Finite Group Databasebeta

← #10826966

Subgroups — #10826966

Order 768.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic, complemented
2C2×#5791C211yesmaximal, characteristic, complemented
3C2×#5239C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5047C211yesmaximal, characteristic, complemented
6C2×#5037C211yesmaximal, characteristic, complemented
7#72126C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#71693C211yesmaximal, characteristic, complemented
11#71685C211yesmaximal, characteristic, complemented
12#71684C211yesmaximal, characteristic, complemented
13#71678C211yesmaximal, characteristic, complemented
14#71586C211yesmaximal, characteristic, complemented
15#71585C211yesmaximal, characteristic, complemented
16#23923—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C3×#525—24no—
21C3×#525—24no—
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#120—21no—
28C2×C3×C4×D4—21no—
29C2×C3×C4×D4—21no—
30C2×C3×#117C2211yescharacteristic
31C2×#953—21no—
32C22×#216C2211yescharacteristic, complemented
33C22×#215C2211yescharacteristic, complemented
34C22×#214C2211yescharacteristic, complemented
35C22×#213C2211yescharacteristic, complemented
36#5791—24no—
37#5791—24no—
38C2×#930C2211yescharacteristic
39C2×#930C2211yescharacteristic
40C2×#929—21no—
41C2×C4×#67—21no—
42C2×C4×#67—21no—
43C2×#926C2211yescharacteristic
44C2×#924C2211yescharacteristic
45C2×#924C2211yescharacteristic
46#5239—24no—
47#5238—24no—
48C2×#835C2211yescharacteristic, complemented
49C2×#835C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51C2×#832C2211yescharacteristic, complemented
52C2×#830C2211yescharacteristic
53C2×#830C2211yescharacteristic
54C2×#830C2211yescharacteristic
55C2×#830C2211yescharacteristic
56C2×#830C2211yescharacteristic
57C2×#830C2211yescharacteristic
58#5047—24no—
59#5037—24no—
60C2×#810C2211yescharacteristic, complemented
61C2×#810C2211yescharacteristic, complemented
62C2×#809C2211yescharacteristic, complemented
63C2×#809C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C2×#525D311yescharacteristic, complemented
70C2×#452—31no—
71C2×#452—31no—
72C2×#449—31no—
73C2×#449—31no—
74#2001—31no—
75#2000—31no—
76#2000—31no—
77#1999—31no—
78#1875—31no—
79#1875—31no—
80#1873—31no—
81#1873—31no—
82#1779—31no—
83C25×C3D411yescharacteristic
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—22no—
96C23×C3×C4—22no—
97C23×C3×C4—22no—
98C23×C3×C4—22no—
99C23×C3×C4—21no—
100C23×C3×C4—41no—
101C23×C3×C4—41no—
102C23×C3×C4D411yescharacteristic
103C23×C3×C4D411yescharacteristic
104C23×C3×C4D411yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C2×#235—22no—
112C2×#235—22no—
113C2×#235—22no—
114C2×#235—22no—
115C2×#235—41no—
116C2×#235—41no—
117C22×D12C2311yescharacteristic
118C22×C4×D3—21no—
119C22×Dic6C2311yescharacteristic
120C3×#123—28no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8D414yescomplemented
125C3×#121—22no—
126C3×#121—22no—
127C3×#121—22no—
128C3×#121D414yescomplemented
129C3×#120—28no—
130C3×C4×D4—28no—
131C3×C4×D4—28no—
132C3×#117—22no—
133C3×#117—22no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C42—21no—
144#953—28no—
145C2×#217—21no—
146C2×#217—21no—
147C2×#217—21no—
148C2×#216—22no—
149C2×#216—22no—
150C2×#216—41no—
151C2×#215—22no—
152C2×#215—22no—
153C2×#215—41no—
154C2×#214—22no—
155C2×#214—22no—
156C2×#214—41no—
157C2×#213—22no—
158C2×#213—22no—
159C2×#213—41no—
160#930—22no—
161#930—22no—
162#930—22no—
163#930D414yescomplemented
164#929—28no—
165C4×#67—28no—
166C4×#67—28no—
167C2×(C2×D3)⋊C4—21no—
168C2×(C2×D3)⋊C4—21no—
169#926—22no—
170#926—22no—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173#924—22no—
174#924—22no—
175#924—22no—
176#924D414yescomplemented
177C2×Dic3⋊C4—21no—
178C2×Dic3⋊C4—21no—
179C2×C4×Dic3—21no—
180C22×C3⋊C8C2311yescharacteristic
181C22×C3⋊C8C2311yescharacteristic
182C22×C3⋊C8C2311yescharacteristic
183C22×C3⋊C8C2311yescharacteristic
184#835—22no—
185#835—22no—
186#832—22no—
187#832—22no—
188#830—22no—
189#830—22no—
190#830—22no—
191#830—22no—
