Finite Group Databasebeta

← C2×#26026070 #36720798

Subgroups — C2×#26026070 #36720798

Order 22784.

2894 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667990C211yesmaximal, characteristic
2C22×C4⋊C4×D89C211yesmaximal, characteristic
3#26026070C2116yesmaximal, direct product factor
4C2×#19151540C211yesmaximal, characteristic, complemented
5C2×#19151539C211yesmaximal, characteristic, complemented
6C2×#19151531C211yesmaximal, characteristic, complemented
7C2×#19151531C211yesmaximal, characteristic, complemented
8C2×#19151528C211yesmaximal, characteristic, complemented
9C2×#19151519C211yesmaximal, characteristic, complemented
10C2×#19151518C211yesmaximal, characteristic, complemented
11C2×#19151472C211yesmaximal, characteristic
12C2×#19151469C211yesmaximal, characteristic
13C2×#19151460C211yesmaximal, characteristic
14C2×#19151460C211yesmaximal, characteristic
15C2×#19151455C211yesmaximal, characteristic
16C2×#398×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C23×C4×D89C2211yescharacteristic
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
32C2×C4⋊C4×D89—28no—
33C2×C4⋊C4×D89C2218yes—
34C22×#13083551C2211yescharacteristic
35C22×#13083551C2211yescharacteristic
36C22×#13083551C2211yescharacteristic
37C22×#13083551C2211yescharacteristic
38#19151540C2218yescomplemented
39#19151539C2218yescomplemented
40#19151531C2218yescomplemented
41#19151531C2218yescomplemented
42#19151528C2218yescomplemented
43#19151519C2218yescomplemented
44#19151518C2218yescomplemented
45#19151472C2218yes—
46#19151469C2218yes—
47#19151460C2218yes—
48#19151460C2218yes—
49#19151455C2218yes—
50C2×#15667919C2211yescharacteristic
51C2×#15667919C2211yescharacteristic
52C2×#15667919C2211yescharacteristic
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×C4⋊C4×C89C2211yescharacteristic
64C22×C4⋊C4×C89C2211yescharacteristic
65#398×C89C2218yescomplemented
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C2×#95×C89C2211yescharacteristic
69C24×D89C2311yescharacteristic
70C22×Dic178—24no—
71C22×Dic178—42no—
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—24no—
84C22×C4×D89—42no—
85C22×C4×D89—42no—
86C22×C4×D89—42no—
87C22×C4×D89—42no—
88C22×C4×D89D418yes—
89C22×C4×D89Q818yescomplemented
90C22×C4×D89C2314yes—
91C22×C4×D89C2314yes—
92C22×C4×D89C2314yes—
93#15667990—232no—
94C2×C4⋊Dic89—24no—
95C2×C4⋊Dic89—42no—
96C2×C4⋊Dic89—42no—
97C2×C4⋊Dic89C2314yes—
98C2×C4⋊Dic89C2314yes—
99C2×C4⋊Dic89C2314yes—
100C2×#13083553—24no—
101C2×#13083553—24no—
102C2×#13083553—24no—
103C2×#13083553—24no—
104C2×#13083553—42no—
105C2×#13083553—42no—
106C2×#13083553C2314yes—
107C2×#13083553C2314yes—
108C2×#13083553C2314yes—
109C2×#13083553C2314yes—
110C2×#13083553C2314yes—
111C2×#13083553C2314yes—
112C4⋊C4×D89—232no—
113C2×#13083551—24no—
114C2×#13083551—24no—
115C2×#13083551—24no—
116C2×#13083551—24no—
117C2×#13083551C2314yes—
118C2×#13083551C2314yes—
119C2×#13083551C2314yes—
120C2×#13083551C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123#15667919C2314yes—
