Finite Group Databasebeta

← #29887963

Subgroups — #29887963

Order 15616.

1482 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454168C211yesmaximal, characteristic
2#21454126C211yesmaximal, characteristic
3#21453742C211yesmaximal, characteristic, complemented
4#21453733C211yesmaximal, characteristic, complemented
5#21453640C211yesmaximal, characteristic, complemented
6#21453636C211yesmaximal, characteristic, complemented
7#21453575C211yesmaximal, characteristic, complemented
8#21453574C211yesmaximal, characteristic, complemented
9#21453406C211yesmaximal, characteristic, complemented
10#21453403C211yesmaximal, characteristic, complemented
11#21453272C211yesmaximal, characteristic, complemented
12#21453264C211yesmaximal, characteristic, complemented
13#21453165C211yesmaximal, characteristic, complemented
14#21452691C211yesmaximal, characteristic, complemented
15#21452683C211yesmaximal, characteristic, complemented
16#21452595C211yesmaximal, characteristic, complemented
17#21452593C211yesmaximal, characteristic, complemented
18#21451633C211yesmaximal, characteristic
19#21451631C211yesmaximal, characteristic
20#21450327C211yesmaximal, characteristic
21#21450323C211yesmaximal, characteristic
22#21450207C211yesmaximal, characteristic
23#21450207C211yesmaximal, characteristic
24#21450201C211yesmaximal, characteristic
25#21450201C211yesmaximal, characteristic
26#21449966C211yesmaximal, characteristic
27#21449955C211yesmaximal, characteristic
28#21448551C211yesmaximal, characteristic
29#21448548C211yesmaximal, characteristic
30#387×D61C211yesmaximal, characteristic
31C61×#2758C211yesmaximal, characteristic, complemented
32C2×#14519775C2211yescharacteristic
33C2×#14519768C2211yescharacteristic
34C2×#14519767C2211yescharacteristic
35C2×#14519767C2211yescharacteristic
36C2×#14519757C2211yescharacteristic
37C2×#14519753C2211yescharacteristic
38C2×C4⋊C4×D61C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C42×D61C2211yescharacteristic
41C61⋊#401C2211yescharacteristic
42C61⋊#401C2211yescharacteristic
43C61⋊#401C2211yescharacteristic
44C61⋊#401C2211yescharacteristic
45#16839704C2211yescharacteristic
46#16839704C2211yescharacteristic
47#16839704C2211yescharacteristic
48#16839704C2211yescharacteristic
49#16839704C2211yescharacteristic
50#16839704C2211yescharacteristic
51#16839703C2211yescharacteristic
52#16839703C2211yescharacteristic
53#16839703C2211yescharacteristic
54#16839703C2211yescharacteristic
55#16839703C2211yescharacteristic
56#16839703C2211yescharacteristic
57#16839702C2211yescharacteristic
58#16839702C2211yescharacteristic
59#16839702C2211yescharacteristic
60#16839701C2211yescharacteristic
61#16839700C2211yescharacteristic
62#16839700C2211yescharacteristic
63#16839700C2211yescharacteristic
64#16839696C2211yescharacteristic
65#16839696C2211yescharacteristic
66#16839696C2211yescharacteristic
67#16839696C2211yescharacteristic
68#16839696C2211yescharacteristic
69#16839696C2211yescharacteristic
70#16839696C2211yescharacteristic
71#16839696C2211yescharacteristic
72#16839695C2211yescharacteristic
73#16839695C2211yescharacteristic
74#16839694C2211yescharacteristic
75#16839694C2211yescharacteristic
76#16839693C2211yescharacteristic
77#16839693C2211yescharacteristic
78#16839693C2211yescharacteristic
79#16839693C2211yescharacteristic
80#16839683C2211yescharacteristic
81#16839682C2211yescharacteristic
82#16839681C2211yescharacteristic
83#16839669C2211yescharacteristic
84#16839668C2211yescharacteristic
85#16839666C2211yescharacteristic
86#16839666C2211yescharacteristic
87#16839660C2211yescharacteristic
88#16839660C2211yescharacteristic
89#16839659C2211yescharacteristic
90#16839659C2211yescharacteristic
91#16839659C2211yescharacteristic
92#16839659C2211yescharacteristic
93#16839659C2211yescharacteristic
