Finite Group Databasebeta

← #11069162

Subgroups — #11069162

Order 768.

2484 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5535C212yesmaximal, complemented
2C3×#2285C211yesmaximal, characteristic, complemented
3#82288C212yesmaximal, complemented
4#82081C211yesmaximal, characteristic, complemented
5C4×#930C211yesmaximal, characteristic, complemented
6#74362C212yesmaximal, complemented
7#74328C212yesmaximal, complemented
8#74198C214yesmaximal, complemented
9#74035C214yesmaximal, complemented
10#73935C212yesmaximal, complemented
11#73887C212yesmaximal, complemented
12#73799C211yesmaximal, characteristic, complemented
13#73780C212yesmaximal, complemented
14C4⋊C4×D12C211yesmaximal, characteristic, complemented
15#73716C211yesmaximal, characteristic, complemented
16#73677C212yesmaximal, complemented
17#73653C211yesmaximal, characteristic, complemented
18#39352—31nomaximal, Sylow
19C2×C3×#117C2212yes—
20C22×C3×C42C2211yescharacteristic
21C2×#930C2212yes—
22C2×#930C2212yes—
23C2×#930C2212yes—
24C2×#930C2211yescharacteristic
25C2×C4×#67C2212yes—
26#5535—216no—
27C2×#895C2212yes—
28C2×#895C2212yes—
29C2×#894C2214yes—
30C2×#894C2214yes—
31C2×#894C2214yes—
32C2×#893C2212yes—
33C2×D3×C4⋊C4C2212yes—
34C2×#884C2214yes—
35C2×#884C2214yes—
36C2×#874C2212yes—
37C2×#874C2211yescharacteristic
38C2×C4×D12C2212yes—
39C2×C4×D12C2211yescharacteristic
40C2×C4×D12C2212yes—
41C2×#870C2212yes—
42C3×#384C2211yescharacteristic
43C3×#384C2211yescharacteristic
44C3×#382C2212yes—
45C3×#380C2212yes—
46C3×#380C2211yescharacteristic
47C3×#380C2211yescharacteristic
48C3×C4×C4⋊C4C2211yescharacteristic
49C3×C4×C4⋊C4C2212yes—
50C3×C4×C4⋊C4C2211yescharacteristic
51#5213C2212yes—
52#5212C2211yescharacteristic
53#4993C2214yes—
54#4993C2214yes—
55#4992C2214yes—
56#4991C2214yes—
57#4989C2214yes—
58#4988C2212yes—
59#4987C2212yes—
60#4975C2212yes—
61#4972C2212yes—
62#4959C2214yes—
63#4959C2214yes—
64#4940C2212yes—
65#4939C2211yescharacteristic
66#4939C2212yes—
67#4939C2212yes—
68#4939C2212yes—
69#4939C2212yes—
70#4939C2212yes—
71C4×(C2×D3)⋊C4C2212yes—
72#4935C2211yescharacteristic
73C4×C4⋊Dic3C2211yescharacteristic
74#4928C2212yes—
75#4928C2212yes—
76#4928C2211yescharacteristic
77#4676C2214yes—
78#4672C2214yes—
79#4671C2214yes—
80#4668C2214yes—
81#4667C2214yes—
82#4665C2214yes—
83#4665C2214yes—
84#4657C2214yes—
85C2×#540—32no—
86#2856—31no—
87#2706—34no—
88#2671—34no—
89#2624—32no—
90#2552—31no—
91#2541—31no—
92#2537—32no—
93#2501—32no—
94#2454—32no—
95#2445—32no—
96#2422—32no—
97#2416—32no—
98#2366—31no—
99D4×C4⋊C4—31no—
100C4×#121—31no—
101#2285D311yescharacteristic, complemented
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C22×#67C2314yes—
106C22×#67C2312yes—
107C22×D12C2312yes—
108C22×D12C2312yes—
109C22×D12C2311yescharacteristic
110C22×D12C2312yes—
111C22×D12C2314yes—
112C22×D12C2314yes—
113C22×C4×D3C2312yes—
114C22×C4×D3C2314yes—
115C22×C4×D3C2314yes—
116C3×#117—28no—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C42—24no—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2312yes—
130C2×C3×C42C2312yes—
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C2×#217C2312yes—
135#930—28no—
136#930—44no—
137#930—44no—
138#930D418yescomplemented
139C4×#67—44no—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×C4×Dic3C2312yes—
165#895—44no—
166#895—44no—
167#894—216no—
168#894—216no—
169#894—48no—
170#893—44no—
171D3×C4⋊C4—44no—
