Finite Group Databasebeta

← #36717468

Subgroups — #36717468

Order 22784.

2318 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26023444C214yesmaximal, complemented
2#26023272C212yesmaximal
3#26023261C212yesmaximal, complemented
4#26023209C211yesmaximal, characteristic, complemented
5#26023201C211yesmaximal, characteristic, complemented
6#26023181C212yesmaximal, complemented
7Q8×C4⋊Dic89C211yesmaximal, characteristic, complemented
8D4×C4⋊Dic89C211yesmaximal, characteristic, complemented
9D4×C4⋊Dic89C212yesmaximal, complemented
10#26022994C212yesmaximal, complemented
11#26022965C212yesmaximal, complemented
12#26022924C214yesmaximal, complemented
13#26022875C212yesmaximal, complemented
14#26022861C212yesmaximal, complemented
15C2×#19151468C211yesmaximal, characteristic, complemented
16#26022650C211yesmaximal, characteristic, complemented
17C2×#529×C89C211yesmaximal, characteristic
18C2×Q8×Dic89C2212yes—
19C2×D4×Dic89C2214yes—
20C2×D4×Dic89C2212yes—
21C2×#15667971C2212yes—
22C22×C4⋊Dic89C2212yes—
23C22×C4⋊Dic89C2212yes—
24C22×C4⋊Dic89C2212yes—
25C22×C4⋊Dic89C2212yes—
26#19151505C2212yes—
27#19151501C2212yes—
28#19151497C2214yes—
29#19151497C2212yes—
30#19151497C2214yes—
31#19151497C2214yes—
32#19151497C2214yes—
33#19151497C2212yes—
34#19151491C2214yes—
35#19151491C2214yes—
36#19151491C2214yes—
37#19151491C2214yes—
38#19151484C2214yes—
39#19151484C2214yes—
40#19151484C2214yes—
41#19151484C2214yes—
42#19151478C2214yes—
43#19151473C2214yes—
44#19151473C2214yes—
45#19151473C2214yes—
46#19151473C2214yes—
47#19151473C2214yes—
48#19151468C2211yescharacteristic
49#19151468C2212yes—
50#19151468C2212yes—
51#19151468C2211yescharacteristic
52#19151468C2212yes—
53#19151468C2212yes—
54#19151466C2212yes—
55#19151464C2212yes—
56#19151464C2211yescharacteristic
57#19151464C2211yescharacteristic
58#19151461C2212yes—
59#19151458C2211yescharacteristic
60#19151458C2212yes—
61#19151458C2212yes—
62#19151458C2211yescharacteristic
63C4⋊C4×Dic89C2212yes—
64C4⋊C4×Dic89C2212yes—
65C4×C4⋊Dic89C2212yes—
66C4×C4⋊Dic89C2211yescharacteristic
67C4×C4⋊Dic89C2211yescharacteristic
68C4×C4⋊Dic89C2212yes—
69C22⋊C4×Dic89C2214yes—
70C4×C22⋊Dic89C2212yes—
71#19151444C2212yes—
72#529×C89C4116yescomplemented
73C2×#126×C89C2212yes—
74C2×#125×C89C2211yescharacteristic
75C2×#124×C89C2211yescharacteristic
76C2×#123×C89C2212yes—
77C2×C22⋊Q8×C89C2211yescharacteristic
78C2×#121×C89C2211yescharacteristic
79C2×C4×Q8×C89C2211yescharacteristic
80C2×C4×D4×C89C2212yes—
81C2×C4×D4×C89C2211yescharacteristic
82C2×#117×C89C2212yes—
