Finite Group Databasebeta

← C2×#13076742 #14960096

Subgroups — C2×#13076742 #14960096

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#13076742C2116yesmaximal, direct product factor
2C2×#10622605C211yesmaximal, characteristic, complemented
3C2×#10622274C211yesmaximal, characteristic, complemented
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622574C211yesmaximal, characteristic, complemented
11C2×#10622572C211yesmaximal, characteristic, complemented
12C2×#10622572C211yesmaximal, characteristic, complemented
13C2×#10622573C211yesmaximal, characteristic
14C2×#10622552C211yesmaximal, characteristic, complemented
15C2×#10622546C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C11×#388C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622607C2218yescomplemented
54#10622605C2218yescomplemented
55#10622574C2218yescomplemented
56#10622574C2218yescomplemented
57#10622573C2218yes—
58#10622572C2218yescomplemented
59#10622572C2218yescomplemented
60#10622561C2218yescomplemented
61#10622552C2218yescomplemented
62#10622546C2218yescomplemented
63#10622288C2218yescomplemented
64#10622287C2218yescomplemented
65#10622285C2218yescomplemented
66#10622274C2218yescomplemented
67C25×C11C2311yescharacteristic
68C24×D11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—42no—
77C22×C22⋊D11—42no—
78C22×C22⋊D11—42no—
79C22×C22⋊D11—42no—
80C22×C22⋊D11—42no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11C2314yes—
83C22×C22⋊D11C2314yes—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×D44—24no—
91C22×D44—42no—
92C22×D44—42no—
93C22×D44C2314yes—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4—42no—
98C2×C11×C22⋊C4—42no—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C42×C11—42no—
103C2×C42×C11C2314yes—
104C2×C22⋊Dic11—42no—
105C2×C22⋊Dic11—42no—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×(C2×D11)⋊C4—42no—
109C2×(C2×D11)⋊C4—42no—
110C2×(C2×D11)⋊C4—42no—
111C2×(C2×D11)⋊C4—42no—
112C2×(C2×D11)⋊C4—42no—
113C2×(C2×D11)⋊C4—42no—
114C2×(C2×D11)⋊C4—42no—
115C2×(C2×D11)⋊C4—42no—
116C2×(C2×D11)⋊C4—42no—
117C2×(C2×D11)⋊C4—42no—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
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⋊Dic11—42no—
131C2×C4⋊Dic11C2314yes—
132C2×C4⋊Dic11C2314yes—
133C2×C4⋊Dic11C2314yes—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—42no—
136C2×Dic11⋊C4—42no—
137C2×Dic11⋊C4—42no—
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×C11C2412yes—
159C24×C11C2411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11C2412yes—
175C23×D11C2412yes—
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—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#4114yes—
194C22×C4×C11C2412yes—
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×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C2×D44—28no—
233C2×D44—44no—
234C2×D44—44no—
235C2×D44—416no—
236C11×C4⋊C4—44no—
237C11×C22⋊C4—28no—
238C11×C22⋊C4—44no—
239C11×C22⋊C4—44no—
240C42×C11—44no—
241C22⋊Dic11—44no—
242C22⋊Dic11—44no—
243(C2×D11)⋊C4—44no—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
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—
255C4⋊Dic11—44no—
256Dic11⋊C4—28no—
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×#390—111no—
274C2×#388D1111yescharacteristic, complemented
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—44no—
284C23×C11—44no—
285C23×C11—44no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11C2×#4112yes—
291C23×C11H(5,𝔽2)12yes—
292C23×C11H(5,𝔽2)12yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C11H(5,𝔽2)12yes—
295C23×C11H(5,𝔽2)12yes—
296C23×C112−1+412yes—
297C23×C11C2511yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—44no—
313C22×D11—44no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—44no—
317C22×D11—44no—
318C22×D11—44no—
319C22×D11—44no—
320C22×D11—44no—
321C22×D11—44no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326C2×C4×C11—28no—
327C2×C4×C11—22no—
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—22no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—44no—
348C2×C4×C11—44no—
349C2×C4×C11C2×#4114yes—
350C22⋊D11—416no—
351C22⋊D11—416no—
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—
