Finite Group Databasebeta

← C2×#26023846 #36722445

Subgroups — C2×#26023846 #36722445

Order 22784.

3246 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×#15668011C211yesmaximal, characteristic, complemented
2C22×#15667990C211yesmaximal, characteristic
3C22×#15667990C211yesmaximal, characteristic
4C22×#15667977C211yesmaximal, characteristic, complemented
5#26023846C2116yesmaximal, direct product factor
6C2×#19151532C211yesmaximal, characteristic, complemented
7C2×#19151522C211yesmaximal, characteristic
8C2×#19151520C211yesmaximal, characteristic
9C2×#19151502C211yesmaximal, characteristic, complemented
10C2×#19151495C211yesmaximal, characteristic, complemented
11C2×#19151494C211yesmaximal, characteristic, complemented
12C2×#19151493C211yesmaximal, characteristic, complemented
13C2×#19151490C211yesmaximal, characteristic
14C2×#19151488C211yesmaximal, characteristic
15C2×#19151445C211yesmaximal, characteristic
16C2×#398×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×Dic178C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C2×#15668011—28no—
21C2×#15668011C2218yescomplemented
22C2×#15667990—28no—
23C2×#15667990—28no—
24C2×#15667990C2218yes—
25C2×#15667990C2218yes—
26C2×#15667977—28no—
27C2×#15667977C2218yescomplemented
28C22×C4⋊Dic89C2211yescharacteristic
29C22×C4⋊Dic89C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C22×#13083553C2211yescharacteristic
33C22×#13083553C2211yescharacteristic
34C22×#13083553C2211yescharacteristic
35C22×#13083553C2211yescharacteristic
36C22×#13083553C2211yescharacteristic
37C22×#13083553C2211yescharacteristic
38C22×#13083551C2211yescharacteristic
39C22×#13083551C2211yescharacteristic
40C22×#13083551C2211yescharacteristic
41C22×#13083551C2211yescharacteristic
42C22×#13083551C2211yescharacteristic
43C22×#13083551C2211yescharacteristic
44C22×C4×Dic89C2211yescharacteristic
45C22×C4×Dic89C2211yescharacteristic
46C22×C4×Dic89C2211yescharacteristic
47C22×C4×Dic89C2211yescharacteristic
48#19151532C2218yescomplemented
49#19151522C2218yes—
50#19151520C2218yes—
51#19151502C2218yescomplemented
52#19151495C2218yescomplemented
53#19151494C2218yescomplemented
54#19151493C2218yescomplemented
55#19151490C2218yes—
56#19151488C2218yes—
57#19151445C2218yes—
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C2×#15667919C2211yescharacteristic
62C2×#15667919C2211yescharacteristic
63C22×C4⋊C4×C89C2211yescharacteristic
64C22×C4⋊C4×C89C2211yescharacteristic
65C22×C4⋊C4×C89C2211yescharacteristic
66C22×C4⋊C4×C89C2211yescharacteristic
67#398×C89C2218yescomplemented
68C2×#95×C89C2211yescharacteristic
69C2×#95×C89C2211yescharacteristic
70C2×#95×C89C2211yescharacteristic
