Finite Group Databasebeta

← #36716888

Subgroups — #36716888

Order 22784.

2772 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26023317C211yesmaximal, characteristic, complemented
2#26023317C212yesmaximal, complemented
3#26023304C214yesmaximal, complemented
4#26023294C212yesmaximal, complemented
5#26023225C212yesmaximal, complemented
6#26023209C211yesmaximal, characteristic, complemented
7#26023201C211yesmaximal, characteristic, complemented
8#26023082C212yesmaximal, complemented
9#26023019C214yesmaximal, complemented
10#26022978C212yesmaximal, complemented
11#127×Dic89C211yesmaximal, characteristic, complemented
12#121×Dic89C212yesmaximal, complemented
13#26022743C212yesmaximal, complemented
14#26022730C211yesmaximal, characteristic, complemented
15#26022613C212yesmaximal, complemented
16C4×D4×Dic89C211yesmaximal, characteristic, complemented
17C2×#550×C89C211yesmaximal, characteristic
18C2×D4×Dic89C2211yescharacteristic
19C2×D4×Dic89C2212yes—
20C2×D4×Dic89C2211yescharacteristic
21C2×D4×Dic89C2212yes—
22C2×D4×Dic89C2214yes—
23C2×D4×Dic89C2212yes—
24C2×D4×Dic89C2212yes—
25C2×D4×Dic89C2212yes—
26C2×#15667971C2212yes—
27C22×C4×Dic89C2212yes—
28#19151505C2212yes—
29#19151505C2211yescharacteristic
30#19151505C2211yescharacteristic
31#19151501C2212yes—
32#19151501C2212yes—
33#19151501C2212yes—
34#19151501C2212yes—
35#19151501C2212yes—
36#19151501C2212yes—
37#19151501C2214yes—
38#19151497C2211yescharacteristic
39#19151497C2211yescharacteristic
40#19151491C2214yes—
41#19151491C2214yes—
42#19151491C2214yes—
43#19151484C2214yes—
44#19151484C2212yes—
45#19151484C2212yes—
46#19151478C2214yes—
47#19151478C2214yes—
48#19151478C2214yes—
49#19151478C2214yes—
50#19151478C2214yes—
51#19151478C2214yes—
52#19151478C2214yes—
53#19151468C2211yescharacteristic
54#19151464C2212yes—
55#19151461C2214yes—
56#19151458C2212yes—
57C4⋊C4×Dic89C2212yes—
58C4⋊C4×Dic89C2212yes—
59C4⋊C4×Dic89C2211yescharacteristic
60C4⋊C4×Dic89C2211yescharacteristic
61C4×C4⋊Dic89C2211yescharacteristic
62C4×C4⋊Dic89C2211yescharacteristic
63C4×C4⋊Dic89C2212yes—
64C4×C4⋊Dic89C2212yes—
65C22⋊C4×Dic89C2212yes—
66C22⋊C4×Dic89C2214yes—
67C22⋊C4×Dic89C2214yes—
68C22⋊C4×Dic89C2212yes—
69C4×C22⋊Dic89C2214yes—
70C4×C22⋊Dic89C2214yes—
71C4×C22⋊Dic89C2212yes—
72#19151444C2212yes—
73C2×#15667919C2214yes—
74C42×Dic89C2211yescharacteristic
75C22×#41×C89C2212yes—
76#550×C89C4116yescomplemented
77C2×#127×C89C2212yes—
78C2×#127×C89C2211yescharacteristic
79C2×#121×C89C2214yes—
80C2×#121×C89C2212yes—
81C2×C4×Q8×C89C2211yescharacteristic
