no—
706C2×Dic61—21no—
707C2×Dic61—21no—
708C2×Dic61—21no—
709C2×Dic61—21no—
710C2×Dic61—21no—
711C2×Dic61—21no—
712C2×Dic61—21no—
713C2×Dic61—21no—
714C2×Dic61—44no—
715C2×Dic61—44no—
716C2×Dic61—44no—
717C2×Dic61—44no—
718C2×Dic61—44no—
719C2×Dic61—44no—
720C2×Dic61—82no—
721C2×Dic61—82no—
722C2×Dic61H(5,𝔽2)12yes—
723C4×D61—82no—
724Dic122—82no—
725#36791—611nomaximal, Sylow
726C22×C61—22no—
727C22×C61—22no—
728C22×C61—22no—
729C22×C61—22no—
730C22×C61—22no—
731C22×C61—22no—
732C22×C61—22no—
733C22×C61—22no—
734C22×C61—22no—
735C22×C61—22no—
736C22×C61—22no—
737C22×C61—22no—
738C22×C61—416no—
739C22×C61—41no—
740C22×C61—41no—
741C22×C61—41no—
742C22×C61—41no—
743C22×C61—41no—
744C22×C61—41no—
745C22×C61—41no—
746C22×C61—41no—
747C22×C61—41no—
748C22×C61—41no—
749C22×C61—41no—
750C22×C61—41no—
751C22×C61—41no—
752C22×C61—41no—
753C22×C61—41no—
754C22×C61—41no—
755C22×C61—41no—
756C22×C61—41no—
757C22×C61—41no—
758C22×C61—41no—
759C22×C61—41no—
760C22×C61—41no—
761C22×C61#53814yes—
762C22×C61C22×#4111yescharacteristic
763C22×C61C2×H(5,𝔽2)11yescharacteristic
764C22×C61C2×H(5,𝔽2)11yescharacteristic
765C22×C61C2×H(5,𝔽2)11yescharacteristic
766C22×C61C2×H(5,𝔽2)11yescharacteristic
767C22×C61C2×2−1+411yescharacteristic
768C22×C61#58511yescharacteristic
769C2×D61—41no—
770C2×D61—41no—
771C2×D61—41no—
772C2×D61—41no—
773C2×D61—41no—
774C2×D61—41no—
775C2×D61—41no—
776C4×C61—22no—
777C4×C61—22no—
778C4×C61—41no—
779C4×C61—41no—
780C4×C61—41no—
781C4×C61—41no—
782C4×C61—41no—
783C4×C61—41no—
784C4×C61—41no—
785C4×C61—41no—
786Dic61—22no—
787Dic61—41no—
788Dic61—41no—
789Dic61—41no—
790Dic61—41no—
791Dic61—41no—
792Dic61—41no—
793Dic61—41no—
794Dic61—41no—
795Dic61—41no—
796Dic61—41no—
797Dic61—41no—
798Dic61—41no—
799Dic61—41no—
800Dic61—41no—
801#2849—611no—
802#2847—611no—
803#2804—611no—
804#2797—611no—
805#2788—611no—
806#2784—611no—
807#2780—611no—
808#2778—611no—
809#2751—611no—
810#2750—611no—
811#2745—611no—
812#2714—611no—
813#2710—611no—
814#2708—611no—
815#2708—611no—
816#2695—611no—
817#2686—611no—
818#2682—611no—
819#2643—611no—
820#2639—611no—
821#2481—611no—
822#2472—611no—
823#2443—611no—
824#2438—611no—
825#2430—611no—
826#2424—611no—
827#2411—611no—
828#2404D6111yescharacteristic, complemented
829#2322—611no—
830#2311—611no—
831C2×#385—611no—
832C2×C61—24no—
833C2×C61—42no—
834C2×C61—42no—
835C2×C61—81no—
836C2×C61—81no—
837C2×C61C2×#53811yescharacteristic
838C2×C61#349211yescharacteristic
839C2×C61#350611yescharacteristic
840C2×C61#353211yescharacteristic
841C2×C61#353411yescharacteristic
842C2×C61#353511yescharacteristic
843C2×C61#353611yescharacteristic
844D61—81no—
845C22×#41C2×D6111yescharacteristic
846C24×C4—611no—
847C2×#126—611no—
848C2×#124—611no—
849C2×#123—611no—
