Finite Group Databasebeta

← #11058606

Subgroups — #11058606

Order 768.

2468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5555C211yesmaximal, characteristic, complemented
2C2×#5479C211yesmaximal, characteristic, complemented
3C3×C4×#121C211yesmaximal, characteristic, complemented
4#82701C212yesmaximal, complemented
5#82415C212yesmaximal, complemented
6#82376C211yesmaximal, characteristic, complemented
7#82353C212yesmaximal, complemented
8#82076C211yesmaximal, characteristic, complemented
9#76294C212yesmaximal, complemented
10#76102C212yesmaximal, complemented
11#75676C214yesmaximal, complemented
12#74804C214yesmaximal, complemented
13#73888C212yesmaximal, complemented
14C4⋊C4×D12C211yesmaximal, characteristic, complemented
15#73722C211yesmaximal, characteristic, complemented
16#73495C212yesmaximal, complemented
17#73486C212yesmaximal, complemented
18#38908—31nomaximal, Sylow
19C22×#237C2212yes—
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2212yes—
23C22×C3×C42C2211yescharacteristic
24C2×#930C2212yes—
25C2×#930C2211yescharacteristic
26C2×#929C2212yes—
27C2×C4×#67C2212yes—
28C22×C4⋊Dic3C2212yes—
29C2×#924C2211yescharacteristic
30C2×#924C2212yes—
31C2×#924C2212yes—
32#5555—28no—
33C2×#897C2212yes—
34C2×D3×C4⋊C4C2212yes—
35C2×#886C2214yes—
36#5479—28no—
37C2×#876C2212yes—
38C2×#875C2211yescharacteristic
39C2×C4×D12C2212yes—
40C2×C4×D12C2211yescharacteristic
41C2×#872C2212yes—
42C2×#870C2211yescharacteristic
43C2×#869C2211yescharacteristic
44C2×C4×Dic6C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#389C2211yescharacteristic
47C3×#388C2212yes—
48C3×#386C2212yes—
49C3×#380C2211yescharacteristic
50C3×C4×C4⋊C4C2211yescharacteristic
51C3×C4×C22⋊C4C2212yes—
52#5223C2214yes—
53#5221C2212yes—
54#5220C2214yes—
55#5212C2212yes—
56#5212C2212yes—
57#5212C2212yes—
58#4992C2214yes—
59#4987C2212yes—
60#4982C2214yes—
61#4973C2212yes—
62#4973C2212yes—
63#4972C2212yes—
64#4959C2214yes—
65#4956C2214yes—
66#4956C2214yes—
67#4956C2214yes—
68#4948C2214yes—
69#4948C2214yes—
70#4946C2214yes—
71#4942C2214yes—
72#4942C2214yes—
73#4936C2212yes—
74#4935C2211yescharacteristic
75#4929C2212yes—
76#4929C2212yes—
77#4928C2212yes—
78#4928C2212yes—
79#4928C2212yes—
80#4675C2214yes—
81#4668C2214yes—
82#4667C2214yes—
83#4660C2214yes—
84#4659C2214yes—
85#4657C2214yes—
86C2×#547—31no—
87C2×#529—31no—
88#2857—31no—
89#2695—34no—
90#2693—34no—
91#2625—32no—
92#2568—31no—
93#2538—31no—
94#2535—32no—
95#2442—32no—
96#2427—32no—
97#2417—32no—
98#2417—32no—
99#2407—32no—
100D4×C4⋊C4—31no—
101#2311—32no—
102C4×#121D311yescharacteristic, complemented
103C22×C3×D4C2312yes—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C22×#67C2314yes—
110C22×#67C2312yes—
111C23×Dic3C2314yes—
112C2×#237—28no—
113C2×#237—28no—
114C2×#237—44no—
115C22×D12C2311yescharacteristic
116C22×C4×D3C2312yes—
117C22×C4×D3C2314yes—
118C22×Dic6C2311yescharacteristic
119C22×Dic6C2312yes—
120C3×#121—24no—
121C3×C4×D4—24no—
122C3×C4×D4—44no—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C22⋊C4C2312yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C42—24no—
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2312yes—
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×#217C2312yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yes—
142#930—24no—
143#930—28no—
144#929—28no—
145C4×#67—28no—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×C4⋊Dic3—28no—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2311yescharacteristic
161#924—24no—
162#924—44no—
163#924—44no—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2312yes—
