Finite Group Databasebeta

← #11633938

Subgroups — #11633938

Order 768.

2534 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5555C211yesmaximal, characteristic, complemented
2C2×#5470C211yesmaximal, characteristic, complemented
3C3×C4×#121C211yesmaximal, characteristic, complemented
4#82701C212yesmaximal, complemented
5#82379C211yesmaximal, characteristic, complemented
6#82377C212yesmaximal, complemented
7#82353C212yesmaximal, complemented
8C4×#930C211yesmaximal, characteristic, complemented
9#76301C212yesmaximal, complemented
10#76216C212yesmaximal, complemented
11#75675C214yesmaximal, complemented
12#74725C214yesmaximal, complemented
13#73936C212yesmaximal, complemented
14#73802C211yesmaximal, characteristic, complemented
15#73650C211yesmaximal, characteristic, complemented
16#73485C212yesmaximal, complemented
17#73465C212yesmaximal, complemented
18#59040—31nomaximal, Sylow
19C22×#237C2212yes—
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2212yes—
23C22×C3×C42C2211yescharacteristic
24C2×#930C2212yes—
25C2×#930C2211yescharacteristic
26C2×C4×#67C2212yes—
27C2×#926C2212yes—
28C22×C4⋊Dic3C2212yes—
29C2×#924C2212yes—
30C2×#924C2212yes—
31C2×#924C2212yes—
32C2×#924C2212yes—
33#5555—28no—
34C2×#897C2212yes—
35C2×#887C2212yes—
36C2×#886C2214yes—
37C2×#875C2212yes—
38C2×C4×D12C2211yescharacteristic
39#5470—28no—
40C2×#870C2212yes—
41C2×#869C2211yescharacteristic
42C2×#869C2211yescharacteristic
43C2×C4×Dic6C2212yes—
44C2×C4×Dic6C2212yes—
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#5213C2212yes—
56#5212C2211yescharacteristic
57#4993C2214yes—
58#4987C2212yes—
59#4987C2212yes—
60#4982C2214yes—
61#4975C2212yes—
62#4973C2212yes—
63#4959C2214yes—
64#4957C2214yes—
65#4957C2214yes—
66#4957C2214yes—
67#4949C2214yes—
68#4948C2214yes—
69#4946C2214yes—
70#4942C2214yes—
71Dic3×C22⋊C4C2214yes—
72#4940C2212yes—
73#4939C2211yescharacteristic
74C4×(C2×D3)⋊C4C2212yes—
75C4×C4⋊Dic3C2211yescharacteristic
76C4×C4⋊Dic3C2212yes—
77#4929C2212yes—
78#4928C2212yes—
79#4928C2211yescharacteristic
80#4676C2214yes—
81#4674C2214yes—
82#4669C2214yes—
83#4655C2214yes—
84#4653C2214yes—
85#4647C2214yes—
86C2×#547—31no—
87C2×#533—31no—
88#2694—34no—
89#2547—31no—
90#2542—31no—
91#2540—32no—
92#2538—32no—
93#2471—34no—
94#2426—32no—
95#2423—32no—
96#2417—32no—
97#2407—32no—
98#2365—31no—
99#2360—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121D311yescharacteristic, complemented
103C22×C3×D4C2312yes—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2312yes—
108C23×C3×C4C2311yescharacteristic
109C22×#67C2314yes—
110C22×#67C2312yes—
111C23×Dic3C2314yes—
112C2×#237—28no—
113C2×#237—28no—
114C2×#237—44no—
115C22×D12C2311yescharacteristic
116C22×C4×D3C2312yes—
117C22×Dic6C2312yes—
118C22×Dic6C2312yes—
119C3×#121—24no—
120C3×C4×D4—24no—
121C3×C4×D4—44no—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C22⋊C4C2312yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C42—24no—
132C2×C3×C42C2312yes—
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C2×#217C2314yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2312yes—
141#930—28no—
142#930—24no—
143C4×#67—44no—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2312yes—
151#926—28no—
152C2×C4⋊Dic3—28no—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2311yescharacteristic
161#924—28no—
162#924—28no—
163#924—28no—