172#884—216no—
173#884—216no—
174#874—28no—
175#874—24no—
176C4×D12—28no—
177C4×D12—24no—
178C4×D12—28no—
179#870—28no—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3×#95C2312yes—
183C3×#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189#540—616no—
190C2×#127—31no—
191C2×#127—32no—
192C2×#125—32no—
193C2×#123—34no—
194C2×#123—34no—
195C2×#123—34no—
196C2×#121—31no—
197C2×#121—32no—
198C2×#121—32no—
199C2×#121—32no—
200C2×#121—32no—
201C2×#121—32no—
202C2×#121—34no—
203C2×#121—34no—
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4—32no—
207C2×C4×D4—31no—
208C2×C4×D4—32no—
209C2×#117C2×D312yes—
210C22×C4⋊C4—32no—
211C22×C42C2×D311yescharacteristic
212#399—34no—
213#399—34no—
214#398—34no—
215#397—34no—
216#396—34no—
217#394—34no—
218#394—34no—
219#394—34no—
220#394—34no—
221#392—34no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—32no—
226#390—32no—
227#390—32no—
228#390—31no—
229#389—32no—
230#389—32no—
231#389—32no—
232#389—31no—
233#388—32no—
234#386—32no—
235#386—34no—
236#386—34no—
237#385—34no—
238#385—34no—
239#384—32no—
240#384—31no—
241#384C2×D311yescharacteristic
242#384C2×D311yescharacteristic
243#382C2×D312yes—
244#380—31no—
245#380—32no—
246#380—34no—
247#380C2×D312yes—
248#380C2×D311yescharacteristic
249#380C2×D311yescharacteristic
250C4×C4⋊C4—31no—
251C4×C4⋊C4C2×D311yescharacteristic
252C4×C4⋊C4C2×D312yes—
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—32no—
255C24×C3C2411yescharacteristic
256C23×D3C2414yes—
257C23×D3C2412yes—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—41no—
266C22×C3×C4C2×D414yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2412yes—
269C22×C3×C4C2411yescharacteristic
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—28no—
278C2×#67—42no—
279C2×#67—42no—
280C2×#67—44no—
281C2×#67—44no—
282C2×#67C2×D418yes—
283C22×Dic3C2412yes—
284C22×Dic3C2412yes—
285C22×Dic3C2414yes—
286C22×Dic3C2412yes—
287C2×D12—22no—
288C2×D12—22no—
289C2×D12—24no—
290C2×D12—24no—
291C2×D12—24no—
292C2×D12—24no—
293C2×D12—24no—
294C2×D12—24no—
295C2×D12—28no—
296C2×D12—28no—
297C2×D12—24no—
298C2×D12—44no—
299C2×D12—44no—
300C2×D12—44no—
301C2×D12—42no—
302C2×D12—42no—
303C2×D12—44no—
304C2×D12C2×D414yes—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—28no—
309C2×C4×D3—28no—
310C2×C4×D3—44no—
311C2×C4×D3—44no—
312C2×C4×D3—44no—
313C2×C4×D3—44no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—24no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—42no—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—24no—
324C3×C42—24no—
325C3×C42—24no—
326C3×C42—22no—
327C3×C42—22no—
328C3×C42—22no—
329C3×C42#4114yes—
330#217—42no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—28no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4C2×D418yes—
344C4⋊Dic3—24no—
345C4⋊Dic3—22no—
346C4⋊Dic3—24no—
347C4⋊Dic3—22no—
348C4⋊Dic3—42no—
349C4⋊Dic3C2×D414yes—
350Dic3⋊C4—28no—
351Dic3⋊C4—28no—
352Dic3⋊C4—44no—
353Dic3⋊C4—44no—
354Dic3⋊C4—42no—
355C4×Dic3—24no—
356C22×D4—32no—
357C22×D4—34no—
358C22×D4—31no—
359C22×D4—32no—
360C22×D4—32no—
361C22×D4—34no—
362C22×D4—34no—
363C22×D4—32no—
364C23×C4—32no—
365C23×C4—34no—
366C23×C4—34no—
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370#127—68no—
371#127—64no—
372#125—68no—
373#123—616no—
374#123—616no—
375#123—128no—
376#121—38no—
377#121—616no—
378#121—616no—
379#121—68no—
380#121—124no—
381#121—124no—
382#121—124no—
