Finite Group Databasebeta

← C2×#26025708 #36724734

Subgroups — C2×#26025708 #36724734

Order 22784.

2334 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
1#26025708C2116yesmaximal, direct product factor
2C2×#19151537C211yesmaximal, characteristic, complemented
3C2×#19151535C211yesmaximal, characteristic
4C2×#19151531C211yesmaximal, characteristic, complemented
5C2×#19151511C211yesmaximal, characteristic
6C2×#19151504C211yesmaximal, characteristic, complemented
7C2×#19151502C211yesmaximal, characteristic, complemented
8C2×#19151488C211yesmaximal, characteristic
9C2×#19151488C211yesmaximal, characteristic
10C2×#19151484C211yesmaximal, characteristic, complemented
11C2×#19151483C211yesmaximal, characteristic, complemented
12C2×#19151469C211yesmaximal, characteristic
13C2×#19151469C211yesmaximal, characteristic
14C2×C4⋊C4×Dic89C211yesmaximal, characteristic, complemented
15C2×C4×#13083551C211yesmaximal, characteristic
16C2×#389×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C22×C4⋊Dic89C2211yescharacteristic
20C22×C4⋊Dic89C2211yescharacteristic
21C22×C4⋊Dic89C2211yescharacteristic
22C22×#13083553C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083551C2211yescharacteristic
25C22×#13083551C2211yescharacteristic
26C22×#13083551C2211yescharacteristic
27C22×#13083551C2211yescharacteristic
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×C4×Dic89C2211yescharacteristic
31C22×C4×Dic89C2211yescharacteristic
32C22×C4×Dic89C2211yescharacteristic
33#19151537C2218yescomplemented
34#19151535C2218yes—
35#19151531C2218yescomplemented
36#19151511C2218yes—
37#19151504C2218yescomplemented
38#19151502C2218yescomplemented
39#19151488C2218yes—
40#19151488C2218yes—
41#19151484C2218yescomplemented
42#19151483C2218yescomplemented
43#19151469C2218yes—
44#19151469C2218yes—
45C4⋊C4×Dic89C2218yescomplemented
46C4×#13083551C2218yes—
47C2×#15667919C2211yescharacteristic
48C2×#15667919C2211yescharacteristic
49C2×#15667919C2211yescharacteristic
50C2×#15667919C2211yescharacteristic
51C2×#15667919C2211yescharacteristic
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C22×C4⋊C4×C89C2211yescharacteristic
60C22×C4⋊C4×C89C2211yescharacteristic
61C22×C4⋊C4×C89C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63C22×C42×C89C2211yescharacteristic
64#389×C89C2218yescomplemented
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C24×D89C2311yescharacteristic
68C22×Dic178—24no—
69C22×Dic178—24no—
70C22×Dic178—42no—
71C22×Dic178C2314yes—
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C22×C4×D89—24no—
80C22×C4×D89—42no—
81C22×C4×D89—42no—
82C22×C4×D89C2314yes—
83C2×C4⋊Dic89—24no—
84C2×C4⋊Dic89—24no—
85C2×C4⋊Dic89—42no—
86C2×C4⋊Dic89C2314yes—
87C2×C4⋊Dic89C2314yes—
88C2×C4⋊Dic89C2314yes—
89C2×#13083553—42no—
90C2×#13083553—42no—
91C2×#13083553C2314yes—
92C2×#13083553C2314yes—
93C2×#13083551—24no—
94C2×#13083551—24no—
95C2×#13083551—24no—
96C2×#13083551—42no—
97C2×#13083551—42no—
98C2×#13083551Q818yescomplemented
99C2×#13083551C2314yes—
100C2×#13083551C2314yes—
101C2×#13083551C2314yes—
102C2×#13083551C2314yes—
103C2×#13083551C2314yes—
104C2×#13083551C2314yes—
105C2×C4×Dic89—24no—
106C2×C4×Dic89—42no—
107C2×C4×Dic89—42no—
108C2×C4×Dic89C2314yes—
109C2×C4×Dic89C2314yes—
110C2×C4×Dic89C2314yes—
111#15667919C2314yes—
112#15667919C2314yes—
113#15667919C2314yes—
114#15667919C2314yes—
115#15667919C2314yes—
116#15667919C2314yes—
117#15667919C2314yes—
118#15667919C2314yes—
119#15667919C2314yes—