83C22×C42×C89C2211yescharacteristic
84C23×Dic89C2314yes—
85C23×Dic89C2314yes—
86Q8×Dic89—44no—
87D4×Dic89—44no—
88D4×Dic89—48no—
89#15667971—44no—
90C2×C4⋊Dic89—44no—
91C2×C4⋊Dic89—44no—
92C2×C4⋊Dic89—44no—
93C2×C4⋊Dic89—44no—
94C2×C4⋊Dic89C2311yescharacteristic
95C2×C4⋊Dic89C2311yescharacteristic
96C2×C4⋊Dic89C2311yescharacteristic
97C2×C4⋊Dic89C2311yescharacteristic
98C2×C4⋊Dic89C2312yes—
99C2×C4⋊Dic89C2312yes—
100C2×C4⋊Dic89C2312yes—
101C2×C4⋊Dic89C2312yes—
102C2×C4⋊Dic89C2312yes—
103C2×C4⋊Dic89C2314yes—
104C2×C4⋊Dic89C2314yes—
105C2×C4⋊Dic89C2314yes—
106C2×C4⋊Dic89C2312yes—
107C2×C4⋊Dic89C2314yes—
108C2×C4⋊Dic89C2314yes—
109C2×C4⋊Dic89C2314yes—
110C2×C22⋊Dic89C2312yes—
111C2×C22⋊Dic89C2312yes—
112C2×C22⋊Dic89C2314yes—
113C2×C22⋊Dic89C2314yes—
114C2×C22⋊Dic89C2314yes—
115C2×C4×Dic89C2312yes—
116C2×C4×Dic89C2312yes—
117C2×C4×Dic89C2314yes—
118C2×C4×Dic89C2314yes—
119C2×C4×Dic89C2314yes—
120#15667919C2312yes—
121#15667919C2312yes—
122#15667919C2312yes—
123#15667919C2312yes—
124#15667919C2312yes—
125#15667919C2312yes—
126#15667919C2314yes—
127#15667919C2314yes—
128#15667919C2312yes—
129#15667919C2312yes—
130#15667919C2314yes—
131#15667919C2314yes—
132#15667919C2314yes—
133#15667919C2314yes—
134C22×Q8×C89C2311yescharacteristic
135C22×D4×C89C2312yes—
136C22×D4×C89C2311yescharacteristic
137C23×C4×C89C2311yescharacteristic
138C23×C4×C89C2311yescharacteristic
139C23×C4×C89C2312yes—
140C23×C4×C89C2311yescharacteristic
141#126×C89C2×C4116yescomplemented
142#125×C89C2×C418yescomplemented
143#124×C89C2×C418yescomplemented
144#123×C89C2×C4116yescomplemented
145C22⋊Q8×C89C2×C418yescomplemented
146#121×C89C2×C418yes—
147C4×Q8×C89C2×C418yescomplemented
148C4×D4×C89C2×C418yescomplemented
149C4×D4×C89C2×C4116yescomplemented
150#117×C89C2×C4116yescomplemented
151C2×C4⋊C4×C89C2311yescharacteristic
152C2×C4⋊C4×C89C2311yescharacteristic
153C2×C4⋊C4×C89C2312yes—
154C2×C4⋊C4×C89C2312yes—
155C2×C4⋊C4×C89C2312yes—
156C2×C4⋊C4×C89C2312yes—
157C2×C22⋊C4×C89C2312yes—
158C2×C22⋊C4×C89C2312yes—
159C2×C22⋊C4×C89C2312yes—
160C2×C22⋊C4×C89C2312yes—
161C2×C22⋊C4×C89C2312yes—
162C2×C42×C89C2×C418yescomplemented
163C2×C42×C89C2311yescharacteristic
164C2×C42×C89C2312yes—
165C2×C42×C89C2311yescharacteristic
166C2×C42×C89C2311yescharacteristic
167C2×C42×C89C2311yescharacteristic
168C22×Dic89—28no—
169C22×Dic89—44no—
170C22×Dic89—44no—
171C22×Dic89—44no—
172C22×Dic89—44no—
173C22×Dic89—44no—
174C22×Dic89C2412yes—
175C22×Dic89C2414yes—
176C22×Dic89C2414yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C4⋊Dic89—22no—
