Finite Group Databasebeta

← C2×#26023329 #36714055

Subgroups — C2×#26023329 #36714055

Order 22784.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667990C211yesmaximal, characteristic
2#26023329C2116yesmaximal, direct product factor
3C2×#19151503C211yesmaximal, characteristic, complemented
4C2×#19151502C211yesmaximal, characteristic, complemented
5C2×#19151485C211yesmaximal, characteristic, complemented
6C2×#19151480C211yesmaximal, characteristic, complemented
7C2×#19151480C211yesmaximal, characteristic, complemented
8C2×#19151472C211yesmaximal, characteristic
9C2×#19151469C211yesmaximal, characteristic
10C2×C4⋊C4×Dic89C211yesmaximal, characteristic, complemented
11C2×C4×#13083553C211yesmaximal, characteristic, complemented
12C2×C4×#13083551C211yesmaximal, characteristic
13C2×#19151445C211yesmaximal, characteristic
14C2×#19151445C211yesmaximal, characteristic
15C2×#95×D89C211yesmaximal, characteristic
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C23×C4×D89C2211yescharacteristic
21C2×#15667990C4116yescomplemented
22C2×#15667990C2218yes—
23C22×C4⋊Dic89C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×C4×Dic89C2211yescharacteristic
33C22×C4×Dic89C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35C22×C4×Dic89C2211yescharacteristic
36C22×C4×Dic89C2211yescharacteristic
37#19151503C2218yescomplemented
38#19151502C2218yescomplemented
39#19151485C2218yescomplemented
40#19151480C2218yescomplemented
41#19151480C2218yescomplemented
42#19151472C2218yes—
43#19151469C2218yes—
44C4⋊C4×Dic89C2218yescomplemented
45C4×#13083553C2218yescomplemented
46C4×#13083551C2218yes—
47#19151445C2218yes—
48#19151445C2218yes—
49C2×#15667919C2211yescharacteristic
50C2×#15667919C2211yescharacteristic
51C2×#15667919C2211yescharacteristic
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59#95×D89C2218yes—
60C22×C4⋊C4×C89C2211yescharacteristic
61C22×C4⋊C4×C89C2211yescharacteristic
62C22×C42×C89C2211yescharacteristic
63#387×C89C2218yescomplemented
64C2×#95×C89C2211yescharacteristic
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C24×D89C2311yescharacteristic
69C22×Dic178—42no—
70C22×Dic178—42no—
71C22×Dic178C2×C418yescomplemented
72C22×Dic178C2314yes—
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C22×C4×D89—24no—
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×D89C2×C418yes—
89C22×C4×D89C2314yes—
90C22×C4×D89C2314yes—
91C22×C4×D89C2314yes—
92#15667990C2×C4164yescomplemented
93C2×C4⋊Dic89—24no—
94C2×C4⋊Dic89C2314yes—
95C2×#13083553—24no—
96C2×#13083553—42no—
97C2×#13083553C2×C418yescomplemented
98C2×#13083553C2×C418yescomplemented
99C2×#13083553C2314yes—
100C2×#13083553C2314yes—
101C2×#13083553C2314yes—
102C2×#13083553C2314yes—
103C2×#13083551—24no—
104C2×#13083551C2×C418yes—
105C2×#13083551C2×C418yes—
106C2×#13083551Q818yescomplemented
107C2×#13083551C2314yes—
108C2×#13083551C2314yes—
109C2×#13083551C2314yes—
110C2×#13083551C2314yes—
111C2×C4×Dic89—24no—
112C2×C4×Dic89—24no—
113C2×C4×Dic89—42no—
114C2×C4×Dic89—42no—
115C2×C4×Dic89—42no—
116C2×C4×Dic89C2314yes—