124#15667919C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131#15667919C2314yes—
132C23×C4×C89C2311yescharacteristic
133C23×C4×C89C2311yescharacteristic
134C23×C4×C89C2311yescharacteristic
135C23×C4×C89C2311yescharacteristic
136C23×C4×C89C2311yescharacteristic
137C23×C4×C89C2311yescharacteristic
138C23×C4×C89C2311yescharacteristic
139C2×C4⋊C4×C89—24no—
140C2×C4⋊C4×C89—24no—
141C2×C4⋊C4×C89—42no—
142C2×C4⋊C4×C89—42no—
143C2×C4⋊C4×C89C2314yes—
144C2×C4⋊C4×C89C2314yes—
145C2×C4⋊C4×C89C2314yes—
146C2×C4⋊C4×C89C2314yes—
147#95×C89C2314yes—
148#95×C89C2314yes—
149#95×C89C2314yes—
150C23×D89—22no—
151C23×D89—22no—
152C23×D89—22no—
153C23×D89—22no—
154C23×D89C2×D414yes—
155C23×D89C2×Q814yes—
156C23×D89#4114yes—
157C23×D89C2412yes—
158C2×Dic178—28no—
159C2×Dic178—44no—
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×Dic89—22no—
179C22×Dic89—22no—
180C22×Dic89—22no—
181C22×Dic89C2×D414yes—
182C22×Dic89C2×Q814yes—
183C22×Dic89C2412yes—
184C22×Dic89C2412yes—
185C22×Dic89C2412yes—
186C22×Dic89C2412yes—
187C22×Dic89C2412yes—
188C22×Dic89C2412yes—
189C22×Dic89C2412yes—
190C2×C4×D89—232no—
191C2×C4×D89—28no—
192C2×C4×D89—28no—
193C2×C4×D89—28no—
194C2×C4×D89—416no—
195C2×C4×D89—44no—
196C2×C4×D89—44no—
197C2×C4×D89—44no—
198C2×C4×D89—44no—
199C2×C4×D89—416no—
200C2×C4×D89C2×D4116yes—
201C2×C4×D89C2×Q8116yescomplemented
202C4⋊Dic89—28no—
203C4⋊Dic89—44no—
204C4⋊Dic89—44no—
205#13083553—28no—
206#13083553—28no—
207#13083553—28no—
208#13083553—28no—
209#13083553—44no—
210#13083553—44no—
211#13083551—28no—
212#13083551—28no—
213#13083551—28no—
214#13083551—28no—
215C24×C89C2411yescharacteristic
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×C89—22no—
234C22×C4×C89—22no—
235C22×C4×C89C2×D414yes—
236C22×C4×C89C2×Q814yes—
237C22×C4×C89C2412yes—
238C22×C4×C89C2412yes—
239C22×C4×C89C2412yes—
240C22×C4×C89C2412yes—
241C22×C4×C89C2412yes—
242C22×C4×C89C2412yes—
243C22×C4×C89C2412yes—
244C4⋊C4×C89—28no—
245C4⋊C4×C89—28no—
246C4⋊C4×C89—44no—
247C4⋊C4×C89—44no—
248C23×C89C22×D412yes—
249C23×C89C22×Q812yes—
250C23×C89C2×#4112yes—
251C23×C89H(5,𝔽2)12yes—
252C23×C89H(5,𝔽2)12yes—
253C23×C892−1+412yes—
254C23×C892−1+412yes—
255C23×C89C2511yescharacteristic
256C22×D89—28no—
257C22×D89—28no—
258C22×D89—28no—
259C22×D89—28no—
260C22×D89—28no—
261C22×D89—28no—
262C22×D89—22no—
263C22×D89—22no—
264C22×D89—22no—
265C22×D89—22no—
266C22×D89C22⋊Q8116yes—
267C22×D89C22×D414yes—
268C22×D89C22×Q814yes—
269C22×D89C2×#4114yes—
270C2×C4×C89—28no—
271C2×C4×C89—28no—
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—22no—
290C2×C4×C89—22no—
291C2×C4×C89—44no—
292C2×C4×C89—44no—
293C2×C4×C89—44no—
294C2×C4×C89—44no—
295C2×C4×C89—44no—
296C2×C4×C89C22×D414yes—
297C2×C4×C89C22×Q814yes—
298C2×Dic89—28no—
299C2×Dic89—28no—
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—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—22no—
318C2×Dic89—22no—
319C2×Dic89—44no—
