Finite Group Databasebeta

← C2×#13076701 #14960081

Subgroups — C2×#13076701 #14960081

Order 2816.

2930 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076701C2116yesmaximal, direct product factor
2C2×C11⋊#401C211yesmaximal, characteristic, complemented
3C2×#10622565C211yesmaximal, characteristic, complemented
4C2×#10622606C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622836C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622569C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
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
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C11×#394C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44#10622836C2218yescomplemented
45#10622836C2218yescomplemented
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#10622607C2218yescomplemented
56#10622606C2218yescomplemented
57#10622574C2218yescomplemented
58#10622573C2218yescomplemented
59#10622573C2218yescomplemented
60#10622572C2218yescomplemented
61#10622569C2218yescomplemented
62#10622569C2218yescomplemented
63#10622566C2218yescomplemented
64#10622565C2218yescomplemented
65#10622278C2218yescomplemented
66C11⋊#401C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C22×D4×C11—42no—
72C22×D4×C11—42no—
73C22×D4×C11—42no—
74C22×D4×C11C2314yes—
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—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×D44—24no—
103C22×D44—42no—
104C22×D44—42no—
105C22×D44C2314yes—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11—42no—
109C22×C4×D11C2314yes—
110C2×C11×C4⋊C4—42no—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4—42no—
114C2×C11×C22⋊C4—42no—
115C2×C11×C22⋊C4—42no—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11—42no—
123C2×C22⋊Dic11—42no—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11—42no—
143C2×C4⋊Dic11C2314yes—
144C2×Dic11⋊C4—42no—
145C2×Dic11⋊C4C2314yes—
146C11×#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2825—111nomaximal, Sylow
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11C2412yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
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#4114yes—
188C23×D11C2412yes—
189C23×D11C2412yes—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—416no—
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×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—416no—
227C2×C22⋊D11—416no—
228C2×C22⋊D11—416no—
229C2×C22⋊D11—416no—
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—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C2×D44—28no—
255C2×D44—44no—
256C2×D44—44no—
257C2×D44—416no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11—416no—
262C11×C4⋊C4—44no—
263C11×C22⋊C4—44no—
264C11×C22⋊C4—44no—
265C11×C22⋊C4—44no—
266C11×C22⋊C4—44no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270C22⋊Dic11—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276(C2×D11)⋊C4—44no—
277(C2×D11)⋊C4—44no—
278C4⋊Dic11—44no—
279Dic11⋊C4—44no—
280#2825—1116no—
281C2×#401—111no—
282C2×#397—111no—
283C2×#397—111no—
284C2×#397—111no—
285C2×#396—111no—
286C2×#394—111no—
287C2×#394—111no—
288C2×#394D1111yescharacteristic, complemented
289C2×#392—111no—
290C2×#392—111no—
291C2×#392—111no—
292C2×#392—111no—
293C2×#386—111no—
294C2×#386—111no—
295C2×#386—111no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11C2×#4112yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C11H(5,𝔽2)12yes—
328C23×C11H(5,𝔽2)12yes—
329C23×C11H(5,𝔽2)12yes—
330C23×C11H(5,𝔽2)12yes—
331C23×C11C2511yescharacteristic
332C22×D11—28no—
333C22×D11—28no—
334C22×D11—28no—
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—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11—44no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11C2×#4114yes—
360D4×C11—416no—
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—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—44no—
379C2×C4×C11—44no—
