Finite Group Databasebeta

← #29886736

Subgroups — #29886736

Order 15616.

1304 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454093C211yesmaximal, characteristic
2#21454070C211yesmaximal, characteristic
3#21454068C211yesmaximal, characteristic
4#21454066C211yesmaximal, characteristic
5#21454064C211yesmaximal, characteristic
6#21454062C211yesmaximal, characteristic
7#21454061C211yesmaximal, characteristic
8#21454060C211yesmaximal, characteristic
9#21454059C211yesmaximal, characteristic
10#21454058C211yesmaximal, characteristic
11#21454057C211yesmaximal, characteristic
12#21454056C211yesmaximal, characteristic
13#21453889C211yesmaximal, characteristic
14#21453888C211yesmaximal, characteristic
15#21453885C211yesmaximal, characteristic
16#21449125C211yesmaximal, characteristic
17#21449125C211yesmaximal, characteristic
18#21449125C211yesmaximal, characteristic
19#21449125C211yesmaximal, characteristic
20#21449125C211yesmaximal, characteristic
21#21449125C211yesmaximal, characteristic
22#21449125C211yesmaximal, characteristic
23#21449123C211yesmaximal, characteristic
24#21449123C211yesmaximal, characteristic
25#21449123C211yesmaximal, characteristic
26#21449123C211yesmaximal, characteristic
27#21449123C211yesmaximal, characteristic
28#21448378C211yesmaximal, characteristic
29#21448376C211yesmaximal, characteristic
30#21448376C211yesmaximal, characteristic
31C61×#2839C211yesmaximal, characteristic
32C2×#14519768C2211yescharacteristic
33C2×#14519767C2211yescharacteristic
34C2×#14519767C2211yescharacteristic
35#16839704C2211yescharacteristic
36#16839704C2211yescharacteristic
37#16839704C2211yescharacteristic
38#16839704C2211yescharacteristic
39#16839704C2211yescharacteristic
40#16839704C2211yescharacteristic
41#16839704C2211yescharacteristic
42#16839704C2211yescharacteristic
43#16839704C2211yescharacteristic
44#16839704C2211yescharacteristic
45#16839704C2211yescharacteristic
46#16839704C2211yescharacteristic
47#16839703C2211yescharacteristic
48#16839703C2211yescharacteristic
49#16839703C2211yescharacteristic
50#16839703C2211yescharacteristic
51#16839703C2211yescharacteristic
52#16839703C2211yescharacteristic
53#16839703C2211yescharacteristic
54#16839703C2211yescharacteristic
55#16839703C2211yescharacteristic
56#16839703C2211yescharacteristic
57#16839703C2211yescharacteristic
58#16839703C2211yescharacteristic
59#16839703C2211yescharacteristic
60#16839703C2211yescharacteristic
61#16839702C2211yescharacteristic
62#16839702C2211yescharacteristic
63#16839702C2211yescharacteristic
64#16839702C2211yescharacteristic
65#16839702C2211yescharacteristic
66#16839701C2211yescharacteristic
67#16839701C2211yescharacteristic
68#16839701C2211yescharacteristic
69#16839701C2211yescharacteristic
70#16839701C2211yescharacteristic
71#16839700C2211yescharacteristic
72#16839700C2211yescharacteristic
73#16839700C2211yescharacteristic
74#16839700C2211yescharacteristic
75#16839700C2211yescharacteristic
76#16839696C2211yescharacteristic
77#16839696C2211yescharacteristic
78#16839696C2211yescharacteristic
79#16839696C2211yescharacteristic