181C4⋊Dic89—24no—
182C4⋊Dic89—24no—
183C4⋊Dic89—24no—
184C4⋊Dic89—22no—
185C4⋊Dic89—24no—
186C4⋊Dic89—22no—
187C4⋊Dic89—22no—
188C4⋊Dic89—44no—
189C4⋊Dic89—44no—
190C4⋊Dic89—44no—
191C4⋊Dic89—44no—
192C4⋊Dic89—42no—
193C4⋊Dic89—44no—
194C4⋊Dic89—42no—
195C4⋊Dic89—44no—
196C22⋊Dic89—24no—
197C22⋊Dic89—24no—
198C22⋊Dic89—44no—
199C22⋊Dic89—44no—
200C22⋊Dic89—44no—
201C4×Dic89—24no—
202C4×Dic89—24no—
203C4×Dic89—44no—
204C4×Dic89—44no—
205C4×Dic89—44no—
206C24×C89C2412yes—
207C24×C89C2411yescharacteristic
208C2×Q8×C89—22no—
209C2×Q8×C89—22no—
210C2×Q8×C89C22×C414yes—
211C2×D4×C89—24no—
212C2×D4×C89—24no—
213C2×D4×C89—22no—
214C2×D4×C89—22no—
215C2×D4×C89C22×C418yes—
216C2×D4×C89C22×C414yes—
217C22×C4×C89—22no—
218C22×C4×C89—22no—
219C22×C4×C89—24no—
220C22×C4×C89—22no—
221C22×C4×C89—22no—
222C22×C4×C89—22no—
223C22×C4×C89—24no—
224C22×C4×C89—22no—
225C22×C4×C89C22×C414yes—
226C22×C4×C89C22×C414yes—
227C22×C4×C89C22×C414yes—
228C22×C4×C89C22×C418yes—
229C22×C4×C89C2411yescharacteristic
230C22×C4×C89C2411yescharacteristic
231C22×C4×C89C2411yescharacteristic
232C22×C4×C89C2411yescharacteristic
233C22×C4×C89C2412yes—
234C22×C4×C89C2412yes—
235C22×C4×C89C2412yes—
236C22×C4×C89C2411yescharacteristic
237C22×C4×C89C2411yescharacteristic
238C4⋊C4×C89C22×C418yes—
239C4⋊C4×C89C22×C418yes—
240C4⋊C4×C89C22×C414yes—
241C4⋊C4×C89C22×C418yes—
242C4⋊C4×C89C22×C414yes—
243C4⋊C4×C89C22×C418yes—
244C22⋊C4×C89C22×C418yes—
245C22⋊C4×C89C22×C418yes—
246C22⋊C4×C89C22×C418yes—
247C22⋊C4×C89C22×C418yes—
248C22⋊C4×C89C22×C418yes—
249C42×C89C22×C414yes—
250C42×C89C22×C414yes—
251C42×C89C22×C414yes—
252C42×C89C22×C414yes—
253C42×C89C22×C418yes—
254C23×C89—21no—
255C23×C89—21no—
256C23×C89—21no—
257C23×C89—21no—
258C23×C89—22no—
259C23×C89—22no—
260C23×C89—22no—
261C23×C89—22no—
262C23×C89—22no—
263C23×C89—22no—
264C23×C89C23×C414yes—
265C23×C89C23×C412yes—
266C23×C89H(5,𝔽2)12yes—
267C23×C892−1+412yes—
268C23×C89C2511yescharacteristic
269Q8×C89—28no—
270D4×C89—216no—
271D4×C89—28no—
272C2×C4×C89—28no—
273C2×C4×C89—22no—
274C2×C4×C89—21no—
275C2×C4×C89—21no—
276C2×C4×C89—21no—
277C2×C4×C89—21no—
278C2×C4×C89—22no—
279C2×C4×C89—22no—
280C2×C4×C89—21no—
281C2×C4×C89—21no—
282C2×C4×C89—22no—
283C2×C4×C89—21no—
284C2×C4×C89—21no—
285C2×C4×C89—22no—
286C2×C4×C89—22no—
287C2×C4×C89—28no—
288C2×C4×C89—216no—
289C2×C4×C89—28no—
290C2×C4×C89C23×C412yes—
291C2×C4×C89C23×C412yes—
292C2×C4×C89C23×C412yes—
293C2×C4×C89C23×C412yes—
294C2×C4×C89C23×C414yes—
295C2×C4×C89C23×C414yes—
296C2×C4×C89C23×C414yes—
