Finite Group Databasebeta

← C2×#13076712 #14959976

Subgroups — C2×#13076712 #14959976

Order 2816.

2542 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076712C2116yesmaximal, direct product factor
2C2×#10622271C211yesmaximal, characteristic, complemented
3C2×#10622599C211yesmaximal, characteristic, complemented
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622561C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622835C211yesmaximal, characteristic, complemented
12C2×#10622836C211yesmaximal, characteristic
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622281C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C11×#394C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44#10622836C2218yes—
45#10622835C2218yescomplemented
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#10622605C2218yescomplemented
56#10622599C2218yescomplemented
57#10622574C2218yescomplemented
58#10622572C2218yescomplemented
59#10622569C2218yescomplemented
60#10622569C2218yescomplemented
61#10622566C2218yescomplemented
62#10622565C2218yescomplemented
63#10622561C2218yescomplemented
64#10622561C2218yescomplemented
65#10622281C2218yescomplemented
66#10622271C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C22×D4×C11—42no—
71C22×D4×C11—42no—
72C22×D4×C11—42no—
73C22×D4×C11C2314yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11C2314yes—
86C22×C22⋊D11C2314yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×C4×D11—42no—
95C22×C4×D11—42no—
96C22×C4×D11—42no—
97C22×C4×D11C2314yes—
98C2×C11×C4⋊C4—42no—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C22⋊C4—42no—
101C2×C11×C22⋊C4—42no—
102C2×C11×C22⋊C4—42no—
103C2×C11×C22⋊C4—42no—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C22⋊Dic11—42no—
109C2×C22⋊Dic11—42no—
110C2×C22⋊Dic11—42no—
111C2×C22⋊Dic11—42no—
112C2×C22⋊Dic11—42no—
113C2×C22⋊Dic11—42no—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×C4⋊Dic11—42no—
129C2×C4⋊Dic11—42no—
130C2×C4⋊Dic11C2314yes—
131C2×C4⋊Dic11C2314yes—
132C2×Dic11⋊C4—42no—
133C2×Dic11⋊C4—42no—
134C2×Dic11⋊C4—42no—
135C2×Dic11⋊C4—42no—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C11×#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2826—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
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×C11C2412yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11#4114yes—
175C23×D11C2412yes—
176C2×D4×C11—44no—
177C2×D4×C11—44no—
178C2×D4×C11—44no—
179C2×D4×C11—416no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C2×C22⋊D11—28no—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—44no—
206C2×C22⋊D11—416no—
207C2×C22⋊D11—416no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C2×C4×D11—44no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C2×C4×D11—416no—
240C11×C4⋊C4—44no—
241C11×C22⋊C4—44no—
242C11×C22⋊C4—44no—
243C11×C22⋊C4—44no—
244C11×C22⋊C4—44no—
245C22⋊Dic11—44no—
246C22⋊Dic11—44no—
247C22⋊Dic11—44no—
248C22⋊Dic11—44no—
249C22⋊Dic11—44no—
250C22⋊Dic11—44no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255C4⋊Dic11—44no—
256C4⋊Dic11—44no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259Dic11⋊C4—44no—
260Dic11⋊C4—44no—
261#2826—1116no—
262C2×#400—111no—
263C2×#400—111no—
264C2×#399—111no—
265C2×#397—111no—
266C2×#397—111no—
267C2×#396—111no—
268C2×#396—111no—
269C2×#394—111no—
270C2×#394—111no—
271C2×#394—111no—
272C2×#394D1111yescharacteristic, complemented
273C2×#392—111no—
274C2×#386—111no—
275C2×#386—111no—
276C2×#385—111no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11C2×#4112yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C11H(5,𝔽2)12yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C112−1+412yes—
