Finite Group Databasebeta

← #30610813

Subgroups — #30610813

Order 15616.

926 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462629C211yesmaximal, characteristic
2#21462514C211yesmaximal, characteristic
3#21461182C211yesmaximal, characteristic, complemented
4#21461181C211yesmaximal, characteristic, complemented
5#21461167C211yesmaximal, characteristic, complemented
6#21461162C211yesmaximal, characteristic, complemented
7#21461161C211yesmaximal, characteristic, complemented
8#21461147C211yesmaximal, characteristic, complemented
9#21461142C211yesmaximal, characteristic, complemented
10#21461141C211yesmaximal, characteristic, complemented
11#21461127C211yesmaximal, characteristic, complemented
12#21461122C211yesmaximal, characteristic, complemented
13#21461121C211yesmaximal, characteristic, complemented
14C2×Q8⋊#92420C211yesmaximal, characteristic, complemented
15Q8×#11758224C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic
23#16840783C2211yescharacteristic
24#16840781C2211yescharacteristic
25#16840780C2211yescharacteristic
26#16840779C2211yescharacteristic
27#16840778C2211yescharacteristic
28#16840778C2211yescharacteristic
29#16840765C2211yescharacteristic
30C2×C4⋊#92420C2211yescharacteristic
31#16840735—21no—
32#16840726—21no—
33C4×#11758213C2211yescharacteristic
34C4×#11758217C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48Q8⋊#92420C2211yescharacteristic
49Q8⋊#92420C2211yescharacteristic
50Q8⋊#92420C2211yescharacteristic
51Q8⋊#92420C2211yescharacteristic
52Q8×Dic122C411yescharacteristic
53#16840487—21no—
54#16840487C411yescharacteristic
55#16840470—21no—
56#16840470—21no—
57#16840470C411yescharacteristic
58#16840470C411yescharacteristic
59#16840469—21no—
60#16840469C411yescharacteristic
61Q8×C22⋊D61C411yescharacteristic
62Q8×C22⋊D61C411yescharacteristic
63#16840317—21no—
64#16840317C2211yescharacteristic
65#16840314—21no—
66#16840314—21no—
67#16840314C2211yescharacteristic
68#16840314C2211yescharacteristic
69C4×#11758224—21no—
70C4×#11758224C2211yescharacteristic
71C2×Q8×Dic61C2211yescharacteristic
72C2×Q8×Dic61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74D4×Q8×C61C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758224D411yescharacteristic
108C2×Q8×D61C2×C411yescharacteristic
109#14519777—21no—
110#14519777C2×C411yescharacteristic
111#14519776—21no—
112#14519776—21no—
113#14519776C2×C411yescharacteristic
114#14519776C2×C411yescharacteristic
115#14519775—21no—
116#14519775—21no—
117#14519775C2×C411yescharacteristic
118#14519775C2×C411yescharacteristic
119#14519768—21no—
120#14519768—21no—
121#14519768—21no—
122#14519767—21no—
123#14519767—21no—
124#14519767—21no—
125#14519767—21no—
126#14519767—21no—
127#14519767—21no—
128#14519757—21no—
129#14519757—21no—
130#14519757—21no—
131#14519756—21no—
132#14519756—21no—
133#14519756C2×C411yescharacteristic
134#14519756C2×C411yescharacteristic
135#14519754—21no—
136#14519754—21no—
137#14519754—21no—
138#14519754—21no—
139#14519754—21no—
140#14519754—21no—
141#14519753—21no—
142#14519753—21no—
143#14519753C2×C411yescharacteristic
144#14519753C2×C411yescharacteristic
145Q8×Dic61—21no—
146Q8×Dic61—21no—
147Q8×Dic61—21no—
148Q8×Dic61—21no—
149Q8×Dic61C2×C411yescharacteristic
150Q8×Dic61C2×C411yescharacteristic
151Q8×Dic61C2×C411yescharacteristic
152Q8×Dic61C2×C411yescharacteristic
153Q8×Dic61C2311yescharacteristic
154Q8×Dic61C2311yescharacteristic
155Q8×Dic61C2311yescharacteristic
156C4×Dic122—21no—
157C4×Dic122—21no—
