Finite Group Databasebeta

← #10947984

Subgroups — #10947984

Order 768.

1252 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87268C211yesmaximal, characteristic
2C2×C3×#410C211yesmaximal, characteristic, complemented
3C2×#5240C211yesmaximal, characteristic, complemented
4#70061C212yesmaximal, complemented
5#70060C214yesmaximal, complemented
6#70059C212yesmaximal, complemented
7#70019C214yesmaximal, complemented
8#33358—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×#235C411yescharacteristic, complemented
11C2×C3×#117—21no—
12#5833—21no—
13#5833—21no—
14#5832C412yescomplemented
15#5832C2212yes—
16#5830C411yescharacteristic, complemented
17#5830C2211yescharacteristic
18#5828—21no—
19#5828—21no—
20#5825C411yescharacteristic, complemented
21#5825C2211yescharacteristic
22#5816C412yescomplemented
23#5805C2212yes—
24#5804—21no—
25#5804—21no—
26#5791—21no—
27#5791—21no—
28C2×#926—21no—
29C2×#926C411yescharacteristic, complemented
30C3×#410—21no—
31C3×#410—21no—
32C3×#410C2212yes—
33C3×#410C2212yescomplemented
34C2×C3×#99—21no—
35C2×C3×#99C2212yescomplemented
36#5240—21no—
37#5240—21no—
38#5240C2212yes—
39#5240C2212yescomplemented
40C2×#834—21no—
41C2×#834C2212yescomplemented
42#4474C2218yescomplemented
43#4473C2218yescomplemented
44#3449—31no—
45C2×#410—31no—
46C2×#410D311yescharacteristic, complemented
47#2129—32no—
48#2128—32no—
49#2127—34no—
50#2126—34no—
51C2×C3×#41—41no—
52C2×C3×#41—41no—
53C2×C3×#41—41no—
54C2×C3×#41—41no—
55C2×C3×#41C2×C411yescharacteristic
56C2×C3×#41C2×C411yescharacteristic
57C2×C3×#41D411yescharacteristic
58C2×C3×#41D411yescharacteristic
59C2×C3×#41D411yescharacteristic
60C2×C3×#41D411yescharacteristic
61C2×C3×#41C2311yescharacteristic
62C2×C3×#41C2311yescharacteristic
63C22×C3×Q8C2×C411yescharacteristic
64C22×C3×D4D411yescharacteristic
65C22×C3×D4D411yescharacteristic
66C22×C3×D4C2311yescharacteristic
67C23×C3×C4C2×C411yescharacteristic
68C23×C3×C4D411yescharacteristic
69C23×C3×C4D411yescharacteristic
70C22×#67—21no—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—41no—
74C2×#235—41no—
75C2×#235—41no—
76C2×#235—41no—
77C2×#235C2×C412yes—
78C2×#235C2×C412yescomplemented
79C22×D12C2×C411yescharacteristic, complemented
80C22×C4×D3—21no—
81C22×Dic6C2×C411yescharacteristic, complemented
82C3×#117—22no—
83C3×#117—22no—
84C3×#117—41no—
85C3×#117—41no—
86C2×C3×C4⋊C4—41no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C42—41no—
89#953—22no—
90#953—22no—
91C2×#217—21no—
92C2×#217—22no—
93#947C2×C412yescomplemented
94#947C2×C412yescomplemented
95#946—22no—
96#946—22no—
97#944C2×C412yescomplemented
98#944C2×C412yescomplemented
99#940C2×C412yes—
100#940C2312yes—
101#939—22no—
102#939—22no—
103#939—22no—
104#939—22no—
105#938—22no—
106#938—22no—
107#937—21no—
108#937—21no—
109#937—21no—
110#937—21no—
111#936C2×C412yes—
112#936C2312yes—
113#935—21no—
114#935—21no—
115#935—21no—
116#935—21no—
117#930—21no—
118#930—21no—
119#930—21no—
120#930—21no—
121#929—22no—
122#929—22no—
123C4×#67—22no—
124C4×#67—22no—
125C4×#67—22no—
126C4×#67—22no—
127#926—21no—
128#926—21no—
129#926—22no—
130#926—22no—
131#926—41no—
132#926—41no—
133#926C2×C412yes—
134#926C2×C411yescharacteristic, complemented
135#926C2×C411yescharacteristic, complemented
136C2×C4⋊Dic3—21no—
137C2×C4⋊Dic3—41no—
138#924—21no—
