Finite Group Databasebeta

← #10993913

Subgroups — #10993913

Order 768.

3120 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5551C211yesmaximal, characteristic, complemented
2C2×#5551C212yesmaximal, complemented
3C2×C4×#235C211yesmaximal, characteristic, complemented
4C3×C4×#121C211yesmaximal, characteristic, complemented
5#82641C212yesmaximal, complemented
6#82376C211yesmaximal, characteristic, complemented
7#82351C212yesmaximal, complemented
8#82076C211yesmaximal, characteristic, complemented
9#76475C212yesmaximal, complemented
10D3×#389C212yesmaximal, complemented
11#75843C214yesmaximal, complemented
12#74895C214yesmaximal, complemented
13#73911C212yesmaximal, complemented
14C4⋊C4×D12C211yesmaximal, characteristic, complemented
15#73711C211yesmaximal, characteristic, complemented
16#73573C212yesmaximal, complemented
17#73488C212yesmaximal, complemented
18#36259—31nomaximal, Sylow
19C22×#235C2212yes—
20C22×#235C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C2×#938C2214yes—
26C2×#938C2212yes—
27C2×C4×#67C2212yes—
28C2×C4×#67C2212yes—
29C2×#926C2211yescharacteristic
30C2×#924C2212yes—
31C2×#924C2212yes—
32C2×#924C2212yes—
33#5551—216no—
34#5551—28no—
35C2×D3×C4⋊C4C2214yes—
36C2×D3×C4⋊C4C2212yes—
37C2×D3×C4⋊C4C2212yes—
38C2×#883C2214yes—
39C2×#883C2214yes—
40C2×#883C2214yes—
41C4×#235—28no—
42C2×C4×D12C2212yes—
43C2×C4×D12C2211yescharacteristic
44C2×C4×D12C2211yescharacteristic
45C2×#872C2212yes—
46C2×C42×D3C2212yes—
47C2×#869C2212yes—
48C2×#869C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#390C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#388C2212yes—
54C3×#386C2212yes—
55C3×#380C2211yescharacteristic
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×C4×C22⋊C4C2212yes—
58#5222C2214yes—
59#5221C2212yes—
60#5212C2212yes—
61#5212C2212yes—
62#5212C2212yes—
63#4987C2212yes—
64#4984C2212yes—
65#4984C2212yes—
66#4976C2214yes—
67#4972C2212yes—
68#4956C2214yes—
69#4956C2214yes—
70#4952C2214yes—
71#4951C2214yes—
72#4948C2214yes—
73#4948C2214yes—
74#4945C2214yes—
75#4935C2211yescharacteristic
76#4929C2212yes—
77#4929C2212yes—
78#4928C2212yes—
79#4928C2212yes—
80#4928C2212yes—
81#4668C2214yes—
82#4664C2214yes—
83D3×#95C2214yes—
84#4661C2214yes—
85#4657C2214yes—
86#4647C2214yes—
87C2×#547—32no—
88C2×#547—31no—
89C2×C4×#41—31no—
90#2857—31no—
91#2854—32no—
92#2546—31no—
93#2538—31no—
94#2486—32no—
95#2429—32no—
96#2425—34no—
97#2416—32no—
98#2415—32no—
99#2413—34no—
100D4×C4⋊C4—31no—
101#2339—32no—
102C4×#121D311yescharacteristic, complemented
103C2×#389—32no—
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2312yes—
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C22×#67C2314yes—
111C22×#67C2312yes—
112C2×#235—24no—
113C2×#235—28no—
114C2×#235—28no—
115C2×#235—24no—
116C2×#235—28no—
117C2×#235D418yescomplemented
118C22×D12C2311yescharacteristic
119C22×C4×D3C2314yes—
120C22×C4×D3C2312yes—
121C22×C4×D3C2314yes—
122C22×C4×D3C2312yes—
123C22×C4×D3C2312yes—
124C22×Dic6C2312yes—
125C22×Dic6C2311yescharacteristic
126C3×#121—24no—
127C3×C4×D4—28no—
128C3×C4×D4—24no—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2312yes—
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C42—24no—
