Finite Group Databasebeta

← C2×#13072583 #14921632

Subgroups — C2×#13072583 #14921632

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×#66928C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3C22×#66949C211yesmaximal, characteristic, complemented
4C22×C4×D44C211yesmaximal, characteristic, complemented
5#13072583C2116yesmaximal, direct product factor
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622269C211yesmaximal, characteristic, complemented
8C2×#10622604C211yesmaximal, characteristic, complemented
9C2×#10622284C211yesmaximal, characteristic
10C2×#10622552C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622553C211yesmaximal, characteristic, complemented
13C2×#10622553C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×#10622281C211yesmaximal, characteristic, complemented
16C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C2×#66949—28no—
47C2×#66949C2218yescomplemented
48C2×#66947—28no—
49C2×#66947C2218yescomplemented
50C2×#66928—28no—
51C2×#66928C2218yescomplemented
52C2×C4×D44—28no—
53C2×C4×D44C2218yescomplemented
54C4×C11×C4⋊C4C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622607C2218yescomplemented
62#10622604C2218yescomplemented
63#10622553C2218yescomplemented
64#10622553C2218yescomplemented
65#10622553C2218yescomplemented
66#10622552C2218yescomplemented
67#10622284C2218yes—
68#10622281C2218yescomplemented
69#10622278C2218yescomplemented
70#10622269C2218yescomplemented
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44—24no—
90C22×D44—24no—
91C22×D44—24no—
92C22×D44—24no—
93C22×D44—42no—
94C22×D44—42no—
95C22×D44C2314yes—
96C22×D44C2314yes—
97C22×D44C2314yes—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11—42no—
104C22×C4×D11C2314yes—
105C22×C4×D11C2314yes—
106C22×Dic22—24no—
107C22×Dic22—24no—
108C22×Dic22—42no—
109C22×Dic22C2314yes—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4D418yescomplemented
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C42×C11—24no—
115C2×C42×C11—24no—
116C2×C42×C11—24no—
117C2×C42×C11C2314yes—
118C2×C42×C11C2314yes—
119C2×C42×C11C2314yes—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
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—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×(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×(C2×D11)⋊C4C2314yes—
146C2×C4⋊Dic11—24no—
147C2×C4⋊Dic11—42no—
148C2×C4⋊Dic11C2314yes—
149C2×C4⋊Dic11C2314yes—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4—24no—
152C2×Dic11⋊C4—24no—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156#66949—232no—
157#66947—232no—
158#66928—232no—
159C4×D44—232no—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2461—111nomaximal, Sylow
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
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×D11C2×D414yes—
188C23×D11#4114yes—
189C23×D11C2412yes—
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—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11C2×D414yes—
208C22×C4×C11C2×D414yes—
209C22×C4×C11C2×D414yes—
210C22×C4×C11C2×D414yes—
211C22×C4×C11#4114yes—
212C22×C4×C11#4114yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11C2×D414yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C2×D44—232no—
241C2×D44—28no—
242C2×D44—28no—
243C2×D44—28no—
244C2×D44—28no—
245C2×D44—28no—
246C2×D44—28no—
247C2×D44—28no—
248C2×D44—44no—
249C2×D44—44no—
250C2×D44—416no—
251C2×D44—416no—
252C2×C4×D11—28no—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—28no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—416no—
259C2×C4×D11—416no—
260C2×Dic22—28no—
261C2×Dic22—28no—
262C2×Dic22—44no—
263C2×Dic22—416no—
264C11×C4⋊C4—28no—
265C11×C4⋊C4C2×D4116yescomplemented
266C42×C11—28no—
267C42×C11—28no—
268C42×C11—28no—
269(C2×D11)⋊C4—28no—
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—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281(C2×D11)⋊C4C2×D4116yescomplemented
282C4⋊Dic11—28no—
283C4⋊Dic11—44no—
284Dic11⋊C4—28no—
285Dic11⋊C4—28no—
286Dic11⋊C4—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×#386—111no—
