Finite Group Databasebeta

← C2×#26022851 #36713012

Subgroups — C2×#26022851 #36713012

Order 22784.

2894 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D89C211yesmaximal, characteristic
2#26022851C2116yesmaximal, direct product factor
3C2×#19151485C211yesmaximal, characteristic, complemented
4C2×#19151484C211yesmaximal, characteristic, complemented
5C2×#19151483C211yesmaximal, characteristic, complemented
6C2×#19151482C211yesmaximal, characteristic, complemented
7C2×#19151481C211yesmaximal, characteristic, complemented
8C2×#19151480C211yesmaximal, characteristic, complemented
9C2×#19151479C211yesmaximal, characteristic, complemented
10C2×#19151460C211yesmaximal, characteristic
11C2×#19151460C211yesmaximal, characteristic
12C2×#19151457C211yesmaximal, characteristic
13C2×#19151455C211yesmaximal, characteristic
14C2×C4×#13083551C211yesmaximal, characteristic
15C2×#19151445C211yesmaximal, characteristic
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×C4×D89C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C22×C4⋊Dic89C2211yescharacteristic
21C22×C4⋊Dic89C2211yescharacteristic
22C22×#13083553C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C2×C4⋊C4×D89C4116yescomplemented
27C2×C4⋊C4×D89C2218yes—
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×C4×Dic89C2211yescharacteristic
33C22×C4×Dic89C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35#19151485C2218yescomplemented
36#19151484C2218yescomplemented
37#19151483C2218yescomplemented
38#19151482C2218yescomplemented
39#19151481C2218yescomplemented
40#19151480C2218yescomplemented
41#19151479C2218yescomplemented
42#19151460C2218yes—
43#19151460C2218yes—
44#19151457C2218yes—
45#19151455C2218yes—
46C4×#13083551C2218yes—
47#19151445C2218yes—
48C2×#15667919C2211yescharacteristic
49C2×#15667919C2211yescharacteristic
50C2×#15667919C2211yescharacteristic
51C2×#15667919C2211yescharacteristic
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C22×C4⋊C4×C89C2211yescharacteristic
61C22×C4⋊C4×C89C2211yescharacteristic
62C22×C42×C89C2211yescharacteristic
63#387×C89C2218yescomplemented
64C2×#95×C89C2211yescharacteristic
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C24×D89C2311yescharacteristic
69C23×Dic89C2311yescharacteristic
70C23×Dic89C2311yescharacteristic
71C23×Dic89C2311yescharacteristic
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C22×C4×D89—24no—
77C22×C4×D89—24no—
78C22×C4×D89—42no—
79C22×C4×D89—42no—
80C22×C4×D89—42no—
81C22×C4×D89—42no—
82C22×C4×D89C2×C418yes—
83C22×C4×D89C2×C418yes—
84C22×C4×D89C2×C418yes—
85C22×C4×D89C2314yes—
86C22×C4×D89C2314yes—
87C22×C4×D89C2314yes—
88C2×C4⋊Dic89—42no—
89C2×C4⋊Dic89C2×C418yes—
