Finite Group Databasebeta

← C2×#13072578 #14921625

Subgroups — C2×#13072578 #14921625

Order 2816.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic, complemented
2C22×#66988C211yesmaximal, characteristic, complemented
3C22×#66931C211yesmaximal, characteristic, complemented
4C22×D4×Dic11C211yesmaximal, characteristic, complemented
5#13072578C2116yesmaximal, direct product factor
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622269C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622834C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622563C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C2×#66989—28no—
37C2×#66989C2218yescomplemented
38C2×#66988—28no—
39C2×#66988C2218yescomplemented
40C2×D4×Dic11—28no—
41C2×D4×Dic11C2218yescomplemented
42C22×C4⋊Dic11C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×C4⋊Dic11C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66931—28no—
53C2×#66931C2218yescomplemented
54C11×#392C2218yes—
55C2×C11×#95C2211yescharacteristic
56#10622835C2218yescomplemented
57#10622834C2218yescomplemented
58#10622833C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622564C2218yescomplemented
65#10622563C2218yescomplemented
66#10622561C2218yescomplemented
67#10622558C2218yescomplemented
68#10622557C2218yescomplemented
69#10622269C2218yescomplemented
70#10622262C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11C2314yes—
84C22×D4×C11C2314yes—
85C22×D4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×Dic11—24no—
91C23×Dic11—24no—
92C23×Dic11—24no—
93C23×Dic11—24no—
94C23×Dic11—42no—
95C23×Dic11—42no—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2314yes—
101C23×Dic11C2314yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×Dic22—24no—
107C22×Dic22—24no—
108C22×Dic22—42no—
109C22×Dic22C2314yes—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11D418yescomplemented
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136#66989—232no—
137#66988—232no—
138D4×Dic11—232no—
139C2×C4⋊Dic11—24no—
140C2×C4⋊Dic11—24no—
141C2×C4⋊Dic11—42no—
142C2×C4⋊Dic11C2314yes—
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2314yes—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4D418yescomplemented
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×C4×Dic11—24no—
154C2×C4×Dic11—24no—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2314yes—
159#66931—232no—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2461—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11C2×D414yes—
187C24×C11#4114yes—
188C24×C11C2412yes—
189C24×C11C2412yes—
190C24×C11C2412yes—
191C24×C11C2411yescharacteristic
192C2×D4×C11—232no—
193C2×D4×C11—28no—
194C2×D4×C11—28no—
195C2×D4×C11—28no—
196C2×D4×C11—28no—
197C2×D4×C11—28no—
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11—416no—
203C2×D4×C11—416no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11C2×D414yes—
214C22×C4×C11#4114yes—
215C22×C4×C11#4114yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×Dic11—28no—
221C22×Dic11—28no—
222C22×Dic11—28no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—28no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11—416no—
247C22×Dic11—416no—
248C22×Dic11C2×D414yes—
249C22×Dic11C2×D414yes—
250C22×Dic11C2×D414yes—
251C22×Dic11C2×D414yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×Dic22—28no—
261C2×Dic22—28no—
262C2×Dic22—44no—
263C2×Dic22—416no—
264C11×C22⋊C4—28no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—28no—
267C22⋊Dic11—28no—
268C22⋊Dic11—28no—
269C22⋊Dic11—28no—
270C22⋊Dic11—28no—
271C22⋊Dic11—28no—
272C22⋊Dic11—28no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—28no—
276C22⋊Dic11C2×D4116yescomplemented
277C4⋊Dic11—28no—
278C4⋊Dic11—28no—
279C4⋊Dic11—44no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4C2×D4116yescomplemented
284C4×Dic11—28no—
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#124—111no—
288C22×#123—111no—
289C22×C22⋊Q8—111no—
290C22×C4×D4—111no—
291#2461—1116no—