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2312yes—
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2312yes—
147C2×#217C2314yes—
148C2×#217C2314yes—
149#938—216no—
150#938—28no—
151C4×#67—28no—
152C4×#67—28no—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2312yes—
156#926—24no—
157C2×C4⋊Dic3C2314yes—
158C2×C4⋊Dic3C2314yes—
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2311yescharacteristic
166#924—28no—
167#924—28no—
168#924—28no—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×Dic3⋊C4C2314yes—
172C2×Dic3⋊C4C2312yes—
173C2×Dic3⋊C4C2312yes—
174C2×Dic3⋊C4C2314yes—
175C2×C4×Dic3C2312yes—
176C2×C4×Dic3C2312yes—
177C2×C4×Dic3C2312yes—
178D3×C4⋊C4—216no—
179D3×C4⋊C4—28no—
180D3×C4⋊C4—28no—
181#883—216no—
182#883—216no—
183#883—216no—
184C4×D12—24no—
185C4×D12—28no—
186C4×D12D418yescomplemented
187#872—28no—
188C42×D3—28no—
189#869—28no—
190#869—24no—
191C4×Dic6—24no—
192C4×Dic6—24no—
193C3×#95C2312yes—
194C3×#95C2312yes—
195C3×#95C2312yes—
196C3⋊#95C2314yes—
197C3⋊#95C2314yes—
198C3⋊#95C2314yes—
199C3⋊#95C2314yes—
200C3⋊#95C2314yes—
201C3⋊#95C2314yes—
202C22×#41—31no—
203C22×#41—32no—
204#547—68no—
205#547—616no—
206C2×C4⋊Q8—31no—
207C2×C4⋊Q8—32no—
208C2×#123—34no—
209C2×#123—34no—
210C2×#123—34no—
211C2×C22⋊Q8—32no—
212C2×C22⋊Q8—32no—
213C2×C22⋊Q8—32no—
214C2×#121—32no—
215C2×#121—34no—
216C2×#121C2×D311yescharacteristic
217C4×#41—68no—
218C2×C4×Q8—31no—
219C2×C4×Q8—31no—
220C2×C4×D4—32no—
221C2×C4×D4—32no—
222C2×C4×D4—31no—
223C2×C4×D4—31no—
224C2×C4×D4—32no—
225C2×C4×D4C2×D312yes—
226C2×C4×D4C2×D311yescharacteristic
227C2×#117—31no—
228C2×#117—32no—
229C22×C4⋊C4—32no—
230C22×C4⋊C4—34no—
231C22×C4⋊C4—32no—
232C22×C42—32no—
233C22×C42C2×D311yescharacteristic
234#398—34no—
235#398—34no—
236#397—34no—
237#396—34no—
238#396—34no—
239#394—34no—
240#391—32no—
241#391—32no—
242#390—32no—
243#390C2×D311yescharacteristic
244#389—32no—
245#389—32no—
246#389—34no—
247#389—32no—
248#389—32no—
249#389—32no—
250#389—32no—
251#389—34no—
252#389C2×D311yescharacteristic
253#388—34no—
254#388—34no—
255#388C2×D312yes—
256#386—34no—
257#386—34no—
258#386C2×D312yes—
259#385—34no—
260#384—31no—
261#381—34no—
262#380—32no—
263#380—32no—
264#380—32no—
265#380—32no—
266#380C2×D311yescharacteristic
267C4×C4⋊C4C2×D311yescharacteristic
268C4×C22⋊C4C2×D312yes—
269C2×#95—34no—
270C24×C3C2412yes—
271C24×C3C2411yescharacteristic
272C23×D3C2412yes—
273C2×C3×D4—24no—
274C2×C3×D4—22no—
275C2×C3×D4—24no—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—42no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—24no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—41no—
290C22×C3×C4C2×D414yes—
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
294C22×C3×C4C2411yescharacteristic
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2412yes—
297C22×C3×C4C2411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—28no—
303C2×#67—28no—
304C2×#67—28no—
305C2×#67C2×D418yes—
306C22×Dic3C2412yes—
307C22×Dic3C2414yes—
308C22×Dic3C2414yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311#235—232no—
312#235—432no—
313C2×D12C2×D414yes—
314C2×D12C2×D414yes—
