Finite Group Databasebeta

← C2×#13072188 #14921909

Subgroups — C2×#13072188 #14921909

Order 2816.

3894 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×#66938C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072188C2116yesmaximal, direct product factor
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622260C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622555C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#397C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66949—28no—
45C2×#66949C2218yescomplemented
46C2×#66938—28no—
47C2×#66938C2218yescomplemented
48C2×#66937—28no—
49C2×#66937C2218yes—
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4C2218yescomplemented
52C11×#397C2218yescomplemented
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#10622600C2218yescomplemented
62#10622574C2218yescomplemented
63#10622571C2218yescomplemented
64#10622555C2218yescomplemented
65#10622288C2218yescomplemented
66#10622285C2218yescomplemented
67#10622279C2218yescomplemented
68#10622278C2218yescomplemented
69#10622260C2218yescomplemented
70#10622259C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11D418yes—
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11—24no—
89C23×Dic11—24no—
90C23×Dic11—42no—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—42no—
101C22×D44C2314yes—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—42no—
108C22×C4×D11C2314yes—
109C22×C4×D11C2314yes—
110C22×Dic22—24no—
111C22×Dic22—24no—
112C22×Dic22—24no—
113C22×Dic22C2314yes—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11C2314yes—
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)⋊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×C4⋊Dic11—42no—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—42no—
145C2×Dic11⋊C4D418yescomplemented
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11—24no—
151C2×C4×Dic11—24no—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2314yes—
154#66949—232no—
155#66938—232no—
156#66937—232no—
157(C22⋊D11)⋊C4—232no—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2427—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11C2×D414yes—
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×D11C2×D414yes—
189C23×D11#4114yes—
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×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11C2×D414yes—
210C22×C4×C11C2412yes—
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—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
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—44no—
240C22×Dic11—416no—
241C22×Dic11C2×D414yes—
242C22×Dic11C2×D414yes—
243C22×Dic11C2×D414yes—
244C22×Dic11#4114yes—
245C22×Dic11#4114yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C2×D44—28no—
253C2×D44—28no—
254C2×D44—44no—
255C2×D44—416no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—44no—
262C2×C4×D11—416no—
263C2×C4×D11—416no—
264C2×Dic22—28no—
265C2×Dic22—28no—
266C2×Dic22—28no—
267C2×Dic22—416no—
268C11×C4⋊C4—28no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—28no—
272C22⋊Dic11—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—
281C4⋊Dic11—44no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—44no—
285Dic11⋊C4C2×D4116yescomplemented
286C4×Dic11—28no—
287C4×Dic11—28no—
288C22×#124—111no—
289C22×C22⋊Q8—111no—
290C22×#121—111no—
291C22×C4×D4—111no—
292#2427—1116no—
293C2×#397—111no—
294C2×#397D1111yescharacteristic, complemented
295C2×#394—111no—
296C2×#394—111no—
297C2×#391—111no—
298C2×#389—111no—
299C2×#386—111no—
300C2×#386—111no—
301C2×#380—111no—
302C2×#380—111no—
303C2×C4×C22⋊C4—111no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11C22×D414yes—
318C23×C11C22×D412yes—
319C23×C11C22×D412yes—
320C23×C11C2×#4112yes—
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—28no—
330C22×D11—28no—
331C22×D11—28no—
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—22no—
343C22×D11—22no—
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—
353C22×D11C2×#4114yes—
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—44no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11C22×D414yes—
378C22⋊D11—232no—
379C22⋊D11—416no—
380C2×Dic11—28no—
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—416no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11#121116yes—
400C2×Dic11C22×D414yes—
401C2×Dic11C22×D414yes—
402C2×Dic11C22×D414yes—
403C2×Dic11C2×#4114yes—
404C2×Dic11C2×#4114yes—
405D44—416no—
406C4×D11—416no—
407C4×D11—416no—
408Dic22—416no—
409C23×Q8—111no—
410C23×D4—111no—
411C23×D4—111no—
412C23×D4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4—111no—
416C2×#124—118no—
417C2×#124—228no—
418C2×C22⋊Q8—118no—
419C2×C22⋊Q8—228no—
420C2×#121—118no—
421C2×#121—228no—
422C2×C4×D4—118no—
423C2×C4×D4—228no—
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⋊C4—111no—
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C42—111no—
443C22×C42—111no—
444#397—118no—
445#397C2×D1118yescomplemented
446#394—118no—
447#394—118no—
448#391—118no—
449#389—118no—
450#386—118no—
451#386—118no—
452#380—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
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1111yescharacteristic
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—42no—
467C22×C11—416no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11C2×#12114yes—
472C22×C11#52914yes—
473C22×C11#54214yes—
474C22×C11#54614yes—
475C22×C11#54614yes—
476C22×C11#54714yes—
477C22×C11#54814yes—
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—24no—
489C2×D11—24no—
490C2×D11—24no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—416no—
494C2×D11—416no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C4×C11—24no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11C2×#12118yes—
513C25—111no—
514C25—111no—
515C25C22×D1111yescharacteristic
516C22×Q8—114no—
517C22×Q8—224no—
518C22×Q8—224no—
519C22×Q8—224no—
520C22×D4—118no—
521C22×D4—114no—
522C22×D4—114no—