297C2×C4×C89C23×C412yes—
298C2×C4×C89C23×C412yes—
299C2×C4×C89H(5,𝔽2)12yes—
300C2×C4×C89H(5,𝔽2)12yes—
301C2×C4×C892−1+412yes—
302C2×C4×C892−1+412yes—
303C2×Dic89—22no—
304C2×Dic89—22no—
305C2×Dic89—22no—
306C2×Dic89—22no—
307C2×Dic89—24no—
308C2×Dic89—24no—
309C2×Dic89—24no—
310C2×Dic89—22no—
311C2×Dic89—24no—
312C2×Dic89—24no—
313C2×Dic89—22no—
314C2×Dic89—24no—
315C2×Dic89—22no—
316C2×Dic89—22no—
317C2×Dic89—22no—
318C2×Dic89—22no—
319C2×Dic89—22no—
320C2×Dic89—22no—
321C2×Dic89—88no—
322C2×Dic89—88no—
323C22×C89—22no—
324C22×C89—22no—
325C22×C89—22no—
326C22×C89—22no—
327C22×C89—22no—
328C22×C89—22no—
329C22×C89—24no—
330C22×C89—24no—
331C22×C89—24no—
332C22×C89—42no—
333C22×C89—42no—
334C22×C89—42no—
335C22×C89—42no—
336C22×C89#52014yes—
337C22×C89C24×C411yescharacteristic
338C22×C89C2×H(5,𝔽2)11yescharacteristic
339C22×C89C2×H(5,𝔽2)11yescharacteristic
340C22×C89C2×H(5,𝔽2)11yescharacteristic
341C22×C89C2×2−1+411yescharacteristic
342C22×C89C2×2−1+411yescharacteristic
343C22×C89C2×2−1+411yescharacteristic
344C4×C89—22no—
345C4×C89—22no—
346C4×C89—24no—
347C4×C89—22no—
348C4×C89—22no—
349C4×C89—24no—
350C4×C89—24no—
351C4×C89#52014yes—
352C4×C89#52014yes—
353Dic89—44no—
354Dic89—42no—
355Dic89—44no—
356Dic89—42no—
357Dic89—42no—
358Dic89—42no—
359#34384—891nomaximal, Sylow
360C2×C89—24no—
361C2×C89—44no—
362C2×C89C2×#52011yescharacteristic
363C2×C89C2×#52011yescharacteristic
364C2×C89C2×#52011yescharacteristic
365C2×C89#354311yescharacteristic
366C2×C89#354411yescharacteristic
367C2×C89#355211yescharacteristic
368C2×C89#355211yescharacteristic
369C2×#529D8911yescharacteristic
370#2383—894no—
371#2361—892no—
372#2360—892no—
373#2355—891no—
374#2354—891no—
375#2352—892no—
376Q8×C4⋊C4—891no—
377D4×C4⋊C4—891no—
378D4×C4⋊C4—892no—
379#2330—892no—
380#2326—892no—
381#2322—894no—
382#2317—892no—
383#2314—892no—
384C2×#384—891no—
385#2283—891no—
386C89#3438411yescharacteristic, complemented, Sylow
387#529Dic89116yescomplemented
388C2×#126C2×D8912yes—
389C2×#125C2×D8911yescharacteristic
390C2×#124C2×D8911yescharacteristic
391C2×#123C2×D8912yes—
392C2×C22⋊Q8C2×D8911yescharacteristic
393C2×#121C2×D8911yescharacteristic
394C2×C4×Q8—892no—
395C2×C4×Q8C2×D8911yescharacteristic
396C2×C4×D4—894no—
397C2×C4×D4—892no—
398C2×C4×D4C2×D8912yes—
399C2×C4×D4C2×D8911yescharacteristic
400C2×#117—892no—
401C2×#117C2×D8912yes—
402C22×C4⋊C4—892no—
403C22×C4⋊C4—892no—
404C22×C4⋊C4—892no—
405C22×C4⋊C4—892no—
406C22×C42C2×D8911yescharacteristic
407#391—892no—
408#390—892no—
409#389—894no—
