Finite Group Databasebeta

← C2×#13072577 #14921628

Subgroups — C2×#13072577 #14921628

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×#66982C211yesmaximal, characteristic, complemented
3C22×#66977C211yesmaximal, characteristic, complemented
4#13072577C2116yesmaximal, direct product factor
5C2×#10622607C211yesmaximal, characteristic, complemented
6C2×#10622592C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C2×C4×D4×C11—28no—
24C2×C4×D4×C11C2218yescomplemented
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66982—28no—
36C2×#66982C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×C4⋊Dic11C2211yescharacteristic
43C2×#66977—28no—
44C2×#66977C2218yescomplemented
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66938—28no—
53C2×#66938C2218yescomplemented
54#10622836C2218yes—
55#10622835C2218yescomplemented
56#10622826C2218yescomplemented
57#10622823C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622607C2218yescomplemented
65#10622592C2218yescomplemented
66#10622570C2218yescomplemented
67#10622564C2218yescomplemented
68#10622557C2218yescomplemented
69#10622553C2218yescomplemented
70C4×Dic11⋊C4C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11C2314yes—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11—42no—
83C23×C4×C11—42no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C23×C4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×Dic22—24no—
107C22×Dic22—24no—
108C22×Dic22—42no—
109C22×Dic22C2314yes—
110C4×D4×C11—232no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4D418yescomplemented
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C42×C11—24no—
118C2×C42×C11C2314yes—
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⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131#66982—232no—
132C2×(C2×D11)⋊C4—24no—
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×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11—24no—
143C2×C4⋊Dic11C2314yes—
144#66977—232no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—42no—
149C2×Dic11⋊C4D418yescomplemented
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11—24no—
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2314yes—
159#66938—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×C11C2×D414yes—
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—22no—
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—28no—
207C22×C4×C11—22no—
208C22×C4×C11—28no—
209C22×C4×C11—28no—
210C22×C4×C11—28no—
211C22×C4×C11—44no—
212C22×C4×C11—44no—
213C22×C4×C11—416no—
214C22×C4×C11—416no—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2×D414yes—
217C22×C4×C11C2×D414yes—
218C22×C4×C11#4114yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—28no—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—416no—
231C2×C22⋊D11—416no—
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—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11C2×D414yes—
251C22×Dic11C2×D414yes—
252C22×Dic11#4114yes—
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×C4⋊C4—28no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4C2×D4116yescomplemented
267C42×C11—28no—
268C22⋊Dic11—28no—
269C22⋊Dic11—28no—
270C22⋊Dic11—28no—
271C22⋊Dic11—28no—
272C22⋊Dic11—28no—
273C22⋊Dic11—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279C4⋊Dic11—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284Dic11⋊C4C2×D4116yescomplemented
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#124—111no—
288C22×#123—111no—
289C22×C22⋊Q8—111no—
290C22×C4×D4D1111yescharacteristic, complemented
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×#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—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11C22×D412yes—
330C23×C11C22×D414yes—
331C23×C11C22×D412yes—
332C23×C11C2×#4114yes—
333C23×C11C2×#4112yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C112−1+412yes—
338C23×C11C2511yescharacteristic
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353D4×C11—232no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
357C2×C4×C11—28no—
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—416no—
371C2×C4×C11—44no—
372C2×C4×C11C22×D414yes—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C22×D414yes—
375C2×C4×C11C2×#4114yes—
376C22⋊D11—416no—
377C22⋊D11—416no—
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—22no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11C22×D414yes—
404C2×Dic11C22×D414yes—
405C2×Dic11C2×#4114yes—
406Dic22—416no—
407C23×Q8—111no—
408C23×D4—111no—
409C23×D4—111no—
410C23×D4C2×D1111yescharacteristic
411C24×C4C2×D1111yescharacteristic
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—28no—
420C2×C4×D4C2×D1118yescomplemented
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⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C42—111no—
442C22×C42—111no—
443C22×C42C2×D1111yescharacteristic
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#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×#95—111no—
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#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—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—88no—
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504Dic11—24no—
505Dic11—24no—
506Dic11—24no—
507Dic11—42no—
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—24no—
