Finite Group Databasebeta

← C2×#26025674 #36724708

Subgroups — C2×#26025674 #36724708

Order 22784.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26025674C2116yesmaximal, direct product factor
2C2×#19151540C211yesmaximal, characteristic, complemented
3C2×#19151520C211yesmaximal, characteristic
4C2×#19151520C211yesmaximal, characteristic
5C2×#19151497C211yesmaximal, characteristic, complemented
6C2×#19151495C211yesmaximal, characteristic, complemented
7C2×#19151494C211yesmaximal, characteristic, complemented
8C2×#19151490C211yesmaximal, characteristic
9C2×#19151488C211yesmaximal, characteristic
10C2×#19151483C211yesmaximal, characteristic, complemented
11C2×#19151479C211yesmaximal, characteristic, complemented
12C2×#19151472C211yesmaximal, characteristic
13C2×#19151469C211yesmaximal, characteristic
14C2×C4⋊C4×Dic89C211yesmaximal, characteristic, complemented
15C2×#19151445C211yesmaximal, characteristic
16C2×#398×C89C211yesmaximal, characteristic, complemented
17C23×C4×D89C2211yescharacteristic
18C22×C4⋊Dic89C2211yescharacteristic
19C22×C4⋊Dic89C2211yescharacteristic
20C22×C4⋊Dic89C2211yescharacteristic
21C22×C4⋊Dic89C2211yescharacteristic
22C22×#13083553C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083551C2211yescharacteristic
27C22×#13083551C2211yescharacteristic
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×C4×Dic89C2211yescharacteristic
33C22×C4×Dic89C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35C22×C4×Dic89C2211yescharacteristic
36#19151540C2218yescomplemented
37#19151520C2218yes—
38#19151520C2218yes—
39#19151497C2218yescomplemented
40#19151495C2218yescomplemented
41#19151494C2218yescomplemented
42#19151490C2218yes—
43#19151488C2218yes—
44#19151483C2218yescomplemented
45#19151479C2218yescomplemented
46#19151472C2218yes—
47#19151469C2218yes—
48C4⋊C4×Dic89C2218yescomplemented
49#19151445C2218yes—
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
63#398×C89C2218yescomplemented
64C2×#95×C89C2211yescharacteristic
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C24×D89C2311yescharacteristic
68C23×Dic89C2311yescharacteristic
69C23×Dic89C2311yescharacteristic
70C23×Dic89C2311yescharacteristic
71C23×Dic89C2311yescharacteristic
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C22×C4×D89—24no—
76C22×C4×D89—42no—
77C22×C4×D89—42no—
78C22×C4×D89C2314yes—
79C2×C4⋊Dic89—24no—
80C2×C4⋊Dic89—24no—
81C2×C4⋊Dic89—24no—
82C2×C4⋊Dic89—42no—
83C2×C4⋊Dic89C2314yes—
84C2×C4⋊Dic89C2314yes—
85C2×C4⋊Dic89C2314yes—
86C2×C4⋊Dic89C2314yes—
87C2×#13083553—24no—
88C2×#13083553—24no—
89C2×#13083553—42no—
90C2×#13083553—42no—
91C2×#13083553C2314yes—
92C2×#13083553C2314yes—
93C2×#13083553C2314yes—
94C2×#13083553C2314yes—
95C2×#13083551—24no—
96C2×#13083551—24no—
97C2×#13083551—24no—
98C2×#13083551—42no—
99C2×#13083551—42no—
100C2×#13083551Q818yes—
101C2×#13083551C2314yes—
102C2×#13083551C2314yes—
103C2×#13083551C2314yes—
104C2×#13083551C2314yes—
105C2×#13083551C2314yes—
106C2×#13083551C2314yes—
107C2×C4×Dic89—24no—
108C2×C4×Dic89—42no—
109C2×C4×Dic89—42no—
110C2×C4×Dic89—42no—
111C2×C4×Dic89C2314yes—
