Finite Group Databasebeta

← C2×#13072355 #14921225

Subgroups — C2×#13072355 #14921225

Order 2816.

4002 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×#66947C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13072355C2116yesmaximal, direct product factor
6C2×#10622605C211yesmaximal, characteristic, complemented
7C2×#10622597C211yesmaximal, characteristic, complemented
8C2×#10622288C211yesmaximal, characteristic, complemented
9C2×#10622285C211yesmaximal, characteristic, complemented
10C2×#10622282C211yesmaximal, characteristic, complemented
11C2×#10622268C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C2×#10622602C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C2×#66983—28no—
29C2×#66983C2218yes—
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×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4—28no—
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2218yescomplemented
47C22×C4×Dic11C2211yescharacteristic
48C2×#66947—28no—
49C2×#66947C2218yescomplemented
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4C2218yescomplemented
52C11×#385C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622605C2218yescomplemented
62#10622602C2218yescomplemented
63#10622597C2218yescomplemented
64#10622571C2218yescomplemented
65#10622571C2218yescomplemented
66#10622571C2218yescomplemented
67#10622288C2218yescomplemented
68#10622285C2218yescomplemented
69#10622282C2218yescomplemented
70#10622268C2218yescomplemented
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×C11C2311yescharacteristic
82C23×C4×C11C2314yes—
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⋊D11D418yes—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11—24no—
93C23×Dic11—24no—
94C23×Dic11—24no—
95C23×Dic11—24no—
96C23×Dic11—24no—
97C23×Dic11—42no—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2314yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2314yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×D44—24no—
107C22×D44—24no—
108C22×D44—42no—
109C22×D44C2314yes—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—42no—
113C22×C4×D11C2314yes—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4—42no—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122#66983—232no—
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—42no—
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×(C2×D11)⋊C4C2314yes—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—232no—
148C2×Dic11⋊C4D418yescomplemented
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×C4×Dic11—24no—
155C2×C4×Dic11C2314yes—
156#66947—232no—
157(C22⋊D11)⋊C4—232no—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2443—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11C2×D414yes—
172C24×C11#4114yes—
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—
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—28no—
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—44no—
212C22×C4×C11—416no—
213C22×C4×C11C2×D414yes—
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—416no—
227C2×C22⋊D11C2×D4116yes—
228C22×Dic11—232no—
229C22×Dic11—28no—
230C22×Dic11—28no—
231C22×Dic11—28no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—28no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—28no—
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—44no—
249C22×Dic11—416no—
250C22×Dic11C2×D414yes—
251C22×Dic11C2×D414yes—
252C22×Dic11C2×D414yes—
253C22×Dic11#4114yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×D44—28no—
261C2×D44—28no—
262C2×D44—44no—
263C2×D44—416no—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—44no—
267C2×C4×D11—416no—
268C11×C4⋊C4—28no—
269C11×C4⋊C4—44no—
270C11×C22⋊C4—28no—
271C11×C22⋊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—44no—
281C4⋊Dic11—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—28no—
286Dic11⋊C4C2×D4116yescomplemented
287C4×Dic11—28no—
288C22×#123—111no—
289C22×#121—111no—
290C22×C4×D4—111no—
291C23×C4⋊C4—111no—
292#2443—1116no—
293C2×#399—111no—
294C2×#398—111no—
295C2×#397—111no—
296C2×#394—111no—
297C2×#388—111no—
298C2×#387—111no—
299C2×#386—111no—
300C2×#386—111no—
301C2×#386—111no—
302C2×#385—111no—
303C2×#385D1111yescharacteristic, complemented
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#123116yescomplemented
315C23×C11C22×D414yes—
316C23×C11C22×D412yes—
