Finite Group Databasebeta

← C2×#26022784 #36712875

Subgroups — C2×#26022784 #36712875

Order 22784.

3854 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667989C211yesmaximal, characteristic
2C22×#15667977C211yesmaximal, characteristic, complemented
3C23×C4×Dic89C211yesmaximal, characteristic
4#26022784C2116yesmaximal, direct product factor
5C2×#19151502C211yesmaximal, characteristic, complemented
6C2×#19151493C211yesmaximal, characteristic, complemented
7C2×#19151483C211yesmaximal, characteristic, complemented
8C2×#19151479C211yesmaximal, characteristic, complemented
9C2×#19151471C211yesmaximal, characteristic
10C2×#19151456C211yesmaximal, characteristic
11C2×C4⋊C4×Dic89C211yesmaximal, characteristic, complemented
12C2×#19151449C211yesmaximal, characteristic, complemented
13C2×#19151449C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic89C211yesmaximal, characteristic
15C2×C22⋊C4×Dic89C211yesmaximal, characteristic
16C2×#385×C89C211yesmaximal, characteristic
17C23×Dic178C2211yescharacteristic
18C24×Dic89C2211yescharacteristic
19C24×Dic89C2211yescharacteristic
20C2×#15667989C4116yescomplemented
21C2×#15667989C2218yes—
22C2×#15667977—28no—
23C2×#15667977C2218yescomplemented
24C22×C4⋊Dic89C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×C22⋊Dic89C2211yescharacteristic
32C22×C22⋊Dic89C2211yescharacteristic
33C22×C4×Dic89—28no—
34C22×C4×Dic89C2211yescharacteristic
35C22×C4×Dic89C2211yescharacteristic
36C22×C4×Dic89C2211yescharacteristic
37C22×C4×Dic89C2211yescharacteristic
38C22×C4×Dic89C2218yes—
39C22×C4×Dic89C2211yescharacteristic
40C22×C4×Dic89C2211yescharacteristic
41C22×C4×Dic89C2211yescharacteristic
42C22×C4×Dic89C2211yescharacteristic
43#19151502C2218yescomplemented
44#19151493C2218yescomplemented
45#19151483C2218yescomplemented
46#19151479C2218yescomplemented
47#19151471C2218yes—
48#19151456C2218yes—
49C4⋊C4×Dic89C2218yescomplemented
50#19151449C2218yescomplemented
51#19151449C2218yescomplemented
52C22⋊C4×Dic89C2218yes—
53C22⋊C4×Dic89C2218yes—
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C2×#15667919C2211yescharacteristic
62C24×C4×C89C2211yescharacteristic
63C22×C4⋊C4×C89C2211yescharacteristic
64C22×C4⋊C4×C89C2211yescharacteristic
65C22×C22⋊C4×C89C2211yescharacteristic
66C22×C22⋊C4×C89C2211yescharacteristic
67#385×C89C2218yes—
68C2×#95×C89C2211yescharacteristic
69C2×#95×C89C2211yescharacteristic
70C22×Dic178—24no—
71C22×Dic178—24no—
72C22×Dic178C2×C418yescomplemented
73C22×Dic178C2314yes—
74C23×Dic89—24no—
75C23×Dic89—24no—
76C23×Dic89—24no—
77C23×Dic89—24no—