192#830—41no—
193#830—41no—
194#810—22no—
195#810—22no—
196#809—22no—
197#809—22no—
198C22×#41—31no—
199C22×#41C2×D311yescharacteristic
200C24×C4C2×D311yescharacteristic
201C22×Q16—31no—
202C22×SD16—31no—
203C22×SD16—31no—
204C22×D8—31no—
205#525—24no—
206#525—24no—
207#525—64no—
208#525—64no—
209C2×#123—21no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8C2×D311yescharacteristic
214C2×C22⋊Q8C2×D311yescharacteristic
215C2×#121—31no—
216C2×#121—31no—
217C2×#121C2×D311yescharacteristic
218C2×#121C2×D311yescharacteristic
219C2×#120—21no—
220C2×#120—61no—
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4—61no—
224C2×C4×D4—61no—
225C2×#117—31no—
226C2×#117C2×D311yescharacteristic
227#452—64no—
228#452—64no—
229#449—64no—
230#449—64no—
231C2×#103—31no—
232C2×#103—31no—
233C2×#103—31no—
234C2×#103—31no—
235C2×#102—31no—
236C2×#102—31no—
237C2×#102—31no—
238C2×#102—31no—
239C2×C22⋊C8—31no—
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8—31no—
245#340—31no—
246#340—31no—
247#340—31no—
248#340—31no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—21no—
253C24×C3—41no—
254C24×C3—41no—
255C24×C3—41no—
256C24×C3—41no—
257C24×C3C2×D411yescharacteristic
258C24×C3C2×D411yescharacteristic
259C24×C3C2×D411yescharacteristic
260C23×D3—21no—
261C3×#41—44no—
262C3×#41—44no—
263C3×#41—44no—
264C3×#41—44no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8C2×D412yes—
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—42no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4C2×D412yes—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—24no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—41no—
311C22×C3×C4—41no—
312C22×C3×C4—41no—
313C22×C3×C4—44no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4—42no—
318C22×C3×C4—42no—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2411yescharacteristic
327C2×#67—24no—
328C2×#67—24no—
329C2×#67—24no—
330C2×#67—42no—
331C2×#67—42no—
332C2×#67—42no—
333C2×#67—42no—
334C2×#67—42no—
335C2×#67—42no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339#235—44no—
340#235—44no—
341#235—44no—
342#235—44no—
343C2×D12—21no—
344C2×D12—21no—
345C2×D12—21no—
346C2×D12—21no—
347C2×D12—21no—
348C2×D12C2×D412yes—
349C2×C4×D3—24no—
350C2×C4×D3—42no—
351C2×C4×D3—42no—
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6—21no—
357C2×Dic6C2×D412yes—
358C3×C4⋊C4—24no—
359C3×C4⋊C4—24no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4C2×D412yes—
363C3×C4⋊C4C2×D412yes—
364C3×C22⋊C4—24no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—24no—
369C3×C42—24no—
370#217—24no—
371#217—24no—
372#217—24no—
373#216—44no—
374#215—44no—
375#214—44no—
376#213—44no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C2×D412yes—
382C4⋊Dic3C2×D412yes—
383Dic3⋊C4—24no—
384Dic3⋊C4—24no—
385C4×Dic3—24no—
386C2×C3⋊C8—21no—
387C2×C3⋊C8—21no—
388C2×C3⋊C8—21no—
389C2×C3⋊C8—21no—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—21no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396C2×C3⋊C8—21no—
397C2×C3⋊C8—21no—
398C25#6711yescharacteristic
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—41no—
404C2×#41—41no—
405C2×#41—62no—
406C2×#41—62no—
407C2×#41—62no—
408C2×#41—62no—
409C2×#41—121no—
410C2×#41—121no—
411C22×Q8—31no—
412C22×Q8C22×D311yescharacteristic
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—31no—
417C22×D4—61no—
418C22×D4—61no—
419C22×D4—61no—
420C22×D4C22×D311yescharacteristic
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—21no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—61no—
429C23×C4#6711yescharacteristic
430C23×C4#6711yescharacteristic
431C23×C4#6711yescharacteristic
432C23×C4C22×D311yescharacteristic
433C23×C4C22×D311yescharacteristic
434C23×C4C22×D311yescharacteristic
435C2×Q16—62no—
436C2×Q16—62no—
437C2×Q16—121no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16—62no—
442C2×SD16—121no—
443C2×SD16—121no—
444C2×D8—62no—
445C2×D8—62no—
446C2×D8—121no—
447C22×C8—31no—
448C22×C8—31no—
449C22×C8—31no—
450C22×C8—31no—
451#123—28no—
