Finite Group Databasebeta

← C2×#13072497 #14921272

Subgroups — C2×#13072497 #14921272

Order 2816.

3894 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×#66982C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13072497C2116yesmaximal, direct product factor
6C2×#10622605C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic
10C2×#10622260C211yesmaximal, characteristic, complemented
11C2×#10622585C211yesmaximal, characteristic, complemented
12C2×#10622558C211yesmaximal, characteristic, complemented
13C2×#10622282C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×#10622602C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×#66982—28no—
30C2×#66982C2218yescomplemented
31C2×C4×C22⋊D11—28no—
32C2×C4×C22⋊D11C2218yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66946—28no—
51C2×#66946C2218yescomplemented
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54C11×#385C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622605C2218yescomplemented
62#10622602C2218yescomplemented
63#10622585C2218yescomplemented
64#10622573C2218yes—
65#10622572C2218yescomplemented
66#10622558C2218yescomplemented
67#10622285C2218yescomplemented
68#10622282C2218yescomplemented
69#10622281C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11—24no—
75C23×C4×C11—24no—
76C23×C4×C11—42no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—24no—
101C22×D44C2314yes—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11C2314yes—
109C22×C4×D11C2314yes—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4—42no—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11D418yescomplemented
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122#66982—232no—
123C4×C22⋊D11—232no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4D418yescomplemented
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×C4⋊Dic11—24no—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×C4×Dic11—24no—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158#66946—232no—
159#66936—232no—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2455—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11C2×D414yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11C2×D414yes—
189C23×D11#4114yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—28no—
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×C11—28no—
210C22×C4×C11—44no—
211C22×C4×C11—416no—
212C22×C4×C11C2×D414yes—
213C22×C4×C11#4114yes—
214C22×C4×C11C2412yes—
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×Dic11C2×D414yes—
243C22×Dic11C2×D414yes—
244C22×Dic11C2×D414yes—
245C22×Dic11#4114yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C2×D44—232no—
253C2×D44—28no—
254C2×D44—28no—
255C2×D44—28no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C2×C4×D11—416no—
263C2×C4×D11—416no—
264C11×C4⋊C4—28no—
265C11×C4⋊C4—44no—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C22⋊Dic11—28no—
269C22⋊Dic11C2×D4116yescomplemented
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—44no—
277(C2×D11)⋊C4C2×D4116yescomplemented
278C4⋊Dic11—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#123—111no—
288C22×#123—111no—
289C22×C4×D4—111no—
290C22×C4×D4—111no—
291#2455—1116no—
292C2×#399—111no—
293C2×#394—111no—
294C2×#394—111no—
295C2×#392—111no—
296C2×#389—111no—
297C2×#389—111no—
298C2×#388—111no—
299C2×#388—111no—
300C2×#385—111no—
301C2×#385—111no—
302C2×#385D1111yescharacteristic, complemented
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—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11C22×D414yes—
317C23×C11C22×D412yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C112−1+412yes—
324C23×C11C2511yescharacteristic
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11C22×D414yes—
352C22×D11C2×#4114yes—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
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—22no—
371C2×C4×C11—416no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11C22×D414yes—
377C2×C4×C11C2×#4114yes—
378C22⋊D11—232no—
379C22⋊D11—416no—
380C2×Dic11—28no—
381C2×Dic11—28no—
382C2×Dic11—28no—
383C2×Dic11—28no—
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×Dic11C22×D414yes—
401C2×Dic11C22×D414yes—
402C2×Dic11C22×D414yes—
403C2×Dic11C2×#4114yes—
404D44—232no—
405C4×D11—416no—
406C4×D11—416no—
407C23×D4—111no—
408C23×D4—111no—
409C23×D4—111no—
410C24×C4—111no—
411C24×C4—111no—
412C24×C4C2×D1111yescharacteristic
413C2×#123—118no—
414C2×#123—118no—
415C2×#123—228no—
416C2×#123—228no—
417C2×C4×D4—118no—
418C2×C4×D4—118no—
419C2×C4×D4—228no—
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×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C42—111no—
443C22×C42—111no—
444#399—118no—
445#394—118no—
446#394—118no—
447#392—118no—
448#389—118no—
449#389—118no—
450#388—118no—
451#388—118no—
452#385—118no—
453#385—118no—
454#385C2×D1118yescomplemented
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—416no—
468C22×C11—42no—
469C22×C11#52514yes—
470C22×C11#52514yes—
471C22×C11#53914yes—
472C22×C11D4214yes—
473C22×C11#54714yes—
474C22×C11#54714yes—
475C22×C11#55914yes—
476C22×C11C23×D411yescharacteristic
477C22×C11C23×D411yescharacteristic
478C22×C11C22×#4111yescharacteristic
479C22×C11C22×#4111yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C2×H(5,𝔽2)11yescharacteristic
482C22×C11C2×2−1+411yescharacteristic
483C2×D11—24no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—416no—
496C2×D11—416no—
497C2×D11—42no—
498C2×D11—42no—
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—42no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511C25—111no—
512C25—111no—
513C25C22×D1111yescharacteristic
514C22×D4—114no—
515C22×D4—114no—
516C22×D4—114no—
517C22×D4—224no—
518C22×D4—224no—
519C22×D4—224no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—442no—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—114no—
