Finite Group Databasebeta

← #10830655

Subgroups — #10830655

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×C3×#546C211yesmaximal, characteristic
2C2×#5239C211yesmaximal, characteristic, complemented
3C2×#5218C211yesmaximal, characteristic, complemented
4C2×#5054C211yesmaximal, characteristic, complemented
5#82375C211yesmaximal, characteristic, complemented
6C2×C4×#214C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72128C211yesmaximal, characteristic, complemented
9#71725C211yesmaximal, characteristic, complemented
10#71700C211yesmaximal, characteristic, complemented
11#71694C211yesmaximal, characteristic, complemented
12#71685C211yesmaximal, characteristic, complemented
13#71680C211yesmaximal, characteristic, complemented
14#71614C211yesmaximal, characteristic, complemented
15#71605C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C3×#546—24no—
20C3×#546—24no—
21C2×C3×#124C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121—21no—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#120—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C22×C3×C22⋊C4—21no—
30C22×#216C2211yescharacteristic, complemented
31C22×#214C2211yescharacteristic
32C22×#214C2211yescharacteristic
33C2×#924C2211yescharacteristic
34C2×#924C2211yescharacteristic, complemented
35C2×C4×Dic6C2211yescharacteristic, complemented
36#5239—24no—
37C2×#835C2211yescharacteristic, complemented
38C2×#835C2211yescharacteristic, complemented
39C2×#835C2211yescharacteristic, complemented
40#5222—21no—
41#5218—24no—
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48#5212C2211yescharacteristic
49#5212C2211yescharacteristic, complemented
50C2×#830C2211yescharacteristic
51C2×#830C2211yescharacteristic
52C2×#830C2211yescharacteristic, complemented
53C2×#830C2211yescharacteristic, complemented
54#5054—24no—
55C4×#214—24no—
56#4983—21no—
57C2×#810C2211yescharacteristic, complemented
58C2×#808C2211yescharacteristic, complemented
59#4944—21no—
60#4944—21no—
61#4936C2211yescharacteristic, complemented
62C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C4×C3⋊C8C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546D311yescharacteristic
67C2×#464—31no—
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—
81C25×C3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—22no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—22no—
95C22×C3×D4—21no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4D411yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4—21no—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C3×#124—22no—
107C3×#124D414yes—
108C3×#123—28no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—22no—
111C3×#121—28no—
112C3×#121—22no—
113C3×#121—22no—
114C3×#120—28no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4D414yes—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4D411yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C22⋊C4—28no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C22⋊C4D411yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×#217—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#216—22no—
136C2×#216—22no—
137C2×#216—41no—
138C2×#214—22no—
139C2×#214—22no—
140C2×#214—22no—
141C2×#214—22no—
142C2×#214—41no—
143C2×#214D414yescomplemented
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147#924—22no—
148#924—22no—
149#924—41no—
150#924—41no—
151C2×Dic3⋊C4—21no—
152C2×Dic3⋊C4—21no—
153C2×Dic3⋊C4—21no—
154C2×C4×Dic3—21no—
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159C4×Dic6—22no—
160C4×Dic6—22no—
161#835—22no—
162#835—22no—
163#835—41no—
164#832—22no—
165#832—22no—
166#832—22no—
167#832—22no—
168#832—22no—
169#832—41no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173C3⋊#95—21no—
174#830—22no—
175#830—22no—
176#830—41no—
177#830—41no—
178#810—22no—
179#808—22no—
180C4⋊(C3⋊C8)—22no—
181C4×C3⋊C8—22no—
182C22×#41C2×D311yescharacteristic
183C23×D4C2×D311yescharacteristic
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16—31no—
187#546—24no—
188#546—24no—
189C2×#124C2×D311yescharacteristic
190C2×#123—21no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8C2×D311yescharacteristic
194C2×#121—21no—
195C2×#121C2×D311yescharacteristic
196C2×#120—21no—
197C2×C4×Q8—31no—
198C2×C4×D4C2×D311yescharacteristic
199C2×C4×D4C2×D311yescharacteristic
200C22×C22⋊C4—21no—
201#464—64no—
202#452—64no—
203#450—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
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—