410#389—894no—
411#389—894no—
412#389—892no—
413#389—894no—
414#389—892no—
415#388—894no—
416#388—894no—
417#388—894no—
418#388—894no—
419#387—894no—
420#387—894no—
421#387—894no—
422#387—894no—
423#386—894no—
424#385—894no—
425#385—894no—
426#385—894no—
427#385—894no—
428#385—894no—
429#384—892no—
430#384—892no—
431#384—892no—
432#384—891no—
433#384—891no—
434#384—892no—
435#383—892no—
436#382—891no—
437#382—891no—
438#382—892no—
439#381—892no—
440#380—892no—
441#380—892no—
442#380—891no—
443#380—891no—
444C4×C4⋊C4—892no—
445C4×C4⋊C4—892no—
446C4×C4⋊C4—892no—
447C4×C4⋊C4—892no—
448C4×C4⋊C4—891no—
449C4×C4⋊C4—891no—
450C4×C22⋊C4—892no—
451C4×C22⋊C4—894no—
452#376—892no—
453C22×Q8C22×D8911yescharacteristic
454C22×D4C22×D8912yes—
455C22×D4C22×D8911yescharacteristic
456C23×C4—894no—
457C23×C4—894no—
458C23×C4C22×D8911yescharacteristic
459C23×C4C22×D8911yescharacteristic
460C23×C4C22×D8911yescharacteristic
461C23×C4C22×D8912yes—
462#126C2×Dic89116yescomplemented
463#125C2×Dic8918yescomplemented
464#124C2×Dic8918yescomplemented
465#123C2×Dic89116yescomplemented
466C22⋊Q8C2×Dic8918yescomplemented
467#121C2×Dic8918yes—
468C4×Q8—3564no—
469C4×Q8C2×Dic8918yescomplemented
470C4×D4—3568no—
471C4×D4—3564no—
472C4×D4C2×Dic8918yescomplemented
473C4×D4C2×Dic89116yescomplemented
474#117—3564no—
475#117C2×Dic89116yescomplemented
476C2×C4⋊C4—892no—
477C2×C4⋊C4—894no—
478C2×C4⋊C4—894no—
479C2×C4⋊C4—894no—
480C2×C4⋊C4—892no—
481C2×C4⋊C4—894no—
482C2×C4⋊C4—894no—
483C2×C4⋊C4—894no—
484C2×C4⋊C4—891no—
485C2×C4⋊C4—892no—
486C2×C4⋊C4—892no—
487C2×C4⋊C4—892no—
488C2×C4⋊C4—892no—
489C2×C4⋊C4—891no—
490C2×C4⋊C4—891no—
491C2×C4⋊C4—891no—
492C2×C4⋊C4—3564no—
493C2×C4⋊C4—3564no—
494C2×C4⋊C4—3564no—
495C2×C4⋊C4—3564no—
496C2×C4⋊C4C22×D8912yes—
497C2×C4⋊C4C22×D8912yes—
498C2×C4⋊C4C22×D8911yescharacteristic
499C2×C4⋊C4C22×D8912yes—
500C2×C4⋊C4C22×D8911yescharacteristic
501C2×C4⋊C4C22×D8912yes—
502C2×C22⋊C4—894no—
503C2×C22⋊C4—894no—
504C2×C22⋊C4—894no—
505C2×C22⋊C4—892no—
506C2×C22⋊C4—892no—
507C2×C22⋊C4C22×D8912yes—
508C2×C22⋊C4C22×D8912yes—
509C2×C22⋊C4C22×D8912yes—
510C2×C22⋊C4C22×D8912yes—
511C2×C22⋊C4C22×D8912yes—
512C2×C42—894no—
513C2×C42—894no—
514C2×C42—894no—
515C2×C42—892no—
516C2×C42—892no—
517C2×C42C2×Dic8918yescomplemented
518C2×C42C22×D8911yescharacteristic
519C2×C42C22×D8912yes—
520C2×C42C22×D8911yescharacteristic
521C2×C42C22×D8911yescharacteristic
522C2×C42C22×D8911yescharacteristic
523#95—892no—
524#95—892no—
525#95—892no—
526#95—892no—
527#95—894no—
528#95—892no—
529#95—892no—
530#95—894no—
