Finite Group Databasebeta

← C2×#13072608 #14921297

Subgroups — C2×#13072608 #14921297

Order 2816.

3958 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072608C2116yesmaximal, direct product factor
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic
9C2×#10622564C211yesmaximal, characteristic, complemented
10C2×#10622283C211yesmaximal, characteristic, complemented
11C2×#10622267C211yesmaximal, characteristic, complemented
12C2×#10622591C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622563C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×D4×Dic11—28no—
34C2×D4×Dic11C2218yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66950—28no—
47C2×#66950C2218yescomplemented
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2218yescomplemented
50C2×#66931—28no—
51C2×#66931C2218yescomplemented
52C11×#394C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54#10622836C2218yes—
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622591C2218yescomplemented
63#10622572C2218yescomplemented
64#10622571C2218yescomplemented
65#10622569C2218yescomplemented
66#10622564C2218yescomplemented
67#10622563C2218yescomplemented
68#10622560C2218yescomplemented
69#10622283C2218yescomplemented
70#10622267C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11C2314yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11—24no—
92C23×Dic11—24no—
93C23×Dic11—24no—
94C23×Dic11—24no—
95C23×Dic11—42no—
96C23×Dic11—42no—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2314yes—
101C23×Dic11C2314yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—42no—
109C22×C4×D11C2314yes—
110C22×Dic22—24no—
111C22×Dic22—24no—
112C22×Dic22—42no—
113C22×Dic22C2314yes—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—42no—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132D4×Dic11—232no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11—24no—
143C2×C4⋊Dic11D418yescomplemented
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4D418yescomplemented
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×C4×Dic11—24no—
152C2×C4×Dic11—24no—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155#66950—232no—
156(C22⋊D11)⋊C4—232no—
157#66931—232no—
158C11×#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2463—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#4114yes—
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×D11#4114yes—
191C23×D11C2412yes—
192C2×D4×C11—232no—
193C2×D4×C11—28no—
194C2×D4×C11—28no—
195C2×D4×C11—28no—
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—22no—
209C22×C4×C11C2×D414yes—
210C22×C4×C11C2×D414yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C2×C22⋊D11—232no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—28no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—416no—
224C22×Dic11—28no—
225C22×Dic11—28no—
226C22×Dic11—28no—
227C22×Dic11—28no—
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×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11—416no—
248C22×Dic11—416no—
249C22×Dic11C2×D414yes—
250C22×Dic11C2×D414yes—
251C22×Dic11C2×D414yes—
252C22×Dic11C2×D414yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—44no—
263C2×C4×D11—416no—
264C2×Dic22—28no—
265C2×Dic22—28no—
266C2×Dic22—44no—
267C2×Dic22—416no—
268C11×C4⋊C4—28no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—28no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—28no—
276C22⋊Dic11—44no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281C4⋊Dic11—28no—
282C4⋊Dic11—28no—
283C4⋊Dic11C2×D4116yescomplemented
284Dic11⋊C4—28no—
285Dic11⋊C4C2×D4116yescomplemented
286C4×Dic11—28no—
287C4×Dic11—28no—
288C22×C22⋊Q8—111no—
289C22×C22⋊Q8—111no—
290C22×C4×D4—111no—
291C22×C4×D4—111no—
292#2463—1116no—
293C2×#394—111no—
294C2×#394D1111yescharacteristic, complemented
295C2×#393—111no—
296C2×#392—111no—
297C2×#388—111no—
298C2×#388—111no—
299C2×#387—111no—
300C2×#387—111no—
301C2×#386—111no—
302C2×#386—111no—
303C2×#385—111no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—28no—
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—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×#4114yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C112−1+412yes—