158C4×Dic122C2×C411yescharacteristic
159C4×Dic122C2×C411yescharacteristic
160#14519742—21no—
161#14519742—21no—
162#14519742—21no—
163#14519742—21no—
164#14519742—21no—
165#14519742D411yescharacteristic
166#14519742C2311yescharacteristic
167D4×Dic61—21no—
168D4×Dic61D411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61C2×C411yescharacteristic
172C4×C22⋊D61C2×C411yescharacteristic
173#14519737—21no—
174#14519737—21no—
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519735—21no—
178#14519735D411yescharacteristic
179#14519733—21no—
180#14519733—21no—
181#14519733D411yescharacteristic
182#14519733D411yescharacteristic
183C2×C4⋊Dic61—21no—
184C2×C4⋊Dic61—21no—
185C2×C4⋊Dic61C2×C411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic
187C4⋊C4×D61—21no—
188C4⋊C4×D61C2×C411yescharacteristic
189C2×C4×Dic61—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194C42×D61C2311yescharacteristic
195C22×Q8×C61C2×C411yescharacteristic
196C22×Q8×C61C2×C411yescharacteristic
197C4⋊Q8×C61—21no—
198C4⋊Q8×C61C2×C411yescharacteristic
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202C22⋊Q8×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61—22no—
209C2×Q8×C61—22no—
210C2×Q8×C61—41no—
211C2×Q8×C61—41no—
212C2×Q8×C61C22×C411yescharacteristic
213C2×Q8×C61C22×C411yescharacteristic
214C2×Q8×C61C22×C411yescharacteristic
215C2×D4×C61C22⋊C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228Q8×D61—22no—
229Q8×D61—41no—
230#11758224—22no—
231#11758224—22no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122C22⋊C411yescharacteristic
242C2×Dic122C22×C411yescharacteristic
243#11758217—42no—
244#11758217—42no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—21no—
252C2×#92420—21no—
253C2×#92420—42no—
254C2×#92420—42no—
255#11758213—42no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C22⋊C411yescharacteristic
262C4⋊C4×C61C22×C411yescharacteristic
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61C22⋊C411yescharacteristic
266C22⋊C4×C61C22⋊C411yescharacteristic
267C42×C61—21no—
268C42×C61C22×C411yescharacteristic
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61C22⋊C411yescharacteristic
272C22⋊Dic61C22⋊C411yescharacteristic
273#11758198—21no—
274#11758198—21no—
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊C411yescharacteristic
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61C22⋊C411yescharacteristic
288C4⋊Dic61C22×C411yescharacteristic
289C4⋊Dic61C22×C411yescharacteristic
290C4⋊Dic61C22×C411yescharacteristic
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2411yescharacteristic
326C23×C61C2×C22⋊C411yescharacteristic
327C23×C61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329Q8×C61—21no—
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—21no—
333Q8×C61—21no—
334Q8×C61—42no—
335Q8×C61—42no—
336Q8×C61#13112yes—
337D4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C22⋊D61—22no—
354C22⋊D61—22no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—81no—
364C2×Dic61—81no—
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61#13712yes—
371C2×Dic61#13712yes—
372C2×Dic61C22×D411yescharacteristic
373C2×Dic61C22×D411yescharacteristic
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—41no—
379C4×D61—42no—
380C4×D61—81no—
381Dic122—22no—
382Dic122—21no—
383Dic122—21no—
384Dic122—42no—
385Dic122—81no—
386Dic122—81no—
387Dic122—81no—
388#92420—22no—
389#92420—41no—
390#92420—41no—
391#92420—41no—
392#92420—41no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#17514—611nomaximal, Sylow