531#95—894no—
532#95—892no—
533#95—892no—
534#95—894no—
535#95—894no—
536#95—894no—
537C24C23×D8912yes—
538C24C23×D8911yescharacteristic
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8C22×Dic8914yes—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4C22×Dic8918yes—
547C2×D4C22×Dic8914yes—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—892no—
557C22×C4—892no—
558C22×C4—892no—
559C22×C4—894no—
560C22×C4—892no—
561C22×C4—894no—
562C22×C4—3564no—
563C22×C4—3564no—
564C22×C4—3564no—
565C22×C4—3564no—
566C22×C4—3564no—
567C22×C4—1788no—
568C22×C4C22×Dic8914yes—
569C22×C4C22×Dic8914yes—
570C22×C4C22×Dic8914yes—
571C22×C4C22×Dic8918yes—
572C22×C4C23×D8912yes—
573C22×C4C23×D8912yes—
574C22×C4C23×D8912yes—
575C22×C4C23×D8911yescharacteristic
576C22×C4C23×D8911yescharacteristic
577C22×C4C23×D8911yescharacteristic
578C22×C4C23×D8911yescharacteristic
579C22×C4C23×D8911yescharacteristic
580C22×C4C23×D8911yescharacteristic
581C4⋊C4—3564no—
582C4⋊C4—3564no—
583C4⋊C4—3564no—
584C4⋊C4—3562no—
585C4⋊C4—3564no—
586C4⋊C4—3562no—
587C4⋊C4—3564no—
588C4⋊C4—3564no—
589C4⋊C4—1782no—
590C4⋊C4—1784no—
591C4⋊C4—1784no—
592C4⋊C4—1784no—
593C4⋊C4—1784no—
594C4⋊C4—1782no—
595C4⋊C4—1782no—
596C4⋊C4—1782no—
597C4⋊C4C22×Dic8918yes—
598C4⋊C4C22×Dic8918yes—
599C4⋊C4C22×Dic8914yes—
600C4⋊C4C22×Dic8918yes—
601C4⋊C4C22×Dic8914yes—
602C4⋊C4C22×Dic8918yes—
603C22⋊C4—3564no—
604C22⋊C4—3564no—
605C22⋊C4—3564no—
606C22⋊C4—1784no—
607C22⋊C4—1784no—
608C22⋊C4C22×Dic8918yes—
609C22⋊C4C22×Dic8918yes—
610C22⋊C4C22×Dic8918yes—
611C22⋊C4C22×Dic8918yes—
612C22⋊C4C22×Dic8918yes—
613C42—3564no—
614C42—3564no—
615C42—3564no—
616C42—1784no—
617C42—1784no—
618C42C22×Dic8914yes—
619C42C22×Dic8914yes—
620C42C22×Dic8914yes—
621C42C22×Dic8914yes—
622C42C22×Dic8918yes—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23C23×Dic8914yes—
634C23C23×Dic8912yes—
635C23#1566805812yes—
636C23#1566805912yes—
637C23C24×D8911yescharacteristic
638Q8—28no—
639D4—216no—
640D4—28no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—216no—
658C2×C4—28no—
659C2×C4—1782no—
660C2×C4—1782no—
661C2×C4—1782no—
662C2×C4—1784no—
663C2×C4—1784no—
664C2×C4—1784no—
665C2×C4—1782no—
666C2×C4—1784no—
667C2×C4—1784no—
668C2×C4—1782no—
669C2×C4—1784no—
670C2×C4—1782no—
671C2×C4—1782no—
672C2×C4—1782no—
673C2×C4—1782no—
674C2×C4—1782no—
675C2×C4—1782no—
676C2×C4—1782no—
677C2×C4—7128no—
678C2×C4—7128no—
679C2×C4C23×Dic8912yes—
680C2×C4C23×Dic8912yes—
681C2×C4C23×Dic8912yes—
682C2×C4C23×Dic8912yes—
683C2×C4C23×Dic8914yes—
684C2×C4C23×Dic8914yes—
