Finite Group Databasebeta

← #10848723

Subgroups — #10848723

Order 768.

1216 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5479C211yesmaximal, characteristic, complemented
2#82077C211yesmaximal, characteristic, complemented
3C2×#4696C211yesmaximal, characteristic, complemented
4C2×#4697C211yesmaximal, characteristic, complemented
5C3×C4×C22⋊C8C211yesmaximal, characteristic, complemented
6#69964C211yesmaximal, characteristic, complemented
7#69962C211yesmaximal, characteristic, complemented
8#69962C211yesmaximal, characteristic, complemented
9#69961C211yesmaximal, characteristic
10#69778C211yesmaximal, characteristic, complemented
11#69773C211yesmaximal, characteristic, complemented
12#68686C211yesmaximal, characteristic, complemented
13#68685C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68672C211yesmaximal, characteristic, complemented
16#25601—31nomaximal, Sylow
17C22×C3×C42C2211yescharacteristic
18C2×#930C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#929—21no—
21C2×C4×#67—21no—
22C2×#924C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C22×Dic12C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C22×#204C2211yescharacteristic
27C22×#204C2211yescharacteristic
28#5479—24no—
29#5479—24no—
30C2×#876—21no—
31C2×#875C2211yescharacteristic
32C2×#875C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C2×#872—21no—
35C2×#870C2211yescharacteristic
36C2×C4×Dic6C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C4×C8C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic
41#5213—21no—
42#5213—21no—
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×#816C2211yescharacteristic
51#4940—21no—
52#4940—21no—
53#4939C2211yescharacteristic
54#4936C2211yescharacteristic
55#4929C2211yescharacteristic
56#4697—24no—
57#4696—24no—
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#529—31no—
65C2×#495—31no—
66C2×#488—31no—
67#2850—31no—
68#2001—31no—
69#2000—31no—
70#2000—31no—
71#1999—31no—
72#1991—31no—
73#1958—31no—
74#1880—31no—
75#1879—31no—
76#1878—31no—
77#1877—31no—
78C4×C22⋊C8D311yescharacteristic, complemented
79C23×C3×C4D411yescharacteristic
80C23×C3×C4D411yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×D12C2311yescharacteristic
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×Dic6C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C2×C3×C42—22no—
94C2×C3×C42—22no—
95C2×C3×C42D411yescharacteristic
96C2×C3×C42D411yescharacteristic
97C2×C3×C42C2311yescharacteristic
98C2×C3×C42C2311yescharacteristic
99C2×#217—21no—
100C2×#217—21no—
101#930—22no—
102#930—22no—
103#930—41no—
104#930—41no—
105#929—28no—
106C4×#67—28no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×C4⋊Dic3C2311yescharacteristic
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120#924—22no—
121#924—22no—
122#924—41no—
123#924—41no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×C4×Dic3—21no—
130C2×Dic12—22no—
131C2×Dic12—22no—
132C2×Dic12—41no—
133C2×D24—22no—
134C2×D24—22no—
135C2×D24—41no—
136C2×#204—22no—
137C2×#204—22no—
138C2×#204—22no—
139C2×#204—22no—
140C2×#204—41no—
141C2×#204—41no—
142#876—28no—
143#875—22no—
144#875—22no—
145#875—22no—
146#875D414yescomplemented
147C4×D12—22no—
148C4×D12—22no—
149#872—28no—
150#870—22no—
151#870D414yescomplemented
152C4×Dic6—22no—
153C4×Dic6—22no—
154C3×C22⋊C8—22no—
155C3×C22⋊C8—22no—
156C3×C4×C8—22no—
157C3×C4×C8—22no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—22no—
163#821—22no—
164#821—41no—
165#821—41no—
166#816—22no—
167#816—22no—
168#816—41no—
169#816—41no—
170C22×Q16—31no—
171C22×SD16—31no—
172C22×SD16—31no—
173C22×D8—31no—
174#529—64no—
175#529—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#124—31no—
179C2×#124—31no—
180C2×#123—61no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184C2×#121—31no—
