Finite Group Databasebeta

← C2×#26023023 #36713302

Subgroups — C2×#26023023 #36713302

Order 22784.

2614 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15668006C211yesmaximal, characteristic
2#26023023C2116yesmaximal, direct product factor
3C2×#19151495C211yesmaximal, characteristic, complemented
4C2×#19151493C211yesmaximal, characteristic, complemented
5C2×#19151490C211yesmaximal, characteristic
6C2×#19151488C211yesmaximal, characteristic
7C2×#19151487C211yesmaximal, characteristic
8C2×#19151485C211yesmaximal, characteristic, complemented
9C2×#19151480C211yesmaximal, characteristic, complemented
10C2×#19151479C211yesmaximal, characteristic, complemented
11C2×#19151472C211yesmaximal, characteristic
12C2×#19151469C211yesmaximal, characteristic
13C2×C4×C4⋊Dic89C211yesmaximal, characteristic, complemented
14C2×#19151449C211yesmaximal, characteristic, complemented
15C2×#19151445C211yesmaximal, characteristic
16C2×#382×C89C211yesmaximal, characteristic, complemented
17C23×C4×D89C2211yescharacteristic
18C2×#15668006C4116yescomplemented
19C2×#15668006C2218yes—
20C22×C4⋊Dic89C2211yescharacteristic
21C22×C4⋊Dic89C2211yescharacteristic
22C22×#13083553C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×#13083551C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35C22×C4×Dic89C2211yescharacteristic
36C22×C4×Dic89C2211yescharacteristic
37C22×C4×Dic89C2211yescharacteristic
38C22×C4×Dic89C2211yescharacteristic
39#19151495C2218yescomplemented
40#19151493C2218yescomplemented
41#19151490C2218yes—
42#19151488C2218yes—
43#19151487C2218yes—
44#19151485C2218yescomplemented
45#19151480C2218yescomplemented
46#19151479C2218yescomplemented
47#19151472C2218yes—
48#19151469C2218yes—
49C4×C4⋊Dic89C2218yescomplemented
50#19151449C2218yescomplemented
51#19151445C2218yes—
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#382×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—42no—
78C22×C4×D89—42no—
79C22×C4×D89C2314yes—
80#15668006C2×C4164yescomplemented
81C2×C4⋊Dic89—24no—
82C2×C4⋊Dic89—24no—
83C2×C4⋊Dic89C2314yes—
84C2×C4⋊Dic89C2314yes—
85C2×#13083553—24no—
86C2×#13083553—42no—
87C2×#13083553—42no—
88C2×#13083553C2×C418yescomplemented
89C2×#13083553C2×C418yescomplemented
90C2×#13083553C2×C418yescomplemented
91C2×#13083553C2314yes—
92C2×#13083553C2314yes—
93C2×#13083553C2314yes—
94C2×#13083553C2314yes—
95C2×#13083553C2314yes—
96C2×#13083553C2314yes—
97C2×#13083551—24no—
98C2×#13083551—42no—
99C2×#13083551—42no—
100C2×#13083551C2×C418yes—
101C2×#13083551C2×C418yes—
102C2×#13083551C2×C418yes—
103C2×#13083551C2314yes—
104C2×#13083551C2314yes—
105C2×#13083551C2314yes—
106C2×#13083551C2314yes—
107C2×#13083551C2314yes—
108C2×#13083551C2314yes—
109C2×C4×Dic89—24no—
110C2×C4×Dic89—42no—
111C2×C4×Dic89—42no—
112C2×C4×Dic89—42no—
113C2×C4×Dic89—42no—
114C2×C4×Dic89C2314yes—
115C2×C4×Dic89C2314yes—
116C2×C4×Dic89C2314yes—
117C2×C4×Dic89C2314yes—
118C2×C4×Dic89C2314yes—
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×C89—42no—
136C2×C4⋊C4×C89C2314yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C42×C89C2×C418yescomplemented
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×D89—22no—
149C23×D89—22no—
150C23×D89C22×C414yes—
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×Dic89C22×C414yes—
169C22×Dic89C22×C414yes—
170C22×Dic89C22×C414yes—
171C22×Dic89#4114yes—
172C22×Dic89#4114yes—