80#16839696C2211yescharacteristic
81#16839696C2211yescharacteristic
82#16839696C2211yescharacteristic
83#16839696C2211yescharacteristic
84#16839696C2211yescharacteristic
85#16839696C2211yescharacteristic
86#16839696C2211yescharacteristic
87#16839696C2211yescharacteristic
88#16839696C2211yescharacteristic
89#16839696C2211yescharacteristic
90#16839695C2211yescharacteristic
91#16839695C2211yescharacteristic
92#16839695C2211yescharacteristic
93#16839695C2211yescharacteristic
94#16839695C2211yescharacteristic
95#16839695C2211yescharacteristic
96#16839695C2211yescharacteristic
97#16839695C2211yescharacteristic
98#16839695C2211yescharacteristic
99#16839695C2211yescharacteristic
100#16839695C2211yescharacteristic
101#16839695C2211yescharacteristic
102#16839694C2211yescharacteristic
103#16839694C2211yescharacteristic
104#16839694C2211yescharacteristic
105#16839694C2211yescharacteristic
106#16839694C2211yescharacteristic
107#16839693C2211yescharacteristic
108#16839693C2211yescharacteristic
109#16839693C2211yescharacteristic
110#16839693C2211yescharacteristic
111#16839693C2211yescharacteristic
112#16839693C2211yescharacteristic
113#16839693C2211yescharacteristic
114#16839692C2211yescharacteristic
115#16839692C2211yescharacteristic
116#16839692C2211yescharacteristic
117#16839692C2211yescharacteristic
118#16839692C2211yescharacteristic
119#16839660C2211yescharacteristic
120#16839659C2211yescharacteristic
121#16839659C2211yescharacteristic
122#16839657C2211yescharacteristic
123#16839657C2211yescharacteristic
124#16839649C2211yescharacteristic
125#16839649C2211yescharacteristic
126#16839647C2211yescharacteristic
127#16839647C2211yescharacteristic
128#16839646C2211yescharacteristic
129#16839646C2211yescharacteristic
130#16839645C2211yescharacteristic
131#16839645C2211yescharacteristic
132#16839643C2211yescharacteristic
133#16839643C2211yescharacteristic
134#16839627C2211yescharacteristic
135#16839626C2211yescharacteristic
136#16839626C2211yescharacteristic
137C4⋊C4×Dic61C2211yescharacteristic
138C4⋊C4×Dic61C2211yescharacteristic
139C4⋊C4×Dic61C2211yescharacteristic
140C4⋊C4×Dic61C2211yescharacteristic
141C4⋊C4×Dic61C2211yescharacteristic
142C4⋊C4×Dic61C2211yescharacteristic
143C4⋊C4×Dic61C2211yescharacteristic
144C4⋊C4×Dic61C2211yescharacteristic
145C4⋊C4×Dic61C2211yescharacteristic
146C4⋊C4×Dic61C2211yescharacteristic
147C4⋊C4×Dic61C2211yescharacteristic
148C4⋊C4×Dic61C2211yescharacteristic
149C4⋊C4×Dic61C2211yescharacteristic
150C4⋊C4×Dic61C2211yescharacteristic
151#16839613C2211yescharacteristic
152#16839613C2211yescharacteristic
153#16839613C2211yescharacteristic
154#16839613C2211yescharacteristic
155#16839613C2211yescharacteristic
156#16839613C2211yescharacteristic
157#16839613C2211yescharacteristic
158#16839613C2211yescharacteristic
159#16839613C2211yescharacteristic
160#16839613C2211yescharacteristic
161#16839613C2211yescharacteristic
162#16839613C2211yescharacteristic
163#16839613C2211yescharacteristic
164#16839613C2211yescharacteristic
165#16839613C2211yescharacteristic
166#16839613C2211yescharacteristic
167#16839607C2211yescharacteristic