82C2×C4×D4×C89C2211yescharacteristic
83C2×C4×D4×C89C2212yes—
84C23×Dic89C2312yes—
85C23×Dic89C2314yes—
86C23×Dic89C2314yes—
87C23×Dic89C2312yes—
88D4×Dic89—24no—
89D4×Dic89—28no—
90D4×Dic89—24no—
91D4×Dic89—28no—
92D4×Dic89—44no—
93D4×Dic89—44no—
94D4×Dic89—44no—
95D4×Dic89—48no—
96#15667971—44no—
97C2×C4⋊Dic89C2311yescharacteristic
98C2×C4⋊Dic89C2312yes—
99C2×C4⋊Dic89C2311yescharacteristic
100C2×C4⋊Dic89C2312yes—
101C2×C4⋊Dic89C2311yescharacteristic
102C2×C4⋊Dic89C2312yes—
103C2×C4⋊Dic89C2312yes—
104C2×C4⋊Dic89C2312yes—
105C2×C4⋊Dic89C2311yescharacteristic
106C2×C22⋊Dic89C2312yes—
107C2×C22⋊Dic89C2314yes—
108C2×C22⋊Dic89C2314yes—
109C2×C22⋊Dic89C2312yes—
110C2×C22⋊Dic89C2314yes—
111C2×C22⋊Dic89C2314yes—
112C2×C22⋊Dic89C2314yes—
113C2×C22⋊Dic89C2314yes—
114C2×C22⋊Dic89C2314yes—
115C2×C22⋊Dic89C2314yes—
116C2×C4×Dic89—44no—
117C2×C4×Dic89C2311yescharacteristic
118C2×C4×Dic89C2311yescharacteristic
119C2×C4×Dic89C2311yescharacteristic
120C2×C4×Dic89C2311yescharacteristic
121C2×C4×Dic89C2312yes—
122C2×C4×Dic89C2312yes—
123C2×C4×Dic89C2311yescharacteristic
124C2×C4×Dic89C2312yes—
125C2×C4×Dic89C2312yes—
126C2×C4×Dic89C2314yes—
127C2×C4×Dic89C2314yes—
128C2×C4×Dic89C2311yescharacteristic
129#15667919C2312yes—
130#15667919C2312yes—
131#15667919C2314yes—
132#15667919C2314yes—
133#15667919C2312yes—
134#15667919C2312yes—
135#15667919C2312yes—
136#15667919C2312yes—
137#15667919C2312yes—
138#15667919C2314yes—
139#15667919C2312yes—
140#15667919C2312yes—
141#15667919C2312yes—
142#15667919C2314yes—
143C2×#41×C89—44no—
144C2×#41×C89—44no—
145C2×#41×C89C2×C4116yescomplemented
146C22×Q8×C89C2311yescharacteristic
147C22×D4×C89C2311yescharacteristic
148C22×D4×C89C2312yes—
149C22×D4×C89C2312yes—
150C22×D4×C89C2314yes—
151C22×D4×C89C2314yes—
152C22×D4×C89C2312yes—
153C23×C4×C89C2312yes—
154C23×C4×C89C2314yes—
155#127×C89C2×C418yescomplemented
156#127×C89C2×C4116yescomplemented
157#121×C89C2×C4116yescomplemented
158#121×C89C2×C4132yescomplemented
159C4×Q8×C89C2×C418yescomplemented
160C4×D4×C89C2×C418yescomplemented
161C4×D4×C89C2×C4116yescomplemented
162C2×C4⋊C4×C89C2311yescharacteristic
163C2×C4⋊C4×C89C2311yescharacteristic
164C2×C4⋊C4×C89C2312yes—
165C2×C22⋊C4×C89C2312yes—
166C2×C22⋊C4×C89C2314yes—
167C2×C42×C89C2311yescharacteristic
168C2×C42×C89C2312yes—
169C22×Dic89—24no—
170C22×Dic89—24no—
171C22×Dic89—24no—
172C22×Dic89—28no—
173C22×Dic89—28no—
174C22×Dic89—42no—
175C22×Dic89—42no—
176C22×Dic89—42no—
177C22×Dic89—44no—
178C22×Dic89—44no—
179C22×Dic89—44no—
180C22×Dic89—44no—
181C22×Dic89C2412yes—
182C22×Dic89C2412yes—