94#16839659C2211yescharacteristic
95#16839659C2211yescharacteristic
96#16839658C2211yescharacteristic
97#16839657C2211yescharacteristic
98#16839657C2211yescharacteristic
99#16839657C2211yescharacteristic
100#16839649C2211yescharacteristic
101#16839649C2211yescharacteristic
102#16839649C2211yescharacteristic
103#16839648C2211yescharacteristic
104#16839648C2211yescharacteristic
105#16839647C2211yescharacteristic
106#16839647C2211yescharacteristic
107#16839647C2211yescharacteristic
108#16839647C2211yescharacteristic
109#16839647C2211yescharacteristic
110#16839646C2211yescharacteristic
111#16839646C2211yescharacteristic
112#16839646C2211yescharacteristic
113#16839646C2211yescharacteristic
114#16839646C2211yescharacteristic
115#16839646C2211yescharacteristic
116#16839645C2211yescharacteristic
117#16839645C2211yescharacteristic
118#16839645C2211yescharacteristic
119#16839645C2211yescharacteristic
120#16839645C2211yescharacteristic
121#16839645C2211yescharacteristic
122#16839645C2211yescharacteristic
123#16839644C2211yescharacteristic
124#16839644C2211yescharacteristic
125#16839644C2211yescharacteristic
126#16839644C2211yescharacteristic
127#16839644C2211yescharacteristic
128#16839644C2211yescharacteristic
129#16839644C2211yescharacteristic
130#16839644C2211yescharacteristic
131#16839643C2211yescharacteristic
132#16839643C2211yescharacteristic
133#16839643C2211yescharacteristic
134#16839643C2211yescharacteristic
135#16839643C2211yescharacteristic
136#16839636C2211yescharacteristic
137#16839636C2211yescharacteristic
138#16839636C2211yescharacteristic
139#16839636C2211yescharacteristic
140#16839636C2211yescharacteristic
141#16839636C2211yescharacteristic
142#16839633C2211yescharacteristic
143#16839633C2211yescharacteristic
144#16839633C2211yescharacteristic
145#16839633C2211yescharacteristic
146#16839633C2211yescharacteristic
147#16839633C2211yescharacteristic
148#16839631C2211yescharacteristic
149#16839629C2211yescharacteristic
150#16839629C2211yescharacteristic
151#16839627C2211yescharacteristic
152#16839626C2211yescharacteristic
153#16839626C2211yescharacteristic
154#16839624C2211yescharacteristic
155#16839624C2211yescharacteristic
156#16839624C2211yescharacteristic
157#16839624C2211yescharacteristic
158#16839621C2211yescharacteristic
159#16839621C2211yescharacteristic
160#16839621C2211yescharacteristic
161#16839621C2211yescharacteristic
162#16839621C2211yescharacteristic
163#16839621C2211yescharacteristic
164C4×#11758198C2211yescharacteristic
165C4×#11758198C2211yescharacteristic
166#16839609C2211yescharacteristic
167#16839609C2211yescharacteristic
168#95×D61C2211yescharacteristic
169#95×D61C2211yescharacteristic
170#95×D61C2211yescharacteristic
171#95×D61C2211yescharacteristic
172C61×#400C2211yescharacteristic
173C61×#400C2211yescharacteristic
174C61×#400C2211yescharacteristic
175C61×#400C2211yescharacteristic
176C61×#400C2211yescharacteristic
177C61×#395C2211yescharacteristic
178C61×#391C2211yescharacteristic
179C61×#391C2211yescharacteristic
180C61×#389C2211yescharacteristic
181C61×#387C2211yescharacteristic
182C61×#387C2211yescharacteristic
183C61×#387C2211yescharacteristic
184C61×#387C2211yescharacteristic
185C61×#383C2211yescharacteristic
186C61×#383C2211yescharacteristic
187C22×Dic122C2311yescharacteristic
188C22×C4×D61C2311yescharacteristic
189C22×C4×D61C2311yescharacteristic
190C22×C4×D61C2311yescharacteristic
191C22×C4×D61C2311yescharacteristic
192C22×C4×D61C2311yescharacteristic
193C22×C4×D61C2311yescharacteristic
194C22×C4×D61C2311yescharacteristic
195#14519775—42no—
196#14519768—42no—
197#14519767—42no—
198#14519767—42no—
199#14519757—24no—
200#14519753—24no—
201C2×C4⋊Dic61C2311yescharacteristic
202C2×C4⋊Dic61C2311yescharacteristic
203C2×C4⋊Dic61C2311yescharacteristic
204C2×C4⋊Dic61C2311yescharacteristic
