Finite Group Databasebeta

← C2×#26025340 #36724531

Subgroups — C2×#26025340 #36724531

Order 22784.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15668004C211yesmaximal, characteristic, complemented
2C22×#15667990C211yesmaximal, characteristic
3#26025340C2116yesmaximal, direct product factor
4C2×#19151533C211yesmaximal, characteristic
5C2×#19151532C211yesmaximal, characteristic, complemented
6C2×#19151522C211yesmaximal, characteristic
7C2×#19151519C211yesmaximal, characteristic, complemented
8C2×#19151502C211yesmaximal, characteristic, complemented
9C2×#19151494C211yesmaximal, characteristic, complemented
10C2×#19151493C211yesmaximal, characteristic, complemented
11C2×#19151490C211yesmaximal, characteristic
12C2×#19151490C211yesmaximal, characteristic
13C2×#19151472C211yesmaximal, characteristic
14C2×#19151449C211yesmaximal, characteristic, complemented
15C2×C4×#13083551C211yesmaximal, characteristic
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C2×#15668004—28no—
20C2×#15668004C2218yescomplemented
21C2×#15667990—28no—
22C2×#15667990C2218yes—
23C22×C4⋊Dic89C2211yescharacteristic
24C22×C4⋊Dic89C2211yescharacteristic
25C22×C4⋊Dic89C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C22×#13083553C2211yescharacteristic
33C22×#13083553C2211yescharacteristic
34C22×#13083551C2211yescharacteristic
35C22×#13083551C2211yescharacteristic
36C22×#13083551C2211yescharacteristic
37C22×#13083551C2211yescharacteristic
38C22×#13083551C2211yescharacteristic
39C22×#13083551C2211yescharacteristic
40C22×C4×Dic89C2211yescharacteristic
41C22×C4×Dic89C2211yescharacteristic
42C22×C4×Dic89C2211yescharacteristic
43#19151533C2218yes—
44#19151532C2218yescomplemented
45#19151522C2218yes—
46#19151519C2218yescomplemented
47#19151502C2218yescomplemented
48#19151494C2218yescomplemented
49#19151493C2218yescomplemented
50#19151490C2218yes—
51#19151490C2218yes—
52#19151472C2218yes—
53#19151449C2218yescomplemented
54C4×#13083551C2218yes—
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
70C22×Dic178—24no—
71C22×Dic178—24no—
72C22×Dic178—42no—
73C22×Dic178C2314yes—
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C23×Dic89C2311yescharacteristic
81C22×C4×D89—24no—
82C22×C4×D89—24no—
83C22×C4×D89—42no—
84C22×C4×D89C2314yes—
85#15668004—232no—
86#15667990—232no—
87C2×C4⋊Dic89—24no—
88C2×C4⋊Dic89—24no—
89C2×C4⋊Dic89—24no—
90C2×C4⋊Dic89C2314yes—
91C2×C4⋊Dic89C2314yes—
92C2×C4⋊Dic89C2314yes—
93C2×#13083553—24no—
94C2×#13083553—24no—
95C2×#13083553—24no—
96C2×#13083553—24no—
97C2×#13083553—24no—
98C2×#13083553—24no—
99C2×#13083553—42no—
100C2×#13083553D418yes—
101C2×#13083553C2314yes—
102C2×#13083553C2314yes—
103C2×#13083553C2314yes—
104C2×#13083553C2314yes—
105C2×#13083553C2314yes—
106C2×#13083553C2314yes—
107C2×#13083553C2314yes—
108C2×#13083553C2314yes—
109C2×#13083551—24no—
110C2×#13083551—24no—
111C2×#13083551—24no—
112C2×#13083551—24no—
113C2×#13083551—42no—
114C2×#13083551Q818yescomplemented
115C2×#13083551C2314yes—
116C2×#13083551C2314yes—
117C2×#13083551C2314yes—
118C2×#13083551C2314yes—
119C2×#13083551C2314yes—
120C2×#13083551C2314yes—