380C2×C4×C11—44no—
381C22⋊D11—416no—
382C22⋊D11—416no—
383C22⋊D11—416no—
384C22⋊D11—416no—
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—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—44no—
404C2×Dic11—44no—
405C2×Dic11—44no—
406C2×Dic11—44no—
407C2×Dic11—44no—
408C2×Dic11—44no—
409D44—416no—
410C4×D11—416no—
411C23×D4—111no—
412C23×D4—111no—
413C23×D4—111no—
414C23×D4—111no—
415C23×D4—111no—
416C23×D4C2×D1111yescharacteristic
417C24×C4—111no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C22⋊C4C2×D1111yescharacteristic
434C22×C22⋊C4C2×D1111yescharacteristic
435C22×C22⋊C4C2×D1111yescharacteristic
436#401—118no—
437#397—118no—
438#397—118no—
439#397—118no—
440#396—118no—
441#394—118no—
442#394—118no—
443#394C2×D1118yescomplemented
444#392—118no—
445#392—118no—
446#392—118no—
447#392—118no—
448#386—118no—
449#386—118no—
450#386—118no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95C2×D1111yescharacteristic
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—88no—
476C22×C11—88no—
477C22×C11#53814yes—
478C22×C11#53814yes—
479C22×C11#53814yes—
480C22×C11#56014yes—
481C22×C11#56014yes—
482C22×C11#56014yes—
483C22×C11#56014yes—
484C22×C11C22×#4111yescharacteristic
485C22×C11C2×H(5,𝔽2)11yescharacteristic
486C22×C11C2×H(5,𝔽2)11yescharacteristic
487C22×C11C2×H(5,𝔽2)11yescharacteristic
488C22×C11C2×H(5,𝔽2)11yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×H(5,𝔽2)11yescharacteristic
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—416no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—88no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517Dic11—42no—
518C25—111no—
519C25—111no—
520C25C22×D1111yescharacteristic
521C25C22×D1111yescharacteristic
522C22×D4—42no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—114no—
526C22×D4—114no—
527C22×D4—114no—
528C22×D4—114no—
529C22×D4—114no—
530C22×D4—224no—
531C22×D4—224no—
532C22×D4—224no—
533C22×D4—442no—
534C22×D4—442no—
535C22×D4—442no—
536C22×D4—442no—
537C22×D4—442no—
538C22×D4—442no—
539C22×D4—442no—
540C22×D4—442no—
541C22×D4—442no—
542C22×D4—442no—
543C22×D4—442no—
544C22×D4—442no—
545C22×D4C22×D1114yes—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—114no—
553C23×C4—442no—
554C23×C4—442no—
555C23×C4—442no—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C2×C4⋊C4—42no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—442no—
565C2×C4⋊C4—442no—
566C2×C4⋊C4C22×D1114yes—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
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—442no—
583C2×C22⋊C4—442no—
584C2×C22⋊C4—442no—
585C2×C22⋊C4—442no—
586C2×C22⋊C4—442no—
587C2×C22⋊C4—442no—
588C2×C22⋊C4—442no—
589C2×C22⋊C4—442no—
590C2×C22⋊C4—442no—
591C2×C22⋊C4—442no—
592C2×C22⋊C4—442no—
593C2×C22⋊C4C22×D1114yes—
594C2×C22⋊C4C22×D1114yes—
595C2×C22⋊C4C22×D1114yes—
596C2×C22⋊C4C22×D1114yes—
597#95—114no—
598#95—114no—
599#95—114no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95C22×D1114yes—
607C2×C11—82no—
608C2×C11—82no—
609C2×C11#282518yescomplemented
610C2×C11C2×#53811yescharacteristic
611C2×C11C2×#53811yescharacteristic
612C2×C11C2×#53811yescharacteristic
613C2×C11C2×#56011yescharacteristic
614C2×C11C2×#56011yescharacteristic
615C2×C11C2×#56011yescharacteristic
616C2×C11C2×#56011yescharacteristic
617D11—44no—
618D11—82no—
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—22no—
632C24—22no—
633C24—114no—
634C24—112no—
635C24—112no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24—222no—
647C24—222no—
648C24—222no—
649C24C23×D1112yes—
650C24C23×D1112yes—
651C24C23×D1111yescharacteristic
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—416no—
656C2×D4—228no—
657C2×D4—228no—
658C2×D4—228no—
659C2×D4—444no—
660C2×D4—444no—
661C2×D4—4416no—
662C2×D4—444no—
663C2×D4—444no—
664C2×D4—444no—
665C2×D4—444no—
666C2×D4—444no—
667C2×D4—444no—
668C2×D4—444no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—444no—
