Finite Group Databasebeta

← #11634146

Subgroups — #11634146

Order 768.

2310 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#533C211yesmaximal, characteristic, complemented
2C2×#5734C211yesmaximal, characteristic, complemented
3#83259C211yesmaximal, characteristic, complemented
4#83240C211yesmaximal, characteristic, complemented
5#83230C211yesmaximal, characteristic, complemented
6#83061C212yesmaximal, complemented
7#83058C212yesmaximal, complemented
8#82813C212yesmaximal, complemented
9#82806C214yesmaximal, complemented
10#82779C212yesmaximal, complemented
11#82495C212yesmaximal, complemented
12#82469C214yesmaximal, complemented
13#82464C212yesmaximal, complemented
14#82276C212yesmaximal, complemented
15#82241C212yesmaximal, complemented
16C4×#930C211yesmaximal, characteristic, complemented
17C4×#930C211yesmaximal, characteristic, complemented
18#59050—31nomaximal, Sylow
19C3×#533—28no—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#125C2212yes—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×C4×Q8C2212yes—
26C2×C3×C4×Q8C2212yes—
27C2×C3×#117C2212yes—
28C22×C3×C42C2211yescharacteristic
29C2×#947C2214yes—
30C2×#947C2212yes—
31C2×#946C2212yes—
32C2×#946C2212yes—
33C2×#930C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×C4×#67C2212yes—
36C2×C4×#67C2212yes—
37#5734—28no—
38C2×#895C2212yes—
39C2×#895C2212yes—
40C2×#892C2212yes—
41C2×#892C2212yes—
42C2×C4×D12C2211yescharacteristic
43C2×C4×D12C2211yescharacteristic
44#5229C2214yes—
45#5229C2212yes—
46#5213C2212yes—
47#5213C2212yes—
48#5212C2211yescharacteristic
49#5212C2211yescharacteristic
50#4994C2214yes—
51#4993C2214yes—
52#4993C2214yes—
53#4992C2214yes—
54#4992C2214yes—
55#4991C2214yes—
56#4990C2214yes—
57#4988C2214yes—
58#4988C2212yes—
59#4987C2212yes—
60#4987C2212yes—
61#4984C2212yes—
62#4984C2212yes—
63#4978C2214yes—
64#4975C2212yes—
65Dic3×C4⋊C4C2212yes—
66Dic3×C4⋊C4C2212yes—
67#4972C2214yes—
68#4961C2214yes—
69#4960C2214yes—
70#4957C2214yes—
71#4944C2214yes—
72#4940C2214yes—
73#4940C2212yes—
74#4940C2212yes—
75#4940C2214yes—
76#4939C2214yes—
77#4939C2211yescharacteristic
78#4939C2211yescharacteristic
79C4×(C2×D3)⋊C4C2212yes—
80C4×(C2×D3)⋊C4C2212yes—
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83C4×Dic3⋊C4C2214yes—
84#4928C2211yescharacteristic
85#4928C2211yescharacteristic
86C2×#555—31no—
87C2×#533D311yescharacteristic, complemented
88#2730—34no—
89#2547—31no—
90#2542—31no—
91#2540—32no—
92#2490—32no—
93#2448—34no—
94#2441—32no—
95#2426—32no—
96#2415—32no—
97#2414—32no—
98#2369—31no—
99#2362—32no—
100#2354—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×Q8C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C22×#67C2312yes—
110C22×D12C2311yescharacteristic
111C22×D12C2311yescharacteristic
112C22×D12C2314yes—
113C22×C4×D3C2312yes—
114C22×C4×D3C2312yes—
115C3×C4⋊Q8—24no—
116C3×C4⋊Q8D418yescomplemented
117C3×#125—28no—
118C3×C22⋊Q8—28no—
119C3×C22⋊Q8—28no—
120C3×C4×Q8—28no—
121C3×C4×Q8—28no—
122C3×#117—28no—
123C2×C3×C4⋊C4C2314yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C22⋊C4C2314yes—
130C2×C3×C42—24no—
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2314yes—
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C2×#217C2312yes—
137C2×#217C2312yes—
138#947—216no—
139#947—44no—
140#946—28no—
141#946—44no—
142#930—24no—
143#930—24no—
144C4×#67—28no—
145C4×#67—44no—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×(C2×D3)⋊C4C2312yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×C4⋊Dic3C2311yescharacteristic
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2314yes—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×Dic3⋊C4C2312yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2312yes—
170C2×Dic3⋊C4C2314yes—
171C2×C4×Dic3C2314yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2314yes—
175#895—28no—
176#895—28no—
177#892—28no—
178#892—28no—
179C4×D12—24no—
180C4×D12—24no—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191#555—68no—
192#533—28no—
193C2×C4⋊Q8C2×D311yescharacteristic
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×#125C2×D312yes—
196C2×#124—34no—
197C2×#124—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8C2×D312yes—
201C2×C22⋊Q8C2×D312yes—
202C2×#121—31no—
203C2×#121—31no—
204C2×#121—32no—
205C2×#121—32no—
206C2×C4×Q8C2×D312yes—
207C2×C4×Q8C2×D312yes—
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×C4×D4—31no—