301C2×#385—111no—
302C2×C4×C4⋊C4D1111yescharacteristic, complemented
303C23×C11C22×D412yes—
304C23×C11C22×D412yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C112−1+412yes—
310C23×C11C2511yescharacteristic
311C22×D11—28no—
312C22×D11—28no—
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
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—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11—44no—
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×D11C22×D414yes—
352C22×D11C2×#4114yes—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
357C2×C4×C11—28no—
358C2×C4×C11—28no—
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—22no—
373C2×C4×C11—22no—
374C2×C4×C11—44no—
375C2×C4×C11C22×D414yes—
376C2×C4×C11C22×D414yes—
377C2×C4×C11C22×D414yes—
378C2×C4×C11C22×D414yes—
379C2×C4×C11C2×#4114yes—
380C2×C4×C11C2×#4114yes—
381C2×Dic11—28no—
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—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11C22×D414yes—
401D44—232no—
402D44—416no—
403D44—416no—
404C4×D11—416no—
405C4×D11—416no—
406Dic22—416no—
407C23×Q8—111no—
408C23×D4—111no—
409C23×D4—111no—
410C23×D4—111no—
411C24×C4—111no—
412C24×C4—111no—
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⋊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⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C42C2×D1111yescharacteristic
442C22×C42C2×D1111yescharacteristic
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⋊C4C2×D1118yescomplemented
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95C2×D1111yescharacteristic
460C2×#95C2×D1111yescharacteristic
461C22×C11#52514yes—
462C22×C11#53214yes—
463C22×C11#54214yes—
464C22×C11D4214yes—
465C22×C11#54714yes—
466C22×C11#54814yes—
467C22×C11#55114yes—
468C22×C11C23×D411yescharacteristic
469C22×C11C23×D411yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C22×C11C2×2−1+411yescharacteristic
475C2×D11—24no—
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—416no—
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—24no—
504C4×C11—24no—
505C4×C11—42no—
506Dic11—24no—
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511C25—111no—
512C25—111no—
513C25—111no—
514C22×Q8—114no—
515C22×Q8—224no—
516C22×Q8—224no—
517C22×Q8—442no—
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—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×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#124—2232no—
551#123—2232no—
552C22⋊Q8—2232no—
553C4×D4—2232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—114no—
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—224no—
564C2×C4⋊C4—442no—
565C2×C4⋊C4D4418yescomplemented
566C2×C4⋊C4C22×D1114yes—
567C2×C4⋊C4C22×D1114yes—
568C2×C22⋊C4—118no—
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—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⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C42—24no—
595C2×C42—24no—
596C2×C42—24no—
597C2×C42C22×D1114yes—
598C2×C42C22×D1114yes—
599C2×C42C22×D1114yes—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95C22×D1114yes—
605#95C22×D1114yes—
606C2×C11#246118yescomplemented
607C2×C11C2×#52511yescharacteristic
608C2×C11C2×#53211yescharacteristic
609C2×C11C2×#54211yescharacteristic
610C2×C11C2×D4211yescharacteristic
611C2×C11C2×#54711yescharacteristic
612C2×C11C2×#54811yescharacteristic
613C2×C11C2×#55111yescharacteristic
614D11—44no—
615D11—44no—
616D11—82no—
617C24—114no—
618C24—114no—
619C24—112no—
620C24—112no—
621C24—112no—
622C24—222no—
623C24—222no—
624C24—222no—
625C24—222no—
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—222no—
640C24—222no—
641C24C23×D1111yescharacteristic
642C2×Q8—228no—
643C2×Q8—228no—
644C2×Q8—444no—
645C2×Q8—4416no—
646C2×D4—228no—
647C2×D4—228no—
648C2×D4—2232no—
649C2×D4—228no—
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—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—114no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—228no—
680C22×C4—228no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
