Finite Group Databasebeta

← C2×#13076704 #14960083

Subgroups — C2×#13076704 #14960083

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#13076704C2116yesmaximal, direct product factor
2C2×C11⋊#401C211yesmaximal, characteristic, complemented
3C2×#10622288C211yesmaximal, characteristic, complemented
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622836C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622833C211yesmaximal, characteristic, complemented
15C2×#10622571C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
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
42C11×#392C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44#10622836C2218yescomplemented
45#10622836C2218yescomplemented
46#10622836C2218yescomplemented
47#10622835C2218yescomplemented
48#10622833C2218yescomplemented
49#10622833C2218yescomplemented
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622574C2218yescomplemented
60#10622572C2218yescomplemented
61#10622571C2218yescomplemented
62#10622566C2218yescomplemented
63#10622565C2218yescomplemented
64#10622561C2218yescomplemented
65#10622288C2218yescomplemented
66C11⋊#401C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C22×D4×C11—24no—
72C22×D4×C11—24no—
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11—42no—
76C22×D4×C11—42no—
77C22×D4×C11—42no—
78C22×D4×C11—42no—
79C22×D4×C11—42no—
80C22×D4×C11C2314yes—
81C22×D4×C11C2314yes—
82C22×D4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C23×Dic11—42no—
100C23×Dic11—42no—
101C23×Dic11—42no—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2314yes—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C22⋊Dic11—42no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11—42no—
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×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4—42no—
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—42no—
143C2×Dic11⋊C4—42no—
144C2×Dic11⋊C4C2314yes—
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×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11#4114yes—
178C24×C11C2412yes—
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×D11C2412yes—
190C2×D4×C11—28no—
191C2×D4×C11—28no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—44no—
199C2×D4×C11—416no—
200C2×D4×C11—416no—
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×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C2×C22⋊D11—28no—
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—44no—
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×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—44no—
252C22×Dic11—44no—
253C22×Dic11—44no—
254C22×Dic11—416no—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C11×C22⋊C4—44no—
263C11×C22⋊C4—44no—
264C11×C22⋊C4—44no—
265C22⋊Dic11—44no—
266C22⋊Dic11—44no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270C22⋊Dic11—44no—
271C22⋊Dic11—44no—
272C22⋊Dic11—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276(C2×D11)⋊C4—44no—
277C4⋊Dic11—44no—
278Dic11⋊C4—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×#394—111no—
289C2×#392—111no—
290C2×#392—111no—
291C2×#392—111no—
292C2×#392D1111yescharacteristic, complemented
293C2×#386—111no—
294C2×#386—111no—
295C2×#386—111no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—28no—
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—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—44no—
320C23×C11—44no—
321C23×C11—44no—
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×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11C2×#4114yes—
338C23×C11C2×#4112yes—
339C23×C11H(5,𝔽2)12yes—
340C23×C11H(5,𝔽2)12yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11H(5,𝔽2)12yes—
344C23×C11H(5,𝔽2)12yes—
345C23×C11C2511yescharacteristic
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—44no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11—44no—
360D4×C11—416no—
361D4×C11—416no—
362D4×C11—416no—
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—44no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—44no—
379C22⋊D11—416no—
380C22⋊D11—416no—
381C22⋊D11—416no—
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—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—416no—
404C2×Dic11—44no—
405C2×Dic11—44no—
406C2×Dic11—44no—
407C2×Dic11—44no—
408C2×Dic11—44no—
409C2×Dic11—44no—
410C2×Dic11—44no—
411C23×D4—111no—
412C23×D4—111no—
413C23×D4—111no—
414C23×D4C2×D1111yescharacteristic
415C23×D4C2×D1111yescharacteristic
416C23×D4C2×D1111yescharacteristic
417C24×C4—111no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
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⋊C4—111no—
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#394—118no—
444#392—118no—
445#392—118no—
446#392—118no—
447#392C2×D1118yescomplemented
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—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—416no—
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—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—88no—
484C22×C11—88no—
485C22×C11#53814yes—
486C22×C11#53814yes—
487C22×C11#53814yes—
488C22×C11#56014yes—
489C22×C11#56014yes—
490C22×C11#56014yes—
491C22×C11#56014yes—
492C22×C11C22×#4111yescharacteristic
493C22×C11C2×H(5,𝔽2)11yescharacteristic
494C22×C11C2×H(5,𝔽2)11yescharacteristic
495C22×C11C2×H(5,𝔽2)11yescharacteristic
496C22×C11C2×H(5,𝔽2)11yescharacteristic
497C22×C11C2×H(5,𝔽2)11yescharacteristic
498C22×C11C2×H(5,𝔽2)11yescharacteristic
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—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517Dic11—42no—
