Finite Group Databasebeta

← #10830657

Subgroups — #10830657

Order 768.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5676C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×#5187C211yesmaximal, characteristic, complemented
4C2×#5169C211yesmaximal, characteristic, complemented
5#82499C211yesmaximal, characteristic, complemented
6C2×C4×#215C211yesmaximal, characteristic, complemented
7#72071C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71725C211yesmaximal, characteristic, complemented
10#70480C211yesmaximal, characteristic, complemented
11#70470C211yesmaximal, characteristic, complemented
12#70274C211yesmaximal, characteristic, complemented
13#70267C211yesmaximal, characteristic, complemented
14#70207C211yesmaximal, characteristic, complemented
15#70198C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×C4×Q8C2211yescharacteristic, complemented
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×#946C2211yescharacteristic, complemented
26C22×#215C2211yescharacteristic
27C2×#938C2211yescharacteristic
28#5676—24no—
29#5676—24no—
30C2×#884—21no—
31C2×#883—21no—
32C2×#882—21no—
33C2×D3×C22⋊C4—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C3×#464—24no—
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic
40C2×#835C2211yescharacteristic, complemented
41C2×#835C2211yescharacteristic, complemented
42C2×#835C2211yescharacteristic, complemented
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5187—24no—
46#5169—24no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C4×#215—24no—
54#4991—21no—
55#4987C2211yescharacteristic
56#4987C2211yescharacteristic, complemented
57#4981—21no—
58C2×#809C2211yescharacteristic
59C2×#808C2211yescharacteristic, complemented
60#4940—21no—
61#4940—21no—
62#4936C2211yescharacteristic, complemented
63C2×C4×C3⋊C8C2211yescharacteristic, complemented
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464D311yescharacteristic, complemented
68C2×#452—31no—
69C2×#450—31no—
70C2×C4×SD16—31no—
71#2536—31no—
72#2035—31no—
73#2034—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×Q8C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239—41no—
92C2×#239—41no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—22no—
97C2×D3×D4—41no—
98C2×D3×D4—41no—
99C22×D12—21no—
100C22×D12D411yescharacteristic
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—41no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—41no—
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C3×#124—22no—
115C3×#124D414yes—
116C3×C4×Q8—22no—
117C3×C4×Q8—22no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C42—21no—
123C2×C3×C42C2311yescharacteristic
124C2×#217—21no—
125#946—22no—
126#946—22no—
127#946—22no—
128#946—22no—
129#946—41no—
130#946—41no—
131C2×#215—22no—
132C2×#215—22no—
133C2×#215D414yescomplemented
134#938—22no—
135#938—22no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4D411yescharacteristic
143C2×(C2×D3)⋊C4D411yescharacteristic
144C2×C4⋊Dic3D411yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4—21no—
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153#884—28no—
154#883—28no—
155#882—28no—
156D3×C22⋊C4—28no—
157C4×D12—22no—
158C4×D12—22no—
159C4×D12—22no—
160C4×D12D414yes—
161C3×C4⋊C8—22no—
162C3×#103—22no—
163C3×#102—22no—
164#835—22no—
165#835—22no—
166#835—41no—
167#832—22no—
168#832—41no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#821—22no—
174#821—22no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—22no—
177(C2×D3)⋊C8—41no—
178(C2×D3)⋊C8—41no—
179#809—22no—
180#808—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×Q16C2×D311yescharacteristic, complemented
185C22×SD16—31no—
186C22×SD16C2×D311yescharacteristic
187#546—64no—
188#546—64no—
189C2×#124C2×D311yescharacteristic
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×Q8C2×D311yescharacteristic, complemented
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#464—24no—
202#452—64no—
203#450—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8C2×D311yescharacteristic, complemented
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103C2×D311yescharacteristic, complemented
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
221C2×C4×C8—31no—
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C23×D3—21no—
233C23×D3—24no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—81no—
239C23×D3—81no—
240C23×D3C2×D411yescharacteristic
241C23×D3C2×D411yescharacteristic
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8C2×D412yes—
253C2×C3×Q8C2×D412yes—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4C2×D412yes—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C2×#67—24no—
