Finite Group Databasebeta

← #10846247

Subgroups — #10846247

Order 768.

1104 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2428C211yesmaximal, characteristic
2C2×#5076C211yesmaximal, characteristic, complemented
3C2×#5041C211yesmaximal, characteristic, complemented
4C2×#5041C211yesmaximal, characteristic, complemented
5C2×C4×#214C211yesmaximal, characteristic, complemented
6#73488C211yesmaximal, characteristic, complemented
7#71762C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#71612C211yesmaximal, characteristic, complemented
11#69660C211yesmaximal, characteristic, complemented
12#69646C211yesmaximal, characteristic, complemented
13#69633C211yesmaximal, characteristic, complemented
14#69618C211yesmaximal, characteristic, complemented
15C22⋊C4×C3⋊C8C211yesmaximal, characteristic, complemented
16#25410—31nomaximal, Sylow
17C2×C3×#127C2211yescharacteristic
18C2×C3×#121—21no—
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#214C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C2×#869C2211yescharacteristic
30C2×C4×Dic6C2211yescharacteristic
31C3×#394—21no—
32C3×#392—21no—
33C3×#390C2211yescharacteristic
34C3×#389C2211yescharacteristic
35C3×#386—21no—
36C3×C4×C22⋊C4C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5076—24no—
43#5041—24no—
44#5041—24no—
45C4×#214—24no—
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#808C2211yescharacteristic
52#4951—21no—
53#4948—21no—
54#4929C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4657—21no—
59#4647—21no—
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#492—31no—
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2429—31no—
69#2428D311yescharacteristic
70#2043—31no—
71#2041—31no—
72#2000—31no—
73#2000—31no—
74#1968—31no—
75#1941—31no—
76#1880—31no—
77#1877—31no—
78C8×C22⋊C4—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C3×#127—22no—
90C3×#127—41no—
91C3×#121—22no—
92C3×#121—22no—
93C3×#121—41no—
94C3×#121—41no—
95C3×#121—44no—
96C3×C4×D4—22no—
97C3×C4×D4—41no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C22⋊C4D411yescharacteristic
108C2×C3×C42C2311yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111C2×#217—21no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—22no—
115C2×#214—22no—
116C2×#214—22no—
117C2×#214—22no—
118C2×#214—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—41no—
122C2×#214—41no—
123C2×#214D414yescomplemented
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128#924—22no—
129#924—22no—
130#924—41no—
131#924—41no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C22×C3⋊C8—22no—
138C22×C3⋊C8—22no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#869—22no—
145#869—41no—
146C4×Dic6—22no—
147C4×Dic6—41no—
148C3×#95—21no—
149C3×#95D411yescharacteristic
150C3×#95D411yescharacteristic
151#832—22no—
152#832—22no—
153#832—22no—
154#832—41no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—22no—
159#810—22no—
160#810—22no—
161#810—22no—
162#810—41no—
163#808—22no—
164#808D414yescomplemented
165C4×C3⋊C8—22no—
166C4×C3⋊C8—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×SD16—31no—
170C22×SD16—31no—
171C23×C8—31no—
172C2×C4⋊Q8—31no—
173C2×#127C2×D311yescharacteristic
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—31no—
176C2×#121—21no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4C2×D311yescharacteristic
181#492—64no—
182#465—64no—
183#465—64no—
184C4×SD16—64no—
185C2×#106—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197C2×C4×C8—31no—
198#398—61no—
199#396—61no—
200#394—21no—
201#392—21no—
202#391—31no—
203#390C2×D311yescharacteristic
204#389—31no—
205#389—61no—
206#389C2×D311yescharacteristic
207#388—61no—
208#386—21no—
209C4×C22⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C2×C3×D4—81no—
240C2×C3×D4C2×D412yes—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4—81no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6C2×D412yes—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—42no—
278C3×C4⋊C4C2×D412yes—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—81no—
285C3×C22⋊C4SD1614yescomplemented
286C3×C42—21no—
287C3×C42—21no—
288C3×C42—21no—
289C3×C42—21no—
290#217—42no—
291#217—42no—
292#214—28no—
293#214—44no—
294#214—44no—
295#214—44no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—42no—
300C4⋊Dic3—42no—
301C4⋊Dic3C2×D412yes—
302Dic3⋊C4—42no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306C4×Dic3—42no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—44no—
316C2×C3⋊C8C2×D412yes—
317C2×C3⋊C8C2×D412yes—
318C2×C3⋊C8#4112yes—
319C2×C3⋊C8#4112yes—
320C22×Q8—31no—
321C22×Q8—31no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C22×D311yescharacteristic
327C22×D4C22×D311yescharacteristic
328C23×C4—21no—
329C23×C4C22×D311yescharacteristic
330C2×SD16—34no—
331C2×SD16—62no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—62no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C22×C8—31no—
343C22×C8—31no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—62no—
347C22×C8—62no—
348C22×C8—62no—
349C4⋊Q8—62no—
350C4⋊Q8—121no—
351#127—22no—
352#127—41no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—22no—
358#121—22no—
359#121—41no—
360#121—41no—
361#121—44no—
362C4×Q8—62no—
363C4×Q8—121no—
364C4×D4—22no—
365C4×D4—41no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4#6711yescharacteristic