121C2×C4×Dic89—24no—
122C2×C4×Dic89—42no—
123C2×C4×Dic89—42no—
124C2×C4×Dic89C2314yes—
125C2×C4×Dic89C2314yes—
126C2×C4×Dic89C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131#15667919C2314yes—
132#15667919C2314yes—
133C23×C4×C89C2311yescharacteristic
134C23×C4×C89C2311yescharacteristic
135C23×C4×C89C2311yescharacteristic
136C23×C4×C89C2311yescharacteristic
137C23×C4×C89C2311yescharacteristic
138C23×C4×C89C2311yescharacteristic
139C23×C4×C89C2311yescharacteristic
140C2×C4⋊C4×C89—24no—
141C2×C4⋊C4×C89—24no—
142C2×C4⋊C4×C89C2314yes—
143C2×C4⋊C4×C89C2314yes—
144C2×C42×C89—24no—
145C2×C42×C89C2314yes—
146#95×C89C2314yes—
147#95×C89C2314yes—
148#95×C89C2314yes—
149#95×C89C2314yes—
150C23×D89—22no—
151C23×D89—22no—
152C23×D89—22no—
153C23×D89—22no—
154C23×D89—22no—
155C23×D89—22no—
156C23×D89C2×Q814yes—
157C23×D89C2412yes—
158C2×Dic178—28no—
159C2×Dic178—28no—
160C2×Dic178—44no—
161C2×Dic178—416no—
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—22no—
175C22×Dic89—22no—
176C22×Dic89—22no—
177C22×Dic89—22no—
178C22×Dic89C2×D414yes—
179C22×Dic89C2×D414yes—
180C22×Dic89C2×Q814yes—
181C22×Dic89#4114yes—
182C22×Dic89#4114yes—
183C22×Dic89C2412yes—
184C22×Dic89C2412yes—
185C22×Dic89C2412yes—
186C22×Dic89C2412yes—
187C22×Dic89C2412yes—
188C22×Dic89C2412yes—
189C22×Dic89C2412yes—
190C2×C4×D89—28no—
191C2×C4×D89—28no—
192C2×C4×D89—44no—
193C2×C4×D89—416no—
194C4⋊Dic89—28no—
195C4⋊Dic89—28no—
196C4⋊Dic89—28no—
197#13083553—28no—
198#13083553—28no—
199#13083553—28no—
200#13083553—28no—
201#13083553—28no—
202#13083553—28no—
203#13083553—44no—
204#13083553C2×D4116yes—
205#13083551—28no—
206#13083551—28no—
207#13083551—28no—
208#13083551—28no—
209#13083551—44no—
210#13083551C2×Q8116yescomplemented
211C4×Dic89—28no—
212C4×Dic89—44no—
213C4×Dic89—44no—
214C24×C89C2411yescharacteristic
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×C89—22no—
224C22×C4×C89—22no—
225C22×C4×C89—22no—
226C22×C4×C89—22no—
227C22×C4×C89—22no—
228C22×C4×C89—22no—
229C22×C4×C89—22no—
230C22×C4×C89—22no—
231C22×C4×C89—22no—
232C22×C4×C89—22no—
233C22×C4×C89C2×D414yes—
234C22×C4×C89C2×Q814yes—
235C22×C4×C89#4114yes—
236C22×C4×C89C2412yes—
237C22×C4×C89C2412yes—
238C22×C4×C89C2412yes—
239C22×C4×C89C2412yes—
240C22×C4×C89C2412yes—
241C22×C4×C89C2412yes—
242C22×C4×C89C2412yes—
243C4⋊C4×C89—28no—
244C4⋊C4×C89—28no—
245C42×C89—28no—
246C23×C89C22×D412yes—
247C23×C89C22×Q812yes—
248C23×C89C2×#4112yes—
249C23×C89C2×#4112yes—
250C23×C89C2×#4112yes—
251C23×C89H(5,𝔽2)12yes—
252C23×C892−1+412yes—
253C23×C89C2511yescharacteristic
254C22×D89—28no—
255C22×D89—28no—
256C22×D89—28no—
257C22×D89—22no—
258C22×D89—22no—
259C22×D89—22no—
260C22×D89—22no—
261C22×D89—22no—
262C22×D89—22no—
263C22×D89—44no—
264C22×D89—44no—
265C22×D89—44no—
266C22×D89—44no—
267C22×D89C22×Q814yes—
268C2×C4×C89—28no—
269C2×C4×C89—28no—
270C2×C4×C89—28no—
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—22no—
282C2×C4×C89—22no—
283C2×C4×C89—22no—
284C2×C4×C89—22no—
285C2×C4×C89—22no—
286C2×C4×C89—22no—
287C2×C4×C89—22no—
288C2×C4×C89—22no—
289C2×C4×C89—44no—
290C2×C4×C89—44no—
291C2×C4×C89—44no—
