Finite Group Databasebeta

← #10901263

Subgroups — #10901263

Order 768.

1138 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic, complemented
2C2×#5028C211yesmaximal, characteristic, complemented
3C2×#5016C211yesmaximal, characteristic, complemented
4#82287C211yesmaximal, characteristic, complemented
5#71794C211yesmaximal, characteristic, complemented
6#71792C211yesmaximal, characteristic, complemented
7#71729C211yesmaximal, characteristic, complemented
8#71728C211yesmaximal, characteristic, complemented
9#71700C211yesmaximal, characteristic, complemented
10#71699C211yesmaximal, characteristic, complemented
11#71685C211yesmaximal, characteristic, complemented
12#71684C211yesmaximal, characteristic
13#71626C211yesmaximal, characteristic, complemented
14#71604C211yesmaximal, characteristic, complemented
15#71583C211yesmaximal, characteristic, complemented
16#29677—31nomaximal, Sylow
17C3×#542—24no—
18C3×#542—24no—
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#126—21no—
21C2×C3×#124—21no—
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C22×#214C2211yescharacteristic
33C22×#213C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×#924C2211yescharacteristic
36C2×#875C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5028—24no—
44#5016—24no—
45#4994—21no—
46#4994—21no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4961—21no—
52#4961—21no—
53#4939C2211yescharacteristic
54#4935C2211yescharacteristic
55#4929C2211yescharacteristic
56C2×C4⋊(C3⋊C8)C2211yescharacteristic
57C2×C4⋊(C3⋊C8)C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#542D311yescharacteristic, complemented
65C2×#464—31no—
66C2×#463—31no—
67#2620—31no—
68#2024—31no—
69#2023—31no—
70#2015—31no—
71#2012—31no—
72#2001—31no—
73#2000—31no—
74#2000—31no—
75#1999—31no—
76#1803—31no—
77#1802—31no—
78#1798—31no—
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×D12C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C3×C4⋊Q8—22no—
89C3×C4⋊Q8—22no—
90C3×#126—28no—
91C3×#124—28no—
92C3×#124—22no—
93C3×#124—22no—
94C3×#123—28no—
95C3×C22⋊Q8—28no—
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—22no—
98C3×#121—22no—
99C3×#121—22no—
100C3×C4×Q8—22no—
101C3×C4×Q8D414yescomplemented
102C3×C4×D4—22no—
103C3×C4×D4D414yescomplemented
104C3×#117—22no—
105C3×#117—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4D411yescharacteristic
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C42—21no—
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#216—22no—
125C2×#216—41no—
126C2×#216—41no—
127C2×#215—22no—
128C2×#215—41no—
129C2×#215—41no—
130C2×#214—22no—
131C2×#214—41no—
132C2×#214—41no—
133C2×#213—22no—
134C2×#213—41no—
135C2×#213—41no—
136#930—41no—
137#930—41no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×C4⋊Dic3—21no—
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147#924—41no—
148#924—41no—
149C2×Dic3⋊C4—21no—
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154#875—22no—
155#875—22no—
156#835—41no—
157#835—41no—
158#832—41no—
159#832—41no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#830—41no—
163#830—41no—
164#810—22no—
165#810—22no—
166#809—22no—
167#809—22no—
168C4⋊(C3⋊C8)—22no—
169C4⋊(C3⋊C8)—22no—
170C22×Q16—31no—
171C22×SD16—31no—
172C22×SD16—31no—
173C22×D8—31no—
174#542—24no—
175#542—24no—
176C2×C4⋊Q8C2×D311yescharacteristic
177C2×#126—21no—
178C2×#124—21no—
179C2×#124—31no—
180C2×#124C2×D311yescharacteristic
181C2×#123—21no—
182C2×C22⋊Q8—21no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×#121—31no—
186C2×#121C2×D311yescharacteristic
187C2×C4×Q8C2×D311yescharacteristic
188C2×C4×D4C2×D311yescharacteristic
189C2×#117C2×D311yescharacteristic
190#464—64no—
191#463—64no—
192C2×C4⋊C8—31no—
193C2×C4⋊C8—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—31no—
201C2×#102—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8—31no—