183C22×Dic89C2414yes—
184C22×Dic89C2411yescharacteristic
185C22×Dic89C2412yes—
186C22×Dic89C2411yescharacteristic
187C22×Dic89C2412yes—
188C22×Dic89C2411yescharacteristic
189C22×Dic89C2411yescharacteristic
190C4⋊Dic89—22no—
191C4⋊Dic89—24no—
192C4⋊Dic89—22no—
193C4⋊Dic89—24no—
194C4⋊Dic89—22no—
195C4⋊Dic89—24no—
196C4⋊Dic89—42no—
197C4⋊Dic89—42no—
198C4⋊Dic89#4114yescomplemented
199C22⋊Dic89—24no—
200C22⋊Dic89—28no—
201C22⋊Dic89—28no—
202C22⋊Dic89—24no—
203C22⋊Dic89—28no—
204C22⋊Dic89—44no—
205C22⋊Dic89—44no—
206C22⋊Dic89—44no—
207C22⋊Dic89—44no—
208C22⋊Dic89—44no—
209C4×Dic89—22no—
210C4×Dic89—24no—
211C4×Dic89—22no—
212C4×Dic89—24no—
213C4×Dic89—22no—
214C4×Dic89—22no—
215C4×Dic89—44no—
216C4×Dic89—44no—
217C4×Dic89—42no—
218C4×Dic89—42no—
219C4×Dic89—41no—
220C4×Dic89#4114yescomplemented
221C24×C89C2412yes—
222C24×C89C2414yes—
223#41×C89—432no—
224C2×Q8×C89—22no—
225C2×Q8×C89—22no—
226C2×Q8×C89C22×C414yes—
227C2×D4×C89—22no—
228C2×D4×C89—24no—
229C2×D4×C89—22no—
230C2×D4×C89—24no—
231C2×D4×C89—24no—
232C2×D4×C89—24no—
233C2×D4×C89—42no—
234C2×D4×C89—44no—
235C2×D4×C89—42no—
236C2×D4×C89—44no—
237C2×D4×C89—44no—
238C2×D4×C89—44no—
239C2×D4×C89C22×C414yes—
240C2×D4×C89C22×C418yes—
241C2×D4×C89C22×C418yes—
242C2×D4×C89C22×C4116yes—
243C2×D4×C89C22×C418yes—
244C2×D4×C89C22×C4116yes—
245C22×C4×C89—24no—
246C22×C4×C89—24no—
247C22×C4×C89—44no—
248C22×C4×C89—44no—
249C22×C4×C89C22×C418yes—
250C22×C4×C89C22×C4116yes—
251C22×C4×C89C2411yescharacteristic
252C22×C4×C89C2412yes—
253C22×C4×C89C2412yes—
254C22×C4×C89C2412yes—
255C22×C4×C89C2411yescharacteristic
256C22×C4×C89C2411yescharacteristic
257C4⋊C4×C89C22×C414yes—
258C4⋊C4×C89C22×C418yes—
259C4⋊C4×C89C22×C414yes—
260C22⋊C4×C89C22×C418yes—
261C22⋊C4×C89C22×C4116yes—
262C42×C89C22×C418yes—
263C42×C89C22×C414yes—
264C23×C89—22no—
265C23×C89—24no—
266C23×C89—22no—
267C23×C89—24no—
268C23×C89—22no—
269C23×C89—22no—
270C23×C89—24no—
271C23×C89—24no—
272C23×C89—24no—
273C23×C89—22no—
274C23×C89—24no—
275C23×C89—22no—
276C23×C89C23×C414yes—
277C23×C89C23×C418yes—
278C23×C89C2511yescharacteristic
279Q8×C89—28no—
280D4×C89—28no—
281D4×C89—216no—
282D4×C89—216no—
283D4×C89—48no—
284D4×C89—416no—
285D4×C89—416no—
286C2×C4×C89—22no—
287C2×C4×C89—22no—
288C2×C4×C89—22no—
289C2×C4×C89—22no—
290C2×C4×C89—21no—
291C2×C4×C89—22no—
292C2×C4×C89—21no—
293C2×C4×C89—22no—
294C2×C4×C89—216no—
295C2×C4×C89—416no—
296C2×C4×C89C23×C412yes—
297C2×C4×C89C23×C414yes—
298C2×C4×C89C23×C414yes—
299C2×C4×C89C23×C414yes—
300C2×C4×C89C23×C412yes—
301C2×C4×C89C23×C412yes—
302C2×C4×C89C2×#4112yes—
