Finite Group Databasebeta

← #36714607

Subgroups — #36714607

Order 22784.

2470 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#13083574C211yesmaximal, characteristic
2#26023204C212yesmaximal, complemented
3#26023178C212yesmaximal, complemented
4#26023177C212yesmaximal, complemented
5C4⋊C4×C22⋊D89C212yesmaximal, complemented
6#26023132C212yesmaximal, complemented
7#26023108C212yesmaximal, complemented
8#26023105C212yesmaximal, complemented
9#26023079C212yesmaximal
10#26022900C212yesmaximal, complemented
11#26022888C212yesmaximal, complemented
12#26022886C212yesmaximal, complemented
13#26022658C211yesmaximal, characteristic, complemented
14#26022650C211yesmaximal, characteristic, complemented
15#26022645C211yesmaximal, characteristic, complemented
16#26022645C211yesmaximal, characteristic, complemented
17#382×D89C211yesmaximal, characteristic, complemented
18#26022610C212yesmaximal, complemented
19C2×#382×C89C211yesmaximal, characteristic, complemented
20C22×#13083574C2211yescharacteristic
21C4×#13083574C4116yescomplemented
22C2×C4×Dic178C2211yescharacteristic
23C2×C4×Dic178C2211yescharacteristic
24C2×C4×D356C2211yescharacteristic
25C2×C4×D356C2211yescharacteristic
26C2×C4×C22⋊D89C2214yes—
27C2×C4×C22⋊D89C2211yescharacteristic
28C2×C4×C22⋊D89C2211yescharacteristic
29C2×C4×C22⋊D89C2211yescharacteristic
30C2×C4×C22⋊D89C2211yescharacteristic
31C2×#15667971C2211yescharacteristic
32C2×#15667970C2212yes—
33C2×#15667969C2211yescharacteristic
34C2×#15667969C2211yescharacteristic
35C2×C4⋊C4×D89C2212yes—
36C2×C42×D89C2211yescharacteristic
37C2×C42×D89C2211yescharacteristic
38#19151502C2214yes—
39#19151493C2214yes—
40#19151488C2214yes—
41#19151487C2214yes—
42#19151483C2214yes—
43#19151481C2214yes—
44#19151480C2214yes—
45#19151479C2214yes—
46#19151477C2214yes—
47#19151476C2214yes—
48#19151471C2214yes—
49#19151469C2214yes—
50#19151467C2212yes—
51#19151466C2212yes—
52#19151465C2212yes—
53#19151465C2212yes—
54#19151464C2211yescharacteristic
55#19151464C2211yescharacteristic
56#19151463C2212yes—
57#19151462C2212yes—
58#19151462C2212yes—
59#19151461C2212yes—
60#19151460C2212yes—
61#19151460C2212yes—
62#19151458C2212yes—
63#19151457C2212yes—
64#19151457C2212yes—
65#19151455C2212yes—
66#19151455C2212yes—
67C4⋊C4×Dic89C2212yes—
68C4⋊C4×Dic89C2212yes—
69C4×C4⋊Dic89C2212yes—
70#19151449C2212yes—
71#19151449C2212yes—
72#19151449C2214yes—
73C4×C22⋊Dic89C2214yes—
74C4×C22⋊Dic89C2212yes—
75#19151445C2214yes—
76#19151445C2212yes—
77#19151445C2212yes—
78#19151444C2212yes—
79#19151443C2212yes—
80#19151443C2212yes—
81#95×D89C2212yes—
82#95×D89C2212yes—
83C22×C4⋊C4×C89C2212yes—
84C22×C42×C89C2211yescharacteristic