204#396—61no—
205#396—61no—
206#394—61no—
207#394—61no—
208#391—31no—
209#390—31no—
210#384—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C2×C3×Q8—24no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—81no—
227C2×C3×Q8—81no—
228C2×C3×Q8C2×D412yes—
229C2×C3×D4—24no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—81no—
236C2×C3×D4—81no—
237C2×C3×D4C2×D412yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
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—24no—
248C22×C3×C4—81no—
249C22×C3×C4—81no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2411yescharacteristic
256C2×#67—42no—
257C2×#67—81no—
258C2×#67—81no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4C2×D412yes—
282C3×C4⋊C4C2×D412yes—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C42—24no—
291C3×C42—21no—
292C3×C42—21no—
293C3×C42C2×D412yes—
294C3×C42C2×D412yes—
295#217—42no—
296#216—44no—
297#215—44no—
298#214—44no—
299#213—44no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—81no—
304(C2×D3)⋊C4—81no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—81no—
310C4⋊Dic3—81no—
311Dic3⋊C4—42no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C22×Q8—21no—
325C22×Q8—31no—
326C22×Q8C22×D311yescharacteristic
327C22×D4—21no—
328C22×D4—31no—
329C22×D4—61no—
330C22×D4C22×D311yescharacteristic
331C23×C4—21no—
332C23×C4C22×D311yescharacteristic
333C2×Q16—62no—
334C2×Q16—121no—
335C2×Q16—121no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—121no—
339C2×SD16—121no—
340C2×SD16—121no—
341C2×SD16—121no—
342C2×D8—62no—
343C2×D8—121no—
344C2×D8—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—31no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351#126—28no—
352#124—28no—
353#124—22no—
354#124—22no—
355#124—62no—
356#124—62no—
357#123—28no—
358C22⋊Q8—28no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—121no—
362C22⋊Q8—121no—
363#121—22no—
364#121—22no—
365#121—121no—
366#121—121no—
367C4×Q8—22no—
368C4×Q8#6714yescomplemented
369C4×D4—22no—
370C4×D4#6714yescomplemented
371#117—22no—
372#117—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4#6711yescharacteristic
382C2×C4⋊C4#6711yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4#6711yescharacteristic
397C2×C22⋊C4#6711yescharacteristic
398C2×C42—21no—
399C2×C42C22×D311yescharacteristic
400C2×C42C22×D311yescharacteristic
401C4⋊C8—62no—
402C4⋊C8—62no—
403#103—62no—
404#103—62no—
405#103—121no—
406#103—121no—
407#102—62no—
408#102—62no—
409#102—121no—
410#102—121no—
411C22⋊C8—121no—
412C22⋊C8—121no—
413#95—61no—
414#95—61no—
415C23×C3—21no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3C22×D411yescharacteristic
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×Q8—84no—
442C3×D4—22no—
443C3×D4—22no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—84no—
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—22no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—84no—
474C2×C3×C4#12012yes—
475C2×C3×C4#12012yes—
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481C2×C3×C42−1+411yescharacteristic
482#67—84no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492D12—41no—
493D12—41no—
494D12—41no—
495D12—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499Dic6—41no—
500C3⋊C8—41no—
501C3⋊C8—41no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—21no—
505C24—61no—
506C24C2×#6711yescharacteristic
507C2×Q8—24no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—81no—
520C2×Q8—81no—
521C2×Q8C2×#6712yes—
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4—122no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4C2×#6712yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4C2×#6711yescharacteristic
556C22×C4C2×#6711yescharacteristic
557C22×C4C2×#6711yescharacteristic
558C22×C4C2×#6711yescharacteristic
559C22×C4C2×#6711yescharacteristic
