Finite Group Databasebeta

← C2×#13074472 #14920481

Subgroups — C2×#13074472 #14920481

Order 2816.

3670 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074472C2116yesmaximal, direct product factor
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622264C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
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×C4×C22⋊D11—28no—
34C2×C4×C22⋊D11C2218yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66938—28no—
45C2×#66938C2218yescomplemented
46C11×#386C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49#10622836C2218yescomplemented
50#10622836C2218yescomplemented
51#10622826C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622573C2218yescomplemented
61#10622573C2218yescomplemented
62#10622569C2218yescomplemented
63#10622565C2218yescomplemented
64#10622560C2218yescomplemented
65#10622288C2218yescomplemented
66#10622286C2218yescomplemented
67#10622278C2218yescomplemented
68#10622264C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—42no—
75C22×D4×C11—42no—
76C22×D4×C11C2314yes—
77C23×C4×C11—24no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C22×D44—24no—
109C22×D44—42no—
110C22×D44—42no—
111C22×D44C2314yes—
112C22×C4×D11—24no—
113C22×C4×D11—42no—
114C22×C4×D11—42no—
115C22×C4×D11C2314yes—
116C22×Dic22—24no—
117C22×Dic22—42no—
118C22×Dic22—42no—
119C22×Dic22C2314yes—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—42no—
122C2×C11×C22⋊C4—42no—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—42no—
129C2×C22⋊Dic11—42no—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C4×C22⋊D11—232no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4—42no—
140C2×(C2×D11)⋊C4—42no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4C2314yes—
151C2×C4×Dic11D418yescomplemented
152C2×C4×Dic11C2314yes—
153#66938—232no—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2631—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
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#4114yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11#4114yes—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C2×D4×C11—28no—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C2×D4×C11—416no—
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—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—28no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—416no—
220C22×C4×C11C2×D414yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C2×C22⋊D11—232no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—416no—
240C2×C22⋊D11—416no—
241C2×C22⋊D11—416no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11C2×D414yes—
259C22×Dic11C2×D414yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×D44—28no—
267C2×D44—44no—
268C2×D44—44no—
269C2×D44—416no—
270C2×C4×D11—28no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—416no—
274C2×Dic22—28no—
275C2×Dic22—44no—
276C2×Dic22—44no—
277C2×Dic22—416no—
278C11×C22⋊C4—28no—
279C11×C22⋊C4—44no—
280C11×C22⋊C4—44no—
281C22⋊Dic11—28no—
282C22⋊Dic11—28no—
283C22⋊Dic11—44no—
284C22⋊Dic11—44no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290(C2×D11)⋊C4—44no—
291(C2×D11)⋊C4—44no—
292Dic11⋊C4—28no—
293C4×Dic11C2×D4116yescomplemented
294C22×#124—111no—
295C22×C4×D4—111no—
296#2631—1116no—
297C2×#397—111no—
298C2×#397—111no—
299C2×#393—111no—
300C2×#393—111no—
301C2×#392—111no—
302C2×#392—111no—
303C2×#392—111no—
304C2×#392—111no—
305C2×#386—111no—
306C2×#386—111no—
307C2×#386—111no—
308C2×#386D1111yescharacteristic, complemented
309C2×#383—111no—
310C23×C11—28no—
311C23×C11—28no—
312C23×C11—28no—
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—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11C22×D412yes—
338C23×C11C2×#4114yes—
339C23×C11C2×#4112yes—
340C23×C11C2×#4112yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11H(5,𝔽2)12yes—
344C23×C11H(5,𝔽2)12yes—
345C23×C11C2511yescharacteristic
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11—44no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11—44no—
372C22×D11—44no—
373C22×D11C2×#4114yes—
374D4×C11—416no—
375C2×C4×C11—28no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—416no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11—44no—
