Finite Group Databasebeta

← C2×#13072186 #14921913

Subgroups — C2×#13072186 #14921913

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×#66931C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072186C2116yesmaximal, direct product factor
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622566C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622585C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622555C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, 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
23C23×Dic22C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66992—28no—
34C2×#66992C2218yes—
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66938—28no—
47C2×#66938C2218yescomplemented
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2218yescomplemented
50C2×#66931—28no—
51C2×#66931C2218yescomplemented
52C11×#394C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54#10622833C2218yescomplemented
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622600C2218yescomplemented
63#10622585C2218yescomplemented
64#10622572C2218yescomplemented
65#10622569C2218yescomplemented
66#10622566C2218yescomplemented
67#10622555C2218yescomplemented
68C22⋊C4×Dic11C2218yescomplemented
69#10622288C2218yescomplemented
70#10622259C2218yescomplemented
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×Dic11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2314yes—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—42no—
109C22×C4×D11C2314yes—
110C22×Dic22—24no—
111C22×Dic22—24no—
112C22×Dic22—24no—
113C22×Dic22C2314yes—
114C2×C11×C4⋊C4—42no—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132#66992—232no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
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—42no—
146C2×Dic11⋊C4D418yescomplemented
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×C4×Dic11—24no—
152C2×C4×Dic11—24no—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155#66938—232no—
156(C22⋊D11)⋊C4—232no—
157#66931—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×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11C2×D414yes—
180C24×C11#4114yes—
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×C11C2×D414yes—
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—28no—
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—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—
264C2×Dic22—28no—
265C2×Dic22—28no—
266C2×Dic22—28no—
267C2×Dic22—416no—
268C11×C4⋊C4—44no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—28no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—28no—
276C22⋊Dic11—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281C4⋊Dic11—28no—
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×#397—111no—
295C2×#394—111no—
296C2×#394D1111yescharacteristic, complemented
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—28no—
308C23×C11—28no—
309C23×C11—28no—
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—22no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11C22×D414yes—
331C23×C11C22×D412yes—
332C23×C11C22×D412yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C112−1+412yes—
339C23×C11C2511yescharacteristic
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11C22×D414yes—
354D4×C11—416no—
355C2×C4×C11—28no—
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—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11C22×D414yes—
375C22⋊D11—232no—
376C22⋊D11—416no—
377C2×Dic11—28no—
378C2×Dic11—28no—
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—22no—
395C2×Dic11—416no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11—416no—
401C2×Dic11#121116yes—
402C2×Dic11C22×D414yes—
403C2×Dic11C22×D414yes—
404C2×Dic11C22×D414yes—
405C2×Dic11C2×#4114yes—
406C2×Dic11C2×#4114yes—
407C4×D11—416no—
408Dic22—416no—
409C23×Q8—111no—
410C23×D4—111no—
411C23×D4—111no—
412C23×D4C2×D1111yescharacteristic
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⋊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#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×#95—111no—
461C2×#95—111no—
462C2×#95C2×D1111yescharacteristic
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—416no—
472C22×C11—416no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11C2×#12114yes—
480C22×C11#52914yes—
481C22×C11#54214yes—
482C22×C11#54614yes—
483C22×C11#54614yes—
484C22×C11#54714yes—
485C22×C11#54814yes—
486C22×C11C23×D411yescharacteristic
487C22×C11C23×D411yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C22×#4111yescharacteristic
490C22×C11C22×#4111yescharacteristic
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11C2×2−1+411yescharacteristic
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—24no—
496C2×D11—42no—
497C2×D11—416no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C4×C11—24no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506Dic11—24no—
507Dic11—24no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11C2×#12118yes—
513C25—111no—
514C25C22×D1111yescharacteristic
515C25C22×D1111yescharacteristic
516C22×Q8—114no—
517C22×Q8—224no—
518C22×Q8—224no—
519C22×Q8—224no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—42no—
523C22×D4—118no—
524C22×D4—114no—
525C22×D4—114no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—224no—
529C22×D4—224no—
530C22×D4—442no—
531C22×D4C22×D1114yes—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—114no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—114no—