205C2×C4⋊Dic61C2311yescharacteristic
206C2×C4⋊Dic61C2311yescharacteristic
207C2×C4⋊Dic61C2311yescharacteristic
208C2×C4⋊Dic61C2311yescharacteristic
209C2×C4⋊Dic61C2311yescharacteristic
210C2×C4⋊Dic61C2311yescharacteristic
211C2×C4⋊Dic61C2311yescharacteristic
212C2×#11758196C2311yescharacteristic
213C2×#11758196C2311yescharacteristic
214C2×#11758196C2311yescharacteristic
215C2×#11758196C2311yescharacteristic
216C2×#11758196C2311yescharacteristic
217C2×#11758196C2311yescharacteristic
218C2×#11758196C2311yescharacteristic
219C2×#11758196C2311yescharacteristic
220C2×#11758196C2311yescharacteristic
221C2×#11758196C2311yescharacteristic
222C2×#11758196C2311yescharacteristic
223C2×#11758196C2311yescharacteristic
224C2×#11758196C2311yescharacteristic
225C2×#11758196C2311yescharacteristic
226C2×#11758196C2311yescharacteristic
227C2×#11758196C2311yescharacteristic
228C2×#11758196C2311yescharacteristic
229C2×#11758196C2311yescharacteristic
230C2×#11758196C2311yescharacteristic
231C2×#11758196C2311yescharacteristic
232C2×#11758196C2311yescharacteristic
233C2×#11758196C2311yescharacteristic
234C2×#11758196C2311yescharacteristic
235C2×#11758196C2311yescharacteristic
236C2×#11758196C2311yescharacteristic
237C2×#11758196C2311yescharacteristic
238C2×#11758196C2311yescharacteristic
239C2×#11758196C2311yescharacteristic
240C2×#11758196C2311yescharacteristic
241C2×#11758196C2311yescharacteristic
242C4⋊C4×D61—24no—
243C4⋊C4×D61—42no—
244C2×#11758198C2311yescharacteristic
245C2×#11758198C2311yescharacteristic
246C2×#11758198C2311yescharacteristic
247C2×#11758198C2311yescharacteristic
248C2×#11758198C2311yescharacteristic
249C2×#11758198C2311yescharacteristic
250C2×#11758198C2311yescharacteristic
251C2×#11758198C2311yescharacteristic
252C2×C4×Dic61C2311yescharacteristic
253C2×C4×Dic61C2311yescharacteristic
254C2×C4×Dic61C2311yescharacteristic
255C2×C4×Dic61C2311yescharacteristic
256C2×C4×Dic61C2311yescharacteristic
257C2×C4×Dic61C2311yescharacteristic
258C2×C4×Dic61C2311yescharacteristic
259C2×C4×Dic61C2311yescharacteristic
260C2×C4×Dic61C2311yescharacteristic
261C42×D61—42no—
262#14519684C2311yescharacteristic
263#14519684C2311yescharacteristic
264#14519684C2311yescharacteristic
265#14519684C2311yescharacteristic
266#14519684C2311yescharacteristic
267#14519684C2311yescharacteristic
268#14519684C2311yescharacteristic
269#14519684C2311yescharacteristic
270#14519684C2311yescharacteristic
271#14519684C2311yescharacteristic
272#14519684C2311yescharacteristic
273#14519684C2311yescharacteristic
274#14519684C2311yescharacteristic
275#14519684C2311yescharacteristic
276#14519684C2311yescharacteristic
277#14519684C2311yescharacteristic
278#14519684C2311yescharacteristic
279#14519684C2311yescharacteristic
280#14519684C2311yescharacteristic
281#14519684C2311yescharacteristic
282#14519684C2311yescharacteristic
283#14519684C2311yescharacteristic
284#14519684C2311yescharacteristic
285#14519684C2311yescharacteristic
286#14519684C2311yescharacteristic
287#14519684C2311yescharacteristic
288#14519684C2311yescharacteristic
289#14519684C2311yescharacteristic
290#14519684C2311yescharacteristic
291#14519684C2311yescharacteristic
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
316C22×Q8×C61C2311yescharacteristic
317C2×C4⋊C4×C61C2311yescharacteristic
318C2×C4⋊C4×C61C2311yescharacteristic
319C2×C4⋊C4×C61C2311yescharacteristic
320C2×C4⋊C4×C61C2311yescharacteristic
321C2×C4⋊C4×C61C2311yescharacteristic
322C2×C4⋊C4×C61C2311yescharacteristic
323C2×C4⋊C4×C61C2311yescharacteristic
324C2×C4⋊C4×C61C2311yescharacteristic
325C2×C4⋊C4×C61C2311yescharacteristic
326C2×C42×C61C2311yescharacteristic
327C2×C42×C61C2311yescharacteristic
328C2×C42×C61C2311yescharacteristic
329#95×C61C2311yescharacteristic
330#95×C61C2311yescharacteristic
331#95×C61C2311yescharacteristic