312C23×C11C2511yescharacteristic
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11C2×#4114yes—
327D4×C11—416no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—44no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—44no—
348C22⋊D11—416no—
349C22⋊D11—416no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11—44no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C2×Dic11—44no—
378C4×D11—416no—
379C23×D4—111no—
380C23×D4—111no—
381C23×D4C2×D1111yescharacteristic
382C24×C4—111no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4C2×D1111yescharacteristic
390C22×C22⋊C4—111no—
391C22×C22⋊C4—111no—
392C22×C22⋊C4—111no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—111no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4C2×D1111yescharacteristic
401C22×C22⋊C4C2×D1111yescharacteristic
402C22×C22⋊C4C2×D1111yescharacteristic
403C22×C22⋊C4C2×D1111yescharacteristic
404#400—118no—
405#400—118no—
406#399—118no—
407#397—118no—
408#397—118no—
409#396—118no—
410#396—118no—
411#394—118no—
412#394—118no—
413#394—118no—
414#394C2×D1118yescomplemented
415#392—118no—
416#386—118no—
417#386—118no—
418#385—118no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95—111no—
427C2×#95—111no—
428C2×#95C2×D1111yescharacteristic
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—88no—
444C22×C11—88no—
445C22×C11#53814yes—
446C22×C11#53814yes—
447C22×C11#53914yes—
448C22×C11#56014yes—
449C22×C11#56014yes—
450C22×C11#56214yes—
451C22×C11#56214yes—
452C22×C11C22×#4111yescharacteristic
453C22×C11C2×H(5,𝔽2)11yescharacteristic
454C22×C11C2×H(5,𝔽2)11yescharacteristic
455C22×C11C2×H(5,𝔽2)11yescharacteristic
456C22×C11C2×H(5,𝔽2)11yescharacteristic
457C22×C11C2×H(5,𝔽2)11yescharacteristic
458C22×C11C2×2−1+411yescharacteristic
459C2×D11—24no—
460C2×D11—24no—
461C2×D11—24no—
462C2×D11—416no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479C25—111no—
480C25C22×D1111yescharacteristic
481C25C22×D1111yescharacteristic
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4—114no—
486C22×D4—114no—
487C22×D4—224no—
488C22×D4—224no—
489C22×D4—442no—
490C22×D4—442no—
491C22×D4—442no—
492C22×D4—442no—
493C22×D4C22×D1114yes—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—114no—
502C23×C4—442no—
503C23×C4—442no—
504C23×C4—442no—
505C23×C4C22×D1111yescharacteristic
506C23×C4C22×D1111yescharacteristic
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C2×C4⋊C4—42no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—442no—
518C2×C4⋊C4—442no—
519C2×C4⋊C4—442no—
520C2×C4⋊C4—442no—
521C2×C4⋊C4—442no—
522C2×C4⋊C4—442no—
523C2×C4⋊C4C22×D1114yes—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—224no—
539C2×C22⋊C4—442no—
540C2×C22⋊C4—442no—
541C2×C22⋊C4—442no—
542C2×C22⋊C4—442no—
543C2×C22⋊C4—442no—
544C2×C22⋊C4—442no—
545C2×C22⋊C4—442no—
546C2×C22⋊C4—442no—
547C2×C22⋊C4—442no—
548C2×C22⋊C4C22×D1114yes—
549C2×C22⋊C4C22×D1114yes—
550C2×C22⋊C4C22×D1114yes—
551C2×C22⋊C4C22×D1114yes—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95C22×D1114yes—
562C2×C11—82no—
563C2×C11—82no—
564C2×C11#282618yescomplemented
565C2×C11C2×#53811yescharacteristic
566C2×C11C2×#53811yescharacteristic
567C2×C11C2×#53911yescharacteristic
568C2×C11C2×#56011yescharacteristic
569C2×C11C2×#56011yescharacteristic
570C2×C11C2×#56211yescharacteristic
571C2×C11C2×#56211yescharacteristic
572D11—44no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—114no—
588C24—112no—
589C24—222no—
590C24—222no—
591C24—222no—
592C24—222no—
593C24—222no—
594C24—222no—
595C24C23×D1112yes—
596C24C23×D1112yes—
597C24C23×D1111yescharacteristic
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—416no—
602C2×D4—228no—
