Finite Group Databasebeta

← C2×#13076744 #14960098

Subgroups — C2×#13076744 #14960098

Order 2816.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076744C2116yesmaximal, direct product factor
2C2×#10622562C211yesmaximal, characteristic, complemented
3C2×#10622597C211yesmaximal, characteristic, complemented
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622572C211yesmaximal, characteristic, complemented
12C2×#10622835C211yesmaximal, characteristic, complemented
13C2×#10622836C211yesmaximal, characteristic
14C2×#10622553C211yesmaximal, characteristic, complemented
15C2×#10622546C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C11×#390C2218yescomplemented
45#10622836C2218yes—
46#10622835C2218yescomplemented
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#10622597C2218yescomplemented
57#10622574C2218yescomplemented
58#10622572C2218yescomplemented
59#10622572C2218yescomplemented
60#10622572C2218yescomplemented
61#10622566C2218yescomplemented
62#10622565C2218yescomplemented
63#10622562C2218yescomplemented
64#10622561C2218yescomplemented
65#10622553C2218yescomplemented
66#10622546C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C22×D4×C11—24no—
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—42no—
80C22×C22⋊D11—42no—
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
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C22⋊C4—42no—
97C2×C11×C22⋊C4—42no—
98C2×C11×C22⋊C4—42no—
99C2×C11×C22⋊C4—42no—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C42×C11—42no—
105C2×C42×C11C2314yes—
106C2×C22⋊Dic11—42no—
107C2×C22⋊Dic11—42no—
108C2×C22⋊Dic11—42no—
109C2×C22⋊Dic11—42no—
110C2×C22⋊Dic11—42no—
111C2×C22⋊Dic11—42no—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2314yes—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4C2314yes—
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—24no—
133C2×Dic11⋊C4—42no—
134C2×Dic11⋊C4—42no—
135C2×Dic11⋊C4—42no—
136C2×Dic11⋊C4—42no—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2829—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—22no—
175C23×D11C2412yes—
176C2×D4×C11—28no—
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#4114yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—44no—
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—
236C11×C4⋊C4—44no—
237C11×C22⋊C4—44no—
238C11×C22⋊C4—44no—
239C11×C22⋊C4—44no—
240C11×C22⋊C4—44no—
241C42×C11—44no—
242C22⋊Dic11—44no—
243C22⋊Dic11—44no—
244C22⋊Dic11—44no—
245C22⋊Dic11—44no—
246C22⋊Dic11—44no—
247C22⋊Dic11—44no—
248(C2×D11)⋊C4—28no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4—44no—
253C4⋊Dic11—44no—
254C4⋊Dic11—44no—
255Dic11⋊C4—28no—
256Dic11⋊C4—44no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259Dic11⋊C4—44no—
260#2829—1116no—
261C2×#399—111no—
262C2×#398—111no—
263C2×#397—111no—
264C2×#397—111no—
265C2×#396—111no—
266C2×#396—111no—
267C2×#394—111no—
268C2×#394—111no—
269C2×#394—111no—
270C2×#394—111no—
271C2×#394—111no—
272C2×#392—111no—
273C2×#390D1111yescharacteristic, complemented
274C2×#388—111no—
275C2×#387—111no—
276C23×C11—22no—
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—44no—
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×C11C2×#4112yes—
305C23×C11H(5,𝔽2)12yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C11H(5,𝔽2)12yes—
310C23×C112−1+412yes—
311C23×C11C2511yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—44no—
320C22×D11—44no—
321C22×D11—44no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326D4×C11—416no—
327C2×C4×C11—28no—
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—44no—
343C2×C4×C11—44no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11C2×#4114yes—
347C22⋊D11—416no—
348C22⋊D11—416no—
349C2×Dic11—22no—
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—44no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11—44no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C23×D4—111no—
378C23×D4—111no—
379C23×D4C2×D1111yescharacteristic
380C22×C4⋊C4—111no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4—111no—
389C22×C22⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
400C22×C22⋊C4C2×D1111yescharacteristic
401C22×C22⋊C4C2×D1111yescharacteristic
402C22×C22⋊C4C2×D1111yescharacteristic
403C22×C42C2×D1111yescharacteristic
404#399—118no—
405#398—118no—
406#397—118no—
407#397—118no—
408#396—118no—
409#396—118no—
410#394—118no—
411#394—118no—
412#394—118no—
413#394—118no—
414#394—118no—
415#392—118no—
416#390C2×D1118yescomplemented
417#388—118no—
418#387—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—
427C22×C11—42no—
428C22×C11—42no—
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—88no—
442C22×C11—88no—
443C22×C11#53814yes—
444C22×C11#54014yes—
445C22×C11#54214yes—
446C22×C11#56014yes—
447C22×C11#56014yes—
448C22×C11#56214yes—
449C22×C11#56214yes—
450C22×C11C22×#4111yescharacteristic
451C22×C11C2×H(5,𝔽2)11yescharacteristic
452C22×C11C2×H(5,𝔽2)11yescharacteristic
453C22×C11C2×H(5,𝔽2)11yescharacteristic
454C22×C11C2×H(5,𝔽2)11yescharacteristic
455C22×C11C2×H(5,𝔽2)11yescharacteristic
456C22×C11C2×2−1+411yescharacteristic
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—88no—
465C4×C11—24no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477C25—111no—
478C25C22×D1111yescharacteristic
479C25C22×D1111yescharacteristic
480C22×D4—24no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—114no—