139#924—21no—
140#924—21no—
141#924—21no—
142C2×C4×Dic3—41no—
143C2×C4×Dic3C2×C412yescomplemented
144C3×#99—22no—
145C3×#99—22no—
146C3×#99—22no—
147C3×#99C2314yes—
148#834—22no—
149#834—22no—
150#834—22no—
151#834C2314yes—
152C22×#41—31no—
153C22×#41C2×D311yescharacteristic
154#537—61no—
155#537—61no—
156#536—31no—
157#536—31no—
158#536—32no—
159#535—31no—
160#535—31no—
161#535—32no—
162#534—61no—
163#534—61no—
164#532—32no—
165#532—32no—
166#525—61no—
167#525—61no—
168#525—61no—
169#525—61no—
170C2×#117—21no—
171C2×#117—31no—
172C2×#117—61no—
173#410—21no—
174#410—21no—
175#410—32no—
176#410—32no—
177#410—61no—
178#410—61no—
179#410C2×D312yes—
180#410C2×D312yescomplemented
181C2×#99—21no—
182C2×#99—32no—
183C2×#99—61no—
184C2×#99C2×D312yescomplemented
185#354—38no—
186#353—38no—
187C24×C3C22⋊C411yescharacteristic
188C24×C3C2×D411yescharacteristic
189C24×C3C2×D411yescharacteristic
190C23×D3—21no—
191C3×#41—41no—
192C3×#41—41no—
193C3×#41—41no—
194C3×#41—41no—
195C3×#41—41no—
196C3×#41—41no—
197C3×#41—41no—
198C3×#41—41no—
199C3×#41—41no—
200C3×#41—41no—
201C3×#41—41no—
202C3×#41—41no—
203C3×#41—41no—
204C3×#41—41no—
205C3×#41—41no—
206C3×#41—41no—
207C2×C3×Q8—41no—
208C2×C3×Q8—41no—
209C2×C3×Q8C22⋊C411yescharacteristic
210C2×C3×Q8C22⋊C411yescharacteristic
211C2×C3×Q8C22×C411yescharacteristic
212C2×C3×Q8C22×C411yescharacteristic
213C2×C3×D4—41no—
214C2×C3×D4—41no—
215C2×C3×D4—41no—
216C2×C3×D4—41no—
217C2×C3×D4—41no—
218C2×C3×D4—41no—
219C2×C3×D4C22⋊C411yescharacteristic
220C2×C3×D4C22⋊C411yescharacteristic
221C2×C3×D4C22⋊C411yescharacteristic
222C2×C3×D4C22⋊C411yescharacteristic
223C2×C3×D4C22×C411yescharacteristic
224C2×C3×D4C2×D411yescharacteristic
225C2×C3×D4C2×D411yescharacteristic
226C2×C3×D4C2×D411yescharacteristic
227C2×C3×D4C2×D411yescharacteristic
228C2×C3×D4C2×D411yescharacteristic
229C2×C3×D4C2×D411yescharacteristic
230C2×C3×D4C2411yescharacteristic
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—42no—
244C22×C3×C4C22⋊C411yescharacteristic
245C22×C3×C4C22⋊C411yescharacteristic
246C22×C3×C4C22⋊C411yescharacteristic
247C22×C3×C4C22⋊C411yescharacteristic
248C22×C3×C4C22⋊C411yescharacteristic
249C22×C3×C4C22⋊C411yescharacteristic
250C22×C3×C4C22⋊C411yescharacteristic
251C22×C3×C4C22⋊C411yescharacteristic
252C22×C3×C4C22⋊C411yescharacteristic
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C22×C411yescharacteristic
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—22no—
264C2×#67—22no—
265C2×#67—22no—
266C2×#67—42no—
267C2×#67—42no—
268C22×Dic3—21no—
269C22×Dic3—22no—
270C22×Dic3—42no—
271#235—42no—
272#235—42no—
273#235—41no—
274#235—41no—
275#235—41no—
276#235—41no—
277#235—42no—
278#235—42no—
279#235—42no—
280#235—42no—
281C2×D12—21no—
282C2×D12—41no—
283C2×D12—41no—
284C2×D12C22×C412yes—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—42no—
288C2×C4×D3—42no—
289C2×Dic6—21no—
290C2×Dic6—41no—
291C2×Dic6—41no—
292C2×Dic6C22×C412yes—
293C3×C4⋊C4—42no—
294C3×C4⋊C4—42no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—42no—
297C3×C42—42no—
298C3×C42—42no—
299#217—22no—
300#217—22no—
301#217—22no—
302#217—21no—
303#217—21no—
304#217—22no—
305#217—22no—
306#217—24no—
307#217—42no—
308(C2×D3)⋊C4—22no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—22no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—22no—