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—228no—
696C22×C4—228no—
697C22×C4—444no—
698C22×C4—444no—
699C22×C4—4416no—
700C22×C4—4416no—
701C22×C4C2×D4414yes—
702C22×C4C2×D4414yes—
703C22×C4C2×D4414yes—
704C22×C4#433914yes—
705C22×C4#433914yes—
706C22×C4D4×D1114yes—
707C22×C4C23×D1112yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—228no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—444no—
720C4⋊C4C2×D44116yescomplemented
721C22⋊C4—1116no—
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⋊C4—228no—
734C42—28no—
735C42—28no—
736C42—28no—
737C11C2×#246111yescharacteristic, complemented, Sylow
738C23—114no—
739C23—114no—
740C23—228no—
741C23—228no—
742C23—228no—
743C23—228no—
744C23—228no—
745C23—228no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—444no—
766C23—444no—
767C23—444no—
768C23—444no—
769C23—444no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23C22×D4412yes—
781C23C2×#433912yes—
782C23C2×#433912yes—
783C23C2×D4×D1112yes—
784C23#6704012yes—
785C23#41×D1112yes—
786C23#6704212yes—
787C23C24×D1111yescharacteristic
788Q8—4416no—
789D4—2232no—
790D4—4416no—
791D4—4416no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
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—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—44no—
814C2×C4—114no—
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—4416no—
831C2×C4—4416no—
832C2×C4—444no—
833C2×C4—444no—
834C2×C4—444no—
835C2×C4—444no—
836C2×C4C22×D4414yes—
837C2×C4C22×D4414yes—
838C2×C4C22×D4414yes—
839C2×C4C2×#433914yes—
840C2×C4C2×#433914yes—
841C2×C4C2×D4×D1114yes—
842C22—224no—
843C22—224no—
844C22—224no—
845C22—224no—
846C22—224no—
847C22—224no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—4416no—
853C22—4416no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—888no—
866C22#1062300814yes—
867C22#1062303814yes—
868C22#1062305814yes—
869C22#1062307814yes—
870C22D4×D4414yes—
871C22#1062310714yes—
872C22#1062311314yes—
873C22C23×D4411yescharacteristic
874C22C22×#433911yescharacteristic
875C22C22×#433911yescharacteristic
876C22C22×D4×D1111yescharacteristic
877C22C2×#6704011yescharacteristic
878C22C2×#41×D1111yescharacteristic
879C22C2×#6704211yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—42no—
887C4—224no—
888C4—442no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—444no—
893C2—444no—
894C2—882no—
895C2#1307258318yesdirect product factor
896C2C2×#1062307811yescharacteristic
897C2C2×#1062300811yescharacteristic
898C2C2×#1062311311yescharacteristic
899C2C2×D4×D4411yescharacteristic
900C2C2×#1062303811yescharacteristic
901C2C2×#1062310711yescharacteristic
902C2C2×#1062305811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66928C2semidirect
2. C22×#66947C2semidirect
3. C22×#66949C2semidirect
4. C22×C4×D44C2semidirect
5. #13072583C2direct (N × H)
6. C2×#10622607C2semidirect
7. C2×#10622269C2semidirect
8. C2×#10622604C2semidirect
10. C2×#10622552C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622553C2semidirect
13. C2×#10622553C2semidirect
14. C2×#10622278C2semidirect
15. C2×#10622281C2semidirect
16. C2×C4×C11×C4⋊C4C2semidirect
47. C2×#66949C22semidirect
49. C2×#66947C22semidirect
51. C2×#66928C22semidirect
53. C2×C4×D44C22semidirect
54. C4×C11×C4⋊C4C22semidirect
61. #10622607C22semidirect
62. #10622604C22semidirect
63. #10622553C22semidirect
64. #10622553C22semidirect
65. #10622553C22semidirect
66. #10622552C22semidirect
68. #10622281C22semidirect
69. #10622278C22semidirect
70. #10622269C22semidirect
111. C2×C11×C4⋊C4D4semidirect
132. C2×(C2×D11)⋊C4D4semidirect
265. C11×C4⋊C4C2×D4semidirect
281. (C2×D11)⋊C4C2×D4semidirect
302. C2×C4×C4⋊C4D11semidirect
454. C4×C4⋊C4C2×D11semidirect
565. C2×C4⋊C4D44semidirect
606. C2×C11#2461semidirect
720. C4⋊C4C2×D44semidirect
737. C11C2×#2461semidirect
895. C2#13072583direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
C22×#669472
C22×#669492
C22×C4×D442
#130725832
C2×#106226072
C2×#106222692
C2×#106226042
C2×#106222842
C2×#106225522
C2×#106225532
C2×#106222782
C2×#106222812
C2×C4×C11×C4⋊C42
C2×#246111