71C24×D89C2311yescharacteristic
72C22×Dic178—24no—
73C22×Dic178—24no—
74C22×Dic178—24no—
75C22×Dic178—24no—
76C22×Dic178—24no—
77C22×Dic178D418yes—
78C22×Dic178C2314yes—
79C22×Dic178C2314yes—
80C23×Dic89C2311yescharacteristic
81C23×Dic89C2311yescharacteristic
82C23×Dic89C2311yescharacteristic
83C23×Dic89C2311yescharacteristic
84C23×Dic89C2311yescharacteristic
85C23×Dic89C2311yescharacteristic
86C23×Dic89C2311yescharacteristic
87C22×C4×D89—24no—
88C22×C4×D89—24no—
89C22×C4×D89—24no—
90C22×C4×D89C2314yes—
91#15668011—232no—
92#15667990—232no—
93#15667990—232no—
94#15667977—232no—
95C2×C4⋊Dic89—24no—
96C2×C4⋊Dic89—24no—
97C2×C4⋊Dic89C2314yes—
98C2×C4⋊Dic89C2314yes—
99C2×#13083553—24no—
100C2×#13083553—24no—
101C2×#13083553—24no—
102C2×#13083553—24no—
103C2×#13083553—24no—
104C2×#13083553—24no—
105C2×#13083553—24no—
106C2×#13083553D418yes—
107C2×#13083553C2314yes—
108C2×#13083553C2314yes—
109C2×#13083553C2314yes—
110C2×#13083553C2314yes—
111C2×#13083553C2314yes—
112C2×#13083553C2314yes—
113C2×#13083553C2314yes—
114C2×#13083553C2314yes—
115C2×#13083551—24no—
116C2×#13083551—24no—
117C2×#13083551—24no—
118C2×#13083551—24no—
119C2×#13083551—24no—
120C2×#13083551Q818yescomplemented
121C2×#13083551C2314yes—
122C2×#13083551C2314yes—
123C2×#13083551C2314yes—
124C2×#13083551C2314yes—
125C2×#13083551C2314yes—
126C2×#13083551C2314yes—
127C2×C4×Dic89—24no—
128C2×C4×Dic89—24no—
129C2×C4×Dic89—24no—
130C2×C4×Dic89—24no—
131C2×C4×Dic89C2314yes—
132C2×C4×Dic89C2314yes—
133C2×C4×Dic89C2314yes—
134C2×C4×Dic89C2314yes—
135#15667919C2314yes—
136#15667919C2314yes—
137#15667919C2314yes—
138#15667919C2314yes—
139#15667919C2314yes—
140C23×C4×C89C2311yescharacteristic
141C23×C4×C89C2311yescharacteristic
142C23×C4×C89C2311yescharacteristic
143C23×C4×C89C2311yescharacteristic
144C23×C4×C89C2311yescharacteristic
145C23×C4×C89C2311yescharacteristic
146C23×C4×C89C2311yescharacteristic
147C2×C4⋊C4×C89—24no—
148C2×C4⋊C4×C89—24no—
149C2×C4⋊C4×C89—24no—
150C2×C4⋊C4×C89—24no—
151C2×C4⋊C4×C89C2314yes—
152C2×C4⋊C4×C89C2314yes—
153C2×C4⋊C4×C89C2314yes—
154C2×C4⋊C4×C89C2314yes—
155#95×C89C2314yes—
156#95×C89C2314yes—
157#95×C89C2314yes—
158C23×D89—22no—
159C23×D89—22no—
160C23×D89—22no—
161C23×D89—22no—
162C23×D89—22no—
163C23×D89—22no—
164C23×D89C2×Q814yes—
165C23×D89C2412yes—
166C2×Dic178—232no—
167C2×Dic178—28no—
168C2×Dic178—28no—
169C2×Dic178—28no—
170C2×Dic178—28no—
171C2×Dic178—28no—
172C2×Dic178—416no—
173C2×Dic178C2×D4116yes—
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×Dic89C2×D414yes—
189C22×Dic89C2×D414yes—
190C22×Dic89C2×D414yes—
191C22×Dic89C2×D414yes—
192C22×Dic89C2×Q814yes—
193C22×Dic89#4114yes—
194C22×Dic89#4114yes—
195C22×Dic89C2412yes—