315C2×D12#4114yes—
316C2×C4×D3—24no—
317C2×C4×D3—24no—
318C2×C4×D3—24no—
319C2×C4×D3—24no—
320C2×C4×D3—24no—
321C2×C4×D3—28no—
322C2×C4×D3—28no—
323C2×C4×D3—28no—
324C2×C4×D3—28no—
325C2×C4×D3—28no—
326C2×C4×D3—24no—
327C2×C4×D3—44no—
328C2×C4×D3—42no—
329C2×C4×D3C2×D418yes—
330C2×C4×D3C2×D418yes—
331C2×Dic6—22no—
332C2×Dic6—22no—
333C2×Dic6—24no—
334C2×Dic6—24no—
335C2×Dic6—24no—
336C2×Dic6C2×D414yes—
337C3×C4⋊C4—24no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4#4114yescomplemented
341C3×C22⋊C4—24no—
342C3×C22⋊C4—24no—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—24no—
345C3×C22⋊C4—24no—
346C3×C42—22no—
347C3×C42—24no—
348C3×C42—22no—
349C3×C42—22no—
350C3×C42C2×D414yes—
351#217—28no—
352#217—28no—
353#217—28no—
354#217—24no—
355#217—44no—
356(C2×D3)⋊C4—24no—
357(C2×D3)⋊C4—28no—
358(C2×D3)⋊C4C2×D418yes—
359C4⋊Dic3—22no—
360C4⋊Dic3—24no—
361C4⋊Dic3—24no—
362C4⋊Dic3—24no—
363C4⋊Dic3—24no—
364C4⋊Dic3—28no—
365C4⋊Dic3—28no—
366C4⋊Dic3—42no—
367C4⋊Dic3C2×D414yes—
368Dic3⋊C4—24no—
369Dic3⋊C4—28no—
370Dic3⋊C4—28no—
371Dic3⋊C4—24no—
372Dic3⋊C4—28no—
373Dic3⋊C4—28no—
374C4×Dic3—24no—
375C4×Dic3—24no—
376C4×Dic3—24no—
377C2×#41—38no—
378C2×#41—64no—
379C2×#41—64no—
380C2×#41—68no—
381C2×#41—68no—
382C2×#41—68no—
383C22×Q8—31no—
384C22×Q8—32no—
385C22×D4—32no—
386C22×D4—34no—
387C22×D4—31no—
388C22×D4C22×D311yescharacteristic
389C22×D4C22×D312yes—
390C23×C4—32no—
391C23×C4—32no—
392C23×C4—34no—
393C23×C4—34no—
394C23×C4—32no—
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D312yes—
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C4⋊Q8—68no—
400C4⋊Q8—64no—
401#123—616no—
402#123—616no—
403#123—616no—
404C22⋊Q8—68no—
405C22⋊Q8—68no—
406C22⋊Q8—68no—
407#121—24no—
408#121—68no—
409#121—616no—
410C4×Q8—64no—
411C4×Q8—64no—
412C4×D4—28no—
413C4×D4—24no—
414C4×D4—38no—
415C4×D4—64no—
416C4×D4—68no—
417C4×D4—68no—
418C4×D4—68no—
419#117—68no—
420#117—64no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—34no—
424C2×C4⋊C4—34no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—34no—
427C2×C4⋊C4—32no—
428C2×C4⋊C4—34no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—32no—
431C2×C4⋊C4—32no—
432C2×C4⋊C4—32no—
433C2×C4⋊C4—32no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—616no—
437C2×C4⋊C4—68no—
438C2×C4⋊C4—68no—
439C2×C4⋊C4C22×D311yescharacteristic
440C2×C4⋊C4C22×D312yes—
441C2×C4⋊C4C22×D311yescharacteristic
442C2×C4⋊C4C22×D311yescharacteristic
443C2×C22⋊C4—32no—
444C2×C22⋊C4—32no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4C22×D312yes—
452C2×C22⋊C4C22×D312yes—
453C2×C22⋊C4C22×D312yes—
454C2×C22⋊C4C22×D312yes—
455C2×C22⋊C4C22×D312yes—
456C2×C42—24no—
457C2×C42—32no—
458C2×C42—32no—
459C2×C42—32no—
460C2×C42—68no—
461C2×C42C22×D311yescharacteristic
462C2×C42C22×D312yes—
463C2×C42C22×D311yescharacteristic
464C2×C42C22×D311yescharacteristic
465C2×C42C22×D311yescharacteristic
466#95—34no—
467#95—34no—
468#95—34no—
469#95—34no—
470#95—34no—
471#95—34no—
472#95C22×D312yes—
473#95C22×D312yes—
474#95C22×D312yes—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3C22×D412yes—
489C23×C3C2511yescharacteristic
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3C22×D414yes—