339C23×C11C2511yescharacteristic
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11C2×#4114yes—
354D4×C11—232no—
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—22no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C22×D414yes—
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—416no—
399C2×Dic11—416no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11C22×D414yes—
404C2×Dic11C22×D414yes—
405C2×Dic11C22×D414yes—
406C2×Dic11C22×D414yes—
407C4×D11—416no—
408Dic22—416no—
409C23×Q8—111no—
410C23×D4—111no—
411C23×D4—111no—
412C23×D4C2×D1111yescharacteristic
413C24×C4—111no—
414C24×C4—111no—
415C24×C4—111no—
416C2×C22⋊Q8—118no—
417C2×C22⋊Q8—118no—
418C2×C22⋊Q8—228no—
419C2×C22⋊Q8—228no—
420C2×C4×D4—118no—
421C2×C4×D4—118no—
422C2×C4×D4—228no—
423C2×C4×D4—228no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4C2×D1111yescharacteristic
442C22×C42—111no—
443C22×C42—111no—
444#394—118no—
445#394C2×D1118yescomplemented
446#393—118no—
447#392—118no—
448#388—118no—
449#388—118no—
450#387—118no—
451#387—118no—
452#386—118no—
453#386—118no—
454#385—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95C2×D1111yescharacteristic
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—416no—
478C22×C11—416no—
479C22×C11#52514yes—
480C22×C11#52514yes—
481C22×C11#53914yes—
482C22×C11D4214yes—
483C22×C11#54814yes—
484C22×C11#54814yes—
485C22×C11#55114yes—
486C22×C11C23×D411yescharacteristic
487C22×C11C23×D411yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C22×#4111yescharacteristic
490C22×C11C22×#4111yescharacteristic
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11C2×2−1+411yescharacteristic
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—24no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—416no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506Dic11—24no—
507Dic11—24no—
508Dic11—24no—
509Dic11—24no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513C25—111no—
514C25C22×D1111yescharacteristic
515C25C22×D1111yescharacteristic
516C22×Q8—114no—
517C22×Q8—224no—
518C22×Q8—224no—
519C22×Q8—442no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—114no—
524C22×D4—114no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—224no—
529C22×D4—224no—
530C22×D4—442no—
531C22×D4C22×D1114yes—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—114no—
540C23×C4—114no—
541C23×C4—114no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—224no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4—442no—
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C22⋊Q8—2232no—
557C22⋊Q8—2232no—
558C4×D4—2232no—
559C4×D4—2232no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—118no—
562C2×C4⋊C4—118no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—224no—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
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—114no—
583C2×C22⋊C4—114no—
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⋊C4—442no—
592C2×C22⋊C4C22×D1114yes—
593C2×C22⋊C4C22×D1114yes—
594C2×C22⋊C4C22×D1114yes—
595C2×C22⋊C4C22×D1114yes—
596C2×C42—114no—
597C2×C42—114no—
598C2×C42—224no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95C22×D1114yes—
608C2×C11—44no—
609C2×C11—44no—
610C2×C11#246318yescomplemented
611C2×C11C2×#52511yescharacteristic
612C2×C11C2×#52511yescharacteristic
613C2×C11C2×#53911yescharacteristic
614C2×C11C2×D4211yescharacteristic
615C2×C11C2×#54811yescharacteristic
616C2×C11C2×#54811yescharacteristic
617C2×C11C2×#55111yescharacteristic
618D11—44no—
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—114no—
632C24—112no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24#434114yes—
640C24#434114yes—
641C24C23×D1112yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×Q8—228no—
645C2×Q8—228no—
646C2×Q8—444no—
647C2×Q8—4416no—
648C2×D4—232no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—2232no—
655C2×D4—228no—
656C2×D4—228no—
657C2×D4—228no—
658C2×D4—444no—
659C2×D4—4416no—
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—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—114no—
674C22×C4—114no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—228no—