166C2×Dic3⋊C4C2312yes—
167C2×Dic3⋊C4C2312yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×C4×Dic3C2312yes—
172#897—28no—
173D3×C4⋊C4—44no—
174#886—216no—
175#876—28no—
176#875—24no—
177C4×D12—44no—
178C4×D12D418yescomplemented
179#872—28no—
180#870—24no—
181#869—24no—
182C4×Dic6—24no—
183C3×#95C2312yes—
184C3×#95C2312yes—
185C3×#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C22×#41—32no—
195#547—68no—
196C2×C4⋊Q8—31no—
197#529—68no—
198C2×#126—32no—
199C2×#125—31no—
200C2×#124—31no—
201C2×#123—32no—
202C2×#123—34no—
203C2×C22⋊Q8—31no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8—32no—
207C2×#121—31no—
208C2×#121—32no—
209C2×#121C2×D311yescharacteristic
210C2×C4×Q8—31no—
211C2×C4×D4—32no—
212C2×C4×D4—31no—
213C2×C4×D4—32no—
214C2×C4×D4C2×D311yescharacteristic
215C2×C4×D4C2×D312yes—
216C2×#117—32no—
217C22×C4⋊C4—32no—
218C22×C4⋊C4—32no—
219C22×C42C2×D311yescharacteristic
220#400—34no—
221#400—34no—
222#398—34no—
223#398—34no—
224#397—34no—
225#397—34no—
226#396—34no—
227#396—34no—
228#394—34no—
229#392—34no—
230#391—32no—
231#391—32no—
232#391—32no—
233#391—32no—
234#390—32no—
235#390C2×D311yescharacteristic
236#389—32no—
237#389—32no—
238#389—32no—
239#389—32no—
240#389C2×D311yescharacteristic
241#388C2×D312yes—
242#386—34no—
243#386—34no—
244#386—34no—
245#386—34no—
246#386C2×D312yes—
247#385—34no—
248#385—34no—
249#384—31no—
250#382—32no—
251#380—32no—
252#380—32no—
253#380—32no—
254#380—32no—
255#380—34no—
256#380—34no—
257#380—34no—
258#380C2×D311yescharacteristic
259C4×C4⋊C4C2×D311yescharacteristic
260C4×C22⋊C4C2×D312yes—
261C24×C3C2412yes—
262C24×C3C2411yescharacteristic
263C23×D3C2412yes—
264C2×C3×D4—24no—
265C2×C3×D4—24no—
266C2×C3×D4—22no—
267C2×C3×D4—22no—
268C2×C3×D4—42no—
269C2×C3×D4#4114yes—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—24no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—24no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—24no—
281C22×C3×C4—41no—
282C22×C3×C4C2412yes—
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2412yes—
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2412yes—
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C22×C3×C4C2411yescharacteristic
290C22×C3×C4C2411yescharacteristic
291C2×#67—28no—
292C2×#67—24no—
293C2×#67—28no—
294C2×#67—24no—
295C2×#67—44no—
296C2×#67—42no—
297C22×Dic3—28no—
298C22×Dic3—28no—
299C22×Dic3—44no—
300C22×Dic3C2412yes—
301C22×Dic3C2414yes—
302C22×Dic3C2412yes—
303C22×Dic3C2414yes—
304C22×Dic3C2412yes—
305#237—432no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12C2×D414yes—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C2×C4×D3—44no—
312C2×C4×D3—44no—
313C2×C4×D3—44no—
314C2×C4×D3C2×D418yes—
315C2×Dic6—22no—
316C2×Dic6—24no—
317C2×Dic6—24no—
318C2×Dic6—22no—
319C2×Dic6—24no—
320C2×Dic6—22no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—42no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330C3×C42—22no—
331C3×C42—22no—
332C3×C42—22no—
333C3×C42—24no—
334C3×C42C2×D414yes—
335#217—24no—
336#217—44no—
337#217—44no—
338#217—44no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4C2×D418yes—
345C4⋊Dic3—22no—
346C4⋊Dic3—24no—
347C4⋊Dic3—24no—
348C4⋊Dic3—24no—
349C4⋊Dic3—24no—
350C4⋊Dic3—28no—
351C4⋊Dic3—42no—
352C4⋊Dic3C2×D414yes—
353Dic3⋊C4—24no—
354Dic3⋊C4—24no—
355Dic3⋊C4—24no—
356Dic3⋊C4—24no—
357Dic3⋊C4—44no—
358Dic3⋊C4—44no—
359Dic3⋊C4—44no—
360C4×Dic3—24no—
361C2×#41—68no—
362C2×#41—68no—
363C2×#41—124no—
364C22×Q8—31no—
365C22×Q8—32no—
366C22×D4—32no—
367C22×D4—34no—
368C22×D4—31no—
369C22×D4C22×D312yes—