292C2×C4×C89—44no—
293C2×C4×C89C22×D414yes—
294C2×C4×C89C22×Q814yes—
295C2×C4×C89C2×#4114yes—
296C2×Dic89—28no—
297C2×Dic89—28no—
298C2×Dic89—28no—
299C2×Dic89—28no—
300C2×Dic89—28no—
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—22no—
310C2×Dic89—22no—
311C2×Dic89—22no—
312C2×Dic89—22no—
313C2×Dic89—22no—
314C2×Dic89—22no—
315C2×Dic89—22no—
316C2×Dic89—22no—
317C2×Dic89—44no—
318C2×Dic89—44no—
319C2×Dic89C22×D414yes—
320C2×Dic89C22×D414yes—
321C2×Dic89C22×Q814yes—
322C2×Dic89C2×#4114yes—
323C2×Dic89C2×#4114yes—
324C4×D89—416no—
325Dic178—416no—
326C22×C89#53214yes—
327C22×C89#53314yes—
328C22×C89#53914yes—
329C22×C89#54614yes—
330C22×C89D4×Q814yes—
331C22×C89#55214yes—
332C22×C89#55414yes—
333C22×C89C23×D411yescharacteristic
334C22×C89C23×Q811yescharacteristic
335C22×C89C22×#4111yescharacteristic
336C22×C89C22×#4111yescharacteristic
337C22×C89C22×#4111yescharacteristic
338C22×C89C2×H(5,𝔽2)11yescharacteristic
339C22×C89C2×2−1+411yescharacteristic
340C2×D89—24no—
341C2×D89—24no—
342C2×D89—24no—
343C2×D89—42no—
344C2×D89—42no—
345C2×D89—42no—
346C2×D89—42no—
347C2×D89—416no—
348C4×C89—24no—
349C4×C89—24no—
350C4×C89—24no—
351C4×C89—42no—
352C4×C89—42no—
353C4×C89—42no—
354C4×C89—42no—
355Dic89—24no—
356Dic89—24no—
357Dic89—24no—
358Dic89—24no—
359Dic89—24no—
360Dic89—42no—
361Dic89—42no—
362C2×#2556—891nomaximal, Sylow
363C2×C89#255618yescomplemented
364C2×C89C2×#53211yescharacteristic
365C2×C89C2×#53311yescharacteristic
366C2×C89C2×#53911yescharacteristic
367C2×C89C2×#54611yescharacteristic
368C2×C89C2×D4×Q811yescharacteristic
369C2×C89C2×#55211yescharacteristic
370C2×C89C2×#55411yescharacteristic
371D89—44no—
372C22×#125—891no—
373C22×C22⋊Q8—891no—
374#2556—8916no—
375C2×#399—891no—
376C2×#398—891no—
377C2×#396—891no—
378C2×#395—891no—
379C2×#391—891no—
380C2×#389—891no—
381C2×#389—891no—
382C2×#388—891no—
383C2×#388—891no—
384C2×#387D8911yescharacteristic, complemented
385C2×#385—891no—
386C2×C4×C4⋊C4—891no—
387C2×C4×C22⋊C4—891no—
388C89C2×#255611yescharacteristic, complemented, Sylow
389C23×Q8—891no—
390C24×C4—891no—
391C2×#125—898no—
392C2×#125—1788no—
393C2×C22⋊Q8—898no—
394C2×C22⋊Q8—1788no—
395C22×C4⋊C4—891no—
396C22×C4⋊C4—891no—
397C22×C4⋊C4—891no—
398C22×C4⋊C4—891no—
399C22×C4⋊C4—891no—
400C22×C4⋊C4—891no—
401C22×C4⋊C4—891no—
402C22×C4⋊C4—891no—
403C22×C4⋊C4—891no—
404C22×C4⋊C4—891no—
405C22×C4⋊C4—891no—
406C22×C4⋊C4C2×D8911yescharacteristic
407C22×C4⋊C4C2×D8911yescharacteristic
408C22×C22⋊C4—891no—
409C22×C22⋊C4—891no—
410C22×C22⋊C4—891no—
411C22×C22⋊C4—891no—
412C22×C22⋊C4—891no—
413C22×C22⋊C4—891no—
414C22×C42—891no—
415C22×C42—891no—
416C22×C42—891no—
417C22×C42C2×D8911yescharacteristic
418#399—898no—
419#398—898no—
420#396—898no—
421#395—898no—
422#391—898no—
423#389—898no—
424#389—898no—
425#388—898no—
426#388—898no—
427#387C2×D8918yescomplemented
428#385—898no—
429C4×C4⋊C4—898no—
430C4×C22⋊C4—898no—
431C2×#95—891no—
432C2×#95—891no—
433C2×#95—891no—
434C2×#95—891no—
435C2×#95—891no—
436C2×#95—891no—
437C2×#95C2×D8911yescharacteristic
438C2×#95C2×D8911yescharacteristic
439C2×#95C2×D8911yescharacteristic