303C2×C4×C89C2×#4112yes—
304C2×C4×C89H(5,𝔽2)12yes—
305C2×C4×C89H(5,𝔽2)12yes—
306C2×Dic89—21no—
307C2×Dic89—21no—
308C2×Dic89—21no—
309C2×Dic89—22no—
310C2×Dic89—21no—
311C2×Dic89—21no—
312C2×Dic89—22no—
313C2×Dic89—21no—
314C2×Dic89—21no—
315C2×Dic89—22no—
316C2×Dic89—22no—
317C2×Dic89—22no—
318C2×Dic89—24no—
319C2×Dic89—22no—
320C2×Dic89—21no—
321C2×Dic89—22no—
322C2×Dic89—24no—
323C2×Dic89—24no—
324C2×Dic89—22no—
325C2×Dic89—22no—
326C2×Dic89—21no—
327C2×Dic89—22no—
328C2×Dic89—22no—
329C2×Dic89—48no—
330C2×Dic89—48no—
331C2×Dic89—88no—
332C2×Dic89—88no—
333C2×Dic89C2×#4112yes—
334C2×Dic89C2×#4112yes—
335C2×Dic89C2×#4114yes—
336C2×Dic89H(5,𝔽2)12yes—
337C22×C89—24no—
338C22×C89—28no—
339C22×C89—24no—
340C22×C89—28no—
341C22×C89—28no—
342C22×C89—24no—
343C22×C89—42no—
344C22×C89—44no—
345C22×C89—44no—
346C22×C89—42no—
347C22×C89—42no—
348C22×C89—44no—
349C22×C89—42no—
350C22×C89—44no—
351C22×C89C24×C411yescharacteristic
352C22×C89C22×#4111yescharacteristic
353C22×C89C22×#4111yescharacteristic
354C22×C89C2×H(5,𝔽2)11yescharacteristic
355C22×C89C2×H(5,𝔽2)11yescharacteristic
356C22×C89C2×H(5,𝔽2)11yescharacteristic
357C22×C89#58511yescharacteristic
358C4×C89—24no—
359C4×C89—24no—
360C4×C89—22no—
361C4×C89—24no—
362C4×C89C4×#4114yes—
363C4×C89#51814yes—
364Dic89—22no—
365Dic89—22no—
366Dic89—22no—
367Dic89—24no—
368Dic89—42no—
369Dic89—44no—
370Dic89—41no—
371Dic89—42no—
372Dic89—42no—
373#34330—891nomaximal, Sylow
374C2×C89—44no—
375C2×C89—48no—
376C2×C89C2×C4×#4111yescharacteristic
377C2×C89C2×#51811yescharacteristic
378C2×C89C4×H(5,𝔽2)11yescharacteristic
379C2×C89#350611yescharacteristic
380C2×C89#350811yescharacteristic
381C2×C89#351711yescharacteristic
382C2×C89#351911yescharacteristic
383C2×#550D8911yescharacteristic
384#2366—891no—
385#2366—892no—
386#2364—894no—
387#2363—892no—
388#2357—892no—
389#2355—891no—
390#2354—891no—
391#2339—892no—
392#2333—894no—
393#2328—892no—
394C4×#127—891no—
395C4×#121—892no—
396#2297—892no—
397#2295—891no—
398#2275—892no—
399C42×D4—891no—
400C89#3433011yescharacteristic, complemented, Sylow
401C22×#41C2×D8912yes—
402#550Dic89116yescomplemented
403C2×#127C2×D8911yescharacteristic
404C2×#127C2×D8912yes—
405C2×#121C2×D8914yes—
406C2×#121C2×D8912yes—
407C2×C4×Q8C2×D8911yescharacteristic
408C2×C4×D4—892no—
409C2×C4×D4—892no—
410C2×C4×D4—892no—
411C2×C4×D4—894no—
412C2×C4×D4—892no—
413C2×C4×D4—891no—
414C2×C4×D4—891no—
415C2×C4×D4—892no—
416C2×C4×D4C2×D8911yescharacteristic
417C2×C4×D4C2×D8912yes—
418C2×#117—892no—
419C22×C42—892no—
420#391—891no—