164#924—44no—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×C4×Dic3C2314yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2314yes—
174#897—28no—
175#887—44no—
176#886—216no—
177#875—44no—
178C4×D12—24no—
179#870—28no—
180#869—24no—
181#869D418yescomplemented
182C4×Dic6—28no—
183C4×Dic6—28no—
184C3×#95C2312yes—
185C3×#95C2312yes—
186C3×#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C22×#41—32no—
195#547—68no—
196#533—68no—
197C2×C4⋊Q8—31no—
198C2×C4⋊Q8—31no—
199C2×#125—32no—
200C2×#124—32no—
201C2×#123—34no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8—32no—
207C2×#121—32no—
208C2×#121—31no—
209C2×#121C2×D311yescharacteristic
210C2×C4×Q8—32no—
211C2×C4×Q8—32no—
212C2×C4×Q8—32no—
213C2×C4×D4—32no—
214C2×C4×D4—31no—
215C2×C4×D4C2×D311yescharacteristic
216C2×C4×D4C2×D312yes—
217C2×#117—32no—
218C22×C4⋊C4—32no—
219C22×C42C2×D311yescharacteristic
220#399—34no—
221#399—34no—
222#398—34no—
223#397—34no—
224#396—34no—
225#396—34no—
226#394—34no—
227#392—34no—
228#391—32no—
229#391—32no—
230#390—32no—
231#390—34no—
232#390—34no—
233#390—34no—
234#390—31no—
235#390C2×D311yescharacteristic
236#389—31no—
237#389—32no—
238#389—34no—
239#389C2×D311yescharacteristic
240#388—32no—
241#388—34no—
242#388C2×D312yes—
243#387—34no—
244#387—34no—
245#386—34no—
246#386—32no—
247#386C2×D312yes—
248#385—34no—
249#384—32no—
250#380—31no—
251#380—32no—
252#380—32no—
253#380—34no—
254#380C2×D311yescharacteristic
255C4×C4⋊C4—32no—
256C4×C4⋊C4—31no—
257C4×C4⋊C4C2×D311yescharacteristic
258C4×C22⋊C4—34no—
259C4×C22⋊C4—32no—
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—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—24no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
284C22×C3×C4C2411yescharacteristic
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—42no—
296C2×#67—44no—
297C22×Dic3—28no—
298C22×Dic3—28no—
299C22×Dic3—44no—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C22×Dic3C2414yes—
303C22×Dic3C2414yes—
304C22×Dic3C2412yes—
305#237—432no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12—22no—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×Dic6—24no—
313C2×Dic6—24no—
314C2×Dic6—24no—
315C2×Dic6—24no—
316C2×Dic6—24no—
317C2×Dic6C2×D418yes—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—42no—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—24no—
325C3×C22⋊C4—42no—
326C3×C22⋊C4—42no—
327C3×C42—22no—
328C3×C42—22no—
329C3×C42—22no—
330C3×C42—24no—
331C3×C42C2×D414yes—
332#217—28no—
333#217—28no—
334#217—44no—
335#217—42no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—28no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—42no—
343C4⋊Dic3—24no—
344C4⋊Dic3—24no—
345C4⋊Dic3—22no—
346C4⋊Dic3—22no—
347C4⋊Dic3—28no—
348C4⋊Dic3C2×D418yes—
349C4⋊Dic3C2×D418yes—
350C4⋊Dic3#4114yescomplemented
351Dic3⋊C4—28no—
352Dic3⋊C4—28no—
353Dic3⋊C4—28no—
354Dic3⋊C4—44no—
355Dic3⋊C4—44no—
356Dic3⋊C4—42no—
357C4×Dic3—24no—
358C4×Dic3—28no—
359C4×Dic3—44no—
360C2×#41—68no—
361C2×#41—68no—
362C2×#41—124no—
363C22×Q8—32no—
364C22×Q8—32no—
365C22×D4—32no—
366C22×D4—34no—
367C22×D4—31no—
368C22×D4C22×D312yes—
369C22×D4C22×D311yescharacteristic
370C23×C4—34no—
371C23×C4—32no—
372C23×C4C22×D312yes—
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C4⋊Q8—38no—
377C4⋊Q8—64no—
378#125—68no—
379#124—124no—
380#123—616no—
381C22⋊Q8—68no—
382C22⋊Q8—68no—