440C2×#95C2×D8911yescharacteristic
441C25—891no—
442C22×Q8—894no—
443C22×Q8—3562no—
444C22×Q8—1784no—
445C22×Q8—1784no—
446C23×C4—891no—
447C23×C4—891no—
448C23×C4—891no—
449C23×C4—891no—
450C23×C4—891no—
451C23×C4—891no—
452C23×C4—891no—
453C23×C4—894no—
454C23×C4—3562no—
455C23×C4—1784no—
456C23×C4—1784no—
457C23×C4C22×D8911yescharacteristic
458C23×C4C22×D8911yescharacteristic
459C23×C4C22×D8911yescharacteristic
460C23×C4C22×D8911yescharacteristic
461C23×C4C22×D8911yescharacteristic
462C23×C4C22×D8911yescharacteristic
463C23×C4C22×D8911yescharacteristic
464#125—17832no—
465C22⋊Q8—17832no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—898no—
469C2×C4⋊C4—894no—
470C2×C4⋊C4—894no—
471C2×C4⋊C4—894no—
472C2×C4⋊C4—894no—
473C2×C4⋊C4—894no—
474C2×C4⋊C4—894no—
475C2×C4⋊C4—894no—
476C2×C4⋊C4—894no—
477C2×C4⋊C4—894no—
478C2×C4⋊C4—894no—
479C2×C4⋊C4—894no—
480C2×C4⋊C4—3562no—
481C2×C4⋊C4—1784no—
482C2×C4⋊C4—1784no—
483C2×C4⋊C4—1784no—
484C2×C4⋊C4—1784no—
485C2×C4⋊C4—1784no—
486C2×C4⋊C4—1784no—
487C2×C4⋊C4—1784no—
488C2×C4⋊C4—1784no—
489C2×C4⋊C4—1784no—
490C2×C4⋊C4C22×D8914yes—
491C2×C4⋊C4C22×D8914yes—
492C2×C22⋊C4—898no—
493C2×C22⋊C4—894no—
494C2×C22⋊C4—894no—
495C2×C22⋊C4—894no—
496C2×C22⋊C4—894no—
497C2×C22⋊C4—894no—
498C2×C22⋊C4—894no—
499C2×C22⋊C4—3562no—
500C2×C22⋊C4—1784no—
501C2×C22⋊C4—1784no—
502C2×C22⋊C4—1784no—
503C2×C22⋊C4—1784no—
504C2×C42—24no—
505C2×C42—894no—
506C2×C42—894no—
507C2×C42—894no—
508C2×C42—3562no—
509C2×C42—3562no—
510C2×C42—1784no—
511C2×C42C22×D8914yes—
512#95—894no—
513#95—894no—
514#95—894no—
515#95—894no—
516#95—894no—
517#95—894no—
518#95C22×D8914yes—
519#95C22×D8914yes—
520#95C22×D8914yes—
521#95C22×D8914yes—
522C24—894no—
523C24—892no—
524C24—1782no—
525C24—1782no—
526C24—1782no—
527C24—1782no—
528C24—1782no—
529C24—1782no—
530C24C23×D8911yescharacteristic
531C2×Q8—3564no—
532C2×Q8—35616no—
533C2×Q8—1788no—
534C2×Q8—1788no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—894no—
554C22×C4—894no—
555C22×C4—894no—
556C22×C4—894no—
557C22×C4—894no—
558C22×C4—892no—
559C22×C4—892no—
560C22×C4—892no—
561C22×C4—892no—
562C22×C4—892no—
563C22×C4—892no—
564C22×C4—892no—
565C22×C4—35616no—
566C22×C4—3564no—
567C22×C4—1788no—
568C22×C4—1782no—
569C22×C4—1782no—
570C22×C4—1782no—
571C22×C4—1782no—
572C22×C4—1782no—
573C22×C4—1782no—
574C22×C4—1788no—
575C22×C4—1782no—
576C22×C4—1782no—
577C22×C4—1782no—
578C22×C4—1782no—
579C22×C4—1782no—
580C22×C4—1782no—
581C22×C4—1782no—
582C22×C4—1782no—
583C22×C4—1782no—
584C22×C4—1782no—
585C22×C4D4×D8914yes—
586C22×C4Q8×D8914yes—
587C22×C4#1308357414yes—
588C22×C4C23×D8912yes—
589C22×C4C23×D8912yes—
590C22×C4C23×D8912yes—
591C22×C4C23×D8912yes—
592C22×C4C23×D8912yes—
593C22×C4C23×D8912yes—
594C22×C4C23×D8912yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—8916no—
598C4⋊C4—3564no—
599C4⋊C4—1788no—
600C4⋊C4—1788no—
601C4⋊C4—1788no—
602C4⋊C4—1788no—
603C4⋊C4—1788no—
604C4⋊C4—1788no—
605C4⋊C4—1788no—
606C4⋊C4—1788no—
607C4⋊C4—1788no—
608C22⋊C4—8916no—
609C22⋊C4—3564no—
610C22⋊C4—1788no—
611C22⋊C4—1788no—
612C22⋊C4—1788no—
613C22⋊C4—1788no—
614C42—28no—