78C23×Dic89C2×C418yes—
79C23×Dic89Q818yescomplemented
80C23×Dic89C2311yescharacteristic
81C23×Dic89C2311yescharacteristic
82C23×Dic89C2311yescharacteristic
83C23×Dic89C2314yes—
84C23×Dic89C2311yescharacteristic
85C23×Dic89C2311yescharacteristic
86C23×Dic89C2311yescharacteristic
87C23×Dic89C2314yes—
88C23×Dic89C2311yescharacteristic
89C23×Dic89C2311yescharacteristic
90#15667989C2×C4164yescomplemented
91#15667977—232no—
92C2×C4⋊Dic89C2×C418yescomplemented
93C2×C4⋊Dic89C2314yes—
94C2×#13083553—24no—
95C2×#13083553—24no—
96C2×#13083553—24no—
97C2×#13083553—24no—
98C2×#13083553C2×C418yescomplemented
99C2×#13083553C2×C418yescomplemented
100C2×#13083553C2314yes—
101C2×#13083553C2314yes—
102C2×#13083553C2314yes—
103C2×#13083553C2314yes—
104C2×#13083553C2314yes—
105C2×#13083553C2314yes—
106C2×C22⋊Dic89—24no—
107C2×C22⋊Dic89C2×C418yes—
108C2×C22⋊Dic89C2314yes—
109C2×C22⋊Dic89C2314yes—
110C2×C4×Dic89—24no—
111C2×C4×Dic89—24no—
112C2×C4×Dic89—24no—
113C2×C4×Dic89—24no—
114C2×C4×Dic89—24no—
115C2×C4×Dic89—24no—
116C2×C4×Dic89—232no—
117C2×C4×Dic89—24no—
118C2×C4×Dic89D418yes—
119C2×C4×Dic89C2314yes—
120C2×C4×Dic89C2314yes—
121C2×C4×Dic89C2314yes—
122C2×C4×Dic89C2314yes—
123C2×C4×Dic89C2314yes—
124C2×C4×Dic89C2314yes—
125C2×C4×Dic89C2314yes—
126C2×C4×Dic89C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131#15667919C2314yes—
132#15667919C2314yes—
133#15667919C2314yes—
134#15667919C2314yes—
135C25×C89C2311yescharacteristic
136C23×C4×C89—24no—
137C23×C4×C89—24no—
138C23×C4×C89—24no—
139C23×C4×C89C2311yescharacteristic
140C23×C4×C89C2314yes—
141C23×C4×C89C2311yescharacteristic
142C23×C4×C89C2311yescharacteristic
143C23×C4×C89C2311yescharacteristic
144C23×C4×C89C2311yescharacteristic
145C23×C4×C89C2311yescharacteristic
146C2×C4⋊C4×C89—24no—
147C2×C4⋊C4×C89—24no—
148C2×C4⋊C4×C89C2314yes—
149C2×C4⋊C4×C89C2314yes—
150C2×C22⋊C4×C89—24no—
151C2×C22⋊C4×C89C2×C418yes—
152C2×C22⋊C4×C89C2314yes—
153C2×C22⋊C4×C89C2314yes—
154#95×C89C2314yes—
155#95×C89C2314yes—
156C2×Dic178—232no—
157C2×Dic178—28no—
158C2×Dic178—28no—
159C2×Dic178C22×C4116yescomplemented
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—232no—
169C22×Dic89—232no—
170C22×Dic89—28no—
171C22×Dic89—28no—
172C22×Dic89—28no—
173C22×Dic89—28no—
174C22×Dic89—22no—
175C22×Dic89—22no—
176C22×Dic89—22no—
177C22×Dic89—22no—
178C22×Dic89—22no—
179C22×Dic89—22no—
180C22×Dic89C22×C4116yes—
181C22×Dic89C22×C414yes—
182C22×Dic89C22×C414yes—
183C22×Dic89C22×C414yes—
184C22×Dic89C22×C414yes—
185C22×Dic89C2×D414yes—
186C22×Dic89C2×D414yes—
