Finite Group Databasebeta

← #29647849

Subgroups — #29647849

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459675C211yesmaximal, characteristic
2#21454903C211yesmaximal, characteristic, complemented
3#21448736C211yesmaximal, characteristic, complemented
4#21444381C211yesmaximal, characteristic, complemented
5#21444377C211yesmaximal, characteristic
6#21444356C211yesmaximal, characteristic, complemented
7#21444355C211yesmaximal, characteristic, complemented
8#21444354C211yesmaximal, characteristic, complemented
9#21444345C211yesmaximal, characteristic, complemented
10#21444344C211yesmaximal, characteristic, complemented
11#21444343C211yesmaximal, characteristic, complemented
12#21444341C211yesmaximal, characteristic, complemented
13#21444316C211yesmaximal, characteristic, complemented
14#21444312C211yesmaximal, characteristic
15C61×#1512C211yesmaximal, characteristic, complemented
16#16840495C411yescharacteristic, complemented
17#16840494C411yescharacteristic, complemented
18#16840489C411yescharacteristic, complemented
19#16840488C411yescharacteristic, complemented
20#16840484C411yescharacteristic, complemented
21#16840481C411yescharacteristic, complemented
22#16840480—21no—
23#16840479—21no—
24#16840471C411yescharacteristic, complemented
25#16840468C411yescharacteristic, complemented
26#16840448—21no—
27#16840445—21no—
28#16840356—21no—
29#16840354—21no—
30#16840334—21no—
31#16840314C2211yescharacteristic
32#16840307C2211yescharacteristic
33#16840298C2211yescharacteristic
34#16840296C2211yescharacteristic
35#16840293C2211yescharacteristic
36#16840241—21no—
37C2×C4×Dic122C2211yescharacteristic
38C2×#14519742—21no—
39#16839891—21no—
40#16839891—21no—
41#16839890—21no—
42#16839890—21no—
43#16839819C2211yescharacteristic
44#16839816C2211yescharacteristic
45#16839816C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839812C2211yescharacteristic
48#16839659—21no—
49#16839659—21no—
50#16839658—21no—
51#16839626C2211yescharacteristic
52#16839626C2211yescharacteristic
53C4×C4⋊Dic61C2211yescharacteristic
54#16839613C2211yescharacteristic
55#16839613C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839499C2211yescharacteristic
59#16839499C2211yescharacteristic
60#16839498C2211yescharacteristic
61#16839498C2211yescharacteristic
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C61×#382C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758224—21no—
76C22×Dic122D411yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519776C2×C411yescharacteristic
80#14519776C2×C411yescharacteristic
81#14519775C2×C411yescharacteristic
82#14519773C2×C411yescharacteristic
83#14519772—21no—
84#14519772—21no—
85#14519771—21no—
86#14519771—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519769—21no—
91#14519769C2×C411yescharacteristic
92#14519768—21no—
93#14519768C2×C411yescharacteristic
94#14519768C2×C411yescharacteristic
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519766C2×C411yescharacteristic
99#14519765C2×C411yescharacteristic
100#14519764C2×C411yescharacteristic
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519761—21no—
105#14519761—21no—
106#14519760—21no—
107#14519760—21no—
108#14519759—21no—
109#14519759—21no—
110#14519758—21no—
111#14519757—21no—
112#14519756—21no—
113#14519756C2311yescharacteristic
114#14519755—21no—
115#14519755—21no—
116#14519755—21no—
117#14519754—21no—
118#14519754—21no—
119#14519754—21no—
120#14519754—21no—
121#14519751C2311yescharacteristic
122#14519749—21no—
123Q8×Dic61C2×C411yescharacteristic
124Q8×Dic61C2×C411yescharacteristic
125C4×Dic122—21no—
126C4×Dic122C2×C411yescharacteristic
127C4×Dic122C2×C411yescharacteristic
128C4×Dic122C2×C411yescharacteristic
129C4×Dic122C2×C411yescharacteristic
130C4×Dic122C2×C411yescharacteristic
131C4×Dic122D411yescharacteristic
132C4×Dic122D411yescharacteristic
133C4×Dic122D411yescharacteristic
