Finite Group Databasebeta

← C2×#26024327 #36722634

Subgroups — C2×#26024327 #36722634

Order 22784.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15668007C211yesmaximal, characteristic
2#26024327C2116yesmaximal, direct product factor
3C2×#19151537C211yesmaximal, characteristic, complemented
4C2×#19151520C211yesmaximal, characteristic
5C2×#19151517C211yesmaximal, characteristic, complemented
6C2×#19151509C211yesmaximal, characteristic
7C2×#19151496C211yesmaximal, characteristic, complemented
8C2×#19151489C211yesmaximal, characteristic
9C2×#19151489C211yesmaximal, characteristic
10C2×#19151489C211yesmaximal, characteristic
11C2×#19151488C211yesmaximal, characteristic
12C2×#19151484C211yesmaximal, characteristic, complemented
13C2×#19151482C211yesmaximal, characteristic, complemented
14C2×#19151479C211yesmaximal, characteristic, complemented
15C2×C4×#13083553C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C89C211yesmaximal, characteristic, complemented
17C2×#15668007—28no—
18C2×#15668007C2218yes—
19C22×C4⋊Dic89C2211yescharacteristic
20C22×C4⋊Dic89C2211yescharacteristic
21C22×#13083553C2211yescharacteristic
22C22×#13083553C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083551C2211yescharacteristic
27C22×#13083551C2211yescharacteristic
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×C4×Dic89C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35#19151537C2218yescomplemented
36#19151520C2218yes—
37#19151517C2218yescomplemented
38#19151509C2218yes—
39#19151496C2218yescomplemented
40#19151489C2218yes—
41#19151489C2218yes—
42#19151489C2218yes—
43#19151488C2218yes—
44#19151484C2218yescomplemented
45#19151482C2218yescomplemented
46#19151479C2218yescomplemented
47C4×#13083553C2218yescomplemented
48C2×#15667919C2211yescharacteristic
49C2×#15667919C2211yescharacteristic
50C2×#15667919C2211yescharacteristic
51C2×#15667919C2211yescharacteristic
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C23×Q8×C89C2211yescharacteristic
61C2×C4×Q8×C89—28no—
62C2×C4×Q8×C89C2218yescomplemented
63C22×C4⋊C4×C89C2211yescharacteristic
64C22×C4⋊C4×C89C2211yescharacteristic
65C22×C4⋊C4×C89C2211yescharacteristic
66C22×C42×C89C2211yescharacteristic
67C22×C42×C89C2211yescharacteristic
68C22×C42×C89C2211yescharacteristic
69C24×D89C2311yescharacteristic
70C23×Dic89C2311yescharacteristic
71C23×Dic89C2311yescharacteristic
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77#15668007—232no—
78C2×C4⋊Dic89—24no—
79C2×C4⋊Dic89—24no—
80C2×C4⋊Dic89C2314yes—
81C2×C4⋊Dic89C2314yes—
82C2×#13083553—24no—
83C2×#13083553—24no—
84C2×#13083553—24no—
85C2×#13083553—24no—
86C2×#13083553—24no—
87C2×#13083553C2314yes—
88C2×#13083553C2314yes—
89C2×#13083553C2314yes—
90C2×#13083553C2314yes—
91C2×#13083553C2314yes—
92C2×#13083551—24no—
93C2×#13083551—24no—
94C2×#13083551—24no—
95C2×#13083551—24no—
96C2×#13083551—24no—
97C2×#13083551—24no—
98C2×#13083551—24no—
99C2×#13083551C2314yes—
100C2×#13083551C2314yes—