320C2×Dic89—44no—
321C2×Dic89—44no—
322C2×Dic89—44no—
323C2×Dic89—44no—
324C2×Dic89C22×D414yes—
325C2×Dic89C22×Q814yes—
326C4×D89—232no—
327C4×D89—416no—
328C4×D89—416no—
329Dic178—416no—
330C22×C89C2×C22⋊Q814yes—
331C22×C89#53414yes—
332C22×C89#53614yes—
333C22×C89#53914yes—
334C22×C89#53914yes—
335C22×C89#54414yes—
336C22×C89#54414yes—
337C22×C89C23×D411yescharacteristic
338C22×C89C23×Q811yescharacteristic
339C22×C89C22×#4111yescharacteristic
340C22×C89C2×H(5,𝔽2)11yescharacteristic
341C22×C89C2×H(5,𝔽2)11yescharacteristic
342C22×C89C2×2−1+411yescharacteristic
343C22×C89C2×2−1+411yescharacteristic
344C2×D89—232no—
345C2×D89—24no—
346C2×D89—24no—
347C2×D89—24no—
348C2×D89—24no—
349C2×D89—24no—
350C2×D89—24no—
351C2×D89C2×C22⋊Q818yes—
352C4×C89—24no—
353C4×C89—24no—
354C4×C89—42no—
355C4×C89—42no—
356C4×C89—42no—
357C4×C89—42no—
358C4×C89—42no—
359Dic89—24no—
360Dic89—24no—
361Dic89—42no—
362Dic89—42no—
363Dic89—42no—
364Dic89—42no—
365Dic89—42no—
366C2×#2627—891nomaximal, Sylow
367C2×C89#262718yescomplemented
368C2×C89C22×C22⋊Q811yescharacteristic
369C2×C89C2×#53411yescharacteristic
370C2×C89C2×#53611yescharacteristic
371C2×C89C2×#53911yescharacteristic
372C2×C89C2×#53911yescharacteristic
373C2×C89C2×#54411yescharacteristic
374C2×C89C2×#54411yescharacteristic
375D89—28no—
376C22×C22⋊Q8—891no—
377C23×C4⋊C4—891no—
378#2627—8916no—
379C2×#400—891no—
380C2×#400—891no—
381C2×#398—891no—
382C2×#398—891no—
383C2×#398—891no—
384C2×#398D8911yescharacteristic, complemented
385C2×#395—891no—
386C2×#395—891no—
387C2×#385—891no—
388C2×#385—891no—
389C2×#381—891no—
390C2×#381—891no—
391C2×#380—891no—
392C89C2×#262711yescharacteristic, complemented, Sylow
393C23×Q8—891no—
394C24×C4—891no—
395C24×C4—891no—
396C24×C4—891no—
397C2×C22⋊Q8—898no—
398C2×C22⋊Q8—1788no—
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⋊C4—891no—
407C22×C4⋊C4—891no—
408C22×C4⋊C4—898no—
409C22×C4⋊C4—1788no—
410C22×C4⋊C4C2×D8911yescharacteristic
411C22×C4⋊C4C2×D8911yescharacteristic
412C22×C4⋊C4C2×D8911yescharacteristic
413C22×C4⋊C4C2×D8911yescharacteristic
414C22×C22⋊C4—891no—
415C22×C22⋊C4—891no—
416C22×C22⋊C4—891no—
417C22×C22⋊C4—891no—
418#400—898no—
419#400—898no—
420#398—898no—
421#398—898no—
422#398—898no—
423#398C2×D8918yescomplemented
424#395—898no—
425#395—898no—
426#385—898no—
427#385—898no—
428#381—898no—
429#381—898no—
430#380—898no—
431C2×#95—891no—
432C2×#95—891no—
433C2×#95—891no—
434C2×#95—891no—
435C2×#95—891no—
436C2×#95—891no—
437C2×#95—891no—
438C2×#95—891no—
439C2×#95—891no—
440C2×#95—891no—
441C2×#95—891no—
442C2×#95C2×D8911yescharacteristic
443C2×#95C2×D8911yescharacteristic
444C2×#95C2×D8911yescharacteristic
445C25—891no—
446C22×Q8—894no—
447C22×Q8—3562no—
448C22×Q8—3562no—
449C22×Q8—1784no—
450C23×C4—891no—
451C23×C4—891no—
452C23×C4—898no—
453C23×C4—894no—
454C23×C4—898no—
455C23×C4—894no—
456C23×C4—891no—
457C23×C4—891no—
458C23×C4—891no—
459C23×C4—891no—
460C23×C4—891no—
461C23×C4—894no—
462C23×C4—3562no—