452#123—68no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—34no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8#6714yescomplemented
461#121—22no—
462#121—22no—
463#121—22no—
464#121—34no—
465#121—62no—
466#121—62no—
467#121—62no—
468#121#6714yescomplemented
469#120—28no—
470#120—68no—
471C4×D4—28no—
472C4×D4—28no—
473C4×D4—68no—
474C4×D4—68no—
475#117—22no—
476#117—22no—
477#117—62no—
478#117—62no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—61no—
484C2×C4⋊C4—61no—
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—61no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C22⋊C4—61no—
497C2×C42—21no—
498C2×C42—61no—
499#103—62no—
500#103—62no—
501#103—62no—
502#103—62no—
503#102—62no—
504#102—62no—
505#102—62no—
506#102—62no—
507C22⋊C8—62no—
508C22⋊C8—62no—
509C22⋊C8—62no—
510C22⋊C8—62no—
511C22⋊C8—121no—
512C22⋊C8—121no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—22no—
532C23×C3—44no—
533C23×C3—44no—
534C23×C3—44no—
535C23×C3—44no—
536C23×C3—44no—
537C23×C3—44no—
538C23×C3—44no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3#12012yes—
546C23×C3#12012yes—
547C23×C3#13512yes—
548C23×C3C22×D411yescharacteristic
549C22×D3—22no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C3×Q8—22no—
557C3×Q8—22no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—48no—
563C3×D4—48no—
564C3×D4—48no—
565C3×D4—41no—
566C3×D4—41no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—21no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—21no—
583C2×C3×C4—22no—
584C2×C3×C4—21no—
585C2×C3×C4—44no—
586C2×C3×C4—44no—
587C2×C3×C4—44no—
588C2×C3×C4—48no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4#12012yes—
600C2×C3×C4#12012yes—
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4H(5,𝔽2)11yescharacteristic
606C2×C3×C4H(5,𝔽2)11yescharacteristic
607#67—48no—
608#67—48no—
609#67—48no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619D12—22no—
620D12—22no—
621D12—41no—
622D12—41no—
623C4×D3—48no—
624Dic6—22no—
625Dic6—22no—
626Dic6—41no—
627Dic6—41no—
628C3⋊C8—41no—
629C3⋊C8—41no—
630C3⋊C8—41no—
631C3⋊C8—41no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24—41no—
640C24—61no—
641C24C2×#6711yescharacteristic
642C24C2×#6711yescharacteristic
643C24C2×#6711yescharacteristic
644#41—44no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—124no—
649#41—124no—
650#41—124no—
651#41—124no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—32no—
658C2×Q8—61no—
659C2×Q8—61no—
660C2×Q8—61no—
661C2×Q8—61no—
662C2×Q8—61no—
663C2×Q8C2×#6712yes—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—32no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—64no—
680C2×D4—64no—
681C2×D4—64no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—122no—
688C2×D4—122no—
689C2×D4—122no—
690C2×D4—122no—
691C2×D4—122no—
692C2×D4—122no—
693C2×D4C2×#6712yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—64no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—122no—
732C22×C4—122no—
733C22×C4D3×D412yes—
734C22×C4D3×D412yes—
735C22×C4C2×#6711yescharacteristic
736C22×C4C2×#6711yescharacteristic
737C22×C4C2×#6711yescharacteristic
738C22×C4C2×#6712yes—
739C22×C4C2×#6712yes—
740C22×C4C23×D311yescharacteristic
741Q16—124no—
742SD16—124no—
743SD16—124no—
744D8—124no—
745C2×C8—61no—
746C2×C8—61no—
747C2×C8—61no—
748C2×C8—61no—
749C2×C8—61no—
750C2×C8—61no—
751C2×C8—61no—
752C2×C8—61no—
753C2×C8—61no—
754C2×C8—61no—
755C2×C8—61no—
756C2×C8—61no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—32no—
762C4⋊C4—32no—
763C4⋊C4—64no—
764C4⋊C4—64no—
765C4⋊C4—61no—
766C4⋊C4—61no—
767C4⋊C4C2×#6712yes—
768C4⋊C4C2×#6712yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—64no—
775C22⋊C4—64no—
776C22⋊C4—64no—
777C22⋊C4—64no—
778C22⋊C4—64no—
779C42—24no—
780C42—64no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—416no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3C2×#12011yescharacteristic
811C22×C3C2×#12011yescharacteristic
812C22×C3#53411yescharacteristic
813C22×C3C2×#13511yescharacteristic
814C22×C3#57511yescharacteristic