332#95×C61C2311yescharacteristic
333#95×C61C2311yescharacteristic
334#95×C61C2311yescharacteristic
335#95×C61C2311yescharacteristic
336#95×C61C2311yescharacteristic
337#95×C61C2311yescharacteristic
338#95×C61C2311yescharacteristic
339#95×C61C2311yescharacteristic
340#95×C61C2311yescharacteristic
341#95×C61C2311yescharacteristic
342#95×C61C2311yescharacteristic
343#95×C61C2311yescharacteristic
344#95×C61C2311yescharacteristic
345#95×C61C2311yescharacteristic
346#95×C61C2311yescharacteristic
347#95×C61C2311yescharacteristic
348#95×C61C2311yescharacteristic
349#95×C61C2311yescharacteristic
350#95×C61C2311yescharacteristic
351C23×D61C2411yescharacteristic
352C2×Q8×C61—22no—
353C2×Q8×C61—41no—
354C2×Q8×C61—41no—
355C22×C4×C61C2411yescharacteristic
356C22×C4×C61C2411yescharacteristic
357C22×C4×C61C2411yescharacteristic
358C22×C4×C61C2411yescharacteristic
359C22×C4×C61C2411yescharacteristic
360C22×C4×C61C2411yescharacteristic
361C22×C4×C61C2411yescharacteristic
362C22×C4×C61C2411yescharacteristic
363C22×C4×C61C2411yescharacteristic
364C22×C4×C61C2411yescharacteristic
365C22×C4×C61C2411yescharacteristic
366C22×C4×C61C2411yescharacteristic
367C22×C4×C61C2411yescharacteristic
368C22×C4×C61C2411yescharacteristic
369C22×C4×C61C2411yescharacteristic
370C22×Dic61C2411yescharacteristic
371C22×Dic61C2411yescharacteristic
372C22×Dic61C2411yescharacteristic
373C22×Dic61C2411yescharacteristic
374C22×Dic61C2411yescharacteristic
375C22×Dic61C2411yescharacteristic
376C22×Dic61C2411yescharacteristic
377C22×Dic61C2411yescharacteristic
378C22×Dic61C2411yescharacteristic
379C22×Dic61C2411yescharacteristic
380C22×Dic61C2411yescharacteristic
381C22×Dic61C2411yescharacteristic
382C22×Dic61C2411yescharacteristic
383C22×Dic61C2411yescharacteristic
384C22×Dic61C2411yescharacteristic
385C2×C4×D61—22no—
386C2×C4×D61—22no—
387C2×C4×D61—22no—
388C2×C4×D61—22no—
389C2×C4×D61—22no—
390C2×C4×D61—22no—
391C2×C4×D61—22no—
392C2×C4×D61—22no—
393C2×C4×D61—22no—
394C2×C4×D61—22no—
395C2×C4×D61—41no—
396C2×C4×D61—41no—
397C2×C4×D61—41no—
398C2×C4×D61—41no—
399C2×C4×D61—41no—
400C2×C4×D61—41no—
401C2×C4×D61—41no—
402C2×C4×D61—41no—
403C2×C4×D61—41no—
404C2×C4×D61—41no—
405C2×C4×D61#4114yes—
406C2×Dic122—22no—
407C2×Dic122—41no—
408C2×Dic122—41no—
409C4⋊C4×C61—22no—
410C4⋊C4×C61—22no—
411C4⋊C4×C61—41no—
412C4⋊C4×C61—41no—
413C4⋊C4×C61—41no—
414C4⋊C4×C61—41no—
415C4⋊C4×C61—41no—
416C4⋊C4×C61—41no—
417C4⋊C4×C61—41no—
418C42×C61—41no—
419C42×C61—41no—
420C42×C61—41no—
421#11758198—22no—
422#11758198—22no—
423#11758198—22no—
424#11758198—22no—
425#11758198—22no—
426#11758198—22no—
427#11758198—22no—
428#11758198—22no—
429C4⋊Dic61—22no—
430C4⋊Dic61—22no—
431C4⋊Dic61—22no—
432C4⋊Dic61—22no—
433C4⋊Dic61—22no—
434C4⋊Dic61—22no—
435C4⋊Dic61—22no—
436C4⋊Dic61—41no—
437C4⋊Dic61—41no—
438C4⋊Dic61—41no—
439C4⋊Dic61—41no—
440#11758196—22no—
441#11758196—22no—
442#11758196—22no—
443#11758196—22no—
444#11758196—22no—
445#11758196—22no—
446#11758196—22no—
447#11758196—22no—
448#11758196—22no—
449#11758196—22no—
450#11758196—22no—
451#11758196—41no—
452#11758196—41no—
453#11758196—41no—
454#11758196—41no—
455#11758196—41no—
456#11758196—41no—
457#11758196—41no—
458#11758196—41no—
459#11758196—41no—
460#11758196—41no—
461#11758196—41no—
462#11758196—41no—
463#11758196—41no—
464#11758196—41no—
465#11758196—41no—
466#11758196—41no—
467#11758196—41no—
468#11758196—41no—
469#11758196—41no—
470C4×Dic61—22no—
471C4×Dic61—22no—
472C4×Dic61—41no—
473C4×Dic61—41no—
474C4×Dic61—41no—
475C4×Dic61—41no—
476C4×Dic61—41no—
477C4×Dic61—41no—
478C4×Dic61—41no—
479C23×C61C2511yescharacteristic
480C22×D61—21no—
481C22×D61—21no—
482C22×D61—21no—
483C22×D61—21no—
484C22×D61C2×#4112yes—
485C22×D612−1+412yes—
486C22×D612−1+412yes—
487Q8×C61—82no—
488C2×C4×C61—21no—
489C2×C4×C61—21no—
490C2×C4×C61—21no—
