Finite Group Databasebeta

← #11069158

Subgroups — #11069158

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×#5619C212yesmaximal, complemented
2C3×C4×#121C211yesmaximal, characteristic, complemented
3#82417C212yesmaximal, complemented
4#82378C211yesmaximal, characteristic, complemented
5#82352C212yesmaximal, complemented
6D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
7#82081C211yesmaximal, characteristic, complemented
8#82062C211yesmaximal, characteristic, complemented
9#76317C212yesmaximal, complemented
10#76016C212yesmaximal, complemented
11#75687C214yesmaximal, complemented
12#74790C214yesmaximal, complemented
13#74033C212yesmaximal, complemented
14#73717C211yesmaximal, characteristic, complemented
15#73653C211yesmaximal, characteristic, complemented
16#73585C212yesmaximal, complemented
17#73516C212yesmaximal, complemented
18#39352—31nomaximal, Sylow
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2212yes—
22C22×C3×C42C2211yescharacteristic
23C2×#940C2212yes—
24C2×#939C2214yes—
25C2×#938C2214yes—
26C2×D4×Dic3C2212yes—
27C2×#930C2212yes—
28C2×#930C2212yes—
29C2×#930C2212yes—
30C2×#930C2212yes—
31C2×#930C2212yes—
32C2×#926C2212yes—
33C22×C4⋊Dic3C2212yes—
34#5619—216no—
35C2×#893C2212yes—
36C2×#890C2212yes—
37C2×#886C2214yes—
38C2×#886C2214yes—
39C2×#883C2214yes—
40C2×#874C2211yescharacteristic
41C2×C4×D12C2212yes—
42C3×#390C2211yescharacteristic
43C3×#389C2211yescharacteristic
44C3×#388C2212yes—
45C3×#386C2212yes—
46C3×#380C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C22⋊C4C2212yes—
49#5212C2212yes—
50#5212C2212yes—
51#5212C2211yescharacteristic
52#5212C2211yescharacteristic
53#4994C2214yes—
54#4988C2212yes—
55#4988C2212yes—
56#4987C2214yes—
57#4984C2212yes—
58#4984C2212yes—
59#4961C2214yes—
60#4961C2214yes—
61#4961C2214yes—
62#4961C2214yes—
63#4960C2214yes—
64#4958C2214yes—
65#4950C2214yes—
66#4939C2212yes—
67#4939C2212yes—
68#4939C2212yes—
69#4939C2212yes—
70#4936C2212yes—
71#4935C2211yescharacteristic
72#4935C2212yes—
73#4935C2211yescharacteristic
74#4935C2211yescharacteristic
75C4×C4⋊Dic3C2212yes—
76C4×C4⋊Dic3C2211yescharacteristic
77C4×C4⋊Dic3C2211yescharacteristic
78#4928C2212yes—
79#4677C2214yes—
80#4677C2214yes—
81#4674C2214yes—
82#4668C2214yes—
83#4665C2214yes—
84#4661C2214yes—
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×#121D311yescharacteristic, complemented
101#2285—31no—
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2312yes—
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2314yes—
109C22×#67C2314yes—
110C22×#67C2314yes—
111C23×Dic3C2314yes—
112C22×D12C2312yes—
113C22×D12C2312yes—
114C22×D12C2312yes—
115C22×C4×D3C2314yes—
116C3×#121D418yescomplemented
117C3×C4×D4—24no—
118C3×C4×D4—44no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C22⋊C4C2312yes—
128C2×C3×C42—24no—
129C2×C3×C42C2312yes—
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C2×#217C2314yes—
135C2×#217C2312yes—
136C2×#217C2312yes—
137#940—28no—
138#939—216no—
139#938—216no—
140D4×Dic3—28no—
141#930—28no—
142#930—44no—
143#930—44no—
144#930—44no—
145#930—44no—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154#926—28no—
155C2×C4⋊Dic3—44no—
156C2×C4⋊Dic3C2314yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2314yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×C4×Dic3C2312yes—
172C2×C4×Dic3C2312yes—
173#893—28no—
174#890—28no—
175#886—216no—
176#886—48no—
177#883—216no—
178#874—24no—
179C4×D12—44no—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3×#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189#540—616no—
190C2×#127—32no—
191C2×#127—31no—
192C2×#125—32no—
193C2×#123—34no—
194C2×#123—34no—
195C2×#123—34no—
196C2×#121—34no—
197C2×#121—34no—
198C2×#121—32no—
199C2×#121—32no—
200C2×#121—32no—
201C2×#121—32no—
202C2×#121—32no—
203C2×#121C2×D311yescharacteristic
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4—32no—
207C2×C4×D4C2×D311yescharacteristic
208C2×C4×D4C2×D312yes—
209C2×#117—32no—
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#390C2×D311yescharacteristic
229#389—32no—
230#389—32no—
231#389—32no—
232#389C2×D311yescharacteristic
233#388C2×D312yes—
234#386—34no—
235#386—34no—
236#386C2×D312yes—
237#385—34no—
238#385—34no—
239#384—31no—
240#384—31no—
241#384—31no—
242#384—32no—
