Finite Group Databasebeta

← #10828694

Subgroups — #10828694

Order 768.

1060 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic
2#82915C211yesmaximal, characteristic, complemented
3#82663C211yesmaximal, characteristic, complemented
4#82207C211yesmaximal, characteristic, complemented
5#71901C211yesmaximal, characteristic, complemented
6#71900C211yesmaximal, characteristic, complemented
7#71852C211yesmaximal, characteristic, complemented
8#71852C211yesmaximal, characteristic, complemented
9#71713C211yesmaximal, characteristic, complemented
10#71683C211yesmaximal, characteristic, complemented
11#71665C211yesmaximal, characteristic, complemented
12#71664C211yesmaximal, characteristic, complemented
13#71647C211yesmaximal, characteristic, complemented
14#71647C211yesmaximal, characteristic, complemented
15#71590C211yesmaximal, characteristic, complemented
16#24084—31nomaximal, Sylow
17C3×#555—21no—
18C3×#553—21no—
19C3×#553—21no—
20C3×#551—22no—
21C3×#547—21no—
22C3×#546—22no—
23C3×#544C2211yescharacteristic
24C3×#542—21no—
25C3×#540—21no—
26C3×#535C2211yescharacteristic
27C3×#532—21no—
28C3×#529—21no—
29C3×#525C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C3×#520C2211yescharacteristic
32C3×#518C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C2×#926C2211yescharacteristic
35C22×#208C2211yescharacteristic
36C2×#837C2211yescharacteristic
37C2×#837C2211yescharacteristic
38#5232C2211yescharacteristic
39#5232C2211yescharacteristic
40#5222—22no—
41#5221C2211yescharacteristic
42#5221C2211yescharacteristic
43C2×#833C2211yescharacteristic
44C2×#833C2211yescharacteristic
45C4×#217C2211yescharacteristic
46#5207C2211yescharacteristic
47#5045—21no—
48#5045—21no—
49#5035—21no—
50#5035—21no—
51#4998—21no—
52#4998—21no—
53#4995C2211yescharacteristic
54#4995C2211yescharacteristic
55#4995C2211yescharacteristic
56#4995C2211yescharacteristic
57#4995C2211yescharacteristic
58#4995C2211yescharacteristic
59#4977C2211yescharacteristic
60#4975C2211yescharacteristic
61#4964—21no—
62#4964—21no—
63#4944—22no—
64#4532C2211yescharacteristic
65#4532C2211yescharacteristic
66#4532C2211yescharacteristic
67#4532C2211yescharacteristic
68#4532C2211yescharacteristic
69#4532C2211yescharacteristic
70#4530C2211yescharacteristic
71#4530C2211yescharacteristic
72#3494D311yescharacteristic
73#3093—31no—
74#2911—31no—
75#2500—31no—
76#2061—31no—
77#2060—31no—
78#2037—31no—
79#2037—31no—
80#1900—31no—
81#1871—31no—
82#1860—31no—
83#1859—31no—
84#1856—31no—
85#1856—31no—
86#1826—31no—
87C2×C3×#41—22no—
88C2×C3×#41C2311yescharacteristic
89C22×C3×D4D412yes—
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C3×C4⋊Q8—21no—
93C3×C4⋊Q8—21no—
94C3×#127—21no—
95C3×#126—22no—
96C3×#126—22no—
97C3×#125—21no—
98C3×#125—21no—
99C3×#124—22no—
100C3×#124—22no—
101C3×#124—21no—
102C3×#123—22no—
103C3×#123—22no—
104C3×#123—22no—
105C3×#123—22no—
106C3×#123—21no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8D411yescharacteristic
110C3×C22⋊Q8D411yescharacteristic
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—22no—
114C3×#121—21no—
115C3×#121—21no—
116C3×#121—21no—
117C3×#121—21no—
118C3×#121—21no—
119C3×#121—21no—
120C3×#121D411yescharacteristic
121C3×#121D411yescharacteristic
122C3×#120—21no—
123C3×#120—22no—
124C3×C4×Q8—21no—
125C3×C4×D4—22no—
126C3×C4×D4—22no—
127C3×C4×D4—21no—
128C3×C4×D4—22no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×#117—22no—
136C3×#117—21no—
137C3×#117—21no—
138C3×#117—21no—
139C3×#117D411yescharacteristic
140C3×#117D411yescharacteristic
141C3×#117C2311yescharacteristic
142C3×#117C2311yescharacteristic
143C3×#117C2311yescharacteristic
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4D411yescharacteristic