85#382×C89C2211yescharacteristic
86#382×C89C2212yes—
87#382×C89C2212yes—
88#382×C89C2212yes—
89#382×C89C2211yescharacteristic
90C2×#95×C89C2212yes—
91C2×#95×C89C2212yes—
92C2×#13083574—28no—
93C2×#13083574C2×C418yes—
94C22×Dic178C2311yescharacteristic
95C22×D356C2311yescharacteristic
96C22×C22⋊D89C2311yescharacteristic
97C22×C22⋊D89C2311yescharacteristic
98C22×C4×D89C2311yescharacteristic
99C22×C4×D89C2311yescharacteristic
100C22×C4×D89C2311yescharacteristic
101C22×C4×D89C2311yescharacteristic
102C22×C4×D89C2314yes—
103C22×C4×D89C2311yescharacteristic
104C22×C4×D89C2311yescharacteristic
105C4×Dic178C2×C418yescomplemented
106C4×Dic178C2×C418yescomplemented
107C4×D356C2×C418yescomplemented
108C4×D356C2×C418yescomplemented
109C4×C22⋊D89—216no—
110C4×C22⋊D89C2×C418yes—
111C4×C22⋊D89C2×C418yes—
112C4×C22⋊D89C2×C418yescomplemented
113C4×C22⋊D89C2×C418yescomplemented
114#15667971C2×C418yescomplemented
115#15667970—44no—
116#15667969C2×C418yescomplemented
117#15667969C2×C418yescomplemented
118C2×C4⋊Dic89C2312yes—
119C2×C4⋊Dic89C2312yes—
120C2×C4⋊Dic89C2311yescharacteristic
121C2×C4⋊Dic89C2311yescharacteristic
122C2×#13083553C2314yes—
123C2×#13083553C2314yes—
124C2×#13083553C2314yes—
125C2×#13083553C2311yescharacteristic
126C2×#13083553C2311yescharacteristic
127C2×#13083553C2311yescharacteristic
128C2×#13083553C2311yescharacteristic
129C4⋊C4×D89—44no—
130C2×C22⋊Dic89C2314yes—
131C2×C22⋊Dic89C2311yescharacteristic
132C2×C22⋊Dic89C2311yescharacteristic
133C2×#13083551C2314yes—
134C2×#13083551C2314yes—
135C2×#13083551C2314yes—
136C2×#13083551C2311yescharacteristic
137C2×#13083551C2311yescharacteristic
138C2×#13083551C2311yescharacteristic
139C2×#13083551C2311yescharacteristic
140C2×C4×Dic89C2314yes—
141C2×C4×Dic89C2314yes—
142C2×C4×Dic89C2314yes—
143C2×C4×Dic89C2314yes—
144C2×C4×Dic89C2311yescharacteristic
145C2×C4×Dic89C2311yescharacteristic
146C2×C4×Dic89C2311yescharacteristic
147C2×C4×Dic89C2311yescharacteristic
148C2×C4×Dic89C2311yescharacteristic
149C2×C4×Dic89C2311yescharacteristic
150C42×D89C2×C418yescomplemented
151C42×D89C2×C418yescomplemented
152#15667919C2312yes—
153#15667919C2312yes—
154#15667919C2314yes—
155#15667919C2314yes—
156#15667919C2312yes—
157#15667919C2314yes—
158#15667919C2312yes—
159#15667919C2314yes—
160#15667919C2314yes—
161#15667919C2314yes—
162#15667919C2314yes—
163#15667919C2314yes—
164C23×C4×C89C2311yescharacteristic
165C23×C4×C89C2311yescharacteristic
166C23×C4×C89C2314yes—
167C23×C4×C89C2311yescharacteristic
168C2×C4⋊C4×C89—44no—
169C2×C4⋊C4×C89C2312yes—
170C2×C4⋊C4×C89C2312yes—
171C2×C4⋊C4×C89C2314yes—
172C2×C42×C89C2×C418yescomplemented
