Finite Group Databasebeta

← C2×#13072590 #14921634

Subgroups — C2×#13072590 #14921634

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×#67000C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13072590C2116yesmaximal, direct product factor
5C2×#10622607C211yesmaximal, characteristic, complemented
6C2×#10622842C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622603C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C2×C11×C22⋊Q8—28no—
24C2×C11×C22⋊Q8C2218yescomplemented
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#67000—28no—
33C2×#67000C2218yescomplemented
34C2×C4×C22⋊D11—28no—
35C2×C4×C22⋊D11C2218yescomplemented
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×C4⋊Dic11C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66947—28no—
53C2×#66947C2218yescomplemented
54#10622842C2218yescomplemented
55#10622826C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622607C2218yescomplemented
63#10622603C2218yescomplemented
64#10622603C2218yescomplemented
65#10622602C2218yescomplemented
66C4⋊C4×Dic11C2218yescomplemented
67#10622574C2218yescomplemented
68#10622573C2218yes—
69#10622570C2218yescomplemented
70#10622558C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×Q8×C11—24no—
75C22×Q8×C11—24no—
76C22×Q8×C11—42no—
77C22×Q8×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
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×D44—24no—
103C22×D44—24no—
104C22×D44—42no—
105C22×D44C2314yes—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—42no—
109C22×C4×D11C2314yes—
110C11×C22⋊Q8—232no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4D418yescomplemented
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125#67000—232no—
126C4×C22⋊D11—232no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4D418yescomplemented
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×C4⋊Dic11—24no—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—42no—
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#66947—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#4114yes—
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×D11—22no—
189C23×D11C2×D414yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
192C2×Q8×C11—28no—
193C2×Q8×C11—28no—
194C2×Q8×C11—44no—
195C2×Q8×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—22no—
209C22×C4×C11—22no—
210C22×C4×C11—28no—
211C22×C4×C11—28no—
212C22×C4×C11—44no—
213C22×C4×C11—416no—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2×D414yes—
217C22×C4×C11C2×D414yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C2×C22⋊D11—232no—
225C2×C22⋊D11—28no—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—44no—
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×Dic11C2×D414yes—
248C22×Dic11#4114yes—
249C22×Dic11#4114yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C2×D44—28no—
257C2×D44—28no—
258C2×D44—44no—
259C2×D44—416no—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—44no—
263C2×C4×D11—416no—
264C11×C4⋊C4—28no—
265C11×C4⋊C4—28no—
266C11×C4⋊C4C2×D4116yescomplemented
267C11×C22⋊C4—28no—
268C11×C22⋊C4—28no—
269C22⋊Dic11—28no—
270C22⋊Dic11—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—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4C2×D4116yescomplemented
280C4⋊Dic11—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284C4×Dic11—28no—
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#124—111no—
288C22×#123—111no—
289C22×C22⋊Q8D1111yescharacteristic, complemented
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×#386—111no—
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—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11C22×D412yes—
317C23×C11C22×D412yes—
318C23×C11C2×#4114yes—
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—22no—
329C22×D11—22no—
330C22×D11—22no—
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—44no—
342C22×D11—44no—
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×D11—44no—
352C22×D11C22×D414yes—
353Q8×C11—416no—
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—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—416no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11C22×D414yes—
376C2×C4×C11C22×D414yes—
377C2×C4×C11C22×D414yes—
378C2×C4×C11C22×D414yes—
379C22⋊D11—232no—
380C22⋊D11—416no—
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—22no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11C22×D414yes—
403C2×Dic11C2×#4114yes—
404C2×Dic11C2×#4114yes—
405D44—416no—
406C4×D11—416no—
407C23×Q8C2×D1111yescharacteristic
408C23×D4—111no—
409C23×D4—111no—
410C23×D4—111no—
411C24×C4—111no—
412C24×C4C2×D1111yescharacteristic
413C2×#124—118no—
414C2×#124—228no—
415C2×#123—118no—
416C2×#123—228no—
417C2×C22⋊Q8—28no—
418C2×C22⋊Q8C2×D1118yescomplemented
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⋊C4C2×D1111yescharacteristic
426C22×C4⋊C4C2×D1111yescharacteristic
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×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#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—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—416no—
469C22×C11#52514yes—
470C22×C11#53214yes—
471C22×C11#54214yes—
472C22×C11D4214yes—
473C22×C11#54714yes—
474C22×C11#54814yes—
475C22×C11#55114yes—
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—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—416no—
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—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511C25—111no—
512C25—111no—
513C25C22×D1111yescharacteristic
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8—42no—
517C22×Q8C22×D1114yes—
518C22×D4—114no—