196C22×Dic89C2412yes—
197C22×Dic89C2412yes—
198C22×Dic89C2412yes—
199C22×Dic89C2412yes—
200C22×Dic89C2412yes—
201C22×Dic89C2412yes—
202C2×C4×D89—28no—
203C2×C4×D89—28no—
204C2×C4×D89—28no—
205C2×C4×D89—416no—
206C4⋊Dic89—28no—
207C4⋊Dic89—28no—
208#13083553—28no—
209#13083553—28no—
210#13083553—28no—
211#13083553—28no—
212#13083553—28no—
213#13083553—28no—
214#13083553—28no—
215#13083553C2×D4116yes—
216#13083551—28no—
217#13083551—28no—
218#13083551—28no—
219#13083551—28no—
220#13083551—28no—
221#13083551C2×Q8116yescomplemented
222C4×Dic89—28no—
223C4×Dic89—28no—
224C4×Dic89—28no—
225C4×Dic89—28no—
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×C89—22no—
244C22×C4×C89—22no—
245C22×C4×C89C2×D414yes—
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×C89—28no—
257C4⋊C4×C89—28no—
258C4⋊C4×C89—28no—
259C23×C89C22×D412yes—
260C23×C89C22×D412yes—
261C23×C89C22×Q812yes—
262C23×C89C2×#4112yes—
263C23×C89C2×#4112yes—
264C23×C892−1+412yes—
265C23×C892−1+412yes—
266C23×C89C2511yescharacteristic
267C22×D89—28no—
268C22×D89—28no—
269C22×D89—28no—
270C22×D89—22no—
271C22×D89—22no—
272C22×D89—22no—
273C22×D89—22no—
274C22×D89—22no—
275C22×D89—22no—
276C22×D89—44no—
277C22×D89—44no—
278C22×D89—44no—
279C22×D89—44no—
280C22×D89C22×Q814yes—
281C2×C4×C89—28no—
282C2×C4×C89—28no—
283C2×C4×C89—28no—
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—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—22no—
302C2×C4×C89—44no—
303C2×C4×C89—44no—
304C2×C4×C89—44no—
305C2×C4×C89—44no—
306C2×C4×C89C22×D414yes—
307C2×C4×C89C22×D414yes—
308C2×C4×C89C22×Q814yes—
309C2×Dic89—28no—
310C2×Dic89—28no—
311C2×Dic89—28no—
312C2×Dic89—28no—
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—22no—
324C2×Dic89—22no—
325C2×Dic89—22no—
326C2×Dic89—22no—
327C2×Dic89—44no—
328C2×Dic89—44no—
329C2×Dic89#121116yes—
330C2×Dic89C22×D414yes—
331C2×Dic89C22×D414yes—
332C2×Dic89C22×D414yes—
333C2×Dic89C22×D414yes—
334C2×Dic89C22×Q814yes—
335C2×Dic89C2×#4114yes—
336C2×Dic89C2×#4114yes—
337C4×D89—416no—
338Dic178—232no—
339Dic178—416no—
340C22×C89C2×#12114yes—
341C22×C89#53314yes—
342C22×C89#54114yes—
343C22×C89#54714yes—
344C22×C89#54814yes—
345C22×C89D4×Q814yes—
346C22×C89D4×Q814yes—
347C22×C89C23×D411yescharacteristic
348C22×C89C23×D411yescharacteristic
349C22×C89C23×Q811yescharacteristic
350C22×C89C22×#4111yescharacteristic
351C22×C89C22×#4111yescharacteristic
352C22×C89C2×2−1+411yescharacteristic
353C22×C89C2×2−1+411yescharacteristic
354C2×D89—24no—
355C2×D89—24no—
356C2×D89—24no—
357C2×D89—42no—
358C2×D89—416no—
359C2×D89—42no—
360C2×D89—42no—
361C2×D89—42no—
362C4×C89—24no—
363C4×C89—24no—
364C4×C89—24no—
365C4×C89—42no—
