Finite Group Databasebeta

← C2×#26023947 #36722252

Subgroups — C2×#26023947 #36722252

Order 22784.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15668010C211yesmaximal, characteristic, complemented
2C22×#15667990C211yesmaximal, characteristic
3C22×#15667988C211yesmaximal, characteristic
4C22×C4⋊C4×D89C211yesmaximal, characteristic
5#26023947C2116yesmaximal, direct product factor
6C2×#19151532C211yesmaximal, characteristic, complemented
7C2×#19151531C211yesmaximal, characteristic, complemented
8C2×#19151519C211yesmaximal, characteristic, complemented
9C2×#19151495C211yesmaximal, characteristic, complemented
10C2×#19151493C211yesmaximal, characteristic, complemented
11C2×#19151472C211yesmaximal, characteristic
12C2×#19151469C211yesmaximal, characteristic
13C2×#19151467C211yesmaximal, characteristic, complemented
14C2×#19151457C211yesmaximal, characteristic
15C2×#19151445C211yesmaximal, characteristic
16C2×#395×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C23×C4×D89C2211yescharacteristic
21C2×#15668010—28no—
22C2×#15668010C2218yescomplemented
23C2×#15667990—28no—
24C2×#15667990C2218yes—
25C2×#15667988—28no—
26C2×#15667988C2218yes—
27C22×C4⋊Dic89C2211yescharacteristic
28C22×C4⋊Dic89C2211yescharacteristic
29C22×C4⋊Dic89C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C22×#13083553C2211yescharacteristic
33C22×#13083553C2211yescharacteristic
34C22×#13083553C2211yescharacteristic
35C22×#13083553C2211yescharacteristic
36C22×#13083553C2211yescharacteristic
37C22×#13083553C2211yescharacteristic
38C22×#13083553C2211yescharacteristic
39C22×#13083553C2211yescharacteristic
40C2×C4⋊C4×D89—28no—
41C2×C4⋊C4×D89C2218yes—
42C22×#13083551C2211yescharacteristic
43C22×#13083551C2211yescharacteristic
44C22×#13083551C2211yescharacteristic
45C22×#13083551C2211yescharacteristic
46C22×C4×Dic89C2211yescharacteristic
47C22×C4×Dic89C2211yescharacteristic
48#19151532C2218yescomplemented
49#19151531C2218yescomplemented
50#19151519C2218yescomplemented
51#19151495C2218yescomplemented
52#19151493C2218yescomplemented
53#19151472C2218yes—
54#19151469C2218yes—
55#19151467C2218yescomplemented
56#19151457C2218yes—
57#19151445C2218yes—
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C2×#15667919C2211yescharacteristic
62C2×#15667919C2211yescharacteristic
63C23×Q8×C89C2211yescharacteristic
64C22×C4⋊C4×C89C2211yescharacteristic
65C22×C4⋊C4×C89C2211yescharacteristic
66C22×C4⋊C4×C89C2211yescharacteristic
67#395×C89C2218yescomplemented
68C2×#95×C89C2211yescharacteristic
69C2×#95×C89C2211yescharacteristic
70C2×#95×C89C2211yescharacteristic