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61#41912yes—
403C22×C61C22×C22⋊C411yescharacteristic
404C2×D61—21no—
405C2×D61—21no—
406C2×D61—21no—
407C4×C61—22no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61C2×#13111yescharacteristic
416C4×C61#56811yescharacteristic
417Dic61—21no—
418Dic61—21no—
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—41no—
423Dic61—41no—
424Dic61—41no—
425Dic61—41no—
426Dic61#41912yes—
427Dic61C2×#13711yescharacteristic
428Dic61C2×#13711yescharacteristic
429Q8×#41—611no—
430#2965—611no—
431#2925—611no—
432#1497—611no—
433#1497—611no—
434#1493—611no—
435#1491—611no—
436#1491—611no—
437#1487—611no—
438#1485—611no—
439#1485—611no—
440#1481—611no—
441#1479—611no—
442#1479—611no—
443C2×Q8⋊C8—611no—
444C2×C61—22no—
445C2×C61—41no—
446C2×C61#288011yescharacteristic
447C2×C61C2×#41911yescharacteristic
448C2×C61#290111yescharacteristic
449D61—41no—
450Q82—611no—
451#557—611no—
452#557—1221no—
453#554—611no—
454#554—611no—
455#554—611no—
456#554—1221no—
457#554—1221no—
458#554—1221no—
459D4×Q8—611no—
460D4×Q8—611no—
461D4×Q8#692311yescharacteristic
462#533—611no—
463#533—611no—
464#533—611no—
465#533—1221no—
466#533—1221no—
467#533—1221no—
468C4×#41—611no—
469C4×#41—1221no—
470C2×C4×Q8—611no—
471C2×C4×Q8—611no—
472C2×C4×Q8—611no—
473#446—1221no—
474#436—1221no—
475#435—1221no—
476#435—1221no—
477#433—1221no—
478#433—1221no—
479#432—611no—
480#432—611no—
481#431—611no—
482#431—611no—
483#431—611no—
484#431—611no—
485#431—611no—
486#423—611no—
487C2×C4⋊C8—611no—
488#408—1221no—
489#405—1221no—
490C4×M16—611no—
491C4×M16—611no—
492C2×C4×C8—611no—
493Q8⋊C8—611no—
494Q8⋊C8—611no—
495Q8⋊C8—611no—
496Q8⋊C8—611no—
497Q8⋊C8—611no—
498Q8⋊C8—611no—
499Q8⋊C8—611no—
500Q8⋊C8—611no—
501Q8⋊C8—611no—
502Q8⋊C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8—611no—
507Q8⋊C8—611no—
508Q8⋊C8—611no—
509C61#1751411yescharacteristic, complemented, Sylow
510C2×#41—611no—
511C22×Q8—611no—
512C22×Q8C2×#692311yescharacteristic
513C22×Q8C2×#692311yescharacteristic
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16—1221no—
517C22×C8—1221no—
518C22×C8—1221no—
519C4⋊Q8—21no—
520C4⋊Q8—611no—
521C4⋊Q8—611no—
522C4⋊Q8—611no—
523C4⋊Q8—611no—
524C4⋊Q8—611no—
525C4⋊Q8—1221no—
526C4⋊Q8—1221no—
527C4⋊Q8—1221no—
528C4⋊Q8—1221no—
529C4⋊Q8—1221no—
530C4⋊Q8C2×#692311yescharacteristic
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#125—1221no—
536#125—1221no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—611no—
543C22⋊Q8—611no—
544C22⋊Q8—611no—
545C22⋊Q8—611no—
546C22⋊Q8—1221no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8C2×#692311yescharacteristic
560C22⋊Q8C2×#692311yescharacteristic
561C4×Q8—611no—
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×Q8—1221no—
583C4×Q8C2×#692311yescharacteristic
584C4×D4—21no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4C2×#692311yescharacteristic
596#117—611no—
597#117—611no—
598#117—611no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C42—611no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—1221no—
614C4⋊C8—611no—
615C4⋊C8—611no—
616C4⋊C8—611no—
617C4⋊C8—611no—
618C4⋊C8—1221no—
619C4⋊C8—1221no—
620C4⋊C8—1221no—
621C4⋊C8—1221no—
622C4⋊C8—1221no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627C22⋊C8—1221no—
628C22⋊C8—1221no—
629C22⋊C8—1221no—
630#97—1221no—
631#97—1221no—
632#97—1221no—
633#97—1221no—
634C4×C8—611no—
635C4×C8—611no—
636C4×C8—611no—
637C4×C8—611no—
638C4×C8—1221no—