101C2×#13083551C2314yes—
102C2×#13083551C2314yes—
103C2×#13083551C2314yes—
104C2×#13083551C2314yes—
105C2×#13083551C2314yes—
106C2×C4×Dic89—24no—
107C2×C4×Dic89—24no—
108C2×C4×Dic89C2314yes—
109C2×C4×Dic89C2314yes—
110#15667919C2314yes—
111#15667919C2314yes—
112#15667919C2314yes—
113#15667919C2314yes—
114#15667919C2314yes—
115#15667919C2314yes—
116#15667919C2314yes—
117#15667919C2314yes—
118#15667919C2314yes—
119#15667919C2314yes—
120#15667919C2314yes—
121#15667919C2314yes—
122C22×Q8×C89—24no—
123C22×Q8×C89—24no—
124C22×Q8×C89—24no—
125C22×Q8×C89C2314yes—
126C23×C4×C89C2311yescharacteristic
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C23×C4×C89C2311yescharacteristic
132C23×C4×C89C2311yescharacteristic
133C4×Q8×C89—232no—
134C2×C4⋊C4×C89—24no—
135C2×C4⋊C4×C89—24no—
136C2×C4⋊C4×C89D418yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C4⋊C4×C89C2314yes—
139C2×C4⋊C4×C89C2314yes—
140C2×C42×C89—24no—
141C2×C42×C89—24no—
142C2×C42×C89—24no—
143C2×C42×C89C2314yes—
144C2×C42×C89C2314yes—
145C2×C42×C89C2314yes—
146C23×D89—22no—
147C23×D89—22no—
148C23×D89—22no—
149C23×D89—22no—
150C23×D89—22no—
151C23×D89—22no—
152C23×D89—22no—
153C23×D89C2412yes—
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×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89#4114yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C22×Dic89C2412yes—
181C22×Dic89C2412yes—
182C4⋊Dic89—28no—
183C4⋊Dic89—28no—
184#13083553—28no—
185#13083553—28no—
186#13083553—28no—
187#13083553—28no—
188#13083553—28no—
189#13083551—28no—
190#13083551—28no—
191#13083551—28no—
192#13083551—28no—
193#13083551—28no—
194#13083551—28no—
195#13083551—28no—
196C4×Dic89—28no—
197C4×Dic89—28no—
198C24×C89C2411yescharacteristic
199C2×Q8×C89—232no—
200C2×Q8×C89—28no—
201C2×Q8×C89—28no—
202C2×Q8×C89—28no—
203C22×C4×C89—22no—
204C22×C4×C89—22no—
205C22×C4×C89—22no—
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×C89C2×D414yes—
219C22×C4×C89C2×D414yes—
220C22×C4×C89C2×D414yes—
221C22×C4×C89#4114yes—
222C22×C4×C89#4114yes—
223C22×C4×C89#4114yes—
224C22×C4×C89C2412yes—
225C22×C4×C89C2412yes—
226C22×C4×C89C2412yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C22×C4×C89C2412yes—
231C4⋊C4×C89—28no—
232C4⋊C4×C89—28no—
233C4⋊C4×C89C2×D4116yes—
234C42×C89—28no—
235C42×C89—28no—
236C42×C89—28no—
237C23×C89C22×D412yes—
238C23×C89C2×#4112yes—
239C23×C89C2×#4112yes—
240C23×C89C2×#4112yes—
241C23×C89C2×#4112yes—
242C23×C892−1+412yes—
243C23×C892−1+412yes—
244C23×C89C2511yescharacteristic
245C22×D89—22no—
246C22×D89—22no—
247C22×D89—22no—
248C22×D89—22no—
249C22×D89—22no—
250C22×D89—22no—
251C22×D89—22no—
252C22×D89—44no—
253C22×D89—44no—
254C22×D89—44no—
255C22×D89—44no—
256C22×D89—44no—
257C22×D89—44no—
258C22×D89—44no—
259Q8×C89—232no—
260C2×C4×C89—28no—
261C2×C4×C89—28no—
262C2×C4×C89—28no—
263C2×C4×C89—28no—
264C2×C4×C89—28no—
265C2×C4×C89—28no—
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—22no—
281C2×C4×C89—44no—