541C23×C4—114no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—224no—
548C23×C4—224no—
549C23×C4—442no—
550C23×C4—442no—
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—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—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—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⋊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#95—114no—
606#95—114no—
607#95C22×D1114yes—
608C2×C11—44no—
609C2×C11—44no—
610C2×C11#242718yescomplemented
611C2×C11C22×#12111yescharacteristic
612C2×C11C2×#52911yescharacteristic
613C2×C11C2×#54211yescharacteristic
614C2×C11C2×#54611yescharacteristic
615C2×C11C2×#54611yescharacteristic
616C2×C11C2×#54711yescharacteristic
617C2×C11C2×#54811yescharacteristic
618D11—44no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—114no—
632C24—112no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24D4×D1114yes—
640C24#434114yes—
641C24C23×D1112yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×Q8—228no—
645C2×Q8—228no—
646C2×Q8—228no—
647C2×Q8—4416no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—44no—
651C2×D4—416no—
652C2×D4—1116no—
653C2×D4—228no—
654C2×D4—2232no—
655C2×D4—228no—
656C2×D4—228no—
657C2×D4—228no—
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—114no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—112no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—228no—
687C22×C4—228no—
688C22×C4—228no—
689C22×C4—228no—
690C22×C4—228no—
691C22×C4—228no—
692C22×C4—222no—
693C22×C4—222no—
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—222no—
708C22×C4—228no—
709C22×C4—444no—
710C22×C4—4416no—
711C22×C4—4416no—
712C22×C4—444no—
713C22×C4—4416no—
714C22×C4D4×D1114yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C4⋊C4—44no—
721C4⋊C4—1116no—
722C4⋊C4—228no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—444no—
726C22⋊C4—28no—
727C22⋊C4—28no—
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—
738C42—228no—
739C42—228no—
740C11C2×#242711yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—114no—
768C23—228no—
769C23—228no—
770C23—228no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23—444no—
781C23C2×D4×D1114yes—
782C23C2×D4×D1112yes—
783C23C2×D4×D1112yes—
784C23C2×#434114yes—
785C23C2×#434112yes—
786C23#6703712yes—
787C23#41×D1112yes—
788C23#41×D1112yes—
789C23#6704312yes—
790C23C24×D1111yescharacteristic
791Q8—4416no—
792D4—416no—
793D4—2232no—
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—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—1116no—
815C2×C4—114no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—114no—
819C2×C4—114no—
820C2×C4—228no—
821C2×C4—228no—
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—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—4416no—
839C2×C4—4416no—
840C2×C4—4416no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4—444no—
845C2×C4C2×D4×D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—416no—
854C22—416no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—224no—
863C22—224no—
864C22—224no—
865C22—442no—
866C22—4416no—
867C22—442no—
868C22—442no—
869C22—442no—
870C22#1062312214yes—
871C22#1062312914yes—
872C22D11×#12114yes—
873C22#1062314114yes—
874C22#1062318014yes—
875C22#1062318614yes—
876C22#1062320014yes—
877C22C22×D4×D1111yescharacteristic
878C22C22×D4×D1111yescharacteristic
879C22C22×#434111yescharacteristic
880C22C2×#6703711yescharacteristic
881C22C2×#41×D1111yescharacteristic
882C22C2×#41×D1111yescharacteristic
883C22C2×#6704311yescharacteristic
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—118no—
890C4—224no—
891C4—224no—
892C4—442no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—44no—
898C2—444no—
899C2#1307218618yesdirect product factor
900C2C2×D11×#12111yescharacteristic
901C2C2×#1062318011yescharacteristic
902C2C2×#1062320011yescharacteristic
903C2C2×#1062312211yescharacteristic
904C2C2×#1062314111yescharacteristic
905C2C2×#1062318611yescharacteristic
906C2C2×#1062312911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#394D11
hypocenterC11C2×#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66931C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072186C2direct (N × H)
6. C2×#10622288C2semidirect
7. C2×#10622566C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622585C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622555C2semidirect
14. C2×#10622600C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
47. C2×#66938C22semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×#66931C22semidirect
52. C11×#394C22semidirect
54. #10622833C22semidirect
62. #10622600C22semidirect
63. #10622585C22semidirect
64. #10622572C22semidirect
65. #10622569C22semidirect
66. #10622566C22semidirect
67. #10622555C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. #10622288C22semidirect
70. #10622259C22semidirect
146. C2×Dic11⋊C4D4semidirect
285. Dic11⋊C4C2×D4semidirect
296. C2×#394D11semidirect
447. #394C2×D11semidirect
610. C2×C11#2427semidirect
740. C11C2×#2427semidirect
899. C2#13072186direct (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×#669312
C22×#669922
C22×(C22⋊D11)⋊C42
#130721862
C2×#106222882
C2×#106225662
C2×#106225722
C2×#106222592
C2×#106225852
C2×#106228332
C2×#106225692
C2×#106225552
C2×#106226002
C2×C22⋊C4×Dic112
C2×C11×#3942
C2×#242711