Finite Group Databasebeta

← C2×#26022786 #36712877

Subgroups — C2×#26022786 #36712877

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×#15667990C211yesmaximal, characteristic
2C22×#15667977C211yesmaximal, characteristic, complemented
3C22×C42×D89C211yesmaximal, characteristic
4#26022786C2116yesmaximal, direct product factor
5C2×#19151502C211yesmaximal, characteristic, complemented
6C2×#19151495C211yesmaximal, characteristic, complemented
7C2×#19151482C211yesmaximal, characteristic, complemented
8C2×#19151472C211yesmaximal, characteristic
9C2×#19151469C211yesmaximal, characteristic
10C2×#19151457C211yesmaximal, characteristic
11C2×C4⋊C4×Dic89C211yesmaximal, characteristic, complemented
12C2×#19151449C211yesmaximal, characteristic, complemented
13C2×#19151449C211yesmaximal, characteristic, complemented
14C2×#19151445C211yesmaximal, characteristic
15C2×#19151445C211yesmaximal, characteristic
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C23×C4×D89C2211yescharacteristic
21C2×#15667990C4116yescomplemented
22C2×#15667990C2218yes—
23C2×#15667977—28no—
24C2×#15667977C2218yescomplemented
25C22×C4⋊Dic89C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×#13083551C2211yescharacteristic
34C22×#13083551C2211yescharacteristic
35C22×#13083551C2211yescharacteristic
36C22×C4×Dic89C2211yescharacteristic
37C22×C4×Dic89C2211yescharacteristic
38C22×C4×Dic89C2211yescharacteristic
39C22×C4×Dic89C2211yescharacteristic
40C22×C4×Dic89C2211yescharacteristic
41C22×C4×Dic89C2211yescharacteristic
42C22×C4×Dic89C2211yescharacteristic
43C2×C42×D89—28no—
44C2×C42×D89C2218yes—
45#19151502C2218yescomplemented
46#19151495C2218yescomplemented
47#19151482C2218yescomplemented
48#19151472C2218yes—
49#19151469C2218yes—
50#19151457C2218yes—
51C4⋊C4×Dic89C2218yescomplemented
52#19151449C2218yescomplemented
53#19151449C2218yescomplemented
54#19151445C2218yes—
55#19151445C2218yes—
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C2×#15667919C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63C22×C4⋊C4×C89C2211yescharacteristic
64C22×C42×C89C2211yescharacteristic
65#387×C89C2218yescomplemented
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C2×#95×C89C2211yescharacteristic
69C2×#95×C89C2211yescharacteristic
70C24×D89C2311yescharacteristic
71C22×Dic178—24no—
72C22×Dic178—24no—
73C22×Dic178C2×C418yescomplemented
74C22×Dic178C2314yes—
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C23×Dic89C2311yescharacteristic
81C23×Dic89C2311yescharacteristic
82C22×C4×D89—24no—
83C22×C4×D89—24no—
84C22×C4×D89—24no—
85C22×C4×D89—24no—
86C22×C4×D89—24no—
87C22×C4×D89—24no—
88C22×C4×D89—24no—
89C22×C4×D89C2×C418yes—
90C22×C4×D89Q818yescomplemented
91C22×C4×D89C2314yes—
92C22×C4×D89C2314yes—
93C22×C4×D89C2314yes—
94#15667990C2×C4164yescomplemented
95#15667977—232no—
96C2×C4⋊Dic89—24no—
97C2×C4⋊Dic89C2314yes—
98C2×#13083553—24no—
99C2×#13083553—24no—
100C2×#13083553—24no—
101C2×#13083553—24no—
102C2×#13083553C2×C418yescomplemented
103C2×#13083553C2×C418yescomplemented
104C2×#13083553C2314yes—
105C2×#13083553C2314yes—
106C2×#13083553C2314yes—
107C2×#13083553C2314yes—
108C2×#13083553C2314yes—