395C2×C4×C11C22×D414yes—
396C22⋊D11—232no—
397C22⋊D11—416no—
398C22⋊D11—416no—
399C22⋊D11—416no—
400C2×Dic11—28no—
401C2×Dic11—28no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—44no—
419C2×Dic11—44no—
420C2×Dic11—44no—
421C2×Dic11—44no—
422C2×Dic11C22×D414yes—
423C2×Dic11C22×D414yes—
424D44—416no—
425C4×D11—416no—
426Dic22—416no—
427C23×Q8—111no—
428C23×D4—111no—
429C23×D4—111no—
430C23×D4—111no—
431C23×D4—111no—
432C23×D4—111no—
433C23×D4C2×D1111yescharacteristic
434C24×C4—111no—
435C24×C4C2×D1111yescharacteristic
436C2×#124—118no—
437C2×#124—228no—
438C2×C4×D4—118no—
439C2×C4×D4—228no—
440C22×C4⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C42—111no—
456#397—118no—
457#397—118no—
458#393—118no—
459#393—118no—
460#392—118no—
461#392—118no—
462#392—118no—
463#392—118no—
464#386—118no—
465#386—118no—
466#386—118no—
467#386C2×D1118yescomplemented
468#383—118no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95C2×D1111yescharacteristic
478C2×#95C2×D1111yescharacteristic
479C22×C11—24no—
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—416no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—88no—
495C22×C11#52514yes—
496C22×C11#53514yes—
497C22×C11#53514yes—
498C22×C11#53814yes—
499C22×C11#53814yes—
500C22×C11#53814yes—
501C22×C11#53814yes—
502C22×C11C23×D411yescharacteristic
503C22×C11C22×#4111yescharacteristic
504C22×C11C22×#4111yescharacteristic
505C22×C11C2×H(5,𝔽2)11yescharacteristic
506C22×C11C2×H(5,𝔽2)11yescharacteristic
507C22×C11C2×H(5,𝔽2)11yescharacteristic
508C22×C11C2×H(5,𝔽2)11yescharacteristic
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—24no—
512C2×D11—416no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—88no—
525C4×C11—24no—
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—42no—
530Dic11—24no—
531Dic11—24no—
532Dic11—42no—
533Dic11—42no—
534Dic11—42no—
535Dic11—42no—
536C25—111no—
537C25—111no—
538C25C22×D1111yescharacteristic
539C25C22×D1111yescharacteristic
540C22×Q8—114no—
541C22×Q8—224no—
542C22×Q8—442no—
543C22×Q8—442no—
544C22×D4—24no—
545C22×D4—42no—
546C22×D4—42no—
547C22×D4—114no—
548C22×D4—114no—
549C22×D4—114no—
550C22×D4—114no—
551C22×D4—114no—
552C22×D4—224no—
553C22×D4—224no—
554C22×D4—224no—
555C22×D4—224no—
556C22×D4—224no—
557C22×D4—224no—
558C22×D4—224no—
559C22×D4—442no—
560C22×D4—442no—
561C22×D4—442no—
562C22×D4—442no—
563C22×D4—442no—
564C22×D4—442no—
565C22×D4—442no—
566C22×D4—442no—
567C22×D4C22×D1114yes—
568C23×C4—24no—
569C23×C4—42no—
570C23×C4—42no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—111no—
576C23×C4—111no—
577C23×C4—114no—
578C23×C4—224no—
579C23×C4—442no—
580C23×C4—442no—
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C23×C4C22×D1111yescharacteristic
586C23×C4C22×D1114yes—
587#124—2232no—
588C4×D4—2232no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—224no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—224no—
609C2×C22⋊C4—224no—
610C2×C22⋊C4—442no—
611C2×C22⋊C4—442no—
612C2×C22⋊C4—442no—
613C2×C22⋊C4—442no—
614C2×C22⋊C4—442no—
615C2×C22⋊C4—442no—
616C2×C22⋊C4C22×D1114yes—
617C2×C22⋊C4C22×D1114yes—
618C2×C22⋊C4C22×D1114yes—
619C2×C42—118no—
620C2×C42—114no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95—114no—
628#95—114no—
629#95C22×D1114yes—
630#95C22×D1114yes—
631C2×C11—44no—
632C2×C11—82no—
633C2×C11#263118yescomplemented
634C2×C11C2×#52511yescharacteristic
635C2×C11C2×#53511yescharacteristic
636C2×C11C2×#53511yescharacteristic
637C2×C11C2×#53811yescharacteristic
638C2×C11C2×#53811yescharacteristic
639C2×C11C2×#53811yescharacteristic
640C2×C11C2×#53811yescharacteristic
641D11—44no—
642D11—82no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—114no—
657C24—112no—
658C24—112no—
659C24—222no—
660C24—222no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24—222no—
669C24—222no—
670C24—222no—
671C24—222no—
672C24#433914yes—
673C24C23×D1112yes—
674C24C23×D1112yes—
675C24C23×D1111yescharacteristic
676C2×Q8—228no—
677C2×Q8—444no—
678C2×Q8—444no—
679C2×Q8—4416no—
680C2×D4—28no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—416no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—228no—