243#382—32no—
244#380—32no—
245#380—32no—
246#380—31no—
247#380—31no—
248#380—34no—
249#380C2×D311yescharacteristic
250C4×C4⋊C4—31no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—31no—
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4C2×D312yes—
255C24×C3C2411yescharacteristic
256C24×C3C2412yes—
257C23×D3C2414yes—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4C2×D414yes—
263C2×C3×D4C2×D418yes—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—24no—
273C22×C3×C4—22no—
274C22×C3×C4—41no—
275C22×C3×C4C2×D414yes—
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C2×#67—28no—
286C2×#67—28no—
287C2×#67—28no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C22×Dic3—28no—
295C22×Dic3—44no—
296C22×Dic3—44no—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2414yes—
302C2×D12—24no—
303C2×D12—24no—
304C2×D12—24no—
305C2×D12—24no—
306C2×D12—24no—
307C2×D12—24no—
308C2×D12—24no—
309C2×D12—42no—
310C2×D12—42no—
311C2×C4×D3—28no—
312C2×C4×D3—44no—
313C2×C4×D3—44no—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—42no—
317C3×C4⋊C4C2×D414yes—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4C2×D418yes—
323C3×C42—22no—
324C3×C42—22no—
325C3×C42—22no—
326C3×C42—24no—
327C3×C42#4114yes—
328#217—28no—
329#217—24no—
330#217—24no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339C4⋊Dic3—24no—
340C4⋊Dic3—24no—
341C4⋊Dic3—28no—
342C4⋊Dic3—24no—
343C4⋊Dic3—22no—
344C4⋊Dic3—24no—
345C4⋊Dic3—22no—
346C4⋊Dic3—24no—
347C4⋊Dic3—22no—
348C4⋊Dic3—22no—
349C4⋊Dic3—44no—
350C4⋊Dic3—44no—
351C4⋊Dic3—42no—
352C4⋊Dic3—42no—
353Dic3⋊C4—28no—
354C4×Dic3—24no—
355C4×Dic3—24no—
356C22×D4—34no—
357C22×D4—34no—
358C22×D4—34no—
359C22×D4—32no—
360C22×D4—32no—
361C22×D4—32no—
362C22×D4C22×D311yescharacteristic
363C22×D4C22×D312yes—
364C23×C4—34no—
365C23×C4—34no—
366C23×C4C22×D312yes—
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—616no—
377#121—616no—
378#121—68no—
379#121—124no—
380#121—124no—
381#121—124no—
382#121—124no—
383#121D1218yescomplemented
384C4×D4—24no—
385C4×D4—44no—
386C4×D4—68no—
387C4×D4—68no—
388C4×D4—124no—
389#117—68no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—124no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D312yes—
409C2×C4⋊C4C22×D311yescharacteristic
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4C22×D312yes—
422C2×C22⋊C4C22×D312yes—
423C2×C22⋊C4C22×D312yes—
424C2×C22⋊C4C22×D312yes—
425C2×C22⋊C4C22×D312yes—
426C2×C42—24no—
427C2×C42—32no—
428C2×C42—32no—
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—32no—
438#95—34no—
439#95—34no—
440#95C22×D312yes—
441#95C22×D312yes—
442#95C22×D312yes—
443C23×C3—22no—
444C23×C3—21no—
445C23×C3—22no—
446C23×C3—21no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3C22×D412yes—
456C23×C3C22×D414yes—
457C23×C3C2511yescharacteristic
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—24no—
465C3×D4—28no—
466C3×D4—48no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—28no—
476C2×C3×C4—21no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—44no—
486C2×C3×C4—44no—
487C2×C3×C4—48no—
488C2×C3×C4C22×D414yes—
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—88no—
499#67—88no—
500#67—88no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—24no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—24no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—88no—
517D12—48no—
518D12—48no—
519D12—84no—
520C4×D3—88no—
521C24—34no—
522C24C23×D311yescharacteristic
523C24C23×D312yes—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—68no—
529C2×D4—68no—
530C2×D4—68no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—64no—
536C2×D4—64no—
537C2×D4—64no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—124no—
541C2×D4—124no—
542C2×D4—124no—
543C2×D4—124no—
544C2×D4—124no—
545C2×D4—124no—
546C2×D4C2×D1214yes—
547C2×D4C2×D1218yes—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—34no—
563C22×C4—41no—
564C22×C4—68no—
565C22×C4—68no—
566C22×C4—124no—
567C22×C4—124no—
568C22×C4—124no—
569C22×C4—124no—
570C22×C4C2×D1214yes—
571C22×C4C23×D311yescharacteristic
572C22×C4C23×D312yes—
573C22×C4C23×D312yes—
574C22×C4C23×D311yescharacteristic
575C22×C4C23×D312yes—
576C22×C4C23×D311yescharacteristic
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D311yescharacteristic