615C42—3564no—
616C42—3564no—
617C42—1788no—
618C23—894no—
619C23—3564no—
620C23—3564no—
621C23—3564no—
622C23—3564no—
623C23—1788no—
624C23—1782no—
625C23—1782no—
626C23—1782no—
627C23—1782no—
628C23—1782no—
629C23—1782no—
630C23—1788no—
631C23—1788no—
632C23C2×D4×D8912yes—
633C23C2×Q8×D8912yes—
634C23#41×D8912yes—
635C23#41×D8912yes—
636C23C2×#1308357412yes—
637C23#1566805812yes—
638C23#1566805912yes—
639C23C24×D8911yescharacteristic
640Q8—35616no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—894no—
667C2×C4—894no—
668C2×C4—894no—
669C2×C4—894no—
670C2×C4—894no—
671C2×C4—35616no—
672C2×C4—3564no—
673C2×C4—3564no—
674C2×C4—1782no—
675C2×C4—1782no—
676C2×C4—1782no—
677C2×C4—1782no—
678C2×C4—1782no—
679C2×C4—1782no—
680C2×C4—1788no—
681C2×C4—1782no—
682C2×C4—1782no—
683C2×C4—1782no—
684C2×C4—1782no—
685C2×C4—1782no—
686C2×C4—1782no—
687C2×C4—1782no—
688C2×C4—1782no—
689C2×C4—1782no—
690C2×C4—1782no—
691C2×C4—1788no—
692C2×C4—1788no—
693C2×C4—1788no—
694C2×C4—1788no—
695C2×C4C2×D4×D8914yes—
696C2×C4C2×Q8×D8914yes—
697C2×C4C2×#1308357414yes—
698C22—3562no—
699C22—3562no—
700C22—35616no—
701C22—3562no—
702C22—3562no—
703C22—1784no—
704C22—1784no—
705C22—1784no—
706C22#1915214514yes—
707C22#1915215414yes—
708C22#1915218914yes—
709C22#1915224014yes—
710C22#1915226114yes—
711C22#1915228114yes—
712C22#1915230814yes—
713C22C22×D4×D8911yescharacteristic
714C22C22×Q8×D8911yescharacteristic
715C22C2×#41×D8911yescharacteristic
716C22C2×#41×D8911yescharacteristic
717C22C22×#1308357411yescharacteristic
718C22C2×#1566805811yescharacteristic
719C22C2×#1566805911yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—3562no—
728C4—3562no—
729C4—1784no—
730C4—1784no—
731C4—1784no—
732C4—1784no—
733C4—1784no—
734C2—3564no—
735C2#2602534018yesdirect product factor
736C2C2×#1915214511yescharacteristic
737C2C2×#1915215411yescharacteristic
738C2C2×#1915218911yescharacteristic
739C2C2×#1915224011yescharacteristic
740C2C2×#1915226111yescharacteristic
741C2C2×#1915228111yescharacteristic
742C2C2×#1915230811yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#387D89
hypocenterC89C2×#2556
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#15668004C2semidirect
3. #26025340C2direct (N × H)
5. C2×#19151532C2semidirect
7. C2×#19151519C2semidirect
8. C2×#19151502C2semidirect
9. C2×#19151494C2semidirect
10. C2×#19151493C2semidirect
14. C2×#19151449C2semidirect
16. C2×#387×C89C2semidirect
20. C2×#15668004C22semidirect
44. #19151532C22semidirect
46. #19151519C22semidirect
47. #19151502C22semidirect
48. #19151494C22semidirect
49. #19151493C22semidirect
53. #19151449C22semidirect
64. #387×C89C22semidirect
114. C2×#13083551Q8semidirect
210. #13083551C2×Q8semidirect
363. C2×C89#2556semidirect
384. C2×#387D89semidirect
388. C89C2×#2556semidirect
427. #387C2×D89semidirect
735. C2#26025340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680042
C22×#156679902
#260253402
C2×#191515332
C2×#191515322
C2×#191515222
C2×#191515192
C2×#191515022
C2×#191514942
C2×#191514932
C2×#191514902
C2×#191514722
C2×#191514492
C2×C4×#130835512
C2×#387×C892
C2×#255689