484C22×D4—114no—
485C22×D4—442no—
486C22×D4—442no—
487C22×D4—442no—
488C22×D4—442no—
489C22×D4—442no—
490C22×D4—442no—
491C22×D4C22×D1114yes—
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4C22×D1111yescharacteristic
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C23×C4C22×D1111yescharacteristic
503C23×C4C22×D1111yescharacteristic
504C2×C4⋊C4—42no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—224no—
513C2×C4⋊C4—442no—
514C2×C4⋊C4—442no—
515C2×C4⋊C4—442no—
516C2×C4⋊C4—442no—
517C2×C4⋊C4—442no—
518C2×C4⋊C4—442no—
519C2×C4⋊C4C22×D1114yes—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
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—224no—
536C2×C22⋊C4—442no—
537C2×C22⋊C4—442no—
538C2×C22⋊C4—442no—
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⋊C4C22×D1114yes—
547C2×C22⋊C4C22×D1114yes—
548C2×C22⋊C4C22×D1114yes—
549C2×C22⋊C4C22×D1114yes—
550C2×C42—42no—
551C2×C42C22×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—
560C2×C11—82no—
561C2×C11—82no—
562C2×C11#282918yescomplemented
563C2×C11C2×#53811yescharacteristic
564C2×C11C2×#54011yescharacteristic
565C2×C11C2×#54211yescharacteristic
566C2×C11C2×#56011yescharacteristic
567C2×C11C2×#56011yescharacteristic
568C2×C11C2×#56211yescharacteristic
569C2×C11C2×#56211yescharacteristic
570D11—82no—
571C24—22no—
572C24—22no—
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—112no—
586C24—222no—
587C24—222no—
588C24—222no—
589C24—222no—
590C24—222no—
591C24—222no—
592C24—222no—
593C24C23×D1112yes—
594C24C23×D1112yes—
595C24C23×D1111yescharacteristic
596C2×D4—28no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—416no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4—444no—
603C2×D4—444no—
604C2×D4—444no—
605C2×D4—444no—
606C2×D4—4416no—
607C2×D4—4416no—
608C22×C4—22no—
609C22×C4—22no—
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—112no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
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#433914yes—
651C22×C4C23×D1112yes—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C4⋊C4—44no—
657C4⋊C4—228no—
658C4⋊C4—444no—
659C4⋊C4—444no—
660C4⋊C4—444no—
661C4⋊C4—444no—
662C4⋊C4—444no—
663C4⋊C4—444no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—228no—
669C22⋊C4—444no—
670C22⋊C4—444no—
671C22⋊C4—444no—
672C22⋊C4—444no—
673C22⋊C4—444no—
674C22⋊C4—444no—
675C22⋊C4—444no—
676C22⋊C4—444no—
677C22⋊C4—444no—
678C22⋊C4—444no—
679C42—44no—
680C11C2×#282911yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—444no—
717C23—444no—
718C23—444no—
719C23—444no—
720C23—444no—
721C23—444no—
722C23—444no—
723C23C2×#433912yes—
724C23#6703712yes—
725C23#6703712yes—
726C23#6703712yes—
727C23#6703712yes—
728C23#6704212yes—
729C23#6704312yes—
730C23C24×D1111yescharacteristic
731D4—416no—
732D4—4416no—
733D4—4416no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
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—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
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—444no—
775C2×C4—444no—
776C2×C4—444no—
777C2×C4—444no—
778C2×C4—444no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4C2×#433914yes—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—88no—
797C22—88no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—888no—
806C22#1062302514yes—
807C22#1062309214yes—
808C22#1062309314yes—
809C22#1062315114yes—
810C22#1062315214yes—
811C22#1062321514yes—
812C22#1062325114yes—
813C22C22×#433911yescharacteristic
814C22C2×#6703711yescharacteristic
815C22C2×#6703711yescharacteristic
816C22C2×#6703711yescharacteristic
817C22C2×#6703711yescharacteristic
818C22C2×#6704211yescharacteristic
819C22C2×#6704311yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4—442no—
829C4—442no—
830C4—442no—
831C4—442no—
832C2—82no—
833C2—82no—
834C2—882no—
835C2#1307674418yesdirect product factor
836C2C2×#1062302511yescharacteristic
837C2C2×#1062309311yescharacteristic
838C2C2×#1062309211yescharacteristic
839C2C2×#1062325111yescharacteristic
840C2C2×#1062315111yescharacteristic
841C2C2×#1062321511yescharacteristic
842C2C2×#1062315211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#390D11
hypocenterC11C2×#2829
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. #13076744C2direct (N × H)
2. C2×#10622562C2semidirect
3. C2×#10622597C2semidirect
4. C2×#10622565C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622572C2semidirect
12. C2×#10622835C2semidirect
14. C2×#10622553C2semidirect
15. C2×#10622546C2semidirect
16. C2×C11×#390C2semidirect
44. C11×#390C22semidirect
46. #10622835C22semidirect
55. #10622607C22semidirect
56. #10622597C22semidirect
57. #10622574C22semidirect
58. #10622572C22semidirect
59. #10622572C22semidirect
60. #10622572C22semidirect
61. #10622566C22semidirect
62. #10622565C22semidirect
63. #10622562C22semidirect
64. #10622561C22semidirect
65. #10622553C22semidirect
66. #10622546C22semidirect
273. C2×#390D11semidirect
416. #390C2×D11semidirect
562. C2×C11#2829semidirect
680. C11C2×#2829semidirect
835. C2#13076744direct (N × H)

Maximal subgroups

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

subgroupindex
#130767442
C2×#106225622
C2×#106225972
C2×#106225652
C2×#106225662
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225532
C2×#106225462
C2×C11×#3902
C2×#282911