317C23×C11C22×D412yes—
318C23×C11C2×#4114yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4114yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C112−1+412yes—
325C23×C11C2511yescharacteristic
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
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—22no—
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×D11—44no—
353C22×D11C22×D414yes—
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—22no—
372C2×C4×C11—416no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11C22×D414yes—
379C22⋊D11—232no—
380C22⋊D11—416no—
381C2×Dic11—232no—
382C2×Dic11—28no—
383C2×Dic11—28no—
384C2×Dic11—28no—
385C2×Dic11—28no—
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—22no—
400C2×Dic11—416no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11C22×D414yes—
404C2×Dic11C22×D414yes—
405C2×Dic11C22×D414yes—
406C2×Dic11C2×#4114yes—
407D44—416no—
408C4×D11—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C24×C4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4C2×D1111yescharacteristic
416C2×#123—118no—
417C2×#123—228no—
418C2×#121—118no—
419C2×#121—228no—
420C2×C4×D4—118no—
421C2×C4×D4—228no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—118no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—228no—
430C22×C4⋊C4C2×D1111yescharacteristic
431C22×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C42—111no—
444#399—118no—
445#398—118no—
446#397—118no—
447#394—118no—
448#388—118no—
449#387—118no—
450#386—118no—
451#386—118no—
452#386—118no—
453#385—118no—
454#385C2×D1118yescomplemented
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1111yescharacteristic
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—232no—
469C22×C11—24no—
470C22×C11C2×#12314yes—
471C22×C11C2×#12318yescomplemented
472C22×C11#52514yes—
473C22×C11#53914yes—
474C22×C11D4214yes—
475C22×C11#54714yes—
476C22×C11#54814yes—
477C22×C11#55314yes—
478C22×C11C23×D411yescharacteristic
479C22×C11C23×D411yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×2−1+411yescharacteristic
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—416no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—88no—
501C4×C11—24no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507Dic11—24no—
508Dic11—24no—
509Dic11—24no—
510Dic11—24no—
511Dic11—42no—
512Dic11—42no—
513C25—111no—
514C25—111no—
515C25C22×D1111yescharacteristic
516C22×D4—118no—
517C22×D4—114no—
518C22×D4—114no—
519C22×D4—114no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—442no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—42no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—114no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—114no—
539C23×C4—114no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—442no—
548C23×C4—442no—
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1114yes—
555C23×C4C22×D1111yescharacteristic
556#123—2232no—
557#121—2232no—
558C4×D4—2232no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—42no—
561C2×C4⋊C4—118no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—2232no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—224no—
571C2×C4⋊C4—224no—
572C2×C4⋊C4—224no—
573C2×C4⋊C4—224no—
574C2×C4⋊C4C22×D1114yes—
575C2×C4⋊C4C22×D1114yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
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—114no—
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×C22⋊C4—224no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4C22×D1114yes—
597C2×C22⋊C4C22×D1114yes—
598C2×C42—114no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95C22×D1114yes—
607#95C22×D1114yes—
608C2×C11—28no—
609C2×C11#244318yescomplemented
610C2×C11C22×#12311yescharacteristic
611C2×C11C2×#52511yescharacteristic
612C2×C11C2×#53911yescharacteristic
613C2×C11C2×D4211yescharacteristic
614C2×C11C2×#54711yescharacteristic
615C2×C11C2×#54811yescharacteristic
616C2×C11C2×#55311yescharacteristic
617D11—44no—
618D11—82no—
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#433914yes—
640C24D4×D1114yes—
641C24#434314yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×D4—1116no—
645C2×D4—228no—
646C2×D4—2232no—
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—444no—
654C2×D4—4416no—
655C2×D4—4416no—
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—22no—
665C22×C4—22no—