603C2×D4—228no—
604C2×D4—444no—
605C2×D4—444no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4—4416no—
609C2×D4—4416no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—444no—
654C22×C4—444no—
655C22×C4—444no—
656C22×C4—4416no—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C22×C4C23×D1112yes—
661C22×C4C23×D1112yes—
662C4⋊C4—44no—
663C4⋊C4—444no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C4⋊C4—444no—
667C4⋊C4—444no—
668C4⋊C4—444no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—228no—
674C22⋊C4—444no—
675C22⋊C4—444no—
676C22⋊C4—444no—
677C22⋊C4—444no—
678C22⋊C4—444no—
679C22⋊C4—444no—
680C22⋊C4—444no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C11C2×#282611yescharacteristic, complemented, Sylow
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—114no—
713C23—228no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—228no—
719C23—222no—
720C23—222no—
721C23—228no—
722C23—444no—
723C23—444no—
724C23—444no—
725C23—444no—
726C23#6703712yes—
727C23#6703712yes—
728C23#6703712yes—
729C23#6703712yes—
730C23#41×D1112yes—
731C23#6704212yes—
732C23#6704312yes—
733C23C24×D1111yescharacteristic
734D4—416no—
735D4—4416no—
736D4—4416no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—4416no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4—444no—
782C2×C4—444no—
783C2×C4—444no—
784C2×C4—444no—
785C2×C4—444no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—88no—
801C22—88no—
802C22—224no—
803C22—224no—
804C22—224no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—4416no—
810C22#1062312614yes—
811C22#1062314414yes—
812C22#1062315114yes—
813C22#1062315214yes—
814C22#1062319114yes—
815C22#1062319814yes—
816C22#1062320914yes—
817C22C2×#6703711yescharacteristic
818C22C2×#6703711yescharacteristic
819C22C2×#6703711yescharacteristic
820C22C2×#6703711yescharacteristic
821C22C2×#41×D1111yescharacteristic
822C22C2×#6704211yescharacteristic
823C22C2×#6704311yescharacteristic
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—442no—
830C4—442no—
831C4—442no—
832C4—442no—
833C4—442no—
834C4—442no—
835C4—442no—
836C2—82no—
837C2—82no—
838C2—444no—
839C2#1307671218yesdirect product factor
840C2C2×#1062314411yescharacteristic
841C2C2×#1062320911yescharacteristic
842C2C2×#1062319111yescharacteristic
843C2C2×#1062315111yescharacteristic
844C2C2×#1062312611yescharacteristic
845C2C2×#1062315211yescharacteristic
846C2C2×#1062319811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#394D11
hypocenterC11C2×#2826
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13076712C2direct (N × H)
2. C2×#10622271C2semidirect
3. C2×#10622599C2semidirect
4. C2×#10622605C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622561C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622835C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622281C2semidirect
16. C2×C11×#394C2semidirect
42. C11×#394C22semidirect
45. #10622835C22semidirect
55. #10622605C22semidirect
56. #10622599C22semidirect
57. #10622574C22semidirect
58. #10622572C22semidirect
59. #10622569C22semidirect
60. #10622569C22semidirect
61. #10622566C22semidirect
62. #10622565C22semidirect
63. #10622561C22semidirect
64. #10622561C22semidirect
65. #10622281C22semidirect
66. #10622271C22semidirect
272. C2×#394D11semidirect
414. #394C2×D11semidirect
564. C2×C11#2826semidirect
683. C11C2×#2826semidirect
839. C2#13076712direct (N × H)

Maximal subgroups

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

subgroupindex
#130767122
C2×#106222712
C2×#106225992
C2×#106226052
C2×#106225652
C2×#106225662
C2×#106225612
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225692
C2×#106222812
C2×C11×#3942
C2×#282611