168#16839607C2211yescharacteristic
169#16839607C2211yescharacteristic
170#16839607C2211yescharacteristic
171C42×Dic61C2211yescharacteristic
172C61×#400C2211yescharacteristic
173C61×#400C2211yescharacteristic
174C61×#400C2211yescharacteristic
175C61×#400C2211yescharacteristic
176C61×#400C2211yescharacteristic
177C61×#400C2211yescharacteristic
178C61×#400C2211yescharacteristic
179C61×#398C2211yescharacteristic
180C61×#398C2211yescharacteristic
181C61×#398C2211yescharacteristic
182C61×#398C2211yescharacteristic
183C61×#398C2211yescharacteristic
184C61×#389C2211yescharacteristic
185C61×#387C2211yescharacteristic
186C61×#387C2211yescharacteristic
187#14519768—24no—
188#14519767—24no—
189#14519767—24no—
190C2×C4⋊Dic61C2311yescharacteristic
191C2×C4⋊Dic61C2311yescharacteristic
192C2×C4⋊Dic61C2311yescharacteristic
193C2×C4⋊Dic61C2311yescharacteristic
194C2×C4⋊Dic61C2311yescharacteristic
195C2×C4⋊Dic61C2311yescharacteristic
196C2×C4⋊Dic61C2311yescharacteristic
197C2×C4⋊Dic61C2311yescharacteristic
198C2×C4⋊Dic61C2311yescharacteristic
199C2×C4⋊Dic61C2311yescharacteristic
200C2×C4⋊Dic61C2311yescharacteristic
201C2×C4⋊Dic61C2311yescharacteristic
202C2×C4⋊Dic61C2311yescharacteristic
203C2×C4⋊Dic61C2311yescharacteristic
204C2×#11758196C2311yescharacteristic
205C2×#11758196C2311yescharacteristic
206C2×#11758196C2311yescharacteristic
207C2×#11758196C2311yescharacteristic
208C2×#11758196C2311yescharacteristic
209C2×#11758196C2311yescharacteristic
210C2×#11758196C2311yescharacteristic
211C2×#11758196C2311yescharacteristic
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×C4×Dic61C2311yescharacteristic
237C2×C4×Dic61C2311yescharacteristic
238C2×C4×Dic61C2311yescharacteristic
239C2×C4×Dic61C2311yescharacteristic
240C2×C4×Dic61C2311yescharacteristic
241C2×C4×Dic61C2311yescharacteristic
242C2×C4×Dic61C2311yescharacteristic
243C2×C4×Dic61C2311yescharacteristic
244C2×C4×Dic61C2311yescharacteristic
245C2×C4×Dic61C2311yescharacteristic
246C2×C4×Dic61C2311yescharacteristic
247C2×C4×Dic61C2311yescharacteristic
248C2×C4×Dic61C2311yescharacteristic
249C2×C4×Dic61C2311yescharacteristic
250C2×C4×Dic61C2311yescharacteristic
251C2×C4×Dic61C2311yescharacteristic
252C2×C4×Dic61C2311yescharacteristic
253C2×C4×Dic61C2311yescharacteristic
254#14519684C2311yescharacteristic
255#14519684C2311yescharacteristic
256#14519684C2311yescharacteristic
257#14519684C2311yescharacteristic
258#14519684C2311yescharacteristic
259#14519684C2311yescharacteristic
260#14519684C2311yescharacteristic
261#14519684C2311yescharacteristic
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
310C2×C4⋊C4×C61C2311yescharacteristic
311C2×C4⋊C4×C61C2311yescharacteristic
312C2×C4⋊C4×C61C2311yescharacteristic
313C2×C4⋊C4×C61C2311yescharacteristic
314C2×C4⋊C4×C61C2311yescharacteristic
315C2×C4⋊C4×C61C2311yescharacteristic
316C2×C4⋊C4×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×C42×C61C2311yescharacteristic
325#95×C61C2311yescharacteristic
326#95×C61C2311yescharacteristic
327#95×C61C2311yescharacteristic
328#95×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