173C2×C42×C89C2311yescharacteristic
174C2×C42×C89C2311yescharacteristic
175C2×C42×C89C2311yescharacteristic
176C2×C42×C89C2311yescharacteristic
177#95×C89C2312yes—
178#95×C89C2312yes—
179#95×C89C2312yes—
180#95×C89C2312yes—
181#95×C89C2314yes—
182#95×C89C2314yes—
183C23×D89C2411yescharacteristic
184C23×D89C2411yescharacteristic
185#13083574—232no—
186C2×Dic178—24no—
187C2×Dic178C22×C414yes—
188C2×D356—24no—
189C2×D356C22×C414yes—
190C2×C22⋊D89—24no—
191C2×C22⋊D89C22×C414yes—
192C2×C22⋊D89C22×C414yes—
193C2×C22⋊D89#4118yes—
194C22×Dic89C2414yes—
195C22×Dic89C2414yes—
196C22×Dic89C2411yescharacteristic
197C22×Dic89C2411yescharacteristic
198C22×Dic89C2411yescharacteristic
199C22×Dic89C2411yescharacteristic
200C22×Dic89C2411yescharacteristic
201C22×Dic89C2411yescharacteristic
202C2×C4×D89—24no—
203C2×C4×D89—22no—
204C2×C4×D89—22no—
205C2×C4×D89—22no—
206C2×C4×D89—22no—
207C2×C4×D89—24no—
208C2×C4×D89—28no—
209C2×C4×D89—42no—
210C2×C4×D89—42no—
211C2×C4×D89—44no—
212C2×C4×D89—44no—
213C2×C4×D89C22×C414yes—
214C2×C4×D89C22×C414yes—
215C2×C4×D89C22×C414yes—
216C2×C4×D89C22×C414yes—
217C2×C4×D89C22×C414yes—
218C2×C4×D89C22×C414yes—
219C4⋊Dic89—24no—
220C4⋊Dic89—24no—
221C4⋊Dic89C22×C414yes—
222C4⋊Dic89C22×C414yes—
223#13083553—28no—
224#13083553—44no—
225#13083553—44no—
226#13083553C22×C414yes—
227#13083553C22×C414yes—
228#13083553C22×C414yes—
229#13083553C22×C414yes—
230C22⋊Dic89—28no—
231C22⋊Dic89C22×C414yes—
232C22⋊Dic89C22×C414yes—
233#13083551—28no—
234#13083551—44no—
235#13083551—44no—
236#13083551C22×C414yes—
237#13083551C22×C414yes—
238#13083551C22×C414yes—
239#13083551C22×C414yes—
240C4×Dic89—28no—
241C4×Dic89—44no—
242C4×Dic89—44no—
243C4×Dic89—44no—
244C4×Dic89C22×C414yes—
245C4×Dic89C22×C414yes—
246C4×Dic89C22×C414yes—
247C4×Dic89C22×C414yes—
248C4×Dic89C22×C414yes—
249C4×Dic89C22×C414yes—
250C24×C89C2411yescharacteristic
251C22×C4×C89—24no—
252C22×C4×C89—22no—
253C22×C4×C89—22no—
254C22×C4×C89—28no—
255C22×C4×C89—42no—
256C22×C4×C89—44no—
257C22×C4×C89—44no—
258C22×C4×C89C22×C414yes—
259C22×C4×C89C22×C414yes—
260C22×C4×C89C22×C414yes—
261C22×C4×C89C2414yes—
262C22×C4×C89C2414yes—
263C22×C4×C89C2411yescharacteristic
264C22×C4×C89C2411yescharacteristic
265C22×C4×C89C2411yescharacteristic
266C22×C4×C89C2411yescharacteristic
267C22×C4×C89C2411yescharacteristic
268C22×C4×C89C2411yescharacteristic
269C4⋊C4×C89—24no—
270C4⋊C4×C89—24no—
271C4⋊C4×C89—44no—
272C42×C89C22×C414yes—
273C42×C89C22×C414yes—
274C42×C89C22×C414yes—
275C42×C89C22×C414yes—
276C23×C89—21no—
277C23×C89—21no—
278C23×C89—22no—
279C23×C89C23×C412yes—
280C23×C89C2×#4114yes—
281C23×C89C2511yescharacteristic
282C22×D89—21no—