639C4×C8—1221no—
640C4×C8—1221no—
641#41—1222no—
642#41—1222no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—41no—
648C2×Q8—41no—
649C2×Q8—611no—
650C2×Q8—611no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—1222no—
656C2×Q8—2441no—
657C2×Q8C22×#692311yescharacteristic
658C2×Q8C22×#692311yescharacteristic
659C2×Q8C22×#692311yescharacteristic
660C2×D4—611no—
661C2×D4—611no—
662C2×D4C22⋊#692311yescharacteristic
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4C22×#692311yescharacteristic
677C22×C4C22×#692311yescharacteristic
678M16—2442no—
679M16—2442no—
680M16—2442no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—2442no—
690C2×C8—2442no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—611no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4C22⋊#692311yescharacteristic
728C4⋊C4C22×#692311yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—611no—
732C22⋊C4—611no—
733C22⋊C4—611no—
734C22⋊C4—611no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4C22⋊#692311yescharacteristic
740C22⋊C4C22⋊#692311yescharacteristic
741C42—21no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—1221no—
752C42—1221no—
753C42—1221no—
754C42—1221no—
755C42—1221no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42C22×#692311yescharacteristic
761C23—611no—
762C23C2×C22⋊#692311yescharacteristic
763C23C2×C22⋊#692311yescharacteristic
764Q8—21no—
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—21no—
769Q8—42no—
770Q8—42no—
771Q8—1222no—
772Q8—1221no—
773Q8—1221no—
774Q8—4881no—
775Q8—4881no—
776Q8—4881no—
777Q8—2442no—
778Q8#1451986412yes—
779D4—22no—
780D4—1222no—
781D4—1222no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—4881no—
812C2×C4—4881no—
813C2×C4—4881no—
814C2×C4—2441no—
815C2×C4—2442no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4C2×C22⋊#692311yescharacteristic
819C2×C4C2×C22⋊#692311yescharacteristic
820C2×C4C2×C22⋊#692311yescharacteristic
821C2×C4C2×C22⋊#692311yescharacteristic
822C2×C4C23×#692311yescharacteristic
823C8—1222no—
824C8—2441no—
825C8—2441no—
826C8—2441no—
827C8—2441no—
828C8—2441no—
829C8—2441no—
830C8—2441no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—1221no—
837C22—1221no—
838C22—1221no—
839C22#1684075512yes—
840C22C22×C22⋊#692311yescharacteristic
841C4—21no—
842C4—21no—
843C4—22no—
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—611no—
850C4—611no—
851C4—612no—
852C4—1221no—
853C4—1221no—
854C4—1221no—
855C4—1221no—
856C4—1221no—
857C4—2441no—
858C4—2441no—
859C4—2441no—
860C4—2441no—
861C4C2×#1451986411yescharacteristic
862C4#1684084011yescharacteristic
863C2—22no—
864C2—41no—
865C2—2441no—
866C2#2146240711yescharacteristic
867C2C2×#1684075511yescharacteristic
868C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758224D4
cosocleC4×Dic61C24
hypercenterD4×Q8#6923
hypocenterC61#17514
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461182C2semidirect
4. #21461181C2semidirect
5. #21461167C2semidirect
6. #21461162C2semidirect
7. #21461161C2semidirect
8. #21461147C2semidirect
9. #21461142C2semidirect
10. #21461141C2semidirect
11. #21461127C2semidirect
12. #21461122C2semidirect
13. #21461121C2semidirect
14. C2×Q8⋊#92420C2semidirect
509. C61#17514semidirect

Maximal subgroups

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

subgroupindex
#214626292
#214625142
#214611822
#214611812
#214611672
#214611622
#214611612
#214611472
#214611422
#214611412
#214611272
#214611222
#214611212
C2×Q8⋊#924202
Q8×#117582242
#1751461