173C22×Dic89C2412yes—
174C22×Dic89C2412yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C2×C4×D89—28no—
181C2×C4×D89—44no—
182C2×C4×D89—44no—
183C2×C4×D89—416no—
184C4⋊Dic89—28no—
185C4⋊Dic89—28no—
186#13083553—28no—
187#13083553—44no—
188#13083553—44no—
189#13083553C22×C4116yescomplemented
190#13083553C22×C4116yescomplemented
191#13083553C22×C4116yescomplemented
192#13083551—28no—
193#13083551—44no—
194#13083551—44no—
195#13083551C22×C4116yes—
196#13083551C22×C4116yes—
197#13083551C22×C4116yes—
198C4×Dic89—28no—
199C4×Dic89—44no—
200C4×Dic89—44no—
201C4×Dic89—44no—
202C4×Dic89—44no—
203C24×C89C2411yescharacteristic
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×C89—22no—
219C22×C4×C89—22no—
220C22×C4×C89—22no—
221C22×C4×C89—22no—
222C22×C4×C89C22×C414yes—
223C22×C4×C89C22×C414yes—
224C22×C4×C89C22×C414yes—
225C22×C4×C89C2412yes—
226C22×C4×C89C2412yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C22×C4×C89C2412yes—
231C22×C4×C89C2412yes—
232C4⋊C4×C89—44no—
233C4⋊C4×C89—44no—
234C42×C89C22×C4116yescomplemented
235C23×C89C23×C412yes—
236C23×C89C2×#4112yes—
237C23×C89C2×#4112yes—
238C23×C89H(5,𝔽2)12yes—
239C23×C89H(5,𝔽2)12yes—
240C23×C892−1+412yes—
241C23×C892−1+412yes—
242C23×C89C2511yescharacteristic
243C22×D89—28no—
244C22×D89—28no—
245C22×D89—28no—
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×D89C23×C414yes—
257C2×C4×C89—28no—
258C2×C4×C89—28no—
259C2×C4×C89—28no—
260C2×C4×C89—22no—
261C2×C4×C89—22no—
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—44no—
279C2×C4×C89—44no—
280C2×C4×C89—44no—
281C2×C4×C89—44no—
282C2×C4×C89C23×C414yes—
283C2×C4×C89C23×C414yes—
284C2×C4×C89C23×C414yes—
285C2×Dic89—28no—
286C2×Dic89—28no—
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—44no—
307C2×Dic89—44no—
308C2×Dic89C23×C414yes—
309C2×Dic89C23×C414yes—
310C2×Dic89C23×C414yes—
311C2×Dic89C2×#4114yes—
312C2×Dic89C2×#4114yes—
313C4×D89—416no—
314C22×C89C4×#4114yes—
315C22×C89#52014yes—
316C22×C89#52014yes—
317C22×C89#53814yes—
318C22×C89#53914yes—
319C22×C89#54114yes—
320C22×C89#54214yes—
321C22×C89C24×C411yescharacteristic
322C22×C89C22×#4111yescharacteristic
323C22×C89C22×#4111yescharacteristic
324C22×C89C2×H(5,𝔽2)11yescharacteristic
325C22×C89C2×H(5,𝔽2)11yescharacteristic
326C22×C89C2×2−1+411yescharacteristic
327C22×C89C2×2−1+411yescharacteristic
328C2×D89—24no—
329C2×D89—24no—
330C2×D89—24no—
331C2×D89—416no—
332C2×D89—42no—
333C2×D89—42no—
334C2×D89—42no—
335C2×D89—42no—
336C4×C89—24no—
337C4×C89—24no—
338C4×C89—24no—
339C4×C89—42no—
340C4×C89—42no—
341C4×C89—42no—
342C4×C89—42no—
343Dic89—24no—
344Dic89—24no—
345Dic89—24no—
346Dic89—24no—
347Dic89—24no—
348Dic89—42no—
349Dic89—42no—
350C2×#2334—891nomaximal, Sylow
351C2×C89#233418yescomplemented
352C2×C89C2×C4×#4111yescharacteristic
353C2×C89C2×#52011yescharacteristic
354C2×C89C2×#52011yescharacteristic
355C2×C89C2×#53811yescharacteristic
356C2×C89C2×#53911yescharacteristic
357C2×C89C2×#54111yescharacteristic
358C2×C89C2×#54211yescharacteristic
359D89—44no—
360C22×#126—891no—
361#2334—8916no—
362C2×#389—891no—
363C2×#389—891no—
364C2×#388—891no—
365C2×#388—891no—
366C2×#388—891no—
367C2×#387—891no—
368C2×#387—891no—
369C2×#387—891no—
370C2×#385—891no—
371C2×#385—891no—
372C2×#382D8911yescharacteristic, complemented
373C2×C4×C4⋊C4—891no—
374C2×C4×C4⋊C4—891no—
375C2×C4×C22⋊C4—891no—
376C89C2×#233411yescharacteristic, complemented, Sylow