71C24×D89C2311yescharacteristic
72C22×Dic178—24no—
73C22×Dic178—24no—
74C22×Dic178—42no—
75C22×Dic178C2314yes—
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C23×Dic89C2311yescharacteristic
81C23×Dic89C2311yescharacteristic
82C23×Dic89C2311yescharacteristic
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×D89—42no—
90C22×C4×D89—42no—
91C22×C4×D89Q818yescomplemented
92C22×C4×D89C2314yes—
93C22×C4×D89C2314yes—
94C22×C4×D89C2314yes—
95#15668010—232no—
96#15667990—232no—
97#15667988—232no—
98C2×C4⋊Dic89—24no—
99C2×C4⋊Dic89—24no—
100C2×C4⋊Dic89—42no—
101C2×C4⋊Dic89C2314yes—
102C2×C4⋊Dic89C2314yes—
103C2×C4⋊Dic89C2314yes—
104C2×#13083553—24no—
105C2×#13083553—24no—
106C2×#13083553—24no—
107C2×#13083553—24no—
108C2×#13083553—24no—
109C2×#13083553—24no—
110C2×#13083553—24no—
111C2×#13083553—24no—
112C2×#13083553—24no—
113C2×#13083553D418yes—
114C2×#13083553C2314yes—
115C2×#13083553C2314yes—
116C2×#13083553C2314yes—
117C2×#13083553C2314yes—
118C2×#13083553C2314yes—
119C2×#13083553C2314yes—
120C2×#13083553C2314yes—
121C2×#13083553C2314yes—
122C2×#13083553C2314yes—
123C2×#13083553C2314yes—
124C4⋊C4×D89—232no—
125C2×#13083551—24no—
126C2×#13083551—24no—
127C2×#13083551D418yes—
128C2×#13083551Q818yescomplemented
129C2×#13083551C2314yes—
130C2×#13083551C2314yes—
131C2×#13083551C2314yes—
132C2×#13083551C2314yes—
133C2×C4×Dic89—24no—
134C2×C4×Dic89—24no—
135C2×C4×Dic89C2314yes—
136C2×C4×Dic89C2314yes—
137#15667919C2314yes—
138#15667919C2314yes—
139#15667919C2314yes—
140#15667919C2314yes—
141#15667919C2314yes—
142C22×Q8×C89—24no—
143C22×Q8×C89—24no—
144C22×Q8×C89—42no—
145C22×Q8×C89C2314yes—
146C23×C4×C89C2311yescharacteristic
147C23×C4×C89C2311yescharacteristic
148C23×C4×C89C2311yescharacteristic
149C23×C4×C89C2311yescharacteristic
150C23×C4×C89C2311yescharacteristic
151C23×C4×C89C2311yescharacteristic
152C23×C4×C89C2311yescharacteristic
153C2×C4⋊C4×C89—24no—
154C2×C4⋊C4×C89—24no—
155C2×C4⋊C4×C89—42no—
156C2×C4⋊C4×C89C2314yes—
157C2×C4⋊C4×C89C2314yes—
158C2×C4⋊C4×C89C2314yes—
159#95×C89C2314yes—
160#95×C89C2314yes—
161#95×C89C2314yes—
162C23×D89—22no—
163C23×D89—22no—
164C23×D89—22no—
165C23×D89—22no—
166C23×D89C2×D414yes—
167C23×D89C2×Q814yes—
168C23×D89C2×Q814yes—
169C23×D89C2412yes—
170C2×Dic178—28no—
171C2×Dic178—28no—
172C2×Dic178—44no—
173C2×Dic178—416no—
174C22×Dic89—22no—
175C22×Dic89—22no—
176C22×Dic89—22no—
177C22×Dic89—22no—
178C22×Dic89—22no—
179C22×Dic89—22no—
180C22×Dic89—22no—
181C22×Dic89—22no—
182C22×Dic89—22no—
183C22×Dic89—22no—
184C22×Dic89—22no—
185C22×Dic89—22no—
186C22×Dic89—22no—