685C2×C4C23×Dic8914yes—
686C2×C4C23×Dic8912yes—
687C2×C4C23×Dic8912yes—
688C2×C4#1566805812yes—
689C2×C4#1566805812yes—
690C2×C4#1566805912yes—
691C2×C4#1566805912yes—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22#1915208114yes—
706C22C24×Dic8911yescharacteristic
707C22C2×#1566805811yescharacteristic
708C22C2×#1566805811yescharacteristic
709C22C2×#1566805811yescharacteristic
710C22C2×#1566805911yescharacteristic
711C22C2×#1566805911yescharacteristic
712C22C2×#1566805911yescharacteristic
713C4—22no—
714C4—22no—
715C4—24no—
716C4—22no—
717C4—22no—
718C4—24no—
719C4—24no—
720C4—3562no—
721C4—3562no—
722C4—3564no—
723C4—3562no—
724C4—3564no—
725C4—3562no—
726C4#1915208114yes—
727C4#1915208114yes—
728C2—24no—
729C2—44no—
730C2C2×#1915208111yescharacteristic
731C2C2×#1915208111yescharacteristic
732C2C2×#1915208111yescharacteristic
733C2#2603458211yescharacteristic
734C2#2603459211yescharacteristic
735C2#2603468911yescharacteristic
736C2#2603469711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC2×#529×C89C2
socle, cosocleC23×C89C25
prime radicalC2×#121×C89C22
hypercenterC2×#529D89
hypocenterC89#34384
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #26023444C2semidirect
3. #26023261C2semidirect
4. #26023209C2semidirect
5. #26023201C2semidirect
6. #26023181C2semidirect
7. Q8×C4⋊Dic89C2semidirect
8. D4×C4⋊Dic89C2semidirect
9. D4×C4⋊Dic89C2semidirect
10. #26022994C2semidirect
11. #26022965C2semidirect
12. #26022924C2semidirect
13. #26022875C2semidirect
14. #26022861C2semidirect
15. C2×#19151468C2semidirect
16. #26022650C2semidirect
72. #529×C89C4semidirect
141. #126×C89C2×C4semidirect
142. #125×C89C2×C4semidirect
143. #124×C89C2×C4semidirect
144. #123×C89C2×C4semidirect
145. C22⋊Q8×C89C2×C4semidirect
147. C4×Q8×C89C2×C4semidirect
148. C4×D4×C89C2×C4semidirect
149. C4×D4×C89C2×C4semidirect
150. #117×C89C2×C4semidirect
162. C2×C42×C89C2×C4semidirect
386. C89#34384semidirect
387. #529Dic89semidirect
462. #126C2×Dic89semidirect
463. #125C2×Dic89semidirect
464. #124C2×Dic89semidirect
465. #123C2×Dic89semidirect
466. C22⋊Q8C2×Dic89semidirect
469. C4×Q8C2×Dic89semidirect
472. C4×D4C2×Dic89semidirect
473. C4×D4C2×Dic89semidirect
475. #117C2×Dic89semidirect
517. C2×C42C2×Dic89semidirect

Maximal subgroups

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

subgroupindex
#260234442
#260232722
#260232612
#260232092
#260232012
#260231812
Q8×C4⋊Dic892
D4×C4⋊Dic892
#260229942
#260229652
#260229242
#260228752
#260228612
C2×#191514682
#260226502
C2×#529×C892
#3438489