Finite Group Databasebeta

← #10848814

Subgroups — #10848814

Order 768.

1158 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×#5682C211yesmaximal, characteristic, complemented
2C2×C3×#495C211yesmaximal, characteristic, complemented
3#83001C211yesmaximal, characteristic, complemented
4C2×#5055C211yesmaximal, characteristic, complemented
5#72071C211yesmaximal, characteristic, complemented
6#72065C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#72048C211yesmaximal, characteristic, complemented
10#72047C211yesmaximal, characteristic, complemented
11#72043C211yesmaximal, characteristic
12#72037C211yesmaximal, characteristic, complemented
13#71726C211yesmaximal, characteristic, complemented
14#69777C211yesmaximal, characteristic, complemented
15#69753C211yesmaximal, characteristic, complemented
16#25610—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C2×#938C2211yescharacteristic
28C2×D4×Dic3C2211yescharacteristic
29#5682—24no—
30#5682—24no—
31C2×#886—21no—
32C2×#885—21no—
33C2×#879—21no—
34C2×#878—21no—
35C2×#872C2211yescharacteristic
36C2×#869C2211yescharacteristic
37C3×#495—24no—
38C2×C3×C4×C8C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5221C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51#5055—24no—
52#4961—21no—
53#4961—21no—
54#4948—21no—
55#4948—21no—
56#4935C2211yescharacteristic
57C2×#803C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#542—31no—
65C2×#495D311yescharacteristic, complemented
66C2×#489—31no—
67#2620—31no—
68#2001—31no—
69#2000—31no—
70#2000—31no—
71#1999—31no—
72#1990—31no—
73#1959—31no—
74#1880—31no—
75#1879—31no—
76#1878—31no—
77#1877—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C22×C4×D3C2311yescharacteristic
87C22×Dic6—21no—
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C2×C3×Q16—41no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—41no—
96C2×C3×SD16—41no—
97C2×C3×D8—22no—
98C2×C3×D8—22no—
99C2×C3×D8—41no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×#124—22no—
103C3×#124—22no—
104C3×#124—22no—
105C3×#124D414yescomplemented
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C42C2311yescharacteristic
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116#946—22no—
117#946—22no—
118#946—41no—
119#946—41no—
120Q8×Dic3—22no—
121Q8×Dic3—22no—
122#938—22no—
123#938—22no—
124#938—41no—
125#938—41no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4D411yescharacteristic
143C2×Dic3⋊C4D411yescharacteristic
144C2×C4×Dic3—21no—
145C2×C4×Dic3C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148#886—28no—
149#885—28no—
150#879—28no—
151#878—28no—
152#872—22no—
153#872—22no—
154#869—22no—
155#869D414yescomplemented
156C3×C4×C8—22no—
157#835—22no—
158#835—22no—
159#835—41no—
160#835—41no—
161#832—22no—
162#832—22no—
163#832—41no—
164#832—41no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—22no—
169#803—22no—
170C22×Q16C2×D311yescharacteristic
171C22×SD16C2×D311yescharacteristic
172C22×SD16C2×D311yescharacteristic
173C22×D8C2×D311yescharacteristic
174#542—64no—
175#542—64no—
176C2×C4⋊Q8—31no—
177C2×#126—61no—
178C2×#124—61no—
179C2×#124C2×D311yescharacteristic
180C2×#124C2×D311yescharacteristic
181C2×#123—61no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8—61no—
185C2×#121—31no—
186C2×#121—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×#117—31no—
190#495—24no—
191#489—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⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×#97—31no—
203C2×C4×C8C2×D311yescharacteristic
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×C3—21no—
219C23×D3C2×D411yescharacteristic
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×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8C2×D412yes—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4C2×D412yes—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2411yescharacteristic
249C2×#67—24no—
250C2×#67—42no—
251C2×#67—81no—
252C2×#67—81no—
253C2×#67—81no—
254C2×#67—81no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—24no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—81no—
261C22×Dic3—81no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×Dic6—24no—
272C2×Dic6—81no—
273C2×Dic6—81no—
274C3×Q16—44no—
275C3×SD16—44no—
276C3×SD16—44no—
277C3×D8—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8#4112yes—
283C2×C3×C8#4112yes—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C42C2×D412yes—
289C3×C42C2×D412yes—
290#217—24no—
291#217—24no—
292#217—42no—
293#217—81no—
294#217—81no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—42no—
299C4⋊Dic3—24no—
300C4⋊Dic3—24no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—81no—
308C4⋊Dic3—81no—
309C4⋊Dic3C2×D412yes—
310C4⋊Dic3C2×D412yes—
311Dic3⋊C4—24no—
312Dic3⋊C4—22no—
313Dic3⋊C4—22no—
314Dic3⋊C4—42no—
315C4×Dic3—24no—
316C4×Dic3—21no—
317C4×Dic3—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—61no—
325C22×Q8C22×D311yescharacteristic
326C22×Q8C22×D311yescharacteristic
327C22×D4—61no—
328C22×D4—61no—
329C22×D4C22×D311yescharacteristic
330C22×D4C22×D311yescharacteristic
331C23×C4—31no—
332C23×C4—61no—
333C2×Q16—22no—
334C2×Q16—22no—
335C2×Q16—41no—
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—41no—
341C2×SD16—41no—
342C2×D8—22no—
343C2×D8—22no—
344C2×D8—41no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—34no—
350C4⋊Q8—62no—
351#126—68no—
352#124—22no—
353#124—22no—
354#124—22no—
355#124—68no—
356#124#6714yescomplemented