187C22×Dic89—22no—
188C22×Dic89—22no—
189C22×Dic89C2×D414yes—
190C22×Dic89C2×D414yes—
191C22×Dic89C2×D414yes—
192C22×Dic89C2×Q814yes—
193C22×Dic89C2×Q814yes—
194C22×Dic89#4114yes—
195C22×Dic89C2412yes—
196C22×Dic89C2412yes—
197C22×Dic89C2412yes—
198C22×Dic89C2412yes—
199C22×Dic89C2412yes—
200C22×Dic89C2412yes—
201C22×Dic89C2412yes—
202C2×C4×D89—232no—
203C2×C4×D89—28no—
204C2×C4×D89—28no—
205C2×C4×D89—28no—
206C2×C4×D89—28no—
207C2×C4×D89—28no—
208C2×C4×D89—28no—
209C2×C4×D89—44no—
210C2×C4×D89—44no—
211C2×C4×D89—416no—
212C2×C4×D89—416no—
213C2×C4×D89C2×Q8116yescomplemented
214C4⋊Dic89—28no—
215C4⋊Dic89—28no—
216C4⋊Dic89—44no—
217#13083553—28no—
218#13083553—28no—
219#13083553—28no—
220#13083553—28no—
221#13083553—28no—
222#13083553—28no—
223#13083553—28no—
224#13083553—28no—
225#13083553—28no—
226#13083553C2×D4116yes—
227#13083551—28no—
228#13083551—28no—
229#13083551C2×D4116yes—
230#13083551C2×Q8116yescomplemented
231C4×Dic89—28no—
232C4×Dic89—28no—
233C24×C89C2411yescharacteristic
234C2×Q8×C89—28no—
235C2×Q8×C89—28no—
236C2×Q8×C89—44no—
237C2×Q8×C89—416no—
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×C89—22no—
245C22×C4×C89—22no—
246C22×C4×C89—22no—
247C22×C4×C89—22no—
248C22×C4×C89—22no—
249C22×C4×C89—22no—
250C22×C4×C89—22no—
251C22×C4×C89—22no—
252C22×C4×C89—22no—
253C22×C4×C89—22no—
254C22×C4×C89—22no—
255C22×C4×C89C2×D414yes—
256C22×C4×C89C2×D414yes—
257C22×C4×C89C2×Q814yes—
258C22×C4×C89C2×Q814yes—
259C22×C4×C89C2412yes—
260C22×C4×C89C2412yes—
261C22×C4×C89C2412yes—
262C22×C4×C89C2412yes—
263C22×C4×C89C2412yes—
264C22×C4×C89C2412yes—
265C22×C4×C89C2412yes—
266C4⋊C4×C89—28no—
267C4⋊C4×C89—28no—
268C4⋊C4×C89—44no—
269C23×C89C22×D412yes—
270C23×C89C22×D412yes—
271C23×C89C22×Q812yes—
272C23×C89C22×Q812yes—
273C23×C89C2×#4112yes—
274C23×C89H(5,𝔽2)12yes—
275C23×C892−1+412yes—
276C23×C89C2511yescharacteristic
277C22×D89—28no—
278C22×D89—28no—
279C22×D89—28no—
280C22×D89—28no—
281C22×D89—28no—
282C22×D89—28no—
283C22×D89—22no—
284C22×D89—22no—
285C22×D89—22no—
286C22×D89—22no—
287C22×D89C4⋊Q8116yescomplemented
288C22×D89C22×D414yes—
289C22×D89C22×Q814yes—
290C22×D89C22×Q814yes—
291Q8×C89—416no—
292C2×C4×C89—28no—
293C2×C4×C89—28no—
294C2×C4×C89—28no—
295C2×C4×C89—28no—
296C2×C4×C89—22no—
297C2×C4×C89—22no—
298C2×C4×C89—22no—
299C2×C4×C89—22no—
300C2×C4×C89—22no—
301C2×C4×C89—22no—
302C2×C4×C89—22no—
303C2×C4×C89—22no—
304C2×C4×C89—22no—
305C2×C4×C89—22no—
306C2×C4×C89—22no—
307C2×C4×C89—22no—
308C2×C4×C89—22no—
309C2×C4×C89—22no—
310C2×C4×C89—22no—
311C2×C4×C89—22no—
312C2×C4×C89—22no—