282C2×C4×C89C22×D414yes—
283C2×C4×C89C22×D414yes—
284C2×C4×C89C22×D414yes—
285C2×C4×C89C2×#4114yes—
286C2×C4×C89C2×#4114yes—
287C2×C4×C89C2×#4114yes—
288C2×Dic89—28no—
289C2×Dic89—22no—
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—22no—
309C2×Dic89—44no—
310C2×Dic89—44no—
311C2×Dic89—44no—
312C2×Dic89—44no—
313C2×Dic89—44no—
314C2×Dic89—44no—
315C2×Dic89C2×#4114yes—
316C22×C89#52514yes—
317C22×C89#52914yes—
318C22×C89#54114yes—
319C22×C89#54714yes—
320C22×C89#54814yes—
321C22×C89#55614yes—
322C22×C89#55614yes—
323C22×C89C23×D411yescharacteristic
324C22×C89C22×#4111yescharacteristic
325C22×C89C22×#4111yescharacteristic
326C22×C89C22×#4111yescharacteristic
327C22×C89C22×#4111yescharacteristic
328C22×C89C2×2−1+411yescharacteristic
329C22×C89C2×2−1+411yescharacteristic
330C2×D89—42no—
331C2×D89—42no—
332C2×D89—42no—
333C2×D89—42no—
334C2×D89—42no—
335C2×D89—42no—
336C2×D89—42no—
337C2×D89—88no—
338C4×C89—24no—
339C4×C89—24no—
340C4×C89—24no—
341C4×C89—24no—
342C4×C89—24no—
343C4×C89—24no—
344C4×C89—42no—
345Dic89—24no—
346Dic89—42no—
347Dic89—42no—
348Dic89—42no—
349Dic89—42no—
350Dic89—42no—
351Dic89—42no—
352C2×#2469—891nomaximal, Sylow
353C2×C89#246918yescomplemented
354C2×C89C2×#52511yescharacteristic
355C2×C89C2×#52911yescharacteristic
356C2×C89C2×#54111yescharacteristic
357C2×C89C2×#54711yescharacteristic
358C2×C89C2×#54811yescharacteristic
359C2×C89C2×#55611yescharacteristic
360C2×C89C2×#55611yescharacteristic
361D89—82no—
362C22×#126—891no—
363C22×C4×Q8D8911yescharacteristic, complemented
364#2469—8916no—
365C2×#400—891no—
366C2×#396—891no—
367C2×#395—891no—
368C2×#393—891no—
369C2×#389—891no—
370C2×#388—891no—
371C2×#388—891no—
372C2×#388—891no—
373C2×#388—891no—
374C2×#387—891no—
375C2×#387—891no—
376C2×#387—891no—
377C2×C4×C4⋊C4—891no—
378C89C2×#246911yescharacteristic, complemented, Sylow
379C23×Q8C2×D8911yescharacteristic
380C2×#126—898no—
381C2×#126—1788no—
382C2×C4×Q8—28no—
383C2×C4×Q8C2×D8918yescomplemented
384C22×C4⋊C4—891no—
385C22×C4⋊C4—891no—
386C22×C4⋊C4—891no—
387C22×C4⋊C4—891no—
388C22×C4⋊C4—891no—
389C22×C4⋊C4—891no—
390C22×C4⋊C4—891no—
391C22×C4⋊C4C2×D8911yescharacteristic
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×C22⋊C4—891no—
399C22×C22⋊C4—891no—
400C22×C22⋊C4—891no—
401C22×C42—891no—
402C22×C42—891no—
403C22×C42C2×D8911yescharacteristic
404C22×C42C2×D8911yescharacteristic
405C22×C42C2×D8911yescharacteristic
406#400—898no—
407#396—898no—
408#395—898no—
409#393—898no—
410#389—898no—
411#388—898no—
412#388—898no—
413#388—898no—
414#388—898no—
415#387—898no—
416#387—898no—
417#387—898no—
418C4×C4⋊C4—898no—
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×#95—891no—
429C2×#95—891no—
430C2×#95—891no—
431C25—891no—
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8C22×D8914yes—
436C23×C4—891no—
437C23×C4—891no—
438C23×C4—891no—
439C23×C4—891no—
440C23×C4—891no—
441C23×C4—891no—
442C23×C4—891no—
443C23×C4C22×D8911yescharacteristic