292C2×#396—111no—
293C2×#395—111no—
294C2×#394—111no—
295C2×#392D1111yescharacteristic
296C2×#390—111no—
297C2×#388—111no—
298C2×#388—111no—
299C2×#388—111no—
300C2×#386—111no—
301C2×#385—111no—
302C2×C4×C4⋊C4—111no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11C22×D414yes—
344C23×C11C22×D412yes—
345C23×C11C22×D412yes—
346C23×C11C2×#4114yes—
347C23×C11C2×#4112yes—
348C23×C11C2×#4112yes—
349C23×C11C2×#4112yes—
350C23×C11H(5,𝔽2)12yes—
351C23×C112−1+412yes—
352C23×C11C2511yescharacteristic
353D4×C11—232no—
354D4×C11—416no—
355D4×C11—416no—
356C2×C4×C11—28no—
357C2×C4×C11—28no—
358C2×C4×C11—28no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—44no—
369C2×C4×C11C22×D414yes—
370C2×C4×C11C2×#4114yes—
371C2×C4×C11C2×#4114yes—
372C2×Dic11—28no—
373C2×Dic11—28no—
374C2×Dic11—28no—
375C2×Dic11—28no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—416no—
397C2×Dic11—416no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11C22×D414yes—
403C2×Dic11C22×D414yes—
404C2×Dic11C22×D414yes—
405C2×Dic11C22×D414yes—
406Dic22—416no—
407C23×Q8—111no—
408C23×D4C2×D1111yescharacteristic
409C23×D4C2×D1111yescharacteristic
410C23×D4C2×D1111yescharacteristic
411C24×C4—111no—
412C24×C4—111no—
413C2×#124—118no—
414C2×#124—228no—
415C2×#123—118no—
416C2×#123—228no—
417C2×C22⋊Q8—118no—
418C2×C22⋊Q8—228no—
419C2×C4×D4—118no—
420C2×C4×D4—228no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C42—111no—
442C22×C42—111no—
443C22×C42—111no—
444#396—118no—
445#395—118no—
446#394—118no—
447#392C2×D1118yes—
448#390—118no—
449#388—118no—
450#388—118no—
451#388—118no—
452#386—118no—
453#385—118no—
454C4×C4⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95C2×D1111yescharacteristic
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—416no—
476C22×C11—416no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—88no—
485C22×C11#52514yes—
486C22×C11#53214yes—
487C22×C11#54214yes—
488C22×C11D4214yes—
489C22×C11#54714yes—
490C22×C11#54814yes—
491C22×C11#55114yes—
492C22×C11C23×D411yescharacteristic
493C22×C11C23×D411yescharacteristic
494C22×C11C22×#4111yescharacteristic
495C22×C11C22×#4111yescharacteristic
496C22×C11C22×#4111yescharacteristic
497C22×C11C2×H(5,𝔽2)11yescharacteristic
498C22×C11C2×2−1+411yescharacteristic
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—42no—
503Dic11—24no—
504Dic11—24no—
505Dic11—24no—
506Dic11—24no—
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511C25C22×D1111yescharacteristic
512C25C22×D1111yescharacteristic
513C25C22×D1111yescharacteristic
514C22×Q8—114no—
515C22×Q8—224no—
516C22×Q8—224no—
517C22×Q8—442no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4C22×D1114yes—
528C22×D4C22×D1114yes—
529C22×D4C22×D1114yes—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—114no—
539C23×C4—114no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4—442no—
545C23×C4—442no—
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#124—2232no—
551#123—2232no—
552C22⋊Q8—2232no—
553C4×D4—2232no—
554C2×C4⋊C4—118no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—224no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—224no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—442no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—118no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4C22×D1114yes—
592C2×C22⋊C4C22×D1114yes—
593C2×C22⋊C4C22×D1114yes—
594C2×C42—114no—
595C2×C42—114no—
596C2×C42—114no—
597C2×C42—224no—
598C2×C42—224no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95C22×D1114yes—
606C2×C11—44no—
607C2×C11—44no—
608C2×C11—82no—
609C2×C11#246118yescomplemented
610C2×C11C2×#52511yescharacteristic
611C2×C11C2×#53211yescharacteristic
612C2×C11C2×#54211yescharacteristic
613C2×C11C2×D4211yescharacteristic
614C2×C11C2×#54711yescharacteristic
615C2×C11C2×#54811yescharacteristic
616C2×C11C2×#55111yescharacteristic
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24D4×D1114yes—
637C24#434114yes—
638C24C23×D1112yes—