313C2×C4×C89—44no—
314C2×C4×C89—44no—
315C2×C4×C89—44no—
316C2×C4×C89C22×D414yes—
317C2×C4×C89C22×D414yes—
318C2×C4×C89C22×Q814yes—
319C2×C4×C89C22×Q814yes—
320C2×Dic89—28no—
321C2×Dic89—28no—
322C2×Dic89—28no—
323C2×Dic89—22no—
324C2×Dic89—22no—
325C2×Dic89—22no—
326C2×Dic89—22no—
327C2×Dic89—22no—
328C2×Dic89—22no—
329C2×Dic89—22no—
330C2×Dic89—22no—
331C2×Dic89—22no—
332C2×Dic89—22no—
333C2×Dic89—22no—
334C2×Dic89—22no—
335C2×Dic89—22no—
336C2×Dic89—22no—
337C2×Dic89—22no—
338C2×Dic89—44no—
339C2×Dic89—44no—
340C2×Dic89—44no—
341C2×Dic89C22⋊Q8116yescomplemented
342C2×Dic89C22×D414yes—
343C2×Dic89C22×D414yes—
344C2×Dic89C22×D414yes—
345C2×Dic89C22×Q814yes—
346C2×Dic89C22×Q814yes—
347C2×Dic89C2×#4114yes—
348C4×D89—232no—
349C4×D89—416no—
350C4×D89—416no—
351Dic178—416no—
352C22×C89C2×C22⋊Q814yes—
353C22×C89C2×C4⋊Q814yes—
354C22×C89#54414yes—
355C22×C89D4214yes—
356C22×C89#54714yes—
357C22×C89D4×Q814yes—
358C22×C89#55414yes—
359C22×C89C23×D411yescharacteristic
360C22×C89C23×D411yescharacteristic
361C22×C89C23×Q811yescharacteristic
362C22×C89C23×Q811yescharacteristic
363C22×C89C22×#4111yescharacteristic
364C22×C89C2×H(5,𝔽2)11yescharacteristic
365C22×C89C2×2−1+411yescharacteristic
366C2×D89—24no—
367C2×D89—24no—
368C2×D89—24no—
369C2×D89—232no—
370C2×D89—24no—
371C2×D89—24no—
372C2×D89—24no—
373C2×D89C2×C4⋊Q818yescomplemented
374C4×C89—24no—
375C4×C89—24no—
376C4×C89—24no—
377C4×C89—24no—
378C4×C89—42no—
379C4×C89—42no—
380C4×C89—42no—
381Dic89—24no—
382Dic89—24no—
383Dic89—24no—
384Dic89—42no—
385Dic89—42no—
386Dic89—42no—
387Dic89C2×C22⋊Q818yescomplemented
388C2×#2440—891nomaximal, Sylow
389C2×C89#244018yescomplemented
390C2×C89C22×C22⋊Q811yescharacteristic
391C2×C89C22×C4⋊Q811yescharacteristic
392C2×C89C2×#54411yescharacteristic
393C2×C89C2×D4211yescharacteristic
394C2×C89C2×#54711yescharacteristic
395C2×C89C2×D4×Q811yescharacteristic
396C2×C89C2×#55411yescharacteristic
397D89—28no—
398C22×C4⋊Q8—891no—
399C22×C22⋊Q8—891no—
400C22×C22⋊Q8—891no—
401C23×C4⋊C4—891no—
402#2440—8916no—
403C2×#398—891no—
404C2×#398—891no—
405C2×#395—891no—
406C2×#395D8911yescharacteristic, complemented
407C2×#389—891no—
408C2×#389—891no—
409C2×#385—891no—
410C2×#385—891no—
411C2×#384—891no—
412C2×#380—891no—
413C2×C4×C22⋊C4—891no—
414C89C2×#244011yescharacteristic, complemented, Sylow
415C23×Q8—891no—
416C23×Q8C2×D8911yescharacteristic
417C24×C4—891no—
418C24×C4—891no—
419C24×C4—891no—
420C2×C4⋊Q8—898no—
421C2×C4⋊Q8—1788no—
422C2×C22⋊Q8—898no—
423C2×C22⋊Q8—898no—
424C2×C22⋊Q8—1788no—
425C2×C22⋊Q8—1788no—
426C22×C4⋊C4—891no—
