Finite Group Databasebeta

← C2×#13072123 #14921641

Subgroups — C2×#13072123 #14921641

Order 2816.

3830 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×#66936C211yesmaximal, characteristic, complemented
2C22×#66988C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072123C2116yesmaximal, direct product factor
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622565C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622260C211yesmaximal, characteristic, complemented
11C2×#10622563C211yesmaximal, characteristic, complemented
12C2×#10622602C211yesmaximal, characteristic, complemented
13C2×#10622589C211yesmaximal, characteristic, complemented
14C2×#10622555C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66992—28no—
33C2×#66992C2218yes—
34C2×#66988—28no—
35C2×#66988C2218yescomplemented
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66936—28no—
51C2×#66936C2218yescomplemented
52C2×(C22⋊D11)⋊C4—28no—
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C11×#394C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622602C2218yescomplemented
62#10622589C2218yescomplemented
63#10622574C2218yescomplemented
64#10622570C2218yescomplemented
65#10622565C2218yescomplemented
66#10622563C2218yescomplemented
67#10622555C2218yescomplemented
68C22⋊C4×Dic11C2218yescomplemented
69#10622288C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—42no—
77C22×D4×C11C2314yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11D418yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11—24no—
92C23×Dic11—24no—
93C23×Dic11—24no—
94C23×Dic11—24no—
95C23×Dic11—24no—
96C23×Dic11—42no—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2314yes—
102C23×Dic11C2314yes—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—42no—
109C22×C4×D11C2314yes—
110C2×C11×C4⋊C4—42no—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11D418yescomplemented
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128#66992—232no—
129#66988—232no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11—24no—
139C2×C4⋊Dic11—42no—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×C4×Dic11—24no—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158#66936—232no—
159(C22⋊D11)⋊C4—232no—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2422—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×C11C2×D414yes—
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×D11C2×D414yes—
191C23×D11C2412yes—
192C2×D4×C11—28no—
193C2×D4×C11—28no—
194C2×D4×C11—44no—
195C2×D4×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#4114yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C2×C22⋊D11—232no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11C2×D4116yes—
224C22×Dic11—28no—
225C22×Dic11—28no—
226C22×Dic11—28no—
227C22×Dic11—28no—
228C22×Dic11—22no—
229C22×Dic11—28no—
230C22×Dic11—22no—
231C22×Dic11—22no—
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—44no—
246C22×Dic11—416no—
247C22×Dic11—416no—
248C22×Dic11C2×D414yes—
249C22×Dic11C2×D414yes—
250C22×Dic11C2×D414yes—
251C22×Dic11#4114yes—
252C22×Dic11#4114yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—44no—
263C2×C4×D11—416no—
264C11×C4⋊C4—44no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C11×C22⋊C4—28no—
269C22⋊Dic11—28no—
270C22⋊Dic11—28no—
271C22⋊Dic11—28no—
272C22⋊Dic11C2×D4116yescomplemented
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277C4⋊Dic11—28no—
278C4⋊Dic11—44no—
279Dic11⋊C4—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#123—111no—
288C22×#123—111no—
289C22×#121—111no—
290C22×C4×D4—111no—
291#2422—1116no—
292C2×#397—111no—
293C2×#397—111no—
294C2×#394—111no—
295C2×#394D1111yescharacteristic, complemented
296C2×#390—111no—
297C2×#389—111no—
298C2×#385—111no—
299C2×#385—111no—
300C2×#384—111no—
301C2×#380—111no—
302C2×C4×C22⋊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×D414yes—
330C23×C11C22×D414yes—
331C23×C11C22×D412yes—
332C23×C11C22×D412yes—
333C23×C11C2×#4112yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C112−1+412yes—
338C23×C11C2511yescharacteristic
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11C22×D414yes—
353D4×C11—416no—
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—44no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11C2×#4114yes—
374C22⋊D11—232no—
375C22⋊D11—416no—
376C2×Dic11—28no—
377C2×Dic11—28no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
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—416no—
395C2×Dic11—44no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11—416no—
400C2×Dic11#123116yescomplemented
401C2×Dic11C22×D414yes—
402C2×Dic11C22×D414yes—
403C2×Dic11C22×D414yes—
404C2×Dic11C2×#4114yes—
405C2×Dic11C2×#4114yes—
406C4×D11—416no—
407C23×D4—111no—
408C23×D4—111no—
409C23×D4C2×D1111yescharacteristic
410C24×C4—111no—
411C24×C4—111no—
412C24×C4—111no—
413C2×#123—118no—
414C2×#123—118no—
415C2×#123—228no—
416C2×#123—228no—
417C2×#121—118no—
418C2×#121—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⋊C4—111no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C42—111no—
443C22×C42—111no—
444#397—118no—
445#397—118no—
446#394—118no—
447#394C2×D1118yescomplemented
448#390—118no—
449#389—118no—
450#385—118no—
451#385—118no—
452#384—118no—
453#380—118no—
454C4×C22⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95C2×D1111yescharacteristic
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—416no—
470C22×C11—416no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11C2×#12314yes—
478C22×C11#53214yes—
479C22×C11#54214yes—
480C22×C11D4214yes—
481C22×C11#54714yes—
482C22×C11#54714yes—
483C22×C11#55314yes—
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—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—42no—
495C2×D11—416no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C4×C11—24no—
500C4×C11—42no—
501C4×C11—42no—
502C4×C11—42no—
503C4×C11—42no—
504Dic11—24no—
505Dic11—24no—
506Dic11—42no—
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11C2×#12318yescomplemented
511C25—111no—