283C22×D89—21no—
284C22×D89—22no—
285C22×D89—22no—
286C22×D89—21no—
287C22×D89—21no—
288C22×D89—22no—
289C22×D89C23×C412yes—
290C22×D89C23×C412yes—
291C22×D89C2×#4114yes—
292C2×C4×C89—28no—
293C2×C4×C89—22no—
294C2×C4×C89—22no—
295C2×C4×C89—21no—
296C2×C4×C89—21no—
297C2×C4×C89—22no—
298C2×C4×C89—22no—
299C2×C4×C89—28no—
300C2×C4×C89—24no—
301C2×C4×C89—24no—
302C2×C4×C89—24no—
303C2×C4×C89—24no—
304C2×C4×C89—24no—
305C2×C4×C89—24no—
306C2×C4×C89—44no—
307C2×C4×C89—88no—
308C2×C4×C89C23×C412yes—
309C2×C4×C89C23×C412yes—
310C2×C4×C89C23×C412yes—
311C2×C4×C89C23×C412yes—
312C2×C4×C89C23×C412yes—
313C2×C4×C89C23×C412yes—
314C2×C4×C89H(5,𝔽2)12yes—
315C2×C4×C892−1+412yes—
316C22⋊D89—28no—
317C22⋊D89#117116yescomplemented
318C2×Dic89—22no—
319C2×Dic89—21no—
320C2×Dic89—21no—
321C2×Dic89—21no—
322C2×Dic89—21no—
323C2×Dic89—22no—
324C2×Dic89—22no—
325C2×Dic89—24no—
326C2×Dic89—24no—
327C2×Dic89—24no—
328C2×Dic89—24no—
329C2×Dic89—24no—
330C2×Dic89—24no—
331C2×Dic89C23×C412yes—
332C2×Dic89C23×C412yes—
333C2×Dic89C23×C412yes—
334C2×Dic89C23×C412yes—
335C2×Dic89C23×C412yes—
336C2×Dic89C23×C412yes—
337C2×Dic89C2×#4114yes—
338D356—28no—
339C4×D89—28no—
340C4×D89—28no—
341C4×D89—28no—
342C4×D89—28no—
343C4×D89—44no—
344C4×D89—44no—
345C4×D89—88no—
346Dic178—28no—
347C22×C89—22no—
348C22×C89—22no—
349C22×C89—24no—
350C22×C89—24no—
351C22×C89C2×#11714yes—
352C22×C89C24×C411yescharacteristic
353C22×C89C22×#4112yes—
354C22×C89C2×H(5,𝔽2)11yescharacteristic
355C22×C89C2×2−1+411yescharacteristic
356C22×C89#58512yes—
357C2×D89—22no—
358C2×D89—22no—
359C2×D89—24no—
360C2×D89—24no—
361C2×D89—22no—
362C2×D89—22no—
363C2×D89—22no—
364C2×D89—42no—
365C2×D89—42no—
366C2×D89C2×#11714yes—
367C4×C89—22no—
368C4×C89—22no—
369C4×C89—22no—
370C4×C89—22no—
371C4×C89—22no—
372C4×C89—44no—
373C4×C89—44no—
374C4×C89#52014yes—
375Dic89—22no—
376Dic89—22no—
377Dic89—22no—
378Dic89—22no—
379Dic89—22no—
380Dic89—44no—
381Dic89—44no—
382Dic89C2×#11714yes—
383#34191—891nomaximal, Sylow
384C2×C89—24no—
385C2×C89C22×#11711yescharacteristic
386C2×C89C2×#52011yescharacteristic
387C2×C89#342811yescharacteristic
388C2×C89#351412yes—
389C2×C89#351512yes—
390D89—24no—
391D89—42no—
392C2×C4×#41—891no—
393#2355—892no—
394#2352—892no—
395#2352—892no—
396D4×C4⋊C4—892no—
397#2346—892no—
398#2343—892no—
399#2343—892no—
400#2339—892no—
401#2320—892no—
402#2318—892no—
403#2318—892no—
404#2285—891no—
405#2283—891no—
406#2283—891no—
407#2283—891no—
408C2×#382—891no—
409C2×#382D8911yescharacteristic, complemented
410#2275—892no—
411C89#3419111yescharacteristic, complemented, Sylow
412C22×#41—891no—
413C4×#41—8916no—
414C2×C4×Q8—891no—
415C2×C4×Q8—891no—