120#15667919C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123C23×C4×C89C2311yescharacteristic
124C23×C4×C89C2311yescharacteristic
125C23×C4×C89C2311yescharacteristic
126C23×C4×C89C2311yescharacteristic
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C2×C4⋊C4×C89—24no—
131C2×C4⋊C4×C89—24no—
132C2×C4⋊C4×C89—24no—
133C2×C4⋊C4×C89—42no—
134C2×C4⋊C4×C89C2314yes—
135C2×C4⋊C4×C89C2314yes—
136C2×C4⋊C4×C89C2314yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C42×C89—42no—
139C2×C42×C89C2314yes—
140#95×C89C2314yes—
141#95×C89C2314yes—
142C23×D89—22no—
143C23×D89—22no—
144C23×D89—22no—
145C23×D89—22no—
146C23×D89—22no—
147C23×D89—22no—
148C23×D89C2×Q814yes—
149C23×D89C2412yes—
150C2×Dic178—28no—
151C2×Dic178—28no—
152C2×Dic178—44no—
153C2×Dic178—416no—
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×Dic89C2×Q814yes—
174C22×Dic89#4114yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C22×Dic89C2412yes—
181C22×Dic89C2412yes—
182C2×C4×D89—28no—
183C2×C4×D89—44no—
184C2×C4×D89—44no—
185C2×C4×D89—416no—
186C4⋊Dic89—28no—
187C4⋊Dic89—28no—
188C4⋊Dic89—44no—
189#13083553—44no—
190#13083553—44no—
191#13083551—28no—
192#13083551—28no—
193#13083551—28no—
194#13083551—44no—
195#13083551—44no—
196#13083551C2×Q8116yescomplemented
197C4×Dic89—28no—
198C4×Dic89—44no—
199C4×Dic89—44no—
200C24×C89C2411yescharacteristic
201C22×C4×C89—22no—
202C22×C4×C89—22no—
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×Q814yes—
219C22×C4×C89#4114yes—
220C22×C4×C89#4114yes—
221C22×C4×C89#4114yes—
222C22×C4×C89C2412yes—
223C22×C4×C89C2412yes—
224C22×C4×C89C2412yes—
225C22×C4×C89C2412yes—
226C22×C4×C89C2412yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C4⋊C4×C89—28no—
230C4⋊C4×C89—28no—
231C4⋊C4×C89—28no—
232C4⋊C4×C89—44no—
233C42×C89—44no—
234C23×C89C22×Q812yes—
235C23×C89C2×#4112yes—
236C23×C89C2×#4112yes—
237C23×C89C2×#4112yes—
238C23×C89C2×#4112yes—
239C23×C89H(5,𝔽2)12yes—
240C23×C89H(5,𝔽2)12yes—
241C23×C89C2511yescharacteristic
242C22×D89—28no—
243C22×D89—28no—
244C22×D89—28no—
245C22×D89—22no—
246C22×D89—22no—
247C22×D89—22no—
248C22×D89—22no—
249C22×D89—22no—
250C22×D89—22no—
251C22×D89—44no—
252C22×D89—44no—
253C22×D89—44no—
254C22×D89—44no—
255C22×D89C22×Q814yes—
256C2×C4×C89—28no—
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—44no—
278C2×C4×C89—44no—
279C2×C4×C89—44no—
280C2×C4×C89C22×Q814yes—
281C2×C4×C89C2×#4114yes—
282C2×C4×C89C2×#4114yes—
283C2×C4×C89C2×#4114yes—
284C2×Dic89—28no—
285C2×Dic89—28no—
286C2×Dic89—22no—
287C2×Dic89—22no—
288C2×Dic89—22no—
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—44no—
306C2×Dic89—44no—
307C2×Dic89—44no—
308C2×Dic89—44no—
309C2×Dic89—44no—
310C2×Dic89C22×Q814yes—
311C2×Dic89C2×#4114yes—
312C4×D89—416no—
313Dic178—416no—
314C22×C89#52914yes—
315C22×C89#53314yes—
316C22×C89#53814yes—
317C22×C89#55114yes—
318C22×C89#55414yes—
319C22×C89#55414yes—
320C22×C89#55914yes—
321C22×C89C23×Q811yescharacteristic
322C22×C89C22×#4111yescharacteristic
323C22×C89C22×#4111yescharacteristic
324C22×C89C22×#4111yescharacteristic
325C22×C89C22×#4111yescharacteristic
326C22×C89C2×H(5,𝔽2)11yescharacteristic
327C22×C89C2×H(5,𝔽2)11yescharacteristic
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—24no—
340C4×C89—42no—
341C4×C89—42no—
342C4×C89—42no—
343Dic89—24no—
344Dic89—24no—
345Dic89—42no—
346Dic89—42no—
347Dic89—42no—
348Dic89—42no—
349Dic89—42no—
350C2×#2589—891nomaximal, Sylow
351C2×C89#258918yescomplemented
352C2×C89C2×#52911yescharacteristic
353C2×C89C2×#53311yescharacteristic
354C2×C89C2×#53811yescharacteristic
