Finite Group Databasebeta

← #10830640

Subgroups — #10830640

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic
2C2×#5239C211yesmaximal, characteristic, complemented
3C2×#5228C211yesmaximal, characteristic, complemented
4C2×#5054C211yesmaximal, characteristic, complemented
5C2×C4×#216C211yesmaximal, characteristic, complemented
6#82375C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72132C211yesmaximal, characteristic, complemented
9#71725C211yesmaximal, characteristic, complemented
10#71700C211yesmaximal, characteristic, complemented
11#71695C211yesmaximal, characteristic, complemented
12#71685C211yesmaximal, characteristic, complemented
13#71679C211yesmaximal, characteristic, complemented
14#71627C211yesmaximal, characteristic, complemented
15#71614C211yesmaximal, characteristic, complemented
16#24246—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C3×#548—24no—
20C3×#548—24no—
21C2×C3×#124—21no—
22C2×C3×#124C2211yescharacteristic
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121—21no—
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4—21no—
29C2×C3×C4×D4C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C22×#214C2211yescharacteristic
33C2×#924C2211yescharacteristic
34C2×#924C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36#5239—24no—
37#5228—24no—
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5222—21no—
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48#5212C2211yescharacteristic
49#5212C2211yescharacteristic
50C2×#830C2211yescharacteristic
51C2×#830C2211yescharacteristic
52C2×#830C2211yescharacteristic
53C2×#830C2211yescharacteristic
54#5054—24no—
55C4×#216—24no—
56#4983—21no—
57C2×#810C2211yescharacteristic
58C2×#807C2211yescharacteristic
59#4944—21no—
60#4944—21no—
61#4936C2211yescharacteristic
62C2×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×C4×C3⋊C8C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548D311yescharacteristic
67C2×#464—31no—
68C2×#452—31no—
69C2×#451—31no—
70C2×C4×Q16—31no—
71#2536—31no—
72#2036—31no—
73#2033—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1805—31no—
79#1788—31no—
80#1787—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—41no—
86C2×C3×#41—41no—
87C22×C3×Q8—22no—
88C22×C3×Q8—22no—
89C22×C3×Q8—21no—
90C22×C3×Q8—22no—
91C22×C3×Q8—22no—
92C22×C3×Q8—41no—
93C22×C3×Q8—41no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4D411yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4—21no—
101C23×C3×C4—21no—
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C3×#124—28no—
106C3×#124—22no—
107C3×#124D414yes—
108C3×C22⋊Q8—28no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—22no—
111C3×#121—28no—
112C3×#121—22no—
113C3×#121—22no—
114C3×C4×Q8—22no—
115C3×C4×Q8D414yes—
116C3×C4×D4—28no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4D411yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4D411yescharacteristic
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C42—21no—
130C2×C3×C42C2311yescharacteristic
131C2×#217—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#216—22no—
136C2×#216—22no—
137C2×#216—22no—
138C2×#216—22no—
139C2×#216—41no—
140C2×#216D414yescomplemented
141C2×#214—22no—
142C2×#214—22no—
143C2×#214—41no—
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—22no—
164#835—22no—
165#835—22no—
166#835—41no—
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#807—22no—
180C4⋊(C3⋊C8)—22no—
181C4×C3⋊C8—22no—
182C22×#41C2×D311yescharacteristic
183C23×Q8C2×D311yescharacteristic
184C22×Q16—31no—
185C22×Q16—31no—
186C22×SD16—31no—
187#548—24no—
188#548—24no—
189C2×#124—21no—
190C2×#124C2×D311yescharacteristic
191C2×C22⋊Q8—21no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×C22⋊Q8C2×D311yescharacteristic
195C2×#121—21no—
196C2×#121C2×D311yescharacteristic
197C2×C4×Q8—31no—
198C2×C4×Q8C2×D311yescharacteristic
199C2×C4×D4—21no—
200C2×C4×D4C2×D311yescharacteristic
201#464—64no—
202#452—64no—
203#451—64no—
204C4×Q16—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#103—31no—