117C2×C4×Dic89C2314yes—
118C2×C4×Dic89C2314yes—
119C2×C4×Dic89C2314yes—
120C2×C4×Dic89C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123#15667919C2314yes—
124#15667919C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131C23×C4×C89C2311yescharacteristic
132C23×C4×C89C2311yescharacteristic
133C23×C4×C89C2311yescharacteristic
134C23×C4×C89C2311yescharacteristic
135C23×C4×C89C2311yescharacteristic
136C23×C4×C89C2311yescharacteristic
137C23×C4×C89C2311yescharacteristic
138C2×C4⋊C4×C89—42no—
139C2×C4⋊C4×C89C2×C418yescomplemented
140C2×C4⋊C4×C89C2314yes—
141C2×C4⋊C4×C89C2314yes—
142C2×C42×C89—42no—
143C2×C42×C89C2314yes—
144#95×C89C2314yes—
145#95×C89C2314yes—
146#95×C89C2314yes—
147#95×C89C2314yes—
148C23×D89—22no—
149C23×D89—22no—
150C23×D89—22no—
151C23×D89—22no—
152C23×D89C22×C414yes—
153C23×D89C2×Q814yes—
154C23×D89#4114yes—
155C23×D89C2412yes—
156C2×Dic178—416no—
157C2×Dic178—44no—
158C2×Dic178—44no—
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—22no—
169C22×Dic89—22no—
170C22×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89—22no—
175C22×Dic89C22×C414yes—
176C22×Dic89C22×C414yes—
177C22×Dic89C22×C414yes—
178C22×Dic89C2×Q814yes—
179C22×Dic89#4114yes—
180C22×Dic89#4114yes—
181C22×Dic89C2412yes—
182C22×Dic89C2412yes—
183C22×Dic89C2412yes—
184C22×Dic89C2412yes—
185C22×Dic89C2412yes—
186C22×Dic89C2412yes—
187C22×Dic89C2412yes—
188C2×C4×D89—28no—
189C2×C4×D89—28no—
190C2×C4×D89—28no—
191C2×C4×D89—28no—
192C2×C4×D89—416no—
193C2×C4×D89—44no—
194C2×C4×D89—44no—
195C2×C4×D89—44no—
196C2×C4×D89—44no—
197C2×C4×D89—416no—
198C2×C4×D89—416no—
199C2×C4×D89C22×C4116yes—
200C4⋊Dic89—28no—
201#13083553—28no—
202#13083553—44no—
203#13083553C22×C4116yescomplemented
204#13083553C22×C4116yescomplemented
205#13083551—28no—
206#13083551C22×C4116yes—
207#13083551C22×C4116yes—
208#13083551C2×Q8116yescomplemented
209C4×Dic89—28no—
210C4×Dic89—28no—
211C4×Dic89—44no—
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×C89C22×C414yes—
233C22×C4×C89C22×C414yes—
234C22×C4×C89C22×C414yes—
235C22×C4×C89C2×Q814yes—
236C22×C4×C89C2412yes—
237C22×C4×C89C2412yes—
238C22×C4×C89C2412yes—
239C22×C4×C89C2412yes—
240C22×C4×C89C2412yes—
241C22×C4×C89C2412yes—
242C22×C4×C89C2412yes—
243C4⋊C4×C89—44no—
244C4⋊C4×C89C22×C4116yescomplemented
245C42×C89—44no—
246C23×C89C23×C412yes—
247C23×C89C22×Q812yes—
248C23×C89C2×#4112yes—
249C23×C89C2×#4112yes—
250C23×C89C2×#4112yes—
251C23×C89H(5,𝔽2)12yes—
252C23×C89H(5,𝔽2)12yes—
253C23×C89C2511yescharacteristic
254C22×D89—28no—
255C22×D89—28no—
256C22×D89—28no—
257C22×D89—28no—
258C22×D89—28no—
259C22×D89—28no—
260C22×D89—22no—
261C22×D89—22no—
262C22×D89—22no—
263C22×D89—22no—
264C22×D89C4×Q8116yes—
265C22×D89C23×C414yes—
266C22×D89C22×Q814yes—
267C22×D89C2×#4114yes—
268C2×C4×C89—28no—
269C2×C4×C89—28no—
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—44no—
290C2×C4×C89—44no—
291C2×C4×C89—44no—
292C2×C4×C89C23×C414yes—
293C2×C4×C89C23×C414yes—
294C2×C4×C89C23×C414yes—
295C2×C4×C89C22×Q814yes—
296C2×Dic89—28no—
297C2×Dic89—28no—
298C2×Dic89—28no—