421#391—892no—
422#391—891no—
423#390—892no—
424#390—892no—
425#390—892no—
426#390—892no—
427#390—892no—
428#390—894no—
429#390—892no—
430#389—891no—
431#389—891no—
432#388—894no—
433#388—894no—
434#388—894no—
435#387—892no—
436#387—894no—
437#387—892no—
438#386—894no—
439#386—894no—
440#386—894no—
441#386—894no—
442#386—894no—
443#386—894no—
444#386—894no—
445#384—891no—
446#382—892no—
447#381—894no—
448#380—892no—
449C4×C4⋊C4—892no—
450C4×C4⋊C4—892no—
451C4×C4⋊C4—891no—
452C4×C4⋊C4—891no—
453C4×C4⋊C4—891no—
454C4×C4⋊C4—891no—
455C4×C4⋊C4—892no—
456C4×C4⋊C4—892no—
457C4×C22⋊C4—894no—
458C4×C22⋊C4—892no—
459C4×C22⋊C4—894no—
460C4×C22⋊C4—892no—
461C4×C22⋊C4—894no—
462C4×C22⋊C4—894no—
463C4×C22⋊C4—892no—
464#376—892no—
465C2×#95—894no—
466C43—891no—
467C2×#41—44no—
468C2×#41—44no—
469C2×#41C2×Dic89116yescomplemented
470C22×Q8C22×D8911yescharacteristic
471C22×D4C22×D8912yes—
472C22×D4C22×D8911yescharacteristic
473C22×D4C22×D8912yes—
474C22×D4C22×D8912yes—
475C22×D4C22×D8914yes—
476C22×D4C22×D8914yes—
477C23×C4—894no—
478C23×C4—894no—
479C23×C4—892no—
480C23×C4—892no—
481C23×C4C22×D8912yes—
482C23×C4C22×D8914yes—
483#127C2×Dic8918yescomplemented
484#127C2×Dic89116yescomplemented
485#121C2×Dic89116yescomplemented
486#121C2×Dic89132yescomplemented
487C4×Q8C2×Dic8918yescomplemented
488C4×D4—3568no—
489C4×D4—3564no—
490C4×D4—3564no—
491C4×D4—3564no—
492C4×D4—1784no—
493C4×D4—1788no—
494C4×D4—1784no—
495C4×D4—1788no—
496C4×D4C2×Dic8918yescomplemented
497C4×D4C2×Dic89116yescomplemented
498#117—3564no—
499C2×C4⋊C4—891no—
500C2×C4⋊C4—892no—
501C2×C4⋊C4—892no—
502C2×C4⋊C4—891no—
503C2×C4⋊C4—892no—
504C2×C4⋊C4—891no—
505C2×C4⋊C4—892no—
506C2×C4⋊C4—891no—
507C2×C4⋊C4—892no—
508C2×C4⋊C4C22×D8911yescharacteristic
509C2×C4⋊C4C22×D8911yescharacteristic
510C2×C4⋊C4C22×D8912yes—
511C2×C22⋊C4—894no—
512C2×C22⋊C4—894no—
513C2×C22⋊C4—894no—
514C2×C22⋊C4—894no—
515C2×C22⋊C4—894no—
516C2×C22⋊C4—894no—
517C2×C22⋊C4—892no—
518C2×C22⋊C4—894no—
519C2×C22⋊C4—892no—
520C2×C22⋊C4—894no—
521C2×C22⋊C4C22×D8912yes—
522C2×C22⋊C4C22×D8914yes—
523C2×C42—891no—
524C2×C42—894no—
525C2×C42—894no—
526C2×C42—891no—
527C2×C42—892no—
528C2×C42—892no—
529C2×C42—891no—
530C2×C42—891no—
531C2×C42—891no—
532C2×C42—892no—
533C2×C42—892no—
534C2×C42—891no—
535C2×C42—3564no—
536C2×C42C22×D8911yescharacteristic
537C2×C42C22×D8912yes—
538#95—892no—
539#95—892no—
540#95—894no—
541#95—894no—
542#95—892no—
543#95—892no—
544#95—892no—
545#95—892no—
546#95—892no—
547#95—892no—
548#95—894no—
549#95—892no—
550#95—894no—
551#95—892no—
552C24C23×D8912yes—