444C23×C4C22×D8911yescharacteristic
445C23×C4C22×D8911yescharacteristic
446C23×C4C22×D8911yescharacteristic
447C23×C4C22×D8911yescharacteristic
448C23×C4C22×D8911yescharacteristic
449C23×C4C22×D8911yescharacteristic
450#126—17832no—
451C4×Q8—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—894no—
455C2×C4⋊C4—894no—
456C2×C4⋊C4—894no—
457C2×C4⋊C4—894no—
458C2×C4⋊C4—894no—
459C2×C4⋊C4—894no—
460C2×C4⋊C4—894no—
461C2×C4⋊C4—1784no—
462C2×C4⋊C4—1784no—
463C2×C4⋊C4—1784no—
464C2×C4⋊C4—1784no—
465C2×C4⋊C4—1784no—
466C2×C4⋊C4—1784no—
467C2×C4⋊C4—1784no—
468C2×C4⋊C4C22⋊D8918yes—
469C2×C4⋊C4C22×D8914yes—
470C2×C4⋊C4C22×D8914yes—
471C2×C4⋊C4C22×D8914yes—
472C2×C22⋊C4—894no—
473C2×C22⋊C4—894no—
474C2×C22⋊C4—894no—
475C2×C22⋊C4—894no—
476C2×C22⋊C4—894no—
477C2×C22⋊C4—894no—
478C2×C22⋊C4—894no—
479C2×C22⋊C4—1784no—
480C2×C22⋊C4—1784no—
481C2×C22⋊C4—1784no—
482C2×C22⋊C4—1784no—
483C2×C22⋊C4—1784no—
484C2×C22⋊C4—1784no—
485C2×C22⋊C4—1784no—
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—24no—
489C2×C42—894no—
490C2×C42—894no—
491C2×C42—1784no—
492C2×C42—1784no—
493C2×C42C22×D8914yes—
494C2×C42C22×D8914yes—
495C2×C42C22×D8914yes—
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#95—894no—
505#95—894no—
506#95—894no—
507#95—894no—
508C24—892no—
509C24—1782no—
510C24—1782no—
511C24—1782no—
512C24—1782no—
513C24—1782no—
514C24—1782no—
515C24—1782no—
516C24C23×D8911yescharacteristic
517C2×Q8—232no—
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—28no—
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—22no—
536C22×C4—894no—
537C22×C4—892no—
538C22×C4—892no—
539C22×C4—892no—
540C22×C4—892no—
541C22×C4—892no—
542C22×C4—892no—
543C22×C4—892no—
544C22×C4—1782no—
545C22×C4—1782no—
546C22×C4—1782no—
547C22×C4—1782no—
548C22×C4—1782no—
549C22×C4—1782no—
550C22×C4—1782no—
551C22×C4—1782no—
552C22×C4—1782no—
553C22×C4—1782no—
554C22×C4—1782no—
555C22×C4—1782no—
556C22×C4—1782no—
557C22×C4—1782no—
558C22×C4—1782no—
559C22×C4—1782no—
560C22×C4—1782no—
561C22×C4—1782no—
562C22×C4—1782no—
563C22×C4—1782no—
564C22×C4C2×C22⋊D8914yes—
565C22×C4C2×C22⋊D8914yes—
566C22×C4C2×C22⋊D8914yes—
567C22×C4#1308357414yes—
568C22×C4#1308357414yes—
569C22×C4#1308357514yes—
570C22×C4C23×D8912yes—
571C22×C4C23×D8912yes—
572C22×C4C23×D8912yes—
573C22×C4C23×D8912yes—
574C22×C4C23×D8912yes—
575C22×C4C23×D8912yes—
576C22×C4C23×D8912yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—1788no—
580C4⋊C4—1788no—
581C4⋊C4—1788no—
582C4⋊C4—1788no—
583C4⋊C4—1788no—
584C4⋊C4—1788no—
585C4⋊C4—1788no—
586C4⋊C4C2×C22⋊D89116yes—
587C22⋊C4—1788no—
588C22⋊C4—1788no—
589C22⋊C4—1788no—
590C22⋊C4—1788no—
591C22⋊C4—1788no—
592C22⋊C4—1788no—
593C22⋊C4—1788no—
594C42—28no—
595C42—28no—
596C42—28no—
597C42—1788no—
598C42—1788no—
599C23—3564no—
600C23—3564no—
601C23—3564no—
602C23—3564no—
603C23—3564no—
604C23—3564no—
605C23—3564no—
606C23—1782no—
607C23—1782no—
608C23—1782no—
609C23—1782no—
610C23—1782no—
611C23—1782no—
612C23—1782no—
613C23C22×C22⋊D8912yes—