383#121—124no—
384C4×D4—68no—
385C4×D4—68no—
386C4×D4—64no—
387C4×D4—124no—
388C4×D4—124no—
389#117—28no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—124no—
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D312yes—
404C2×C4⋊C4C22×D312yes—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D312yes—
409C2×C4⋊C4C22×D312yes—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4C22×D312yes—
425C2×C22⋊C4C22×D312yes—
426C2×C42—24no—
427C2×C42—32no—
428C2×C42C22×D312yes—
429C2×C42C22×D312yes—
430C2×C42C22×D311yescharacteristic
431C2×C42C22×D311yescharacteristic
432C2×C42C22×D311yescharacteristic
433C2×C42C22×D311yescharacteristic
434#95—32no—
435#95—32no—
436#95—32no—
437#95—34no—
438#95—34no—
439#95C22×D312yes—
440#95C22×D312yes—
441#95C22×D312yes—
442#95C22×D312yes—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3C22×D412yes—
450C23×C3C2511yescharacteristic
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3C22×D414yes—
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—28no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—44no—
488C2×C3×C4—44no—
489C2×C3×C4C22×D412yes—
490C2×C3×C4C22×D412yes—
491C2×C3×C4C2×#4112yes—
492C2×C3×C4C2×#4112yes—
493C2×C3×C4C2×#4112yes—
494C2×C3×C4H(5,𝔽2)12yes—
495C2×C3×C4H(5,𝔽2)12yes—
496C2×C3×C4H(5,𝔽2)12yes—
497C2×C3×C42−1+412yes—
498#67—48no—
499#67—88no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—24no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—24no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3C22×D414yes—
512D12—28no—
513D12—48no—
514D12—48no—
515D12—84no—
516D12—88no—
517D12—88no—
518C4×D3—48no—
519C4×D3—88no—
520C4×D3—88no—
521C24—32no—
522C24—34no—
523C24C23×D311yescharacteristic
524C2×D4—38no—
525C2×D4—34no—
526C2×D4—68no—
527C2×D4—68no—
528C2×D4—68no—
529C2×D4—62no—
530C2×D4—64no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—62no—
535C2×D4—64no—
536C2×D4—64no—
537C2×D4—64no—
538C2×D4—122no—
539C2×D4—124no—
540C2×D4—124no—
541C2×D4—124no—
542C2×D4—122no—
543C2×D4—124no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—124no—
547C2×D4—124no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—34no—
559C22×C4—41no—
560C22×C4—68no—
561C22×C4—68no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—124no—
566C22×C4—124no—
567C22×C4—124no—
568C22×C4—124no—
569C22×C4D3×D414yes—
570C22×C4C23×D312yes—
571C22×C4C23×D312yes—
572C22×C4C23×D311yescharacteristic
573C22×C4C23×D312yes—
574C22×C4C23×D312yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D311yescharacteristic
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—24no—
587C4⋊C4—34no—
588C4⋊C4—42no—
589C4⋊C4—68no—
590C4⋊C4—68no—
591C4⋊C4—62no—
592C4⋊C4—64no—
593C4⋊C4—62no—
594C4⋊C4—64no—
595C4⋊C4—124no—
596C4⋊C4—122no—
597C4⋊C4—122no—
598C4⋊C4—124no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—38no—
602C22⋊C4—68no—
603C22⋊C4—68no—
604C22⋊C4—64no—
605C22⋊C4—68no—
606C22⋊C4—68no—
607C22⋊C4—64no—
608C22⋊C4—124no—
609C22⋊C4—122no—
610C22⋊C4—124no—
611C22⋊C4—124no—
612C22⋊C4—124no—
613C22⋊C4—124no—
614C22⋊C4—122no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—24no—
619C42—24no—
620C42—64no—
621C42#23514yes—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3C23×D411yescharacteristic
630C22×C3C22×#4111yescharacteristic
631C22×C3C2×H(5,𝔽2)11yescharacteristic
632C22×C3C2×H(5,𝔽2)11yescharacteristic
633C22×C3C2×H(5,𝔽2)11yescharacteristic