187C22×Dic89C2×Q814yes—
188C22×Dic89C2×Q814yes—
189C22×Dic89C2×Q8116yescomplemented
190C22×Dic89#4114yes—
191C22×Dic89#4114yes—
192C22×Dic89C2412yes—
193C22×Dic89C2412yes—
194C22×Dic89C2412yes—
195C22×Dic89C2412yes—
196C22×Dic89C2412yes—
197C22×Dic89C2412yes—
198C22×Dic89C2412yes—
199C22×Dic89C2412yes—
200C4⋊Dic89C22×C4116yescomplemented
201#13083553—28no—
202#13083553—28no—
203#13083553—28no—
204#13083553—28no—
205#13083553C22×C4116yescomplemented
206#13083553C22×C4116yescomplemented
207C22⋊Dic89—28no—
208C22⋊Dic89C22×C4116yes—
209C4×Dic89—28no—
210C4×Dic89—28no—
211C4×Dic89—28no—
212C4×Dic89—28no—
213C4×Dic89—28no—
214C4×Dic89—28no—
215C4×Dic89—28no—
216C4×Dic89C2×D4116yes—
217C24×C89—22no—
218C24×C89—22no—
219C24×C89—22no—
220C24×C89—22no—
221C24×C89C22×C414yes—
222C24×C89C2×Q814yes—
223C24×C89#4114yes—
224C24×C89C2412yes—
225C24×C89C2411yescharacteristic
226C22×C4×C89—232no—
227C22×C4×C89—22no—
228C22×C4×C89—22no—
229C22×C4×C89—22no—
230C22×C4×C89—22no—
231C22×C4×C89—28no—
232C22×C4×C89—22no—
233C22×C4×C89—22no—
234C22×C4×C89—22no—
235C22×C4×C89—22no—
236C22×C4×C89—28no—
237C22×C4×C89—28no—
238C22×C4×C89—22no—
239C22×C4×C89—22no—
240C22×C4×C89—22no—
241C22×C4×C89—22no—
242C22×C4×C89—22no—
243C22×C4×C89—22no—
244C22×C4×C89C22×C414yes—
245C22×C4×C89C22×C414yes—
246C22×C4×C89C2×D414yes—
247C22×C4×C89#4114yes—
248C22×C4×C89C2412yes—
249C22×C4×C89C2412yes—
250C22×C4×C89C2412yes—
251C22×C4×C89C2412yes—
252C22×C4×C89C2412yes—
253C22×C4×C89C2412yes—
254C4⋊C4×C89—28no—
255C4⋊C4×C89—28no—
256C22⋊C4×C89—28no—
257C22⋊C4×C89C22×C4116yes—
258C23×C89—28no—
259C23×C89—28no—
260C23×C89—28no—
261C23×C89—28no—
262C23×C89—28no—
263C23×C89—28no—
264C23×C89—22no—
265C23×C89—22no—
266C23×C89—22no—
267C23×C89—22no—
268C23×C89C4×Q8116yescomplemented
269C23×C89C23×C414yes—
270C23×C89C23×C412yes—
271C23×C89C22×D412yes—
272C23×C89C22×Q814yes—
273C23×C89C22×Q812yes—
274C23×C89C2×#4112yes—
275C23×C89C2×#4112yes—
276C23×C89C2×#4114yes—
277C23×C89C2×#4112yes—
278C23×C89C2×#4112yes—
279C23×C89C2511yescharacteristic
280C2×C4×C89—232no—
281C2×C4×C89—28no—
282C2×C4×C89—28no—
283C2×C4×C89—28no—
284C2×C4×C89—28no—
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—22no—
292C2×C4×C89—22no—
293C2×C4×C89—22no—
294C2×C4×C89—22no—
295C2×C4×C89—22no—
296C2×C4×C89—22no—
297C2×C4×C89—22no—
298C2×C4×C89—22no—
299C2×C4×C89—44no—
300C2×C4×C89—44no—
301C2×C4×C89C23×C414yes—
302C2×C4×C89C23×C414yes—
303C2×C4×C89C22×D414yes—
304C2×C4×C89C2×#4114yes—
305C2×Dic89—28no—
306C2×Dic89—28no—
307C2×Dic89—28no—
308C2×Dic89—28no—