687C2×D4—228no—
688C2×D4—2232no—
689C2×D4—228no—
690C2×D4—228no—
691C2×D4—228no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4—4416no—
695C2×D4—444no—
696C2×D4—444no—
697C2×D4—444no—
698C2×D4—444no—
699C2×D4—444no—
700C2×D4—444no—
701C2×D4—4416no—
702C2×D4—4416no—
703C2×D4—4416no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—416no—
722C22×C4—114no—
723C22×C4—114no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—228no—
747C22×C4—444no—
748C22×C4—444no—
749C22×C4—4416no—
750C22×C4D4×D1114yes—
751C22×C4C23×D1112yes—
752C22×C4C23×D1112yes—
753C22×C4C23×D1112yes—
754C22×C4C23×D1112yes—
755C22×C4C23×D1112yes—
756C4⋊C4—228no—
757C22⋊C4—28no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—228no—
761C22⋊C4—228no—
762C22⋊C4—228no—
763C22⋊C4—228no—
764C22⋊C4—228no—
765C22⋊C4—444no—
766C22⋊C4—444no—
767C22⋊C4—444no—
768C22⋊C4—444no—
769C22⋊C4—444no—
770C22⋊C4—444no—
771C42—1116no—
772C11C2×#263111yescharacteristic, complemented, Sylow
773C23—28no—
774C23—28no—
775C23—28no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—114no—
801C23—228no—
802C23—228no—
803C23—222no—
804C23—228no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23—444no—
821C23—444no—
822C23—444no—
823C23—444no—
824C23—444no—
825C23—444no—
826C23—444no—
827C23—444no—
828C23C2×#433914yes—
829C23C2×#433912yes—
830C23C2×D4×D1112yes—
831C23#6703712yes—
832C23#6703712yes—
833C23#6703712yes—
834C23#41×D1112yes—
835C23#6704212yes—
836C23C24×D1111yescharacteristic
837Q8—4416no—
838D4—416no—
839D4—2232no—
840D4—4416no—
841D4—4416no—
842D4—4416no—
843D4—4416no—
844C2×C4—28no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—416no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—114no—
865C2×C4—114no—
866C2×C4—228no—
867C2×C4—228no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—4416no—
885C2×C4—444no—
886C2×C4—444no—
887C2×C4—444no—
888C2×C4—444no—
889C2×C4C2×D4×D1114yes—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—416no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—88no—
906C22—224no—
907C22—224no—
908C22—224no—
909C22—4416no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—888no—
922C22#1062302514yes—
923C22#1062307814yes—
924C22#1062309114yes—
925C22#1062312314yes—
926C22#1062313814yes—
927C22#1062314414yes—
928C22#1062318814yes—
929C22C22×#433911yescharacteristic
930C22C22×D4×D1111yescharacteristic
931C22C2×#6703711yescharacteristic
932C22C2×#6703711yescharacteristic
933C22C2×#6703711yescharacteristic
934C22C2×#41×D1111yescharacteristic
935C22C2×#6704211yescharacteristic
936C4—24no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—224no—
942C4—224no—
943C4—442no—
944C4—442no—
945C4—442no—
946C4—442no—
947C2—44no—
948C2—82no—
949C2—444no—
950C2—882no—
951C2#1307447218yesdirect product factor
952C2C2×#1062307811yescharacteristic
953C2C2×#1062312311yescharacteristic
954C2C2×#1062313811yescharacteristic
955C2C2×#1062314411yescharacteristic
956C2C2×#1062309111yescharacteristic
957C2C2×#1062318811yescharacteristic
958C2C2×#1062302511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2631
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074472C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622286C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622264C2semidirect
16. C2×C11×#386C2semidirect
34. C2×C4×C22⋊D11C22semidirect
45. C2×#66938C22semidirect
46. C11×#386C22semidirect
49. #10622836C22semidirect
50. #10622836C22semidirect
51. #10622826C22semidirect
60. #10622573C22semidirect
61. #10622573C22semidirect
62. #10622569C22semidirect
63. #10622565C22semidirect
64. #10622560C22semidirect
65. #10622288C22semidirect
66. #10622286C22semidirect
67. #10622278C22semidirect
68. #10622264C22semidirect
151. C2×C4×Dic11D4semidirect
293. C4×Dic11C2×D4semidirect
308. C2×#386D11semidirect
467. #386C2×D11semidirect
633. C2×C11#2631semidirect
772. C11C2×#2631semidirect
951. C2#13074472direct (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×C4×C22⋊D112
#130744722
C2×#106222882
C2×#106225652
C2×#106222862
C2×#106225602
C2×#106225732
C2×#106228362
C2×#106228262
C2×#106222782
C2×#106225692
C2×#106222642
C2×C11×#3862
C2×#263111