134C4×Dic122D411yescharacteristic
135#14519742—21no—
136#14519742—21no—
137#14519742—44no—
138#14519742C2×C411yescharacteristic
139#14519742C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141D4×Dic61—21no—
142D4×Dic61C2×C411yescharacteristic
143D4×Dic61C2×C411yescharacteristic
144#14519739C2×C411yescharacteristic
145#14519739C2×C411yescharacteristic
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148#14519737—21no—
149#14519737—21no—
150#14519737—21no—
151#14519735—21no—
152#14519734—21no—
153#14519734—21no—
154#14519733—21no—
155#14519733—21no—
156#14519733—21no—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61D411yescharacteristic
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196—21no—
162C2×#11758196—21no—
163C2×#11758196—21no—
164C2×#11758196D411yescharacteristic
165C2×#11758196D411yescharacteristic
166C4⋊C4×D61—21no—
167C2×C4×Dic61—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61C2311yescharacteristic
171C2×C4×Dic61C2311yescharacteristic
172C4⋊#92418—21no—
173#14519706—21no—
174#14519706—21no—
175#14519706—21no—
176#14519706—21no—
177C22⋊#92418C2311yescharacteristic
178C22⋊#92418C2311yescharacteristic
179#14519688—21no—
180#14519687—21no—
181#14519687—21no—
182C8×Dic61—21no—
183C8×Dic61—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684C2311yescharacteristic
187#14519684C2311yescharacteristic
188#126×C61—21no—
189#125×C61C2×C411yescharacteristic
190#124×C61C2×C411yescharacteristic
191#123×C61—21no—
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2311yescharacteristic
194C4×Q8×C61C2×C411yescharacteristic
195C4×D4×C61—21no—
196C4×D4×C61C2×C411yescharacteristic
197#117×C61—21no—
198C2×C4⋊C4×C61—21no—
199C2×C42×C61C2311yescharacteristic
200C4⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#97×C61—21no—
204#95×C61—21no—
205#95×C61C2311yescharacteristic
206#95×C61C2311yescharacteristic
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227#11758224—42no—
228#11758224—42no—
229C2×D244C22×C411yescharacteristic
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×Dic122—22no—
234C2×Dic122—22no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122C22⋊C411yescharacteristic
238C2×Dic122C22⋊C411yescharacteristic
239C2×Dic122C22⋊C411yescharacteristic
240C2×Dic122C22⋊C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—42no—
249C4⋊C4×C61C22×C411yescharacteristic
250C4⋊C4×C61C22×C411yescharacteristic
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C42×C61—21no—
257C42×C61C22×C411yescharacteristic
258C42×C61C22×C411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—42no—
279C4⋊Dic61C22⋊C411yescharacteristic
280C4⋊Dic61C22⋊C411yescharacteristic
281C4⋊Dic61C22⋊C411yescharacteristic
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22×C411yescharacteristic
284C4⋊Dic61C22×C411yescharacteristic
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—42no—
298#11758196—42no—
299#11758196—42no—
300#11758196—42no—
301#11758196C22⋊C411yescharacteristic
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—42no—
315C4×Dic61—42no—
316C4×Dic61—42no—
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C2×#92418—21no—
326C2×#92418—21no—
327C23×C61—21no—
328C23×C61C22×D411yescharacteristic
329C22×D61—21no—
330Q8×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—41no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—81no—
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C22⋊D61—41no—
355C22⋊D61—41no—
356C22⋊D61—42no—
357C22⋊D61—81no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—22no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—42no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—81no—
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61AGL(1,ℤ/8)12yes—
382C2×Dic61#13712yes—
383D244—41no—
384C4×D61—42no—
385C4×D61—81no—
386C4×D61—81no—
387Dic122—22no—
388Dic122—22no—
389Dic122—22no—
390Dic122—22no—
