Finite Group Databasebeta

← #10827581

Subgroups — #10827581

Order 768.

1222 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5641C211yesmaximal, characteristic
2C2×#5186C211yesmaximal, characteristic, complemented
3#82751C211yesmaximal, characteristic
4C2×#4802C211yesmaximal, characteristic, complemented
5C3×#2001C211yesmaximal, characteristic, complemented
6#72065C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71693C211yesmaximal, characteristic, complemented
9#70271C211yesmaximal, characteristic, complemented
10#70239C211yesmaximal, characteristic, complemented
11#70231C211yesmaximal, characteristic, complemented
12#69958C211yesmaximal, characteristic
13#69931C211yesmaximal, characteristic, complemented
14#68910C211yesmaximal, characteristic, complemented
15#68813C211yesmaximal, characteristic, complemented
16#23980—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C2×#926C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28#5641—24no—
29#5641—24no—
30C2×#898—21no—
31C2×#892C2211yescharacteristic
32C2×#888C2211yescharacteristic
33C2×#887—21no—
34C2×#885—21no—
35C2×#879—21no—
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5186—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48#4989—21no—
49#4987C2211yescharacteristic
50#4979—21no—
51#4973C2211yescharacteristic
52C2×#810C2211yescharacteristic
53#4956—21no—
54#4947—21no—
55#4802—24no—
56C3×#340C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#556—31no—
65C2×#451—31no—
66C2×#419—31no—
67#2409—31no—
68#2024—31no—
69#2024—31no—
70#2001—31no—
71#2001D311yescharacteristic, complemented
72#1894—31no—
73#1878—31no—
74#1878—31no—
75#1873—31no—
76#1873—31no—
77#1870—31no—
78#1825—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67D411yescharacteristic
83C2×D3×Q8—22no—
84C2×D3×Q8—22no—
85C2×D3×Q8—22no—
86C2×D3×Q8—22no—
87C2×D3×Q8—41no—
88C2×D3×Q8—41no—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×Dic6—21no—
92C22×Dic6—21no—
93C22×Dic6C2311yescharacteristic
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16—41no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—41no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217D411yescharacteristic
112#946—22no—
113#946D414yes—
114Q8×Dic3—22no—
115Q8×Dic3—22no—
116C2×#216—22no—
117C2×#216—22no—
118C2×#216—41no—
119C4×#67—22no—
120C4×#67—22no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4D411yescharacteristic
125#926—22no—
126#926—22no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—22no—
132#924—41no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4D411yescharacteristic
137C2×C4×Dic3—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—41no—
145C2×ΓL(1,𝔽25)—41no—
146#898—28no—
147#892—22no—
148#892D414yes—
149#888—22no—
150#888—22no—
151#887—28no—
152#885—28no—
153#879—28no—
154C3×#103—22no—
155C3×#103—41no—
156C3×C22⋊C8—41no—
157#835—22no—
158#835—22no—
159#835—41no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165#830—41no—
166(C2×D3)⋊C8—22no—
167#816—22no—
168#816—22no—
169#810—22no—
170C23×Q8—31no—
171C22×Q16—31no—
172C22×Q16C2×D311yescharacteristic
173C22×M16—31no—
174#556—64no—
175#556—64no—
176C2×C4⋊Q8—31no—
177C2×#126—61no—
178C2×#126—61no—
179C2×#124—61no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×C22⋊Q8C2×D311yescharacteristic
184C2×C4×Q8—31no—
185C2×C4×Q8—61no—
186C2×C4×D4—31no—
187C2×#117—31no—
188C2×#117—31no—
189#451—64no—
190#419—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103C2×D311yescharacteristic
198C2×#103C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202#395—61no—
203#393—61no—
204#391—31no—
205#391—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8C2×D412yes—