345C22×C4×C61C2411yescharacteristic
346C22×C4×C61C2411yescharacteristic
347C22×C4×C61C2411yescharacteristic
348C22×C4×C61C2411yescharacteristic
349C22×C4×C61C2411yescharacteristic
350C22×C4×C61C2411yescharacteristic
351C22×C4×C61C2411yescharacteristic
352C22×C4×C61C2411yescharacteristic
353C22×C4×C61C2411yescharacteristic
354C22×C4×C61C2411yescharacteristic
355C22×C4×C61C2411yescharacteristic
356C22×C4×C61C2411yescharacteristic
357C22×C4×C61C2411yescharacteristic
358C22×C4×C61C2411yescharacteristic
359C22×C4×C61C2411yescharacteristic
360C22×Dic61C2411yescharacteristic
361C22×Dic61C2411yescharacteristic
362C22×Dic61C2411yescharacteristic
363C22×Dic61C2411yescharacteristic
364C22×Dic61C2411yescharacteristic
365C22×Dic61C2411yescharacteristic
366C22×Dic61C2411yescharacteristic
367C22×Dic61C2411yescharacteristic
368C22×Dic61C2411yescharacteristic
369C22×Dic61C2411yescharacteristic
370C22×Dic61C2411yescharacteristic
371C22×Dic61C2411yescharacteristic
372C22×Dic61C2411yescharacteristic
373C22×Dic61C2411yescharacteristic
374C22×Dic61C2411yescharacteristic
375C22×Dic61C2411yescharacteristic
376C4⋊C4×C61—22no—
377C4⋊C4×C61—22no—
378C4⋊C4×C61—22no—
379C4⋊C4×C61—41no—
380C4⋊C4×C61—41no—
381C4⋊C4×C61—41no—
382C4⋊C4×C61—41no—
383C4⋊C4×C61—41no—
384C4⋊C4×C61—41no—
385C4⋊C4×C61—41no—
386C4⋊C4×C61—41no—
387C4⋊C4×C61—41no—
388C4⋊C4×C61—41no—
389C4⋊C4×C61—41no—
390C42×C61—41no—
391C4⋊Dic61—22no—
392C4⋊Dic61—22no—
393C4⋊Dic61—22no—
394C4⋊Dic61—22no—
395C4⋊Dic61—22no—
396C4⋊Dic61—41no—
397C4⋊Dic61—41no—
398C4⋊Dic61—41no—
399C4⋊Dic61—41no—
400C4⋊Dic61—41no—
401C4⋊Dic61—41no—
402C4⋊Dic61—41no—
403C4⋊Dic61—41no—
404C4⋊Dic61—41no—
405#11758196—22no—
406#11758196—22no—
407#11758196—22no—
408#11758196—22no—
409#11758196—22no—
410#11758196—22no—
411#11758196—22no—
412#11758196—22no—
413#11758196—22no—
414#11758196—22no—
415#11758196—41no—
416#11758196—41no—
417#11758196—41no—
418#11758196—41no—
419#11758196—41no—
420#11758196—41no—
421#11758196—41no—
422#11758196—41no—
423#11758196—41no—
424#11758196—41no—
425#11758196—41no—
426#11758196—41no—
427#11758196—41no—
428#11758196—41no—
429#11758196—41no—
430#11758196—41no—
431#11758196—41no—
432#11758196—41no—
433#11758196—41no—
434#11758196—41no—
435#11758196—41no—
436#11758196—41no—
437C4×Dic61—22no—
438C4×Dic61—22no—
439C4×Dic61—22no—
440C4×Dic61—22no—
441C4×Dic61—22no—
442C4×Dic61—22no—
443C4×Dic61—22no—
444C4×Dic61—22no—
445C4×Dic61—22no—
446C4×Dic61—22no—
447C4×Dic61—22no—
448C4×Dic61—22no—
449C4×Dic61—22no—
450C4×Dic61—22no—
451C4×Dic61—22no—
452C4×Dic61—41no—
453C4×Dic61—41no—
454C4×Dic61#4114yes—
455C23×C61C2511yescharacteristic
456C2×C4×C61—21no—
457C2×C4×C61—21no—
458C2×C4×C61—21no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—21no—
470C2×C4×C61—21no—
471C2×C4×C61—21no—
472C2×C4×C61—21no—
473C2×C4×C61—21no—
474C2×C4×C61—21no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—21no—
480C2×C4×C61—21no—
481C2×C4×C61—21no—
482C2×C4×C61—21no—
483C2×C4×C61—21no—
484C2×C4×C61—21no—
485C2×C4×C61—21no—
486C2×C4×C61—21no—
487C2×C4×C61—21no—
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×C61C2×#4112yes—
