Finite Group Databasebeta

← C2×#26024421 #36722879

Subgroups — C2×#26024421 #36722879

Order 22784.

2638 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×#15668002C211yesmaximal, characteristic, complemented
2C22×#15667970C211yesmaximal, characteristic
3#26024421C2116yesmaximal, direct product factor
4C2×#19151538C211yesmaximal, characteristic, complemented
5C2×#19151530C211yesmaximal, characteristic, complemented
6C2×#19151525C211yesmaximal, characteristic
7C2×#19151520C211yesmaximal, characteristic
8C2×#19151497C211yesmaximal, characteristic, complemented
9C2×#19151490C211yesmaximal, characteristic
10C2×#19151489C211yesmaximal, characteristic
11C2×#19151483C211yesmaximal, characteristic, complemented
12C2×#19151483C211yesmaximal, characteristic, complemented
13C2×#19151472C211yesmaximal, characteristic
14C2×#19151472C211yesmaximal, characteristic
15C2×C4×C4⋊Dic89C211yesmaximal, characteristic, complemented
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×C4×D89C2211yescharacteristic
18C2×#15668002—28no—
19C2×#15668002C2218yescomplemented
20C2×#15667970—28no—
21C2×#15667970C2218yes—
22C22×C4⋊Dic89C2211yescharacteristic
23C22×C4⋊Dic89C2211yescharacteristic
24C22×C4⋊Dic89C2211yescharacteristic
25C22×C4⋊Dic89C2211yescharacteristic
26C22×C4⋊Dic89C2211yescharacteristic
27C22×C4⋊Dic89C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×#13083551C2211yescharacteristic
34C22×#13083551C2211yescharacteristic
35C22×#13083551C2211yescharacteristic
36C22×#13083551C2211yescharacteristic
37C22×#13083551C2211yescharacteristic
38C22×C4×Dic89C2211yescharacteristic
39C22×C4×Dic89C2211yescharacteristic
40C22×C4×Dic89C2211yescharacteristic
41#19151538C2218yescomplemented
42#19151530C2218yescomplemented
43#19151525C2218yes—
44#19151520C2218yes—
45#19151497C2218yescomplemented
46#19151490C2218yes—
47#19151489C2218yes—
48#19151483C2218yescomplemented
49#19151483C2218yescomplemented
50#19151472C2218yes—
51#19151472C2218yes—
52C4×C4⋊Dic89C2218yescomplemented
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C22×C4⋊C4×C89C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63C22×C42×C89C2211yescharacteristic
64#387×C89C2218yescomplemented
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C2×#95×C89C2211yescharacteristic
69C24×D89C2311yescharacteristic
70C23×Dic89C2311yescharacteristic
71C23×Dic89C2311yescharacteristic
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C22×C4×D89—24no—
78C22×C4×D89—24no—
79C22×C4×D89—24no—
80C22×C4×D89C2314yes—
81#15668002—232no—
82#15667970—232no—
83C2×C4⋊Dic89—24no—
84C2×C4⋊Dic89—24no—
85C2×C4⋊Dic89—24no—
86C2×C4⋊Dic89—24no—
87C2×C4⋊Dic89—24no—
88C2×C4⋊Dic89—24no—
89C2×C4⋊Dic89C2314yes—
90C2×C4⋊Dic89C2314yes—
91C2×C4⋊Dic89C2314yes—
92C2×C4⋊Dic89C2314yes—
93C2×C4⋊Dic89C2314yes—
94C2×C4⋊Dic89C2314yes—
95C2×#13083553—24no—
96C2×#13083553—24no—
97C2×#13083553—24no—
98C2×#13083553—24no—
99C2×#13083553C2314yes—
100C2×#13083553C2314yes—
101C2×#13083553C2314yes—
102C2×#13083553C2314yes—
103C2×#13083551—24no—
104C2×#13083551—24no—
105C2×#13083551—24no—
106C2×#13083551—24no—
107C2×#13083551—24no—
108C2×#13083551—24no—
109C2×#13083551C2314yes—
110C2×#13083551C2314yes—
111C2×#13083551C2314yes—
112C2×#13083551C2314yes—
113C2×#13083551C2314yes—