357#123—68no—
358C22⋊Q8—68no—
359C22⋊Q8—62no—
360C22⋊Q8—62no—
361C22⋊Q8—121no—
362C22⋊Q8—121no—
363#121—62no—
364#121—62no—
365#121—121no—
366#121—121no—
367C4×Q8—62no—
368C4×Q8—62no—
369C4×D4—62no—
370C4×D4—62no—
371#117—62no—
372#117—62no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—31no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—31no—
399C2×C42—61no—
400C2×C42C22×D311yescharacteristic
401#103—62no—
402#103—62no—
403#103—121no—
404#103—121no—
405#102—62no—
406#102—62no—
407#102—121no—
408#102—121no—
409C22⋊C8—62no—
410C22⋊C8—62no—
411#97—62no—
412C4×C8—22no—
413#95—61no—
414#95—61no—
415C23×C3—22no—
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×C3—41no—
429C23×C3C22×D411yescharacteristic
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4#12012yes—
464C2×C3×C4#12012yes—
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471#67—84no—
472#67—84no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—84no—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499Dic6—84no—
500C3×C8—22no—
501C3×C8—22no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—21no—
505C24—21no—
506C24—31no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—64no—
519C2×Q8—241no—
520C2×Q8—241no—
521C2×Q8C2×#6712yes—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—64no—
534C2×D4—122no—
535C2×D4—241no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4C2×#6712yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—64no—
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—241no—
557C22×C4—241no—
558C22×C4D3×D411yescharacteristic
559C22×C4D3×D411yescharacteristic
560C22×C4C23×D311yescharacteristic
561Q16—44no—
562SD16—44no—
563SD16—44no—
564D8—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8#23712yes—
576C2×C8#23712yes—
577C4⋊C4—32no—
578C4⋊C4—32no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—64no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—122no—
591C4⋊C4—241no—
592C4⋊C4—241no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—62no—
601C22⋊C4—62no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C42—64no—
607C42—61no—
608C42—61no—
609C42D3×D412yes—
610C42C2×#6712yes—
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×C3C2×#12011yescharacteristic
626C22×C3#53211yescharacteristic
627C22×C3#53511yescharacteristic
628C22×C3#57611yescharacteristic
629C22×C3#57711yescharacteristic
630C22×C3#57711yescharacteristic
631C22×C3#57811yescharacteristic
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—42no—
642C3×C4—81no—
643C3×C4#54611yescharacteristic
644C3×C4#54611yescharacteristic
645C3×C4#55011yescharacteristic
646C3×C4#55011yescharacteristic
647Dic3—41no—
648Dic3—42no—
649Dic3—42no—
650Dic3—41no—
651Dic3—41no—
652Dic3—81no—
653Dic3—81no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23C2×D3×D411yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—244no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—244no—
694D4—244no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—62no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—61no—
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×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—244no—
731C2×C4#93712yes—
732C2×C4#93712yes—
733C2×C4C2×D3×D411yescharacteristic
734C2×C4C2×#23711yescharacteristic
735C2×C4C2×#23711yescharacteristic
736C2×C4#100411yescharacteristic
737C2×C4#100411yescharacteristic
738C2×C4C22×#6711yescharacteristic
739C8—22no—
740C8—22no—
741C8—121no—
742C8—121no—
743C2×C3—82no—
744C2×C3—161no—
745C2×C3#243111yescharacteristic
746C2×C3#301211yescharacteristic
747C2×C3#301311yescharacteristic
748C2×C3#317311yescharacteristic
749C2×C3#317511yescharacteristic
750C2×C3#322411yescharacteristic
751C2×C3#322511yescharacteristic
752D3—81no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22#571511yescharacteristic
775C22#571611yescharacteristic
776C22#576911yescharacteristic
777C22#577011yescharacteristic
778C22#577011yescharacteristic
779C22#577111yescharacteristic
780C22C2×#93711yescharacteristic
781C4—22no—
782C4—22no—
783C4—42no—
784C4—81no—
785C4—121no—
786C4—122no—
787C4—122no—
788C4—121no—
789C4—121no—
790C4—241no—
791C4—241no—
792C4#571811yescharacteristic
793C4#571811yescharacteristic
794C4#580611yescharacteristic
795C4#580611yescharacteristic
796C3#2561011yescharacteristic, complemented, Sylow
797C2—82no—
798C2—161no—
799C2—241no—
800C2#8181011yescharacteristic
801C2#8181111yescharacteristic
802C2#8182711yescharacteristic
803C2#8182811yescharacteristic
804C2#8318711yescharacteristic
805C2#8391211yescharacteristic
806C2#8391311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#495C2
socleC23×C3C22×D4
prime radical#72043C2
hypercenterC2×#495D3
hypocenterC3#25610
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#5682C2semidirect
2. C2×C3×#495C2semidirect
3. #83001C2semidirect
4. C2×#5055C2semidirect
5. #72071C2semidirect
6. #72065C2semidirect
7. #72054C2semidirect
8. #72054C2semidirect
9. #72048C2semidirect
10. #72047C2semidirect
12. #72037C2semidirect
13. #71726C2semidirect
14. #69777C2semidirect
15. #69753C2semidirect
65. C2×#495D3semidirect
105. C3×#124D4semidirect
155. #869D4semidirect
356. #124#67semidirect
796. C3#25610semidirect

Maximal subgroups

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

subgroupindex
C2×#56822
C2×C3×#4952
#830012
C2×#50552
#720712
#720652
#720542
#720482
#720472
#720432
#720372
#717262
#697772
#697532
#256103