299C2×Dic89—28no—
300C2×Dic89—28no—
301C2×Dic89—28no—
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×Dic89C23×C414yes—
319C2×Dic89C23×C414yes—
320C2×Dic89C23×C414yes—
321C2×Dic89C22×Q814yes—
322C2×Dic89C2×#4114yes—
323C2×Dic89C2×#4114yes—
324C4×D89—416no—
325C4×D89—416no—
326C4×D89—416no—
327Dic178—416no—
328C22×C89C2×C4×Q814yes—
329C22×C89C4×#4114yes—
330C22×C89#51814yes—
331C22×C89#55114yes—
332C22×C89#55114yes—
333C22×C89#55414yes—
334C22×C89#55414yes—
335C22×C89C24×C411yescharacteristic
336C22×C89C23×Q811yescharacteristic
337C22×C89C22×#4111yescharacteristic
338C22×C89C22×#4111yescharacteristic
339C22×C89C22×#4111yescharacteristic
340C22×C89C2×H(5,𝔽2)11yescharacteristic
341C22×C89C2×H(5,𝔽2)11yescharacteristic
342C2×D89—232no—
343C2×D89—24no—
344C2×D89—24no—
345C2×D89—24no—
346C2×D89—24no—
347C2×D89—24no—
348C2×D89—24no—
349C2×D89C2×C4×Q818yes—
350C4×C89—24no—
351C4×C89—24no—
352C4×C89—24no—
353C4×C89—24no—
354C4×C89—42no—
355C4×C89—42no—
356C4×C89—42no—
357Dic89—24no—
358Dic89—24no—
359Dic89—24no—
360Dic89—24no—
361Dic89—24no—
362Dic89—24no—
363Dic89—42no—
364C2×#2368—891nomaximal, Sylow
365C2×C89#236818yescomplemented
366C2×C89C22×C4×Q811yescharacteristic
367C2×C89C2×C4×#4111yescharacteristic
368C2×C89C2×#51811yescharacteristic
369C2×C89C2×#55111yescharacteristic
370C2×C89C2×#55111yescharacteristic
371C2×C89C2×#55411yescharacteristic
372C2×C89C2×#55411yescharacteristic
373D89—28no—
374C22×C22⋊Q8—891no—
375#2368—8916no—
376C2×#391—891no—
377C2×#391—891no—
378C2×#387—891no—
379C2×#387—891no—
380C2×#387—891no—
381C2×#387D8911yescharacteristic, complemented
382C2×#385—891no—
383C2×#385—891no—
384C2×C4×C4⋊C4—891no—
385C2×C4×C4⋊C4—891no—
386C2×C4×C22⋊C4—891no—
387C2×C4×C22⋊C4—891no—
388C2×C4×C22⋊C4—891no—
389C22×#95—891no—
390C89C2×#236811yescharacteristic, complemented, Sylow
391C23×Q8—891no—
392C24×C4—891no—
393C24×C4—891no—
394C24×C4—891no—
395C2×C22⋊Q8—8916no—
396C2×C22⋊Q8—898no—
397C22×C4⋊C4—891no—
398C22×C4⋊C4—891no—
399C22×C4⋊C4—891no—
400C22×C4⋊C4—891no—
401C22×C4⋊C4—891no—
402C22×C4⋊C4C2×D8911yescharacteristic
403C22×C4⋊C4C2×D8911yescharacteristic
404C22×C22⋊C4—891no—
405C22×C22⋊C4—891no—
406C22×C22⋊C4—891no—
407C22×C22⋊C4—891no—
408C22×C42—891no—
409C22×C42—891no—
410C22×C42—891no—
411C22×C42—891no—
412C22×C42—891no—
413C22×C42C2×D8911yescharacteristic
414#391—898no—
415#391—898no—
416#387—898no—
417#387—898no—
418#387—898no—
419#387C2×D8918yescomplemented
420#385—898no—
421#385—898no—
422C4×C4⋊C4—898no—
423C4×C4⋊C4—898no—
424C4×C22⋊C4—898no—
425C4×C22⋊C4—898no—
426C4×C22⋊C4—898no—
427C2×#95—891no—
428C2×#95—891no—
429C2×#95—891no—
430C2×#95—891no—
431C2×#95—891no—
432C2×#95—891no—
433C2×#95—891no—
434C2×#95—891no—
435C2×#95—891no—
436C2×#95—891no—
437C2×#95—898no—
438C2×#95C2×D8911yescharacteristic
439C2×#95C2×D8911yescharacteristic
440C2×#95C2×D8911yescharacteristic
441C2×#95C2×D8911yescharacteristic
442C25—891no—
443C22×Q8—898no—
444C22×Q8—894no—
445C22×Q8—3562no—
446C22×Q8—3562no—
447C23×C4—891no—
448C23×C4—891no—
449C23×C4—891no—
450C23×C4—891no—
451C23×C4—891no—