185C2×C4×Q8—31no—
186C2×C4×D4—31no—
187C2×C4×D4—61no—
188C2×#117—61no—
189C22×C42C2×D311yescharacteristic
190#495—64no—
191#488—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×C22⋊C8C2×D311yescharacteristic
201C2×C22⋊C8C2×D311yescharacteristic
202C2×C4×C8C2×D311yescharacteristic
203C2×C4×C8C2×D311yescharacteristic
204#391—31no—
205#390—31no—
206#388—61no—
207#388—61no—
208#386—61no—
209#386—61no—
210#382—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336C2×D311yescharacteristic
216#336C2×D311yescharacteristic
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—41no—
231C22×C3×C4—41no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12C2×D412yes—
262C2×C4×D3—24no—
263C2×C4×D3—42no—
264C2×C4×D3—42no—
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×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6C2×D412yes—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8#4112yes—
288C2×C3×C8#4112yes—
289C3×C42—22no—
290C3×C42—22no—
291C3×C42—21no—
292C3×C42—21no—
293C3×C42C2×D412yes—
294C3×C42C2×D412yes—
295#217—24no—
296#217—42no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3C2×D412yes—
313C4⋊Dic3C2×D412yes—
314Dic3⋊C4—24no—
315Dic3⋊C4—24no—
316Dic3⋊C4—24no—
317Dic3⋊C4—24no—
318Dic3⋊C4—42no—
319C4×Dic3—24no—
320Dic12—44no—
321D24—44no—
322#204—44no—
323#204—44no—
324C22×Q8—31no—
325C22×Q8—31no—
326C22×D4—31no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C23×C4—61no—
331C23×C4D1211yescharacteristic
332C23×C4D1211yescharacteristic
333C23×C4C22×D311yescharacteristic
334C2×Q16—62no—
335C2×Q16—62no—
336C2×Q16—121no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—121no—
342C2×SD16—121no—
343C2×D8—62no—
344C2×D8—62no—
345C2×D8—121no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C22×C8C22×D311yescharacteristic
350#126—68no—
351#125—34no—
352#125—62no—
353#124—34no—
354#124—62no—
355#124—62no—
356#124—62no—
357#123—68no—
358C22⋊Q8—62no—
359C22⋊Q8—62no—
360C22⋊Q8—121no—
361C22⋊Q8—121no—
362#121—62no—
363#121—62no—
364#121—121no—
365#121—121no—
366C4×Q8—62no—
367C4×Q8—62no—
368C4×D4—62no—
369C4×D4—62no—
370C4×D4—68no—
371#117—68no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—61no—
395C2×C42D1211yescharacteristic
396C2×C42D1211yescharacteristic
397C2×C42C22×D311yescharacteristic
398C2×C42C22×D311yescharacteristic
399#103—62no—
400#103—62no—
401#103—121no—
402#103—121no—
403#102—62no—
404#102—62no—
405#102—121no—
406#102—121no—
407C22⋊C8—22no—
408C22⋊C8—22no—
409C4×C8—22no—
410C4×C8—22no—
411#95—61no—
412#95—61no—
413#95—61no—
414#95—61no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3#13512yes—
422C23×C3C22×D411yescharacteristic
423C22×D3—22no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
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—44no—
450C2×C3×C4—44no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4#12012yes—
456C2×C3×C4#12012yes—
457C2×C3×C4#13512yes—
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4H(5,𝔽2)11yescharacteristic
463C2×C3×C4H(5,𝔽2)11yescharacteristic
464#67—48no—
465#67—84no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484D12—22no—
485D12—22no—
486D12—41no—
487D12—41no—
488D12—41no—
489D12—41no—
490D12—41no—
491D12—41no—
492C4×D3—48no—
493Dic6—22no—
494Dic6—22no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499Dic6—41no—
500Dic6—41no—
501C3×C8—22no—
502C3×C8—22no—
503C3×C8—41no—
504C3×C8—41no—
505C24—61no—
506C24—61no—
507C24C2×D1211yescharacteristic
508C2×Q8—32no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×D4—32no—
521C2×D4—64no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—64no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—122no—
558C22×C4—122no—
559C22×C4C2×D1211yescharacteristic
560C22×C4C2×D1211yescharacteristic
561C22×C4C2×D1211yescharacteristic
