Finite Group Databasebeta

← C2×#13074685 #14920274

Subgroups — C2×#13074685 #14920274

Order 2816.

2394 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074685C2116yesmaximal, direct product factor
2C2×C11⋊#401C211yesmaximal, characteristic, complemented
3C2×#10622597C211yesmaximal, characteristic, complemented
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic
7C2×#10622604C211yesmaximal, characteristic
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622844C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622282C211yesmaximal, characteristic, complemented
12C2×#10622265C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#391C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C11×#391C2218yescomplemented
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43#10622844C2218yescomplemented
44#10622844C2218yescomplemented
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622604C2218yes—
56#10622597C2218yescomplemented
57#10622553C2218yescomplemented
58C4×(C2×D11)⋊C4C2218yescomplemented
59#10622288C2218yescomplemented
60#10622287C2218yescomplemented
61#10622285C2218yes—
62#10622282C2218yescomplemented
63#10622281C2218yescomplemented
64#10622278C2218yes—
65C11⋊#401C2218yescomplemented
66#10622265C2218yescomplemented
67C24×D11C2311yescharacteristic
68C24×D11C2311yescharacteristic
69C22×Q8×C11—24no—
70C22×Q8×C11—42no—
71C22×Q8×C11—42no—
72C22×Q8×C11C2314yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C22×D44—24no—
87C22×D44—42no—
88C22×D44—42no—
89C22×D44C2314yes—
90C22×C4×D11—24no—
91C22×C4×D11—42no—
92C22×C4×D11—42no—
93C22×C4×D11C2314yes—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4C2314yes—
96C2×C42×C11—42no—
97C2×C42×C11C2314yes—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—42no—
104C2×(C2×D11)⋊C4—42no—
105C2×(C2×D11)⋊C4—42no—
106C2×(C2×D11)⋊C4—42no—
107C2×(C2×D11)⋊C4—42no—
108C2×(C2×D11)⋊C4—42no—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×C4⋊Dic11—42no—
121C2×C4⋊Dic11C2314yes—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4—42no—
124C2×Dic11⋊C4—42no—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×C4×Dic11—42no—
129C2×C4×Dic11C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C2×#2653—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11#4114yes—
160C23×D11C2412yes—
161C23×D11C2412yes—
162C2×Q8×C11—28no—
163C2×Q8×C11—44no—
164C2×Q8×C11—44no—
165C2×Q8×C11—416no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11#4114yes—
186C22×C4×C11#4114yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C2×D44—28no—
219C2×D44—44no—
220C2×D44—44no—
221C2×D44—416no—
222C2×C4×D11—28no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—416no—
226C11×C4⋊C4—44no—
227C42×C11—44no—
228(C2×D11)⋊C4—28no—
229(C2×D11)⋊C4—28no—
230(C2×D11)⋊C4—28no—
231(C2×D11)⋊C4—28no—
232(C2×D11)⋊C4—28no—
233(C2×D11)⋊C4—44no—
234(C2×D11)⋊C4—44no—
235(C2×D11)⋊C4—44no—
236(C2×D11)⋊C4—44no—
237(C2×D11)⋊C4—44no—
238(C2×D11)⋊C4—44no—
239C4⋊Dic11—44no—
240Dic11⋊C4—28no—
241Dic11⋊C4—44no—
242Dic11⋊C4—44no—
243C4×Dic11—44no—
244#2653—1116no—
245C2×#401—111no—
246C2×#398—111no—
247C2×#397—111no—
248C2×#397—111no—
249C2×#394—111no—
250C2×#394—111no—
251C2×#393—111no—
252C2×#393—111no—
253C2×#391D1111yescharacteristic, complemented
254C2×#388—111no—
255C2×#388—111no—
256C2×#387—111no—
257C2×#386—111no—
258C2×#385—111no—
259C2×C4×C22⋊C4—111no—
260C23×C11C2×#4112yes—
261C23×C11C2×#4112yes—
262C23×C11C2×#4112yes—
263C23×C11H(5,𝔽2)12yes—
264C23×C11H(5,𝔽2)12yes—
265C23×C11H(5,𝔽2)12yes—
266C23×C112−1+412yes—
267C23×C11C2511yescharacteristic
268C22×D11—28no—
269C22×D11—28no—
270C22×D11—28no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—22no—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—44no—
285C22×D11—44no—
286C22×D11—44no—
287C22×D11—44no—