452C23×C4—891no—
453C23×C4—898no—
454C23×C4—894no—
455C23×C4—891no—
456C23×C4—894no—
457C23×C4—894no—
458C23×C4—3562no—
459C23×C4—3562no—
460C23×C4—3562no—
461C23×C4—3562no—
462C23×C4—1784no—
463C23×C4—1784no—
464C23×C4—1784no—
465C23×C4—1784no—
466C23×C4C22×D8911yescharacteristic
467C23×C4C22×D8911yescharacteristic
468C23×C4C22×D8911yescharacteristic
469C23×C4C22×D8911yescharacteristic
470C23×C4C22×D8911yescharacteristic
471C23×C4C22×D8911yescharacteristic
472C23×C4C22×D8911yescharacteristic
473C22⋊Q8—8964no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—898no—
476C2×C4⋊C4—898no—
477C2×C4⋊C4—894no—
478C2×C4⋊C4—894no—
479C2×C4⋊C4—894no—
480C2×C4⋊C4—894no—
481C2×C4⋊C4—894no—
482C2×C4⋊C4—3562no—
483C2×C4⋊C4—1784no—
484C2×C4⋊C4—1784no—
485C2×C4⋊C4C4×D8918yescomplemented
486C2×C4⋊C4C22×D8914yes—
487C2×C4⋊C4C22×D8914yes—
488C2×C22⋊C4—898no—
489C2×C22⋊C4—898no—
490C2×C22⋊C4—898no—
491C2×C22⋊C4—894no—
492C2×C22⋊C4—894no—
493C2×C22⋊C4—894no—
494C2×C22⋊C4—894no—
495C2×C22⋊C4—1784no—
496C2×C42—42no—
497C2×C42—894no—
498C2×C42—894no—
499C2×C42—894no—
500C2×C42—894no—
501C2×C42—894no—
502C2×C42—3562no—
503C2×C42—3562no—
504C2×C42—3562no—
505C2×C42—1784no—
506C2×C42—1784no—
507C2×C42C22×D8914yes—
508#95—894no—
509#95—894no—
510#95—894no—
511#95—894no—
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—894no—
524C24—894no—
525C24—892no—
526C24—1782no—
527C24—1782no—
528C24—1782no—
529C24—1782no—
530C24C23×D8911yescharacteristic
531C2×Q8—8916no—
532C2×Q8—3564no—
533C2×Q8—3564no—
534C2×Q8—35616no—
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—894no—
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—8916no—
565C22×C4—892no—
566C22×C4—3564no—
567C22×C4—3564no—
568C22×C4—35616no—
569C22×C4—3564no—
570C22×C4—3564no—
571C22×C4—35616no—
572C22×C4—35616no—
573C22×C4—1788no—
574C22×C4—1788no—
575C22×C4—1788no—
576C22×C4—1788no—
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×C4—1782no—
586C22×C4—1782no—
587C22×C4—1782no—
588C22×C4—1782no—
589C22×C4—1782no—
590C22×C4—1782no—
591C22×C4—1782no—
592C22×C4C2×C4×D8914yes—
593C22×C4C2×C4×D8914yes—
594C22×C4C2×C4×D8914yes—
595C22×C4Q8×D8914yes—
596C22×C4C23×D8912yes—
597C22×C4C23×D8912yes—
598C22×C4C23×D8912yes—
599C22×C4C23×D8912yes—
600C22×C4C23×D8912yes—
601C22×C4C23×D8912yes—
602C22×C4C23×D8912yes—
603C4⋊C4—44no—
604C4⋊C4—8916no—
605C4⋊C4—8916no—
606C4⋊C4—3564no—
607C4⋊C4—1788no—
608C4⋊C4—1788no—
609C4⋊C4C2×C4×D89116yescomplemented
610C22⋊C4—8916no—
611C22⋊C4—8916no—
612C22⋊C4—8916no—
613C22⋊C4—1788no—
614C42—44no—
615C42—3564no—
616C42—3564no—
617C42—3564no—
618C42—1788no—
619C42—1788no—
620C23—894no—
621C23—894no—
622C23—894no—
623C23—8916no—
624C23—1782no—
625C23—1782no—
626C23—1782no—
627C23—1782no—
628C23—1788no—
629C23—1788no—
630C23—1788no—
631C23—1788no—
632C23—1788no—
633C23—1788no—
634C23C22×C4×D8912yes—
635C23C2×Q8×D8912yes—
636C23#41×D8912yes—
637C23#41×D8912yes—
638C23#41×D8912yes—
639C23#1566805712yes—
640C23#1566805812yes—
641C23C24×D8911yescharacteristic
642Q8—35616no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—28no—