211C2×C4×D4—31no—
212C2×#117—32no—
213C2×#117—32no—
214C2×#117C2×D312yes—
215C22×C42C2×D311yescharacteristic
216#399—34no—
217#399—34no—
218#397—34no—
219#397—34no—
220#396—34no—
221#394—34no—
222#394—34no—
223#392—34no—
224#391—32no—
225#391—34no—
226#390—32no—
227#390—34no—
228#390—34no—
229#390—34no—
230#390—31no—
231#390—31no—
232#389—32no—
233#389—32no—
234#389—34no—
235#389—31no—
236#389—31no—
237#388—34no—
238#388—34no—
239#388—34no—
240#388—34no—
241#388—32no—
242#388—32no—
243#387—34no—
244#386—32no—
245#386—32no—
246#384—32no—
247#380—31no—
248#380—31no—
249#380—32no—
250#380—32no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—34no—
254C4×C4⋊C4—31no—
255C4×C4⋊C4—31no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C24×C3C2411yescharacteristic
259C23×D3C2412yes—
260C23×D3C2412yes—
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—42no—
265C2×C3×Q8—42no—
266C2×C3×Q8C2×D418yes—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—41no—
274C22×C3×C4—41no—
275C22×C3×C4#4114yes—
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2414yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2414yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—42no—
288C2×#67—42no—
289C2×#67—42no—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296C2×D12—22no—
297C2×D12—22no—
298C2×D12—22no—
299C2×D12—22no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—28no—
303C2×D12—44no—
304C2×D12—44no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—28no—
313C3×C4⋊C4—28no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4C2×D418yes—
316C3×C4⋊C4C2×D418yes—
317C3×C22⋊C4—28no—
318C3×C42—22no—
319C3×C42—22no—
320C3×C42—22no—
321C3×C42—28no—
322C3×C42C2×D414yes—
323#217—24no—
324#217—42no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—28no—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—42no—
334(C2×D3)⋊C4—42no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339C4⋊Dic3—22no—
340C4⋊Dic3—22no—
341C4⋊Dic3—22no—
342C4⋊Dic3—22no—
343C4⋊Dic3—22no—
344C4⋊Dic3—44no—
345C4⋊Dic3#4114yes—
346Dic3⋊C4—24no—
347Dic3⋊C4—28no—
348Dic3⋊C4—42no—
349Dic3⋊C4—44no—
350C4×Dic3—28no—
351C4×Dic3—24no—
352C4×Dic3—24no—
353C4×Dic3—44no—
354C22×Q8C22×D312yes—
355C22×Q8C22×D312yes—
356C22×D4—32no—
357C22×D4—32no—
358C22×D4—31no—
359C22×D4—31no—
360C22×D4—34no—
361C23×C4—32no—
362C23×C4—32no—
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C4⋊Q8—24no—
367C4⋊Q8#6718yescomplemented
368#125—28no—
369#124—616no—
370#124—124no—
371C22⋊Q8—28no—
372C22⋊Q8—28no—
373C22⋊Q8—68no—
374C22⋊Q8—124no—
375#121—64no—
376#121—64no—
377#121—68no—
378#121—68no—
379C4×Q8—28no—
380C4×Q8—28no—
381C4×D4—68no—
382C4×D4—64no—
383C4×D4—64no—
384C4×D4—124no—
385#117—28no—
386#117—68no—
387#117—68no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4C22×D312yes—
400C2×C4⋊C4C22×D314yes—
401C2×C4⋊C4C22×D314yes—
402C2×C4⋊C4C22×D312yes—
403C2×C4⋊C4C22×D312yes—
404C2×C4⋊C4C22×D312yes—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4C22×D314yes—
422C2×C42—24no—
423C2×C42—34no—
424C2×C42—32no—
425C2×C42—32no—
426C2×C42—34no—
427C2×C42C22×D314yes—
428C2×C42C22×D311yescharacteristic
429C2×C42C22×D311yescharacteristic
430C2×C42C22×D311yescharacteristic
431C2×C42C22×D311yescharacteristic
432#95—32no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—34no—
437#95—32no—
438#95—32no—
439#95—34no—
440#95—34no—
441#95—34no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3C2×#4112yes—
449C23×C3C2511yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C3×Q8—48no—
465C3×Q8—48no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—28no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—24no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—44no—
483C2×C3×C4—44no—
484C2×C3×C4C22×D418yes—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C2×#4112yes—
489C2×C3×C4C2×#4112yes—
490C2×C3×C4C2×#4112yes—
491C2×C3×C4H(5,𝔽2)12yes—
492C2×C3×C42−1+412yes—
493#67—48no—
494#67—48no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3C2×#4114yes—
513D12—44no—
514D12—44no—
515D12—88no—
516C4×D3—48no—
517C4×D3—48no—
518C24—32no—
519C24—32no—
520C24C23×D311yescharacteristic
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—24no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8C2×#6718yes—
527C2×D4—64no—
528C2×D4—64no—
529C2×D4—64no—
530C2×D4—62no—