109C2×#13083553C2314yes—
110C2×#13083551—24no—
111C2×#13083551—24no—
112C2×#13083551C2×C418yes—
113C2×#13083551C2×C418yes—
114C2×#13083551C2314yes—
115C2×#13083551C2314yes—
116C2×#13083551C2314yes—
117C2×#13083551C2314yes—
118C2×C4×Dic89—24no—
119C2×C4×Dic89—24no—
120C2×C4×Dic89—24no—
121C2×C4×Dic89—24no—
122C2×C4×Dic89—24no—
123C2×C4×Dic89—24no—
124C2×C4×Dic89D418yes—
125C2×C4×Dic89C2314yes—
126C2×C4×Dic89C2314yes—
127C2×C4×Dic89C2314yes—
128C2×C4×Dic89C2314yes—
129C2×C4×Dic89C2314yes—
130C2×C4×Dic89C2314yes—
131C2×C4×Dic89C2314yes—
132C42×D89—232no—
133#15667919C2314yes—
134#15667919C2314yes—
135#15667919C2314yes—
136#15667919C2314yes—
137#15667919C2314yes—
138#15667919C2314yes—
139C23×C4×C89C2311yescharacteristic
140C23×C4×C89C2311yescharacteristic
141C23×C4×C89C2311yescharacteristic
142C23×C4×C89C2311yescharacteristic
143C23×C4×C89C2311yescharacteristic
144C23×C4×C89C2311yescharacteristic
145C23×C4×C89C2311yescharacteristic
146C2×C4⋊C4×C89—24no—
147C2×C4⋊C4×C89C2×C418yescomplemented
148C2×C4⋊C4×C89C2314yes—
149C2×C4⋊C4×C89C2314yes—
150C2×C42×C89—24no—
151C2×C42×C89C2314yes—
152#95×C89C2314yes—
153#95×C89C2314yes—
154#95×C89C2314yes—
155#95×C89C2314yes—
156C23×D89—22no—
157C23×D89—22no—
158C23×D89—22no—
159C23×D89—22no—
160C23×D89C22×C414yes—
161C23×D89C2×Q814yes—
162C23×D89#4114yes—
163C23×D89C2412yes—
164C2×Dic178—232no—
165C2×Dic178—28no—
166C2×Dic178—28no—
167C2×Dic178C22×C4116yescomplemented
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×Dic89C22×C414yes—
181C22×Dic89C22×C414yes—
182C22×Dic89C22×C414yes—
183C22×Dic89C2×D414yes—
184C22×Dic89C2×D414yes—
185C22×Dic89C2×Q814yes—
186C22×Dic89#4114yes—
187C22×Dic89#4114yes—
188C22×Dic89#4114yes—
189C22×Dic89C2412yes—
190C22×Dic89C2412yes—
191C22×Dic89C2412yes—
192C22×Dic89C2412yes—
193C22×Dic89C2412yes—
194C22×Dic89C2412yes—
195C22×Dic89C2412yes—
196C2×C4×D89—232no—
197C2×C4×D89—28no—
198C2×C4×D89—28no—
199C2×C4×D89—232no—
200C2×C4×D89—232no—
201C2×C4×D89—28no—
202C2×C4×D89—28no—
203C2×C4×D89—28no—
204C2×C4×D89—28no—
205C2×C4×D89—28no—
206C2×C4×D89C22×C4116yes—
207C2×C4×D89C2×Q8116yescomplemented
208C4⋊Dic89—28no—
209#13083553—28no—
210#13083553—28no—
211#13083553—28no—
212#13083553—28no—
213#13083553C22×C4116yescomplemented
214#13083553C22×C4116yescomplemented
215#13083551—28no—
216#13083551—28no—
217#13083551C22×C4116yes—
218#13083551C22×C4116yes—
219C4×Dic89—28no—
220C4×Dic89—28no—
221C4×Dic89—28no—
222C4×Dic89—28no—
223C4×Dic89—28no—
224C4×Dic89—28no—
225C4×Dic89C2×D4116yes—
226C24×C89C2411yescharacteristic
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×C89—22no—
236C22×C4×C89—22no—
237C22×C4×C89—22no—
238C22×C4×C89—22no—
239C22×C4×C89—22no—
240C22×C4×C89—22no—
241C22×C4×C89—22no—
242C22×C4×C89—22no—
243C22×C4×C89C22×C414yes—
244C22×C4×C89C22×C414yes—
245C22×C4×C89C22×C414yes—
246C22×C4×C89C2×D414yes—
247C22×C4×C89C2×Q814yes—
248C22×C4×C89C2412yes—
249C22×C4×C89C2412yes—
250C22×C4×C89C2412yes—
251C22×C4×C89C2412yes—
252C22×C4×C89C2412yes—
253C22×C4×C89C2412yes—
254C22×C4×C89C2412yes—
255C4⋊C4×C89—28no—
256C4⋊C4×C89C22×C4116yescomplemented
257C42×C89—28no—
258C23×C89C23×C412yes—