370C22×D4C22×D311yescharacteristic
371C23×C4—32no—
372C23×C4—34no—
373C23×C4—34no—
374C23×C4C22×D312yes—
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C4⋊Q8—64no—
379#126—68no—
380#125—64no—
381#124—64no—
382#123—616no—
383#123—68no—
384C22⋊Q8—68no—
385C22⋊Q8—64no—
386C22⋊Q8—124no—
387C22⋊Q8—124no—
388#121—24no—
389#121—64no—
390#121—68no—
391C4×Q8—64no—
392C4×D4—24no—
393C4×D4—38no—
394C4×D4—44no—
395C4×D4—68no—
396C4×D4—124no—
397#117—68no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—68no—
414C2×C4⋊C4—124no—
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D312yes—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4C22×D312yes—
430C2×C22⋊C4C22×D312yes—
431C2×C22⋊C4C22×D312yes—
432C2×C22⋊C4C22×D312yes—
433C2×C22⋊C4C22×D312yes—
434C2×C42—24no—
435C2×C42—32no—
436C2×C42C22×D311yescharacteristic
437C2×C42C22×D312yes—
438C2×C42C22×D311yescharacteristic
439C2×C42C22×D311yescharacteristic
440C2×C42C22×D311yescharacteristic
441#95—34no—
442#95—34no—
443#95—34no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95C22×D312yes—
450#95C22×D312yes—
451#95C22×D312yes—
452C23×C3—21no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—22no—
457C23×C3—21no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—21no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—21no—
464C23×C3C2×#4114yes—
465C23×C32−1+412yes—
466C23×C3C2511yescharacteristic
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3C22×D414yes—
474C3×D4—28no—
475C3×D4—48no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—44no—
497C2×C3×C4—44no—
498C2×C3×C4—48no—
499C2×C3×C4—44no—
500C2×C3×C4C22×D412yes—
501C2×C3×C4C22×D412yes—
502C2×C3×C4C22×D412yes—
503C2×C3×C4C2×#4112yes—
504C2×C3×C4H(5,𝔽2)12yes—
505C2×C3×C4H(5,𝔽2)12yes—
506C2×C3×C42−1+412yes—
507#67—416no—
508#67—48no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—22no—
517C2×Dic3—24no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—24no—
522C2×Dic3—22no—
523C2×Dic3—416no—
524C2×Dic3C22×D414yes—
525D12—28no—
526C4×D3—216no—
527C4×D3—88no—
528Dic6—44no—
529Dic6—48no—
530C24—32no—
531C24C23×D312yes—
532C24C23×D311yescharacteristic
533#41—1232no—
534C2×Q8—64no—
535C2×Q8—62no—
536C2×Q8—64no—
537C2×Q8—62no—
538C2×Q8—64no—
539C2×Q8—62no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—34no—
545C2×D4—42no—
546C2×D4—64no—
547C2×D4—68no—
548C2×D4—68no—
549C2×D4—64no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—124no—
553C2×D4—122no—
554C2×D4#23514yes—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—32no—
567C22×C4—38no—
568C22×C4—32no—
569C22×C4—34no—
570C22×C4—32no—
571C22×C4—34no—
572C22×C4—41no—
573C22×C4—68no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—68no—
577C22×C4—124no—
578C22×C4—124no—
579C22×C4—124no—
580C22×C4—124no—
581C22×C4C23×D312yes—
582C22×C4C23×D311yescharacteristic
583C22×C4C23×D312yes—
584C22×C4C23×D311yescharacteristic
585C22×C4C23×D312yes—
586C22×C4C23×D311yescharacteristic
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589C22×C4C23×D311yescharacteristic
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—34no—
594C4⋊C4—42no—
595C4⋊C4—68no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—62no—
601C4⋊C4—64no—
602C4⋊C4—64no—
603C4⋊C4—64no—
604C4⋊C4—64no—
605C4⋊C4—124no—
606C4⋊C4—124no—
607C4⋊C4—124no—
608C4⋊C4—122no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—38no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—64no—
618C22⋊C4—68no—
619C22⋊C4—64no—
620C22⋊C4—124no—
621C22⋊C4—124no—
622C22⋊C4—124no—
623C22⋊C4—124no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—24no—