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—
124C23×C4×C89C2311yescharacteristic
125C23×C4×C89C2311yescharacteristic
126C23×C4×C89C2311yescharacteristic
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C2×C4⋊C4×C89—24no—
132C2×C4⋊C4×C89—24no—
133C2×C4⋊C4×C89—42no—
134C2×C4⋊C4×C89—42no—
135C2×C4⋊C4×C89C2314yes—
136C2×C4⋊C4×C89C2314yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C4⋊C4×C89C2314yes—
139#95×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—
150C22×Dic89—22no—
151C22×Dic89—22no—
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×Dic89C2×Q814yes—
169C22×Dic89#4114yes—
170C22×Dic89#4114yes—
171C22×Dic89C2412yes—
172C22×Dic89C2412yes—
173C22×Dic89C2412yes—
174C22×Dic89C2412yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C2×C4×D89—28no—
179C2×C4×D89—44no—
180C2×C4×D89—44no—
181C2×C4×D89—416no—
182C4⋊Dic89—28no—
183C4⋊Dic89—28no—
184C4⋊Dic89—28no—
185C4⋊Dic89—44no—
186#13083553—28no—
187#13083553—28no—
188#13083553—44no—
189#13083553—44no—
190#13083551—28no—
191#13083551—28no—
192#13083551—28no—
193#13083551—44no—
194#13083551—44no—
195#13083551C2×Q8116yes—
196C4×Dic89—28no—
197C4×Dic89—44no—
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×C89—22no—
219C22×C4×C89C2×Q814yes—
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—44no—
232C4⋊C4×C89—44no—
233C23×C89C22×Q812yes—
234C23×C89C2×#4112yes—
235C23×C89C2×#4112yes—
236C23×C89C2×#4112yes—
237C23×C89C2×#4112yes—
238C23×C89H(5,𝔽2)12yes—
239C23×C89H(5,𝔽2)12yes—
240C23×C89C2511yescharacteristic
241C22×D89—28no—
242C22×D89—28no—
243C22×D89—28no—
244C22×D89—22no—
245C22×D89—22no—
246C22×D89—22no—
247C22×D89—22no—
248C22×D89—22no—
249C22×D89—22no—
250C22×D89—44no—
251C22×D89—44no—
252C22×D89—44no—
253C22×D89—44no—
254C22×D89C22×Q814yes—
255C2×C4×C89—28no—
256C2×C4×C89—28no—
257C2×C4×C89—28no—
258C2×C4×C89—22no—
259C2×C4×C89—22no—
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—44no—
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×Dic89—28no—
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—44no—
305C2×Dic89—44no—
306C2×Dic89—44no—
307C2×Dic89—44no—
308C2×Dic89C22×Q814yes—
309C2×Dic89C2×#4114yes—
310C2×Dic89C2×#4114yes—
311C4×D89—416no—
312C22×C89#52914yes—
313C22×C89#53314yes—
314C22×C89#53814yes—
315C22×C89#55314yes—
316C22×C89#55314yes—
317C22×C89#55414yes—
318C22×C89#55414yes—
319C22×C89C23×Q811yescharacteristic
320C22×C89C22×#4111yescharacteristic
321C22×C89C22×#4111yescharacteristic
322C22×C89C22×#4111yescharacteristic
323C22×C89C22×#4111yescharacteristic
324C22×C89C2×H(5,𝔽2)11yescharacteristic
325C22×C89C2×H(5,𝔽2)11yescharacteristic
326C2×D89—24no—
327C2×D89—24no—
328C2×D89—24no—
329C2×D89—416no—
330C2×D89—42no—
331C2×D89—42no—
332C2×D89—42no—
333C2×D89—42no—
334C4×C89—24no—
335C4×C89—24no—
336C4×C89—24no—
337C4×C89—42no—
338C4×C89—42no—
339C4×C89—42no—
340C4×C89—42no—
341Dic89—24no—
342Dic89—24no—
343Dic89—24no—
344Dic89—42no—
345Dic89—42no—
346Dic89—42no—
347Dic89—42no—
348C2×#2587—891nomaximal, Sylow
349C2×C89#258718yescomplemented
350C2×C89C2×#52911yescharacteristic
351C2×C89C2×#53311yescharacteristic
352C2×C89C2×#53811yescharacteristic
