Finite Group Databasebeta

← C2×#13074458 #14920159

Subgroups — C2×#13074458 #14920159

Order 2816.

3218 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66939C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074458C2116yesmaximal, direct product factor
4C2×#10622270C211yesmaximal, characteristic, complemented
5C2×#10622289C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622268C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#397C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66939—28no—
45C2×#66939C2218yescomplemented
46C2×(C22⋊D11)⋊C4—28no—
47C2×(C22⋊D11)⋊C4C2218yescomplemented
48C11×#397C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622607C2218yescomplemented
58#10622603C2218yescomplemented
59#10622573C2218yes—
60#10622572C2218yescomplemented
61#10622572C2218yescomplemented
62#10622555C2218yescomplemented
63#10622289C2218yescomplemented
64#10622285C2218yescomplemented
65#10622281C2218yescomplemented
66#10622278C2218yescomplemented
67#10622270C2218yescomplemented
68#10622268C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—24no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11C2314yes—
85C22×C22⋊D11C2314yes—
86C23×Dic11—42no—
87C23×Dic11—42no—
88C23×Dic11D418yescomplemented
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2314yes—
96C22×D44—24no—
97C22×D44—42no—
98C22×D44—42no—
99C22×D44C2314yes—
100C22×C4×D11—24no—
101C22×C4×D11—42no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C2×C11×C4⋊C4—42no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C22⋊Dic11—42no—
113C2×C22⋊Dic11C2314yes—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×C4⋊Dic11—24no—
133C2×C4⋊Dic11—24no—
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2314yes—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—42no—
139C2×Dic11⋊C4—42no—
140C2×Dic11⋊C4—42no—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—24no—
147C2×C4×Dic11C2314yes—
148#66939—232no—
149(C22⋊D11)⋊C4—232no—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11×#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2630—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11C2×D414yes—
166C24×C11C2412yes—
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#4114yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
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×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—232no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—416no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
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—416no—
232C22×Dic11—44no—
233C22×Dic11—44no—
234C22×Dic11C2×D414yes—
235C22×Dic11C2×D414yes—
236C22×Dic11C2×D4116yescomplemented
237C22×Dic11#4114yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×D44—28no—
245C2×D44—44no—
246C2×D44—44no—
247C2×D44—416no—
248C2×C4×D11—28no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C11×C4⋊C4—44no—
253C11×C22⋊C4—28no—
254C11×C22⋊C4—28no—
255C11×C22⋊C4—44no—
256C22⋊Dic11—44no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266C4⋊Dic11—28no—
267C4⋊Dic11—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—28no—
270Dic11⋊C4—44no—
271Dic11⋊C4—44no—
272Dic11⋊C4—44no—
273C4×Dic11—28no—
274C22×#123—111no—
275C22×C4×D4—111no—
276#2630—1116no—
277C2×#398—111no—
278C2×#397D1111yescharacteristic, complemented
279C2×#396—111no—
280C2×#396—111no—
281C2×#394—111no—
282C2×#394—111no—
283C2×#394—111no—
284C2×#392—111no—
285C2×#388—111no—
286C2×#387—111no—
287C2×#386—111no—
288C2×#385—111no—
289C2×#380—111no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11C22×D414yes—
304C23×C11C22×D412yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C11H(5,𝔽2)12yes—
310C23×C112−1+412yes—
311C23×C11C2511yescharacteristic
312C22×D11—28no—
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—22no—
316C22×D11—22no—
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—44no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11C2×#4114yes—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C22⋊D11—232no—
365C22⋊D11—416no—
366C2×Dic11—28no—
367C2×Dic11—28no—
368C2×Dic11—28no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—416no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11C22×D414yes—
389C2×Dic11C22×D414yes—
390C2×Dic11C2×#4114yes—
391D44—416no—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4—111no—
396C24×C4—111no—
397C24×C4—111no—
398C2×#123—118no—
399C2×#123—228no—
400C2×C4×D4—118no—
401C2×C4×D4—228no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4C2×D1111yescharacteristic
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4C2×D1111yescharacteristic
423C22×C42—111no—
424#398—118no—
425#397C2×D1118yescomplemented
426#396—118no—
427#396—118no—
428#394—118no—
429#394—118no—
430#394—118no—
431#392—118no—
432#388—118no—
433#387—118no—
434#386—118no—
435#385—118no—
436#380—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95C2×D1111yescharacteristic
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—416no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11#52514yes—
454C22×C11#53414yes—
455C22×C11#53714yes—
456C22×C11#53814yes—
457C22×C11#53914yes—
458C22×C11#54014yes—
459C22×C11#54214yes—
460C22×C11C23×D411yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C22×#4111yescharacteristic
463C22×C11C2×H(5,𝔽2)11yescharacteristic
464C22×C11C2×H(5,𝔽2)11yescharacteristic
465C22×C11C2×H(5,𝔽2)11yescharacteristic
466C22×C11C2×2−1+411yescharacteristic
467C2×D11—24no—
468C2×D11—24no—
469C2×D11—24no—
470C2×D11—416no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—88no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—42no—