850C2×#123—611no—
851C2×#123—611no—
852C2×#123—611no—
853C2×C22⋊Q8—611no—
854C2×#121—611no—
855C2×#121—611no—
856C2×#121—611no—
857C2×#121—611no—
858C2×#121—611no—
859C2×#120—611no—
860C2×#120C2×D6111yescharacteristic
861C2×#120C2×D6111yescharacteristic
862C2×C4×D4—611no—
863C2×#117—611no—
864C22×C4⋊C4—611no—
865C22×C4⋊C4—611no—
866C22×C22⋊C4—611no—
867C22×C22⋊C4C2×D6111yescharacteristic
868#401—611no—
869#400—611no—
870#400—611no—
871#400—611no—
872#400—611no—
873#400—611no—
874#400—611no—
875#400—611no—
876#400—611no—
877#399—611no—
878#398—611no—
879#398—611no—
880#398—611no—
881#397—611no—
882#397—611no—
883#397—611no—
884#397—611no—
885#397—611no—
886#397—611no—
887#397—611no—
888#397—611no—
889#396—611no—
890#396—611no—
891#396—611no—
892#396—611no—
893#396—611no—
894#395—611no—
895#395—611no—
896#394—611no—
897#394—611no—
898#394—611no—
899#394—611no—
900#394—611no—
901#394—611no—
902#394—611no—
903#394—611no—
904#394—611no—
905#394—611no—
906#393—611no—
907#393—611no—
908#393—611no—
909#393—611no—
910#393C2×D6111yescharacteristic
911#393C2×D6111yescharacteristic
912#392—611no—
913#392—611no—
914#392C2×D6111yescharacteristic
915#392C2×D6111yescharacteristic
916#391—611no—
917#391—611no—
918#391—611no—
919#390—611no—
920#390—611no—
921#390—611no—
922#390—611no—
923#390—611no—
924#390—611no—
925#389—611no—
926#389—611no—
927#389—611no—
928#388—611no—
929#388—611no—
930#388—611no—
931#388—611no—
932#388—611no—
933#388—611no—
934#388—611no—
935#388—611no—
936#388—611no—
937#387—611no—
938#387—611no—
939#387—611no—
940#387—611no—
941#387—611no—
942#387—611no—
943#387—611no—
944#386—611no—
945#386—611no—
946#386—611no—
947#386—611no—
948#386—611no—
949#386—611no—
950#386—611no—
951#386—611no—
952#386—611no—
953#386—611no—
954#386—611no—
955#386—611no—
956#386—611no—
957#386—611no—
958#386—611no—
959#386—611no—
960#386—611no—
961#386C2×D6111yescharacteristic
962#386C2×D6111yescharacteristic
963#386C2×D6111yescharacteristic
964#386C2×D6111yescharacteristic
965#386C2×D6111yescharacteristic
966#386C2×D6111yescharacteristic
967#385—611no—
968#385—611no—
969#385—611no—
970#385—611no—
971#385—611no—
972#385—611no—
973#385—611no—
974#385—611no—
975#385—611no—
976#385—611no—
977#385—611no—
978#385—611no—
979#385—611no—
980#385—611no—
981#385—611no—
982#385—611no—
983#385—611no—
984#385—611no—
985#385—611no—
986#381—611no—
987#381—611no—
988#381C2×D6111yescharacteristic
989#380—611no—
990#380—611no—
991#380—611no—
992#380—611no—
993#380—611no—
994#380—611no—
995#380—611no—
996#379—611no—
997C4×C22⋊C4—611no—
998C2×#95—611no—
999C2×#95—611no—
1000C61#3679111yescharacteristic, complemented, Sylow
1001C25C22×D6111yescharacteristic
1002C2×#41—24no—
1003C2×#41—42no—
1004C2×#41—42no—