259C23×C89C22×D412yes—
260C23×C89C22×Q812yes—
261C23×C89C2×#4112yes—
262C23×C89C2×#4112yes—
263C23×C89C2×#4112yes—
264C23×C89C2×#4112yes—
265C23×C89C2511yescharacteristic
266C22×D89—28no—
267C22×D89—28no—
268C22×D89—28no—
269C22×D89—28no—
270C22×D89—28no—
271C22×D89—28no—
272C22×D89—22no—
273C22×D89—22no—
274C22×D89—22no—
275C22×D89—22no—
276C22×D89C4×Q8116yescomplemented
277C22×D89C23×C414yes—
278C22×D89C22×Q814yes—
279C22×D89C2×#4114yes—
280C2×C4×C89—28no—
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—22no—
300C2×C4×C89—22no—
301C2×C4×C89—44no—
302C2×C4×C89—44no—
303C2×C4×C89C23×C414yes—
304C2×C4×C89C23×C414yes—
305C2×C4×C89C23×C414yes—
306C2×C4×C89C22×D414yes—
307C2×C4×C89C22×Q814yes—
308C2×Dic89—28no—
309C2×Dic89—28no—
310C2×Dic89—28no—
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—22no—
320C2×Dic89—22no—
321C2×Dic89—22no—
322C2×Dic89—22no—
323C2×Dic89—44no—
324C2×Dic89—44no—
325C2×Dic89C4×D4116yes—
326C2×Dic89C22⋊Q8116yescomplemented
327C2×Dic89C23×C414yes—
328C2×Dic89C23×C414yes—
329C2×Dic89C23×C414yes—
330C2×Dic89C22×D414yes—
331C2×Dic89C22×D414yes—
332C2×Dic89C22×Q814yes—
333C2×Dic89C2×#4114yes—
334C2×Dic89C2×#4114yes—
335C2×Dic89C2×#4114yes—
336C4×D89—232no—
337C4×D89—232no—
338C4×D89—232no—
339Dic178—232no—
340C22×C89C2×C4×D414yes—
341C22×C89C2×C4×Q814yes—
342C22×C89C4×#4114yes—
343C22×C89C2×C22⋊Q814yes—
344C22×C89#52514yes—
345C22×C89#52914yes—
346C22×C89#53314yes—
347C22×C89C24×C411yescharacteristic
348C22×C89C23×D411yescharacteristic
349C22×C89C23×Q811yescharacteristic
350C22×C89C22×#4111yescharacteristic
351C22×C89C22×#4111yescharacteristic
352C22×C89C22×#4111yescharacteristic
353C22×C89C22×#4111yescharacteristic
354C2×D89—24no—
355C2×D89—24no—
356C2×D89—24no—
357C2×D89—24no—
358C2×D89—24no—
359C2×D89—24no—
360C2×D89—232no—
361C2×D89C2×C4×Q818yescomplemented
362C4×C89—24no—
363C4×C89—24no—
364C4×C89—24no—
365C4×C89—24no—
366C4×C89—24no—
367C4×C89—42no—
368C4×C89—42no—
369Dic89—24no—
370Dic89—24no—
371Dic89—24no—
372Dic89—42no—
373Dic89—42no—
374Dic89C2×C4×D418yes—
375Dic89C2×C22⋊Q818yescomplemented
376C2×C4×C22⋊Q8—891nomaximal, Sylow
377C2×C89C4×C22⋊Q818yescomplemented
378C2×C89C22×C4×D411yescharacteristic
379C2×C89C22×C4×Q811yescharacteristic
380C2×C89C2×C4×#4111yescharacteristic
381C2×C89C22×C22⋊Q811yescharacteristic
382C2×C89C2×#52511yescharacteristic
383C2×C89C2×#52911yescharacteristic
384C2×C89C2×#53311yescharacteristic
385D89—28no—
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×#387D8911yescharacteristic, complemented
394C2×#385—891no—
395C2×#385—891no—
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×C4—891no—
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⋊C4—891no—
423C22×C22⋊C4—891no—
424C22×C42—891no—
425C22×C42—891no—
426C22×C42—891no—
427C22×C42—891no—
428C22×C42—891no—
429C22×C42—891no—
430C22×C42—891no—
431C22×C42—898no—
432C22×C42—1788no—
433C22×C42C2×D8911yescharacteristic
434#391—898no—
435#389—898no—
436#387—898no—
437#387C2×D8918yescomplemented
438#385—898no—
439#385—898no—
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×#95C2×D8911yescharacteristic
453C2×#95C2×D8911yescharacteristic