501C2×Dic61—21no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—21no—
505C2×Dic61—21no—
506C2×Dic61—21no—
507C2×Dic61—21no—
508C2×Dic61—21no—
509C2×Dic61—21no—
510C2×Dic61—21no—
511C2×Dic61—21no—
512C2×Dic61—21no—
513C2×Dic61—21no—
514C2×Dic61—21no—
515C2×Dic61—21no—
516C2×Dic61—21no—
517C2×Dic61—21no—
518C2×Dic61—21no—
519C2×Dic61—21no—
520C2×Dic61—21no—
521C2×Dic61—21no—
522C2×Dic61—21no—
523C2×Dic61—21no—
524C2×Dic61—21no—
525C2×Dic61—21no—
526C2×Dic61—21no—
527C2×Dic61—21no—
528C2×Dic61—21no—
529C2×Dic61—21no—
530C2×Dic61—21no—
531C2×Dic61—21no—
532C2×Dic61—21no—
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×Dic61C2×#4112yes—
545C2×Dic61C2×#4112yes—
546C2×Dic612−1+412yes—
547C2×Dic612−1+412yes—
548C2×Dic612−1+412yes—
549#36701—611nomaximal, Sylow
550C22×C61C22×#4111yescharacteristic
551C22×C61C2×2−1+411yescharacteristic
552C22×C61C2×2−1+411yescharacteristic
553C22×C61C2×2−1+411yescharacteristic
554C22×C61#58511yescharacteristic
555C22×C61#58511yescharacteristic
556C22×C61#58511yescharacteristic
557C4×C61—22no—
558C4×C61—41no—
559C4×C61—41no—
560C4×C61—41no—
561C4×C61—41no—
562C4×C61—41no—
563C4×C61—41no—
564C4×C61—41no—
565C4×C61—41no—
566C4×C61—41no—
567C4×C61—41no—
568C4×C61—41no—
569C4×C61—41no—
570C4×C61—41no—
571C4×C61—41no—
572Dic61—22no—
573Dic61—22no—
574Dic61—41no—
575Dic61—41no—
576Dic61—41no—
577Dic61—41no—
578Dic61—41no—
579Dic61—41no—
580Dic61—41no—
581Dic61—41no—
582Dic61—41no—
583Dic61—41no—
584Dic61—41no—
585Dic61—41no—
586Dic61—41no—
587Dic61#56414yes—
588#2845—611no—
589#2839—611no—
590#2839—611no—
591#2839—611no—
592#2839—611no—
593#2839—611no—
594#2839—611no—
595#2839—611no—
596#2839—611no—
597#2839—611no—
598#2839—611no—
599#2839—611no—
600#2839D6111yescharacteristic
601#2822—611no—
602#2822—611no—
603#2822—611no—
604#2402—611no—
605#2402—611no—
606#2402—611no—
607#2402—611no—
608#2402—611no—
609#2402—611no—
610#2402—611no—
611#2402—611no—
612#2402—611no—
613#2402—611no—
614#2402—611no—
615#2402—611no—
616C4×#125—611no—
617C4×#125—611no—
618C4×#125—611no—
619C2×C61#346111yescharacteristic
620C2×C61#346111yescharacteristic
621C2×C61#346111yescharacteristic
622C2×C61C2×#56411yescharacteristic
623C2×C61#353111yescharacteristic
624C2×C61#353111yescharacteristic
625C2×C61#353111yescharacteristic
626C2×#125—611no—
627C2×#125—611no—
628C2×#125—611no—
629#400—611no—
630#400—611no—
631#400—611no—
632#400—611no—
633#400—611no—
634#400—611no—
635#400—611no—
636#400—611no—
637#400—611no—
638#400—611no—
639#400—611no—
640#400—611no—
641#400—611no—
642#400—611no—
643#400—611no—
644#400—611no—
645#400—611no—
646#400—611no—
647#400—611no—
648#400—611no—
649#400—611no—
650#400—611no—
651#400—611no—
652#400—611no—
653#400—611no—
654#400—611no—
655#400—611no—
656#400—611no—
657#400—611no—
658#400—611no—
659#400—611no—
660#400—611no—
661#400—611no—
662#400—611no—
663#400—611no—
664#400—611no—
665#400—611no—
666#400—611no—
667#400—611no—
668#400—611no—
669#400—611no—
670#400C2×D6111yescharacteristic
671#400C2×D6111yescharacteristic
672#400C2×D6111yescharacteristic
673#400C2×D6111yescharacteristic