1005C22×Q8—611no—
1006C22×Q8C22×D6111yescharacteristic
1007C22×D4—611no—
1008C22×D4—611no—
1009C22×D4—611no—
1010C22×D4—611no—
1011C22×D4—611no—
1012C22×D4C22×D6111yescharacteristic
1013C22×D4C22×D6111yescharacteristic
1014C22×D4C22×D6111yescharacteristic
1015C22×D4C22×D6111yescharacteristic
1016C22×D4C22×D6111yescharacteristic
1017C22×D4C22×D6111yescharacteristic
1018C22×D4C22×D6111yescharacteristic
1019C23×C4—611no—
1020C23×C4—611no—
1021C23×C4—611no—
1022C23×C4—611no—
1023C23×C4—611no—
1024C23×C4—611no—
1025C23×C4—611no—
1026C23×C4—611no—
1027C23×C4—611no—
1028C23×C4—2442no—
1029C23×C4—2442no—
1030C23×C4—2442no—
1031C23×C4C22×D6111yescharacteristic
1032C23×C4C22×D6111yescharacteristic
1033C23×C4C22×D6111yescharacteristic
1034C23×C4C22×D6111yescharacteristic
1035#126—2442no—
1036#124—2442no—
1037#123—1224no—
1038#123—2442no—
1039#123—2442no—
1040#123—2442no—
1041C22⋊Q8—2442no—
1042#121—2442no—
1043#121—2442no—
1044#121—2442no—
1045#121—2442no—
1046#121—2442no—
1047#120—42no—
1048#120—42no—
1049#120—2442no—
1050C4×D4—2442no—
1051#117—2442no—
1052C2×C4⋊C4—611no—
1053C2×C4⋊C4—611no—
1054C2×C4⋊C4—611no—
1055C2×C4⋊C4—611no—
1056C2×C4⋊C4—611no—
1057C2×C4⋊C4—611no—
1058C2×C4⋊C4—611no—
1059C2×C4⋊C4—611no—
1060C2×C4⋊C4—611no—
1061C2×C4⋊C4—611no—
1062C2×C4⋊C4—611no—
1063C2×C4⋊C4—611no—
1064C2×C4⋊C4—611no—
1065C2×C4⋊C4—611no—
1066C2×C4⋊C4—611no—
1067C2×C4⋊C4—611no—
1068C2×C4⋊C4—611no—
1069C2×C4⋊C4—611no—
1070C2×C4⋊C4—611no—
1071C2×C4⋊C4—611no—
1072C2×C4⋊C4—611no—
1073C2×C4⋊C4—611no—
1074C2×C4⋊C4—611no—
1075C2×C4⋊C4—611no—
1076C2×C4⋊C4—611no—
1077C2×C4⋊C4—611no—
1078C2×C4⋊C4—611no—
1079C2×C4⋊C4—611no—
1080C2×C4⋊C4—2442no—
1081C2×C4⋊C4—2442no—
1082C2×C22⋊C4—24no—
1083C2×C22⋊C4—611no—
1084C2×C22⋊C4—611no—
1085C2×C22⋊C4—611no—
1086C2×C22⋊C4—611no—
1087C2×C22⋊C4—611no—
1088C2×C22⋊C4—611no—
1089C2×C22⋊C4—611no—
1090C2×C22⋊C4—611no—
1091C2×C22⋊C4—611no—
1092C2×C22⋊C4—611no—
1093C2×C22⋊C4—611no—
1094C2×C22⋊C4—611no—
1095C2×C22⋊C4—611no—
1096C2×C22⋊C4—611no—
1097C2×C22⋊C4—611no—
1098C2×C22⋊C4—611no—
1099C2×C22⋊C4—611no—
1100C2×C22⋊C4—611no—
1101C2×C22⋊C4—611no—
1102C2×C22⋊C4—611no—
1103C2×C22⋊C4—611no—
1104C2×C22⋊C4—611no—
1105C2×C22⋊C4—611no—
1106C2×C22⋊C4—611no—
1107C2×C22⋊C4—611no—
1108C2×C22⋊C4—611no—
1109C2×C22⋊C4—611no—
1110C2×C22⋊C4—611no—
1111C2×C22⋊C4—611no—
1112C2×C22⋊C4—611no—
1113C2×C22⋊C4—611no—
1114C2×C22⋊C4—611no—
1115C2×C22⋊C4—611no—
1116C2×C22⋊C4—611no—
1117C2×C22⋊C4—611no—
1118C2×C22⋊C4—611no—
1119C2×C22⋊C4—2442no—
1120C2×C22⋊C4C22×D6111yescharacteristic
1121C2×C22⋊C4C22×D6111yescharacteristic
1122C2×C22⋊C4C22×D6111yescharacteristic
1123C2×C22⋊C4C22×D6111yescharacteristic
1124C2×C22⋊C4C22×D6111yescharacteristic
1125C2×C22⋊C4C22×D6111yescharacteristic