521C22×D4—114no—
522C22×D4—114no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—442no—
528C22×D4—442no—
529C22×D4C22×D1114yes—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—42no—
535C23×C4—42no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1114yes—
545C23×C4C22×D1114yes—
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#124—2232no—
551#123—2232no—
552C22⋊Q8—2232no—
553C4×D4—232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—118no—
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—442no—
567C2×C4⋊C4C22×D1114yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
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—224no—
581C2×C22⋊C4—224no—
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⋊D1118yescomplemented
592C2×C22⋊C4C22×D1114yes—
593C2×C22⋊C4C22×D1114yes—
594C2×C42—24no—
595C2×C42—114no—
596C2×C42—114no—
597C2×C42—224no—
598C2×C42—224no—
599C2×C42C22×D1114yes—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606C2×C11—44no—
607C2×C11—44no—
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—82no—
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—112no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24#433914yes—
638C24C2×C22⋊D1114yes—
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—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—444no—
655C2×D4—444no—
656C2×D4—4416no—
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—28no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—416no—
676C22×C4—416no—
677C22×C4—114no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
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—222no—
704C22×C4—222no—
705C22×C4#433914yes—
706C22×C4D4×D1114yes—
707C22×C4C2×C22⋊D1114yes—
708C22×C4C2×C22⋊D1114yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—1116no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—444no—
721C22⋊C4—28no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—228no—
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⋊C4C2×C22⋊D11116yescomplemented
734C42—28no—
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—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
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—
778C23C2×#433914yes—
779C23C2×#433912yes—
780C23C2×#433912yes—
781C23C2×D4×D1112yes—
782C23#6703712yes—
783C23#41×D1112yes—
784C23#6704312yes—
785C23C22×C22⋊D1114yes—
786C23C22×C22⋊D1112yes—
787C23C24×D1111yescharacteristic
788Q8—4416no—
789D4—232no—
790D4—4416no—
791D4—4416no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
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—416no—
809C2×C4—44no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—228no—
814C2×C4—228no—
815C2×C4—228no—
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—222no—
834C2×C4—444no—
835C2×C4—444no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4C2×#433914yes—
839C2×C4C2×D4×D1114yes—
840C2×C4C22×C22⋊D1114yes—
841C2×C4C22×C22⋊D1114yes—
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—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—888no—
866C22#1062307914yes—
867C22#1062308314yes—
868C22#1062308714yes—
869C22#1062309214yes—
870C22#1062332214yes—
871C22D4×C22⋊D1114yes—
872C22#1062335514yes—
873C22C22×#433911yescharacteristic
874C22C22×#433911yescharacteristic
875C22C22×D4×D1111yescharacteristic
876C22C2×#6703711yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#6704311yescharacteristic
879C22C23×C22⋊D1111yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—224no—
886C4—224no—
887C4—224no—
888C4—442no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—44no—
893C2—44no—
894C2—882no—
895C2#1307257718yesdirect product factor
896C2C2×#1062332211yescharacteristic
897C2C2×#1062307911yescharacteristic
898C2C2×#1062309211yescharacteristic
899C2C2×D4×C22⋊D1111yescharacteristic
900C2C2×#1062335511yescharacteristic
901C2C2×#1062308311yescharacteristic
902C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC22×C4×D4D11
hypocenterC11C2×#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66982C2semidirect
3. C22×#66977C2semidirect
4. #13072577C2direct (N × H)
5. C2×#10622607C2semidirect
6. C2×#10622592C2semidirect
7. C2×#10622835C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622823C2semidirect
15. C2×C4×Dic11⋊C4C2semidirect
16. C22×C4×D4×C11C2semidirect
24. C2×C4×D4×C11C22semidirect
36. C2×#66982C22semidirect
44. C2×#66977C22semidirect
53. C2×#66938C22semidirect
55. #10622835C22semidirect
56. #10622826C22semidirect
57. #10622823C22semidirect
64. #10622607C22semidirect
65. #10622592C22semidirect
66. #10622570C22semidirect
67. #10622564C22semidirect
68. #10622557C22semidirect
69. #10622553C22semidirect
70. C4×Dic11⋊C4C22semidirect
114. C2×C11×C22⋊C4D4semidirect
149. C2×Dic11⋊C4D4semidirect
266. C11×C22⋊C4C2×D4semidirect
284. Dic11⋊C4C2×D4semidirect
290. C22×C4×D4D11semidirect
420. C2×C4×D4C2×D11semidirect
591. C2×C22⋊C4C22⋊D11semidirect
608. C2×C11#2461semidirect
733. C22⋊C4C2×C22⋊D11semidirect
737. C11C2×#2461semidirect
895. C2#13072577direct (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×#669822
C22×#669772
#130725772
C2×#106226072
C2×#106225922
C2×#106228352
C2×#106228362
C2×#106225702
C2×#106225642
C2×#106225532
C2×#106225572
C2×#106228262
C2×#106228232
C2×C4×Dic11⋊C42
C22×C4×D4×C112
C2×#246111