212C2×#103—31no—
213C2×#103—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×C3C2×D411yescharacteristic
233C24×C3C2×D411yescharacteristic
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C2×C3×Q8—24no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—42no—
248C2×C3×Q8—42no—
249C2×C3×Q8—44no—
250C2×C3×Q8—44no—
251C2×C3×Q8—44no—
252C2×C3×Q8—44no—
253C2×C3×Q8C2×D412yes—
254C2×C3×Q8C2×D412yes—
255C2×C3×Q8C2×D412yes—
256C2×C3×Q8#4112yes—
257C2×C3×D4—24no—
258C2×C3×D4—24no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—41no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4C2×D412yes—
272C22×C3×C4—21no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
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—42no—
290C22×C3×C4—42no—
291C22×C3×C4—42no—
292C22×C3×C4—42no—
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2411yescharacteristic
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6C2×D412yes—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4C2×D412yes—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C42—24no—
320C3×C42C2×D412yes—
321C3×C42C2×D412yes—
322#217—42no—
323#217—42no—
324#217—42no—
325#217—42no—
326#216—28no—
327#216—44no—
328#214—44no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335Dic3⋊C4—42no—
336Dic3⋊C4—42no—
337Dic3⋊C4—42no—
338C4×Dic3—42no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8C2×D412yes—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—41no—
356C2×#41—41no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—31no—
363C22×Q8—41no—
364C22×Q8—41no—
365C22×Q8C22×D311yescharacteristic
366C22×Q8C22×D311yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4#6711yescharacteristic
370C22×D4C22×D311yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C2×Q16—34no—
376C2×Q16—62no—
377C2×Q16—62no—
378C2×Q16—62no—
379C2×Q16—62no—
380C2×Q16—121no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—121no—
384C22×C8—31no—
385C22×C8—31no—
386C22×C8—31no—
387C22×C8—31no—
388#124—28no—
389#124—22no—
390#124#6714yes—
391C22⋊Q8—28no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—62no—
395C22⋊Q8—62no—
396C22⋊Q8—121no—
397C22⋊Q8—121no—
398#121—28no—
399#121—22no—
400#121—22no—
401C4×Q8—22no—
402C4×Q8—62no—
403C4×Q8—62no—
404C4×Q8#6714yes—
405C4×D4—28no—
406C4×D4—22no—
407C4×D4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4#6711yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4#6711yescharacteristic
427C2×C22⋊C4#6711yescharacteristic
428C2×C42—21no—
429C2×C42—61no—
430C2×C42C22×D311yescharacteristic
431#107—62no—
432C4⋊C8—62no—
433#103—62no—
434#103—62no—
435#103—62no—
436#103—62no—
437#103—62no—
438#103—62no—
439#103—121no—
440#102—62no—
441#102—62no—
442#102—121no—
443C22⋊C8—62no—
444C22⋊C8—62no—
445C22⋊C8—121no—
446C22⋊C8—121no—
447C4×C8—62no—
448#95—61no—
449#95—61no—
450#95—61no—
451#95—61no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—22no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3#13512yes—
473C23×C3C22×D411yescharacteristic
474C3×Q8—22no—
475C3×Q8—22no—
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—22no—
479C3×Q8—48no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8#12114yes—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—44no—
486C3×D4—48no—
487C3×D4—48no—
488C3×D4—41no—
489C3×D4—41no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—48no—
506C2×C3×C4—48no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
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
527C2×Dic3—22no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539Dic6—22no—
540Dic6—22no—
541Dic6—41no—
542Dic6—41no—
543C3⋊C8—22no—
544C3⋊C8—41no—
545C3⋊C8—41no—
546C3⋊C8—41no—
547C24—21no—
548C24C2×#6711yescharacteristic
549C24C2×#6711yescharacteristic
550#41—44no—
551#41—44no—
552#41—44no—
553#41—44no—
554C2×Q8—24no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—32no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×Q8—61no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8D3×D412yes—
