Finite Group Databasebeta

← #10848719

Subgroups — #10848719

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×#5680C211yesmaximal, characteristic, complemented
2C2×C3×#495C211yesmaximal, characteristic, complemented
3#83008C211yesmaximal, characteristic, complemented
4C2×#5056C211yesmaximal, 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#71725C211yesmaximal, characteristic, complemented
14#69778C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
16#25601—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#5680—24no—
30#5680—24no—
31C2×#883—21no—
32C2×#67⋊C4—21no—
33C2×#879—21no—
34C2×#877—21no—
35C2×C42×D3C2211yescharacteristic
36C2×#870C2211yescharacteristic
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#5056—24no—
52#4956—21no—
53#4956—21no—
54#4944—21no—
55#4944—21no—
56#4936C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#529—31no—
65C2×#495D311yescharacteristic, complemented
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⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C22×C4×D3D411yescharacteristic
87C22×C4×D3D411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C2×C3×Q16—22no—
90C2×C3×Q16—22no—
91C2×C3×Q16—41no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—41no—
97C2×C3×SD16—41no—
98C2×C3×D8—22no—
99C2×C3×D8—22no—
100C2×C3×D8—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×#124—22no—
104C3×#124—22no—
105C3×#124—22no—
106C3×#124D414yescomplemented
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C42C2311yescharacteristic
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117#946—22no—
118#946—22no—
119#946—41no—
120#946—41no—
121Q8×Dic3—22no—
122Q8×Dic3—22no—
123#938—22no—
124#938—22no—
125#938—41no—
126#938—41no—
127D4×Dic3—22no—
128D4×Dic3—22no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3D411yescharacteristic
142C2×C4×Dic3D411yescharacteristic
143C2×C4×Dic3C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#883—28no—
147#67⋊C4—28no—
148#879—28no—
149#877—28no—
150C42×D3—22no—
151C42×D3—22no—
152#870—22no—
153#870D414yescomplemented
154C3×C4×C8—22no—
155#835—22no—
156#835—22no—
157#835—41no—
158#835—41no—
159#832—22no—
160#832—22no—
161#832—41no—
162#832—41no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—22no—
169C4×C3⋊C8—22no—
170C22×Q16C2×D311yescharacteristic
171C22×SD16C2×D311yescharacteristic
172C22×SD16C2×D311yescharacteristic
173C22×D8C2×D311yescharacteristic
174#529—64no—
175#529—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#124C2×D311yescharacteristic
179C2×#124C2×D311yescharacteristic
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×C42—31no—
190#495—24no—
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⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×C4×C8—31no—
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#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—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C22×Dic3—24no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—42no—
261C22×Dic3—42no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×C4×D3—22no—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—22no—
275C2×C4×D3—41no—
276C2×C4×D3—41no—
277C3×Q16—44no—
278C3×SD16—44no—
279C3×SD16—44no—
280C3×D8—44no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8#4112yes—
286C2×C3×C8#4112yes—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C42C2×D412yes—
292C3×C42C2×D412yes—
293#217—24no—
294#217—24no—
295#217—42no—
296#217—42no—
297#217—42no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—42no—
300C4⋊Dic3—24no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3C2×D412yes—
308C4⋊Dic3C2×D412yes—
309Dic3⋊C4—24no—
310Dic3⋊C4—24no—
311Dic3⋊C4—24no—
312Dic3⋊C4—42no—
313C4×Dic3—24no—
314C4×Dic3—22no—
315C4×Dic3—22no—
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×Q8C22×D311yescharacteristic
325C22×Q8C22×D311yescharacteristic
326C22×D4—61no—
327C22×D4—61no—
328C22×D4C22×D311yescharacteristic
329C22×D4C22×D311yescharacteristic
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—61no—
334C2×Q16—22no—
335C2×Q16—22no—
336C2×Q16—41no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—41no—
342C2×SD16—41no—
343C2×D8—22no—
344C2×D8—22no—
345C2×D8—41no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8C22×D311yescharacteristic
349C22×C8C22×D311yescharacteristic
350#126—68no—
351#125—34no—
352#125—62no—
353#124—22no—
354#124—22no—
355#124—22no—
356#124#6714yescomplemented
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—68no—
369C4×D4—62no—
370C4×D4—62no—
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—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
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—31no—
393C2×C42—31no—
394C2×C42—31no—
395C2×C42—61no—
396C2×C42—62no—
397C2×C42—62no—
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—62no—