518C25—111no—
519C25C22×D1111yescharacteristic
520C25C22×D1111yescharacteristic
521C25C22×D1111yescharacteristic
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—42no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4—42no—
528C22×D4—42no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4—114no—
532C22×D4—114no—
533C22×D4—114no—
534C22×D4—224no—
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×D4C22×D1114yes—
544C22×D4C22×D1114yes—
545C22×D4C22×D1114yes—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—114no—
554C23×C4—442no—
555C23×C4—442no—
556C23×C4—442no—
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C2×C4⋊C4—114no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—442no—
565C2×C4⋊C4—442no—
566C2×C4⋊C4—442no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—114no—
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⋊C4—442no—
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—44no—
608C2×C11—82no—
609C2×C11—82no—
610C2×C11#282518yescomplemented
611C2×C11C2×#53811yescharacteristic
612C2×C11C2×#53811yescharacteristic
613C2×C11C2×#53811yescharacteristic
614C2×C11C2×#56011yescharacteristic
615C2×C11C2×#56011yescharacteristic
616C2×C11C2×#56011yescharacteristic
617C2×C11C2×#56011yescharacteristic
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—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—112no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24—222no—
647C24#434114yes—
648C24C23×D1112yes—
649C24C23×D1112yes—
650C24C23×D1112yes—
651C24C23×D1111yescharacteristic
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—44no—
660C2×D4—44no—
661C2×D4—416no—
662C2×D4—416no—
663C2×D4—416no—
664C2×D4—228no—
665C2×D4—444no—
666C2×D4—444no—
667C2×D4—444no—
668C2×D4—444no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—444no—
672C2×D4—444no—
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—112no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
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—222no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—222no—
716C22×C4—444no—
717C22×C4—444no—
718C22×C4—444no—
719C22×C4—4416no—
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C22×C4C23×D1112yes—
723C22×C4C23×D1112yes—
724C4⋊C4—444no—
725C4⋊C4—444no—
726C4⋊C4—444no—
727C22⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—444no—
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—28no—
744C23—28no—
745C23—28no—
746C23—22no—
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—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—444no—
792C23—444no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23—444no—
797C23—444no—
798C23C2×#434114yes—
799C23C2×#434112yes—
800C23#6703712yes—
801C23#6703712yes—
802C23#6703712yes—
803C23#6703712yes—
804C23#6703712yes—
805C23#6704212yes—
806C23C24×D1111yescharacteristic
807D4—416no—
808D4—416no—
809D4—416no—
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—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
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—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—4416no—
851C2×C4—444no—
852C2×C4—444no—
853C2×C4—444no—
854C2×C4—444no—
855C2×C4—444no—
856C2×C4—444no—
857C2×C4—444no—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—416no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—88no—
881C22—88no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—888no—
890C22#1062312414yes—
891C22#1062312414yes—
892C22#1062312614yes—
893C22#1062314814yes—
894C22#1062315114yes—
895C22#1062315114yes—
896C22#1062325114yes—
897C22C22×#434111yescharacteristic
898C22C2×#6703711yescharacteristic
899C22C2×#6703711yescharacteristic
900C22C2×#6703711yescharacteristic
901C22C2×#6703711yescharacteristic
902C22C2×#6703711yescharacteristic
903C22C2×#6704211yescharacteristic
904C4—42no—
905C4—42no—
906C4—42no—
907C4—42no—
908C4—442no—
909C4—442no—
910C4—442no—
911C4—442no—
912C4—442no—
913C4—442no—
914C4—442no—
915C2—44no—
916C2—82no—
917C2—82no—
918C2—882no—
919C2#1307670418yesdirect product factor
920C2C2×#1062312411yescharacteristic
921C2C2×#1062312411yescharacteristic
922C2C2×#1062314811yescharacteristic
923C2C2×#1062325111yescharacteristic
924C2C2×#1062315111yescharacteristic
925C2C2×#1062315111yescharacteristic
926C2C2×#1062312611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2825
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13076704C2direct (N × H)
2. C2×C11⋊#401C2semidirect
3. C2×#10622288C2semidirect
4. C2×#10622565C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622836C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622833C2semidirect
15. C2×#10622571C2semidirect
16. C2×C11×#392C2semidirect
42. C11×#392C22semidirect
44. #10622836C22semidirect
45. #10622836C22semidirect
46. #10622836C22semidirect
47. #10622835C22semidirect
48. #10622833C22semidirect
49. #10622833C22semidirect
59. #10622574C22semidirect
60. #10622572C22semidirect
61. #10622571C22semidirect
62. #10622566C22semidirect
63. #10622565C22semidirect
64. #10622561C22semidirect
65. #10622288C22semidirect
66. C11⋊#401C22semidirect
292. C2×#392D11semidirect
447. #392C2×D11semidirect
610. C2×C11#2825semidirect
742. C11C2×#2825semidirect
919. C2#13076704direct (N × H)

Maximal subgroups

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

subgroupindex
#130767042
C2×C11⋊#4012
C2×#106222882
C2×#106225652
C2×#106225662
C2×#106225612
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106228332
C2×#106225712
C2×C11×#3922
C2×#282511