391Dic122—42no—
392Dic122—41no—
393Dic122—81no—
394C8×C61—41no—
395C8×C61—41no—
396#92418—41no—
397#92418—41no—
398#17628—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61C22×C22⋊C411yescharacteristic
405C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C61C2×#13711yescharacteristic
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—41no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61—81no—
420C4×C61—81no—
421Dic61—21no—
422Dic61—21no—
423Dic61—21no—
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—42no—
428Dic61—41no—
429Dic61—41no—
430Dic61—41no—
431Dic61—81no—
432Dic61#41712yes—
433Dic61#41712yes—
434#3507—611no—
435#2983—611no—
436#2351—611no—
437#1518—611no—
438#1517—611no—
439#1512—611no—
440#1512—611no—
441#1512—611no—
442#1512D6111yescharacteristic, complemented
443#1509—611no—
444#1509—611no—
445#1509—611no—
446#1509—611no—
447#1503—611no—
448#1502—611no—
449C2×C61—21no—
450C2×C61—21no—
451C2×C61—81no—
452C2×C61#288411yescharacteristic
453C2×C61C2×#41711yescharacteristic
454C2×C61#290111yescharacteristic
455D61—81no—
456#559—611no—
457#559—611no—
458#557—611no—
459#557—611no—
460#556—611no—
461#556—611no—
462#556—1221no—
463#556—1221no—
464#554—611no—
465#554—611no—
466#552—1221no—
467#552—1221no—
468#539—1221no—
469#539—1221no—
470#536—1221no—
471#533—611no—
472#532—611no—
473#529—611no—
474#529—611no—
475#529—611no—
476#529C2×D6111yescharacteristic
477#520—1221no—
478C2×C4×Q8—611no—
479C2×C4×Q8—1221no—
480#446—1221no—
481#446—1221no—
482#446—1221no—
483#446—1221no—
484#432—611no—
485#432—611no—
486#432—611no—
487#432C2×D6111yescharacteristic
488#431—611no—
489#431—611no—
490#389—1221no—
491#389—1221no—
492#389—1221no—
493#382—611no—
494#382—611no—
495#382C2×D6111yescharacteristic
496C4×C4⋊C4—611no—
497C4×C4⋊C4—611no—
498C4×C4⋊C4—611no—
499#328—611no—
500#328—611no—
501#328—611no—
502#328—611no—
503#328—611no—
504#328—611no—
505#328C2×D6111yescharacteristic
506#328C2×D6111yescharacteristic
507#327—611no—
508#327—611no—
509#327—611no—
510#327—611no—
511#327—611no—
512#327—611no—
513#327C2×D6111yescharacteristic
514#327C2×D6111yescharacteristic
515C61#1762811yescharacteristic, complemented, Sylow
516C2×#41—1221no—
517C22×Q8—611no—
518C4⋊Q8—611no—
519C4⋊Q8—611no—
520C4⋊Q8—611no—
521C4⋊Q8—1221no—
522C4⋊Q8—1221no—
523#127—611no—
524#126—21no—
525#126—1221no—
526#126—1221no—
527#126—1221no—
528#126—1221no—
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#125—611no—
533#125—611no—
534#125—611no—
535#125—1221no—
536#125—1221no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125C4×D6111yescharacteristic
541#124—611no—
542#124—611no—
543#124—611no—
544#124—1221no—
545#124—1221no—
546#124—1221no—
547#124C4×D6111yescharacteristic
548#123—21no—
549#123—1221no—
550#123—1221no—
551#123—1221no—
552#123—1221no—
553#123—1221no—
554#123—1221no—
555#123—1221no—
556C22⋊Q8—611no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563C22⋊Q8—1221no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8C22×D6111yescharacteristic
567#121—611no—
568#121—1221no—
569#121C22×D6111yescharacteristic
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—611no—
575C4×Q8—611no—
576C4×Q8—611no—
577C4×Q8—611no—
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×Q8—1221no—
586C4×Q8—2444no—
587C4×Q8C4×D6111yescharacteristic
588C4×D4—21no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—611no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4C4×D6111yescharacteristic
601#117—21no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—1221no—
622C2×C42—1221no—
623C2×C42—1221no—
624C2×C42C22×D6111yescharacteristic
625C4⋊C8—21no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C22⋊C8—611no—
632C22⋊C8—611no—
633C22⋊C8C22×D6111yescharacteristic
634C22⋊C8C22×D6111yescharacteristic
635#97—21no—
636#97—1221no—
637#97—1221no—
638#97—1221no—
639C4×C8—1221no—