315C4⋊Dic3—42no—
316C4⋊Dic3—42no—
317Dic3⋊C4—22no—
318Dic3⋊C4—22no—
319Dic3⋊C4—22no—
320Dic3⋊C4—22no—
321C4×Dic3—22no—
322C4×Dic3—42no—
323C4×Dic3—42no—
324C4×Dic3C22×C412yes—
325C4×Dic3C22×C412yes—
326C2×#41—32no—
327C2×#41—32no—
328C2×#41—41no—
329C2×#41—41no—
330C2×#41—41no—
331C2×#41—41no—
332C2×#41—61no—
333C2×#41—61no—
334C2×#41—121no—
335C2×#41—121no—
336C2×#41—121no—
337C2×#41—121no—
338C2×#41C4×D311yescharacteristic
339C2×#41C4×D311yescharacteristic
340C2×#41D1211yescharacteristic
341C2×#41D1211yescharacteristic
342C2×#41#6711yescharacteristic
343C2×#41#6711yescharacteristic
344C2×#41C22×D311yescharacteristic
345C2×#41C22×D311yescharacteristic
346C22×Q8—31no—
347C22×Q8C4×D311yescharacteristic
348C22×D4—31no—
349C22×D4—61no—
350C22×D4D1211yescharacteristic
351C22×D4#6711yescharacteristic
352C22×D4C22×D311yescharacteristic
353C23×C4—61no—
354C23×C4C4×D311yescharacteristic
355C23×C4D1211yescharacteristic
356C23×C4#6711yescharacteristic
357C4⋊Q8—32no—
358C4⋊Q8—32no—
359#127—32no—
360#127—32no—
361#124—32no—
362#124—32no—
363#124—32no—
364#124—32no—
365#123—61no—
366#123—61no—
367#123—61no—
368#123—61no—
369#123—62no—
370#123—62no—
371C22⋊Q8—62no—
372C22⋊Q8—62no—
373C22⋊Q8—61no—
374C22⋊Q8—61no—
375C22⋊Q8—61no—
376C22⋊Q8—61no—
377#121—62no—
378#121—62no—
379#121—62no—
380#121—62no—
381#121—62no—
382#121—62no—
383#121—61no—
384#121—61no—
385#121—61no—
386#121—61no—
387#120—62no—
388#120—62no—
389#120—61no—
390#120—61no—
391#120—61no—
392#120—61no—
393C4×D4—62no—
394C4×D4—62no—
395C4×D4—62no—
396C4×D4—62no—
397#117—22no—
398#117—22no—
399#117—32no—
400#117—31no—
401#117—31no—
402#117—41no—
403#117—41no—
404#117—61no—
405#117—61no—
406#117—62no—
407#117—62no—
408#117—121no—
409#117—121no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—121no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—62no—
416C2×C42—32no—
417C2×C42—41no—
418C2×C42—121no—
419#99—22no—
420#99—22no—
421#99—22no—
422#99—34no—
423#99—62no—
424#99—62no—
425#99—62no—
426#99C22×D314yes—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—81no—
434C23×C3—81no—
435C23×C3—81no—
436C23×C3C2×C22⋊C411yescharacteristic
437C23×C3C2×C22⋊C411yescharacteristic
438C23×C3C2×C22⋊C411yescharacteristic
439C23×C3C2×C22⋊C411yescharacteristic
440C23×C3C2×C22⋊C411yescharacteristic
441C23×C3C22×D411yescharacteristic
442C23×C3C22×D411yescharacteristic
443C22×D3—22no—
444C22×D3—42no—
445C22×D3—82no—
446C3×Q8—41no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—41no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—41no—
461C3×D4—41no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—44no—
493C2×C3×C4—84no—
494C2×C3×C4#9911yescharacteristic
495C2×C3×C4#9911yescharacteristic
496C2×C3×C4#9911yescharacteristic
497C2×C3×C4#9911yescharacteristic
498C2×C3×C4C2×C22⋊C411yescharacteristic
499C2×C3×C4C2×C22⋊C411yescharacteristic
500C2×C3×C4C2×C22⋊C411yescharacteristic
501C2×C3×C4C2×C22⋊C411yescharacteristic
502C2×C3×C4C2×C22⋊C411yescharacteristic
503C2×C3×C4C2×C22⋊C411yescharacteristic
504C2×C3×C4C2×C22⋊C411yescharacteristic
505C2×C3×C4C23×C411yescharacteristic
506#67—44no—
507#67—42no—
508#67—42no—
509#67—82no—
510#67—82no—
511#67—82no—
512#67—82no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—42no—
517C2×Dic3—44no—