1126C2×C22⋊C4C22×D6111yescharacteristic
1127C2×C22⋊C4C22×D6111yescharacteristic
1128C2×C22⋊C4C22×D6111yescharacteristic
1129C2×C22⋊C4C22×D6111yescharacteristic
1130C2×C22⋊C4C22×D6111yescharacteristic
1131C2×C22⋊C4C22×D6111yescharacteristic
1132C2×C22⋊C4C22×D6111yescharacteristic
1133C2×C22⋊C4C22×D6111yescharacteristic
1134C2×C42—611no—
1135C2×C42—611no—
1136C2×C42—611no—
1137C2×C42—611no—
1138C2×C42—611no—
1139#95—611no—
1140#95—611no—
1141#95—611no—
1142#95—611no—
1143#95—611no—
1144#95—611no—
1145#95—611no—
1146#95—611no—
1147#95—611no—
1148#95—611no—
1149#95—611no—
1150#95—611no—
1151#95—611no—
1152#95—611no—
1153#95—611no—
1154#95—611no—
1155#95—611no—
1156#95—611no—
1157#95—611no—
1158#95—611no—
1159#95—611no—
1160#95—611no—
1161#95—611no—
1162#95—611no—
1163#95—611no—
1164#95—611no—
1165#95—611no—
1166#95—611no—
1167#95—611no—
1168#95—611no—
1169#95—611no—
1170#95—611no—
1171#95—611no—
1172#95—611no—
1173#95—611no—
1174#95—611no—
1175#95C22×D6111yescharacteristic
1176#95C22×D6111yescharacteristic
1177#95C22×D6111yescharacteristic
1178#95C22×D6111yescharacteristic
1179#95C22×D6111yescharacteristic
1180#95C22×D6111yescharacteristic
1181#95C22×D6111yescharacteristic
1182#95C22×D6111yescharacteristic
1183C24—22no—
1184C24—22no—
1185C24—22no—
1186C24—22no—
1187C24—22no—
1188C24—41no—
1189C24—41no—
1190C24—611no—
1191C24C23×D6111yescharacteristic
1192C24C23×D6111yescharacteristic
1193C24C23×D6111yescharacteristic
1194C24C23×D6111yescharacteristic
1195C24C23×D6111yescharacteristic
1196#41—416no—
1197C2×Q8—22no—
1198C2×Q8—41no—
1199C2×Q8—41no—
1200C2×Q8—2441no—
1201C2×Q8—2441no—
1202C2×Q8—2441no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—22no—
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—41no—
1215C2×D4—41no—
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—41no—
1224C2×D4—1222no—
1225C2×D4—1222no—
1226C2×D4—1222no—
1227C2×D4—1222no—
1228C2×D4—1222no—
1229C2×D4—1222no—
1230C2×D4—2441no—
1231C2×D4—2441no—
1232C2×D4—2441no—
1233C2×D4—2441no—
1234C2×D4—2441no—
1235C2×D4—2441no—
1236C2×D4—2441no—
1237C2×D4—2441no—
1238C2×D4—2441no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—41no—
1245C22×C4—41no—
1246C22×C4—41no—
1247C22×C4—41no—
1248C22×C4—41no—
1249C22×C4—41no—
1250C22×C4—611no—
1251C22×C4—611no—
1252C22×C4—611no—
1253C22×C4—611no—
1254C22×C4—611no—
1255C22×C4—611no—
1256C22×C4—611no—
1257C22×C4—611no—
1258C22×C4—611no—
1259C22×C4—611no—
1260C22×C4—611no—
1261C22×C4—611no—
1262C22×C4—611no—
1263C22×C4—611no—
1264C22×C4—611no—
1265C22×C4—1222no—
1266C22×C4—1222no—
1267C22×C4—1222no—
1268C22×C4—1222no—
1269C22×C4—1222no—
1270C22×C4—1222no—
1271C22×C4—1222no—
1272C22×C4—1222no—
1273C22×C4—1222no—
1274C22×C4—2441no—
1275C22×C4—2441no—
1276C22×C4—2441no—
1277C22×C4—2441no—