512C25C22×D1111yescharacteristic
513C25C22×D1111yescharacteristic
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—42no—
517C22×D4—118no—
518C22×D4—114no—
519C22×D4—114no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—442no—
525C22×D4C22×D1114yes—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—114no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—114no—
535C23×C4—114no—
536C23×C4—224no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—442no—
544C23×C4—442no—
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#123—2232no—
551#123—2232no—
552#121—2232no—
553C4×D4—2232no—
554C2×C4⋊C4—42no—
555C2×C4⋊C4—114no—
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—114no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—224no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—442no—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—118no—
577C2×C22⋊C4—114no—
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—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×C22⋊C4C22×D1114yes—
595C2×C22⋊C4C22×D1114yes—
596C2×C42—114no—
597C2×C42—114no—
598C2×C42—224no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95C22×D1114yes—
606C2×C11—44no—
607C2×C11—44no—
608C2×C11#242218yescomplemented
609C2×C11C22×#12311yescharacteristic
610C2×C11C2×#53211yescharacteristic
611C2×C11C2×#54211yescharacteristic
612C2×C11C2×D4211yescharacteristic
613C2×C11C2×#54711yescharacteristic
614C2×C11C2×#54711yescharacteristic
615C2×C11C2×#55311yescharacteristic
616D11—44no—
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—114no—
630C24—112no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24D4×D1114yes—
638C24D4×D1114yes—
639C24C23×D1112yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×D4—28no—
643C2×D4—28no—
644C2×D4—44no—
645C2×D4—416no—
646C2×D4—1116no—
647C2×D4—2232no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—444no—
653C2×D4—4416no—
654C22×C4—22no—
655C22×C4—22no—
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—22no—
667C22×C4—22no—
668C22×C4—114no—
669C22×C4—114no—
670C22×C4—114no—
671C22×C4—112no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—228no—
681C22×C4—228no—
682C22×C4—228no—
683C22×C4—228no—
684C22×C4—228no—
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—228no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—444no—
704C22×C4—4416no—
705C22×C4—4416no—
706C22×C4—444no—
707C22×C4—4416no—
708C22×C4#434114yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—44no—
715C4⋊C4—228no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—228no—
721C4⋊C4—228no—
722C4⋊C4—444no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—1116no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C42—228no—
736C42—228no—
737C11C2×#242211yescharacteristic, 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—114no—
765C23—228no—
766C23—228no—
767C23—228no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23C2×D4×D1114yes—
779C23C2×D4×D1114yes—
780C23C2×D4×D1112yes—
781C23C2×D4×D1112yes—
782C23C2×#434112yes—
783C23#6703712yes—
784C23#41×D1112yes—
785C23#41×D1112yes—
786C23#6704312yes—
787C23C24×D1111yescharacteristic
788D4—416no—
789D4—2232no—
790D4—4416no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
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—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—1116no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—228no—
817C2×C4—228no—
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—4416no—
835C2×C4—4416no—
836C2×C4—4416no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4C2×#434114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—224no—
859C22—224no—
860C22—224no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—4416no—
866C22#1062312114yes—
867C22#1062312714yes—
868C22#1062313214yes—
869C22#1062314214yes—
870C22D11×#12314yes—
871C22#1062318614yes—
872C22#1062320014yes—
873C22C22×D4×D1111yescharacteristic
874C22C22×D4×D1111yescharacteristic
875C22C22×#434111yescharacteristic
876C22C2×#6703711yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#41×D1111yescharacteristic
879C22C2×#6704311yescharacteristic
880C4—24no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—118no—
886C4—224no—
887C4—224no—
888C4—442no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—44no—
893C2—44no—
894C2—444no—
895C2#1307212318yesdirect product factor
896C2C2×D11×#12311yescharacteristic
897C2C2×#1062312711yescharacteristic
898C2C2×#1062320011yescharacteristic
899C2C2×#1062312111yescharacteristic
900C2C2×#1062318611yescharacteristic
901C2C2×#1062314211yescharacteristic
902C2C2×#1062313211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#394D11
hypocenterC11C2×#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66988C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072123C2direct (N × H)
6. C2×#10622288C2semidirect
7. C2×#10622565C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622260C2semidirect
11. C2×#10622563C2semidirect
12. C2×#10622602C2semidirect
13. C2×#10622589C2semidirect
14. C2×#10622555C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
35. C2×#66988C22semidirect
51. C2×#66936C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C11×#394C22semidirect
61. #10622602C22semidirect
62. #10622589C22semidirect
63. #10622574C22semidirect
64. #10622570C22semidirect
65. #10622565C22semidirect
66. #10622563C22semidirect
67. #10622555C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. #10622288C22semidirect
70. #10622260C22semidirect
123. C2×C22⋊Dic11D4semidirect
272. C22⋊Dic11C2×D4semidirect
295. C2×#394D11semidirect
400. C2×Dic11#123semidirect
447. #394C2×D11semidirect
510. Dic11C2×#123semidirect
608. C2×C11#2422semidirect
737. C11C2×#2422semidirect
895. C2#13072123direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669882
C22×#669922
C22×(C22⋊D11)⋊C42
#130721232
C2×#106222882
C2×#106225652
C2×#106225742
C2×#106225702
C2×#106222602
C2×#106225632
C2×#106226022
C2×#106225892
C2×#106225552
C2×C22⋊C4×Dic112
C2×C11×#3942
C2×#242211