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—232no—
318C2×Dic89—232no—
319C2×Dic89—22no—
320C2×Dic89—22no—
321C2×Dic89—22no—
322C2×Dic89—22no—
323C2×Dic89—22no—
324C2×Dic89—22no—
325C2×Dic89—44no—
326C2×Dic89—44no—
327C2×Dic89C4×D4116yes—
328C2×Dic89C22⋊Q8116yescomplemented
329C2×Dic89C23×C414yes—
330C2×Dic89C23×C414yes—
331C2×Dic89C23×C414yes—
332C2×Dic89C23×C414yes—
333C2×Dic89C22×D414yes—
334C2×Dic89C22×D414yes—
335C2×Dic89C22×Q814yes—
336C2×Dic89C22×Q814yes—
337C2×Dic89C2×#4114yes—
338C2×Dic89C2×#4114yes—
339Dic178—232no—
340C22×C89—24no—
341C22×C89—24no—
342C22×C89—24no—
343C22×C89—24no—
344C22×C89—24no—
345C22×C89—24no—
346C22×C89—232no—
347C22×C89C2×C4×D414yes—
348C22×C89C2×C4×Q814yes—
349C22×C89C2×C4×Q818yescomplemented
350C22×C89C4×#4114yes—
351C22×C89C2×C22⋊Q814yes—
352C22×C89#52514yes—
353C22×C89#52914yes—
354C22×C89#53314yes—
355C22×C89C24×C411yescharacteristic
356C22×C89C23×D411yescharacteristic
357C22×C89C23×Q811yescharacteristic
358C22×C89C22×#4111yescharacteristic
359C22×C89C22×#4111yescharacteristic
360C22×C89C22×#4111yescharacteristic
361C22×C89C22×#4111yescharacteristic
362C4×C89—24no—
363C4×C89—24no—
364C4×C89—24no—
365C4×C89—24no—
366C4×C89—42no—
367C4×C89—42no—
368Dic89—24no—
369Dic89—24no—
370Dic89—24no—
371Dic89—24no—
372Dic89—42no—
373Dic89—42no—
374Dic89C2×C4×D418yes—
375Dic89C2×C22⋊Q818yescomplemented
376C2×C4×C22⋊Q8—891nomaximal, Sylow
377C2×C89—28no—
378C2×C89C4×C22⋊Q818yescomplemented
379C2×C89C22×C4×D411yescharacteristic
380C2×C89C22×C4×Q811yescharacteristic
381C2×C89C2×C4×#4111yescharacteristic
382C2×C89C22×C22⋊Q811yescharacteristic
383C2×C89C2×#52511yescharacteristic
384C2×C89C2×#52911yescharacteristic
385C2×C89C2×#53311yescharacteristic
386C22×C22⋊Q8—891no—
387C22×C4×Q8—891no—
388C23×C42—891no—
389C4×C22⋊Q8—8916no—
390C2×#391—891no—
391C2×#389—891no—
392C2×#387—891no—
393C2×#387—891no—
394C2×#385—891no—
395C2×#385D8911yescharacteristic
396C2×#380—891no—
397C2×C4×C4⋊C4—891no—
398C2×C4×C4⋊C4—891no—
399C2×C4×C4⋊C4—891no—
400C2×C4×C22⋊C4—891no—
401C2×C4×C22⋊C4—891no—
402C89C2×C4×C22⋊Q811yescharacteristic, complemented, Sylow
403C23×Q8—891no—
404C24×C4—891no—
405C24×C4—891no—
406C24×C4C2×D8911yescharacteristic
407C2×C22⋊Q8—8916no—
408C2×C22⋊Q8—898no—
409C2×C4×Q8—898no—
410C2×C4×Q8—1788no—
411C22×C4⋊C4—891no—
412C22×C4⋊C4—891no—
413C22×C4⋊C4—891no—
414C22×C4⋊C4—891no—
415C22×C4⋊C4—891no—
416C22×C4⋊C4—891no—
417C22×C4⋊C4—891no—
418C22×C4⋊C4C2×D8911yescharacteristic
419C22×C4⋊C4C2×D8911yescharacteristic
420C22×C22⋊C4—891no—
421C22×C22⋊C4—891no—