815C22×C3#57511yescharacteristic
816C22×C3#57511yescharacteristic
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—81no—
821C2×D3—81no—
822C2×D3—81no—
823C2×D3—81no—
824C3×C4—22no—
825C3×C4—22no—
826C3×C4—41no—
827C3×C4—42no—
828C3×C4—42no—
829C3×C4—42no—
830C3×C4D4211yescharacteristic
831C3×C4D4211yescharacteristic
832C3×C4D4211yescharacteristic
833C3×C4D4211yescharacteristic
834Dic3—42no—
835Dic3—42no—
836Dic3—42no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—22no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—62no—
870C23—121no—
871C23—121no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23#93712yes—
877C23#95012yes—
878C23#95312yes—
879C23C22×#6711yescharacteristic
880Q8—22no—
881Q8—22no—
882Q8—41no—
883Q8—41no—
884Q8—62no—
885Q8—62no—
886Q8—121no—
887Q8—121no—
888D4—22no—
889D4—22no—
890D4—48no—
891D4—48no—
892D4—48no—
893D4—41no—
894D4—41no—
895D4—62no—
896D4—62no—
897D4—128no—
898D4—128no—
899D4—128no—
900D4—121no—
901D4—121no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—48no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—62no—
935C2×C4—62no—
936C2×C4—62no—
937C2×C4—128no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4#93712yes—
945C2×C4#95312yes—
946C2×C4C2×D3×D411yescharacteristic
947C2×C4C2×D3×D411yescharacteristic
948C2×C4#100411yescharacteristic
949C2×C4#100411yescharacteristic
950C2×C4C22×#6711yescharacteristic
951C2×C4C22×#6711yescharacteristic
952C8—121no—
953C8—121no—
954C8—121no—
955C8—121no—
956C2×C3—42no—
957C2×C3—42no—
958C2×C3—42no—
959C2×C3—82no—
960C2×C3#240311yescharacteristic
961C2×C3#300211yescharacteristic
962C2×C3#300211yescharacteristic
963C2×C3#300511yescharacteristic
964C2×C3#300511yescharacteristic
965C2×C3#319111yescharacteristic
966C2×C3#319711yescharacteristic
967D3—82no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—416no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—122no—
998C22—122no—
999C22—122no—
1000C22—241no—
1001C22—241no—
1002C22—241no—
1003C22—241no—
1004C22C2×#93711yescharacteristic
1005C22#580411yescharacteristic
1006C22C2×#95011yescharacteristic
1007C22#582211yescharacteristic
1008C22#582211yescharacteristic
1009C22#582211yescharacteristic
1010C22C2×#95311yescharacteristic
1011C4—22no—
1012C4—22no—
1013C4—41no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4D4×#6711yescharacteristic
1021C4D4×#6711yescharacteristic
1022C4D4×#6711yescharacteristic
1023C4D4×#6711yescharacteristic
1024C3#2392311yescharacteristic, complemented, Sylow
1025C2—42no—
1026C2—42no—
1027C2—42no—
1028C2—82no—
1029C2—242no—
1030C2#8292611yescharacteristic
1031C2#8292811yescharacteristic
1032C2#8293011yescharacteristic
1033C2#8293211yescharacteristic
1034C2#8405211yescharacteristic
1035C2#8408011yescharacteristic
1036C2#8408111yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#525C2
socleC23×C3C22×D4
hypercenterC2×#525D3
hypocenterC3#23923
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×C3×#525C2semidirect
2. C2×#5791C2semidirect
3. C2×#5239C2semidirect
4. C2×#5238C2semidirect
5. C2×#5047C2semidirect
6. C2×#5037C2semidirect
7. #72126C2semidirect
8. #71700C2semidirect
9. #71699C2semidirect
10. #71693C2semidirect
11. #71685C2semidirect
12. #71684C2semidirect
13. #71678C2semidirect
14. #71586C2semidirect
15. #71585C2semidirect
32. C22×#216C22semidirect
33. C22×#215C22semidirect
34. C22×#214C22semidirect
35. C22×#213C22semidirect
48. C2×#835C22semidirect
49. C2×#835C22semidirect
50. C2×#832C22semidirect
51. C2×#832C22semidirect
60. C2×#810C22semidirect
61. C2×#810C22semidirect
62. C2×#809C22semidirect
63. C2×#809C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
69. C2×#525D3semidirect
124. C3×C22⋊Q8D4semidirect
128. C3×#121D4semidirect
163. #930D4semidirect
176. #924D4semidirect
460. C22⋊Q8#67semidirect
468. #121#67semidirect
1024. C3#23923semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C2×#57912
C2×#52392
C2×#52382
C2×#50472
C2×#50372
#721262
#717002
#716992
#716932
#716852
#716842
#716782
#715862
#715852
#239233