454C2×#95C2×D8911yescharacteristic
455C2×#95C2×D8911yescharacteristic
456C25—891no—
457C22×Q8—898no—
458C22×Q8—894no—
459C22×Q8—1784no—
460C22×Q8—1784no—
461C23×C4—891no—
462C23×C4—891no—
463C23×C4—891no—
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—894no—
473C23×C4—1784no—
474C23×C4—1784no—
475C23×C4—1784no—
476C23×C4—1784no—
477C23×C4—1784no—
478C23×C4—1784no—
479C23×C4—1784no—
480C23×C4C22×D8911yescharacteristic
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—898no—
491C2×C4⋊C4—898no—
492C2×C4⋊C4—894no—
493C2×C4⋊C4—894no—
494C2×C4⋊C4—894no—
495C2×C4⋊C4—894no—
496C2×C4⋊C4—894no—
497C2×C4⋊C4—894no—
498C2×C4⋊C4—894no—
499C2×C4⋊C4—1784no—
500C2×C4⋊C4—1784no—
501C2×C4⋊C4—1784no—
502C2×C4⋊C4—1784no—
503C2×C4⋊C4—1784no—
504C2×C4⋊C4C4×D8918yescomplemented
505C2×C4⋊C4C22×D8914yes—
506C2×C4⋊C4C22×D8914yes—
507C2×C22⋊C4—898no—
508C2×C22⋊C4—898no—
509C2×C22⋊C4—894no—
510C2×C22⋊C4—894no—
511C2×C22⋊C4—894no—
512C2×C22⋊C4—894no—
513C2×C22⋊C4—1784no—
514C2×C22⋊C4—1784no—
515C2×C42—24no—
516C2×C42—898no—
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×C42C22×D8914yes—
532#95—894no—
533#95—894no—
534#95—894no—
535#95—894no—
536#95—894no—
537#95—894no—
538#95C22×D8914yes—
539#95C22×D8914yes—
540#95C22×D8914yes—
541#95C22×D8914yes—
542C24—894no—
543C24—894no—
544C24—894no—
545C24—892no—
546C24—1782no—
547C24—1782no—
548C24—1782no—
549C24—1782no—
550C24C23×D8911yescharacteristic
551C2×Q8—8916no—
552C2×Q8—1788no—
553C2×Q8—1788no—
554C2×Q8—17832no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—894no—
572C22×C4—894no—
573C22×C4—894no—
574C22×C4—894no—
575C22×C4—894no—
576C22×C4—894no—
577C22×C4—892no—
578C22×C4—892no—
579C22×C4—894no—
580C22×C4—894no—
581C22×C4—894no—
582C22×C4—892no—
583C22×C4—892no—
584C22×C4—892no—
585C22×C4—8916no—
586C22×C4—8916no—
587C22×C4—892no—
588C22×C4—892no—
589C22×C4—1788no—
590C22×C4—1788no—
591C22×C4—1788no—
592C22×C4—1788no—
593C22×C4—1788no—
594C22×C4—17832no—
595C22×C4—17832no—
596C22×C4—1788no—
597C22×C4—17832no—
598C22×C4—1782no—
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—1788no—
611C22×C4C2×C4×D8914yes—
612C22×C4C2×C4×D8914yes—
613C22×C4C2×C4×D8914yes—
614C22×C4D4×D8914yes—
615C22×C4Q8×D8914yes—
616C22×C4C23×D8912yes—
617C22×C4C23×D8912yes—
618C22×C4C23×D8912yes—
619C22×C4C23×D8912yes—
620C22×C4C23×D8912yes—
621C22×C4C23×D8912yes—
622C22×C4C23×D8912yes—
623C4⋊C4—28no—
624C4⋊C4—8916no—
625C4⋊C4—8916no—
626C4⋊C4—1788no—
627C4⋊C4—1788no—
628C4⋊C4—1788no—
629C4⋊C4—1788no—
630C4⋊C4—1788no—
631C4⋊C4C2×C4×D89116yescomplemented
632C22⋊C4—8916no—
633C22⋊C4—8916no—
634C22⋊C4—1788no—
635C22⋊C4—1788no—
636C42—28no—
637C42—8916no—
638C42—1788no—
639C42—1788no—
640C42—1788no—
641C42—1788no—
642C42—1788no—
643C42—1788no—
644C23—894no—
645C23—894no—
646C23—894no—
647C23—8916no—
648C23—1788no—
649C23—1788no—
650C23—1782no—
651C23—1782no—
652C23—1782no—
653C23—1782no—
654C23—1788no—
655C23—1788no—
656C23—1788no—
657C23—1788no—
658C23C22×C4×D8912yes—
659C23C2×D4×D8912yes—
660C23C2×Q8×D8912yes—
661C23#41×D8912yes—
662C23#41×D8912yes—
663C23#41×D8912yes—
664C23#41×D8912yes—
665C23C24×D8911yescharacteristic