422C22×C22⋊C4C2×D8911yescharacteristic
423C22×C22⋊C4C2×D8911yescharacteristic
424C22×C42—891no—
425C22×C42—891no—
426C22×C42—891no—
427C22×C42—891no—
428C22×C42—898no—
429C22×C42—891no—
430C22×C42—891no—
431C22×C42—891no—
432C22×C42—891no—
433C22×C42—1788no—
434#391—898no—
435#389—898no—
436#387—898no—
437#387—898no—
438#385—898no—
439#385C2×D8918yes—
440#380—898no—
441C4×C4⋊C4—898no—
442C4×C4⋊C4—898no—
443C4×C4⋊C4—898no—
444C4×C22⋊C4—898no—
445C4×C22⋊C4—898no—
446C2×#95—891no—
447C2×#95—891no—
448C2×#95—891no—
449C2×#95—891no—
450C2×#95—891no—
451C2×#95—891no—
452C2×#95—891no—
453C2×#95—891no—
454C2×#95C2×D8911yescharacteristic
455C2×#95C2×D8911yescharacteristic
456C25C22×D8911yescharacteristic
457C22×Q8—898no—
458C22×Q8—894no—
459C22×Q8—1784no—
460C22×Q8—1784no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—891no—
465C23×C4—891no—
466C23×C4—898no—
467C23×C4—898no—
468C23×C4—894no—
469C23×C4—894no—
470C23×C4—891no—
471C23×C4—891no—
472C23×C4—891no—
473C23×C4—891no—
474C23×C4—891no—
475C23×C4—891no—
476C23×C4—1784no—
477C23×C4—1784no—
478C23×C4—1784no—
479C23×C4—1784no—
480C23×C4C22×D8914yes—
481C23×C4C22×D8911yescharacteristic
482C23×C4C22×D8911yescharacteristic
483C23×C4C22×D8911yescharacteristic
484C23×C4C22×D8911yescharacteristic
485C23×C4C22×D8911yescharacteristic
486C23×C4C22×D8911yescharacteristic
487C22⋊Q8—8964no—
488C4×Q8—17832no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—898no—
492C2×C4⋊C4—898no—
493C2×C4⋊C4—898no—
494C2×C4⋊C4—894no—
495C2×C4⋊C4—894no—
496C2×C4⋊C4—894no—
497C2×C4⋊C4—894no—
498C2×C4⋊C4—894no—
499C2×C4⋊C4—894no—
500C2×C4⋊C4—894no—
501C2×C4⋊C4—1784no—
502C2×C4⋊C4—1784no—
503C2×C4⋊C4—1784no—
504C2×C4⋊C4—1784no—
505C2×C4⋊C4C22×D8914yes—
506C2×C4⋊C4C22×D8914yes—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—898no—
509C2×C22⋊C4—894no—
510C2×C22⋊C4—894no—
511C2×C22⋊C4—1784no—
512C2×C22⋊C4C4×D8918yes—
513C2×C22⋊C4C22×D8914yes—
514C2×C22⋊C4C22×D8914yes—
515C2×C42—898no—
516C2×C42—894no—
517C2×C42—894no—
518C2×C42—894no—
519C2×C42—894no—
520C2×C42—894no—
521C2×C42—894no—
522C2×C42—894no—
523C2×C42—894no—
524C2×C42—17832no—
525C2×C42—1784no—
526C2×C42—1784no—
527C2×C42—1784no—
528C2×C42—1784no—
529C2×C42—1784no—
530C2×C42—1784no—
531C2×C42—1784no—
532#95—894no—
533#95—894no—
534#95—894no—
535#95—894no—
536#95—894no—
537#95—894no—
538#95—894no—
539#95—894no—
540#95C22×D8914yes—
541#95C22×D8914yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×C4×D8914yes—
547C24Q8×D8914yes—
548C24#1308357314yes—
549C24C23×D8912yes—
550C24C23×D8911yescharacteristic
551C2×Q8—8916no—