489Dic11—24no—
490Dic11—24no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25—111no—
497C25C22×D1111yescharacteristic
498C22×D4—114no—
499C22×D4—114no—
500C22×D4—114no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—442no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4—442no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—118no—
514C23×C4—114no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—114no—
519C23×C4—224no—
520C23×C4—442no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4—442no—
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530#123—2232no—
531C4×D4—2232no—
532C2×C4⋊C4—42no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—442no—
545C2×C4⋊C4—442no—
546C2×C4⋊C4—442no—
547C2×C4⋊C4C22×D1114yes—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4—442no—
571C2×C22⋊C4C22×D1114yes—
572C2×C22⋊C4C22×D1114yes—
573C2×C22⋊C4C22×D1114yes—
574C2×C42—114no—
575C2×C42—224no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95C22×D1114yes—
582#95C22×D1114yes—
583#95C22×D1114yes—
584C2×C11—44no—
585C2×C11#263018yescomplemented
586C2×C11C2×#52511yescharacteristic
587C2×C11C2×#53411yescharacteristic
588C2×C11C2×#53711yescharacteristic
589C2×C11C2×#53811yescharacteristic
590C2×C11C2×#53911yescharacteristic
591C2×C11C2×#54011yescharacteristic
592C2×C11C2×#54211yescharacteristic
593D11—44no—
594D11—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—114no—
602C24—112no—
603C24—112no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24D4×D1114yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×D4—228no—
621C2×D4—228no—
622C2×D4—228no—
623C2×D4—2232no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—4416no—
629C2×D4—444no—
630C2×D4—444no—
631C2×D4—4416no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—114no—
651C22×C4—114no—
652C22×C4—114no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—1116no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—228no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—444no—
677C22×C4—444no—
678C22×C4—4416no—
679C22×C4—4416no—
680C22×C4—444no—
681C22×C4—444no—
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C4⋊C4—44no—
689C4⋊C4—228no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—228no—
693C4⋊C4—444no—
694C4⋊C4—444no—
695C4⋊C4—444no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—44no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C42—228no—
710C11C2×#263011yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—114no—
725C23—228no—
726C23—228no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—228no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—444no—
742C23—444no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23C2×D4×D1114yes—
753C23C2×D4×D1112yes—
754C23#6703712yes—
755C23#41×D1112yes—
756C23#41×D1112yes—
757C23#6704212yes—
758C23#6704212yes—
759C23#6704312yes—
760C23C24×D1111yescharacteristic
761D4—2232no—
762D4—4416no—
763D4—4416no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—114no—
789C2×C4—114no—
790C2×C4—114no—
791C2×C4—228no—
792C2×C4—228no—
793C2×C4—228no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—4416no—
810C2×C4—4416no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4—444no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—224no—
823C22—224no—
824C22—224no—
825C22—4416no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—888no—
838C22#1062312814yes—
839C22#1062318414yes—
840C22#1062318714yes—
841C22#1062319414yes—
842C22#1062320914yes—
843C22#1062323814yes—
844C22#1062324114yes—
845C22C22×D4×D1111yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C2×#41×D1111yescharacteristic
848C22C2×#41×D1111yescharacteristic
849C22C2×#6704211yescharacteristic
850C22C2×#6704211yescharacteristic
851C22C2×#6704311yescharacteristic
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—224no—
859C4—224no—
860C4—224no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—444no—
866C2—882no—
867C2#1307445818yesdirect product factor
868C2C2×#1062318711yescharacteristic
869C2C2×#1062318411yescharacteristic
870C2C2×#1062312811yescharacteristic
871C2C2×#1062320911yescharacteristic
872C2C2×#1062323811yescharacteristic
873C2C2×#1062319411yescharacteristic
874C2C2×#1062324111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#397D11
hypocenterC11C2×#2630
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66939C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074458C2direct (N × H)
4. C2×#10622270C2semidirect
5. C2×#10622289C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622572C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622268C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622281C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#397C2semidirect
45. C2×#66939C22semidirect
47. C2×(C22⋊D11)⋊C4C22semidirect
48. C11×#397C22semidirect
57. #10622607C22semidirect
58. #10622603C22semidirect
60. #10622572C22semidirect
61. #10622572C22semidirect
62. #10622555C22semidirect
63. #10622289C22semidirect
64. #10622285C22semidirect
65. #10622281C22semidirect
66. #10622278C22semidirect
67. #10622270C22semidirect
68. #10622268C22semidirect
88. C23×Dic11D4semidirect
236. C22×Dic11C2×D4semidirect
278. C2×#397D11semidirect
425. #397C2×D11semidirect
585. C2×C11#2630semidirect
710. C11C2×#2630semidirect
867. C2#13074458direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669392
C22×(C22⋊D11)⋊C42
#130744582
C2×#106222702
C2×#106222892
C2×#106226072
C2×#106222852
C2×#106225722
C2×#106225732
C2×#106226032
C2×#106222682
C2×#106222782
C2×#106222812
C2×#106225552
C2×C11×#3972
C2×#263011