377C24×C4—891no—
378C2×#126—8916no—
379C2×#126—898no—
380C22×C4⋊C4—891no—
381C22×C4⋊C4—891no—
382C22×C4⋊C4—891no—
383C22×C4⋊C4—891no—
384C22×C4⋊C4—891no—
385C22×C4⋊C4—891no—
386C22×C4⋊C4—891no—
387C22×C4⋊C4—891no—
388C22×C4⋊C4C2×D8911yescharacteristic
389C22×C4⋊C4C2×D8911yescharacteristic
390C22×C22⋊C4—891no—
391C22×C22⋊C4—891no—
392C22×C22⋊C4—891no—
393C22×C22⋊C4—891no—
394C22×C22⋊C4—891no—
395C22×C22⋊C4—891no—
396C22×C42—891no—
397C22×C42—891no—
398C22×C42—891no—
399C22×C42—891no—
400C22×C42—891no—
401C22×C42C2×D8911yescharacteristic
402#389—898no—
403#389—898no—
404#388—898no—
405#388—898no—
406#388—898no—
407#387—898no—
408#387—898no—
409#387—898no—
410#385—898no—
411#385—898no—
412#382C2×D8918yescomplemented
413C4×C4⋊C4—898no—
414C4×C4⋊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×#95C2×D8911yescharacteristic
425C2×#95C2×D8911yescharacteristic
426C2×#95C2×D8911yescharacteristic
427C2×#95C2×D8911yescharacteristic
428C25—891no—
429C23×C4—891no—
430C23×C4—891no—
431C23×C4—891no—
432C23×C4—891no—
433C23×C4—891no—
434C23×C4—891no—
435C23×C4—891no—
436C23×C4—894no—
437C23×C4—3562no—
438C23×C4—3562no—
439C23×C4—1784no—
440C23×C4C22×D8911yescharacteristic
441C23×C4C22×D8911yescharacteristic
442C23×C4C22×D8911yescharacteristic
443C23×C4C22×D8911yescharacteristic
444C23×C4C22×D8911yescharacteristic
445C23×C4C22×D8911yescharacteristic
446C23×C4C22×D8911yescharacteristic
447#126—8964no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—898no—
451C2×C4⋊C4—898no—
452C2×C4⋊C4—898no—
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—3562no—
462C2×C4⋊C4—3562no—
463C2×C4⋊C4—1784no—
464C2×C4⋊C4—1784no—
465C2×C4⋊C4—1784no—
466C2×C4⋊C4C22×D8914yes—
467C2×C4⋊C4C22×D8914yes—
468C2×C22⋊C4—898no—
469C2×C22⋊C4—898no—
470C2×C22⋊C4—898no—
471C2×C22⋊C4—894no—
472C2×C22⋊C4—894no—
473C2×C22⋊C4—894no—
474C2×C22⋊C4—894no—
475C2×C22⋊C4—894no—
476C2×C22⋊C4—894no—
477C2×C22⋊C4—3562no—
478C2×C22⋊C4—3562no—
479C2×C22⋊C4—1784no—
480C2×C42—894no—
481C2×C42—894no—
482C2×C42—894no—
483C2×C42—894no—
484C2×C42—894no—
485C2×C42—3562no—
486C2×C42—3562no—
487C2×C42—3562no—
488C2×C42—3562no—
489C2×C42—1784no—
490C2×C42C4×D8918yescomplemented
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#95C22×D8914yes—
501#95C22×D8914yes—
502#95C22×D8914yes—
503#95C22×D8914yes—
504C24—894no—
505C24—892no—
506C24—1782no—
507C24—1782no—
508C24—1782no—
509C24—1782no—
510C24—1782no—
511C24—1782no—
512C24C23×D8911yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
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—894no—
532C22×C4—894no—
533C22×C4—894no—
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—3564no—
544C22×C4—3564no—
545C22×C4—35616no—
546C22×C4—1788no—
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×C4C2×C4×D8914yes—
564C22×C4C2×C4×D8914yes—
565C22×C4C2×C4×D8914yes—
566C22×C4C23×D8912yes—
567C22×C4C23×D8912yes—
568C22×C4C23×D8912yes—
569C22×C4C23×D8912yes—
570C22×C4C23×D8912yes—
571C22×C4C23×D8912yes—
572C22×C4C23×D8912yes—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—8916no—
576C4⋊C4—8916no—
577C4⋊C4—8916no—
578C4⋊C4—3564no—
579C4⋊C4—3564no—
580C4⋊C4—1788no—
581C4⋊C4—1788no—
582C4⋊C4—1788no—
583C22⋊C4—8916no—
584C22⋊C4—8916no—
585C22⋊C4—8916no—
586C22⋊C4—3564no—
587C22⋊C4—3564no—
588C22⋊C4—1788no—
589C42—3564no—
590C42—3564no—
591C42—3564no—
592C42—3564no—
593C42—1788no—