427C22×C4⋊C4—891no—
428C22×C4⋊C4—891no—
429C22×C4⋊C4—891no—
430C22×C4⋊C4—891no—
431C22×C4⋊C4—891no—
432C22×C4⋊C4—891no—
433C22×C4⋊C4—891no—
434C22×C4⋊C4—891no—
435C22×C4⋊C4—891no—
436C22×C4⋊C4—891no—
437C22×C4⋊C4—891no—
438C22×C4⋊C4—891no—
439C22×C4⋊C4—898no—
440C22×C4⋊C4—1788no—
441C22×C4⋊C4C2×D8911yescharacteristic
442C22×C4⋊C4C2×D8911yescharacteristic
443C22×C4⋊C4C2×D8911yescharacteristic
444C22×C22⋊C4—891no—
445C22×C22⋊C4—891no—
446C22×C22⋊C4—891no—
447C22×C22⋊C4—891no—
448C22×C42—891no—
449C22×C42—891no—
450#398—898no—
451#398—898no—
452#395—898no—
453#395C2×D8918yescomplemented
454#389—898no—
455#389—898no—
456#385—898no—
457#385—898no—
458#384—898no—
459#380—898no—
460C4×C22⋊C4—898no—
461C2×#95—891no—
462C2×#95—891no—
463C2×#95—891no—
464C2×#95—891no—
465C2×#95—891no—
466C2×#95C2×D8911yescharacteristic
467C2×#95C2×D8911yescharacteristic
468C2×#95C2×D8911yescharacteristic
469C25—891no—
470C22×Q8—24no—
471C22×Q8—24no—
472C22×Q8—42no—
473C22×Q8—894no—
474C22×Q8—3562no—
475C22×Q8—1784no—
476C22×Q8—1784no—
477C22×Q8C22×D8914yes—
478C23×C4—891no—
479C23×C4—891no—
480C23×C4—891no—
481C23×C4—891no—
482C23×C4—898no—
483C23×C4—894no—
484C23×C4—891no—
485C23×C4—891no—
486C23×C4—891no—
487C23×C4—894no—
488C23×C4—894no—
489C23×C4—3562no—
490C23×C4—3562no—
491C23×C4—1784no—
492C23×C4—1784no—
493C23×C4—1784no—
494C23×C4—1784no—
495C23×C4—1784no—
496C23×C4—1784no—
497C23×C4C22×D8911yescharacteristic
498C23×C4C22×D8911yescharacteristic
499C23×C4C22×D8911yescharacteristic
500C23×C4C22×D8911yescharacteristic
501C23×C4C22×D8911yescharacteristic
502C23×C4C22×D8911yescharacteristic
503C23×C4C22×D8911yescharacteristic
504C4⋊Q8—17832no—
505C22⋊Q8—17832no—
506C22⋊Q8—17832no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—898no—
511C2×C4⋊C4—894no—
512C2×C4⋊C4—894no—
513C2×C4⋊C4—894no—
514C2×C4⋊C4—894no—
515C2×C4⋊C4—894no—
516C2×C4⋊C4—894no—
517C2×C4⋊C4—894no—
518C2×C4⋊C4—894no—
519C2×C4⋊C4—894no—
520C2×C4⋊C4—894no—
521C2×C4⋊C4—894no—
522C2×C4⋊C4—894no—
523C2×C4⋊C4—894no—
524C2×C4⋊C4—3562no—
525C2×C4⋊C4—17832no—
526C2×C4⋊C4—1784no—
527C2×C4⋊C4—1784no—
528C2×C4⋊C4—1784no—
529C2×C4⋊C4—1784no—
530C2×C4⋊C4—1784no—
531C2×C4⋊C4—1784no—
532C2×C4⋊C4—1784no—
533C2×C4⋊C4—1784no—
534C2×C4⋊C4—1784no—
535C2×C4⋊C4—1784no—
536C2×C4⋊C4—1784no—
537C2×C4⋊C4C22×D8914yes—
538C2×C4⋊C4C22×D8914yes—
539C2×C4⋊C4C22×D8914yes—
540C2×C22⋊C4—898no—
541C2×C22⋊C4—898no—
542C2×C22⋊C4—894no—
543C2×C22⋊C4—894no—
544C2×C22⋊C4—894no—
545C2×C22⋊C4—894no—
546C2×C22⋊C4—1784no—
547C2×C22⋊C4—1784no—
548C2×C42—894no—
549C2×C42—894no—
550C2×C42—1784no—
551C2×C42—1784no—