523C22×D4—114no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—224no—
529C22×D4—224no—
530C22×D4—442no—
531C22×D4—442no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—114no—
539C23×C4—114no—
540C23×C4—114no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—224no—
548C23×C4—442no—
549C23×C4—442no—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556#124—2232no—
557C22⋊Q8—2232no—
558#121—2232no—
559C4×D4—2232no—
560C2×C4⋊C4—24no—
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—224no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—442no—
570C2×C4⋊C4—442no—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
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—114no—
583C2×C22⋊C4—114no—
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⋊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—
606#95C22×D1114yes—
607#95C22×D1114yes—
608C2×C11—44no—
609C2×C11#242718yescomplemented
610C2×C11C22×#12111yescharacteristic
611C2×C11C2×#52911yescharacteristic
612C2×C11C2×#54211yescharacteristic
613C2×C11C2×#54611yescharacteristic
614C2×C11C2×#54611yescharacteristic
615C2×C11C2×#54711yescharacteristic
616C2×C11C2×#54811yescharacteristic
617D11—44no—
618D11—44no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—114no—
626C24—114no—
627C24—112no—
628C24—112no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24—222no—
641C24D4×D1114yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×Q8—228no—
645C2×Q8—228no—
646C2×Q8—228no—
647C2×Q8—4416no—
648C2×D4—1116no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—2232no—
653C2×D4—228no—
654C2×D4—228no—
655C2×D4—228no—
656C2×D4—444no—
657C2×D4—4416no—
658C2×D4—444no—
659C2×D4—4416no—
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—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—114no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—112no—
681C22×C4—114no—
682C22×C4—114no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—228no—
689C22×C4—228no—
690C22×C4—228no—
691C22×C4—228no—
692C22×C4—228no—
693C22×C4—228no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
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—222no—
707C22×C4—228no—
708C22×C4—444no—
709C22×C4—4416no—
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—1116no—
722C4⋊C4—228no—
723C4⋊C4—228no—
724C4⋊C4—444no—
725C4⋊C4—444no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—228no—
736C22⋊C4—228no—
737C22⋊C4—228no—
738C42—228no—
739C42—228no—
740C11C2×#242711yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—114no—
755C23—114no—
756C23—228no—
757C23—228no—
758C23—228no—
759C23—228no—
760C23—228no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—228no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23—444no—
781C23—444no—
782C23C2×D4×D1114yes—
783C23C2×D4×D1112yes—
784C23C2×D4×D1112yes—
785C23#41×D1112yes—
786C23#41×D1112yes—
787C23#41×D1112yes—
788C23#6704212yes—
789C23#6704312yes—
790C23C24×D1111yescharacteristic
791Q8—4416no—
792D4—2232no—
793D4—4416no—
794D4—4416no—
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—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—1116no—
819C2×C4—114no—
820C2×C4—114no—
821C2×C4—114no—
822C2×C4—114no—
823C2×C4—114no—
824C2×C4—228no—
825C2×C4—228no—
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—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—4416no—
840C2×C4—4416no—
841C2×C4—4416no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4—444no—
845C2×C4C2×D4×D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—416no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—224no—
855C22—224no—
856C22—224no—
857C22—224no—
858C22—224no—
859C22—224no—
860C22—442no—
861C22—4416no—
862C22—4416no—
863C22—442no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22—442no—
870C22D11×#12114yes—
871C22#1062318514yes—
872C22#1062318514yes—
873C22#1062318614yes—
874C22#1062320814yes—
875C22#1062323714yes—
876C22#1062324114yes—
877C22C22×D4×D1111yescharacteristic
878C22C22×D4×D1111yescharacteristic
879C22C2×#41×D1111yescharacteristic
880C22C2×#41×D1111yescharacteristic
881C22C2×#41×D1111yescharacteristic
882C22C2×#6704211yescharacteristic
883C22C2×#6704311yescharacteristic
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—118no—
891C4—224no—
892C4—224no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—444no—
898C2—444no—
899C2#1307218818yesdirect product factor
900C2C2×D11×#12111yescharacteristic
901C2C2×#1062323711yescharacteristic
902C2C2×#1062324111yescharacteristic
903C2C2×#1062318511yescharacteristic
904C2C2×#1062318511yescharacteristic
905C2C2×#1062318611yescharacteristic
906C2C2×#1062320811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#397D11
hypocenterC11C2×#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66949C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072188C2direct (N × H)
6. C2×#10622288C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622260C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622555C2semidirect
14. C2×#10622600C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#397C2semidirect
45. C2×#66949C22semidirect
47. C2×#66938C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
52. C11×#397C22semidirect
61. #10622600C22semidirect
62. #10622574C22semidirect
63. #10622571C22semidirect
64. #10622555C22semidirect
65. #10622288C22semidirect
66. #10622285C22semidirect
67. #10622279C22semidirect
68. #10622278C22semidirect
69. #10622260C22semidirect
70. #10622259C22semidirect
145. C2×Dic11⋊C4D4semidirect
285. Dic11⋊C4C2×D4semidirect
294. C2×#397D11semidirect
445. #397C2×D11semidirect
609. C2×C11#2427semidirect
740. C11C2×#2427semidirect
899. C2#13072188direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669492
C22×#669372
C22×(C22⋊D11)⋊C42
#130721882
C2×#106222882
C2×#106222852
C2×#106225742
C2×#106222592
C2×#106222602
C2×#106222782
C2×#106225712
C2×#106225552
C2×#106226002
C2×#106222792
C2×C11×#3972
C2×#242711