536C23×C4—114no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—224no—
541C23×C4—442no—
542C23×C4—442no—
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1114yes—
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#123—2232no—
551#123—2232no—
552C4×D4—2232no—
553C4×D4—2232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—42no—
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—114no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—224no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4C22×D1114yes—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—118no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—118no—
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—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—442no—
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#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11—44no—
607C2×C11#245518yescomplemented
608C2×C11C2×#52511yescharacteristic
609C2×C11C2×#52511yescharacteristic
610C2×C11C2×#53911yescharacteristic
611C2×C11C2×D4211yescharacteristic
612C2×C11C2×#54711yescharacteristic
613C2×C11C2×#54711yescharacteristic
614C2×C11C2×#55911yescharacteristic
615D11—44no—
616D11—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—114no—
624C24—114no—
625C24—112no—
626C24—112no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24D4×D1114yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×D4—228no—
643C2×D4—228no—
644C2×D4—2232no—
645C2×D4—228no—
646C2×D4—228no—
647C2×D4—2232no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—444no—
653C2×D4—4416no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—28no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
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—228no—
685C22×C4—228no—
686C22×C4—228no—
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—228no—
702C22×C4—444no—
703C22×C4—444no—
704C22×C4—4416no—
705C22×C4—4416no—
706C22×C4#433914yes—
707C22×C4D4×D1114yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—44no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—228no—
721C4⋊C4—228no—
722C4⋊C4—228no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—1116no—
726C22⋊C4—1116no—
727C22⋊C4—228no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—444no—
735C42—228no—
736C42—228no—
737C11C2×#245511yescharacteristic, complemented, Sylow
738C23—28no—
739C23—28no—
740C23—28no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—114no—
752C23—114no—
753C23—228no—
754C23—228no—
755C23—228no—
756C23—228no—
757C23—228no—
758C23—228no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23C2×#433912yes—
780C23C2×D4×D1114yes—
781C23C2×D4×D1112yes—
782C23C2×D4×D1112yes—
783C23#6703712yes—
784C23#6704012yes—
785C23#41×D1112yes—
786C23#41×D1112yes—
787C23C24×D1111yescharacteristic
788D4—2232no—
789D4—2232no—
790D4—4416no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
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—22no—
808C2×C4—22no—
809C2×C4—416no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—228no—
819C2×C4—228no—
820C2×C4—228no—
821C2×C4—228no—
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—4416no—
837C2×C4—4416no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4C2×#433914yes—
841C2×C4C2×D4×D1114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—42no—
850C22—224no—
851C22—224no—
852C22—224no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—4416no—
860C22—4416no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22#1062303814yes—
867C22#1062307814yes—
868C22#1062309014yes—
869C22#1062312114yes—
870C22#1062316214yes—
871C22#1062316914yes—
872C22#1062318714yes—
873C22C22×#433911yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C22×D4×D1111yescharacteristic
876C22C2×#6703711yescharacteristic
877C22C2×#6704011yescharacteristic
878C22C2×#41×D1111yescharacteristic
879C22C2×#41×D1111yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—224no—
887C4—224no—
888C4—224no—
889C4—224no—
890C4—442no—
891C4—442no—
892C2—44no—
893C2—444no—
894C2—444no—
895C2#1307249718yesdirect product factor
896C2C2×#1062318711yescharacteristic
897C2C2×#1062307811yescharacteristic
898C2C2×#1062316911yescharacteristic
899C2C2×#1062312111yescharacteristic
900C2C2×#1062303811yescharacteristic
901C2C2×#1062316211yescharacteristic
902C2C2×#1062309011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#385D11
hypocenterC11C2×#2455
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. C22×#66936C2semidirect
3. C22×#66946C2semidirect
4. C22×C4×C22⋊D11C2semidirect
5. #13072497C2direct (N × H)
6. C2×#10622605C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622572C2semidirect
10. C2×#10622260C2semidirect
11. C2×#10622585C2semidirect
12. C2×#10622558C2semidirect
13. C2×#10622282C2semidirect
14. C2×#10622281C2semidirect
15. C2×#10622602C2semidirect
16. C2×C11×#385C2semidirect
30. C2×#66982C22semidirect
32. C2×C4×C22⋊D11C22semidirect
51. C2×#66946C22semidirect
53. C2×#66936C22semidirect
54. C11×#385C22semidirect
61. #10622605C22semidirect
62. #10622602C22semidirect
63. #10622585C22semidirect
65. #10622572C22semidirect
66. #10622558C22semidirect
67. #10622285C22semidirect
68. #10622282C22semidirect
69. #10622281C22semidirect
70. #10622260C22semidirect
119. C2×C22⋊Dic11D4semidirect
131. C2×(C2×D11)⋊C4D4semidirect
269. C22⋊Dic11C2×D4semidirect
277. (C2×D11)⋊C4C2×D4semidirect
302. C2×#385D11semidirect
454. #385C2×D11semidirect
607. C2×C11#2455semidirect
737. C11C2×#2455semidirect
895. C2#13072497direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669362
C22×#669462
C22×C4×C22⋊D112
#130724972
C2×#106226052
C2×#106222852
C2×#106225722
C2×#106225732
C2×#106222602
C2×#106225852
C2×#106225582
C2×#106222822
C2×#106222812
C2×#106226022
C2×C11×#3852
C2×#245511