288C22×D11—44no—
289C22×D11—44no—
290C22×D11—44no—
291C22×D11—44no—
292C22×D11—44no—
293C22×D11—44no—
294C22×D11—44no—
295C22×D11C2×#4114yes—
296Q8×C11—416no—
297C2×C4×C11—28no—
298C2×C4×C11—28no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—44no—
319C2×C4×C11—44no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11C2×#4114yes—
324C2×C4×C11C2×#4114yes—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—44no—
344C2×Dic11—44no—
345C2×Dic11—44no—
346C2×Dic11—44no—
347C2×Dic11—44no—
348C2×Dic11—44no—
349D44—416no—
350C4×D11—416no—
351C23×Q8C2×D1111yescharacteristic
352C23×D4—111no—
353C24×C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4C2×D1111yescharacteristic
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—111no—
369C22×C22⋊C4—111no—
370C22×C42—111no—
371C22×C42C2×D1111yescharacteristic
372#401—118no—
373#398—118no—
374#397—118no—
375#397—118no—
376#394—118no—
377#394—118no—
378#393—118no—
379#393—118no—
380#391C2×D1118yescomplemented
381#388—118no—
382#388—118no—
383#387—118no—
384#386—118no—
385#385—118no—
386C4×C22⋊C4—118no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95—111no—
397C2×#95C2×D1111yescharacteristic
398C2×#95C2×D1111yescharacteristic
399C2×#95C2×D1111yescharacteristic
400C2×#95C2×D1111yescharacteristic
401C22×C11#52914yes—
402C22×C11#53814yes—
403C22×C11#53814yes—
404C22×C11#53814yes—
405C22×C11#53914yes—
406C22×C11#54214yes—
407C22×C11#54214yes—
408C22×C11C22×#4111yescharacteristic
409C22×C11C22×#4111yescharacteristic
410C22×C11C22×#4111yescharacteristic
411C22×C11C2×H(5,𝔽2)11yescharacteristic
412C22×C11C2×H(5,𝔽2)11yescharacteristic
413C22×C11C2×H(5,𝔽2)11yescharacteristic
414C22×C11C2×2−1+411yescharacteristic
415C2×D11—24no—
416C2×D11—24no—
417C2×D11—24no—
418C2×D11—416no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—88no—
431C4×C11—24no—
432C4×C11—24no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443Dic11—42no—
444C25—111no—
445C25—111no—
446C22×Q8—24no—
447C22×Q8—42no—
448C22×Q8—42no—
449C22×Q8C22×D1114yes—
450C22×D4—114no—
451C22×D4—224no—
452C22×D4—442no—
453C22×D4—442no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—114no—
461C23×C4—224no—
462C23×C4—442no—
463C23×C4—442no—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C2×C4⋊C4—42no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—224no—
477C2×C4⋊C4—442no—
478C2×C4⋊C4—442no—
479C2×C4⋊C4—442no—
480C2×C4⋊C4C22×D1114yes—
481C2×C22⋊C4—114no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—114no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—114no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—114no—
490C2×C22⋊C4—114no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—224no—
495C2×C22⋊C4—224no—
496C2×C22⋊C4—224no—
497C2×C22⋊C4—442no—
498C2×C22⋊C4—442no—
499C2×C22⋊C4—442no—
500C2×C22⋊C4—442no—
501C2×C22⋊C4—442no—
502C2×C22⋊C4—442no—
503C2×C42—42no—
504C2×C42—114no—
505C2×C42—442no—
506C2×C42C22×D1114yes—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95—114no—
514#95—114no—
515#95—114no—
516#95—114no—
517#95C22×D1114yes—
518#95C22×D1114yes—
519#95C22×D1114yes—
520#95C22×D1114yes—
521C2×C11#265318yescomplemented
522C2×C11C2×#52911yescharacteristic
523C2×C11C2×#53811yescharacteristic
524C2×C11C2×#53811yescharacteristic
525C2×C11C2×#53811yescharacteristic
526C2×C11C2×#53911yescharacteristic
527C2×C11C2×#54211yescharacteristic
528C2×C11C2×#54211yescharacteristic
529D11—44no—
530D11—82no—
531C24—114no—
532C24—112no—
533C24—112no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24—222no—
543C24—222no—
544C24—222no—
545C24—222no—
546C24—222no—
547C24C23×D1111yescharacteristic
548C2×Q8—28no—
549C2×Q8—44no—
550C2×Q8—44no—
551C2×Q8—416no—
552C2×D4—228no—
553C2×D4—444no—
554C2×D4—444no—
555C2×D4—4416no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—228no—