114C2×#13083551C2314yes—
115C2×C4×Dic89—24no—
116C2×C4×Dic89—24no—
117C2×C4×Dic89—24no—
118C2×C4×Dic89C2314yes—
119C2×C4×Dic89C2314yes—
120C2×C4×Dic89C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123#15667919C2314yes—
124#15667919C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C23×C4×C89C2311yescharacteristic
132C23×C4×C89C2311yescharacteristic
133C23×C4×C89C2311yescharacteristic
134C23×C4×C89C2311yescharacteristic
135C23×C4×C89C2311yescharacteristic
136C2×C4⋊C4×C89—24no—
137C2×C4⋊C4×C89D418yes—
138C2×C4⋊C4×C89C2314yes—
139C2×C4⋊C4×C89C2314yes—
140C2×C42×C89—24no—
141C2×C42×C89C2314yes—
142#95×C89C2314yes—
143#95×C89C2314yes—
144#95×C89C2314yes—
145#95×C89C2314yes—
146C23×D89—22no—
147C23×D89—22no—
148C23×D89—22no—
149C23×D89—22no—
150C23×D89—22no—
151C23×D89—22no—
152C23×D89#4114yes—
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#4114yes—
174C22×Dic89#4114yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C22×Dic89C2412yes—
181C22×Dic89C2412yes—
182C2×C4×D89—232no—
183C2×C4×D89—28no—
184C2×C4×D89—28no—
185C2×C4×D89—28no—
186C4⋊Dic89—28no—
187C4⋊Dic89—28no—
188C4⋊Dic89—28no—
189C4⋊Dic89—28no—
190C4⋊Dic89—28no—
191C4⋊Dic89—28no—
192#13083553—28no—
193#13083553—28no—
194#13083553—28no—
195#13083553—28no—
196#13083551—28no—
197#13083551—28no—
198#13083551—28no—
199#13083551—28no—
200#13083551—28no—
201#13083551—28no—
202C4×Dic89—28no—
203C4×Dic89—28no—
204C4×Dic89—28no—
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×C89C2×D414yes—
224C22×C4×C89C2×D414yes—
225C22×C4×C89C2×D414yes—
226C22×C4×C89#4114yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C22×C4×C89C2412yes—
231C22×C4×C89C2412yes—
232C22×C4×C89C2412yes—
233C22×C4×C89C2412yes—
234C4⋊C4×C89—28no—
235C4⋊C4×C89C2×D4116yes—
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—28no—
246C22×D89—28no—
247C22×D89—28no—
248C22×D89—22no—
249C22×D89—22no—
250C22×D89—22no—
251C22×D89—22no—
252C22×D89—22no—
253C22×D89—22no—
254C22×D89—44no—
255C22×D89—44no—
256C22×D89—44no—
257C22×D89—44no—
258C22×D89C2×#4114yes—
259C2×C4×C89—28no—
260C2×C4×C89—28no—
261C2×C4×C89—28no—
262C2×C4×C89—28no—
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×C89C22×D414yes—
284C2×C4×C89C22×D414yes—
285C2×C4×C89C22×D414yes—
286C2×C4×C89C2×#4114yes—
287C2×Dic89—28no—
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—44no—
309C2×Dic89—44no—
310C2×Dic89—44no—
311C2×Dic89—44no—
312C2×Dic89—44no—
313C2×Dic89C2×#4114yes—
314C2×Dic89C2×#4114yes—
315C4×D89—232no—
316C22×C89#52514yes—
317C22×C89#52914yes—
318C22×C89#54114yes—
319C22×C89#54714yes—
320C22×C89#54814yes—
321C22×C89#55214yes—
322C22×C89#55214yes—
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—24no—
331C2×D89—24no—
332C2×D89—24no—
333C2×D89—42no—
334C2×D89—42no—
335C2×D89—42no—
336C2×D89—42no—
337C2×D89—416no—
338C4×C89—24no—
339C4×C89—24no—
340C4×C89—24no—
341C4×C89—24no—
342C4×C89—42no—
343C4×C89—42no—
344C4×C89—42no—
345Dic89—24no—
346Dic89—24no—
347Dic89—42no—
348Dic89—42no—
349Dic89—42no—
350Dic89—42no—
351Dic89—42no—
352C2×#2475—891nomaximal, Sylow
353C2×C89#247518yescomplemented
354C2×C89C2×#52511yescharacteristic
355C2×C89C2×#52911yescharacteristic
356C2×C89C2×#54111yescharacteristic
357C2×C89C2×#54711yescharacteristic