383C22⋊Q8—68no—
384C22⋊Q8—68no—
385C22⋊Q8—124no—
386#121—24no—
387#121—68no—
388#121—64no—
389C4×Q8—68no—
390C4×Q8—68no—
391C4×Q8—124no—
392C4×D4—24no—
393C4×D4—44no—
394C4×D4—64no—
395C4×D4—124no—
396#117—68no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—68no—
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D312yes—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4C22×D312yes—
428C2×C22⋊C4C22×D312yes—
429C2×C22⋊C4C22×D312yes—
430C2×C22⋊C4C22×D312yes—
431C2×C22⋊C4C22×D312yes—
432C2×C42—24no—
433C2×C42—34no—
434C2×C42—32no—
435C2×C42—34no—
436C2×C42C22×D312yes—
437C2×C42C22×D311yescharacteristic
438C2×C42C22×D311yescharacteristic
439C2×C42C22×D311yescharacteristic
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—34no—
444#95—34no—
445#95—32no—
446#95—34no—
447#95—34no—
448#95C22×D312yes—
449#95C22×D312yes—
450#95C22×D312yes—
451C23×C3—21no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—22no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—21no—
462C23×C3—22no—
463C23×C3C2×#4114yes—
464C23×C32−1+412yes—
465C23×C3C2511yescharacteristic
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C3×D4—28no—
474C3×D4—48no—
475C2×C3×C4—28no—
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—22no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—44no—
496C2×C3×C4—44no—
497C2×C3×C4—48no—
498C2×C3×C4C22×D412yes—
499C2×C3×C4C22×D412yes—
500C2×C3×C4C22×D412yes—
501C2×C3×C4C2×#4112yes—
502C2×C3×C4C2×#4112yes—
503C2×C3×C4H(5,𝔽2)12yes—
504C2×C3×C4H(5,𝔽2)12yes—
505C2×C3×C42−1+412yes—
506#67—416no—
507#67—48no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—24no—
511C2×Dic3—22no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3—24no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—416no—
522C2×Dic3C22×D418yes—
523C2×Dic3C2×#4114yes—
524D12—44no—
525C4×D3—48no—
526Dic6—216no—
527Dic6—48no—
528C24—32no—
529C24C23×D312yes—
530C24C23×D311yescharacteristic
531#41—1232no—
532C2×Q8—38no—
533C2×Q8—64no—
534C2×Q8—64no—
535C2×Q8—64no—
536C2×Q8—64no—
537C2×Q8—64no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—42no—
543C2×D4—68no—
544C2×D4—64no—
545C2×D4—68no—
546C2×D4—64no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—62no—
550C2×D4—122no—
551C2×D4—124no—
552C2×D4#23514yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—32no—
566C22×C4—34no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—34no—
570C22×C4—68no—
571C22×C4—68no—
572C22×C4—64no—
573C22×C4—64no—
574C22×C4—64no—
575C22×C4—124no—
576C22×C4C23×D312yes—
577C22×C4C23×D312yes—
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D311yescharacteristic
580C22×C4C23×D312yes—
581C22×C4C23×D311yescharacteristic
582C22×C4C23×D311yescharacteristic
583C22×C4C23×D311yescharacteristic
584C22×C4C23×D311yescharacteristic
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—38no—
589C4⋊C4—38no—
590C4⋊C4—34no—
591C4⋊C4—42no—
592C4⋊C4—68no—
593C4⋊C4—68no—
594C4⋊C4—68no—
595C4⋊C4—68no—
596C4⋊C4—62no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—62no—
600C4⋊C4—122no—
601C4⋊C4—124no—
602C4⋊C4—124no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—68no—
609C22⋊C4—64no—
610C22⋊C4—68no—
611C22⋊C4—68no—
612C22⋊C4—64no—
613C22⋊C4—64no—
614C22⋊C4—122no—
615C22⋊C4—124no—
616C22⋊C4—124no—
617C22⋊C4—122no—
618C22⋊C4—124no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—24no—