491C2×C4×C61—21no—
492C2×C4×C61—21no—
493C2×C4×C61—21no—
494C2×C4×C61—21no—
495C2×C4×C61—21no—
496C2×C4×C61—21no—
497C2×C4×C61—21no—
498C2×C4×C61—21no—
499C2×C4×C61—21no—
500C2×C4×C61—21no—
501C2×C4×C61—21no—
502C2×C4×C61—21no—
503C2×C4×C61—21no—
504C2×C4×C61—21no—
505C2×C4×C61—21no—
506C2×C4×C61—21no—
507C2×C4×C61—21no—
508C2×C4×C61—21no—
509C2×C4×C61—21no—
510C2×C4×C61—21no—
511C2×C4×C61—21no—
512C2×C4×C61—21no—
513C2×C4×C61—21no—
514C2×C4×C61—21no—
515C2×C4×C61—21no—
516C2×C4×C61—21no—
517C2×C4×C61—21no—
518C2×C4×C61—21no—
519C2×C4×C61—21no—
520C2×C4×C61—21no—
521C2×C4×C61—21no—
522C2×C4×C61—21no—
523C2×C4×C61—21no—
524C2×C4×C61—21no—
525C2×C4×C61—21no—
526C2×C4×C61—21no—
527C2×C4×C61—21no—
528C2×C4×C61—21no—
529C2×C4×C61—21no—
530C2×C4×C61—21no—
531C2×C4×C61—21no—
532C2×C4×C61C2×#4112yes—
533C2×Dic61—21no—
534C2×Dic61—21no—
535C2×Dic61—21no—
536C2×Dic61—21no—
537C2×Dic61—21no—
538C2×Dic61—21no—
539C2×Dic61—21no—
540C2×Dic61—21no—
541C2×Dic61—21no—
542C2×Dic61—21no—
543C2×Dic61—21no—
544C2×Dic61—21no—
545C2×Dic61—21no—
546C2×Dic61—21no—
547C2×Dic61—21no—
548C2×Dic61—21no—
549C2×Dic61—21no—
550C2×Dic61—21no—
551C2×Dic61—21no—
552C2×Dic61—21no—
553C2×Dic61—21no—
554C2×Dic61—21no—
555C2×Dic61—21no—
556C2×Dic61—21no—
557C2×Dic61—21no—
558C2×Dic61—21no—
559C2×Dic61—21no—
560C2×Dic61—21no—
561C2×Dic61—21no—
562C2×Dic61—21no—
563C2×Dic61—21no—
564C2×Dic61—21no—
565C2×Dic61—21no—
566C2×Dic61—21no—
567C2×Dic61—21no—
568C2×Dic61—21no—
569C2×Dic61—21no—
570C2×Dic61—21no—
571C2×Dic61—21no—
572C2×Dic61—21no—
573C2×Dic61—21no—
574C2×Dic61—21no—
575C2×Dic61C2×#4112yes—
576C2×Dic61H(5,𝔽2)12yes—
577C2×Dic612−1+412yes—
578C4×D61—44no—
579C4×D61—44no—
580C4×D61—44no—
581C4×D61—44no—
582C4×D61—44no—
583C4×D61—82no—
584C4×D61—82no—
585Dic122—82no—
586#36762—611nomaximal, Sylow
587C22×C61C22×#4111yescharacteristic
588C22×C61C2×H(5,𝔽2)11yescharacteristic
589C22×C61C2×2−1+411yescharacteristic
590C22×C61C2×2−1+411yescharacteristic
591C22×C61C2×2−1+411yescharacteristic
592C22×C61#58511yescharacteristic
593C22×C61#58511yescharacteristic
594C2×D61—22no—
595C2×D61—22no—
596C2×D61—22no—
597C2×D61—22no—
598C2×D61—22no—
599C2×D61—22no—
600C2×D61#54114yes—
601C4×C61—22no—
602C4×C61—41no—
603C4×C61—41no—
604C4×C61—41no—
605C4×C61—41no—
606C4×C61—41no—
607C4×C61—41no—
608C4×C61—41no—
609C4×C61—41no—
610C4×C61—41no—
611C4×C61—41no—
612C4×C61—41no—
613C4×C61—41no—
614C4×C61—41no—
615C4×C61—41no—
616Dic61—22no—
617Dic61—22no—
618Dic61—22no—
619Dic61—41no—
620Dic61—41no—
621Dic61—41no—
622Dic61—41no—
623Dic61—41no—
624Dic61—41no—
625Dic61—41no—
626Dic61—41no—
627Dic61—41no—
628Dic61—41no—
629Dic61—41no—
630Dic61—41no—
631#2857—611no—
632#2851—611no—
633#2802—611no—
634#2802—611no—
635#2794—611no—
636#2794—611no—
637#2789—611no—
638#2789—611no—
639#2776—611no—
640#2776—611no—
641#2766—611no—
642#2766—611no—
643#2758—611no—
644#2758D6111yescharacteristic, complemented
645#2719—611no—
646#2719—611no—
647#2713—611no—
648#2713—611no—
649#2627—611no—
650#2627—611no—
651#2505—611no—
652#2505—611no—
653#2493—611no—
654#2493—611no—
655#2493—611no—
656#2493—611no—
657#2473—611no—
658#2473—611no—
659#2329—611no—
660#2329—611no—
661C2×#387—611no—
662C2×C61C2×#54111yescharacteristic
663C2×C61#350511yescharacteristic
664C2×C61#350711yescharacteristic
665C2×C61#353511yescharacteristic
666C2×C61#353811yescharacteristic
667C2×C61#356311yescharacteristic
668C2×C61#356411yescharacteristic
669D61—24no—
670C2×C4⋊Q8—611no—
671C2×#125—611no—
672C2×#125—611no—
673C2×#125—611no—
674C2×C22⋊Q8—611no—
675C2×C22⋊Q8—611no—
676C22×C4⋊C4—611no—
677C22×C4⋊C4—611no—
678C22×C42—611no—
679#401—611no—
680#401—611no—
681#401—611no—
682#401—611no—
683#400—611no—
684#400—611no—
685#400—611no—
686#400—611no—
687#400—611no—
688#400—611no—
689#400—611no—
690#400—611no—
691#400—611no—
692#400—611no—