408C22⋊C8—62no—
409C4×C8—22no—
410C4×C8—62no—
411#95—61no—
412#95—61no—
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#13512yes—
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—48no—
472#67—84no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—48no—
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#13512yes—
495C4×D3—44no—
496C4×D3—44no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501C3×C8—22no—
502C3×C8—22no—
503C3⋊C8—41no—
504C3⋊C8—41no—
505C24—21no—
506C24—21no—
507C24—31no—
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—21no—
519C2×Q8C2×#6712yes—
520C2×D4—21no—
521C2×D4—21no—
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—64no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4C2×#6712yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—64no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—121no—
559C22×C4—121no—
560C22×C4—122no—
561C22×C4—122no—
562C22×C4D3×D411yescharacteristic
563C22×C4D3×D411yescharacteristic
564C22×C4C23×D311yescharacteristic
565Q16—44no—
566SD16—44no—
567SD16—44no—
568D8—44no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8#23712yes—
580C2×C8#23712yes—
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—24no—
595C22⋊C4—24no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—64no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—64no—
606C42—62no—
607C42—62no—
608C42—61no—
609C42—61no—
610C42D3×D412yes—
611C42C2×#6712yes—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
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—81no—
626C22×C3C2×#12011yescharacteristic
627C22×C3#53211yescharacteristic
628C22×C3#53511yescharacteristic
629C22×C3C2×#13511yescharacteristic
630C22×C3C2×#13511yescharacteristic
631C22×C3#57511yescharacteristic
632C22×C3#57511yescharacteristic
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—81no—
644C3×C4#54611yescharacteristic
645C3×C4#54611yescharacteristic
646C3×C4#55011yescharacteristic
647C3×C4#55011yescharacteristic
648Dic3—22no—
649Dic3—41no—
650Dic3—41no—
651Dic3—42no—
652Dic3—42no—
653Dic3—81no—
654Dic3—81no—
655C23—22no—
656C23—32no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23C2×D3×D411yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—128no—
694D4—244no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—32no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—124no—
717C2×C4—124no—
718C2×C4—128no—
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—121no—
733C2×C4#93712yes—
734C2×C4#93712yes—
735C2×C4C2×D3×D411yescharacteristic
736C2×C4C2×#23711yescharacteristic
737C2×C4C2×#23711yescharacteristic
738C2×C4#100411yescharacteristic
739C2×C4#100411yescharacteristic
740C2×C4C22×#6711yescharacteristic
741C8—22no—
742C8—22no—
743C8—121no—
744C8—121no—
745C2×C3—82no—
746C2×C3—161no—
747C2×C3#243111yescharacteristic
748C2×C3#300211yescharacteristic
749C2×C3#300211yescharacteristic
750C2×C3#316811yescharacteristic
751C2×C3#318311yescharacteristic
752C2×C3#321111yescharacteristic
753C2×C3#321211yescharacteristic
754D3—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—62no—
759C22—62no—
760C22—62no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22#571511yescharacteristic
777C22#571611yescharacteristic
778C22D3×#13511yescharacteristic
779C22D3×#13511yescharacteristic
780C22#576811yescharacteristic
781C22#576811yescharacteristic
782C22C2×#93711yescharacteristic
783C4—22no—
784C4—22no—
785C4—42no—
786C4—62no—
787C4—81no—
788C4—121no—
789C4—122no—
790C4—122no—
791C4—121no—
792C4—241no—
793C4—241no—
794C4#571811yescharacteristic
795C4#571811yescharacteristic
796C4#580611yescharacteristic
797C4#580611yescharacteristic
798C3#2560111yescharacteristic, complemented, Sylow
799C2—82no—
800C2—122no—
801C2—161no—
802C2#8180911yescharacteristic
803C2#8181211yescharacteristic
804C2#8182511yescharacteristic
805C2#8182611yescharacteristic
806C2#8318711yescharacteristic
807C2#8391111yescharacteristic
808C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#495C2
socleC23×C3C22×D4
prime radical#72043C2
hypercenterC2×#495D3
hypocenterC3#25601
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×#5680C2semidirect
2. C2×C3×#495C2semidirect
3. #83008C2semidirect
4. C2×#5056C2semidirect
5. #72071C2semidirect
6. #72065C2semidirect
7. #72054C2semidirect
8. #72054C2semidirect
9. #72048C2semidirect
10. #72047C2semidirect
12. #72037C2semidirect
13. #71725C2semidirect
14. #69778C2semidirect
15. C4×(C2×D3)⋊C8C2semidirect
65. C2×#495D3semidirect
106. C3×#124D4semidirect
153. #870D4semidirect
356. #124#67semidirect
798. C3#25601semidirect

Maximal subgroups

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

subgroupindex
C2×#56802
C2×C3×#4952
#830082
C2×#50562
#720712
#720652
#720542
#720482
#720472
#720432
#720372
#717252
#697782
C4×(C2×D3)⋊C82
#256013