358C2×C89C2×#54811yescharacteristic
359C2×C89C2×#55211yescharacteristic
360C2×C89C2×#55211yescharacteristic
361D89—44no—
362C22×#125—891no—
363C22×#117—891no—
364#2475—8916no—
365C2×#400—891no—
366C2×#398—891no—
367C2×#397—891no—
368C2×#396—891no—
369C2×#389—891no—
370C2×#388—891no—
371C2×#388—891no—
372C2×#387—891no—
373C2×#387—891no—
374C2×#387D8911yescharacteristic, complemented
375C2×#385—891no—
376C2×#385—891no—
377C2×C4×C4⋊C4—891no—
378C89C2×#247511yescharacteristic, complemented, Sylow
379C24×C4—891no—
380C2×#125—898no—
381C2×#125—1788no—
382C2×#117—898no—
383C2×#117—1788no—
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⋊C4—891no—
392C22×C4⋊C4—891no—
393C22×C4⋊C4—891no—
394C22×C4⋊C4C2×D8911yescharacteristic
395C22×C4⋊C4C2×D8911yescharacteristic
396C22×C22⋊C4—891no—
397C22×C22⋊C4—891no—
398C22×C22⋊C4—891no—
399C22×C22⋊C4—891no—
400C22×C22⋊C4—891no—
401C22×C22⋊C4—891no—
402C22×C42—891no—
403C22×C42—891no—
404C22×C42—891no—
405C22×C42C2×D8911yescharacteristic
406#400—898no—
407#398—898no—
408#397—898no—
409#396—898no—
410#389—898no—
411#388—898no—
412#388—898no—
413#387—898no—
414#387—898no—
415#387C2×D8918yescomplemented
416#385—898no—
417#385—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×#95C2×D8911yescharacteristic
428C2×#95C2×D8911yescharacteristic
429C2×#95C2×D8911yescharacteristic
430C2×#95C2×D8911yescharacteristic
431C25—891no—
432C23×C4—891no—
433C23×C4—891no—
434C23×C4—891no—
435C23×C4—891no—
436C23×C4—891no—
437C23×C4—891no—
438C23×C4—891no—
439C23×C4—894no—
440C23×C4—1784no—
441C23×C4—1784no—
442C23×C4—1784no—
443C23×C4C22×D8911yescharacteristic
444C23×C4C22×D8911yescharacteristic
445C23×C4C22×D8911yescharacteristic
446C23×C4C22×D8911yescharacteristic
447C23×C4C22×D8911yescharacteristic
448C23×C4C22×D8911yescharacteristic
449C23×C4C22×D8911yescharacteristic
450#125—17832no—
451#117—17832no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—894no—
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—894no—
462C2×C4⋊C4—894no—
463C2×C4⋊C4—1784no—
464C2×C4⋊C4—1784no—
465C2×C4⋊C4—1784no—
466C2×C4⋊C4—1784no—
467C2×C4⋊C4—1784no—
468C2×C4⋊C4—1784no—
469C2×C4⋊C4—1784no—
470C2×C4⋊C4—1784no—
471C2×C4⋊C4—1784no—
472C2×C4⋊C4—1784no—
473C2×C4⋊C4D35618yes—
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—894no—
481C2×C22⋊C4—894no—
482C2×C22⋊C4—1784no—
483C2×C22⋊C4—1784no—
484C2×C22⋊C4—1784no—
485C2×C22⋊C4—1784no—
486C2×C22⋊C4—1784no—
487C2×C22⋊C4—1784no—
488C2×C42—24no—
489C2×C42—894no—
490C2×C42—894no—
491C2×C42—894no—
492C2×C42—1784no—
493C2×C42—1784no—
494C2×C42—1784no—
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#95C22×D8914yes—
505#95C22×D8914yes—
506#95C22×D8914yes—
507#95C22×D8914yes—
508C24—894no—
509C24—892no—
510C24—1782no—
511C24—1782no—
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—894no—
535C22×C4—894no—
536C22×C4—892no—
537C22×C4—892no—
538C22×C4—892no—
539C22×C4—892no—
540C22×C4—892no—
541C22×C4—892no—
542C22×C4—892no—
543C22×C4—1788no—
544C22×C4—1788no—
545C22×C4—17832no—
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×C4—1782no—
565C22×C4—1788no—
566C22×C4C2×D35614yes—
567C22×C4C2×D35614yes—
568C22×C4C2×D35614yes—
569C22×C4#1308357314yes—
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—1788no—