355C2×C89C2×#55111yescharacteristic
356C2×C89C2×#55411yescharacteristic
357C2×C89C2×#55411yescharacteristic
358C2×C89C2×#55911yescharacteristic
359D89—44no—
360#2589—8916no—
361C2×#400—891no—
362C2×#399—891no—
363C2×#398—891no—
364C2×#393—891no—
365C2×#391—891no—
366C2×#391—891no—
367C2×#389D8911yescharacteristic, complemented
368C2×#388—891no—
369C2×#388—891no—
370C2×#387—891no—
371C2×#387—891no—
372C2×#385—891no—
373C2×#385—891no—
374C2×C4×C4⋊C4—891no—
375C2×C4×C22⋊C4—891no—
376C89C2×#258911yescharacteristic, complemented, Sylow
377C23×Q8—891no—
378C24×C4—891no—
379C22×C4⋊C4—891no—
380C22×C4⋊C4—891no—
381C22×C4⋊C4—891no—
382C22×C4⋊C4—891no—
383C22×C4⋊C4—891no—
384C22×C4⋊C4C2×D8911yescharacteristic
385C22×C4⋊C4C2×D8911yescharacteristic
386C22×C4⋊C4C2×D8911yescharacteristic
387C22×C4⋊C4C2×D8911yescharacteristic
388C22×C22⋊C4—891no—
389C22×C22⋊C4—891no—
390C22×C22⋊C4—891no—
391C22×C22⋊C4—891no—
392C22×C22⋊C4—891no—
393C22×C22⋊C4—891no—
394C22×C42—891no—
395C22×C42—891no—
396C22×C42—891no—
397C22×C42C2×D8911yescharacteristic
398#400—898no—
399#399—898no—
400#398—898no—
401#393—898no—
402#391—898no—
403#391—898no—
404#389C2×D8918yescomplemented
405#388—898no—
406#388—898no—
407#387—898no—
408#387—898no—
409#385—898no—
410#385—898no—
411C4×C4⋊C4—898no—
412C4×C22⋊C4—898no—
413C2×#95—891no—
414C2×#95—891no—
415C2×#95—891no—
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×#95C2×D8911yescharacteristic
426C2×#95C2×D8911yescharacteristic
427C25—891no—
428C22×Q8—894no—
429C22×Q8—3562no—
430C22×Q8—1784no—
431C22×Q8—1784no—
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—3562no—
441C23×C4—3562no—
442C23×C4—1784no—
443C23×C4C22×D8911yescharacteristic
444C23×C4C22×D8911yescharacteristic
445C23×C4C22×D8911yescharacteristic
446C23×C4C22×D8911yescharacteristic
447C23×C4C22×D8911yescharacteristic
448C23×C4C22×D8911yescharacteristic
449C23×C4C22×D8911yescharacteristic
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—894no—
455C2×C4⋊C4—894no—
456C2×C4⋊C4—894no—
457C2×C4⋊C4—894no—
458C2×C4⋊C4—894no—
459C2×C4⋊C4—3562no—
460C2×C4⋊C4—3562no—
461C2×C4⋊C4—3562no—
462C2×C4⋊C4—1784no—
463C2×C4⋊C4—1784no—
464C2×C4⋊C4C22×D8914yes—
465C2×C4⋊C4C22×D8914yes—
466C2×C4⋊C4C22×D8914yes—
467C2×C4⋊C4C22×D8914yes—
468C2×C22⋊C4—898no—
469C2×C22⋊C4—894no—
470C2×C22⋊C4—894no—
471C2×C22⋊C4—894no—
472C2×C22⋊C4—894no—
473C2×C22⋊C4—894no—
474C2×C22⋊C4—894no—
475C2×C22⋊C4—3562no—
476C2×C22⋊C4—3562no—
477C2×C22⋊C4—1784no—
478C2×C22⋊C4—1784no—
479C2×C22⋊C4—1784no—
480C2×C42—42no—
481C2×C42—894no—
482C2×C42—894no—
483C2×C42—894no—
484C2×C42—3562no—
485C2×C42—3562no—
486C2×C42—1784no—
487C2×C42C22×D8914yes—
488#95—894no—
489#95—894no—
490#95—894no—
491#95—894no—
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—
502C24—894no—
503C24—892no—
504C24—1782no—
505C24—1782no—
506C24—1782no—
507C24—1782no—
508C24—1782no—
509C24—1782no—
510C24C23×D8911yescharacteristic
511C2×Q8—35616no—
512C2×Q8—3564no—
513C2×Q8—1788no—
514C2×Q8—1788no—
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—22no—
532C22×C4—894no—
533C22×C4—894no—
534C22×C4—892no—
535C22×C4—892no—
536C22×C4—892no—
537C22×C4—892no—
538C22×C4—892no—
539C22×C4—892no—
540C22×C4—892no—
541C22×C4—35616no—
542C22×C4—3564no—
543C22×C4—3564no—
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—1788no—
560C22×C4—1782no—
561C22×C4—1782no—
562C22×C4—1782no—
563C22×C4—1782no—
564C22×C4Q8×D8914yes—
565C22×C4#1308357314yes—
566C22×C4#1308357414yes—
567C22×C4#1308357514yes—
568C22×C4C23×D8912yes—