232C24×C3—24no—
233C24×C3—21no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3C2×D411yescharacteristic
241C24×C3C2×D411yescharacteristic
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8C2×D412yes—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—22no—
255C2×C3×D4—24no—
256C2×C3×D4—22no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—41no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
268C2×C3×D4—44no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—44no—
274C2×C3×D4—81no—
275C2×C3×D4—81no—
276C2×C3×D4C2×D412yes—
277C2×C3×D4C2×D412yes—
278C2×C3×D4C2×D412yes—
279C2×C3×D4#4112yes—
280C22×C3×C4—24no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
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—21no—
295C22×C3×C4—24no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—81no—
299C22×C3×C4—81no—
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6C2×D412yes—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4C2×D412yes—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—22no—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—24no—
325C3×C22⋊C4—22no—
326C3×C42C2×D412yes—
327C3×C42C2×D412yes—
328#217—42no—
329#217—42no—
330#217—42no—
331#217—42no—
332#216—44no—
333#214—28no—
334#214—44no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341Dic3⋊C4—42no—
342Dic3⋊C4—42no—
343Dic3⋊C4—42no—
344C4×Dic3—42no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
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—21no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—41no—
363C2×#41—41no—
364C22×Q8—31no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—21no—
373C22×D4—41no—
374C22×D4—41no—
375C22×D4#6711yescharacteristic
376C22×D4C22×D311yescharacteristic
377C22×D4C22×D311yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C2×Q16—62no—
383C2×Q16—62no—
384C2×Q16—121no—
385C2×SD16—34no—
386C2×SD16—62no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—121no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8—31no—
394C22×C8—31no—
395#124—22no—
396#124#6714yes—
397#123—28no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—28no—
405#121—22no—
406#121—22no—
407#120—28no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4#6714yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4#6711yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—28no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4#6711yescharacteristic
434C2×C22⋊C4#6711yescharacteristic
435C2×C42—61no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—62no—
439#103—62no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—62no—
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—21no—
459C23×C3—22no—
460C23×C3—21no—
461C23×C3—22no—
462C23×C3—21no—
463C23×C3—22no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—22no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—48no—
476C23×C3—48no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—84no—
488C23×C3—84no—
489C23×C3—84no—
490C23×C3—84no—
491C23×C3—84no—
492C23×C3#13512yes—
493C23×C3C22×D411yescharacteristic
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—44no—
504C3×D4—48no—
505C3×D4—48no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—84no—
509C3×D4#12114yes—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—48no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—84no—
536C2×C3×C4#12012yes—
537C2×C3×C4#12012yes—
538C2×C3×C4C22×D411yescharacteristic
539C2×C3×C4C22×D411yescharacteristic
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C2×#4111yescharacteristic
542C2×C3×C4H(5,𝔽2)11yescharacteristic
543C2×C3×C4H(5,𝔽2)11yescharacteristic
544C2×Dic3—22no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556Dic6—22no—
557Dic6—22no—
558Dic6—41no—
559Dic6—41no—
560C3⋊C8—22no—
561C3⋊C8—41no—
562C3⋊C8—41no—
563C3⋊C8—41no—
564C24—21no—
565C24—24no—
566C24—21no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24C2×#6711yescharacteristic
574C24C2×#6711yescharacteristic
575#41—44no—
576#41—44no—
577#41—44no—
578#41—44no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—32no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8C2×#6712yes—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4D3×D412yes—
616C2×D4#23712yes—
617C2×D4C2×#6712yes—
618C2×D4C2×#6712yes—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4C2×#6711yescharacteristic
644C22×C4C2×#6711yescharacteristic
645C22×C4C2×#6711yescharacteristic