90C2×C4⋊Dic89C2314yes—
91C2×C4⋊Dic89C2314yes—
92C2×#13083553—42no—
93C2×#13083553—42no—
94C2×#13083553C2×C418yes—
95C2×#13083553C2×C418yes—
96C2×#13083553C2314yes—
97C2×#13083553C2314yes—
98C2×#13083553C2314yes—
99C2×#13083553C2314yes—
100C4⋊C4×D89C2×C4164yescomplemented
101C2×#13083551—24no—
102C2×#13083551—24no—
103C2×#13083551—24no—
104C2×#13083551—24no—
105C2×#13083551C2314yes—
106C2×#13083551C2314yes—
107C2×#13083551C2314yes—
108C2×#13083551C2314yes—
109C2×C4×Dic89—42no—
110C2×C4×Dic89—42no—
111C2×C4×Dic89—42no—
112C2×C4×Dic89C2314yes—
113C2×C4×Dic89C2314yes—
114C2×C4×Dic89C2314yes—
115#15667919C2314yes—
116#15667919C2314yes—
117#15667919C2314yes—
118#15667919C2314yes—
119#15667919C2314yes—
120#15667919C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123#15667919C2314yes—
124#15667919C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C23×C4×C89C2311yescharacteristic
132C23×C4×C89C2311yescharacteristic
133C23×C4×C89C2311yescharacteristic
134C2×C4⋊C4×C89—42no—
135C2×C4⋊C4×C89C2×C418yes—
136C2×C4⋊C4×C89C2314yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C42×C89—42no—
139C2×C42×C89C2314yes—
140#95×C89C2314yes—
141#95×C89C2314yes—
142#95×C89C2314yes—
143#95×C89C2314yes—
144C23×D89—22no—
145C23×D89—22no—
146C23×D89—22no—
147C23×D89—22no—
148C23×D89C22×C414yes—
149C23×D89#4114yes—
150C23×D89#4114yes—
151C23×D89C2412yes—
152C22×Dic89—22no—
153C22×Dic89—22no—
154C22×Dic89—22no—
155C22×Dic89—22no—
156C22×Dic89—22no—
157C22×Dic89—22no—
158C22×Dic89—22no—
159C22×Dic89—22no—
160C22×Dic89—22no—
161C22×Dic89—22no—
162C22×Dic89—22no—
163C22×Dic89—22no—
164C22×Dic89—22no—
165C22×Dic89—22no—
166C22×Dic89—22no—
167C22×Dic89—22no—
168C22×Dic89—22no—
169C22×Dic89—22no—
170C22×Dic89C22×C414yes—
171C22×Dic89C22×C414yes—
172C22×Dic89C22×C414yes—
173C22×Dic89C2412yes—
174C22×Dic89C2412yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C2×C4×D89—232no—
181C2×C4×D89—28no—
182C2×C4×D89—28no—
183C2×C4×D89—416no—
184C2×C4×D89—416no—
185C2×C4×D89—44no—
186C2×C4×D89—44no—
187C2×C4×D89—44no—
188C2×C4×D89—44no—
189C2×C4×D89C22×C4116yes—
190C2×C4×D89C22×C4116yes—
191C2×C4×D89C22×C4116yes—
192C4⋊Dic89—44no—
193C4⋊Dic89C22×C4116yes—
194#13083553—44no—
195#13083553—44no—
196#13083553C22×C4116yes—
197#13083553C22×C4116yes—
198#13083551—28no—
199#13083551—28no—
200#13083551—28no—
201#13083551—28no—
202C4×Dic89—44no—
203C4×Dic89—44no—
204C4×Dic89—44no—
205C24×C89C2411yescharacteristic
206C22×C4×C89—22no—
207C22×C4×C89—22no—
208C22×C4×C89—22no—
209C22×C4×C89—22no—
210C22×C4×C89—22no—
211C22×C4×C89—22no—
212C22×C4×C89—22no—
213C22×C4×C89—22no—
214C22×C4×C89—22no—
215C22×C4×C89—22no—
216C22×C4×C89—22no—
217C22×C4×C89—22no—