531C2×D4—62no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—62no—
535C2×D4—62no—
536C2×D4—68no—
537C2×D4—124no—
538C2×D4—124no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—64no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—64no—
561C22×C4—64no—
562C22×C4#23914yes—
563C22×C4C23×D311yescharacteristic
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D314yes—
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D314yes—
569C22×C4C23×D311yescharacteristic
570C22×C4C23×D311yescharacteristic
571C4⋊C4—24no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—24no—
575C4⋊C4—34no—
576C4⋊C4—68no—
577C4⋊C4—64no—
578C4⋊C4—62no—
579C4⋊C4—62no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—122no—
584C4⋊C4—124no—
585C4⋊C4—124no—
586C4⋊C4C2×#6718yes—
587C4⋊C4C2×#6718yes—
588C22⋊C4—28no—
589C22⋊C4—64no—
590C22⋊C4—68no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—68no—
595C22⋊C4—68no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—122no—
599C22⋊C4—124no—
600C22⋊C4—124no—
601C22⋊C4—124no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—28no—
609C42—64no—
610C42—64no—
611C42—68no—
612C42—124no—
613C42C2×#6714yes—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3C23×D411yescharacteristic
622C22×C3C22×#4111yescharacteristic
623C22×C3C22×#4111yescharacteristic
624C22×C3C2×H(5,𝔽2)11yescharacteristic
625C22×C3C2×2−1+411yescharacteristic
626C22×C3#58511yescharacteristic
627C22×C3#58511yescharacteristic
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C3×C4—22no—
643C3×C4—28no—
644C3×C4—22no—
645C3×C4—41no—
646C3×C4—44no—
647C3×C4—41no—
648C3×C4#54814yes—
649C3×C4#55014yes—
650Dic3—24no—
651Dic3—42no—
652Dic3—42no—
653Dic3—42no—
654Dic3—42no—
655Dic3—42no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—62no—
663C23—62no—
664C23—62no—
665C23—62no—
666C23—62no—
667C23—62no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23C2×#23912yes—
677C23C24×D311yescharacteristic
678Q8—48no—
679Q8—48no—
680D4—128no—
681D4—128no—
682D4—124no—
683D4—124no—
684D4—248no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—28no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—24no—
701C2×C4—34no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—128no—
722C2×C4—128no—
723C2×C4C2×#23912yes—
724C2×C4C2×#23912yes—
725C2×C4#100712yes—
726C2×C4D3×#4112yes—
727C2×C4#100912yes—
728C2×C4C22×#6718yes—
729C2×C4C22×#6712yes—
730C2×C4C22×#6712yes—
731C2×C4C22×#6712yes—
732C2×C3—42no—
733C2×C3C2×#54811yescharacteristic
734C2×C3C2×#55011yescharacteristic
735C2×C3#347511yescharacteristic
736C2×C3#348511yescharacteristic
737C2×C3#350611yescharacteristic
738C2×C3#351811yescharacteristic
739C2×C3#354711yescharacteristic
740D3—82no—
741D3—82no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—122no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22C22×#23911yescharacteristic
764C22C2×#100711yescharacteristic
765C22C2×D3×#4111yescharacteristic
766C22C2×#100911yescharacteristic
767C22#596411yescharacteristic
768C22#596411yescharacteristic
769C22C23×#6711yescharacteristic
770C4—22no—
771C4—22no—
772C4—28no—
773C4—41no—
774C4—44no—
775C4—41no—
776C4—64no—
777C4—122no—
778C4—122no—
779C4—122no—
780C4—122no—
781C4—122no—
782C4#581714yes—
783C4#583414yes—
784C3#5905011yescharacteristic, complemented, Sylow
785C2—42no—
786C2—242no—
787C2—242no—
788C2#8625911yescharacteristic
789C2#8626511yescharacteristic
790C2#8627611yescharacteristic
791C2#8628711yescharacteristic
792C2C2×#581711yescharacteristic
793C2C2×#583411yescharacteristic
794C2#8727311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#533C2
hypercenterC2×#533D3
hypocenterC3#59050
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C3×#533C2semidirect
2. C2×#5734C2semidirect
3. #83259C2semidirect
4. #83240C2semidirect
5. #83230C2semidirect
6. #83061C2semidirect
7. #83058C2semidirect
8. #82813C2semidirect
9. #82806C2semidirect
10. #82779C2semidirect
11. #82495C2semidirect
12. #82469C2semidirect
13. #82464C2semidirect
14. #82276C2semidirect
15. #82241C2semidirect
16. C4×#930C2semidirect
17. C4×#930C2semidirect
87. C2×#533D3semidirect
116. C3×C4⋊Q8D4semidirect
367. C4⋊Q8#67semidirect
784. C3#59050semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5332
C2×#57342
#832592
#832402
#832302
#830612
#830582
#828132
#828062
#827792
#824952
#824692
#824642
#822762
#822412
C4×#9302
#590503