646C22×C4C2×#6711yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—68no—
650SD16—124no—
651C2×C8—32no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C4⋊C4—24no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—122no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4C2×#6712yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—22no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—122no—
688C42C2×#6712yes—
689C42C2×#6712yes—
690C22×C3—24no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—41no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—41no—
703C22×C3—42no—
704C22×C3—41no—
705C22×C3—42no—
706C22×C3—41no—
707C22×C3—42no—
708C22×C3—41no—
709C22×C3—42no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—816no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3C2×#12011yescharacteristic
720C22×C3D4211yescharacteristic
721C22×C3#54611yescharacteristic
722C22×C3C2×#13511yescharacteristic
723C22×C3#57511yescharacteristic
724C22×C3#57711yescharacteristic
725C22×C3#57711yescharacteristic
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4C2×#12111yescharacteristic
733C3×C4#53511yescharacteristic
734C3×C4D4211yescharacteristic
735C3×C4#54611yescharacteristic
736Dic3—42no—
737Dic3—81no—
738Dic3—81no—
739Dic3—81no—
740C23—21no—
741C23—22no—
742C23—21no—
743C23—22no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—48no—
758C23—48no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23—84no—
774C23#95012yes—
775C23C22×#6711yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—41no—
779Q8—41no—
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—44no—
790D4—48no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—84no—
795D4#93814yes—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—62no—
822C2×C4—84no—
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—121no—
834C2×C4#95312yes—
835C2×C4#95312yes—
836C2×C4C2×D3×D411yescharacteristic
837C2×C4C2×#23711yescharacteristic
838C2×C4#100411yescharacteristic
839C2×C4#100411yescharacteristic
840C2×C4C22×#6711yescharacteristic
841C2×C4C22×#6711yescharacteristic
842C8—62no—
843C8—121no—
844C8—121no—
845C8—121no—
846C2×C3—42no—
847C2×C3—44no—
848C2×C3—81no—
849C2×C3—82no—
850C2×C3#240811yescharacteristic
851C2×C3#300211yescharacteristic
852C2×C3#300911yescharacteristic
853C2×C3#327511yescharacteristic
854C2×C3#328211yescharacteristic
855C2×C3#329611yescharacteristic
856C2×C3#332311yescharacteristic
857C22—22no—
858C22—22no—
859C22—24no—
860C22—22no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—42no—
877C22—41no—
878C22—42no—
879C22—41no—
880C22—42no—
881C22—816no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22D4×#6711yescharacteristic
887C22#580611yescharacteristic
888C22C2×#95011yescharacteristic
889C22#582211yescharacteristic
890C22#583611yescharacteristic
891C22#583611yescharacteristic
892C22C2×#95311yescharacteristic
893C4—22no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—122no—
900C4—241no—
901C4—241no—
902C4—241no—
903C4C2×#93811yescharacteristic
904C4D4×#6711yescharacteristic
905C4#580511yescharacteristic
906C4#580611yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2#8349411yescharacteristic
913C2#8350111yescharacteristic
914C2#8350811yescharacteristic
915C2#8350911yescharacteristic
916C2#8405311yescharacteristic
917C2#8408011yescharacteristic
918C2#8410511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#546C2
socleC23×C3C22×D4
hypercenterC2×#546D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
2. C2×#5239C2semidirect
3. C2×#5218C2semidirect
4. C2×#5054C2semidirect
5. #82375C2semidirect
6. C2×C4×#214C2semidirect
7. #72135C2semidirect
8. #72128C2semidirect
9. #71725C2semidirect
10. #71700C2semidirect
11. #71694C2semidirect
12. #71685C2semidirect
13. #71680C2semidirect
14. #71614C2semidirect
15. #71605C2semidirect
30. C22×#216C22semidirect
34. C2×#924C22semidirect
35. C2×C4×Dic6C22semidirect
37. C2×#835C22semidirect
38. C2×#835C22semidirect
39. C2×#835C22semidirect
49. #5212C22semidirect
52. C2×#830C22semidirect
53. C2×#830C22semidirect
57. C2×#810C22semidirect
58. C2×#808C22semidirect
61. #4936C22semidirect
62. C2×C4⋊(C3⋊C8)C22semidirect
63. C2×C4×C3⋊C8C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
143. C2×#214D4semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5462
C2×#52392
C2×#52182
C2×#50542
#823752
C2×C4×#2142
#721352
#721282
#717252
#717002
#716942
#716852
#716802
#716142
#716052
#242473