552#95—894no—
553#95—894no—
554#95—894no—
555#95—894no—
556#95—894no—
557#95C22×D8914yes—
558#95C22×D8914yes—
559#95C22×D8914yes—
560C24—894no—
561C24—894no—
562C24—894no—
563C24—892no—
564C24—1782no—
565C24—1782no—
566C24—1782no—
567C24—1782no—
568C24C23×D8911yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×Q8—35616no—
574C2×Q8—3564no—
575C2×Q8—1788no—
576C2×Q8—1788no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—894no—
595C22×C4—894no—
596C22×C4—894no—
597C22×C4—892no—
598C22×C4—894no—
599C22×C4—894no—
600C22×C4—894no—
601C22×C4—892no—
602C22×C4—892no—
603C22×C4—892no—
604C22×C4—8916no—
605C22×C4—892no—
606C22×C4—892no—
607C22×C4—892no—
608C22×C4—35616no—
609C22×C4—3564no—
610C22×C4—3564no—
611C22×C4—35616no—
612C22×C4—1788no—
613C22×C4—1788no—
614C22×C4—1788no—
615C22×C4—17832no—
616C22×C4—1788no—
617C22×C4—1788no—
618C22×C4—1782no—
619C22×C4—1782no—
620C22×C4—1782no—
621C22×C4—1782no—
622C22×C4—1782no—
623C22×C4—1782no—
624C22×C4—1782no—
625C22×C4—1782no—
626C22×C4—1782no—
627C22×C4—1788no—
628C22×C4—1782no—
629C22×C4—1782no—
630C22×C4—1782no—
631C22×C4—1782no—
632C22×C4—1782no—
633C22×C4—1782no—
634C22×C4D4×D8914yes—
635C22×C4D4×D8914yes—
636C22×C4Q8×D8914yes—
637C22×C4Q8×D8914yes—
638C22×C4C23×D8912yes—
639C22×C4C23×D8912yes—
640C22×C4C23×D8912yes—
641C22×C4C23×D8912yes—
642C22×C4C23×D8912yes—
643C22×C4C23×D8912yes—
644C22×C4C23×D8912yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—44no—
648C4⋊C4—8916no—
649C4⋊C4—3564no—
650C4⋊C4—1788no—
651C4⋊C4—1788no—
652C4⋊C4—1788no—
653C4⋊C4—1788no—
654C4⋊C4—1788no—
655C4⋊C4—1788no—
656C4⋊C4—1788no—
657C4⋊C4—1788no—
658C4⋊C4—1788no—
659C4⋊C4—1788no—
660C4⋊C4—1788no—
661C22⋊C4—8916no—
662C22⋊C4—8916no—
663C22⋊C4—1788no—
664C22⋊C4—1788no—
665C42—1788no—
666C42—1788no—
667C23—8916no—
668C23—894no—
669C23—894no—
670C23—894no—
671C23—1782no—
672C23—1782no—
673C23—1782no—
674C23—1782no—
675C23—1788no—
676C23—1788no—
677C23—1788no—
678C23—1788no—
679C23—1788no—
680C23—1788no—
681C23C2×D4×D8912yes—
682C23C2×D4×D8912yes—
683C23C2×Q8×D8912yes—
684C23C2×Q8×D8912yes—
685C23#41×D8912yes—
686C23#1566805712yes—
687C23#1566806012yes—
688C23C24×D8911yescharacteristic
689Q8—416no—
690Q8—35616no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—894no—
716C2×C4—894no—
717C2×C4—894no—
718C2×C4—8916no—
719C2×C4—894no—
720C2×C4—894no—
721C2×C4—894no—
722C2×C4—35616no—
723C2×C4—35616no—
724C2×C4—3564no—
725C2×C4—3564no—
726C2×C4—3564no—
727C2×C4—17832no—
728C2×C4—1782no—
729C2×C4—1782no—
730C2×C4—1782no—
731C2×C4—1782no—
732C2×C4—1782no—
733C2×C4—1782no—