685C22×C4—228no—
686C22×C4—228no—
687C22×C4—228no—
688C22×C4—228no—
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—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—228no—
707C22×C4—444no—
708C22×C4—4416no—
709C22×C4—444no—
710C22×C4—444no—
711C22×C4—4416no—
712C22×C4—4416no—
713C22×C4D4×D1114yes—
714C22×C4D4×D1114yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C4⋊C4—28no—
721C4⋊C4—1116no—
722C4⋊C4—1116no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—228no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—228no—
736C22⋊C4—228no—
737C22⋊C4—444no—
738C42—228no—
739C42—228no—
740C11C2×#246311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—28no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—28no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—114no—
768C23—228no—
769C23—222no—
770C23—222no—
771C23—228no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—228no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23—444no—
781C23C2×D4×D1112yes—
782C23C2×D4×D1112yes—
783C23C2×#434114yes—
784C23C2×#434114yes—
785C23C2×#434112yes—
786C23C2×#434112yes—
787C23#41×D1112yes—
788C23#6704212yes—
789C23#6704312yes—
790C23C24×D1111yescharacteristic
791Q8—4416no—
792D4—232no—
793D4—2232no—
794D4—4416no—
795C2×C4—28no—
796C2×C4—28no—
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—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—114no—
817C2×C4—228no—
818C2×C4—228no—
819C2×C4—228no—
820C2×C4—228no—
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—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—4416no—
839C2×C4—4416no—
840C2×C4—4416no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4C2×D4×D1114yes—
845C2×C4C2×D4×D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—416no—
858C22—416no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—224no—
863C22—224no—
864C22—224no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—4416no—
869C22—442no—
870C22#1062311714yes—
871C22#1062312914yes—
872C22#1062313714yes—
873C22#1062314014yes—
874C22#1062318914yes—
875C22#1062319614yes—
876C22#1062320814yes—
877C22C22×D4×D1111yescharacteristic
878C22C22×D4×D1111yescharacteristic
879C22C22×#434111yescharacteristic
880C22C22×#434111yescharacteristic
881C22C2×#41×D1111yescharacteristic
882C22C2×#6704211yescharacteristic
883C22C2×#6704311yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—224no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—44no—
898C2—444no—
899C2#1307260818yesdirect product factor
900C2C2×#1062311711yescharacteristic
901C2C2×#1062313711yescharacteristic
902C2C2×#1062319611yescharacteristic
903C2C2×#1062314011yescharacteristic
904C2C2×#1062312911yescharacteristic
905C2C2×#1062320811yescharacteristic
906C2C2×#1062318911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#394D11
hypocenterC11C2×#2463
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66950C2semidirect
2. C22×#66931C2semidirect
3. C22×D4×Dic11C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072608C2direct (N × H)
6. C2×#10622572C2semidirect
7. C2×#10622560C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622267C2semidirect
12. C2×#10622591C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622563C2semidirect
16. C2×C11×#394C2semidirect
34. C2×D4×Dic11C22semidirect
47. C2×#66950C22semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×#66931C22semidirect
52. C11×#394C22semidirect
62. #10622591C22semidirect
63. #10622572C22semidirect
64. #10622571C22semidirect
65. #10622569C22semidirect
66. #10622564C22semidirect
67. #10622563C22semidirect
68. #10622560C22semidirect
69. #10622283C22semidirect
70. #10622267C22semidirect
143. C2×C4⋊Dic11D4semidirect
148. C2×Dic11⋊C4D4semidirect
283. C4⋊Dic11C2×D4semidirect
285. Dic11⋊C4C2×D4semidirect
294. C2×#394D11semidirect
445. #394C2×D11semidirect
610. C2×C11#2463semidirect
740. C11C2×#2463semidirect
899. C2#13072608direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#669312
C22×D4×Dic112
C22×(C22⋊D11)⋊C42
#130726082
C2×#106225722
C2×#106225602
C2×#106228362
C2×#106225642
C2×#106222832
C2×#106222672
C2×#106225912
C2×#106225712
C2×#106225692
C2×#106225632
C2×C11×#3942
C2×#246311