230C2×C3×Q8#4112yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—22no—
244C2×#67—22no—
245C2×#67—41no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253D3×Q8—28no—
254D3×Q8—44no—
255D3×Q8—44no—
256D3×Q8—44no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3C2×D412yes—
265C2×C4×D3C2×D412yes—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—24no—
271C2×Dic6—21no—
272C2×Dic6—42no—
273C2×Dic6—42no—
274C2×Dic6—42no—
275C2×Dic6—42no—
276C2×Dic6—42no—
277C2×Dic6#4112yes—
278C3×Q16—44no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—42no—
290C3×C4⋊C4C2×D412yes—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—42no—
293#217—24no—
294#217—22no—
295#217—42no—
296#216—44no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—42no—
301C4⋊Dic3—24no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3C2×D412yes—
307C4⋊Dic3C2×D412yes—
308Dic3⋊C4—24no—
309Dic3⋊C4—24no—
310Dic3⋊C4—22no—
311Dic3⋊C4—42no—
312C4×Dic3—24no—
313C4×Dic3—24no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C4×Dic3—24no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323ΓL(1,𝔽25)—44no—
324C22×Q8—31no—
325C22×Q8—61no—
326C22×Q8—61no—
327C22×Q8—62no—
328C22×Q8—62no—
329C22×Q8—62no—
330C22×Q8—62no—
331C22×Q8—121no—
332C22×Q8—121no—
333C22×Q8C22×D311yescharacteristic
334C22×Q8C22×D311yescharacteristic
335C22×D4—31no—
336C23×C4—31no—
337C23×C4—61no—
338C23×C4C22×D311yescharacteristic
339C2×Q16—22no—
340C2×Q16—22no—
341C2×Q16—41no—
342C2×Q16—62no—
343C2×Q16—62no—
344C2×Q16—121no—
345C2×M16—62no—
346C2×M16—121no—
347C2×M16—121no—
348C22×C8—31no—
349C22×C8—31no—
350C22×C8C22×D311yescharacteristic
351C22×C8C22×D311yescharacteristic
352C4⋊Q8—62no—
353C4⋊Q8—62no—
354#126—68no—
355#126—68no—
356#124—68no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—34no—
361C22⋊Q8—41no—
362C22⋊Q8—62no—
363C22⋊Q8—62no—
364C22⋊Q8—121no—
365C4×Q8—68no—
366C4×Q8—62no—
367C4×Q8—62no—
368C4×D4—62no—
369C4×D4—62no—
370#117—34no—
371#117—62no—
372#117—62no—
373#117—62no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C42—31no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42—61no—
399#103—22no—
400#103—41no—
401#103—62no—
402#103—62no—
403#103—62no—
404#103—62no—
405#103—62no—
406#103—121no—
407C22⋊C8—41no—
408C22⋊C8—62no—
409C22⋊C8—121no—
410#95—61no—
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—21no—
422C23×C3C22×D411yescharacteristic
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3#12012yes—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8—22no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×Q8—41no—
437C3×Q8—41no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4H(5,𝔽2)11yescharacteristic
462C2×C3×C4H(5,𝔽2)11yescharacteristic
463#67—44no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—22no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
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#12012yes—
484C2×Dic3#13712yes—
485C4×D3—22no—
486C4×D3—22no—
487C4×D3—22no—
488C4×D3—22no—
489C4×D3—48no—
490Dic6—22no—
491Dic6—22no—
492Dic6—48no—
493Dic6—48no—
494Dic6—41no—
495Dic6—41no—
496C3×C8—41no—
497C3×C8—41no—
498C3⋊C8—41no—
499C3⋊C8—41no—
500C24—31no—
501C24D3×D411yescharacteristic
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—32no—
513C2×Q8—64no—
514C2×Q8—61no—
515C2×Q8—68no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×Q8—122no—
521C2×Q8—122no—
522C2×Q8—122no—
523C2×Q8—122no—
524C2×Q8—122no—
525C2×Q8—124no—
526C2×Q8—124no—
527C2×Q8—124no—
528C2×Q8D3×D412yes—
529C2×Q8#23712yes—
530C2×D4—62no—
531C2×D4—62no—
532C2×D4—121no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—32no—
546C22×C4—32no—
547C22×C4—31no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—122no—
557C22×C4—122no—