218C22×C4×C89—22no—
219C22×C4×C89—22no—
220C22×C4×C89—22no—
221C22×C4×C89—22no—
222C22×C4×C89—22no—
223C22×C4×C89—22no—
224C22×C4×C89C22×C414yes—
225C22×C4×C89C22×C414yes—
226C22×C4×C89C22×C414yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C22×C4×C89C2412yes—
231C22×C4×C89C2412yes—
232C22×C4×C89C2412yes—
233C22×C4×C89C2412yes—
234C4⋊C4×C89—44no—
235C4⋊C4×C89C22×C4116yes—
236C42×C89—44no—
237C23×C89C23×C412yes—
238C23×C89C2×#4112yes—
239C23×C89C2×#4112yes—
240C23×C89H(5,𝔽2)12yes—
241C23×C89H(5,𝔽2)12yes—
242C23×C892−1+412yes—
243C23×C892−1+412yes—
244C23×C89C2511yescharacteristic
245C22×D89—28no—
246C22×D89—28no—
247C22×D89—28no—
248C22×D89—28no—
249C22×D89—28no—
250C22×D89—28no—
251C22×D89—22no—
252C22×D89—22no—
253C22×D89—22no—
254C22×D89—22no—
255C22×D89#117116yes—
256C22×D89C23×C414yes—
257C22×D89C2×#4114yes—
258C22×D89C2×#4114yes—
259C2×C4×C89—28no—
260C2×C4×C89—28no—
261C2×C4×C89—28no—
262C2×C4×C89—22no—
263C2×C4×C89—22no—
264C2×C4×C89—22no—
265C2×C4×C89—22no—
266C2×C4×C89—22no—
267C2×C4×C89—22no—
268C2×C4×C89—22no—
269C2×C4×C89—22no—
270C2×C4×C89—22no—
271C2×C4×C89—22no—
272C2×C4×C89—22no—
273C2×C4×C89—22no—
274C2×C4×C89—22no—
275C2×C4×C89—22no—
276C2×C4×C89—22no—
277C2×C4×C89—22no—
278C2×C4×C89—22no—
279C2×C4×C89—22no—
280C2×C4×C89—44no—
281C2×C4×C89—44no—
282C2×C4×C89—44no—
283C2×C4×C89—44no—
284C2×C4×C89C23×C414yes—
285C2×C4×C89C23×C414yes—
286C2×C4×C89C23×C414yes—
287C2×Dic89—28no—
288C2×Dic89—28no—
289C2×Dic89—28no—
290C2×Dic89—22no—
291C2×Dic89—22no—
292C2×Dic89—22no—
293C2×Dic89—22no—
294C2×Dic89—22no—
295C2×Dic89—22no—
296C2×Dic89—22no—
297C2×Dic89—22no—
298C2×Dic89—22no—
299C2×Dic89—22no—
300C2×Dic89—22no—
301C2×Dic89—22no—
302C2×Dic89—22no—
303C2×Dic89—22no—
304C2×Dic89—22no—
305C2×Dic89—22no—
306C2×Dic89—22no—
307C2×Dic89—22no—
308C2×Dic89—44no—
309C2×Dic89—44no—
310C2×Dic89—44no—
311C2×Dic89—44no—
312C2×Dic89C23×C414yes—
313C2×Dic89C23×C414yes—
314C2×Dic89C23×C414yes—
315C4×D89—232no—
316C4×D89—416no—
317C4×D89—416no—
318C22×C89C2×#11714yes—
319C22×C89#51814yes—
320C22×C89#51914yes—
321C22×C89#53914yes—
322C22×C89#53914yes—
323C22×C89#53914yes—
324C22×C89#53914yes—
325C22×C89C24×C411yescharacteristic
326C22×C89C22×#4111yescharacteristic
327C22×C89C22×#4111yescharacteristic
328C22×C89C2×H(5,𝔽2)11yescharacteristic
329C22×C89C2×H(5,𝔽2)11yescharacteristic
330C22×C89C2×2−1+411yescharacteristic
331C22×C89C2×2−1+411yescharacteristic
332C2×D89—232no—
333C2×D89—24no—
334C2×D89—24no—
335C2×D89—24no—
336C2×D89—24no—
337C2×D89—24no—
338C2×D89—24no—
339C2×D89C2×#11718yes—
340C4×C89—24no—
341C4×C89—24no—
342C4×C89—24no—
343C4×C89—42no—
344C4×C89—42no—
345C4×C89—42no—
346C4×C89—42no—