614C23#41×D8912yes—
615C23C2×#1308357412yes—
616C23C2×#1308357412yes—
617C23C2×#1308357512yes—
618C23#1566805912yes—
619C23#1566806012yes—
620C23C24×D8911yescharacteristic
621Q8—232no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—28no—
635C2×C4—28no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—28no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—894no—
645C2×C4—3564no—
646C2×C4—3564no—
647C2×C4—3564no—
648C2×C4—3564no—
649C2×C4—3564no—
650C2×C4—3564no—
651C2×C4—1782no—
652C2×C4—1782no—
653C2×C4—1782no—
654C2×C4—1782no—
655C2×C4—1782no—
656C2×C4—1782no—
657C2×C4—1782no—
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—1788no—
670C2×C4—1782no—
671C2×C4—1782no—
672C2×C4C22×C22⋊D8914yes—
673C2×C4C22×C22⋊D8914yes—
674C2×C4C22×C22⋊D8914yes—
675C2×C4C2×#1308357414yes—
676C2×C4C2×#1308357414yes—
677C2×C4C2×#1308357514yes—
678C22—3562no—
679C22—3562no—
680C22—3562no—
681C22—3562no—
682C22—3562no—
683C22—3562no—
684C22—3562no—
685C22—7128no—
686C22#1915210914yes—
687C22#1915213514yes—
688C22#1915220614yes—
689C22#1915224714yes—
690C22#1915225914yes—
691C22#1915232014yes—
692C22#1915232114yes—
693C22C23×C22⋊D8911yescharacteristic
694C22C2×#41×D8911yescharacteristic
695C22C22×#1308357411yescharacteristic
696C22C22×#1308357411yescharacteristic
697C22C22×#1308357511yescharacteristic
698C22C2×#1566805911yescharacteristic
699C22C2×#1566806011yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—24no—
705C4—24no—
706C4—42no—
707C4—3562no—
708C4—3562no—
709C4—3562no—
710C4—3562no—
711C4—3562no—
712C4—3562no—
713C4—1784no—
714C2—7122no—
715C2#2602432718yesdirect product factor
716C2C2×#1915210911yescharacteristic
717C2C2×#1915213511yescharacteristic
718C2C2×#1915220611yescharacteristic
719C2C2×#1915224711yescharacteristic
720C2C2×#1915225911yescharacteristic
721C2C2×#1915232011yescharacteristic
722C2C2×#1915232111yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC22×C4×Q8×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC22×C4×Q8D89
hypocenterC89C2×#2469
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #26024327C2direct (N × H)
3. C2×#19151537C2semidirect
5. C2×#19151517C2semidirect
7. C2×#19151496C2semidirect
12. C2×#19151484C2semidirect
13. C2×#19151482C2semidirect
14. C2×#19151479C2semidirect
15. C2×C4×#13083553C2semidirect
16. C22×C4×Q8×C89C2semidirect
35. #19151537C22semidirect
37. #19151517C22semidirect
39. #19151496C22semidirect
44. #19151484C22semidirect
45. #19151482C22semidirect
46. #19151479C22semidirect
47. C4×#13083553C22semidirect
62. C2×C4×Q8×C89C22semidirect
353. C2×C89#2469semidirect
363. C22×C4×Q8D89semidirect
378. C89C2×#2469semidirect
383. C2×C4×Q8C2×D89semidirect
715. C2#26024327direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680072
#260243272
C2×#191515372
C2×#191515202
C2×#191515172
C2×#191515092
C2×#191514962
C2×#191514892
C2×#191514882
C2×#191514842
C2×#191514822
C2×#191514792
C2×C4×#130835532
C22×C4×Q8×C892
C2×#246989