693#400—611no—
694#400—611no—
695#400—611no—
696#400—611no—
697#400—611no—
698#400—611no—
699#400—611no—
700#400—611no—
701#400—611no—
702#400C2×D6111yescharacteristic
703#400C2×D6111yescharacteristic
704#400C2×D6111yescharacteristic
705#400C2×D6111yescharacteristic
706#400C2×D6111yescharacteristic
707#398—611no—
708#398—611no—
709#398—611no—
710#398—611no—
711#398—611no—
712#398—611no—
713#398—611no—
714#398—611no—
715#398—611no—
716#398—611no—
717#398—611no—
718#398—611no—
719#398—611no—
720#398—611no—
721#398—611no—
722#398—611no—
723#395—611no—
724#395—611no—
725#395—611no—
726#395C2×D6111yescharacteristic
727#391—611no—
728#391—611no—
729#391—611no—
730#391—611no—
731#391C2×D6111yescharacteristic
732#391C2×D6111yescharacteristic
733#389—611no—
734#389—611no—
735#389—611no—
736#389—611no—
737#389—611no—
738#389—611no—
739#389—611no—
740#389—611no—
741#389—611no—
742#389—611no—
743#389—611no—
744#389—611no—
745#389—611no—
746#389C2×D6111yescharacteristic
747#387—611no—
748#387—611no—
749#387—611no—
750#387—611no—
751#387—611no—
752#387—611no—
753#387—611no—
754#387—611no—
755#387—611no—
756#387—611no—
757#387—611no—
758#387—611no—
759#387—611no—
760#387—611no—
761#387—611no—
762#387—611no—
763#387—611no—
764#387—611no—
765#387—611no—
766#387—611no—
767#387—611no—
768#387—611no—
769#387—611no—
770#387—611no—
771#387—611no—
772#387—611no—
773#387—611no—
774#387—611no—
775#387—611no—
776#387—611no—
777#387—611no—
778#387—611no—
779#387—611no—
780#387—611no—
781#387—611no—
782#387—611no—
783#387C2×D6111yescharacteristic
784#387C2×D6111yescharacteristic
785#387C2×D6111yescharacteristic
786#387C2×D6111yescharacteristic
787#385—611no—
788#385—611no—
789#385—611no—
790#385—611no—
791#385—611no—
792#385—611no—
793#385—611no—
794#385—611no—
795#385—611no—
796#385—611no—
797#385—611no—
798#385—611no—
799#384—611no—
800#383—611no—
801#383—611no—
802#383C2×D6111yescharacteristic
803#383C2×D6111yescharacteristic
804#382—611no—
805#382—611no—
806#382—611no—
807#381—611no—
808#381—611no—
809#381—611no—
810#381—611no—
811#380—611no—
812#380—611no—
813#380—611no—
814#380—611no—
815#380—611no—
816#380—611no—
817C4×C22⋊C4—611no—
818C4×C22⋊C4—611no—
819C4×C22⋊C4—611no—
820C4×C22⋊C4—611no—
821C2×#95—611no—
822C2×#95—611no—
823C2×#95—611no—
824C2×#95—611no—
825C61#3676211yescharacteristic, complemented, Sylow
826C22×Q8—611no—
827C22×Q8C22×D6111yescharacteristic
828C23×C4—611no—
829C23×C4—611no—
830C23×C4—611no—
831C23×C4—611no—
832C23×C4—611no—
833C23×C4—611no—
834C23×C4—611no—
835C4⋊Q8—2442no—
836#125—2442no—
837#125—2442no—
838#125—2442no—
839C22⋊Q8—1224no—
840C22⋊Q8—1224no—
841C2×C4⋊C4—611no—
842C2×C4⋊C4—611no—
843C2×C4⋊C4—611no—
844C2×C4⋊C4—611no—
845C2×C4⋊C4—611no—
846C2×C4⋊C4—611no—
847C2×C4⋊C4—611no—
848C2×C4⋊C4—611no—
849C2×C4⋊C4—611no—
850C2×C4⋊C4—611no—
851C2×C4⋊C4—611no—
852C2×C4⋊C4—611no—
853C2×C4⋊C4—611no—
854C2×C4⋊C4—611no—
855C2×C4⋊C4—611no—
856C2×C4⋊C4—611no—
857C2×C4⋊C4—611no—
858C2×C4⋊C4—611no—
859C2×C4⋊C4—611no—
860C2×C4⋊C4—611no—
861C2×C4⋊C4—611no—
862C2×C4⋊C4—611no—
863C2×C4⋊C4—611no—
864C2×C4⋊C4—611no—
865C2×C4⋊C4—611no—
866C2×C4⋊C4—611no—
867C2×C4⋊C4—611no—
868C2×C4⋊C4—611no—
869C2×C4⋊C4—611no—
870C2×C4⋊C4—611no—
871C2×C4⋊C4—611no—
872C2×C4⋊C4—611no—
873C2×C4⋊C4—611no—
874C2×C4⋊C4—611no—
875C2×C4⋊C4—611no—
876C2×C4⋊C4—611no—
877C2×C4⋊C4—611no—
878C2×C4⋊C4—611no—
879C2×C4⋊C4—611no—
880C2×C4⋊C4—611no—
881C2×C4⋊C4—611no—
882C2×C4⋊C4—1224no—
883C2×C4⋊C4—2442no—
884C2×C4⋊C4C22×D6111yescharacteristic
885C2×C4⋊C4C22×D6111yescharacteristic
886C2×C4⋊C4C22×D6111yescharacteristic
887C2×C4⋊C4C22×D6111yescharacteristic
888C2×C4⋊C4C22×D6111yescharacteristic
889C2×C4⋊C4C22×D6111yescharacteristic
890C2×C4⋊C4C22×D6111yescharacteristic
891C2×C4⋊C4C22×D6111yescharacteristic
892C2×C4⋊C4C22×D6111yescharacteristic