674#400C2×D6111yescharacteristic
675#400C2×D6111yescharacteristic
676#400C2×D6111yescharacteristic
677#398—611no—
678#398—611no—
679#398—611no—
680#398—611no—
681#398—611no—
682#398—611no—
683#398—611no—
684#398—611no—
685#398—611no—
686#398—611no—
687#398—611no—
688#398—611no—
689#398—611no—
690#398—611no—
691#398—611no—
692#398—611no—
693#398—611no—
694#398—611no—
695#398—611no—
696#398—611no—
697#398—611no—
698#398—611no—
699#398—611no—
700#398—611no—
701#398—611no—
702#398—611no—
703#398—611no—
704#398—611no—
705#398—611no—
706#398—611no—
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#398C2×D6111yescharacteristic
721#398C2×D6111yescharacteristic
722#398C2×D6111yescharacteristic
723#398C2×D6111yescharacteristic
724#398C2×D6111yescharacteristic
725#389—611no—
726#389—611no—
727#389—611no—
728#389—611no—
729#389—611no—
730#389C2×D6111yescharacteristic
731#387—611no—
732#387—611no—
733#387—611no—
734#387—611no—
735#387—611no—
736#387—611no—
737#387—611no—
738#387—611no—
739#387—611no—
740#387—611no—
741#387C2×D6111yescharacteristic
742#387C2×D6111yescharacteristic
743#382—611no—
744#382—611no—
745#382—611no—
746C4×C4⋊C4—611no—
747C4×C4⋊C4—611no—
748C4×C4⋊C4—611no—
749C4×C4⋊C4—611no—
750C4×C4⋊C4—611no—
751C4×C4⋊C4—611no—
752C4×C4⋊C4—611no—
753C4×C4⋊C4—611no—
754C4×C4⋊C4—611no—
755C4×C4⋊C4—611no—
756C4×C4⋊C4—611no—
757C4×C4⋊C4—611no—
758C4×C4⋊C4—611no—
759C4×C4⋊C4—611no—
760C4×C4⋊C4—611no—
761C4×C4⋊C4—611no—
762C4×C4⋊C4—611no—
763C4×C4⋊C4—611no—
764C4×C4⋊C4—611no—
765C4×C4⋊C4—611no—
766C4×C4⋊C4—611no—
767C4×C4⋊C4—611no—
768C4×C4⋊C4—611no—
769C4×C4⋊C4—611no—
770C4×C4⋊C4—611no—
771C4×C4⋊C4—611no—
772C4×C4⋊C4—611no—
773C4×C4⋊C4—611no—
774C4×C4⋊C4—611no—
775C4×C4⋊C4—611no—
776#376—611no—
777#376—611no—
778#376—611no—
779#376—611no—
780C43—611no—
781C61#3670111yescharacteristic, complemented, Sylow
782#125—1224no—
783#125—1224no—
784#125—1224no—
785C2×C4⋊C4—611no—
786C2×C4⋊C4—611no—
787C2×C4⋊C4—611no—
788C2×C4⋊C4—611no—
789C2×C4⋊C4—611no—
790C2×C4⋊C4—611no—
791C2×C4⋊C4—611no—
792C2×C4⋊C4—611no—
793C2×C4⋊C4—611no—
794C2×C4⋊C4—611no—
795C2×C4⋊C4—611no—
796C2×C4⋊C4—611no—
797C2×C4⋊C4—611no—
798C2×C4⋊C4—611no—
799C2×C4⋊C4—611no—
800C2×C4⋊C4—611no—
801C2×C4⋊C4—611no—
802C2×C4⋊C4—611no—
803C2×C4⋊C4—611no—
804C2×C4⋊C4—611no—
805C2×C4⋊C4—611no—
806C2×C4⋊C4—611no—
807C2×C4⋊C4—611no—
808C2×C4⋊C4—611no—
809C2×C4⋊C4—611no—
810C2×C4⋊C4—611no—
811C2×C4⋊C4—611no—
812C2×C4⋊C4—611no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—611no—
815C2×C4⋊C4—611no—
816C2×C4⋊C4—611no—
817C2×C4⋊C4—611no—
818C2×C4⋊C4—611no—
819C2×C4⋊C4—611no—
820C2×C4⋊C4—611no—
821C2×C4⋊C4—611no—
822C2×C4⋊C4—611no—
823C2×C4⋊C4—611no—
824C2×C4⋊C4—611no—
825C2×C4⋊C4—611no—
826C2×C4⋊C4—611no—
827C2×C4⋊C4—611no—
828C2×C4⋊C4—611no—
829C2×C4⋊C4—611no—
830C2×C4⋊C4—611no—
831C2×C4⋊C4C22×D6111yescharacteristic
832C2×C4⋊C4C22×D6111yescharacteristic
833C2×C4⋊C4C22×D6111yescharacteristic
834C2×C4⋊C4C22×D6111yescharacteristic
835C2×C4⋊C4C22×D6111yescharacteristic
836C2×C4⋊C4C22×D6111yescharacteristic
837C2×C4⋊C4C22×D6111yescharacteristic
838C2×C4⋊C4C22×D6111yescharacteristic