495C22×D3C22×D414yes—
496C22×D3C2×#4114yes—
497C3×D4—48no—
498C3×D4—44no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—28no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—21no—
517C2×C3×C4—44no—
518C2×C3×C4—48no—
519C2×C3×C4—44no—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C22×D412yes—
522C2×C3×C4C22×D412yes—
523C2×C3×C4C22×D412yes—
524C2×C3×C4C22×D412yes—
525C2×C3×C4C2×#4114yes—
526C2×C3×C4C2×#4112yes—
527C2×C3×C4C2×#4112yes—
528C2×C3×C42−1+412yes—
529C2×C3×C42−1+412yes—
530#67—216no—
531#67—416no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—24no—
538C2×Dic3—24no—
539C2×Dic3—24no—
540C2×Dic3—24no—
541C2×Dic3—24no—
542C2×Dic3—22no—
543C2×Dic3—24no—
544C2×Dic3—22no—
545C2×Dic3C22×D414yes—
546C2×Dic3C22×D414yes—
547D12#121116yescomplemented
548C4×D3—216no—
549C4×D3—216no—
550C4×D3—416no—
551C4×D3—48no—
552C4×D3—416no—
553Dic6—28no—
554Dic6—48no—
555C24—32no—
556C24C23×D312yes—
557C24C23×D311yescharacteristic
558#41—632no—
559#41—1232no—
560C2×Q8—34no—
561C2×Q8—62no—
562C2×Q8—64no—
563C2×Q8—64no—
564C2×Q8—62no—
565C2×Q8—64no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—38no—
572C2×D4—34no—
573C2×D4—34no—
574C2×D4—34no—
575C2×D4—42no—
576C2×D4—64no—
577C2×D4—64no—
578C2×D4—68no—
579C2×D4—68no—
580C2×D4—68no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—38no—
594C22×C4—38no—
595C22×C4—32no—
596C22×C4—34no—
597C22×C4—34no—
598C22×C4—41no—
599C22×C4—64no—
600C22×C4—64no—
601C22×C4—64no—
602C22×C4—68no—
603C22×C4—68no—
604C22×C4—68no—
605C22×C4—68no—
606C22×C4—64no—
607C22×C4—64no—
608C22×C4—68no—
609C22×C4—64no—
610C22×C4—122no—
611C22×C4—124no—
612C22×C4D3×D414yes—
613C22×C4C23×D311yescharacteristic
614C22×C4C23×D312yes—
615C22×C4C23×D312yes—
616C22×C4C23×D312yes—
617C22×C4C23×D311yescharacteristic
618C22×C4C23×D311yescharacteristic
619C22×C4C23×D311yescharacteristic
620C22×C4C23×D311yescharacteristic
621C22×C4C23×D311yescharacteristic
622C4⋊C4—24no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—34no—
626C4⋊C4—68no—
627C4⋊C4—68no—
628C4⋊C4—68no—
629C4⋊C4—64no—
630C4⋊C4—68no—
631C4⋊C4—68no—
632C4⋊C4—64no—
633C4⋊C4—64no—
634C4⋊C4—68no—
635C4⋊C4—64no—
636C4⋊C4—62no—
637C4⋊C4—64no—
638C4⋊C4—64no—
639C4⋊C4—122no—
640C4⋊C4#23514yescomplemented
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—38no—
647C22⋊C4—64no—
648C22⋊C4—68no—
649C22⋊C4—64no—
650C22⋊C4—68no—
651C22⋊C4—68no—
652C22⋊C4—68no—
653C22⋊C4—124no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—24no—
658C42—64no—
659C42—64no—
660C42—64no—
661C42D3×D414yes—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3C23×D411yescharacteristic
677C22×C3C23×D411yescharacteristic
678C22×C3C22×#4111yescharacteristic
679C22×C3C22×#4111yescharacteristic
680C22×C3C2×2−1+411yescharacteristic
681C22×C3C2×2−1+411yescharacteristic
682C22×C3#58511yescharacteristic
683C2×D3—24no—
684C2×D3—24no—
685C2×D3—24no—
686C2×D3—24no—
687C2×D3—24no—
688C2×D3—24no—
689C2×D3C2×#12118yes—
690C3×C4—22no—
691C3×C4—24no—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—42no—
695C3×C4—41no—
696C3×C4—42no—
697C3×C4C2×#12114yes—
698C3×C4#54714yescomplemented
699Dic3—24no—
700Dic3—24no—
701Dic3—44no—