600C22×C4—444no—
601C22×C4—444no—
602C22×C4—4416no—
603C22×C4#433914yes—
604C22×C4#434314yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1112yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1112yes—
610C22×C4C23×D1112yes—
611C22×C4C23×D1112yes—
612C4⋊C4—44no—
613C4⋊C4—228no—
614C4⋊C4—444no—
615C4⋊C4—444no—
616C4⋊C4—444no—
617C22⋊C4—228no—
618C22⋊C4—228no—
619C22⋊C4—228no—
620C22⋊C4—228no—
621C22⋊C4—228no—
622C22⋊C4—444no—
623C22⋊C4—444no—
624C22⋊C4—444no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C22⋊C4—444no—
628C42—44no—
629C42—444no—
630C11C2×#265311yescharacteristic, complemented, Sylow
631C23—114no—
632C23—228no—
633C23—228no—
634C23—222no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—228no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—222no—
647C23—222no—
648C23—444no—
649C23—444no—
650C23—444no—
651C23—444no—
652C23—444no—
653C23—444no—
654C23—444no—
655C23—444no—
656C23—444no—
657C23—444no—
658C23—444no—
659C23C2×#433912yes—
660C23#6703712yes—
661C23#6703712yes—
662C23C2×#434312yes—
663C23#6704012yes—
664C23#41×D1112yes—
665C23#6704212yes—
666C23C24×D1111yescharacteristic
667Q8—416no—
668D4—4416no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—4416no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—444no—
717C2×C4—444no—
718C2×C4—444no—
719C2×C4—444no—
720C2×C4C2×#433914yes—
721C2×C4C2×#434314yes—
722C22—224no—
723C22—224no—
724C22—224no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—4416no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—888no—
738C22#1062302514yes—
739C22#1062311114yes—
740C22#1062311314yes—
741C22#1062316914yes—
742C22#1062317514yes—
743C22#1062320914yes—
744C22#1062326414yes—
745C22C22×#433911yescharacteristic
746C22C2×#6703711yescharacteristic
747C22C2×#6703711yescharacteristic
748C22C22×#434311yescharacteristic
749C22C2×#6704011yescharacteristic
750C22C2×#41×D1111yescharacteristic
751C22C2×#6704211yescharacteristic
752C4—24no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—442no—
760C4—442no—
761C4—442no—
762C4—442no—
763C4—442no—
764C4—442no—
765C2—444no—
766C2—882no—
767C2#1307468518yesdirect product factor
768C2C2×#1062311111yescharacteristic
769C2C2×#1062320911yescharacteristic
770C2C2×#1062302511yescharacteristic
771C2C2×#1062317511yescharacteristic
772C2C2×#1062316911yescharacteristic
773C2C2×#1062311311yescharacteristic
774C2C2×#1062326411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#391C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#391D11
hypocenterC11C2×#2653
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #13074685C2direct (N × H)
2. C2×C11⋊#401C2semidirect
3. C2×#10622597C2semidirect
4. C2×#10622288C2semidirect
5. C2×#10622287C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622844C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622282C2semidirect
12. C2×#10622265C2semidirect
14. C2×#10622281C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#391C2semidirect
38. C11×#391C22semidirect
43. #10622844C22semidirect
44. #10622844C22semidirect
56. #10622597C22semidirect
57. #10622553C22semidirect
58. C4×(C2×D11)⋊C4C22semidirect
59. #10622288C22semidirect
60. #10622287C22semidirect
62. #10622282C22semidirect
63. #10622281C22semidirect
65. C11⋊#401C22semidirect
66. #10622265C22semidirect
253. C2×#391D11semidirect
380. #391C2×D11semidirect
521. C2×C11#2653semidirect
630. C11C2×#2653semidirect
767. C2#13074685direct (N × H)

Maximal subgroups

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

subgroupindex
#130746852
C2×C11⋊#4012
C2×#106225972
C2×#106222882
C2×#106222872
C2×#106222852
C2×#106226042
C2×#106228442
C2×#106225532
C2×#106222822
C2×#106222652
C2×#106222782
C2×#106222812
C2×C4×(C2×D11)⋊C42
C2×C11×#3912
C2×#265311