640C4×C8—1221no—
641#95—21no—
642#95—611no—
643#95—611no—
644#95—1221no—
645#95—1221no—
646#95C22×D6111yescharacteristic
647#95C22×D6111yescharacteristic
648#41—2442no—
649#41—2442no—
650C2×Q8—611no—
651C2×Q8—611no—
652C2×Q8—611no—
653C2×Q8—611no—
654C2×Q8—611no—
655C2×Q8—1222no—
656C2×Q8—1222no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—611no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4C2×C4×D6111yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4D4×D6111yescharacteristic
681C22×C4D4×D6111yescharacteristic
682C22×C4C23×D6111yescharacteristic
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—1221no—
686C2×C8—1221no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—611no—
693C4⋊C4—611no—
694C4⋊C4—611no—
695C4⋊C4—611no—
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—611no—
705C4⋊C4—611no—
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—2442no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4—2442no—
726C4⋊C4—2442no—
727C4⋊C4C2×C4×D6111yescharacteristic
728C4⋊C4C2×C4×D6111yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C42—21no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—2442no—
762C42—2442no—
763C42—2442no—
764C42C2×C4×D6111yescharacteristic
765C42C2×C4×D6111yescharacteristic
766C42D4×D6111yescharacteristic
767C42D4×D6111yescharacteristic
768C23—21no—
769C23—1221no—
770C23C2×D4×D6111yescharacteristic
771Q8—41no—
772Q8—1222no—
773Q8—1222no—
774Q8—1222no—
775Q8—1222no—
776Q8—4881no—
777Q8—2441no—
778Q8—2442no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—4881no—
783D4—2441no—
784D4—2442no—
785D4—2441no—
786D4—2441no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—81no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—612no—
804C2×C4—612no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1222no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—4881no—
818C2×C4—4881no—
819C2×C4—4881no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4C22⋊C4×D6111yescharacteristic
830C2×C4C22⋊C4×D6111yescharacteristic
831C2×C4C22⋊C4×D6111yescharacteristic
832C2×C4C22⋊C4×D6111yescharacteristic
833C2×C4C22×C4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C8—41no—
836C8—41no—
837C8—2441no—
838C8—2441no—
839C22—21no—
840C22—21no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—2441no—
845C22—2441no—
846C22—2441no—
847C22C2×C22⋊C4×D6111yescharacteristic
848C22AGL(1,ℤ/8)×D6111yescharacteristic
849C22#137×D6111yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—81no—
860C4—81no—
861C4—612no—
862C4—612no—
863C4—1221no—
864C4—1221no—
865C4—1221no—
866C4—1221no—
867C4—1221no—
868C4—1221no—
869C4—4881no—
870C4—2442no—
871C4—2441no—
872C4—2441no—
873C4—2441no—
874C2—21no—
875C2—21no—
876C2—81no—
877C2—4881no—
878C2#2145428111yescharacteristic
879C2#417×D6111yescharacteristic
880C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1512C2
socleC22×C61C22×C22⋊C4
prime radical#16840307C22
cosocleC22×C4×C61C24
hypercenter#1512D61
hypocenterC61#17628
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #21454903C2semidirect
3. #21448736C2semidirect
4. #21444381C2semidirect
6. #21444356C2semidirect
7. #21444355C2semidirect
8. #21444354C2semidirect
9. #21444345C2semidirect
10. #21444344C2semidirect
11. #21444343C2semidirect
12. #21444341C2semidirect
13. #21444316C2semidirect
15. C61×#1512C2semidirect
16. #16840495C4semidirect
17. #16840494C4semidirect
18. #16840489C4semidirect
19. #16840488C4semidirect
20. #16840484C4semidirect
21. #16840481C4semidirect
24. #16840471C4semidirect
25. #16840468C4semidirect
442. #1512D61semidirect
515. C61#17628semidirect

Maximal subgroups

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

subgroupindex
#214596752
#214549032
#214487362
#214443812
#214443772
#214443562
#214443552
#214443542
#214443452
#214443442
#214443432
#214443412
#214443162
#214443122
C61×#15122
#1762861