666C22×C4—28no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—44no—
676C22×C4—416no—
677C22×C4—114no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—114no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—228no—
688C22×C4—228no—
689C22×C4—228no—
690C22×C4—228no—
691C22×C4—228no—
692C22×C4—2232no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—228no—
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—222no—
708C22×C4—222no—
709C22×C4—444no—
710C22×C4—4416no—
711C22×C4—444no—
712C22×C4—4416no—
713C22×C4D4×D1114yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C4⋊C4—28no—
721C4⋊C4—44no—
722C4⋊C4—1116no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—228no—
726C4⋊C4—228no—
727C4⋊C4—228no—
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—228no—
738C22⋊C4—444no—
739C42—228no—
740C11C2×#244311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
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—
779C23#66947116yescomplemented
780C23C2×#433914yes—
781C23C2×#433912yes—
782C23C2×D4×D1114yes—
783C23C2×D4×D1112yes—
784C23C2×D4×D1112yes—
785C23#6703712yes—
786C23C2×#434314yes—
787C23C2×#434312yes—
788C23#41×D1112yes—
789C23#6704312yes—
790C23C24×D1111yescharacteristic
791D4—2232no—
792D4—4416no—
793D4—4416no—
794C2×C4—28no—
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—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—416no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—114no—
819C2×C4—114no—
820C2×C4—114no—
821C2×C4—114no—
822C2×C4—2232no—
823C2×C4—228no—
824C2×C4—228no—
825C2×C4—228no—
826C2×C4—228no—
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—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—4416no—
842C2×C4—4416no—
843C2×C4—444no—
844C2×C4—444no—
845C2×C4C2×D4×D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—232no—
853C22—224no—
854C22—224no—
855C22—224no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—4416no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—888no—
869C22C2×#6694714yes—
870C22C2×#6694718yescomplemented
871C22#1062307114yes—
872C22#1062308314yes—
873C22#1062312114yes—
874C22#1062315814yes—
875C22#1062317614yes—
876C22#1062318614yes—
877C22C22×#433911yescharacteristic
878C22C22×D4×D1111yescharacteristic
879C22C22×D4×D1111yescharacteristic
880C22C2×#6703711yescharacteristic
881C22C22×#434311yescharacteristic
882C22C2×#41×D1111yescharacteristic
883C22C2×#6704311yescharacteristic
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—224no—
891C4—224no—
892C4—224no—
893C4—224no—
894C4—442no—
895C4—442no—
896C2—28no—
897C2—444no—
898C2—882no—
899C2#1307235518yesdirect product factor
900C2C22×#6694711yescharacteristic
901C2C2×#1062315811yescharacteristic
902C2C2×#1062317611yescharacteristic
903C2C2×#1062312111yescharacteristic
904C2C2×#1062318611yescharacteristic
905C2C2×#1062308311yescharacteristic
906C2C2×#1062307111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC22×#66983C2
hypercenterC2×#385D11
hypocenterC11C2×#2443
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. C23×Dic11⋊C4C2semidirect
5. #13072355C2direct (N × H)
6. C2×#10622605C2semidirect
7. C2×#10622597C2semidirect
8. C2×#10622288C2semidirect
9. C2×#10622285C2semidirect
10. C2×#10622282C2semidirect
11. C2×#10622268C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622571C2semidirect
15. C2×#10622602C2semidirect
16. C2×C11×#385C2semidirect
46. C22×Dic11⋊C4C22semidirect
49. C2×#66947C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
52. C11×#385C22semidirect
61. #10622605C22semidirect
62. #10622602C22semidirect
63. #10622597C22semidirect
64. #10622571C22semidirect
65. #10622571C22semidirect
66. #10622571C22semidirect
67. #10622288C22semidirect
68. #10622285C22semidirect
69. #10622282C22semidirect
70. #10622268C22semidirect
148. C2×Dic11⋊C4D4semidirect
286. Dic11⋊C4C2×D4semidirect
303. C2×#385D11semidirect
314. C23×C11#123semidirect
454. #385C2×D11semidirect
471. C22×C11C2×#123semidirect
609. C2×C11#2443semidirect
740. C11C2×#2443semidirect
779. C23#66947semidirect
870. C22C2×#66947semidirect
899. C2#13072355direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669832
C22×(C22⋊D11)⋊C42
C23×Dic11⋊C42
#130723552
C2×#106226052
C2×#106225972
C2×#106222882
C2×#106222852
C2×#106222822
C2×#106222682
C2×#106225712
C2×#106226022
C2×C11×#3852
C2×#244311