569C22×C4C23×D8912yes—
570C22×C4C23×D8912yes—
571C22×C4C23×D8912yes—
572C22×C4C23×D8912yes—
573C22×C4C23×D8912yes—
574C22×C4C23×D8912yes—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—44no—
579C4⋊C4—3564no—
580C4⋊C4—3564no—
581C4⋊C4—3564no—
582C4⋊C4—1788no—
583C4⋊C4—1788no—
584C22⋊C4—8916no—
585C22⋊C4—3564no—
586C22⋊C4—3564no—
587C22⋊C4—1788no—
588C22⋊C4—1788no—
589C22⋊C4—1788no—
590C42—44no—
591C42—3564no—
592C42—3564no—
593C42—1788no—
594C23—894no—
595C23—3564no—
596C23—3564no—
597C23—3564no—
598C23—3564no—
599C23—1788no—
600C23—1782no—
601C23—1782no—
602C23—1782no—
603C23—1782no—
604C23—1782no—
605C23—1782no—
606C23—1788no—
607C23—1788no—
608C23C2×Q8×D8912yes—
609C23#41×D8912yes—
610C23C2×#1308357312yes—
611C23C2×#1308357412yes—
612C23C2×#1308357512yes—
613C23#1566805712yes—
614C23#1566805812yes—
615C23C24×D8911yescharacteristic
616Q8—35616no—
617C2×C4—28no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—28no—
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—894no—
642C2×C4—894no—
643C2×C4—35616no—
644C2×C4—3564no—
645C2×C4—3564no—
646C2×C4—3564no—
647C2×C4—3564no—
648C2×C4—3564no—
649C2×C4—1782no—
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—1782no—
667C2×C4—1782no—
668C2×C4—1788no—
669C2×C4—1788no—
670C2×C4C2×Q8×D8914yes—
671C2×C4C2×#1308357314yes—
672C2×C4C2×#1308357414yes—
673C2×C4C2×#1308357514yes—
674C22—3562no—
675C22—3562no—
676C22—3562no—
677C22—3562no—
678C22—35616no—
679C22—1784no—
680C22—1784no—
681C22—1784no—
682C22#1915212814yes—
683C22#1915215314yes—
684C22#1915218514yes—
685C22#1915227514yes—
686C22#1915230314yes—
687C22#1915230414yes—
688C22#1915233314yes—
689C22C22×Q8×D8911yescharacteristic
690C22C2×#41×D8911yescharacteristic
691C22C22×#1308357311yescharacteristic
692C22C22×#1308357411yescharacteristic
693C22C22×#1308357511yescharacteristic
694C22C2×#1566805711yescharacteristic
695C22C2×#1566805811yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3562no—
704C4—3562no—
705C4—3562no—
706C4—3562no—
707C4—3562no—
708C4—1784no—
709C4—1784no—
710C2—3564no—
711C2#2602570818yesdirect product factor
712C2C2×#1915212811yescharacteristic
713C2C2×#1915215311yescharacteristic
714C2C2×#1915218511yescharacteristic
715C2C2×#1915227511yescharacteristic
716C2C2×#1915230311yescharacteristic
717C2C2×#1915230411yescharacteristic
718C2C2×#1915233311yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#389×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#389D89
hypocenterC89C2×#2589
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. #26025708C2direct (N × H)
2. C2×#19151537C2semidirect
4. C2×#19151531C2semidirect
6. C2×#19151504C2semidirect
7. C2×#19151502C2semidirect
10. C2×#19151484C2semidirect
11. C2×#19151483C2semidirect
14. C2×C4⋊C4×Dic89C2semidirect
16. C2×#389×C89C2semidirect
33. #19151537C22semidirect
35. #19151531C22semidirect
37. #19151504C22semidirect
38. #19151502C22semidirect
41. #19151484C22semidirect
42. #19151483C22semidirect
45. C4⋊C4×Dic89C22semidirect
64. #389×C89C22semidirect
98. C2×#13083551Q8semidirect
196. #13083551C2×Q8semidirect
351. C2×C89#2589semidirect
367. C2×#389D89semidirect
376. C89C2×#2589semidirect
404. #389C2×D89semidirect
711. C2#26025708direct (N × H)

Maximal subgroups

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

subgroupindex
#260257082
C2×#191515372
C2×#191515352
C2×#191515312
C2×#191515112
C2×#191515042
C2×#191515022
C2×#191514882
C2×#191514842
C2×#191514832
C2×#191514692
C2×C4⋊C4×Dic892
C2×C4×#130835512
C2×#389×C892
C2×#258989