267C2×#67—24no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—81no—
271C2×#67—81no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3C2×D411yescharacteristic
276C22×Dic3C2×D411yescharacteristic
277#239—44no—
278#239—44no—
279#239—44no—
280#239—44no—
281D3×D4—44no—
282D3×D4—44no—
283D3×D4—44no—
284D3×D4—44no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—24no—
289C2×D12—22no—
290C2×D12—22no—
291C2×D12—41no—
292C2×D12—42no—
293C2×D12—42no—
294C2×D12C2×D412yes—
295C2×D12C2×D412yes—
296C2×D12#4112yes—
297C2×C4×D3—24no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—24no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3—81no—
314C2×C4×D3—81no—
315C3×Q16—44no—
316C3×SD16—44no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—42no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C42—42no—
329C3×C42C2×D412yes—
330C3×C42C2×D412yes—
331#217—24no—
332#215—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—22no—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341C4⋊Dic3—22no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3C2×D412yes—
348Dic3⋊C4—24no—
349Dic3⋊C4—42no—
350Dic3⋊C4—42no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8C2×D412yes—
357C25—61no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—62no—
362C2×#41—121no—
363C2×#41—121no—
364C22×Q8C22×D311yescharacteristic
365C22×Q8C22×D311yescharacteristic
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—61no—
374C22×D4—62no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4C22×D311yescharacteristic
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—61no—
381C23×C4—61no—
382C2×Q16—22no—
383C2×Q16—22no—
384C2×Q16—41no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—34no—
388C2×SD16—41no—
389C2×SD16—62no—
390C2×SD16—62no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395#124—22no—
396#124#6714yes—
397#123—68no—
398C22⋊Q8—62no—
399C22⋊Q8—62no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—68no—
405#121—62no—
406#121—62no—
407#120—68no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—68no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—21no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—22no—
439#103—22no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—22no—
444#102—62no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—62no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—61no—
455#95—61no—
456#95—61no—
457#95—61no—
458C23×C3—22no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3C22×D411yescharacteristic
466C22×D3—21no—
467C22×D3—22no—
468C22×D3—21no—
469C22×D3—22no—
470C22×D3—21no—
471C22×D3—22no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—48no—
483C22×D3—48no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—84no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3#13512yes—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—22no—
497C3×Q8—22no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—41no—
505C3×D4—41no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4#12012yes—
520C2×C3×C4#12012yes—
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C2×#4111yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C2×C3×C4H(5,𝔽2)11yescharacteristic
527#67—48no—
528#67—84no—
529C2×Dic3—21no—
530C2×Dic3—22no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544D12—22no—
545D12—22no—
546D12—22no—
547D12—44no—
548D12—48no—
549D12#12114yes—
550C4×D3—48no—
551C4×D3—41no—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—41no—
556C4×D3—41no—
557C4×D3—41no—
558C4×D3—41no—
559C4×D3—84no—
560C3×C8—41no—
561C3×C8—41no—
562C3⋊C8—22no—
563C3⋊C8—41no—
564C24—21no—
565C24—31no—
566C24—31no—
567C24—64no—
568C24—61no—
569C24—122no—
570C24—122no—
571C24—122no—
572C24—122no—
573C24—241no—
574C24—241no—
575#41—124no—
576#41—124no—
577#41—124no—
578#41—124no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8D3×D412yes—
590C2×Q8C2×#6712yes—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—32no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—62no—
600C2×D4—64no—
601C2×D4—64no—
602C2×D4—64no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—121no—
608C2×D4—122no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—122no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—124no—
616C2×D4—241no—
617C2×D4—241no—
618C2×D4C2×#6712yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—64no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—64no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—122no—
642C22×C4—122no—
643C22×C4—241no—
644C22×C4—241no—
645C22×C4D3×D411yescharacteristic
646C22×C4D3×D411yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—44no—
649SD16—44no—
