Finite Group Databasebeta

← C2×#13072588 #14921638

Subgroups — C2×#13072588 #14921638

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×#66938C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3C22×#66977C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13072588C2116yesmaximal, direct product factor
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622269C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic
10C2×#10622834C211yesmaximal, characteristic, complemented
11C2×#10622558C211yesmaximal, characteristic, complemented
12C2×#10622564C211yesmaximal, characteristic, complemented
13C2×#10622283C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
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
32C2×C4×C22⋊D11—28no—
33C2×C4×C22⋊D11C2218yescomplemented
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C2×#66977—28no—
42C2×#66977C2218yescomplemented
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66938—28no—
51C2×#66938C2218yescomplemented
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54C11×#386C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57#10622836C2218yes—
58#10622834C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63#10622572C2218yescomplemented
64#10622564C2218yescomplemented
65#10622561C2218yescomplemented
66#10622558C2218yescomplemented
67#10622283C2218yescomplemented
68#10622281C2218yescomplemented
69#10622269C2218yescomplemented
70#10622262C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—42no—
77C22×D4×C11C2314yes—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—42no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—42no—
105C22×C4×D11C2314yes—
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⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C4×C22⋊D11—232no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4D418yescomplemented
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11—24no—
138C2×C4⋊Dic11—24no—
139C2×C4⋊Dic11—42no—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×C4⋊Dic11C2314yes—
143#66977—232no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4D418yescomplemented
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11—24no—
153C2×C4×Dic11—24no—
154C2×C4×Dic11—24no—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158#66938—232no—
159#66936—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#4114yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11C2×D414yes—
191C23×D11C2412yes—
192C2×D4×C11—28no—
193C2×D4×C11—28no—
194C2×D4×C11—44no—
195C2×D4×C11—416no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—28no—
209C22×C4×C11—28no—
210C22×C4×C11—44no—
211C22×C4×C11—416no—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2×D414yes—
214C22×C4×C11#4114yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C2×C22⋊D11—232no—
221C2×C22⋊D11—28no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—28no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—416no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
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—22no—
245C22×Dic11C2×D414yes—
246C22×Dic11C2×D414yes—
247C22×Dic11C2×D414yes—
248C22×Dic11#4114yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—44no—
259C2×C4×D11—416no—
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—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4C2×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×#392—111no—
296C2×#390—111no—
297C2×#388—111no—
298C2×#388—111no—
299C2×#388—111no—
300C2×#386D1111yescharacteristic, complemented
301C2×#385—111no—
302C2×C4×C4⋊C4—111no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
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—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11C22×D412yes—
331C23×C11C22×D412yes—
332C23×C11C2×#4112yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C112−1+412yes—
338C23×C11C2511yescharacteristic
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11C22×D414yes—
353D4×C11—416no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
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—22no—
369C2×C4×C11—416no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11C22×D414yes—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C2×#4114yes—
375C22⋊D11—232no—
376C22⋊D11—416no—
377C2×Dic11—28no—
378C2×Dic11—28no—
379C2×Dic11—28no—
380C2×Dic11—28no—
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—22no—
397C2×Dic11—22no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11C22×D414yes—
402C2×Dic11C22×D414yes—
403C2×Dic11C22×D414yes—
404C2×Dic11C2×#4114yes—
405C4×D11—416no—
406Dic22—416no—
407C23×Q8—111no—
408C23×D4—111no—
409C23×D4—111no—
410C23×D4C2×D1111yescharacteristic
411C24×C4—111no—
412C24×C4C2×D1111yescharacteristic
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#392—118no—
448#390—118no—
449#388—118no—
450#388—118no—
451#388—118no—
452#386C2×D1118yescomplemented
453#385—118no—
454C4×C4⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95C2×D1111yescharacteristic
460C2×#95C2×D1111yescharacteristic
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—416no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—88no—
477C22×C11#52514yes—
478C22×C11#53214yes—
479C22×C11#54214yes—
480C22×C11D4214yes—
481C22×C11#54714yes—
482C22×C11#54814yes—
483C22×C11#55114yes—
484C22×C11C23×D411yescharacteristic
485C22×C11C23×D411yescharacteristic
486C22×C11C22×#4111yescharacteristic
487C22×C11C22×#4111yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×2−1+411yescharacteristic