519C22×D4—114no—
520C22×D4—114no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—442no—
529C22×D4—442no—
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—114no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—442no—
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1114yes—
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#124—2232no—
551#123—2232no—
552C22⋊Q8—232no—
553C4×D4—2232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—224no—
561C2×C4⋊C4—224no—
562C2×C4⋊C4—224no—
563C2×C4⋊C4—442no—
564C2×C4⋊C4C22⋊D1118yescomplemented
565C2×C4⋊C4C22×D1114yes—
566C2×C4⋊C4C22×D1114yes—
567C2×C4⋊C4C22×D1114yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—118no—
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—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⋊C4—224no—
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#95—114no—
606C2×C11—44no—
607C2×C11#246118yescomplemented
608C2×C11C2×#52511yescharacteristic
609C2×C11C2×#53211yescharacteristic
610C2×C11C2×#54211yescharacteristic
611C2×C11C2×D4211yescharacteristic
612C2×C11C2×#54711yescharacteristic
613C2×C11C2×#54811yescharacteristic
614C2×C11C2×#55111yescharacteristic
615D11—44no—
616D11—82no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—114no—
624C24—112no—
625C24—112no—
626C24—222no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24#434314yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×Q8—28no—
643C2×Q8—28no—
644C2×Q8—44no—
645C2×Q8—416no—
646C2×D4—228no—
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—2232no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—444no—
655C2×D4—4416no—
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—22no—
671C22×C4—22no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—44no—
675C22×C4—416no—
676C22×C4—114no—
677C22×C4—114no—
678C22×C4—114no—
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—228no—
702C22×C4—444no—
703C22×C4—4416no—
704C22×C4D4×D1114yes—
705C22×C4C2×C22⋊D1114yes—
706C22×C4C2×C22⋊D1114yes—
707C22×C4C2×C22⋊D1114yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—444no—
720C4⋊C4C2×C22⋊D11116yescomplemented
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—1116no—
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⋊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—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—114no—
752C23—228no—
753C23—228no—
754C23—228no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—444no—
769C23—444no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23C2×D4×D1112yes—
780C23#6703712yes—
781C23C2×#434314yes—
782C23C2×#434312yes—
783C23#6704012yes—
784C23#41×D1112yes—
785C23#41×D1112yes—
786C23C22×C22⋊D1112yes—
787C23C24×D1111yescharacteristic
788Q8—416no—
789D4—2232no—
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—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—416no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—228no—
817C2×C4—228no—
818C2×C4—228no—
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—4416no—
835C2×C4—444no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4C2×D4×D1114yes—
839C2×C4C22×C22⋊D1114yes—
840C2×C4C22×C22⋊D1114yes—
841C2×C4C22×C22⋊D1114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—42no—
850C22—224no—
851C22—224no—
852C22—224no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—4416no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—888no—
866C22#1062315814yes—
867C22#1062316214yes—
868C22#1062316814yes—
869C22#1062317114yes—
870C22D4×C22⋊D1114yes—
871C22#1062334814yes—
872C22#1062336314yes—
873C22C22×D4×D1111yescharacteristic
874C22C2×#6703711yescharacteristic
875C22C22×#434311yescharacteristic
876C22C2×#6704011yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#41×D1111yescharacteristic
879C22C23×C22⋊D1111yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—224no—
887C4—224no—
888C4—224no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—44no—
893C2—444no—
894C2—882no—
895C2#1307259018yesdirect product factor
896C2C2×#1062315811yescharacteristic
897C2C2×#1062336311yescharacteristic
898C2C2×#1062317111yescharacteristic
899C2C2×D4×C22⋊D1111yescharacteristic
900C2C2×#1062316211yescharacteristic
901C2C2×#1062334811yescharacteristic
902C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66947C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13072590C2direct (N × H)
5. C2×#10622607C2semidirect
6. C2×#10622842C2semidirect
7. C2×#10622574C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622603C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622602C2semidirect
15. C2×C4⋊C4×Dic11C2semidirect
16. C22×C11×C22⋊Q8C2semidirect
24. C2×C11×C22⋊Q8C22semidirect
33. C2×#67000C22semidirect
35. C2×C4×C22⋊D11C22semidirect
53. C2×#66947C22semidirect
54. #10622842C22semidirect
55. #10622826C22semidirect
62. #10622607C22semidirect
63. #10622603C22semidirect
64. #10622603C22semidirect
65. #10622602C22semidirect
66. C4⋊C4×Dic11C22semidirect
67. #10622574C22semidirect
69. #10622570C22semidirect
70. #10622558C22semidirect
113. C2×C11×C4⋊C4D4semidirect
135. C2×(C2×D11)⋊C4D4semidirect
266. C11×C4⋊C4C2×D4semidirect
279. (C2×D11)⋊C4C2×D4semidirect
289. C22×C22⋊Q8D11semidirect
418. C2×C22⋊Q8C2×D11semidirect
564. C2×C4⋊C4C22⋊D11semidirect
607. C2×C11#2461semidirect
720. C4⋊C4C2×C22⋊D11semidirect
737. C11C2×#2461semidirect
895. C2#13072590direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#669472
C22×C4×C22⋊D112
#130725902
C2×#106226072
C2×#106228422
C2×#106225742
C2×#106225732
C2×#106225702
C2×#106225582
C2×#106226032
C2×#106228262
C2×#106226022
C2×C4⋊C4×Dic112
C22×C11×C22⋊Q82
C2×#246111