146C2×C3×C4⋊C4D411yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—22no—
150C2×C3×C22⋊C4D412yes—
151C2×C3×C42—21no—
152C2×#217—22no—
153C2×#217—21no—
154C2×#217—21no—
155C2×#217—22no—
156#926—21no—
157#926—21no—
158#926—21no—
159#926—21no—
160C2×C4⋊Dic3C2311yescharacteristic
161C2×C4⋊Dic3C2311yescharacteristic
162C2×Dic3⋊C4—22no—
163C2×C4×Dic3—21no—
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2311yescharacteristic
166C2×#208—21no—
167C2×#208—22no—
168C2×#208—22no—
169C2×#208C2311yescharacteristic
170C2×#208C2311yescharacteristic
171C2×#208C2311yescharacteristic
172C2×#208C2311yescharacteristic
173C22×C3⋊C8—21no—
174#837—22no—
175#837—22no—
176#835—21no—
177#835—21no—
178#833—22no—
179#833—22no—
180#832—21no—
181#832—21no—
182C3⋊#95—21no—
183C3⋊#95—22no—
184#830—21no—
185#830—21no—
186#808—21no—
187#808—21no—
188#808—21no—
189#808—21no—
190#808—21no—
191#808—21no—
192#807—21no—
193#807—21no—
194#807—21no—
195#807—21no—
196#807—21no—
197#807—21no—
198C22×M16—31no—
199#555—21no—
200#553—21no—
201#553—21no—
202#551—22no—
203#547—21no—
204#546—22no—
205#544C2×D311yescharacteristic
206#542—21no—
207#540—21no—
208#535C2×D311yescharacteristic
209#532—21no—
210#529—21no—
211#525C2×D311yescharacteristic
212C2×#121C2×D311yescharacteristic
213#520C2×D311yescharacteristic
214#518C2×D311yescharacteristic
215C2×#117—31no—
216C2×#117C2×D311yescharacteristic
217#485—61no—
218#485—61no—
219#482—61no—
220#482—61no—
221#428—31no—
222#428—31no—
223#428—31no—
224#428—31no—
225#428—31no—
226#428—31no—
227#428—61no—
228#428—61no—
229#427—61no—
230#427—61no—
231C2×#104—31no—
232C2×#104—31no—
233#417—31no—
234#417—31no—
235C2×#100—31no—
236C2×#100—31no—
237#407—31no—
238#394—62no—
239#390—31no—
240#390—31no—
241#388—62no—
242#384—31no—
243#382—31no—
244C4×C22⋊C4—31no—
245#343—31no—
246#343—31no—
247#339—31no—
248#339—31no—
249#339—31no—
250#339—31no—
251#339—31no—
252#339—31no—
253C24×C3C2×D412yes—
254C24×C3C2×D411yescharacteristic
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—21no—
259C3×#41—84no—
260C2×C3×Q8—22no—
261C2×C3×Q8C2×D411yescharacteristic
262C2×C3×D4—21no—
263C2×C3×D4—22no—
264C2×C3×D4—21no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—82no—
276C2×C3×D4C2×D411yescharacteristic
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4C2×D411yescharacteristic
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2×D411yescharacteristic
290C22×C3×C4C2×D411yescharacteristic
291C22×C3×C4C2×D411yescharacteristic
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2411yescharacteristic
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—22no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—22no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4C2×D411yescharacteristic
309C3×C4⋊C4C2×D411yescharacteristic
310C3×C4⋊C4C2×D411yescharacteristic
311C3×C4⋊C4C2×D411yescharacteristic
312C3×C4⋊C4C2×D411yescharacteristic
313C3×C4⋊C4C2×D411yescharacteristic
314C3×C22⋊C4—22no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—21no—
320C3×C22⋊C4—21no—
321C3×C22⋊C4—21no—
322C3×C22⋊C4—21no—
323C3×C22⋊C4—21no—
324C3×C22⋊C4—21no—
325C3×C22⋊C4—21no—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—22no—
328C3×C22⋊C4—21no—
329C3×C22⋊C4—21no—
330C3×C42—22no—
331C3×C42—21no—
332C3×C42—21no—
333C3×C42—21no—
334C3×C42—21no—
335C3×C42—21no—
336#217—42no—
337#217—44no—
338#217—41no—
339#217—41no—
340#217—82no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345Dic3⋊C4—82no—
346C4×Dic3—21no—
347C4×Dic3—21no—
348C4×Dic3—21no—
349C4×Dic3—21no—
350C4×Dic3—41no—
351C4×Dic3—41no—
352#208—24no—
353#208—21no—
354#208—21no—
355#208—21no—
356#208—21no—
357#208—21no—
358#208—21no—
359#208#4112yescomplemented
360#208#4112yescomplemented
361C2×C3⋊C8—24no—
362C2×C3⋊C8—21no—
363C2×C3⋊C8—21no—