347Dic89—24no—
348Dic89—24no—
349Dic89—24no—
350Dic89—42no—
351Dic89—42no—
352Dic89—42no—
353Dic89—42no—
354C2×#2313—891nomaximal, Sylow
355C2×C89#231318yescomplemented
356C2×C89C22×#11711yescharacteristic
357C2×C89C2×#51811yescharacteristic
358C2×C89C2×#51911yescharacteristic
359C2×C89C2×#53911yescharacteristic
360C2×C89C2×#53911yescharacteristic
361C2×C89C2×#53911yescharacteristic
362C2×C89C2×#53911yescharacteristic
363D89—28no—
364C23×C4⋊C4—891no—
365#2313—8916no—
366C2×#387—891no—
367C2×#387—891no—
368C2×#387—891no—
369C2×#387—891no—
370C2×#387—891no—
371C2×#387—891no—
372C2×#387—891no—
373C2×#387D8911yescharacteristic, complemented
374C2×#381—891no—
375C2×#381—891no—
376C2×#380—891no—
377C2×#380—891no—
378C2×C4×C22⋊C4—891no—
379C2×C4×C22⋊C4—891no—
380C89C2×#231311yescharacteristic, complemented, Sylow
381C24×C4—891no—
382C24×C4—891no—
383C24×C4—891no—
384C22×C4⋊C4—891no—
385C22×C4⋊C4—891no—
386C22×C4⋊C4—891no—
387C22×C4⋊C4—8916no—
388C22×C4⋊C4—898no—
389C22×C4⋊C4—891no—
390C22×C4⋊C4—891no—
391C22×C4⋊C4—891no—
392C22×C4⋊C4C2×D8911yescharacteristic
393C22×C4⋊C4C2×D8911yescharacteristic
394C22×C22⋊C4—891no—
395C22×C22⋊C4—891no—
396C22×C22⋊C4—891no—
397C22×C22⋊C4—891no—
398C22×C42—891no—
399C22×C42—891no—
400C22×C42—891no—
401C22×C42C2×D8911yescharacteristic
402#387—898no—
403#387—898no—
404#387—898no—
405#387—898no—
406#387—898no—
407#387—898no—
408#387—898no—
409#387C2×D8918yescomplemented
410#381—898no—
411#381—898no—
412#380—898no—
413#380—898no—
414C4×C22⋊C4—898no—
415C4×C22⋊C4—898no—
416C2×#95—891no—
417C2×#95—891no—
418C2×#95—891no—
419C2×#95—891no—
420C2×#95—891no—
421C2×#95—891no—
422C2×#95—891no—
423C2×#95—891no—
424C2×#95—891no—
425C2×#95—891no—
426C2×#95—891no—
427C2×#95—891no—
428C2×#95C2×D8911yescharacteristic
429C2×#95C2×D8911yescharacteristic
430C2×#95C2×D8911yescharacteristic
431C2×#95C2×D8911yescharacteristic
432C25—891no—
433C23×C4—891no—
434C23×C4—891no—
435C23×C4—891no—
436C23×C4—898no—
437C23×C4—898no—
438C23×C4—894no—
439C23×C4—894no—
440C23×C4—898no—
441C23×C4—894no—
442C23×C4—891no—
443C23×C4—891no—
444C23×C4—891no—
445C23×C4—891no—
446C23×C4—3562no—
447C23×C4—3562no—
448C23×C4—3562no—
449C23×C4—3562no—
450C23×C4—1784no—
451C23×C4—1784no—
452C23×C4C22×D8911yescharacteristic
453C23×C4C22×D8911yescharacteristic
454C23×C4C22×D8911yescharacteristic
455C23×C4C22×D8911yescharacteristic
456C23×C4C22×D8911yescharacteristic
457C23×C4C22×D8911yescharacteristic
458C23×C4C22×D8911yescharacteristic
459C2×C4⋊C4—42no—
460C2×C4⋊C4—898no—
461C2×C4⋊C4—898no—
462C2×C4⋊C4—898no—
463C2×C4⋊C4—894no—
464C2×C4⋊C4—894no—
465C2×C4⋊C4—894no—
466C2×C4⋊C4—8964no—
467C2×C4⋊C4—894no—
468C2×C4⋊C4—894no—