560C22×C4C23×D311yescharacteristic
561Q16—124no—
562SD16—124no—
563SD16—124no—
564D8—124no—
565C2×C8—61no—
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—61no—
575C2×C8—61no—
576C2×C8—61no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—122no—
589C4⋊C4—241no—
590C4⋊C4—241no—
591C4⋊C4C2×#6712yes—
592C4⋊C4C2×#6712yes—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42C2×#6712yes—
610C42C2×#6712yes—
611C22×C3—41no—
612C22×C3—42no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—42no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3C2×#12011yescharacteristic
626C22×C3#53511yescharacteristic
627C22×C3#53711yescharacteristic
628C22×C3#57611yescharacteristic
629C22×C3#57711yescharacteristic
630C22×C3#57711yescharacteristic
631C22×C3#57811yescharacteristic
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—41no—
642C3×C4—42no—
643C3×C4—41no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4#53511yescharacteristic
648C3×C4#53511yescharacteristic
649C3×C4#53711yescharacteristic
650C3×C4#53711yescharacteristic
651Dic3—81no—
652Dic3—81no—
653Dic3—81no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23C22×#6711yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—41no—
679Q8—41no—
680Q8—84no—
681Q8—121no—
682Q8—121no—
683Q8—121no—
684Q8—121no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—84no—
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—22no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
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#95312yes—
732C2×C4#95312yes—
733C2×C4#100911yescharacteristic
734C2×C4#100911yescharacteristic
735C2×C4#100911yescharacteristic
736C2×C4#101011yescharacteristic
737C2×C4C22×#6711yescharacteristic
738C2×C4C22×#6711yescharacteristic
739C8—121no—
740C8—121no—
741C8—121no—
742C8—121no—
743C2×C3—81no—
744C2×C3—82no—
745C2×C3#261511yescharacteristic
746C2×C3#301211yescharacteristic
747C2×C3#301311yescharacteristic
748C2×C3#322411yescharacteristic
749C2×C3#322511yescharacteristic
750C2×C3#326211yescharacteristic
751C2×C3#326311yescharacteristic
752D3—161no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—241no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22—241no—
773C22—241no—
774C22#583011yescharacteristic
775C22#583311yescharacteristic
776C22#583511yescharacteristic
777C22#583611yescharacteristic
778C22#583711yescharacteristic
779C22#583811yescharacteristic
780C22C2×#95311yescharacteristic
781C4—22no—
782C4—22no—
783C4—41no—
784C4—42no—
785C4—41no—
786C4—42no—
787C4—42no—
788C4—41no—
789C4—241no—
790C4—241no—
791C4—241no—
792C4#583011yescharacteristic
793C4#583011yescharacteristic
794C4#583311yescharacteristic
795C4#583311yescharacteristic
796C3#2967711yescharacteristic, complemented, Sylow
797C2—81no—
798C2—82no—
799C2—481no—
800C2#8346311yescharacteristic
801C2#8346411yescharacteristic
802C2#8346611yescharacteristic
803C2#8346911yescharacteristic
804C2#8409811yescharacteristic
805C2#8410211yescharacteristic
806C2#8411411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#542C2
socleC23×C3C22×D4
prime radical#71684C2
hypercenterC2×#542D3
hypocenterC3#29677
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C3×#542C2semidirect
2. C2×#5028C2semidirect
3. C2×#5016C2semidirect
4. #82287C2semidirect
5. #71794C2semidirect
6. #71792C2semidirect
7. #71729C2semidirect
8. #71728C2semidirect
9. #71700C2semidirect
10. #71699C2semidirect
11. #71685C2semidirect
13. #71626C2semidirect
14. #71604C2semidirect
15. #71583C2semidirect
64. C2×#542D3semidirect
101. C3×C4×Q8D4semidirect
103. C3×C4×D4D4semidirect
368. C4×Q8#67semidirect
370. C4×D4#67semidirect
796. C3#29677semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×#50282
C2×#50162
#822872
#717942
#717922
#717292
#717282
#717002
#716992
#716852
#716842
#716262
#716042
#715832
#296773