634C22×C3C2×2−1+411yescharacteristic
635C22×C3#58511yescharacteristic
636C2×D3—24no—
637C2×D3—24no—
638C2×D3—24no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—44no—
644C2×D3—44no—
645C2×D3—44no—
646C2×D3—44no—
647C2×D3—44no—
648C2×D3—44no—
649C2×D3—44no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—41no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4#54014yescomplemented
659C3×C4#54714yes—
660Dic3—24no—
661Dic3—42no—
662Dic3—44no—
663Dic3—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—34no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—64no—
682C23—64no—
683C23—64no—
684C23C2×D3×D412yes—
685C23C24×D311yescharacteristic
686D4—68no—
687D4—128no—
688D4—128no—
689D4—128no—
690D4—244no—
691D4—248no—
692D4—248no—
693D4—248no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—28no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—34no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—64no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—64no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—128no—
731C2×C4—248no—
732C2×C4—248no—
733C2×C4C2×#23512yes—
734C2×C4C2×#23512yes—
735C2×C4C2×#23512yes—
736C2×C4C2×D3×D412yes—
737C2×C4C2×D3×D412yes—
738C2×C4#100712yes—
739C2×C4#100912yes—
740C2×C4#100912yes—
741C2×C4#100912yes—
742C2×C3—42no—
743C2×C3C2×#54011yescharacteristic
744C2×C3C2×#54711yescharacteristic
745C2×C3#349411yescharacteristic
746C2×C3#349611yescharacteristic
747C2×C3#349811yescharacteristic
748C2×C3#354811yescharacteristic
749C2×C3#355411yescharacteristic
750D3—44no—
751D3—84no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—64no—
760C22—64no—
761C22—64no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22—122no—
766C22—124no—
767C22—124no—
768C22—124no—
769C22—124no—
770C22—124no—
771C22—124no—
772C22—124no—
773C22C22×#23511yescharacteristic
774C22C22×D3×D411yescharacteristic
775C22C2×#100711yescharacteristic
776C22C2×#100911yescharacteristic
777C22C2×#100911yescharacteristic
778C22C2×#100911yescharacteristic
779C22#596411yescharacteristic
780C4—22no—
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—41no—
788C4—64no—
789C4—122no—
790C4—124no—
791C4—122no—
792C4#550714yes—
793C4#553514yescomplemented
794C3#3935211yescharacteristic, complemented, Sylow
795C2—42no—
796C2—124no—
797C2—244no—
798C2C2×#550711yescharacteristic
799C2C2×#553511yescharacteristic
800C2#8574711yescharacteristic
801C2#8624111yescharacteristic
802C2#8624211yescharacteristic
803C2#8628811yescharacteristic
804C2#8628911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2285C2
hypercenter#2285D3
hypocenterC3#39352
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
1. C2×#5535C2semidirect
2. C3×#2285C2semidirect
3. #82288C2semidirect
4. #82081C2semidirect
5. C4×#930C2semidirect
6. #74362C2semidirect
7. #74328C2semidirect
8. #74198C2semidirect
9. #74035C2semidirect
10. #73935C2semidirect
11. #73887C2semidirect
12. #73799C2semidirect
13. #73780C2semidirect
14. C4⋊C4×D12C2semidirect
15. #73716C2semidirect
16. #73677C2semidirect
17. #73653C2semidirect
101. #2285D3semidirect
138. #930D4semidirect
658. C3×C4#540semidirect
793. C4#5535semidirect
794. C3#39352semidirect

Maximal subgroups

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

subgroupindex
C2×#55352
C3×#22852
#822882
#820812
C4×#9302
#743622
#743282
#741982
#740352
#739352
#738872
#737992
#737802
C4⋊C4×D122
#737162
#736772
#736532
#393523