562C22×C4C2×D1211yescharacteristic
563C22×C4C2×D1211yescharacteristic
564C22×C4C23×D311yescharacteristic
565Q16—124no—
566SD16—124no—
567SD16—124no—
568D8—124no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8#23512yes—
580C2×C8#23512yes—
581C4⋊C4—32no—
582C4⋊C4—32no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—22no—
606C42—22no—
607C42—21no—
608C42—21no—
609C42—64no—
610C42D3×D412yes—
611C42D3×D412yes—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3C2×#12011yescharacteristic
620C22×C3#53211yescharacteristic
621C22×C3#53511yescharacteristic
622C22×C3C2×#13511yescharacteristic
623C22×C3C2×#13511yescharacteristic
624C22×C3#57511yescharacteristic
625C22×C3#57511yescharacteristic
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4#54611yescharacteristic
646C3×C4#54611yescharacteristic
647C3×C4#55011yescharacteristic
648C3×C4#55011yescharacteristic
649Dic3—42no—
650Dic3—42no—
651Dic3—42no—
652Dic3—81no—
653Dic3—81no—
654Dic3—81no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—62no—
662C23—121no—
663C23—121no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23#90412yes—
676C23C22×D1211yescharacteristic
677Q8—62no—
678Q8—62no—
679Q8—121no—
680Q8—121no—
681Q8—121no—
682Q8—121no—
683Q8—121no—
684Q8—121no—
685D4—62no—
686D4—62no—
687D4—128no—
688D4—121no—
689D4—121no—
690D4—121no—
691D4—121no—
692D4—121no—
693D4—121no—
694D4—244no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—128no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4#88212yes—
733C2×C4#88212yes—
734C2×C4#90412yes—
735C2×C4C2×#23511yescharacteristic
736C2×C4C2×#23511yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4#100911yescharacteristic
740C2×C4#100911yescharacteristic
741C8—22no—
742C8—22no—
743C8—41no—
744C8—41no—
745C2×C3—42no—
746C2×C3#243111yescharacteristic
747C2×C3#300211yescharacteristic
748C2×C3#300211yescharacteristic
749C2×C3#316811yescharacteristic
750C2×C3#318311yescharacteristic
751C2×C3#321111yescharacteristic
752C2×C3#321211yescharacteristic
753D3—82no—
754D3—161no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22—241no—
766C22—241no—
767C22—241no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22#547711yescharacteristic
777C22C2×#88211yescharacteristic
778C22#552511yescharacteristic
779C22C2×#90411yescharacteristic
780C22C2×#90411yescharacteristic
781C22#574811yescharacteristic
782C22#574811yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—122no—
789C4—122no—
790C4—122no—
791C4—241no—
792C4—241no—
793C4—241no—
794C4#555011yescharacteristic
795C4#555011yescharacteristic
796C4#555311yescharacteristic
797C4#555311yescharacteristic
798C3#2560111yescharacteristic, complemented, Sylow
799C2—42no—
800C2—242no—
801C2—481no—
802C2#7358611yescharacteristic
803C2#7846911yescharacteristic
804C2#7853411yescharacteristic
805C2#7861011yescharacteristic
806C2#7861011yescharacteristic
807C2#7930711yescharacteristic
808C2#7930811yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C4×C22⋊C8C2
socleC23×C3C22×D4
prime radical#69961C2
hypercenterC4×C22⋊C8D3
hypocenterC3#25601
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#5479C2semidirect
2. #82077C2semidirect
3. C2×#4696C2semidirect
4. C2×#4697C2semidirect
5. C3×C4×C22⋊C8C2semidirect
6. #69964C2semidirect
7. #69962C2semidirect
8. #69962C2semidirect
10. #69778C2semidirect
11. #69773C2semidirect
12. #68686C2semidirect
13. #68685C2semidirect
14. #68673C2semidirect
15. #68672C2semidirect
78. C4×C22⋊C8D3semidirect
146. #875D4semidirect
151. #870D4semidirect
798. C3#25601semidirect

Maximal subgroups

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

subgroupindex
C2×#54792
#820772
C2×#46962
C2×#46972
C3×C4×C22⋊C82
#699642
#699622
#699612
#697782
#697732
#686862
#686852
#686732
#686722
#256013