893C2×C22⋊C4—611no—
894C2×C22⋊C4—611no—
895C2×C22⋊C4—611no—
896C2×C22⋊C4—611no—
897C2×C22⋊C4—611no—
898C2×C22⋊C4—611no—
899C2×C22⋊C4—611no—
900C2×C22⋊C4—611no—
901C2×C42—611no—
902C2×C42—611no—
903C2×C42—611no—
904C2×C42—611no—
905C2×C42—611no—
906C2×C42—611no—
907C2×C42—611no—
908C2×C42—611no—
909C2×C42—611no—
910C2×C42—2442no—
911C2×C42C22×D6111yescharacteristic
912C2×C42C22×D6111yescharacteristic
913C2×C42C22×D6111yescharacteristic
914#95—611no—
915#95—611no—
916#95—611no—
917#95—611no—
918#95—611no—
919#95—611no—
920#95—611no—
921#95—611no—
922#95—611no—
923#95—611no—
924#95—611no—
925#95—611no—
926#95—611no—
927#95—611no—
928#95—611no—
929#95—611no—
930#95—611no—
931#95—611no—
932#95—611no—
933#95—611no—
934#95—611no—
935#95—611no—
936#95—611no—
937#95—611no—
938#95—611no—
939#95—611no—
940#95—611no—
941#95—611no—
942#95—611no—
943#95—611no—
944#95—611no—
945#95—611no—
946#95—611no—
947#95—611no—
948#95—611no—
949#95—611no—
950#95—611no—
951#95—611no—
952#95—611no—
953#95—611no—
954#95—611no—
955#95—611no—
956#95—611no—
957#95—611no—
958#95—611no—
959#95—611no—
960#95—611no—
961#95—611no—
962#95—611no—
963#95—611no—
964#95—611no—
965#95—611no—
966#95—611no—
967#95—611no—
968#95C22×D6111yescharacteristic
969#95C22×D6111yescharacteristic
970#95C22×D6111yescharacteristic
971#95C22×D6111yescharacteristic
972#95C22×D6111yescharacteristic
973#95C22×D6111yescharacteristic
974#95C22×D6111yescharacteristic
975#95C22×D6111yescharacteristic
976#95C22×D6111yescharacteristic
977#95C22×D6111yescharacteristic
978#95C22×D6111yescharacteristic
979#95C22×D6111yescharacteristic
980#95C22×D6111yescharacteristic
981#95C22×D6111yescharacteristic
982#95C22×D6111yescharacteristic
983#95C22×D6111yescharacteristic
984#95C22×D6111yescharacteristic
985#95C22×D6111yescharacteristic
986#95C22×D6111yescharacteristic
987#95C22×D6111yescharacteristic
988#95C22×D6111yescharacteristic
989#95C22×D6111yescharacteristic
990C24—611no—
991C2×Q8—22no—
992C2×Q8—41no—
993C2×Q8—41no—
994C2×Q8—1222no—
995C2×Q8—2441no—
996C2×Q8—2441no—
997C22×C4—611no—
998C22×C4—611no—
999C22×C4—611no—
1000C22×C4—614no—
1001C22×C4—611no—
1002C22×C4—611no—
1003C22×C4—611no—
1004C22×C4—611no—
1005C22×C4—611no—
1006C22×C4—611no—
1007C22×C4—611no—
1008C22×C4—611no—
1009C22×C4—611no—
1010C22×C4—611no—
1011C22×C4—611no—
1012C22×C4—611no—
1013C22×C4—1222no—
1014C22×C4—1222no—
1015C22×C4—1222no—
1016C22×C4—1222no—
1017C22×C4—1222no—
1018C22×C4—1222no—
1019C22×C4—1222no—
1020C22×C4—1222no—
1021C22×C4—1222no—
1022C22×C4—1222no—
1023C22×C4—2441no—
1024C22×C4—2441no—
1025C22×C4—2441no—
1026C22×C4—2441no—
1027C22×C4—2441no—
1028C22×C4—2441no—
1029C22×C4—2441no—
1030C22×C4—2441no—
1031C22×C4—2441no—
1032C22×C4—2441no—
1033C22×C4C23×D6111yescharacteristic
1034C22×C4C23×D6111yescharacteristic
1035C22×C4C23×D6111yescharacteristic
1036C22×C4C23×D6111yescharacteristic
1037C22×C4C23×D6111yescharacteristic
1038C22×C4C23×D6111yescharacteristic
1039C22×C4C23×D6111yescharacteristic
1040C22×C4C23×D6111yescharacteristic
1041C22×C4C23×D6111yescharacteristic
1042C22×C4C23×D6111yescharacteristic
1043C22×C4C23×D6111yescharacteristic
1044C22×C4C23×D6111yescharacteristic
1045C22×C4C23×D6111yescharacteristic
1046C22×C4C23×D6111yescharacteristic
1047C22×C4C23×D6111yescharacteristic
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—1222no—
1058C4⋊C4—1222no—
1059C4⋊C4—1222no—
1060C4⋊C4—1222no—
1061C4⋊C4—1222no—
1062C4⋊C4—1222no—
1063C4⋊C4—1222no—
1064C4⋊C4—1222no—
1065C4⋊C4—1222no—
1066C4⋊C4—1222no—
1067C4⋊C4—1222no—
1068C4⋊C4—1222no—
1069C4⋊C4—1222no—
1070C4⋊C4—1222no—
1071C4⋊C4—1222no—
1072C4⋊C4—1222no—
1073C4⋊C4—1222no—
1074C4⋊C4—1222no—
1075C4⋊C4—2441no—
1076C4⋊C4—2441no—
1077C4⋊C4—2441no—
1078C4⋊C4—2441no—
1079C4⋊C4—2441no—
1080C4⋊C4—2441no—
1081C4⋊C4—2441no—
1082C4⋊C4—2441no—
1083C4⋊C4—2441no—