650SD16—68no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—32no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—32no—
666C4⋊C4—42no—
667C4⋊C4—64no—
668C4⋊C4—62no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—61no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—62no—
681C22⋊C4—62no—
682C22⋊C4—64no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—42no—
688C42D3×D412yes—
689C42C2×#6712yes—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3C2×#12011yescharacteristic
698C22×C3D4211yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3C2×#13511yescharacteristic
701C22×C3#57511yescharacteristic
702C22×C3#57711yescharacteristic
703C22×C3#57711yescharacteristic
704C2×D3—24no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—41no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—41no—
717C2×D3—42no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—816no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—81no—
731C3×C4C2×#12111yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4D4211yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—41no—
736Dic3—41no—
737Dic3—42no—
738Dic3—81no—
739Dic3—81no—
740C23—22no—
741C23—32no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—62no—
753C23—61no—
754C23—62no—
755C23—61no—
756C23—62no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23—128no—
765C23—128no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23—244no—
775C23C2×D3×D411yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784D4—22no—
785D4—22no—
786D4—34no—
787D4—41no—
788D4—41no—
789D4—62no—
790D4—62no—
791D4—62no—
792D4—124no—
793D4—128no—
794D4—128no—
795D4—244no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—128no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—244no—
834C2×C4#93712yes—
835C2×C4#93712yes—
836C2×C4C2×D3×D411yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4#100411yescharacteristic
839C2×C4D3×#4111yescharacteristic
840C2×C4#100911yescharacteristic
841C2×C4C22×#6711yescharacteristic
842C8—41no—
843C8—41no—
844C8—62no—
845C8—121no—
846C2×C3—82no—
847C2×C3#240811yescharacteristic
848C2×C3#300211yescharacteristic
849C2×C3#300911yescharacteristic
850C2×C3#327511yescharacteristic
851C2×C3#328211yescharacteristic
852C2×C3#329611yescharacteristic
853C2×C3#332311yescharacteristic
854D3—42no—
855D3—44no—
856D3—81no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—62no—
861C22—64no—
862C22—62no—
863C22—62no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—122no—
869C22—121no—
870C22—122no—
871C22—121no—
872C22—122no—
873C22—121no—
874C22—122no—
875C22—121no—
876C22—122no—
877C22—122no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—2416no—
886C22#560911yescharacteristic
887C22#561211yescharacteristic
888C22D3×#13511yescharacteristic
889C22#576811yescharacteristic
890C22#577811yescharacteristic
891C22#577811yescharacteristic
892C22C2×#93711yescharacteristic
893C4—22no—
894C4—22no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—122no—
899C4—121no—
900C4—121no—
901C4—241no—
902C4—241no—
903C4D3×#12111yescharacteristic
904C4#560711yescharacteristic
905C4D4×#6711yescharacteristic
906C4#582911yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—82no—
909C2—122no—
910C2—124no—
911C2—241no—
912C2#8061511yescharacteristic
913C2#8062111yescharacteristic
914C2#8062911yescharacteristic
915C2#8063011yescharacteristic
916C2#8264011yescharacteristic
917C2#8391111yescharacteristic
918C2#8398211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#464C2
socleC23×C3C22×D4
prime radicalC2×#5676C2
hypercenterC2×#464D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×C3×#464C2semidirect
3. C2×#5187C2semidirect
4. C2×#5169C2semidirect
5. #82499C2semidirect
6. C2×C4×#215C2semidirect
7. #72071C2semidirect
8. #72054C2semidirect
9. #71725C2semidirect
10. #70480C2semidirect
11. #70470C2semidirect
12. #70274C2semidirect
13. #70267C2semidirect
14. #70207C2semidirect
15. #70198C2semidirect
19. C22×C3×Q16C22semidirect
22. C2×C3×C4×Q8C22semidirect
25. C2×#946C22semidirect
37. C2×C3×C4⋊C8C22semidirect
38. C2×C3×#103C22semidirect
40. C2×#835C22semidirect
41. C2×#835C22semidirect
42. C2×#835C22semidirect
51. C2×(C2×D3)⋊C8C22semidirect
52. C2×(C2×D3)⋊C8C22semidirect
56. #4987C22semidirect
59. C2×#808C22semidirect
62. #4936C22semidirect
63. C2×C4×C3⋊C8C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
67. C2×#464D3semidirect
133. C2×#215D4semidirect
184. C22×Q16C2×D3semidirect
197. C2×C4×Q8C2×D3semidirect
206. C2×C4⋊C8C2×D3semidirect
210. C2×#103C2×D3semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×#56762
C2×C3×#4642
C2×#51872
C2×#51692
#824992
C2×C4×#2152
#720712
#720542
#717252
#704802
#704702
#702742
#702672
#702072
#701982
#242473