672C2×D4—4416no—
673C2×D4—4416no—
674C2×D4—4416no—
675C2×D4—4416no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—112no—
696C22×C4—112no—
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—222no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—444no—
716C22×C4—444no—
717C22×C4—444no—
718C22×C4—4416no—
719C22×C4C23×D1112yes—
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C22×C4C23×D1112yes—
723C22×C4C23×D1112yes—
724C4⋊C4—44no—
725C4⋊C4—444no—
726C4⋊C4—444no—
727C22⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—444no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C22⋊C4—444no—
738C22⋊C4—444no—
739C22⋊C4—444no—
740C22⋊C4—444no—
741C22⋊C4—444no—
742C11C2×#282511yescharacteristic, complemented, Sylow
743C23—22no—
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—22no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—114no—
772C23—228no—
773C23—228no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—228no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—444no—
789C23—444no—
790C23—444no—
791C23—444no—
792C23—444no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23—444no—
797C23—444no—
798C23—444no—
799C23#6703712yes—
800C23#6703712yes—
801C23#6703712yes—
802C23#6703712yes—
803C23#41×D1112yes—
804C23#6704212yes—
805C23#6704212yes—
806C23C24×D1111yescharacteristic
807D4—416no—
808D4—4416no—
809D4—4416no—
810D4—4416no—
811D4—4416no—
812D4—4416no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—4416no—
852C2×C4—444no—
853C2×C4—444no—
854C2×C4—444no—
855C2×C4—444no—
856C2×C4—444no—
857C2×C4—444no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—88no—
873C22—88no—
874C22—224no—
875C22—224no—
876C22—224no—
877C22—442no—
878C22—442no—
879C22—442no—
880C22—442no—
881C22—4416no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—888no—
890C22#1062312614yes—
891C22#1062314414yes—
892C22#1062315114yes—
893C22#1062315114yes—
894C22#1062318814yes—
895C22#1062319714yes—
896C22#1062320914yes—
897C22C2×#6703711yescharacteristic
898C22C2×#6703711yescharacteristic
899C22C2×#6703711yescharacteristic
900C22C2×#6703711yescharacteristic
901C22C2×#41×D1111yescharacteristic
902C22C2×#6704211yescharacteristic
903C22C2×#6704211yescharacteristic
904C4—42no—
905C4—42no—
906C4—42no—
907C4—42no—
908C4—42no—
909C4—442no—
910C4—442no—
911C4—442no—
912C4—442no—
913C4—442no—
914C4—442no—
915C2—82no—
916C2—82no—
917C2—444no—
918C2—882no—
919C2#1307670118yesdirect product factor
920C2C2×#1062314411yescharacteristic
921C2C2×#1062320911yescharacteristic
922C2C2×#1062318811yescharacteristic
923C2C2×#1062315111yescharacteristic
924C2C2×#1062315111yescharacteristic
925C2C2×#1062312611yescharacteristic
926C2C2×#1062319711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2825
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13076701C2direct (N × H)
2. C2×C11⋊#401C2semidirect
3. C2×#10622565C2semidirect
4. C2×#10622606C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622836C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622569C2semidirect
16. C2×C11×#394C2semidirect
42. C11×#394C22semidirect
44. #10622836C22semidirect
45. #10622836C22semidirect
55. #10622607C22semidirect
56. #10622606C22semidirect
57. #10622574C22semidirect
58. #10622573C22semidirect
59. #10622573C22semidirect
60. #10622572C22semidirect
61. #10622569C22semidirect
62. #10622569C22semidirect
63. #10622566C22semidirect
64. #10622565C22semidirect
65. #10622278C22semidirect
66. C11⋊#401C22semidirect
288. C2×#394D11semidirect
443. #394C2×D11semidirect
609. C2×C11#2825semidirect
742. C11C2×#2825semidirect
919. C2#13076701direct (N × H)

Maximal subgroups

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

subgroupindex
#130767012
C2×C11⋊#4012
C2×#106225652
C2×#106226062
C2×#106225662
C2×#106226072
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106222782
C2×#106225692
C2×C11×#3942
C2×#282511