639C24C23×D1112yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×Q8—228no—
643C2×Q8—228no—
644C2×Q8—444no—
645C2×Q8—4416no—
646C2×D4—232no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—416no—
657C2×D4—416no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—114no—
668C22×C4—114no—
669C22×C4—114no—
670C22×C4—114no—
671C22×C4—112no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—228no—
680C22×C4—228no—
681C22×C4—228no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—228no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—444no—
704C22×C4—444no—
705C22×C4—4416no—
706C22×C4—4416no—
707C22×C4D4×D1114yes—
708C22×C4#434114yes—
709C22×C4#434114yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—1116no—
715C4⋊C4—228no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—444no—
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—28no—
724C22⋊C4—1116no—
725C22⋊C4—228no—
726C22⋊C4—228no—
727C22⋊C4—228no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C42—228no—
735C42—228no—
736C42—228no—
737C11C2×#246111yescharacteristic, complemented, Sylow
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23C2×D4×D1114yes—
779C23C2×D4×D1112yes—
780C23C2×D4×D1112yes—
781C23C2×#434114yes—
782C23C2×#434112yes—
783C23C2×#434112yes—
784C23C2×#434112yes—
785C23#6703712yes—
786C23#6704312yes—
787C23C24×D1111yescharacteristic
788Q8—4416no—
789D4—232no—
790D4—416no—
791D4—416no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—44no—
805C2×C4—114no—
806C2×C4—114no—
807C2×C4—114no—
808C2×C4—114no—
809C2×C4—228no—
810C2×C4—228no—
811C2×C4—228no—
812C2×C4—228no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—4416no—
834C2×C4—4416no—
835C2×C4—444no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4C2×D4×D1114yes—
840C2×C4C2×#434114yes—
841C2×C4C2×#434114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—416no—
854C22—416no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—88no—
866C22#1062311714yes—
867C22#1062311814yes—
868C22#1062312114yes—
869C22#1062312914yes—
870C22#1062313414yes—
871C22#1062314214yes—
872C22#1062324714yes—
873C22C22×D4×D1111yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C22×#434111yescharacteristic
876C22C22×#434111yescharacteristic
877C22C22×#434111yescharacteristic
878C22C2×#6703711yescharacteristic
879C22C2×#6704311yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—224no—
885C4—224no—
886C4—224no—
887C4—224no—
888C4—442no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—44no—
893C2—44no—
894C2—82no—
895C2#1307257818yesdirect product factor
896C2C2×#1062311711yescharacteristic
897C2C2×#1062324711yescharacteristic
898C2C2×#1062313411yescharacteristic
899C2C2×#1062312111yescharacteristic
900C2C2×#1062314211yescharacteristic
901C2C2×#1062312911yescharacteristic
902C2C2×#1062311811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×#66988C2semidirect
3. C22×#66931C2semidirect
4. C22×D4×Dic11C2semidirect
5. #13072578C2direct (N × H)
6. C2×#10622561C2semidirect
7. C2×#10622269C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622563C2semidirect
15. C2×#10622262C2semidirect
37. C2×#66989C22semidirect
39. C2×#66988C22semidirect
41. C2×D4×Dic11C22semidirect
53. C2×#66931C22semidirect
56. #10622835C22semidirect
57. #10622834C22semidirect
58. #10622833C22semidirect
64. #10622564C22semidirect
65. #10622563C22semidirect
66. #10622561C22semidirect
67. #10622558C22semidirect
68. #10622557C22semidirect
69. #10622269C22semidirect
70. #10622262C22semidirect
125. C2×C22⋊Dic11D4semidirect
148. C2×Dic11⋊C4D4semidirect
276. C22⋊Dic11C2×D4semidirect
283. Dic11⋊C4C2×D4semidirect
609. C2×C11#2461semidirect
737. C11C2×#2461semidirect
895. C2#13072578direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×#669882
C22×#669312
C22×D4×Dic112
#130725782
C2×#106225612
C2×#106222692
C2×#106228352
C2×#106228342
C2×#106225582
C2×#106225642
C2×#106225572
C2×#106228332
C2×#106225632
C2×#106222622
C2×C11×#3922
C2×#246111