628C42—64no—
629C42D3×D414yes—
630C22×C3—24no—
631C22×C3—22no—
632C22×C3—24no—
633C22×C3—22no—
634C22×C3—24no—
635C22×C3—22no—
636C22×C3—41no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3C23×D411yescharacteristic
645C22×C3C22×#4111yescharacteristic
646C22×C3C2×H(5,𝔽2)11yescharacteristic
647C22×C3C2×H(5,𝔽2)11yescharacteristic
648C22×C3C2×2−1+411yescharacteristic
649C22×C3C2×2−1+411yescharacteristic
650C22×C3#58511yescharacteristic
651C2×D3—24no—
652C2×D3—24no—
653C2×D3—24no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C3×C4—22no—
659C3×C4—41no—
660C3×C4—42no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4#53714yes—
666C3×C4#54614yes—
667Dic3—24no—
668Dic3—42no—
669Dic3—44no—
670Dic3—42no—
671Dic3—44no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—34no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23C2×#23514yes—
692C23#101012yes—
693C23C24×D311yescharacteristic
694Q8—128no—
695Q8—124no—
696D4—28no—
697D4—48no—
698D4—68no—
699D4—1216no—
700D4—128no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—34no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—48no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—616no—
729C2×C4—64no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—62no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—64no—
741C2×C4—1216no—
742C2×C4—248no—
743C2×C4C2×#23512yes—
744C2×C4C2×D3×D412yes—
745C2×C4C2×D3×D412yes—
746C2×C4C2×D3×D412yes—
747C2×C4#100412yes—
748C2×C4#100912yes—
749C2×C4#101012yes—
750C2×C3—44no—
751C2×C3—42no—
752C2×C3C2×#53711yescharacteristic
753C2×C3C2×#54611yescharacteristic
754C2×C3#348911yescharacteristic
755C2×C3#351511yescharacteristic
756C2×C3#352011yescharacteristic
757C2×C3#354611yescharacteristic
758C2×C3#355211yescharacteristic
759D3—44no—
760C22—22no—
761C22—24no—
762C22—24no—
763C22—22no—
764C22—24no—
765C22—22no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—64no—
775C22—64no—
776C22—64no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22—122no—
781C22C22×#23511yescharacteristic
782C22C22×D3×D411yescharacteristic
783C22C2×#100411yescharacteristic
784C22C2×#100911yescharacteristic
785C22C2×#101011yescharacteristic
786C22C2×#101011yescharacteristic
787C22#596411yescharacteristic
788C4—22no—
789C4—42no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—42no—
795C4—64no—
796C4—124no—
797C4—122no—
798C4—122no—
799C4—124no—
800C4#555014yes—
801C4#560814yes—
802C3#3890811yescharacteristic, complemented, Sylow
803C2—42no—
804C2—44no—
805C2—124no—
806C2#8576711yescharacteristic
807C2C2×#555011yescharacteristic
808C2#8583111yescharacteristic
809C2C2×#560811yescharacteristic
810C2#8604211yescharacteristic
811C2#8613411yescharacteristic
812C2#8624911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
hypercenterC4×#121D3
hypocenterC3#38908
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#5555C2semidirect
2. C2×#5479C2semidirect
3. C3×C4×#121C2semidirect
4. #82701C2semidirect
5. #82415C2semidirect
6. #82376C2semidirect
7. #82353C2semidirect
8. #82076C2semidirect
9. #76294C2semidirect
10. #76102C2semidirect
11. #75676C2semidirect
12. #74804C2semidirect
13. #73888C2semidirect
14. C4⋊C4×D12C2semidirect
15. #73722C2semidirect
16. #73495C2semidirect
17. #73486C2semidirect
102. C4×#121D3semidirect
178. C4×D12D4semidirect
802. C3#38908semidirect

Maximal subgroups

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

subgroupindex
C2×#55552
C2×#54792
C3×C4×#1212
#827012
#824152
#823762
#823532
#820762
#762942
#761022
#756762
#748042
#738882
C4⋊C4×D122
#737222
#734952
#734862
#389083