576C2×Q8#23712yes—
577C2×Q8C2×#6712yes—
578C2×Q8C2×#6712yes—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4C2×#6712yes—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4C2×#6711yescharacteristic
620C22×C4C2×#6711yescharacteristic
621C22×C4C2×#6711yescharacteristic
622C22×C4C2×#6711yescharacteristic
623C22×C4C23×D311yescharacteristic
624Q16—68no—
625Q16—124no—
626SD16—124no—
627C2×C8—32no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8—61no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—61no—
638C2×C8—61no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—122no—
650C4⋊C4—122no—
651C4⋊C4—122no—
652C4⋊C4C2×#6712yes—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—122no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C42—24no—
664C42—122no—
665C42C2×#6712yes—
666C42C2×#6712yes—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—42no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3C2×#12011yescharacteristic
689C22×C3D4211yescharacteristic
690C22×C3#54611yescharacteristic
691C22×C3C2×#13511yescharacteristic
692C22×C3#57511yescharacteristic
693C22×C3#57811yescharacteristic
694C22×C3#57811yescharacteristic
695C3×C4—24no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—42no—
701C3×C4—42no—
702C3×C4C2×#12111yescharacteristic
703C3×C4#53511yescharacteristic
704C3×C4D4211yescharacteristic
705C3×C4#54611yescharacteristic
706Dic3—42no—
707Dic3—81no—
708Dic3—81no—
709Dic3—81no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23#95012yes—
731C23C22×#6711yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—48no—
738Q8—41no—
739Q8—41no—
740Q8—62no—
741Q8—62no—
742Q8—121no—
743Q8—121no—
744Q8#93814yes—
745D4—22no—
746D4—22no—
747D4—44no—
748D4—48no—
749D4—48no—
750D4—41no—
751D4—41no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—62no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4#95312yes—
794C2×C4#95312yes—
795C2×C4C2×D3×D411yescharacteristic
796C2×C4C2×#23711yescharacteristic
797C2×C4#100411yescharacteristic
798C2×C4#100411yescharacteristic
799C2×C4C22×#6711yescharacteristic
800C2×C4C22×#6711yescharacteristic
801C8—62no—
802C8—121no—
803C8—121no—
804C8—121no—
805C2×C3—42no—
806C2×C3—81no—
807C2×C3—82no—
808C2×C3#240811yescharacteristic
809C2×C3#300211yescharacteristic
810C2×C3#301111yescharacteristic
811C2×C3#327711yescharacteristic
812C2×C3#328511yescharacteristic
813C2×C3#330011yescharacteristic
814C2×C3#332711yescharacteristic
815C22—22no—
816C22—22no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22D4×#6711yescharacteristic
837C22#580611yescharacteristic
838C22C2×#95011yescharacteristic
839C22#582211yescharacteristic
840C22#583811yescharacteristic
841C22#583811yescharacteristic
842C22C2×#95311yescharacteristic
843C4—24no—
844C4—22no—
845C4—22no—
846C4—41no—
847C4—41no—
848C4—42no—
849C4—42no—
850C4—122no—
851C4—241no—
852C4—241no—
853C4—241no—
854C4C2×#93811yescharacteristic
855C4D4×#6711yescharacteristic
856C4#580511yescharacteristic
857C4#580611yescharacteristic
858C3#2424611yescharacteristic, complemented, Sylow
859C2—42no—
860C2—81no—
861C2—82no—
862C2#8353411yescharacteristic
863C2#8354111yescharacteristic
864C2#8354811yescharacteristic
865C2#8354911yescharacteristic
866C2#8405311yescharacteristic
867C2#8408011yescharacteristic
868C2#8411711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#548C2
socleC23×C3C22×D4
hypercenterC2×#548D3
hypocenterC3#24246
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
2. C2×#5239C2semidirect
3. C2×#5228C2semidirect
4. C2×#5054C2semidirect
5. C2×C4×#216C2semidirect
6. #82375C2semidirect
7. #72135C2semidirect
8. #72132C2semidirect
9. #71725C2semidirect
10. #71700C2semidirect
11. #71695C2semidirect
12. #71685C2semidirect
13. #71679C2semidirect
14. #71627C2semidirect
15. #71614C2semidirect
140. C2×#216D4semidirect
858. C3#24246semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C2×#52392
C2×#52282
C2×#50542
C2×C4×#2162
#823752
#721352
#721322
#717252
#717002
#716952
#716852
#716792
#716272
#716142
#242463