839C2×C4⋊C4C22×D6111yescharacteristic
840C2×C4⋊C4C22×D6111yescharacteristic
841C2×C4⋊C4C22×D6111yescharacteristic
842C2×C4⋊C4C22×D6111yescharacteristic
843C2×C4⋊C4C22×D6111yescharacteristic
844C2×C4⋊C4C22×D6111yescharacteristic
845C2×C42—611no—
846C2×C42—611no—
847C2×C42—611no—
848C2×C42—611no—
849C2×C42—611no—
850C2×C42—611no—
851C2×C42—611no—
852C2×C42—611no—
853C2×C42—611no—
854C2×C42—611no—
855C2×C42—611no—
856C2×C42—611no—
857C2×C42—611no—
858C2×C42—611no—
859C2×C42—611no—
860C2×C42—611no—
861C2×C42—611no—
862C2×C42—611no—
863C2×C42C22×D6111yescharacteristic
864#95—611no—
865#95—611no—
866#95—611no—
867#95—611no—
868#95—611no—
869#95—611no—
870#95—611no—
871#95—611no—
872#95—611no—
873#95—611no—
874#95—611no—
875#95—611no—
876#95—611no—
877#95—611no—
878#95—611no—
879#95—611no—
880#95—611no—
881#95—611no—
882#95—611no—
883#95—611no—
884#95—611no—
885#95—611no—
886#95—611no—
887#95—611no—
888#95—611no—
889#95—611no—
890#95—611no—
891#95—611no—
892#95—611no—
893#95—611no—
894#95—611no—
895#95—611no—
896#95—611no—
897#95—611no—
898#95—611no—
899#95—611no—
900#95—611no—
901#95—611no—
902#95—611no—
903#95—611no—
904#95—611no—
905#95—611no—
906#95—611no—
907#95—611no—
908#95—611no—
909#95—611no—
910#95—611no—
911#95—611no—
912#95—611no—
913#95—611no—
914#95—611no—
915#95—611no—
916#95—611no—
917#95—611no—
918#95—611no—
919#95—611no—
920#95C22×D6111yescharacteristic
921#95C22×D6111yescharacteristic
922#95C22×D6111yescharacteristic
923#95C22×D6111yescharacteristic
924#95C22×D6111yescharacteristic
925#95C22×D6111yescharacteristic
926#95C22×D6111yescharacteristic
927#95C22×D6111yescharacteristic
928#95C22×D6111yescharacteristic
929#95C22×D6111yescharacteristic
930#95C22×D6111yescharacteristic
931#95C22×D6111yescharacteristic
932#95C22×D6111yescharacteristic
933#95C22×D6111yescharacteristic
934#95C22×D6111yescharacteristic
935#95C22×D6111yescharacteristic
936#95C22×D6111yescharacteristic
937#95C22×D6111yescharacteristic
938#95C22×D6111yescharacteristic
939#95C22×D6111yescharacteristic
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—611no—
946C22×C4—611no—
947C22×C4—611no—
948C22×C4—611no—
949C22×C4—611no—
950C22×C4—611no—
951C22×C4—611no—
952C22×C4—611no—
953C22×C4—611no—
954C22×C4—611no—
955C22×C4—611no—
956C22×C4C23×D6111yescharacteristic
957C22×C4C23×D6111yescharacteristic
958C22×C4C23×D6111yescharacteristic
959C22×C4C23×D6111yescharacteristic
960C22×C4C23×D6111yescharacteristic
961C22×C4C23×D6111yescharacteristic
962C22×C4C23×D6111yescharacteristic
963C22×C4C23×D6111yescharacteristic
964C22×C4C23×D6111yescharacteristic
965C22×C4C23×D6111yescharacteristic
966C22×C4C23×D6111yescharacteristic
967C22×C4C23×D6111yescharacteristic
968C22×C4C23×D6111yescharacteristic
969C22×C4C23×D6111yescharacteristic
970C22×C4C23×D6111yescharacteristic
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—1222no—
986C4⋊C4—1222no—
987C4⋊C4—1222no—
988C4⋊C4—1222no—
989C4⋊C4—1222no—
990C4⋊C4—1222no—
991C4⋊C4—1222no—
992C4⋊C4—1222no—
993C4⋊C4—1222no—
994C4⋊C4—1222no—
995C4⋊C4—1222no—
996C4⋊C4—1222no—
997C4⋊C4—1222no—
998C4⋊C4—1222no—
999C4⋊C4—1222no—