553C24C23×D8914yes—
554#41—432no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8C22×Dic8914yes—
558C2×D4—22no—
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C22×Dic8914yes—
571C2×D4C22×Dic8918yes—
572C2×D4C22×Dic8918yes—
573C2×D4C22×Dic89116yes—
574C2×D4C22×Dic8918yes—
575C2×D4C22×Dic89116yes—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—891no—
581C22×C4—891no—
582C22×C4—892no—
583C22×C4—891no—
584C22×C4—892no—
585C22×C4—892no—
586C22×C4—892no—
587C22×C4—891no—
588C22×C4—894no—
589C22×C4—3562no—
590C22×C4—3562no—
591C22×C4—3562no—
592C22×C4—3564no—
593C22×C4—3564no—
594C22×C4—3564no—
595C22×C4—3564no—
596C22×C4—1784no—
597C22×C4—1784no—
598C22×C4—1784no—
599C22×C4—1788no—
600C22×C4—1788no—
601C22×C4C22×Dic8918yes—
602C22×C4C22×Dic89116yes—
603C22×C4C23×D8912yes—
604C22×C4C23×D8912yes—
605C22×C4C23×D8912yes—
606C22×C4C23×D8911yescharacteristic
607C22×C4C23×D8911yescharacteristic
608C22×C4C23×D8911yescharacteristic
609C4⋊C4—894no—
610C4⋊C4—3562no—
611C4⋊C4—3562no—
612C4⋊C4—1784no—
613C4⋊C4—1782no—
614C4⋊C4—1784no—
615C4⋊C4—1782no—
616C4⋊C4—1784no—
617C4⋊C4—1782no—
618C4⋊C4C22×Dic8914yes—
619C4⋊C4C22×Dic8918yes—
620C4⋊C4C22×Dic8914yes—
621C22⋊C4—3564no—
622C22⋊C4—3564no—
623C22⋊C4—3564no—
624C22⋊C4—3564no—
625C22⋊C4—3564no—
626C22⋊C4—1788no—
627C22⋊C4—1788no—
628C22⋊C4—1784no—
629C22⋊C4—1784no—
630C22⋊C4—1788no—
631C22⋊C4C22×Dic8918yes—
632C22⋊C4C22×Dic89116yes—
633C42—894no—
634C42—3562no—
635C42—3562no—
636C42—3564no—
637C42—3564no—
638C42—3561no—
639C42—1782no—
640C42—1784no—
641C42—1782no—
642C42—1782no—
643C42—1784no—
644C42—1782no—
645C42C22×Dic8918yes—
646C42C22×Dic8914yes—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23C23×Dic8914yes—
660C23C23×Dic8918yes—
661C23C24×D8911yescharacteristic
662Q8—28no—
663D4—28no—
664D4—216no—
665D4—216no—
666D4—416no—
667D4—48no—
668D4—416no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—216no—
678C2×C4—416no—
679C2×C4—892no—
680C2×C4—892no—
681C2×C4—894no—
682C2×C4—892no—
683C2×C4—3568no—
684C2×C4—3568no—
685C2×C4—1782no—
686C2×C4—1781no—
687C2×C4—1782no—
688C2×C4—1782no—
689C2×C4—1784no—
690C2×C4—1784no—
691C2×C4—1782no—
692C2×C4—1782no—
693C2×C4—1782no—
694C2×C4—1784no—
695C2×C4—1781no—
696C2×C4—1782no—
697C2×C4—1781no—
698C2×C4—1782no—
699C2×C4—1782no—
700C2×C4—1781no—
701C2×C4—1782no—
702C2×C4—1781no—
703C2×C4—1781no—
704C2×C4—1781no—
705C2×C4—1782no—
706C2×C4—1781no—
707C2×C4—1781no—
708C2×C4—7128no—
709C2×C4—7128no—
710C2×C4C23×Dic8914yes—
711C2×C4C23×Dic8912yes—
712C2×C4C23×Dic8914yes—
713C2×C4C23×Dic8914yes—