353C2×C89C2×#55311yescharacteristic
354C2×C89C2×#55311yescharacteristic
355C2×C89C2×#55411yescharacteristic
356C2×C89C2×#55411yescharacteristic
357D89—44no—
358#2587—8916no—
359C2×#400—891no—
360C2×#398D8911yescharacteristic, complemented
361C2×#396—891no—
362C2×#396—891no—
363C2×#389—891no—
364C2×#389—891no—
365C2×#389—891no—
366C2×#388—891no—
367C2×#388—891no—
368C2×#387—891no—
369C2×#387—891no—
370C2×#385—891no—
371C2×#385—891no—
372C2×C4×C4⋊C4—891no—
373C2×C4×C22⋊C4—891no—
374C89C2×#258711yescharacteristic, complemented, Sylow
375C24×C4—891no—
376C22×C4⋊C4—891no—
377C22×C4⋊C4—891no—
378C22×C4⋊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×C42—891no—
398#400—898no—
399#398C2×D8918yescomplemented
400#396—898no—
401#396—898no—
402#389—898no—
403#389—898no—
404#389—898no—
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×#95C2×D8911yescharacteristic
423C2×#95C2×D8911yescharacteristic
424C2×#95C2×D8911yescharacteristic
425C25—891no—
426C23×C4—891no—
427C23×C4—891no—
428C23×C4—891no—
429C23×C4—891no—
430C23×C4—891no—
431C23×C4—891no—
432C23×C4—891no—
433C23×C4—894no—
434C23×C4—3562no—
435C23×C4—3562no—
436C23×C4—1784no—
437C23×C4C22×D8911yescharacteristic
438C23×C4C22×D8911yescharacteristic
439C23×C4C22×D8911yescharacteristic
440C23×C4C22×D8911yescharacteristic
441C23×C4C22×D8911yescharacteristic
442C23×C4C22×D8911yescharacteristic
443C23×C4C22×D8911yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—894no—
449C2×C4⋊C4—894no—
450C2×C4⋊C4—894no—
451C2×C4⋊C4—894no—
452C2×C4⋊C4—894no—
453C2×C4⋊C4—894no—
454C2×C4⋊C4—894no—
455C2×C4⋊C4—894no—
456C2×C4⋊C4—3562no—
457C2×C4⋊C4—3562no—
458C2×C4⋊C4—3562no—
459C2×C4⋊C4—1784no—
460C2×C4⋊C4—1784no—
461C2×C4⋊C4—1784no—
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—894no—
481C2×C42—894no—
482C2×C42—894no—
483C2×C42—894no—
484C2×C42—3562no—
485C2×C42—3562no—
486C2×C42—3562no—
487C2×C42—1784no—
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#95C22×D8914yes—
498#95C22×D8914yes—
499#95C22×D8914yes—
500C24—894no—
501C24—892no—
502C24—1782no—
503C24—1782no—
504C24—1782no—
505C24—1782no—
506C24—1782no—
507C24—1782no—
508C24C23×D8911yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
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—894no—
528C22×C4—894no—
529C22×C4—894no—
530C22×C4—892no—
531C22×C4—892no—
532C22×C4—892no—
533C22×C4—892no—
534C22×C4—892no—
535C22×C4—892no—
536C22×C4—892no—
537C22×C4—3564no—
538C22×C4—3564no—
539C22×C4—35616no—
540C22×C4—1788no—
541C22×C4—1782no—
542C22×C4—1782no—
543C22×C4—1782no—
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×C4Q8×D8914yes—
560C22×C4#1308357314yes—
561C22×C4#1308357514yes—
562C22×C4C23×D8912yes—
563C22×C4C23×D8912yes—
564C22×C4C23×D8912yes—
565C22×C4C23×D8912yes—
566C22×C4C23×D8912yes—
567C22×C4C23×D8912yes—
568C22×C4C23×D8912yes—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—3564no—
574C4⋊C4—3564no—
575C4⋊C4—3564no—
576C4⋊C4—1788no—
577C4⋊C4—1788no—
578C4⋊C4—1788no—
579C4⋊C4—1788no—
580C4⋊C4—1788no—
581C22⋊C4—8916no—
582C22⋊C4—3564no—
583C22⋊C4—3564no—
584C22⋊C4—1788no—
585C22⋊C4—1788no—