366C4×C89—42no—
367C4×C89—42no—
368C4×C89—42no—
369Dic89—24no—
370Dic89—24no—
371Dic89—24no—
372Dic89—24no—
373Dic89—42no—
374Dic89—42no—
375Dic89C2×#12118yes—
376C2×#2429—891nomaximal, Sylow
377C2×C89#242918yescomplemented
378C2×C89C22×#12111yescharacteristic
379C2×C89C2×#53311yescharacteristic
380C2×C89C2×#54111yescharacteristic
381C2×C89C2×#54711yescharacteristic
382C2×C89C2×#54811yescharacteristic
383C2×C89C2×D4×Q811yescharacteristic
384C2×C89C2×D4×Q811yescharacteristic
385D89—44no—
386C22×C4⋊Q8—891no—
387C22×C22⋊Q8—891no—
388C22×C22⋊Q8—891no—
389C22×C4×Q8—891no—
390#2429—8916no—
391C2×#398—891no—
392C2×#398D8911yescharacteristic, complemented
393C2×#396—891no—
394C2×#396—891no—
395C2×#391—891no—
396C2×#389—891no—
397C2×#389—891no—
398C2×#389—891no—
399C2×#388—891no—
400C2×#388—891no—
401C2×C4×C22⋊C4—891no—
402C89C2×#242911yescharacteristic, complemented, Sylow
403C23×Q8—891no—
404C23×Q8—891no—
405C24×C4—891no—
406C2×C4⋊Q8—898no—
407C2×C4⋊Q8—1788no—
408C2×C22⋊Q8—898no—
409C2×C22⋊Q8—898no—
410C2×C22⋊Q8—1788no—
411C2×C22⋊Q8—1788no—
412C2×C4×Q8—898no—
413C2×C4×Q8—1788no—
414C22×C4⋊C4—891no—
415C22×C4⋊C4—891no—
416C22×C4⋊C4—891no—
417C22×C4⋊C4—891no—
418C22×C4⋊C4—891no—
419C22×C4⋊C4—891no—
420C22×C4⋊C4—891no—
421C22×C4⋊C4—891no—
422C22×C4⋊C4—891no—
423C22×C4⋊C4—891no—
424C22×C4⋊C4C2×D8911yescharacteristic
425C22×C4⋊C4C2×D8911yescharacteristic
426C22×C4⋊C4C2×D8911yescharacteristic
427C22×C4⋊C4C2×D8911yescharacteristic
428C22×C22⋊C4—891no—
429C22×C22⋊C4—891no—
430C22×C22⋊C4—891no—
431C22×C22⋊C4—891no—
432C22×C22⋊C4—891no—
433C22×C22⋊C4—891no—
434C22×C42—891no—
435C22×C42—891no—
436C22×C42—891no—
437C22×C42—891no—
438#398—898no—
439#398C2×D8918yescomplemented
440#396—898no—
441#396—898no—
442#391—898no—
443#389—898no—
444#389—898no—
445#389—898no—
446#388—898no—
447#388—898no—
448C4×C22⋊C4—898no—
449C2×#95—891no—
450C2×#95—891no—
451C2×#95—891no—
452C2×#95—891no—
453C2×#95—891no—
454C2×#95C2×D8911yescharacteristic
455C2×#95C2×D8911yescharacteristic
456C2×#95C2×D8911yescharacteristic
457C25—891no—
458C22×Q8—898no—
459C22×Q8—894no—
460C22×Q8—894no—
461C22×Q8—1784no—
462C22×Q8—1784no—
463C22×Q8—1784no—
464C22×Q8—1784no—
465C22×Q8—1784no—
466C23×C4—891no—
467C23×C4—891no—
468C23×C4—891no—
469C23×C4—891no—
470C23×C4—891no—
471C23×C4—891no—
472C23×C4—891no—
473C23×C4—894no—
474C23×C4—1784no—
475C23×C4—1784no—
476C23×C4—1784no—
477C23×C4C22×D8911yescharacteristic
478C23×C4C22×D8911yescharacteristic
479C23×C4C22×D8911yescharacteristic
480C23×C4C22×D8911yescharacteristic
481C23×C4C22×D8911yescharacteristic
482C23×C4C22×D8911yescharacteristic
483C23×C4C22×D8911yescharacteristic
484C4⋊Q8—17832no—
485C22⋊Q8—17832no—