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—42no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—68no—
587C4⋊C4—68no—
588C4⋊C4—62no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—64no—
592C4⋊C4—62no—
593C4⋊C4—64no—
594C4⋊C4—124no—
595C4⋊C4—122no—
596C4⋊C4—124no—
597C4⋊C4—122no—
598C4⋊C4C2×D1214yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—68no—
606C22⋊C4—68no—
607C22⋊C4—68no—
608C22⋊C4—68no—
609C22⋊C4—124no—
610C22⋊C4—124no—
611C22⋊C4—124no—
612C22⋊C4—124no—
613C22⋊C4—124no—
614C22⋊C4C2×D1218yes—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—24no—
619C42—64no—
620C42—64no—
621C42#23714yes—
622C22×C3—22no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—22no—
626C22×C3—24no—
627C22×C3—22no—
628C22×C3—42no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—41no—
634C22×C3—42no—
635C22×C3—41no—
636C22×C3C23×D411yescharacteristic
637C22×C3C22×#4111yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×H(5,𝔽2)11yescharacteristic
640C22×C3C2×H(5,𝔽2)11yescharacteristic
641C22×C3C2×2−1+411yescharacteristic
642C22×C3#58511yescharacteristic
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—24no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4#54014yescomplemented
658C3×C4#54714yes—
659Dic3—42no—
660Dic3—42no—
661Dic3—42no—
662Dic3—44no—
663Dic3—42no—
664C23—22no—
665C23—21no—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—22no—
676C23—64no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—64no—
682C23—64no—
683C23C22×D1212yes—
684C23C22×D1214yes—
685C23C24×D311yescharacteristic
686D4—28no—
687D4—48no—
688D4—128no—
689D4—128no—
690D4—244no—
691D4—248no—
692D4—248no—
693D4—248no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—64no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—64no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—248no—
731C2×C4—248no—
732C2×C4C22×D1212yes—
733C2×C4C22×D1214yes—
734C2×C4C22×D1212yes—
735C2×C4C2×#23712yes—
736C2×C4C2×#23712yes—
737C2×C4C2×#23712yes—
738C2×C4#100412yes—
739C2×C4#100912yes—
740C2×C4#100912yes—
741C2×C4#101012yes—
742C2×C3—42no—
743C2×C3—44no—
744C2×C3C2×#54011yescharacteristic
745C2×C3C2×#54711yescharacteristic
746C2×C3#349411yescharacteristic
747C2×C3#349611yescharacteristic
748C2×C3#349811yescharacteristic
749C2×C3#354811yescharacteristic
750C2×C3#355411yescharacteristic
751D3—84no—
752C22—22no—
753C22—24no—
754C22—24no—
755C22—22no—
756C22—22no—
757C22—24no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—124no—
767C22—124no—
768C22—124no—
769C22—124no—
770C22—124no—
771C22—124no—
772C22—124no—
773C22C23×D1211yescharacteristic
774C22C22×#23711yescharacteristic
775C22C2×#100411yescharacteristic
776C22C2×#100911yescharacteristic
777C22C2×#100911yescharacteristic
778C22C2×#101011yescharacteristic
779C22#596411yescharacteristic
780C4—22no—
781C4—22no—
782C4—24no—
783C4—22no—
784C4—41no—
785C4—42no—
786C4—42no—
787C4—122no—
788C4—122no—
789C4—122no—
790C4—124no—
791C4—122no—
792C4#555514yes—
793C4#561914yescomplemented
794C3#3935211yescharacteristic, complemented, Sylow
795C2—42no—
796C2—44no—
797C2—244no—
798C2C2×#555511yescharacteristic
799C2#8578611yescharacteristic
800C2#8584611yescharacteristic
801C2C2×#561911yescharacteristic
802C2#8602711yescharacteristic
803C2#8613711yescharacteristic
804C2#8625111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
hypercenterC4×#121D3
hypocenterC3#39352
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#5619C2semidirect
2. C3×C4×#121C2semidirect
3. #82417C2semidirect
4. #82378C2semidirect
5. #82352C2semidirect
6. D4×C4⋊Dic3C2semidirect
7. #82081C2semidirect
8. #82062C2semidirect
9. #76317C2semidirect
10. #76016C2semidirect
11. #75687C2semidirect
12. #74790C2semidirect
13. #74033C2semidirect
14. #73717C2semidirect
15. #73653C2semidirect
16. #73585C2semidirect
17. #73516C2semidirect
100. C4×#121D3semidirect
116. C3×#121D4semidirect
383. #121D12semidirect
657. C3×C4#540semidirect
793. C4#5619semidirect
794. C3#39352semidirect

Maximal subgroups

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

subgroupindex
C2×#56192
C3×C4×#1212
#824172
#823782
#823522
D4×C4⋊Dic32
#820812
#820622
#763172
#760162
#756872
#747902
#740332
#737172
#736532
#735852
#735162
#393523