586C22⋊C4—1788no—
587C42—3564no—
588C42—3564no—
589C42—3564no—
590C42—1788no—
591C23—894no—
592C23—3564no—
593C23—3564no—
594C23—3564no—
595C23—3564no—
596C23—1788no—
597C23—1782no—
598C23—1782no—
599C23—1782no—
600C23—1782no—
601C23—1782no—
602C23—1782no—
603C23—1788no—
604C23—1788no—
605C23C2×Q8×D8912yes—
606C23#41×D8912yes—
607C23#41×D8912yes—
608C23C2×#1308357312yes—
609C23C2×#1308357512yes—
610C23#1566805712yes—
611C23#1566805812yes—
612C23C24×D8911yescharacteristic
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—28no—
621C2×C4—28no—
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—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—894no—
639C2×C4—894no—
640C2×C4—894no—
641C2×C4—35616no—
642C2×C4—3564no—
643C2×C4—3564no—
644C2×C4—3564no—
645C2×C4—3564no—
646C2×C4—1782no—
647C2×C4—1782no—
648C2×C4—1782no—
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—1788no—
665C2×C4—1788no—
666C2×C4—1788no—
667C2×C4C2×Q8×D8914yes—
668C2×C4C2×#1308357314yes—
669C2×C4C2×#1308357514yes—
670C22—3562no—
671C22—3562no—
672C22—3562no—
673C22—3562no—
674C22—35616no—
675C22—1784no—
676C22—1784no—
677C22—1784no—
678C22#1915213414yes—
679C22#1915215414yes—
680C22#1915218414yes—
681C22#1915229114yes—
682C22#1915230114yes—
683C22#1915230614yes—
684C22#1915230914yes—
685C22C22×Q8×D8911yescharacteristic
686C22C2×#41×D8911yescharacteristic
687C22C2×#41×D8911yescharacteristic
688C22C22×#1308357311yescharacteristic
689C22C22×#1308357511yescharacteristic
690C22C2×#1566805711yescharacteristic
691C22C2×#1566805811yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—3562no—
700C4—3562no—
701C4—3562no—
702C4—3562no—
703C4—1784no—
704C4—1784no—
705C4—1784no—
706C2—3564no—
707C2#2602567418yesdirect product factor
708C2C2×#1915213411yescharacteristic
709C2C2×#1915215411yescharacteristic
710C2C2×#1915218411yescharacteristic
711C2C2×#1915229111yescharacteristic
712C2C2×#1915230111yescharacteristic
713C2C2×#1915230611yescharacteristic
714C2C2×#1915230911yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#398×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#398D89
hypocenterC89C2×#2587
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #26025674C2direct (N × H)
2. C2×#19151540C2semidirect
5. C2×#19151497C2semidirect
6. C2×#19151495C2semidirect
7. C2×#19151494C2semidirect
10. C2×#19151483C2semidirect
11. C2×#19151479C2semidirect
14. C2×C4⋊C4×Dic89C2semidirect
16. C2×#398×C89C2semidirect
36. #19151540C22semidirect
39. #19151497C22semidirect
40. #19151495C22semidirect
41. #19151494C22semidirect
44. #19151483C22semidirect
45. #19151479C22semidirect
48. C4⋊C4×Dic89C22semidirect
63. #398×C89C22semidirect
349. C2×C89#2587semidirect
360. C2×#398D89semidirect
374. C89C2×#2587semidirect
399. #398C2×D89semidirect
707. C2#26025674direct (N × H)

Maximal subgroups

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

subgroupindex
#260256742
C2×#191515402
C2×#191515202
C2×#191514972
C2×#191514952
C2×#191514942
C2×#191514902
C2×#191514882
C2×#191514832
C2×#191514792
C2×#191514722
C2×#191514692
C2×C4⋊C4×Dic892
C2×#191514452
C2×#398×C892
C2×#258789