364C2×C3⋊C8—21no—
365C2×C3⋊C8—21no—
366C2×#41—22no—
367C2×#41C22×D311yescharacteristic
368C22×D4#6712yes—
369C22×D4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C2×M16—31no—
372C2×M16—31no—
373C2×M16—31no—
374C2×M16—31no—
375C2×M16—62no—
376C2×M16—62no—
377C2×M16—61no—
378C22×C8—61no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381#127—21no—
382#126—22no—
383#126—22no—
384#125—21no—
385#125—21no—
386#124—22no—
387#124—22no—
388#124—21no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—21no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8#6711yescharacteristic
397C22⋊Q8#6711yescharacteristic
398#121—22no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121#6711yescharacteristic
408#121#6711yescharacteristic
409#120—21no—
410#120—22no—
411C4×Q8—21no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—21no—
415C4×D4—22no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422#117—22no—
423#117—21no—
424#117—21no—
425#117—21no—
426#117—61no—
427#117—61no—
428#117—61no—
429#117—61no—
430#117#6711yescharacteristic
431#117#6711yescharacteristic
432#117C22×D311yescharacteristic
433#117C22×D311yescharacteristic
434#117C22×D311yescharacteristic
435C2×C4⋊C4—21no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4#6711yescharacteristic
440C2×C4⋊C4#6711yescharacteristic
441C2×C4⋊C4C22×D311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—61no—
445C2×C22⋊C4—61no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4#6712yes—
449C2×C42—21no—
450C2×C42—31no—
451C2×C42—31no—
452C2×C42—61no—
453#107—61no—
454#107—61no—
455#107—61no—
456#107—61no—
457#107—61no—
458#107—61no—
459#106—61no—
460#106—61no—
461#106—61no—
462#106—61no—
463#106—61no—
464#106—61no—
465#104—62no—
466#104—62no—
467#103—61no—
468#103—61no—
469#102—61no—
470#102—61no—
471#100—62no—
472#100—62no—
473C22⋊C8—61no—
474C22⋊C8—61no—
475#95—61no—
476#95—62no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—22no—
480C23×C3—21no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—42no—
486C23×C3—42no—
487C23×C3#12011yescharacteristic
488C23×C3#12011yescharacteristic
489C23×C3C22×D411yescharacteristic
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—82no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—44no—
496C3×D4—42no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—81no—
504C3×D4—82no—
505C3×D4—82no—
506C3×D4—82no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—22no—
525C2×C3×C4—42no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—42no—
529C2×C3×C4—81no—
530C2×C3×C4—82no—
531C2×C3×C4—82no—
532C2×C3×C4—82no—
533C2×C3×C4#12011yescharacteristic
534C2×C3×C4#12011yescharacteristic
535C2×C3×C4C22×D411yescharacteristic
536C2×C3×C4C22×D411yescharacteristic
537C2×C3×C4C2×#4111yescharacteristic
538C2×C3×C4C2×#4111yescharacteristic
539C2×C3×C42−1+411yescharacteristic
540C2×C3×C42−1+411yescharacteristic
541C2×Dic3—22no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—42no—
545C2×Dic3—41no—
546C2×Dic3—42no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C3⋊C8—22no—
552C3⋊C8—22no—
553C3⋊C8—41no—
554C3⋊C8—41no—
555C24C2×#6712yes—
556C24C2×#6711yescharacteristic
557#41—21no—
558#41—21no—
559#41—21no—
560#41—21no—
561#41—84no—
562C2×Q8—22no—
563C2×Q8C2×#6711yescharacteristic
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—82no—
578C2×D4C2×#6711yescharacteristic
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4C2×#6711yescharacteristic
594C22×C4C2×#6711yescharacteristic
595C22×C4C2×#6711yescharacteristic
596C22×C4C2×#6711yescharacteristic
597C22×C4C2×#6711yescharacteristic
598C22×C4C2×#6712yes—
599C22×C4C23×D311yescharacteristic
600M16—32no—
601M16—32no—
602M16—64no—
603M16—61no—
604M16—61no—
605M16—61no—
606M16—61no—
607M16—61no—
608M16—61no—