469C2×C4⋊C4—894no—
470C2×C4⋊C4—3562no—
471C2×C4⋊C4—3562no—
472C2×C4⋊C4—3562no—
473C2×C4⋊C4C4×D8918yes—
474C2×C4⋊C4C22×D8914yes—
475C2×C4⋊C4C22×D8914yes—
476C2×C22⋊C4—894no—
477C2×C22⋊C4—894no—
478C2×C22⋊C4—894no—
479C2×C22⋊C4—894no—
480C2×C22⋊C4—1784no—
481C2×C22⋊C4—1784no—
482C2×C22⋊C4—1784no—
483C2×C22⋊C4—1784no—
484C2×C42—42no—
485C2×C42—894no—
486C2×C42—894no—
487C2×C42—894no—
488C2×C42—3562no—
489C2×C42—3562no—
490C2×C42—3562no—
491C2×C42C22×D8914yes—
492#95—894no—
493#95—894no—
494#95—894no—
495#95—894no—
496#95—894no—
497#95—894no—
498#95—894no—
499#95—894no—
500#95—894no—
501#95—894no—
502#95—894no—
503#95—894no—
504#95C22×D8914yes—
505#95C22×D8914yes—
506#95C22×D8914yes—
507#95C22×D8914yes—
508C24—894no—
509C24—894no—
510C24—894no—
511C24—892no—
512C24—1782no—
513C24—1782no—
514C24—1782no—
515C24—1782no—
516C24C23×D8911yescharacteristic
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—894no—
536C22×C4—894no—
537C22×C4—894no—
538C22×C4—892no—
539C22×C4—892no—
540C22×C4—892no—
541C22×C4—8916no—
542C22×C4—8916no—
543C22×C4—8916no—
544C22×C4—892no—
545C22×C4—892no—
546C22×C4—892no—
547C22×C4—892no—
548C22×C4—3564no—
549C22×C4—3564no—
550C22×C4—3564no—
551C22×C4—3564no—
552C22×C4—35616no—
553C22×C4—35616no—
554C22×C4—1788no—
555C22×C4—1788no—
556C22×C4—17832no—
557C22×C4—1782no—
558C22×C4—1782no—
559C22×C4—1782no—
560C22×C4—1782no—
561C22×C4—1782no—
562C22×C4—1782no—
563C22×C4—1782no—
564C22×C4—1782no—
565C22×C4—1782no—
566C22×C4—1782no—
567C22×C4—1782no—
568C22×C4—1782no—
569C22×C4—1782no—
570C22×C4—1782no—
571C22×C4—1782no—
572C22×C4—1782no—
573C22×C4—1782no—
574C22×C4—1782no—
575C22×C4C2×C4×D8914yes—
576C22×C4C2×C4×D8914yes—
577C22×C4C2×C4×D8914yes—
578C22×C4C23×D8912yes—
579C22×C4C23×D8912yes—
580C22×C4C23×D8912yes—
581C22×C4C23×D8912yes—
582C22×C4C23×D8912yes—
583C22×C4C23×D8912yes—
584C22×C4C23×D8912yes—
585C4⋊C4—44no—
586C4⋊C4—8916no—
587C4⋊C4—8916no—
588C4⋊C4—8916no—
589C4⋊C4—3564no—
590C4⋊C4—3564no—
591C4⋊C4—3564no—
592C4⋊C4C2×C4×D89116yes—
593C22⋊C4—1788no—
594C22⋊C4—1788no—
595C22⋊C4—1788no—
596C22⋊C4—1788no—
597C42—44no—
598C42—3564no—
599C42—3564no—
600C42—3564no—
601C23—894no—
602C23—894no—
603C23—894no—
604C23—8916no—
605C23—1782no—
606C23—1782no—
607C23—1782no—
608C23—1782no—
609C23—1788no—
610C23—1788no—
611C23—1788no—
612C23—1788no—
613C23—1788no—
614C23—1788no—
615C23C22×C4×D8912yes—
616C23#41×D8912yes—
617C23#41×D8912yes—
618C23#1566805712yes—
619C23#1566805812yes—
620C23#1566805912yes—
621C23#1566806012yes—
622C23C24×D8911yescharacteristic
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—28no—
630C2×C4—28no—
631C2×C4—28no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—894no—