518C2×Dic3—82no—
519C2×Dic3—84no—
520D12—42no—
521D12—41no—
522D12—41no—
523C4×D3—44no—
524C4×D3—42no—
525C4×D3—42no—
526Dic6—41no—
527Dic6—41no—
528Dic6—42no—
529C24—61no—
530C24(C2×D3)⋊C411yescharacteristic
531C24C2×D1211yescharacteristic
532C24C2×#6711yescharacteristic
533#41—41no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—41no—
538#41—41no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—122no—
550#41—122no—
551#41—122no—
552#41—122no—
553#41—122no—
554#41—122no—
555#41—121no—
556#41—121no—
557#41—121no—
558#41—121no—
559C2×Q8—32no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—61no—
563C2×Q8—121no—
564C2×Q8—121no—
565C2×Q8(C2×D3)⋊C411yescharacteristic
566C2×Q8(C2×D3)⋊C411yescharacteristic
567C2×Q8C2×C4×D311yescharacteristic
568C2×Q8C2×C4×D311yescharacteristic
569C2×D4—32no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—62no—
577C2×D4—62no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—62no—
581C2×D4—62no—
582C2×D4—61no—
583C2×D4—121no—
584C2×D4—121no—
585C2×D4—122no—
586C2×D4—122no—
587C2×D4(C2×D3)⋊C411yescharacteristic
588C2×D4(C2×D3)⋊C411yescharacteristic
589C2×D4(C2×D3)⋊C411yescharacteristic
590C2×D4(C2×D3)⋊C411yescharacteristic
591C2×D4C2×C4×D311yescharacteristic
592C2×D4C2×D1211yescharacteristic
593C2×D4C2×D1211yescharacteristic
594C2×D4C2×D1211yescharacteristic
595C2×D4C2×#6711yescharacteristic
596C2×D4C2×#6711yescharacteristic
597C2×D4C2×#6711yescharacteristic
598C2×D4C23×D311yescharacteristic
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—61no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4(C2×D3)⋊C411yescharacteristic
620C22×C4(C2×D3)⋊C411yescharacteristic
621C22×C4(C2×D3)⋊C411yescharacteristic
622C22×C4(C2×D3)⋊C411yescharacteristic
623C22×C4(C2×D3)⋊C411yescharacteristic
624C22×C4(C2×D3)⋊C411yescharacteristic
625C22×C4(C2×D3)⋊C411yescharacteristic
626C22×C4(C2×D3)⋊C411yescharacteristic
627C22×C4(C2×D3)⋊C411yescharacteristic
628C22×C4C2×C4×D311yescharacteristic
629C22×C4C2×C4×D311yescharacteristic
630C22×C4C2×C4×D311yescharacteristic
631C22×C4C2×D1211yescharacteristic
632C22×C4C2×D1211yescharacteristic
633C22×C4C2×#6711yescharacteristic
634C22×C4C2×#6711yescharacteristic
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—62no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—62no—
641C4⋊C4—62no—
642C4⋊C4—62no—
643C4⋊C4—62no—
644C4⋊C4—122no—
645C4⋊C4—122no—
646C22⋊C4—24no—
647C22⋊C4—42no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—62no—
651C22⋊C4—62no—
652C22⋊C4—62no—
653C22⋊C4—62no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C22⋊C4—62no—
658C22⋊C4—62no—
659C22⋊C4—64no—
660C22⋊C4—122no—
661C42—32no—
662C42—32no—
663C42—42no—
664C42—42no—
665C42—62no—
666C42—122no—
667C42—122no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3C2×#9911yescharacteristic
688C22×C3C2×#9911yescharacteristic
689C22×C3C22×C22⋊C411yescharacteristic
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—42no—
693C2×D3—84no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—84no—
701C3×C4C2×#9911yescharacteristic
702C3×C4C2×#9911yescharacteristic
703C3×C4C2×#9911yescharacteristic
704C3×C4C2×#9911yescharacteristic
705Dic3—42no—
706Dic3—42no—
707Dic3—42no—
708Dic3—84no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—62no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—122no—