594C42C2×C4×D89116yescomplemented
595C23—894no—
596C23—3564no—
597C23—3564no—
598C23—3564no—
599C23—3564no—
600C23—1782no—
601C23—1782no—
602C23—1782no—
603C23—1782no—
604C23—1782no—
605C23—1782no—
606C23—1788no—
607C23—1788no—
608C23—1788no—
609C23C22×C4×D8912yes—
610C23#41×D8912yes—
611C23#41×D8912yes—
612C23#1566805712yes—
613C23#1566805812yes—
614C23#1566805912yes—
615C23#1566806012yes—
616C23C24×D8911yescharacteristic
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
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—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—894no—
643C2×C4—894no—
644C2×C4—894no—
645C2×C4—894no—
646C2×C4—894no—
647C2×C4—35616no—
648C2×C4—3564no—
649C2×C4—3564no—
650C2×C4—1782no—
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—1788no—
667C2×C4—1788no—
668C2×C4—1788no—
669C2×C4—1788no—
670C2×C4—1788no—
671C2×C4C22×C4×D8914yes—
672C2×C4C22×C4×D8914yes—
673C2×C4C22×C4×D8914yes—
674C22—35616no—
675C22—3562no—
676C22—3562no—
677C22—3562no—
678C22—3562no—
679C22—1784no—
680C22—1784no—
681C22—1784no—
682C22#1915206614yes—
683C22#1915207814yes—
684C22#1915207914yes—
685C22#1915218214yes—
686C22#1915219614yes—
687C22#1915220714yes—
688C22#1915221214yes—
689C22C23×C4×D8911yescharacteristic
690C22C2×#41×D8911yescharacteristic
691C22C2×#41×D8911yescharacteristic
692C22C2×#1566805711yescharacteristic
693C22C2×#1566805811yescharacteristic
694C22C2×#1566805911yescharacteristic
695C22C2×#1566806011yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3562no—
704C4—3562no—
705C4—1784no—
706C4—1784no—
707C4—1784no—
708C4—1784no—
709C4—1784no—
710C2—3564no—
711C2#2602302318yesdirect product factor
712C2C2×#1915206611yescharacteristic
713C2C2×#1915207811yescharacteristic
714C2C2×#1915207911yescharacteristic
715C2C2×#1915218211yescharacteristic
716C2C2×#1915219611yescharacteristic
717C2C2×#1915220711yescharacteristic
718C2C2×#1915221211yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#382×C89C2
socleC24×C89C24
prime radicalC24×D89C23
cosocleC23×C89C25
hypercenterC2×#382D89
hypocenterC89C2×#2334
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #26023023C2direct (N × H)
3. C2×#19151495C2semidirect
4. C2×#19151493C2semidirect
8. C2×#19151485C2semidirect
9. C2×#19151480C2semidirect
10. C2×#19151479C2semidirect
13. C2×C4×C4⋊Dic89C2semidirect
14. C2×#19151449C2semidirect
16. C2×#382×C89C2semidirect
18. C2×#15668006C4semidirect
39. #19151495C22semidirect
40. #19151493C22semidirect
44. #19151485C22semidirect
45. #19151480C22semidirect
46. #19151479C22semidirect
49. C4×C4⋊Dic89C22semidirect
50. #19151449C22semidirect
63. #382×C89C22semidirect
80. #15668006C2×C4semidirect
88. C2×#13083553C2×C4semidirect
89. C2×#13083553C2×C4semidirect
90. C2×#13083553C2×C4semidirect
138. C2×C42×C89C2×C4semidirect
189. #13083553C22×C4semidirect
190. #13083553C22×C4semidirect
191. #13083553C22×C4semidirect
234. C42×C89C22×C4semidirect
351. C2×C89#2334semidirect
372. C2×#382D89semidirect
376. C89C2×#2334semidirect
412. #382C2×D89semidirect
490. C2×C42C4×D89semidirect
594. C42C2×C4×D89semidirect
711. C2#26023023direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680062
#260230232
C2×#191514952
C2×#191514932
C2×#191514902
C2×#191514882
C2×#191514872
C2×#191514852
C2×#191514802
C2×#191514792
C2×#191514722
C2×#191514692
C2×C4×C4⋊Dic892
C2×#191514492
C2×#191514452
C2×#382×C892
C2×#233489