385C2×C22⋊C4#6711yescharacteristic
386C2×C42—61no—
387C2×C42C22×D311yescharacteristic
388C2×C42C22×D311yescharacteristic
389#106—34no—
390#106—62no—
391#103—62no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399C22⋊C8—62no—
400C4×C8—62no—
401C4×C8—62no—
402#95—21no—
403#95—61no—
404#95—61no—
405#95—61no—
406#95#6711yescharacteristic
407#95#6711yescharacteristic
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—22no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3C2×SD1612yes—
429C23×C3C22×D411yescharacteristic
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—41no—
433C3×D4—41no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—41no—
438C3×D4—84no—
439C3×D4—84no—
440C3×D4—84no—
441C3×D4—84no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—84no—
465C2×C3×C4C2×SD1612yes—
466C2×C3×C4C2×SD1612yes—
467C2×C3×C4#13512yes—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486Dic6—22no—
487Dic6—22no—
488Dic6—41no—
489Dic6—41no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494C3⋊C8—22no—
495C3⋊C8—41no—
496C3⋊C8—41no—
497C3⋊C8#12114yescomplemented
498C24—21no—
499C24—21no—
500C24C2×#6711yescharacteristic
501C2×Q8—32no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4D3×D412yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—81no—
552C22×C4C2×#6711yescharacteristic
553C22×C4C2×#6711yescharacteristic
554C22×C4C2×#6711yescharacteristic
555C22×C4C2×#6711yescharacteristic
556C22×C4C2×#6711yescharacteristic
557C22×C4C23×D311yescharacteristic
558SD16—68no—
559SD16—124no—
560SD16—124no—
561SD16—124no—
562C2×C8—32no—
563C2×C8—32no—
564C2×C8—32no—
565C2×C8—32no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—124no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—32no—
579C4⋊C4—42no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—122no—
584C4⋊C4—122no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4—122no—
589C4⋊C4D3×D412yes—
590C22⋊C4—22no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—122no—
597C22⋊C4—122no—
598C22⋊C4#21414yescomplemented
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—122no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3#53211yescharacteristic
626C22×C3D4211yescharacteristic
627C22×C3D4211yescharacteristic
628C22×C3C22×SD1611yescharacteristic
629C22×C3C2×#13511yescharacteristic
630C22×C3#57711yescharacteristic
631C22×C3#57711yescharacteristic
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—41no—
636C3×C4—42no—
637C3×C4—41no—
638C3×C4—81no—
639C3×C4C2×#12111yescharacteristic
640C3×C4#54011yescharacteristic
641C3×C4#54611yescharacteristic
642C3×C4#55011yescharacteristic
643Dic3—42no—
644Dic3—42no—
645Dic3—81no—
646Dic3—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C2×#21412yes—
668C23C22×#6711yescharacteristic
669Q8—62no—
670Q8—62no—
671Q8—121no—
672Q8—121no—
673Q8—121no—
674Q8—121no—
675Q8—121no—
676Q8—121no—
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—84no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4C2×#21412yes—
725C2×C4C2×#21412yes—
726C2×C4#95012yes—
727C2×C4C2×D3×D411yescharacteristic
728C2×C4C2×D3×D411yescharacteristic
729C2×C4#100411yescharacteristic
730C2×C4#100411yescharacteristic
731C2×C4D3×#4111yescharacteristic
732C2×C4D3×#4111yescharacteristic
733C8—34no—
734C8—62no—
735C8—121no—
736C8—121no—
737C2×C3—42no—
738C2×C3—82no—
739C2×C3—161no—
740C2×C3#242811yescharacteristic
741C2×C3#316711yescharacteristic
742C2×C3#317411yescharacteristic
743C2×C3D4×SD1611yescharacteristic
744C2×C3D4×SD1611yescharacteristic
745C2×C3#328211yescharacteristic
746C2×C3#328411yescharacteristic
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22C22×#21411yescharacteristic
769C22D4×#6711yescharacteristic
770C22D4×#6711yescharacteristic
771C22C2×#95011yescharacteristic
772C22#583211yescharacteristic
773C22#583611yescharacteristic
774C22#583611yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—41no—
780C4—41no—
781C4—81no—
782C4—122no—
783C4—122no—
784C4—241no—
785C4—241no—
786C4#559911yescharacteristic
787C4D3×#12111yescharacteristic
788C4#561011yescharacteristic
789C4#561511yescharacteristic
790C3#2541011yescharacteristic, complemented, Sylow
791C2—42no—
792C2—82no—
793C2—161no—
794C2#8265011yescharacteristic
795C2#8329011yescharacteristic
796C2#8343111yescharacteristic
797C2D4×#21411yescharacteristic
798C2D4×#21411yescharacteristic
799C2#8350911yescharacteristic
800C2#8357911yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#2428C2
socleC23×C3C22×D4
hypercenter#2428D3
hypocenterC3#25410
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2428

Complements

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

NH ≅ G/Ntype
2. C2×#5076C2semidirect
3. C2×#5041C2semidirect
4. C2×#5041C2semidirect
5. C2×C4×#214C2semidirect
6. #73488C2semidirect
7. #71762C2semidirect
8. #71685C2semidirect
9. #71685C2semidirect
10. #71612C2semidirect
11. #69660C2semidirect
12. #69646C2semidirect
13. #69633C2semidirect
14. #69618C2semidirect
15. C22⋊C4×C3⋊C8C2semidirect
123. C2×#214D4semidirect
164. #808D4semidirect
285. C3×C22⋊C4SD16semidirect
497. C3⋊C8#121semidirect
598. C22⋊C4#214semidirect
790. C3#25410semidirect

Maximal subgroups

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

subgroupindex
C3×#24282
C2×#50762
C2×#50412
C2×C4×#2142
#734882
#717622
#716852
#716122
#696602
#696462
#696332
#696182
C22⋊C4×C3⋊C82
#254103