1278C22×C4—2441no—
1279C22×C4—2441no—
1280C22×C4—2441no—
1281C22×C4—2441no—
1282C22×C4—2441no—
1283C22×C4—2441no—
1284C22×C4—2441no—
1285C22×C4—2441no—
1286C22×C4—2441no—
1287C22×C4—2441no—
1288C22×C4—2441no—
1289C22×C4—2441no—
1290C22×C4—2441no—
1291C22×C4—2441no—
1292C22×C4—24416no—
1293C22×C4#1175822414yes—
1294C22×C4C23×D6111yescharacteristic
1295C22×C4C23×D6111yescharacteristic
1296C22×C4C23×D6111yescharacteristic
1297C22×C4C23×D6111yescharacteristic
1298C22×C4C23×D6111yescharacteristic
1299C22×C4C23×D6111yescharacteristic
1300C22×C4C23×D6111yescharacteristic
1301C22×C4C23×D6111yescharacteristic
1302C22×C4C23×D6111yescharacteristic
1303C22×C4C23×D6111yescharacteristic
1304C4⋊C4—1222no—
1305C4⋊C4—1222no—
1306C4⋊C4—1222no—
1307C4⋊C4—1222no—
1308C4⋊C4—1222no—
1309C4⋊C4—1222no—
1310C4⋊C4—2441no—
1311C4⋊C4—2441no—
1312C4⋊C4—2441no—
1313C4⋊C4—2441no—
1314C4⋊C4—2441no—
1315C4⋊C4—2441no—
1316C4⋊C4—2441no—
1317C4⋊C4—2441no—
1318C4⋊C4—2441no—
1319C4⋊C4—2441no—
1320C4⋊C4—2441no—
1321C4⋊C4—2441no—
1322C4⋊C4—2441no—
1323C4⋊C4—2441no—
1324C4⋊C4—2441no—
1325C4⋊C4—2441no—
1326C4⋊C4—2441no—
1327C4⋊C4—2441no—
1328C4⋊C4—2441no—
1329C4⋊C4—2441no—
1330C4⋊C4—2441no—
1331C4⋊C4—2441no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—41no—
1346C22⋊C4—1222no—
1347C22⋊C4—1222no—
1348C22⋊C4—1222no—
1349C22⋊C4—1222no—
1350C22⋊C4—1222no—
1351C22⋊C4—1222no—
1352C22⋊C4—1222no—
1353C22⋊C4—1222no—
1354C22⋊C4—1222no—
1355C22⋊C4—1222no—
1356C22⋊C4—2441no—
1357C22⋊C4—2441no—
1358C22⋊C4—2441no—
1359C22⋊C4—2441no—
1360C22⋊C4—2441no—
1361C22⋊C4—2441no—
1362C22⋊C4—2441no—
1363C22⋊C4—2441no—
1364C22⋊C4—2441no—
1365C22⋊C4—2441no—
1366C22⋊C4—2441no—
1367C22⋊C4—2441no—
1368C22⋊C4—2441no—
1369C22⋊C4—2441no—
1370C22⋊C4—2441no—
1371C22⋊C4—2441no—
1372C22⋊C4—2441no—
1373C22⋊C4—2441no—
1374C22⋊C4—2441no—
1375C22⋊C4—2441no—
1376C22⋊C4—2441no—
1377C22⋊C4—2441no—
1378C22⋊C4—2441no—
1379C22⋊C4—2441no—
1380C22⋊C4—2441no—
1381C22⋊C4—2441no—
1382C42—2441no—
1383C42—2441no—
1384C42—2441no—
1385C42—2441no—
1386C42—2441no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—28no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—44no—
1419C23—44no—
1420C23—44no—
1421C23—44no—
1422C23—44no—
1423C23—44no—
1424C23—1221no—
1425C23—1221no—
1426C23—1221no—
1427C23—1221no—
1428C23—1221no—
1429C23—1221no—
1430C23—1221no—
1431C23C2×#1175822412yes—
1432C23#1451982212yes—
1433C23#1451982212yes—
1434C23#1451982312yes—
1435C23#1451982412yes—
1436C23C24×D6111yescharacteristic
1437Q8—44no—
1438Q8—4882no—
1439D4—44no—
1440D4—44no—
1441D4—44no—
1442D4—82no—
1443D4—82no—
1444D4—82no—
1445D4—82no—
1446D4—4882no—
1447D4—4882no—
1448D4—4882no—
1449D4—4882no—
1450D4—2444no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—28no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—44no—