558C22×C4—122no—
559C22×C4D3×D411yescharacteristic
560C22×C4C23×D311yescharacteristic
561Q16—44no—
562Q16—124no—
563M16—124no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—32no—
581C4⋊C4—32no—
582C4⋊C4—42no—
583C4⋊C4—62no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4D3×D412yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—62no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—62no—
599C22⋊C4—64no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C42—64no—
603C42—64no—
604C42—64no—
605C42—61no—
606C42—61no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3C2×#12011yescharacteristic
615C22×C3#54611yescharacteristic
616C22×C3#54611yescharacteristic
617C22×C3C2×#13711yescharacteristic
618C22×C3#57511yescharacteristic
619C22×C3#57811yescharacteristic
620C22×C3#57811yescharacteristic
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C3×C4—42no—
629C3×C4—41no—
630C3×C4—42no—
631C3×C4—42no—
632C3×C4—81no—
633C3×C4#52511yescharacteristic
634C3×C4#53511yescharacteristic
635C3×C4#54611yescharacteristic
636C3×C4#54611yescharacteristic
637Dic3—22no—
638Dic3—22no—
639Dic3—42no—
640Dic3—42no—
641Dic3—41no—
642Dic3—42no—
643Dic3—81no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—32no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23C2×D3×D411yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—62no—
668Q8—62no—
669Q8—128no—
670Q8—128no—
671Q8—121no—
672Q8—121no—
673D4—124no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—61no—
708C2×C4—62no—
709C2×C4—128no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4C2×D3×D411yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×#23711yescharacteristic
722C2×C4#100411yescharacteristic
723C2×C4#100411yescharacteristic
724C2×C4D3×#4111yescharacteristic
725C8—41no—
726C8—41no—
727C8—121no—
728C8—121no—
729C2×C3—81no—
730C2×C3#240411yescharacteristic
731C2×C3#300711yescharacteristic
732C2×C3#301111yescharacteristic
733C2×C3#331311yescharacteristic
734C2×C3#331311yescharacteristic
735C2×C3#332811yescharacteristic
736C2×C3#332811yescharacteristic
737D3—42no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—62no—
746C22—62no—
747C22—62no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22D3×#12011yescharacteristic
753C22#559111yescharacteristic
754C22#561011yescharacteristic
755C22#576611yescharacteristic
756C22#576811yescharacteristic
757C22D3×#13711yescharacteristic
758C22#577911yescharacteristic
759C4—42no—
760C4—41no—
761C4—42no—
762C4—42no—
763C4—62no—
764C4—62no—
765C4—81no—
766C4—121no—
767C4—122no—
768C4—122no—
769C4—122no—
770C4—241no—
771C4#559111yescharacteristic
772C4#560611yescharacteristic
773C4#561011yescharacteristic
774C4#571511yescharacteristic
775C3#2398011yescharacteristic, complemented, Sylow
776C2—81no—
777C2—122no—
778C2#7675411yescharacteristic
779C2#8018511yescharacteristic
780C2#8020011yescharacteristic
781C2#8022811yescharacteristic
782C2#8025111yescharacteristic
783C2#8078311yescharacteristic
784C2#8092711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC22×#67D4
hypercenter#2001D3
hypocenterC3#23980
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#5186C2semidirect
4. C2×#4802C2semidirect
5. C3×#2001C2semidirect
6. #72065C2semidirect
7. #71700C2semidirect
8. #71693C2semidirect
9. #70271C2semidirect
10. #70239C2semidirect
11. #70231C2semidirect
13. #69931C2semidirect
14. #68910C2semidirect
15. #68813C2semidirect
71. #2001D3semidirect
775. C3#23980semidirect

Maximal subgroups

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

subgroupindex
C2×#56412
C2×#51862
#827512
C2×#48022
C3×#20012
#720652
#717002
#716932
#702712
#702392
#702312
#699582
#699312
#689102
#688132
#239803