552C2×Q8—1788no—
553C2×Q8—1788no—
554C2×Q8—17832no—
555C22×C4—232no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—894no—
574C22×C4—894no—
575C22×C4—894no—
576C22×C4—894no—
577C22×C4—894no—
578C22×C4—894no—
579C22×C4—892no—
580C22×C4—892no—
581C22×C4—894no—
582C22×C4—894no—
583C22×C4—894no—
584C22×C4—8916no—
585C22×C4—894no—
586C22×C4—8916no—
587C22×C4—892no—
588C22×C4—892no—
589C22×C4—892no—
590C22×C4—892no—
591C22×C4—892no—
592C22×C4—892no—
593C22×C4—1788no—
594C22×C4—1788no—
595C22×C4—1788no—
596C22×C4—1788no—
597C22×C4—17832no—
598C22×C4—17832no—
599C22×C4—1782no—
600C22×C4—1782no—
601C22×C4—1782no—
602C22×C4—1782no—
603C22×C4—1782no—
604C22×C4—1782no—
605C22×C4—1782no—
606C22×C4—1782no—
607C22×C4—1782no—
608C22×C4—1782no—
609C22×C4—1782no—
610C22×C4—1782no—
611C22×C4—1782no—
612C22×C4—1782no—
613C22×C4C2×C4×D8914yes—
614C22×C4C2×C4×D8914yes—
615C22×C4D4×D8914yes—
616C22×C4#1308357314yes—
617C22×C4C23×D8912yes—
618C22×C4C23×D8912yes—
619C22×C4C23×D8912yes—
620C22×C4C23×D8912yes—
621C22×C4C23×D8912yes—
622C22×C4C23×D8912yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—8916no—
626C4⋊C4—8916no—
627C4⋊C4—8916no—
628C4⋊C4—1788no—
629C4⋊C4—1788no—
630C4⋊C4—1788no—
631C4⋊C4—1788no—
632C22⋊C4—28no—
633C22⋊C4—8916no—
634C22⋊C4—1788no—
635C22⋊C4C2×C4×D89116yes—
636C42—8916no—
637C42—1788no—
638C42—1788no—
639C42—1788no—
640C42—1788no—
641C42—1788no—
642C42—1788no—
643C42—1788no—
644C23—28no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23#15667977116yescomplemented
655C23C22×C4×D8914yes—
656C23C22×C4×D8912yes—
657C23C2×D4×D8912yes—
658C23C2×Q8×D8914yes—
659C23C2×Q8×D8912yes—
660C23#41×D8912yes—
661C23#41×D8912yes—
662C23C2×#1308357314yes—
663C23C2×#1308357312yes—
664C23C2×#1308357312yes—
665C23C24×D8911yescharacteristic
666Q8—17832no—
667C2×C4—232no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—894no—
689C2×C4—894no—
690C2×C4—894no—
691C2×C4—894no—
692C2×C4—894no—
693C2×C4—894no—
694C2×C4—8916no—
695C2×C4—8916no—
696C2×C4—894no—
697C2×C4—894no—
698C2×C4—894no—
699C2×C4—894no—
700C2×C4—3564no—
701C2×C4—3564no—
702C2×C4—17832no—
703C2×C4—17832no—
704C2×C4—1782no—
705C2×C4—1782no—
706C2×C4—1782no—
707C2×C4—1782no—
708C2×C4—1782no—
709C2×C4—1782no—
710C2×C4—1782no—
711C2×C4—1782no—
712C2×C4—1782no—
713C2×C4—1782no—
714C2×C4—1782no—
715C2×C4—1782no—
716C2×C4—1782no—
717C2×C4—1782no—
718C2×C4—1788no—
719C2×C4—1788no—
720C2×C4—1788no—
721C2×C4—1788no—
722C2×C4C22×C4×D8914yes—
723C2×C4C22×C4×D8914yes—
724C2×C4C2×D4×D8914yes—