1481C2×C4—44no—
1482C2×C4—44no—
1483C2×C4—612no—
1484C2×C4—1221no—
1485C2×C4—1221no—
1486C2×C4—1221no—
1487C2×C4—1221no—
1488C2×C4—1221no—
1489C2×C4—1221no—
1490C2×C4—1221no—
1491C2×C4—1221no—
1492C2×C4—1221no—
1493C2×C4—1221no—
1494C2×C4—1221no—
1495C2×C4—1221no—
1496C2×C4—1221no—
1497C2×C4—1221no—
1498C2×C4—1221no—
1499C2×C4—1221no—
1500C2×C4—1221no—
1501C2×C4—1221no—
1502C2×C4—1221no—
1503C2×C4—1221no—
1504C2×C4—1221no—
1505C2×C4—1221no—
1506C2×C4—1221no—
1507C2×C4—1221no—
1508C2×C4—1221no—
1509C2×C4—1221no—
1510C2×C4—1221no—
1511C2×C4—1221no—
1512C2×C4—1221no—
1513C2×C4—1221no—
1514C2×C4—1221no—
1515C2×C4—1221no—
1516C2×C4—1221no—
1517C2×C4—1221no—
1518C2×C4—1221no—
1519C2×C4—1221no—
1520C2×C4—1221no—
1521C2×C4—1221no—
1522C2×C4—1221no—
1523C2×C4—1221no—
1524C2×C4—1221no—
1525C2×C4—1221no—
1526C2×C4—1221no—
1527C2×C4—1221no—
1528C2×C4—4882no—
1529C2×C4—4882no—
1530C2×C4—4882no—
1531C2×C4—2444no—
1532C2×C4—2444no—
1533C2×C4—2444no—
1534C2×C4—2444no—
1535C2×C4—2444no—
1536C2×C4—2444no—
1537C2×C4C2×#1175822412yes—
1538C2×C4C2×#1175822412yes—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—416no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—2441no—
1575C22—2441no—
1576C22—2441no—
1577C22—2441no—
1578C22—2441no—
1579C22—2441no—
1580C22—2441no—
1581C22#1684034714yes—
1582C22C22×#1175822411yescharacteristic
1583C22H(5,𝔽2)×D6111yescharacteristic
1584C22C2×#1451982211yescharacteristic
1585C22C2×#1451982211yescharacteristic
1586C22C2×#1451982311yescharacteristic
1587C22C2×#1451982411yescharacteristic
1588C22#1684059711yescharacteristic
1589C4—22no—
1590C4—22no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—1222no—
1600C4—2441no—
1601C4—2441no—
1602C4—2441no—
1603C4—2441no—
1604C4—2441no—
1605C4—2441no—
1606C4—2441no—
1607C4—2441no—
1608C4—2441no—
1609C4—2441no—
1610C4—2441no—
1611C4—2441no—
1612C4—2441no—
1613C4—2441no—
1614C2—24no—
1615C2—42no—
1616C2—42no—
1617C2—81no—
1618C2—81no—
1619C2—4881no—
1620C2C2×#1684034711yescharacteristic
1621C2#2145952511yescharacteristic
1622C2#2145967011yescharacteristic
1623C2#2145996811yescharacteristic
1624C2#2146000511yescharacteristic
1625C2#2146001611yescharacteristic
1626C2#2146003411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2404C2
hypercenter#2404D61
hypocenterC61#36791
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2404

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21454109C2semidirect
2. #21454099C2semidirect
3. #21453760C2semidirect
4. #21453678C2semidirect
5. #21453570C2semidirect
6. #21453517C2semidirect
7. #21453471C2semidirect
8. #21453437C2semidirect
9. #21453078C2semidirect
10. #21453051C2semidirect
11. #21452994C2semidirect