416C2×C4×D4—891no—
417C2×C4×D4—891no—
418C2×C4×D4—891no—
419C2×C4×D4—891no—
420C2×C4×D4—894no—
421C2×C4×D4—891no—
422C2×C4×D4—891no—
423C2×#117—891no—
424C2×#117—892no—
425C2×#117—891no—
426C2×#117—891no—
427C22×C4⋊C4—892no—
428C22×C4⋊C4C2×D8912yes—
429C22×C42—891no—
430C22×C42—891no—
431C22×C42C2×D8911yescharacteristic
432#391—894no—
433#389—894no—
434#388—894no—
435#388—894no—
436#387—894no—
437#387—894no—
438#387—894no—
439#387—894no—
440#386—894no—
441#386—894no—
442#385—894no—
443#385—894no—
444#384—892no—
445#383—892no—
446#383—892no—
447#383—892no—
448#382—892no—
449#382—891no—
450#382—891no—
451#382—892no—
452#382—892no—
453#382C2×D8912yes—
454#382C2×D8912yes—
455#382C2×D8912yes—
456#382C2×D8911yescharacteristic
457#382C2×D8911yescharacteristic
458#381—892no—
459#381—892no—
460#381—892no—
461#380—892no—
462#380—892no—
463#380—892no—
464#380—892no—
465#380—892no—
466C4×C4⋊C4—892no—
467C4×C4⋊C4—892no—
468C4×C4⋊C4—892no—
469C4×C4⋊C4—892no—
470C4×C4⋊C4—892no—
471C4×C4⋊C4—894no—
472C4×C22⋊C4—892no—
473C4×C22⋊C4—894no—
474C4×C22⋊C4—892no—
475C4×C22⋊C4—892no—
476C4×C22⋊C4—894no—
477#376—892no—
478#376—892no—
479#376—892no—
480C2×#95—892no—
481C2×#95—892no—
482C2×#95C2×D8912yes—
483C2×#95C2×D8912yes—
484C2×#41—898no—
485C2×#41—1788no—
486C22×Q8—891no—
487C22×D4—891no—
488C22×D4—891no—
489C22×D4—891no—
490C23×C4—891no—
491C23×C4—891no—
492C23×C4—891no—
493C23×C4—891no—
494C23×C4—891no—
495C23×C4—891no—
496C23×C4—894no—
497C23×C4C22×D8911yescharacteristic
498C23×C4C22×D8911yescharacteristic
499C23×C4C22×D8914yes—
500C23×C4C22×D8911yescharacteristic
501C4×Q8—898no—
502C4×Q8—898no—
503C4×D4—898no—
504C4×D4—898no—
505C4×D4—898no—
506C4×D4—898no—
507C4×D4—898no—
508C4×D4—898no—
509C4×D4—17816no—
510#117—898no—
511#117—898no—
512#117—898no—
513#117—3564no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4—891no—
516C2×C4⋊C4—891no—
517C2×C4⋊C4—891no—
518C2×C4⋊C4—891no—
519C2×C4⋊C4—891no—
520C2×C4⋊C4—891no—
521C2×C4⋊C4—894no—
522C2×C4⋊C4—894no—
523C2×C4⋊C4—892no—
524C2×C4⋊C4—894no—
525C2×C4⋊C4—892no—
526C2×C4⋊C4—3564no—
527C2×C4⋊C4C22×D8912yes—
528C2×C4⋊C4C22×D8912yes—
529C2×C4⋊C4C22×D8914yes—
530C2×C22⋊C4—891no—
531C2×C22⋊C4—891no—
532C2×C22⋊C4—891no—
533C2×C22⋊C4—891no—
534C2×C22⋊C4—891no—
535C2×C22⋊C4—891no—
536C2×C22⋊C4—894no—
537C2×C22⋊C4—894no—
538C2×C22⋊C4—894no—
539C2×C22⋊C4—894no—
540C2×C42—891no—
541C2×C42—891no—
542C2×C42—891no—
543C2×C42—891no—
544C2×C42—891no—
545C2×C42—891no—
546C2×C42—898no—
547C2×C42—898no—
548C2×C42—894no—
549C2×C42—894no—
550C2×C42—894no—
551C2×C42—894no—
552C2×C42C4×D8918yescomplemented
553C2×C42C22×D8911yescharacteristic
554C2×C42C22×D8911yescharacteristic