720C23—242no—
721C23C2×(C2×D3)⋊C411yescharacteristic
722C23C2×(C2×D3)⋊C411yescharacteristic
723C23C2×(C2×D3)⋊C411yescharacteristic
724C23C2×(C2×D3)⋊C411yescharacteristic
725C23C2×(C2×D3)⋊C411yescharacteristic
726C23C22×D1211yescharacteristic
727C23C22×#6711yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—122no—
733Q8—121no—
734Q8—121no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—122no—
748D4—124no—
749D4—122no—
750D4—122no—
751D4—121no—
752D4—121no—
753D4—242no—
754D4—242no—
755D4—242no—
756D4—242no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—44no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—84no—
792C2×C4—124no—
793C2×C4—122no—
794C2×C4—122no—
795C2×C4—122no—
796C2×C4—124no—
797C2×C4—242no—
798C2×C4—244no—
799C2×C4#80611yescharacteristic
800C2×C4#80611yescharacteristic
801C2×C4#80611yescharacteristic
802C2×C4#80611yescharacteristic
803C2×C4C2×(C2×D3)⋊C411yescharacteristic
804C2×C4C2×(C2×D3)⋊C411yescharacteristic
805C2×C4C2×(C2×D3)⋊C411yescharacteristic
806C2×C4C2×(C2×D3)⋊C411yescharacteristic
807C2×C4C2×(C2×D3)⋊C411yescharacteristic
808C2×C4C2×(C2×D3)⋊C411yescharacteristic
809C2×C4C2×(C2×D3)⋊C411yescharacteristic
810C2×C4C22×C4×D311yescharacteristic
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—41no—
815C2×C3—41no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—41no—
819C2×C3—41no—
820C2×C3C22×#9911yescharacteristic
821D3—82no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—122no—
842C22—122no—
843C22—122no—
844C22—244no—
845C22C2×#80611yescharacteristic
846C22C2×#80611yescharacteristic
847C22C22×(C2×D3)⋊C411yescharacteristic
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—84no—
855C4—122no—
856C4—122no—
857C4—122no—
858C4—244no—
859C4C2×#80611yescharacteristic
860C4C2×#80611yescharacteristic
861C4C2×#80611yescharacteristic
862C4C2×#80611yescharacteristic
863C3#3335811yescharacteristic, complemented, Sylow
864C2—21no—
865C2—21no—
866C2—21no—
867C2—41no—
868C2—41no—
869C2—41no—
870C2—41no—
871C2—41no—
872C2—41no—
873C2—242no—
874C2C22×#80611yescharacteristic
subgroupG/H
centerC4C2×#806
commutatorC2×C3×C4C23×C4
FrattiniC2×D4C23×D3
FittingC2×C3×#410C2
socleC2×C3C22×#99
prime radical#87268C2
cosocleC2×C3×D4C24
hypercenterC2×#410D3
hypocenterC3#33358
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×C3×#410C2semidirect
3. C2×#5240C2semidirect
4. #70061C2semidirect
5. #70060C2semidirect
6. #70059C2semidirect
7. #70019C2semidirect
10. C22×#235C4semidirect
14. #5832C4semidirect
16. #5830C4semidirect
20. #5825C4semidirect
22. #5816C4semidirect
29. C2×#926C4semidirect
33. C3×#410C22semidirect
35. C2×C3×#99C22semidirect
39. #5240C22semidirect
41. C2×#834C22semidirect
42. #4474C22semidirect
43. #4473C22semidirect
46. C2×#410D3semidirect
78. C2×#235C2×C4semidirect
79. C22×D12C2×C4semidirect
81. C22×Dic6C2×C4semidirect
93. #947C2×C4semidirect
94. #947C2×C4semidirect
97. #944C2×C4semidirect
98. #944C2×C4semidirect
134. #926C2×C4semidirect
135. #926C2×C4semidirect
143. C2×C4×Dic3C2×C4semidirect
180. #410C2×D3semidirect
184. C2×#99C2×D3semidirect
863. C3#33358semidirect

Maximal subgroups

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

subgroupindex
#872682
C2×C3×#4102
C2×#52402
#700612
#700602
#700592
#700192
#333583