12. #21452617C2semidirect
13. #21452563C2semidirect
14. #21452535C2semidirect
15. #21452532C2semidirect
16. #21452349C2semidirect
17. #21452223C2semidirect
18. #21452186C2semidirect
19. #21451774C2semidirect
20. #21451749C2semidirect
21. #21450079C2semidirect
22. #21449944C2semidirect
23. #21449560C2semidirect
24. #21449497C2semidirect
25. #21449423C2semidirect
26. #21449351C2semidirect
27. #21449204C2semidirect
28. #21448485C2semidirect
29. #21448411C2semidirect
30. C2×#16839637C2semidirect
31. C61×#2404C2semidirect
33. C2×#14519770C22semidirect
36. C2×#14519759C22semidirect
51. C61⋊#401C22semidirect
52. #16839704C22semidirect
53. #16839704C22semidirect
54. #16839704C22semidirect
55. #16839704C22semidirect
56. #16839703C22semidirect
57. #16839703C22semidirect
58. #16839702C22semidirect
59. #16839702C22semidirect
60. #16839698C22semidirect
61. #16839696C22semidirect
62. #16839696C22semidirect
63. #16839694C22semidirect
64. #16839691C22semidirect
65. #16839690C22semidirect
66. #16839690C22semidirect
67. #16839690C22semidirect
68. #16839689C22semidirect
70. #16839687C22semidirect
71. #16839687C22semidirect
75. #16839685C22semidirect
76. #16839685C22semidirect
77. #16839683C22semidirect
78. #16839681C22semidirect
82. #16839678C22semidirect
83. #16839678C22semidirect
84. #16839677C22semidirect
88. #16839676C22semidirect
89. #16839675C22semidirect
91. #16839674C22semidirect
92. #16839673C22semidirect
94. #16839670C22semidirect
95. #16839669C22semidirect
96. #16839669C22semidirect
97. #16839666C22semidirect
100. #16839665C22semidirect
101. #16839665C22semidirect
104. #16839659C22semidirect
105. #16839659C22semidirect
106. #16839659C22semidirect
111. #16839655C22semidirect
112. #16839655C22semidirect
113. #16839654C22semidirect
114. #16839654C22semidirect
116. #16839649C22semidirect
117. #16839649C22semidirect
118. #16839649C22semidirect
119. #16839649C22semidirect
120. #16839647C22semidirect
121. #16839645C22semidirect
122. #16839645C22semidirect
134. #16839641C22semidirect
135. #16839641C22semidirect
149. #16839636C22semidirect
150. #16839636C22semidirect
151. #16839636C22semidirect
153. #16839635C22semidirect
154. #16839635C22semidirect
161. #16839622C22semidirect
162. #16839622C22semidirect
163. #16839622C22semidirect
164. #16839622C22semidirect
828. #2404D61semidirect
1000. C61#36791semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214541092
#214540992
#214537602
#214536782
#214535702
#214535172
#214534712
#214534372
#214530782
#214530512
#214529942
#214526172
#214525632
#214525352
#214525322
#214523492
#214522232
#214521862
#214517742
#214517492
#214500792
#214499442
#214495602
#214494972
#214494232
#214493512
#214492042
#214484852
#214484112
C2×#168396372
C61×#24042
#3679161