734C2×C4—1782no—
735C2×C4—1782no—
736C2×C4—1782no—
737C2×C4—1782no—
738C2×C4—1782no—
739C2×C4—1782no—
740C2×C4—1782no—
741C2×C4—1782no—
742C2×C4—1782no—
743C2×C4—1788no—
744C2×C4—1788no—
745C2×C4—1788no—
746C2×C4C2×D4×D8914yes—
747C2×C4C2×D4×D8914yes—
748C2×C4C2×Q8×D8914yes—
749C2×C4C2×Q8×D8914yes—
750C22—898no—
751C22—17832no—
752C22—1784no—
753C22—1784no—
754C22—1784no—
755C22—1784no—
756C22—1784no—
757C22—1784no—
758C22C22⋊Q8×D8914yes—
759C22C4⋊Q8×D8914yes—
760C22#1915222514yes—
761C22#1915223014yes—
762C22#1915225014yes—
763C22#1915226314yes—
764C22#1915230214yes—
765C22C22×D4×D8911yescharacteristic
766C22C22×D4×D8911yescharacteristic
767C22C22×Q8×D8911yescharacteristic
768C22C22×Q8×D8911yescharacteristic
769C22C2×#41×D8911yescharacteristic
770C22C2×#1566805711yescharacteristic
771C22C2×#1566806011yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—898no—
780C4—3562no—
781C4—3562no—
782C4—3562no—
783C4—1784no—
784C4—1784no—
785C4—1784no—
786C2—1788no—
787C2#2602394718yesdirect product factor
788C2C2×C22⋊Q8×D8911yescharacteristic
789C2C2×C4⋊Q8×D8911yescharacteristic
790C2C2×#1915222511yescharacteristic
791C2C2×#1915223011yescharacteristic
792C2C2×#1915225011yescharacteristic
793C2C2×#1915226311yescharacteristic
794C2C2×#1915230211yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#395×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#395D89
hypocenterC89C2×#2440
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#15668010C2semidirect
5. #26023947C2direct (N × H)
6. C2×#19151532C2semidirect
7. C2×#19151531C2semidirect
8. C2×#19151519C2semidirect
9. C2×#19151495C2semidirect
10. C2×#19151493C2semidirect
13. C2×#19151467C2semidirect
16. C2×#395×C89C2semidirect
22. C2×#15668010C22semidirect
48. #19151532C22semidirect
49. #19151531C22semidirect
50. #19151519C22semidirect
51. #19151495C22semidirect
52. #19151493C22semidirect
55. #19151467C22semidirect
67. #395×C89C22semidirect
91. C22×C4×D89Q8semidirect
128. C2×#13083551Q8semidirect
213. C2×C4×D89C2×Q8semidirect
230. #13083551C2×Q8semidirect
287. C22×D89C4⋊Q8semidirect
341. C2×Dic89C22⋊Q8semidirect
373. C2×D89C2×C4⋊Q8semidirect
387. Dic89C2×C22⋊Q8semidirect
389. C2×C89#2440semidirect
406. C2×#395D89semidirect
414. C89C2×#2440semidirect
453. #395C2×D89semidirect
787. C2#26023947direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680102
C22×#156679902
C22×#156679882
C22×C4⋊C4×D892
#260239472
C2×#191515322
C2×#191515312
C2×#191515192
C2×#191514952
C2×#191514932
C2×#191514722
C2×#191514692
C2×#191514672
C2×#191514572
C2×#191514452
C2×#395×C892
C2×#244089