555C2×C42C22×D8911yescharacteristic
556C2×C42C22×D8911yescharacteristic
557#95—892no—
558#95—892no—
559#95—894no—
560#95—894no—
561#95—892no—
562#95—894no—
563#95—892no—
564#95—894no—
565#95—894no—
566#95—894no—
567#95—894no—
568#95—894no—
569#95C22×D8912yes—
570#95C22×D8912yes—
571#95C22×D8912yes—
572#95C22×D8912yes—
573#95C22×D8914yes—
574#95C22×D8914yes—
575C24—891no—
576C24—891no—
577C24C23×D8911yescharacteristic
578#41—17832no—
579C2×Q8—894no—
580C2×Q8—1784no—
581C2×D4—894no—
582C2×D4—898no—
583C2×D4—894no—
584C2×D4—894no—
585C2×D4—1784no—
586C2×D4—1784no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—891no—
595C22×C4—891no—
596C22×C4—891no—
597C22×C4—891no—
598C22×C4—891no—
599C22×C4—891no—
600C22×C4—894no—
601C22×C4—894no—
602C22×C4—894no—
603C22×C4—894no—
604C22×C4—894no—
605C22×C4—894no—
606C22×C4—894no—
607C22×C4—894no—
608C22×C4—3562no—
609C22×C4—3562no—
610C22×C4—3564no—
611C22×C4—3564no—
612C22×C4—1784no—
613C22×C4—1784no—
614C22×C4—1788no—
615C22×C4—1782no—
616C22×C4—1782no—
617C22×C4—1782no—
618C22×C4—1782no—
619C22×C4C2×C4×D8914yes—
620C22×C4C2×C4×D8914yes—
621C22×C4C2×C4×D8914yes—
622C22×C4C23×D8914yes—
623C22×C4C23×D8914yes—
624C22×C4C23×D8911yescharacteristic
625C22×C4C23×D8911yescharacteristic
626C22×C4C23×D8911yescharacteristic
627C22×C4C23×D8911yescharacteristic
628C22×C4C23×D8911yescharacteristic
629C22×C4C23×D8911yescharacteristic
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—44no—
633C4⋊C4—894no—
634C4⋊C4—894no—
635C4⋊C4—894no—
636C4⋊C4—894no—
637C4⋊C4—894no—
638C4⋊C4—894no—
639C4⋊C4—3564no—
640C4⋊C4—3564no—
641C4⋊C4—1788no—
642C4⋊C4—1784no—
643C4⋊C4—1784no—
644C22⋊C4—894no—
645C22⋊C4—894no—
646C22⋊C4—894no—
647C22⋊C4—894no—
648C22⋊C4—894no—
649C22⋊C4—894no—
650C22⋊C4—3564no—
651C22⋊C4—3564no—
652C22⋊C4—1788no—
653C22⋊C4—1788no—
654C42—894no—
655C42—894no—
656C42—894no—
657C42—894no—
658C42—894no—
659C42—894no—
660C42—3564no—
661C42—3564no—
662C42—3564no—
663C42—1788no—
664C42C2×C4×D8914yes—
665C42C2×C4×D8914yes—
666C42C2×C4×D8914yes—
667C42C2×C4×D8914yes—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—892no—
672C23—894no—
673C23—892no—
674C23—1782no—
675C23—1781no—
676C23—1781no—
677C23—1782no—
678C23—1781no—
679C23—1781no—
680C23—1782no—
681C23C22×C4×D8912yes—
682C23#41×D8914yes—
683C23C24×D8911yescharacteristic
684Q8—1788no—
685D4—8916no—
686D4—1788no—
687D4—1788no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—44no—
703C2×C4—88no—
704C2×C4—892no—
705C2×C4—894no—
706C2×C4—892no—
707C2×C4—892no—
708C2×C4—892no—
709C2×C4—892no—
710C2×C4—892no—
711C2×C4—3564no—
712C2×C4—3564no—
713C2×C4—1788no—
714C2×C4—1788no—