666Q8—17832no—
667C2×C4—22no—
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—22no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—894no—
691C2×C4—894no—
692C2×C4—894no—
693C2×C4—894no—
694C2×C4—894no—
695C2×C4—894no—
696C2×C4—8916no—
697C2×C4—8916no—
698C2×C4—894no—
699C2×C4—894no—
700C2×C4—894no—
701C2×C4—3564no—
702C2×C4—3564no—
703C2×C4—17832no—
704C2×C4—17832no—
705C2×C4—17832no—
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×C4C22×C4×D8914yes—
722C2×C4C22×C4×D8914yes—
723C2×C4C22×C4×D8914yes—
724C2×C4C2×D4×D8914yes—
725C2×C4C2×Q8×D8914yes—
726C22—898no—
727C22—1784no—
728C22—1784no—
729C22—1784no—
730C22—1784no—
731C22—1784no—
732C22—17832no—
733C22—1784no—
734C22C4×D4×D8914yes—
735C22C4×Q8×D8914yes—
736C22#1915206614yes—
737C22C22⋊Q8×D8914yes—
738C22#1915210614yes—
739C22#1915213114yes—
740C22#1915215414yes—
741C22C23×C4×D8911yescharacteristic
742C22C22×D4×D8911yescharacteristic
743C22C22×Q8×D8911yescharacteristic
744C22C2×#41×D8911yescharacteristic
745C22C2×#41×D8911yescharacteristic
746C22C2×#41×D8911yescharacteristic
747C22C2×#41×D8911yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—42no—
755C4—898no—
756C4—898no—
757C4—3562no—
758C4—3562no—
759C4—1784no—
760C4—1784no—
761C4—1784no—
762C2—1788no—
763C2#2602278618yesdirect product factor
764C2C2×C4×D4×D8911yescharacteristic
765C2C2×C4×Q8×D8911yescharacteristic
766C2C2×#1915206611yescharacteristic
767C2C2×C22⋊Q8×D8911yescharacteristic
768C2C2×#1915210611yescharacteristic
769C2C2×#1915213111yescharacteristic
770C2C2×#1915215411yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
cosocleC23×C89C25
hypercenterC2×#387D89
hypocenterC89C2×C4×C22⋊Q8
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×#15667977C2semidirect
4. #26022786C2direct (N × H)
5. C2×#19151502C2semidirect
6. C2×#19151495C2semidirect
7. C2×#19151482C2semidirect
11. C2×C4⋊C4×Dic89C2semidirect
12. C2×#19151449C2semidirect
13. C2×#19151449C2semidirect
16. C2×#387×C89C2semidirect
21. C2×#15667990C4semidirect
24. C2×#15667977C22semidirect
45. #19151502C22semidirect
46. #19151495C22semidirect
47. #19151482C22semidirect
51. C4⋊C4×Dic89C22semidirect
52. #19151449C22semidirect
53. #19151449C22semidirect
65. #387×C89C22semidirect
73. C22×Dic178C2×C4semidirect
90. C22×C4×D89Q8semidirect
94. #15667990C2×C4semidirect
102. C2×#13083553C2×C4semidirect
103. C2×#13083553C2×C4semidirect
147. C2×C4⋊C4×C89C2×C4semidirect
167. C2×Dic178C22×C4semidirect
207. C2×C4×D89C2×Q8semidirect
213. #13083553C22×C4semidirect
214. #13083553C22×C4semidirect
256. C4⋊C4×C89C22×C4semidirect
276. C22×D89C4×Q8semidirect
326. C2×Dic89C22⋊Q8semidirect
361. C2×D89C2×C4×Q8semidirect
375. Dic89C2×C22⋊Q8semidirect
377. C2×C89C4×C22⋊Q8semidirect
393. C2×#387D89semidirect
402. C89C2×C4×C22⋊Q8semidirect
437. #387C2×D89semidirect
504. C2×C4⋊C4C4×D89semidirect
631. C4⋊C4C2×C4×D89semidirect
763. C2#26022786direct (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×#156679772
C22×C42×D892
#260227862
C2×#191515022
C2×#191514952
C2×#191514822
C2×#191514722
C2×#191514692
C2×#191514572
C2×C4⋊C4×Dic892
C2×#191514492
C2×#191514452
C2×#387×C892
C2×C4×C22⋊Q889