725C2×C4C2×#1308357314yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—232no—
732C22—24no—
733C22C4×D4×D8914yes—
734C22C2×#1566797714yes—
735C22C2×#1566797718yescomplemented
736C22C4×#1308357314yes—
737C22C22⋊Q8×D8914yes—
738C22#1915210414yes—
739C22#1915212514yes—
740C22#1915215014yes—
741C22C23×C4×D8911yescharacteristic
742C22C22×D4×D8911yescharacteristic
743C22C22×Q8×D8911yescharacteristic
744C22C2×#41×D8911yescharacteristic
745C22C2×#41×D8911yescharacteristic
746C22C22×#1308357311yescharacteristic
747C22C22×#1308357311yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—898no—
755C4—898no—
756C4—3562no—
757C4—3562no—
758C4—1784no—
759C4—1784no—
760C4—1784no—
761C4—1784no—
762C2—28no—
763C2#2602278418yesdirect product factor
764C2C2×C4×D4×D8911yescharacteristic
765C2C22×#1566797711yescharacteristic
766C2C2×C4×#1308357311yescharacteristic
767C2C2×C22⋊Q8×D8911yescharacteristic
768C2C2×#1915210411yescharacteristic
769C2C2×#1915212511yescharacteristic
770C2C2×#1915215011yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#385×C89C2
socleC24×C89C24
prime radicalC25×C89C23
cosocleC23×C89C25
hypercenterC2×#385D89
hypocenterC89C2×C4×C22⋊Q8
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#15667977C2semidirect
4. #26022784C2direct (N × H)
5. C2×#19151502C2semidirect
6. C2×#19151493C2semidirect
7. C2×#19151483C2semidirect
8. C2×#19151479C2semidirect
11. C2×C4⋊C4×Dic89C2semidirect
12. C2×#19151449C2semidirect
13. C2×#19151449C2semidirect
20. C2×#15667989C4semidirect
23. C2×#15667977C22semidirect
43. #19151502C22semidirect
44. #19151493C22semidirect
45. #19151483C22semidirect
46. #19151479C22semidirect
49. C4⋊C4×Dic89C22semidirect
50. #19151449C22semidirect
51. #19151449C22semidirect
72. C22×Dic178C2×C4semidirect
79. C23×Dic89Q8semidirect
90. #15667989C2×C4semidirect
92. C2×C4⋊Dic89C2×C4semidirect
98. C2×#13083553C2×C4semidirect
99. C2×#13083553C2×C4semidirect
159. C2×Dic178C22×C4semidirect
189. C22×Dic89C2×Q8semidirect
200. C4⋊Dic89C22×C4semidirect
205. #13083553C22×C4semidirect
206. #13083553C22×C4semidirect
268. C23×C89C4×Q8semidirect
328. C2×Dic89C22⋊Q8semidirect
349. C22×C89C2×C4×Q8semidirect
375. Dic89C2×C22⋊Q8semidirect
378. C2×C89C4×C22⋊Q8semidirect
402. C89C2×C4×C22⋊Q8semidirect
654. C23#15667977semidirect
735. C22C2×#15667977semidirect
763. C2#26022784direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679892
C22×#156679772
C23×C4×Dic892
#260227842
C2×#191515022
C2×#191514932
C2×#191514832
C2×#191514792
C2×#191514712
C2×#191514562
C2×C4⋊C4×Dic892
C2×#191514492
C2×C22⋊C4×Dic892
C2×#385×C892
C2×C4×C22⋊Q889