609C2×C8—64no—
610C2×C8—61no—
611C2×C8—61no—
612C2×C8—61no—
613C2×C8—61no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—242no—
629C4⋊C4C2×#6711yescharacteristic
630C4⋊C4C2×#6711yescharacteristic
631C4⋊C4C2×#6711yescharacteristic
632C4⋊C4C2×#6711yescharacteristic
633C4⋊C4C2×#6711yescharacteristic
634C4⋊C4C2×#6711yescharacteristic
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—122no—
652C22⋊C4—124no—
653C22⋊C4—121no—
654C22⋊C4—121no—
655C22⋊C4—242no—
656C42—22no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—61no—
663C42—61no—
664C42—61no—
665C42—61no—
666C42—121no—
667C42—121no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—41no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—42no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—82no—
685C22×C3—82no—
686C22×C3C2×#12011yescharacteristic
687C22×C3#54711yescharacteristic
688C22×C3#54711yescharacteristic
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—42no—
698C3×C4—41no—
699C3×C4#52511yescharacteristic
700C3×C4#53611yescharacteristic
701C3×C4#54711yescharacteristic
702C3×C4#54711yescharacteristic
703Dic3—42no—
704Dic3—81no—
705Dic3—81no—
706Dic3—81no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23#95311yescharacteristic
718C23#95311yescharacteristic
719C23C22×#6711yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—82no—
723D4—21no—
724D4—21no—
725D4—44no—
726D4—42no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—82no—
734D4—81no—
735D4—82no—
736D4—82no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—62no—
760C2×C4—81no—
761C2×C4—82no—
762C2×C4—82no—
763C2×C4—82no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—122no—
768C2×C4—121no—
769C2×C4—122no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4#95311yescharacteristic
774C2×C4#95311yescharacteristic
775C2×C4D3×#4111yescharacteristic
776C2×C4D3×#4111yescharacteristic
777C2×C4#101011yescharacteristic
778C2×C4#101011yescharacteristic
779C2×C4C22×#6711yescharacteristic
780C2×C4C22×#6711yescharacteristic
781C8—62no—
782C8—62no—
783C8—121no—
784C8—121no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—81no—
790C2×C3—82no—
791C2×C3#240611yescharacteristic
792C2×C3#301811yescharacteristic
793C2×C3#301911yescharacteristic
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22#582411yescharacteristic
813C22#582411yescharacteristic
814C22C2×#95311yescharacteristic
815C4—21no—
816C4—21no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—42no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—122no—
826C4—241no—
827C4—241no—
828C4—241no—
829C4#582411yescharacteristic
830C4#582411yescharacteristic
831C4#582511yescharacteristic
832C4#582811yescharacteristic
833C3#2408411yescharacteristic, complemented, Sylow
834C2—21no—
835C2—21no—
836C2—41no—
837C2—41no—
838C2—82no—
839C2—81no—
840C2#8409011yescharacteristic
841C2#8410411yescharacteristic
842C2#8412111yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#3494C2
socleC22×C3C2×#120
hypercenter#3494D3
hypocenterC3#24084
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3494

Complements

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

NH ≅ G/Ntype
2. #82915C2semidirect
3. #82663C2semidirect
4. #82207C2semidirect
5. #71901C2semidirect
6. #71900C2semidirect
7. #71852C2semidirect
8. #71852C2semidirect
9. #71713C2semidirect
10. #71683C2semidirect
11. #71665C2semidirect
12. #71664C2semidirect
13. #71647C2semidirect
14. #71647C2semidirect
15. #71590C2semidirect
359. #208#41semidirect
360. #208#41semidirect
833. C3#24084semidirect

Maximal subgroups

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

subgroupindex
C3×#34942
#829152
#826632
#822072
#719012
#719002
#718522
#717132
#716832
#716652
#716642
#716472
#715902
#240843