1084C4⋊C4—2441no—
1085C4⋊C4—2441no—
1086C4⋊C4—2441no—
1087C4⋊C4—2441no—
1088C4⋊C4—2441no—
1089C4⋊C4—2441no—
1090C4⋊C4—2441no—
1091C4⋊C4—2441no—
1092C4⋊C4—2441no—
1093C4⋊C4—2441no—
1094C4⋊C4—2441no—
1095C4⋊C4—2441no—
1096C4⋊C4—2441no—
1097C4⋊C4—2441no—
1098C22⋊C4—1222no—
1099C22⋊C4—1222no—
1100C22⋊C4—1222no—
1101C22⋊C4—1222no—
1102C22⋊C4—1222no—
1103C22⋊C4—1222no—
1104C22⋊C4—1222no—
1105C22⋊C4—1222no—
1106C42—41no—
1107C42—41no—
1108C42—41no—
1109C42—1222no—
1110C42—1222no—
1111C42—2441no—
1112C42—2441no—
1113C42—2441no—
1114C42—2441no—
1115C42—2441no—
1116C42—2441no—
1117C42—2441no—
1118C23—612no—
1119C23—612no—
1120C23—612no—
1121C23—1221no—
1122C23—1221no—
1123C23—1221no—
1124C23—1221no—
1125C23C24×D6111yescharacteristic
1126Q8—82no—
1127Q8—4882no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—612no—
1173C2×C4—612no—
1174C2×C4—612no—
1175C2×C4—1221no—
1176C2×C4—1221no—
1177C2×C4—1221no—
1178C2×C4—1221no—
1179C2×C4—1221no—
1180C2×C4—1221no—
1181C2×C4—1221no—
1182C2×C4—1221no—
1183C2×C4—1221no—
1184C2×C4—1221no—
1185C2×C4—1221no—
1186C2×C4—1221no—
1187C2×C4—1221no—
1188C2×C4—1221no—
1189C2×C4—1221no—
1190C2×C4—1221no—
1191C2×C4—1221no—
1192C2×C4—1221no—
1193C2×C4—1221no—
1194C2×C4—1221no—
1195C2×C4—1221no—
1196C2×C4—1221no—
1197C2×C4—1221no—
1198C2×C4—1221no—
1199C2×C4—1221no—
1200C2×C4—1221no—
1201C2×C4—1221no—
1202C2×C4—1221no—
1203C2×C4—1221no—
1204C2×C4—1221no—
1205C2×C4—1221no—
1206C2×C4—1221no—
1207C2×C4—1221no—
1208C2×C4—1221no—
1209C2×C4—1221no—
1210C2×C4—1221no—
1211C2×C4—1221no—
1212C2×C4—1221no—
1213C2×C4—1221no—
1214C2×C4—1221no—
1215C2×C4—1221no—
1216C2×C4—1221no—
1217C2×C4—4882no—
1218C2×C4—4882no—
1219C2×C4—2444no—
1220C2×C4—2444no—
1221C2×C4—2444no—
1222C2×C4—2444no—
1223C2×C4—2444no—
1224C2×C4#41×D6112yes—
1225C22—614no—
1226C22—1222no—
1227C22—1222no—
1228C22—1222no—
1229C22—1222no—
1230C22—1222no—
1231C22—1222no—
1232C22C2×#41×D6111yescharacteristic
1233C22H(5,𝔽2)×D6111yescharacteristic
1234C222−1+4×D6111yescharacteristic
1235C222−1+4×D6111yescharacteristic
1236C222−1+4×D6111yescharacteristic
1237C22#1684059811yescharacteristic
1238C22#1684059811yescharacteristic
1239C4—22no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—1222no—
1255C4—1222no—
1256C4—1222no—
1257C4—2441no—
1258C4—2441no—
1259C4—2441no—
1260C4—2441no—
1261C4—2441no—
1262C4—2441no—
1263C4—2441no—
1264C4—2441no—
1265C4—2441no—
1266C4—2441no—
1267C4—2441no—
1268C4—2441no—
1269C2—1224no—
1270C2#541×D6111yescharacteristic
1271C2#2145965011yescharacteristic
1272C2#2145968011yescharacteristic
1273C2#2146002111yescharacteristic
1274C2#2146006311yescharacteristic
1275C2#2146041711yescharacteristic
1276C2#2146043011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2758C2
prime radicalC23×D61C24
hypercenter#2758D61
hypocenterC61#36762
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2758

Complements

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

NH ≅ G/Ntype
3. #21453742C2semidirect
4. #21453733C2semidirect
5. #21453640C2semidirect
6. #21453636C2semidirect
7. #21453575C2semidirect
8. #21453574C2semidirect
9. #21453406C2semidirect
10. #21453403C2semidirect
11. #21453272C2semidirect
12. #21453264C2semidirect
13. #21453165C2semidirect
14. #21452691C2semidirect
15. #21452683C2semidirect
16. #21452595C2semidirect
17. #21452593C2semidirect
31. C61×#2758C2semidirect
644. #2758D61semidirect
825. C61#36762semidirect

Maximal subgroups

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

subgroupindex
#214541682
#214541262
#214537422
#214537332
#214536402
#214536362
#214535752
#214535742
#214534062
#214534032
#214532722
#214532642
#214531652
#214526912
#214526832
#214525952
#214525932
#214516332
#214516312
#214503272
#214503232
#214502072
#214502012
#214499662
#214499552
#214485512
#214485482
#387×D612
C61×#27582
#3676261