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—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—894no—
668C2×C4—894no—
669C2×C4—894no—
670C2×C4—894no—
671C2×C4—894no—
672C2×C4—894no—
673C2×C4—35616no—
674C2×C4—35616no—
675C2×C4—35616no—
676C2×C4—3564no—
677C2×C4—1782no—
678C2×C4—1782no—
679C2×C4—1782no—
680C2×C4—1782no—
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—1782no—
692C2×C4—1788no—
693C2×C4—1788no—
694C2×C4—1788no—
695C2×C4—1788no—
696C2×C4—1788no—
697C2×C4—1788no—
698C2×C4C22×C4×D8914yes—
699C2×C4C22×C4×D8914yes—
700C2×C4C22×C4×D8914yes—
701C2×C4C2×Q8×D8914yes—
702C22—898no—
703C22—1784no—
704C22—1784no—
705C22—1784no—
706C22—1784no—
707C22—1784no—
708C22—1784no—
709C22—17832no—
710C22C4×Q8×D8914yes—
711C22#1915206614yes—
712C22#1915207014yes—
713C22#1915227314yes—
714C22#1915227614yes—
715C22#1915230214yes—
716C22#1915230414yes—
717C22C23×C4×D8911yescharacteristic
718C22C22×Q8×D8911yescharacteristic
719C22C2×#41×D8911yescharacteristic
720C22C2×#41×D8911yescharacteristic
721C22C2×#41×D8911yescharacteristic
722C22C2×#1566805711yescharacteristic
723C22C2×#1566805811yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—3562no—
732C4—1784no—
733C4—1784no—
734C4—1784no—
735C4—1784no—
736C4—1784no—
737C4—1784no—
738C2—1788no—
739C2#2602332918yesdirect product factor
740C2C2×C4×Q8×D8911yescharacteristic
741C2C2×#1915206611yescharacteristic
742C2C2×#1915207011yescharacteristic
743C2C2×#1915227311yescharacteristic
744C2C2×#1915227611yescharacteristic
745C2C2×#1915230211yescharacteristic
746C2C2×#1915230411yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
cosocleC23×C89C25
hypercenterC2×#387D89
hypocenterC89C2×#2368
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #26023329C2direct (N × H)
3. C2×#19151503C2semidirect
4. C2×#19151502C2semidirect
5. C2×#19151485C2semidirect
6. C2×#19151480C2semidirect
7. C2×#19151480C2semidirect
10. C2×C4⋊C4×Dic89C2semidirect
11. C2×C4×#13083553C2semidirect
16. C2×#387×C89C2semidirect
21. C2×#15667990C4semidirect
37. #19151503C22semidirect
38. #19151502C22semidirect
39. #19151485C22semidirect
40. #19151480C22semidirect
41. #19151480C22semidirect
44. C4⋊C4×Dic89C22semidirect
45. C4×#13083553C22semidirect
63. #387×C89C22semidirect
71. C22×Dic178C2×C4semidirect
92. #15667990C2×C4semidirect
97. C2×#13083553C2×C4semidirect
98. C2×#13083553C2×C4semidirect
106. C2×#13083551Q8semidirect
139. C2×C4⋊C4×C89C2×C4semidirect
159. C2×Dic178C22×C4semidirect
203. #13083553C22×C4semidirect
204. #13083553C22×C4semidirect
208. #13083551C2×Q8semidirect
244. C4⋊C4×C89C22×C4semidirect
365. C2×C89#2368semidirect
381. C2×#387D89semidirect
390. C89C2×#2368semidirect
419. #387C2×D89semidirect
485. C2×C4⋊C4C4×D89semidirect
609. C4⋊C4C2×C4×D89semidirect
739. C2#26023329direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679902
#260233292
C2×#191515032
C2×#191515022
C2×#191514852
C2×#191514802
C2×#191514722
C2×#191514692
C2×C4⋊C4×Dic892
C2×C4×#130835532
C2×C4×#130835512
C2×#191514452
C2×#95×D892
C2×#387×C892
C2×#236889