714C2×C4C23×Dic8912yes—
715C2×C4C23×Dic8912yes—
716C2×C4#41×D8912yes—
717C2×C4#41×D8912yes—
718C2×C4#1566805712yes—
719C2×C4#1566805712yes—
720C22—24no—
721C22—28no—
722C22—24no—
723C22—28no—
724C22—24no—
725C22—28no—
726C22—42no—
727C22—44no—
728C22—42no—
729C22—44no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—42no—
734C22C24×Dic8911yescharacteristic
735C22C2×#41×D8911yescharacteristic
736C22C2×#41×D8911yescharacteristic
737C22H(5,𝔽2)×D8911yescharacteristic
738C22C2×#1566805711yescharacteristic
739C22C2×#1566805711yescharacteristic
740C22#1915243311yescharacteristic
741C4—24no—
742C4—24no—
743C4—24no—
744C4—22no—
745C4—3562no—
746C4—3561no—
747C4—3562no—
748C4—3562no—
749C4—3564no—
750C4—1782no—
751C4—1784no—
752C4—1782no—
753C4—1782no—
754C4#41×Dic8914yes—
755C4#1915207314yes—
756C2—44no—
757C2—48no—
758C2C2×#41×Dic8911yescharacteristic
759C2C2×#1915207311yescharacteristic
760C2H(5,𝔽2)×Dic8911yescharacteristic
761C2#2603409611yescharacteristic
762C2#2603412211yescharacteristic
763C2#2603425511yescharacteristic
764C2#2603428311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
Fitting, prime radicalC2×#550×C89C2
socle, cosocleC23×C89C25
hypercenterC2×#550D89
hypocenterC89#34330
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #26023317C2semidirect
2. #26023317C2semidirect
3. #26023304C2semidirect
4. #26023294C2semidirect
5. #26023225C2semidirect
6. #26023209C2semidirect
7. #26023201C2semidirect
8. #26023082C2semidirect
9. #26023019C2semidirect
10. #26022978C2semidirect
11. #127×Dic89C2semidirect
12. #121×Dic89C2semidirect
13. #26022743C2semidirect
14. #26022730C2semidirect
15. #26022613C2semidirect
16. C4×D4×Dic89C2semidirect
76. #550×C89C4semidirect
145. C2×#41×C89C2×C4semidirect
155. #127×C89C2×C4semidirect
156. #127×C89C2×C4semidirect
157. #121×C89C2×C4semidirect
158. #121×C89C2×C4semidirect
159. C4×Q8×C89C2×C4semidirect
160. C4×D4×C89C2×C4semidirect
161. C4×D4×C89C2×C4semidirect
198. C4⋊Dic89#41semidirect
220. C4×Dic89#41semidirect
400. C89#34330semidirect
402. #550Dic89semidirect
469. C2×#41C2×Dic89semidirect
483. #127C2×Dic89semidirect
484. #127C2×Dic89semidirect
485. #121C2×Dic89semidirect
486. #121C2×Dic89semidirect
487. C4×Q8C2×Dic89semidirect
496. C4×D4C2×Dic89semidirect
497. C4×D4C2×Dic89semidirect

Maximal subgroups

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

subgroupindex
#260233172
#260233042
#260232942
#260232252
#260232092
#260232012
#260230822
#260230192
#260229782
#127×Dic892
#121×Dic892
#260227432
#260227302
#260226132
C4×D4×Dic892
C2×#550×C892
#3433089