463C23×C4—3562no—
464C23×C4—3562no—
465C23×C4—3562no—
466C23×C4—1784no—
467C23×C4—1784no—
468C23×C4—1784no—
469C23×C4C22×D8911yescharacteristic
470C23×C4C22×D8911yescharacteristic
471C23×C4C22×D8911yescharacteristic
472C23×C4C22×D8911yescharacteristic
473C23×C4C22×D8911yescharacteristic
474C23×C4C22×D8911yescharacteristic
475C23×C4C22×D8911yescharacteristic
476C22⋊Q8—17832no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—894no—
482C2×C4⋊C4—894no—
483C2×C4⋊C4—894no—
484C2×C4⋊C4—894no—
485C2×C4⋊C4—894no—
486C2×C4⋊C4—894no—
487C2×C4⋊C4—894no—
488C2×C4⋊C4—894no—
489C2×C4⋊C4—894no—
490C2×C4⋊C4—3562no—
491C2×C4⋊C4—3562no—
492C2×C4⋊C4—3562no—
493C2×C4⋊C4—3562no—
494C2×C4⋊C4—17832no—
495C2×C4⋊C4—1784no—
496C2×C4⋊C4—1784no—
497C2×C4⋊C4—1784no—
498C2×C4⋊C4—1784no—
499C2×C4⋊C4—1784no—
500C2×C4⋊C4C22×D8914yes—
501C2×C4⋊C4C22×D8914yes—
502C2×C4⋊C4C22×D8914yes—
503C2×C4⋊C4C22×D8914yes—
504C2×C22⋊C4—894no—
505C2×C22⋊C4—894no—
506C2×C22⋊C4—894no—
507C2×C22⋊C4—894no—
508C2×C22⋊C4—1784no—
509C2×C22⋊C4—1784no—
510C2×C22⋊C4—1784no—
511C2×C22⋊C4—1784no—
512#95—894no—
513#95—894no—
514#95—894no—
515#95—894no—
516#95—894no—
517#95—894no—
518#95—894no—
519#95—894no—
520#95—894no—
521#95—894no—
522#95—894no—
523#95C22×D8914yes—
524#95C22×D8914yes—
525#95C22×D8914yes—
526C24—894no—
527C24—894no—
528C24—894no—
529C24—892no—
530C24—1782no—
531C24—1782no—
532C24—1782no—
533C24—1782no—
534C24C23×D8911yescharacteristic
535C2×Q8—3564no—
536C2×Q8—3564no—
537C2×Q8—35616no—
538C2×Q8—1788no—
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—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—894no—
559C22×C4—894no—
560C22×C4—892no—
561C22×C4—892no—
562C22×C4—8916no—
563C22×C4—8916no—
564C22×C4—892no—
565C22×C4—892no—
566C22×C4—892no—
567C22×C4—892no—
568C22×C4—892no—
569C22×C4—35616no—
570C22×C4—3564no—
571C22×C4—3564no—
572C22×C4—3564no—
573C22×C4—3564no—
574C22×C4—35616no—
575C22×C4—1788no—
576C22×C4—1788no—
577C22×C4—1788no—
578C22×C4—17832no—
579C22×C4—1782no—
580C22×C4—1782no—
581C22×C4—1782no—
582C22×C4—1782no—
583C22×C4—1782no—
584C22×C4—1782no—
585C22×C4—1782no—
586C22×C4—1782no—
587C22×C4—1782no—
588C22×C4—1782no—
589C22×C4—1782no—
590C22×C4—1782no—
591C22×C4—1782no—
592C22×C4—1782no—
593C22×C4—1782no—
594C22×C4—1782no—
595C22×C4—1782no—
596C22×C4—1782no—
597C22×C4—1782no—
598C22×C4D4×D8914yes—
599C22×C4Q8×D8914yes—
600C22×C4C23×D8912yes—
601C22×C4C23×D8912yes—
602C22×C4C23×D8912yes—
603C22×C4C23×D8912yes—
604C22×C4C23×D8912yes—
605C22×C4C23×D8912yes—
606C22×C4C23×D8912yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—3564no—
612C4⋊C4—3564no—
613C4⋊C4—3564no—
614C4⋊C4—3564no—
615C4⋊C4—1788no—
616C4⋊C4—1788no—
617C4⋊C4—1788no—
618C4⋊C4—1788no—
619C4⋊C4—1788no—
620C22⋊C4—1788no—
621C22⋊C4—1788no—
622C22⋊C4—1788no—
623C22⋊C4—1788no—
624C23—894no—
625C23—894no—
626C23—894no—
627C23—8916no—
628C23—1788no—
629C23—1788no—
630C23—1782no—
631C23—1782no—
632C23—1782no—
633C23—1782no—
634C23—1788no—