1000C4⋊C4—2441no—
1001C4⋊C4—2441no—
1002C4⋊C4—2441no—
1003C4⋊C4—2441no—
1004C4⋊C4—2441no—
1005C4⋊C4—2441no—
1006C4⋊C4—2441no—
1007C4⋊C4—2441no—
1008C4⋊C4—2441no—
1009C4⋊C4—2441no—
1010C4⋊C4—2441no—
1011C4⋊C4—2441no—
1012C4⋊C4—2441no—
1013C4⋊C4—2441no—
1014C4⋊C4—2441no—
1015C4⋊C4—2441no—
1016C4⋊C4—2441no—
1017C4⋊C4—2441no—
1018C4⋊C4—2441no—
1019C4⋊C4—2441no—
1020C4⋊C4—2441no—
1021C4⋊C4—2441no—
1022C4⋊C4—2441no—
1023C4⋊C4—2441no—
1024C4⋊C4—2441no—
1025C4⋊C4—2441no—
1026C4⋊C4—2441no—
1027C4⋊C4—2441no—
1028C4⋊C4—2441no—
1029C4⋊C4—2441no—
1030C4⋊C4—2441no—
1031C42—41no—
1032C42—614no—
1033C42—1222no—
1034C42—1222no—
1035C42—1222no—
1036C42—1222no—
1037C42—1222no—
1038C42—1222no—
1039C42—1222no—
1040C42—1222no—
1041C42—1222no—
1042C42—1222no—
1043C42—1222no—
1044C42—1222no—
1045C42—1222no—
1046C42—1222no—
1047C42—1222no—
1048C42—2441no—
1049C42—2441no—
1050C23C24×D6111yescharacteristic
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—612no—
1096C2×C4—612no—
1097C2×C4—612no—
1098C2×C4—612no—
1099C2×C4—612no—
1100C2×C4—1221no—
1101C2×C4—1221no—
1102C2×C4—1221no—
1103C2×C4—1221no—
1104C2×C4—1221no—
1105C2×C4—1221no—
1106C2×C4—1221no—
1107C2×C4—1221no—
1108C2×C4—1221no—
1109C2×C4—1221no—
1110C2×C4—1221no—
1111C2×C4—1221no—
1112C2×C4—1221no—
1113C2×C4—1221no—
1114C2×C4—1221no—
1115C2×C4—1221no—
1116C2×C4—1221no—
1117C2×C4—1221no—
1118C2×C4—1221no—
1119C2×C4—1221no—
1120C2×C4—1221no—
1121C2×C4—1221no—
1122C2×C4—1221no—
1123C2×C4—1221no—
1124C2×C4—1221no—
1125C2×C4—1221no—
1126C2×C4—1221no—
1127C2×C4—1221no—
1128C2×C4—1221no—
1129C2×C4—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—1221no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4#41×D6112yes—
1144C22C2×#41×D6111yescharacteristic
1145C222−1+4×D6111yescharacteristic
1146C222−1+4×D6111yescharacteristic
1147C222−1+4×D6111yescharacteristic
1148C22#1684059711yescharacteristic
1149C22#1684059711yescharacteristic
1150C22#1684059911yescharacteristic
1151C4—22no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—614no—
1167C4—1222no—
1168C4—1222no—
1169C4—2441no—
1170C4—2441no—
1171C4—2441no—
1172C4—2441no—
1173C4—2441no—
1174C4—2441no—
1175C4—2441no—
1176C4—2441no—
1177C4—2441no—
1178C4—2441no—
1179C4—2441no—
1180C4—2441no—
1181C4—2441no—
1182C2#2145924511yescharacteristic
1183C2#2145924911yescharacteristic
1184C2#2145925111yescharacteristic
1185C2#564×D6111yescharacteristic
1186C2#2145996311yescharacteristic
1187C2#2145996511yescharacteristic
1188C2#2145996511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, prime radical, cosocleC23×C61C25
FittingC61×#2839C2
hypercenter#2839D61
hypocenterC61#36701
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2839

Complements

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

NH ≅ G/Ntype
781. C61#36701semidirect

Maximal subgroups

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

subgroupindex
#214540932
#214540702
#214540682
#214540662
#214540642
#214540622
#214540612
#214540602
#214540592
#214540582
#214540572
#214540562
#214538892
#214538882
#214538852
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