623C42—68no—
624C42—64no—
625C42—124no—
626C42D3×D414yes—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—24no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3C23×D411yescharacteristic
642C22×C3C22×#4111yescharacteristic
643C22×C3C22×#4111yescharacteristic
644C22×C3C2×H(5,𝔽2)11yescharacteristic
645C22×C3C2×H(5,𝔽2)11yescharacteristic
646C22×C3C2×2−1+411yescharacteristic
647C22×C3C2×2−1+411yescharacteristic
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4#54614yes—
663C3×C4#55014yes—
664Dic3—28no—
665Dic3—24no—
666Dic3—42no—
667Dic3—44no—
668Dic3—42no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—22no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—21no—
680C23—22no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23C2×#23514yes—
689C23#101012yes—
690C23C24×D311yescharacteristic
691Q8—616no—
692Q8—128no—
693D4—28no—
694D4—48no—
695D4—1216no—
696D4—128no—
697D4—124no—
698C2×C4—28no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—38no—
719C2×C4—34no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—48no—
723C2×C4—64no—
724C2×C4—62no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—62no—
730C2×C4—64no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—1216no—
737C2×C4—128no—
738C2×C4C2×#23512yes—
739C2×C4C2×D3×D412yes—
740C2×C4C2×D3×D412yes—
741C2×C4C2×D3×D412yes—
742C2×C4#100412yes—
743C2×C4D3×#4112yes—
744C2×C4#100912yes—
745C2×C4#101012yes—
746C2×C3—44no—
747C2×C3—42no—
748C2×C3C2×#54611yescharacteristic
749C2×C3C2×#55011yescharacteristic
750C2×C3#348211yescharacteristic
751C2×C3#348611yescharacteristic
752C2×C3#352011yescharacteristic
753C2×C3#352011yescharacteristic
754C2×C3#354811yescharacteristic
755D3—82no—
756C22—22no—
757C22—22no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—22no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22C22×#23511yescharacteristic
778C22C22×D3×D411yescharacteristic
779C22C2×#100411yescharacteristic
780C22C2×D3×#4111yescharacteristic
781C22C2×#100911yescharacteristic
782C22C2×#101011yescharacteristic
783C22C2×#101011yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—42no—
791C4—68no—
792C4—64no—
793C4—122no—
794C4—124no—
795C4—122no—
796C4#555014yes—
797C4#559914yes—
798C3#5904011yescharacteristic, complemented, Sylow
799C2—42no—
800C2—44no—
801C2—242no—
802C2#8576711yescharacteristic
803C2C2×#555011yescharacteristic
804C2#8582611yescharacteristic
805C2C2×#559911yescharacteristic
806C2#8602211yescharacteristic
807C2#8616711yescharacteristic
808C2#8625111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
hypercenterC4×#121D3
hypocenterC3#59040
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×#5470C2semidirect
3. C3×C4×#121C2semidirect
4. #82701C2semidirect
5. #82379C2semidirect
6. #82377C2semidirect
7. #82353C2semidirect
8. C4×#930C2semidirect
9. #76301C2semidirect
10. #76216C2semidirect
11. #75675C2semidirect
12. #74725C2semidirect
13. #73936C2semidirect
14. #73802C2semidirect
15. #73650C2semidirect
16. #73485C2semidirect
17. #73465C2semidirect
102. C4×#121D3semidirect
181. #869D4semidirect
350. C4⋊Dic3#41semidirect
798. C3#59040semidirect

Maximal subgroups

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

subgroupindex
C2×#55552
C2×#54702
C3×C4×#1212
#827012
#823792
#823772
#823532
C4×#9302
#763012
#762162
#756752
#747252
#739362
#738022
#736502
#734852
#734652
#590403