486C22⋊Q8—17832no—
487C4×Q8—17832no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—898no—
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—894no—
500C2×C4⋊C4—894no—
501C2×C4⋊C4—894no—
502C2×C4⋊C4—894no—
503C2×C4⋊C4—1784no—
504C2×C4⋊C4—1784no—
505C2×C4⋊C4—1784no—
506C2×C4⋊C4—1784no—
507C2×C4⋊C4—1784no—
508C2×C4⋊C4—1784no—
509C2×C4⋊C4—1784no—
510C2×C4⋊C4—1784no—
511C2×C4⋊C4—1784no—
512C2×C4⋊C4C22×D8914yes—
513C2×C4⋊C4C22×D8914yes—
514C2×C4⋊C4C22×D8914yes—
515C2×C4⋊C4C22×D8914yes—
516C2×C22⋊C4—898no—
517C2×C22⋊C4—894no—
518C2×C22⋊C4—894no—
519C2×C22⋊C4—894no—
520C2×C22⋊C4—894no—
521C2×C22⋊C4—894no—
522C2×C22⋊C4—894no—
523C2×C22⋊C4—1784no—
524C2×C22⋊C4—1784no—
525C2×C22⋊C4—1784no—
526C2×C22⋊C4—1784no—
527C2×C22⋊C4—1784no—
528C2×C42—894no—
529C2×C42—894no—
530C2×C42—894no—
531C2×C42—894no—
532C2×C42—1784no—
533C2×C42—1784no—
534C2×C42—1784no—
535C2×C42—1784no—
536#95—894no—
537#95—894no—
538#95—894no—
539#95—894no—
540#95—894no—
541#95C22×D8914yes—
542#95C22×D8914yes—
543#95C22×D8914yes—
544C24—894no—
545C24—892no—
546C24—1782no—
547C24—1782no—
548C24—1782no—
549C24—1782no—
550C24—1782no—
551C24—1782no—
552C24C23×D8911yescharacteristic
553C2×Q8—8916no—
554C2×Q8—35616no—
555C2×Q8—1788no—
556C2×Q8—1788no—
557C2×Q8—1788no—
558C2×Q8—1788no—
559C2×Q8—1788no—
560C2×Q8—17832no—
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—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—894no—
580C22×C4—894no—
581C22×C4—894no—
582C22×C4—892no—
583C22×C4—894no—
584C22×C4—894no—
585C22×C4—894no—
586C22×C4—894no—
587C22×C4—892no—
588C22×C4—892no—
589C22×C4—892no—
590C22×C4—892no—
591C22×C4—892no—
592C22×C4—892no—
593C22×C4—35616no—
594C22×C4—1788no—
595C22×C4—1788no—
596C22×C4—1788no—
597C22×C4—1782no—
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—1782no—
611C22×C4D4×D8914yes—
612C22×C4D4×D8914yes—
613C22×C4Q8×D8914yes—
614C22×C4C23×D8912yes—
615C22×C4C23×D8912yes—
616C22×C4C23×D8912yes—
617C22×C4C23×D8912yes—
618C22×C4C23×D8912yes—
619C22×C4C23×D8912yes—
620C22×C4C23×D8912yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—8916no—
626C4⋊C4—1788no—
627C4⋊C4—1788no—
628C4⋊C4—1788no—
629C4⋊C4—1788no—
630C4⋊C4—1788no—
631C4⋊C4—1788no—
632C4⋊C4—1788no—
633C4⋊C4—1788no—
634C4⋊C4—1788no—
635C22⋊C4—8916no—
636C22⋊C4—1788no—
637C22⋊C4—1788no—
638C22⋊C4—1788no—
639C22⋊C4—1788no—
640C22⋊C4—1788no—
641C42—1788no—
642C42—1788no—
643C42—1788no—
644C42—1788no—
645C23—894no—
646C23—3564no—
647C23—3564no—
648C23—3564no—
649C23—3564no—
650C23—1788no—
651C23—1782no—
652C23—1782no—
653C23—1782no—
654C23—1782no—
655C23—1782no—
656C23—1782no—
657C23—1788no—
658C23—1788no—
659C23C2×D4×D8912yes—
660C23C2×D4×D8912yes—
661C23C2×Q8×D8912yes—