649C2×C4—894no—
650C2×C4—894no—
651C2×C4—35616no—
652C2×C4—35616no—
653C2×C4—3564no—
654C2×C4—3564no—
655C2×C4—3564no—
656C2×C4—3564no—
657C2×C4—17832no—
658C2×C4—1782no—
659C2×C4—1782no—
660C2×C4—1782no—
661C2×C4—1782no—
662C2×C4—1782no—
663C2×C4—1782no—
664C2×C4—1782no—
665C2×C4—1782no—
666C2×C4—1782no—
667C2×C4—1782no—
668C2×C4—1782no—
669C2×C4—1782no—
670C2×C4—1782no—
671C2×C4—1782no—
672C2×C4—1782no—
673C2×C4—1782no—
674C2×C4—1782no—
675C2×C4—1782no—
676C2×C4—1788no—
677C2×C4—1788no—
678C2×C4—1788no—
679C2×C4C22×C4×D8914yes—
680C2×C4C22×C4×D8914yes—
681C2×C4C22×C4×D8914yes—
682C22—898no—
683C22—1784no—
684C22—1784no—
685C22—1784no—
686C22—1784no—
687C22—1784no—
688C22—17832no—
689C22—1784no—
690C22#117×D8914yes—
691C22#1915207014yes—
692C22#1915207414yes—
693C22#1915218914yes—
694C22#1915219114yes—
695C22#1915219414yes—
696C22#1915219614yes—
697C22C23×C4×D8911yescharacteristic
698C22C2×#41×D8911yescharacteristic
699C22C2×#41×D8911yescharacteristic
700C22C2×#1566805711yescharacteristic
701C22C2×#1566805811yescharacteristic
702C22C2×#1566805911yescharacteristic
703C22C2×#1566806011yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—3562no—
712C4—3562no—
713C4—3562no—
714C4—3562no—
715C4—1784no—
716C4—1784no—
717C4—1784no—
718C2—1788no—
719C2#2602285118yesdirect product factor
720C2C2×#117×D8911yescharacteristic
721C2C2×#1915207011yescharacteristic
722C2C2×#1915207411yescharacteristic
723C2C2×#1915218911yescharacteristic
724C2C2×#1915219111yescharacteristic
725C2C2×#1915219411yescharacteristic
726C2C2×#1915219611yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
cosocleC23×C89C25
hypercenterC2×#387D89
hypocenterC89C2×#2313
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #26022851C2direct (N × H)
3. C2×#19151485C2semidirect
4. C2×#19151484C2semidirect
5. C2×#19151483C2semidirect
6. C2×#19151482C2semidirect
7. C2×#19151481C2semidirect
8. C2×#19151480C2semidirect
9. C2×#19151479C2semidirect
16. C2×#387×C89C2semidirect
26. C2×C4⋊C4×D89C4semidirect
35. #19151485C22semidirect
36. #19151484C22semidirect
37. #19151483C22semidirect
38. #19151482C22semidirect
39. #19151481C22semidirect
40. #19151480C22semidirect
41. #19151479C22semidirect
63. #387×C89C22semidirect
100. C4⋊C4×D89C2×C4semidirect
355. C2×C89#2313semidirect
373. C2×#387D89semidirect
380. C89C2×#2313semidirect
409. #387C2×D89semidirect
719. C2#26022851direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D892
#260228512
C2×#191514852
C2×#191514842
C2×#191514832
C2×#191514822
C2×#191514812
C2×#191514802
C2×#191514792
C2×#191514602
C2×#191514572
C2×#191514552
C2×C4×#130835512
C2×#191514452
C2×#387×C892
C2×#231389