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—416no—
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—42no—
503C4×C11—42no—
504Dic11—24no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511C25—111no—
512C25C22×D1111yescharacteristic
513C25C22×D1111yescharacteristic
514C22×Q8—114no—
515C22×Q8—224no—
516C22×Q8—224no—
517C22×Q8—442no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—42no—
521C22×D4—114no—
522C22×D4—114no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—442no—
529C22×D4C22×D1114yes—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—42no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—114no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—442no—
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1114yes—
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#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11—44no—
607C2×C11—82no—
608C2×C11#246118yescomplemented
609C2×C11C2×#52511yescharacteristic
610C2×C11C2×#53211yescharacteristic
611C2×C11C2×#54211yescharacteristic
612C2×C11C2×D4211yescharacteristic
613C2×C11C2×#54711yescharacteristic
614C2×C11C2×#54811yescharacteristic
615C2×C11C2×#55111yescharacteristic
616D11—44no—
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—114no—
631C24—112no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24#434114yes—
639C24C23×D1112yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×Q8—228no—
643C2×Q8—228no—
644C2×Q8—444no—
645C2×Q8—4416no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—44no—
649C2×D4—416no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—2232no—
654C2×D4—228no—
655C2×D4—228no—
656C2×D4—444no—
657C2×D4—4416no—
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—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—44no—
673C22×C4—416no—
674C22×C4—114no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—114no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—228no—
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—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—228no—
704C22×C4—444no—
705C22×C4—4416no—
706C22×C4#433914yes—
707C22×C4D4×D1114yes—
708C22×C4D4×D1114yes—
709C22×C4C23×D1112yes—
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—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—114no—
766C23—228no—
767C23—228no—
768C23—228no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23C2×#433912yes—
780C23C2×D4×D1112yes—
781C23C2×D4×D1112yes—
782C23C2×#434114yes—
783C23C2×#434112yes—
784C23#6703712yes—
785C23#41×D1112yes—
786C23#6704312yes—
787C23C24×D1111yescharacteristic
788Q8—4416no—
789D4—416no—
790D4—2232no—
791D4—4416no—
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—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—416no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—228no—
815C2×C4—228no—
816C2×C4—228no—
817C2×C4—228no—
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—222no—
834C2×C4—222no—
835C2×C4—4416no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4C2×#433914yes—
840C2×C4C2×D4×D1114yes—
841C2×C4C2×D4×D1114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—88no—
858C22—224no—
859C22—224no—
860C22—224no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—4416no—
865C22—442no—
866C22#1062302614yes—
867C22#1062307914yes—
868C22#1062308214yes—
869C22#1062312114yes—
870C22#1062312914yes—
871C22#1062313714yes—
872C22#1062319314yes—
873C22C22×#433911yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C22×D4×D1111yescharacteristic
876C22C22×#434111yescharacteristic
877C22C2×#6703711yescharacteristic
878C22C2×#41×D1111yescharacteristic
879C22C2×#6704311yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—224no—
886C4—224no—
887C4—224no—
888C4—224no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—44no—
893C2—82no—
894C2—444no—
895C2#1307258818yesdirect product factor
896C2C2×#1062313711yescharacteristic
897C2C2×#1062307911yescharacteristic
898C2C2×#1062319311yescharacteristic
899C2C2×#1062312111yescharacteristic
900C2C2×#1062308211yescharacteristic
901C2C2×#1062312911yescharacteristic
902C2C2×#1062302611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11C2×#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66936C2semidirect
3. C22×#66977C2semidirect
4. C22×C4×C22⋊D11C2semidirect
5. #13072588C2direct (N × H)
6. C2×#10622561C2semidirect
7. C2×#10622269C2semidirect
8. C2×#10622572C2semidirect
10. C2×#10622834C2semidirect
11. C2×#10622558C2semidirect
12. C2×#10622564C2semidirect
13. C2×#10622283C2semidirect
14. C2×#10622281C2semidirect
15. C2×#10622262C2semidirect
16. C2×C11×#386C2semidirect
33. C2×C4×C22⋊D11C22semidirect
42. C2×#66977C22semidirect
51. C2×#66938C22semidirect
53. C2×#66936C22semidirect
54. C11×#386C22semidirect
58. #10622834C22semidirect
63. #10622572C22semidirect
64. #10622564C22semidirect
65. #10622561C22semidirect
66. #10622558C22semidirect
67. #10622283C22semidirect
68. #10622281C22semidirect
69. #10622269C22semidirect
70. #10622262C22semidirect
132. C2×(C2×D11)⋊C4D4semidirect
147. C2×Dic11⋊C4D4semidirect
276. (C2×D11)⋊C4C2×D4semidirect
283. Dic11⋊C4C2×D4semidirect
300. C2×#386D11semidirect
452. #386C2×D11semidirect
608. C2×C11#2461semidirect
737. C11C2×#2461semidirect
895. C2#13072588direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669362
C22×#669772
C22×C4×C22⋊D112
#130725882
C2×#106225612
C2×#106222692
C2×#106225722
C2×#106228362
C2×#106228342
C2×#106225582
C2×#106225642
C2×#106222832
C2×#106222812
C2×#106222622
C2×C11×#3862
C2×#246111