579C4⋊C4—1788no—
580C4⋊C4—1788no—
581C4⋊C4—1788no—
582C4⋊C4—1788no—
583C4⋊C4—1788no—
584C4⋊C4—1788no—
585C4⋊C4—1788no—
586C4⋊C4—1788no—
587C4⋊C4—1788no—
588C4⋊C4C2×D356116yes—
589C22⋊C4—1788no—
590C22⋊C4—1788no—
591C22⋊C4—1788no—
592C22⋊C4—1788no—
593C22⋊C4—1788no—
594C22⋊C4—1788no—
595C42—28no—
596C42—1788no—
597C42—1788no—
598C42—1788no—
599C23—894no—
600C23—3564no—
601C23—3564no—
602C23—3564no—
603C23—3564no—
604C23—1782no—
605C23—1782no—
606C23—1782no—
607C23—1782no—
608C23—1782no—
609C23—1782no—
610C23—1788no—
611C23—1788no—
612C23—1788no—
613C23C22×D35612yes—
614C23#41×D8912yes—
615C23#41×D8912yes—
616C23#41×D8912yes—
617C23C2×#1308357312yes—
618C23#1566805912yes—
619C23#1566806012yes—
620C23C24×D8911yescharacteristic
621C2×C4—22no—
622C2×C4—22no—
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—28no—
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—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—894no—
646C2×C4—894no—
647C2×C4—3564no—
648C2×C4—3564no—
649C2×C4—3564no—
650C2×C4—3564no—
651C2×C4—3564no—
652C2×C4—17832no—
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—1782no—
670C2×C4—1782no—
671C2×C4—1782no—
672C2×C4—1788no—
673C2×C4—1788no—
674C2×C4C22×D35614yes—
675C2×C4C22×D35614yes—
676C2×C4C22×D35614yes—
677C2×C4C2×#1308357314yes—
678C22—3562no—
679C22—3562no—
680C22—3562no—
681C22—3562no—
682C22—35616no—
683C22—1784no—
684C22—1784no—
685C22—1784no—
686C22#1915211014yes—
687C22#1915212514yes—
688C22#1915220714yes—
689C22#1915225214yes—
690C22#1915226014yes—
691C22#1915228214yes—
692C22#1915228414yes—
693C22C23×D35611yescharacteristic
694C22C2×#41×D8911yescharacteristic
695C22C2×#41×D8911yescharacteristic
696C22C2×#41×D8911yescharacteristic
697C22C22×#1308357311yescharacteristic
698C22C2×#1566805911yescharacteristic
699C22C2×#1566806011yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3562no—
708C4—3562no—
709C4—3562no—
710C4—3562no—
711C4—3562no—
712C4—1784no—
713C4—1784no—
714C2—3564no—
715C2#2602442118yesdirect product factor
716C2C2×#1915211011yescharacteristic
717C2C2×#1915212511yescharacteristic
718C2C2×#1915220711yescharacteristic
719C2C2×#1915225211yescharacteristic
720C2C2×#1915226011yescharacteristic
721C2C2×#1915228211yescharacteristic
722C2C2×#1915228411yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#387D89
hypocenterC89C2×#2475
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#15668002C2semidirect
3. #26024421C2direct (N × H)
4. C2×#19151538C2semidirect
5. C2×#19151530C2semidirect
8. C2×#19151497C2semidirect
11. C2×#19151483C2semidirect
12. C2×#19151483C2semidirect
15. C2×C4×C4⋊Dic89C2semidirect
16. C2×#387×C89C2semidirect
19. C2×#15668002C22semidirect
41. #19151538C22semidirect
42. #19151530C22semidirect
45. #19151497C22semidirect
48. #19151483C22semidirect
49. #19151483C22semidirect
52. C4×C4⋊Dic89C22semidirect
64. #387×C89C22semidirect
353. C2×C89#2475semidirect
374. C2×#387D89semidirect
378. C89C2×#2475semidirect
415. #387C2×D89semidirect
715. C2#26024421direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680022
C22×#156679702
#260244212
C2×#191515382
C2×#191515302
C2×#191515252
C2×#191515202
C2×#191514972
C2×#191514902
C2×#191514892
C2×#191514832
C2×#191514722
C2×C4×C4⋊Dic892
C2×#387×C892
C2×#247589