702Dic3—44no—
703Dic3—42no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—34no—
718C23—34no—
719C23—34no—
720C23—62no—
721C23—62no—
722C23—62no—
723C23—62no—
724C23C2×D3×D412yes—
725C23C24×D311yescharacteristic
726Q8—68no—
727Q8—128no—
728D4—316no—
729D4—48no—
730D4—44no—
731D4—616no—
732D4—1216no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—28no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—34no—
752C2×C4—34no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—48no—
756C2×C4—616no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—616no—
762C2×C4—64no—
763C2×C4—62no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—64no—
767C2×C4—64no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—64no—
771C2×C4—1216no—
772C2×C4—128no—
773C2×C4—1216no—
774C2×C4C2×#23514yes—
775C2×C4C2×#23512yes—
776C2×C4C2×D3×D412yes—
777C2×C4C2×D3×D412yes—
778C2×C4C2×D3×D412yes—
779C2×C4C2×D3×D412yes—
780C2×C4C2×D3×D412yes—
781C2×C4D3×#4112yes—
782C2×C4#101012yes—
783C2×C4#101012yes—
784C2×C3—42no—
785C2×C3—82no—
786C2×C3C22×#12111yescharacteristic
787C2×C3C2×#54711yescharacteristic
788C2×C3D4×#4111yescharacteristic
789C2×C3#348211yescharacteristic
790C2×C3#348911yescharacteristic
791C2×C3#349911yescharacteristic
792C2×C3#351511yescharacteristic
793D3—28no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—38no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—64no—
810C22—64no—
811C22—64no—
812C22—64no—
813C22—64no—
814C22—64no—
815C22C22×#23511yescharacteristic
816C22C22×D3×D411yescharacteristic
817C22C22×D3×D411yescharacteristic
818C22C2×D3×#4111yescharacteristic
819C22C2×#101011yescharacteristic
820C22C2×#101011yescharacteristic
821C22#596411yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—64no—
830C4—64no—
831C4—124no—
832C4—122no—
833C4—124no—
834C4#555114yescomplemented
835C4D3×#12114yes—
836C3#3625911yescharacteristic, complemented, Sylow
837C2—42no—
838C2—68no—
839C2—82no—
840C2C2×#555111yescharacteristic
841C2D4×#23511yescharacteristic
842C2#8584411yescharacteristic
843C2C2×D3×#12111yescharacteristic
844C2#8604211yescharacteristic
845C2#8616511yescharacteristic
846C2#8624311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
hypercenterC4×#121D3
hypocenterC3#36259
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#5551C2semidirect
2. C2×#5551C2semidirect
3. C2×C4×#235C2semidirect
4. C3×C4×#121C2semidirect
5. #82641C2semidirect
6. #82376C2semidirect
7. #82351C2semidirect
8. #82076C2semidirect
9. #76475C2semidirect
10. D3×#389C2semidirect
11. #75843C2semidirect
12. #74895C2semidirect
13. #73911C2semidirect
14. C4⋊C4×D12C2semidirect
15. #73711C2semidirect
16. #73573C2semidirect
17. #73488C2semidirect
102. C4×#121D3semidirect
117. C2×#235D4semidirect
186. C4×D12D4semidirect
340. C3×C4⋊C4#41semidirect
547. D12#121semidirect
640. C4⋊C4#235semidirect
698. C3×C4#547semidirect
834. C4#5551semidirect
836. C3#36259semidirect

Maximal subgroups

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

subgroupindex
C2×#55512
C2×C4×#2352
C3×C4×#1212
#826412
#823762
#823512
#820762
#764752
D3×#3892
#758432
#748952
#739112
C4⋊C4×D122
#737112
#735732
#734882
#362593