662C23#41×D8912yes—
663C23#41×D8912yes—
664C23#1566805912yes—
665C23#1566806012yes—
666C23C24×D8911yescharacteristic
667Q8—35616no—
668Q8—17832no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—894no—
695C2×C4—894no—
696C2×C4—894no—
697C2×C4—8916no—
698C2×C4—894no—
699C2×C4—894no—
700C2×C4—894no—
701C2×C4—894no—
702C2×C4—35616no—
703C2×C4—3564no—
704C2×C4—3564no—
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—1782no—
719C2×C4—1788no—
720C2×C4—1788no—
721C2×C4—1788no—
722C2×C4—1788no—
723C2×C4C2×D4×D8914yes—
724C2×C4C2×D4×D8914yes—
725C2×C4C2×Q8×D8914yes—
726C22—3562no—
727C22—3562no—
728C22—3562no—
729C22—35616no—
730C22—3562no—
731C22—1784no—
732C22—1784no—
733C22—1784no—
734C22#121×D8914yes—
735C22#1915215414yes—
736C22#1915220714yes—
737C22#1915224614yes—
738C22#1915225814yes—
739C22#1915226114yes—
740C22#1915226314yes—
741C22C22×D4×D8911yescharacteristic
742C22C22×D4×D8911yescharacteristic
743C22C22×Q8×D8911yescharacteristic
744C22C2×#41×D8911yescharacteristic
745C22C2×#41×D8911yescharacteristic
746C22C2×#1566805911yescharacteristic
747C22C2×#1566806011yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—898no—
756C4—3562no—
757C4—3562no—
758C4—1784no—
759C4—1784no—
760C4—1784no—
761C4—1784no—
762C2—3564no—
763C2#2602384618yesdirect product factor
764C2C2×#121×D8911yescharacteristic
765C2C2×#1915215411yescharacteristic
766C2C2×#1915220711yescharacteristic
767C2C2×#1915224611yescharacteristic
768C2C2×#1915225811yescharacteristic
769C2C2×#1915226111yescharacteristic
770C2C2×#1915226311yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#398×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#398D89
hypocenterC89C2×#2429
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#15668011C2semidirect
4. C22×#15667977C2semidirect
5. #26023846C2direct (N × H)
6. C2×#19151532C2semidirect
9. C2×#19151502C2semidirect
10. C2×#19151495C2semidirect
11. C2×#19151494C2semidirect
12. C2×#19151493C2semidirect
16. C2×#398×C89C2semidirect
21. C2×#15668011C22semidirect
27. C2×#15667977C22semidirect
48. #19151532C22semidirect
51. #19151502C22semidirect
52. #19151495C22semidirect
53. #19151494C22semidirect
54. #19151493C22semidirect
67. #398×C89C22semidirect
120. C2×#13083551Q8semidirect
221. #13083551C2×Q8semidirect
377. C2×C89#2429semidirect
392. C2×#398D89semidirect
402. C89C2×#2429semidirect
439. #398C2×D89semidirect
763. C2#26023846direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680112
C22×#156679902
C22×#156679772
#260238462
C2×#191515322
C2×#191515222
C2×#191515202
C2×#191515022
C2×#191514952
C2×#191514942
C2×#191514932
C2×#191514902
C2×#191514882
C2×#191514452
C2×#398×C892
C2×#242989