715C2×C4—1784no—
716C2×C4—1784no—
717C2×C4—1784no—
718C2×C4—1784no—
719C2×C4—1784no—
720C2×C4—1784no—
721C2×C4—1782no—
722C2×C4—1781no—
723C2×C4—1781no—
724C2×C4—1781no—
725C2×C4—1781no—
726C2×C4—1782no—
727C2×C4—1782no—
728C2×C4—1788no—
729C2×C4—1788no—
730C2×C4—7128no—
731C2×C4C22×C4×D8912yes—
732C2×C4C22×C4×D8912yes—
733C2×C4C22×C4×D8912yes—
734C2×C4C22×C4×D8912yes—
735C2×C4C22×C4×D8912yes—
736C2×C4C22×C4×D8912yes—
737C2×C4#1566805712yes—
738C2×C4#1566806012yes—
739C22—24no—
740C22—22no—
741C22—22no—
742C22—24no—
743C22—894no—
744C22—3562no—
745C22—3562no—
746C22—1782no—
747C22—1782no—
748C22—1782no—
749C22—1784no—
750C22—1782no—
751C22—1782no—
752C22—1784no—
753C22#117×D8914yes—
754C22C23×C4×D8911yescharacteristic
755C22C2×#41×D8912yes—
756C22C2×#1566805711yescharacteristic
757C22C2×#1566806011yescharacteristic
758C22#1915243412yes—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—44no—
765C4—44no—
766C4—894no—
767C4—3564no—
768C4—3564no—
769C4—1782no—
770C4—1782no—
771C4—1782no—
772C4—1782no—
773C4—1782no—
774C4#1915207914yes—
775C2—24no—
776C2—3562no—
777C2—1784no—
778C2C2×#117×D8911yescharacteristic
779C2C2×#1915207911yescharacteristic
780C2#2603345311yescharacteristic
781C2#2603420712yes—
782C2#2603422412yes—
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC2×#382×C89C2
socle, cosocleC23×C89C25
prime radicalC22×#13083574C22
hypercenterC2×#382D89
hypocenterC89#34191
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #26023204C2semidirect
3. #26023178C2semidirect
4. #26023177C2semidirect
5. C4⋊C4×C22⋊D89C2semidirect
6. #26023132C2semidirect
7. #26023108C2semidirect
8. #26023105C2semidirect
10. #26022900C2semidirect
11. #26022888C2semidirect
12. #26022886C2semidirect
13. #26022658C2semidirect
14. #26022650C2semidirect
15. #26022645C2semidirect
16. #26022645C2semidirect
17. #382×D89C2semidirect
18. #26022610C2semidirect
19. C2×#382×C89C2semidirect
21. C4×#13083574C4semidirect
105. C4×Dic178C2×C4semidirect
106. C4×Dic178C2×C4semidirect
107. C4×D356C2×C4semidirect
108. C4×D356C2×C4semidirect
112. C4×C22⋊D89C2×C4semidirect
113. C4×C22⋊D89C2×C4semidirect
114. #15667971C2×C4semidirect
116. #15667969C2×C4semidirect
117. #15667969C2×C4semidirect
150. C42×D89C2×C4semidirect
151. C42×D89C2×C4semidirect
172. C2×C42×C89C2×C4semidirect
317. C22⋊D89#117semidirect
409. C2×#382D89semidirect
411. C89#34191semidirect
552. C2×C42C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#130835742
#260232042
#260231782
#260231772
C4⋊C4×C22⋊D892
#260231322
#260231082
#260231052
#260230792
#260229002
#260228882
#260228862
#260226582
#260226502
#260226452
#382×D892
#260226102
C2×#382×C892
#3419189