635C23—1788no—
636C23—1788no—
637C23—1788no—
638C23C2×D4×D8912yes—
639C23C2×Q8×D8912yes—
640C23#41×D8912yes—
641C23#1566805712yes—
642C23#1566805812yes—
643C23#1566805912yes—
644C23#1566806012yes—
645C23C24×D8911yescharacteristic
646Q8—35616no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
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—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—894no—
674C2×C4—894no—
675C2×C4—35616no—
676C2×C4—35616no—
677C2×C4—3564no—
678C2×C4—3564no—
679C2×C4—3564no—
680C2×C4—3564no—
681C2×C4—3564no—
682C2×C4—17832no—
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—1782no—
692C2×C4—1782no—
693C2×C4—1782no—
694C2×C4—1782no—
695C2×C4—1782no—
696C2×C4—1782no—
697C2×C4—1782no—
698C2×C4—1788no—
699C2×C4—1782no—
700C2×C4—1782no—
701C2×C4—1782no—
702C2×C4—1782no—
703C2×C4—1788no—
704C2×C4C2×D4×D8914yes—
705C2×C4C2×Q8×D8914yes—
706C22—898no—
707C22—17832no—
708C22—1784no—
709C22—1784no—
710C22—1784no—
711C22—1784no—
712C22—1784no—
713C22—1784no—
714C22C22⋊Q8×D8914yes—
715C22#1915215614yes—
716C22#1915217114yes—
717C22#1915219114yes—
718C22#1915219614yes—
719C22#1915222514yes—
720C22#1915222814yes—
721C22C22×D4×D8911yescharacteristic
722C22C22×Q8×D8911yescharacteristic
723C22C2×#41×D8911yescharacteristic
724C22C2×#1566805711yescharacteristic
725C22C2×#1566805811yescharacteristic
726C22C2×#1566805911yescharacteristic
727C22C2×#1566806011yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—3562no—
736C4—3562no—
737C4—3562no—
738C4—3562no—
739C4—3562no—
740C4—1784no—
741C4—1784no—
742C2—1788no—
743C2#2602607018yesdirect product factor
744C2C2×C22⋊Q8×D8911yescharacteristic
745C2C2×#1915215611yescharacteristic
746C2C2×#1915217111yescharacteristic
747C2C2×#1915219111yescharacteristic
748C2C2×#1915219611yescharacteristic
749C2C2×#1915222511yescharacteristic
750C2C2×#1915222811yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#398×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#398D89
hypocenterC89C2×#2627
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #26026070C2direct (N × H)
4. C2×#19151540C2semidirect
5. C2×#19151539C2semidirect
6. C2×#19151531C2semidirect
7. C2×#19151531C2semidirect
8. C2×#19151528C2semidirect
9. C2×#19151519C2semidirect
10. C2×#19151518C2semidirect
16. C2×#398×C89C2semidirect
38. #19151540C22semidirect
39. #19151539C22semidirect
40. #19151531C22semidirect
41. #19151531C22semidirect
42. #19151528C22semidirect
43. #19151519C22semidirect
44. #19151518C22semidirect
65. #398×C89C22semidirect
89. C22×C4×D89Q8semidirect
201. C2×C4×D89C2×Q8semidirect
367. C2×C89#2627semidirect
384. C2×#398D89semidirect
392. C89C2×#2627semidirect
423. #398C2×D89semidirect
743. C2#26026070direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679902
C22×C4⋊C4×D892
#260260702
C2×#191515402
C2×#191515392
C2×#191515312
C2×#191515282
C2×#191515192
C2×#191515182
C2×#191514722
C2×#191514692
C2×#191514602
C2×#191514552
C2×#398×C892
C2×#262789