376D44—416no—
377C23×D4—111no—
378C23×D4—111no—
379C23×D4—111no—
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⋊C4—111no—
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#390—118no—
417#388C2×D1118yescomplemented
418#387—118no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95C2×D1111yescharacteristic
426C2×#95C2×D1111yescharacteristic
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—88no—
435C22×C11#53814yes—
436C22×C11#54014yes—
437C22×C11#54214yes—
438C22×C11#56014yes—
439C22×C11#56014yes—
440C22×C11#56214yes—
441C22×C11#56214yes—
442C22×C11C22×#4111yescharacteristic
443C22×C11C2×H(5,𝔽2)11yescharacteristic
444C22×C11C2×H(5,𝔽2)11yescharacteristic
445C22×C11C2×H(5,𝔽2)11yescharacteristic
446C22×C11C2×H(5,𝔽2)11yescharacteristic
447C22×C11C2×H(5,𝔽2)11yescharacteristic
448C22×C11C2×2−1+411yescharacteristic
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—88no—
464C2×D11—88no—
465C4×C11—24no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477C25—111no—
478C25—111no—
479C25C22×D1111yescharacteristic
480C22×D4—114no—
481C22×D4—114no—
482C22×D4—114no—
483C22×D4—224no—
484C22×D4—442no—
485C22×D4—442no—
486C22×D4—442no—
487C22×D4—442no—
488C22×D4—442no—
489C22×D4—442no—
490C22×D4—442no—
491C22×D4—442no—
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4C22×D1111yescharacteristic
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—24no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—114no—
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—442no—
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⋊C4—442no—
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#95C22×D1114yes—
559#95C22×D1114yes—
560C2×C11—82no—
561C2×C11#282918yescomplemented
562C2×C11C2×#53811yescharacteristic
563C2×C11C2×#54011yescharacteristic
564C2×C11C2×#54211yescharacteristic
565C2×C11C2×#56011yescharacteristic
566C2×C11C2×#56011yescharacteristic
567C2×C11C2×#56211yescharacteristic
568C2×C11C2×#56211yescharacteristic
569D11—82no—
570D11—82no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—112no—
579C24—112no—
580C24—222no—
581C24—222no—
582C24—222no—
583C24—222no—
584C24—222no—
585C24—222no—
586C24—222no—
587C24—222no—
588C24—222no—
589C24—222no—
590C24—222no—
591C24—222no—
592C24—222no—
593C24—222no—
594C24C23×D1112yes—
595C24C23×D1111yescharacteristic
596C2×D4—228no—
597C2×D4—444no—
598C2×D4—444no—
599C2×D4—4416no—
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—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—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#433914yes—
650C22×C4C23×D1112yes—
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—28no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—444no—
668C22⋊C4—444no—
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—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—222no—
703C23—222no—
704C23—222no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—444no—
710C23—444no—
711C23—444no—
712C23—444no—
713C23—444no—
714C23—444no—
715C23—444no—
716C23—444no—
717C23—444no—
718C23—444no—
719C23—444no—
720C23—444no—
721C23—444no—
722C23—444no—
723C23C2×#433912yes—
724C23#6703712yes—
725C23#6703712yes—
726C23#6704212yes—
727C23#6704212yes—
728C23#6704212yes—
729C23#6704312yes—
730C23C24×D1111yescharacteristic
731D4—4416no—
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—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—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—88no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—442no—
804C22—888no—
805C22—888no—
806C22#1062306514yes—
807C22#1062309114yes—
808C22#1062309314yes—
809C22#1062315114yes—
810C22#1062319814yes—
811C22#1062321514yes—
812C22#1062324214yes—
813C22C22×#433911yescharacteristic
814C22C2×#6703711yescharacteristic
815C22C2×#6703711yescharacteristic
816C22C2×#6704211yescharacteristic
817C22C2×#6704211yescharacteristic
818C22C2×#6704211yescharacteristic
819C22C2×#6704311yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—442no—
827C4—442no—
828C4—442no—
829C4—442no—
830C4—442no—
831C4—442no—
832C2—82no—
833C2—882no—
834C2—882no—
835C2#1307674218yesdirect product factor
836C2C2×#1062309111yescharacteristic
837C2C2×#1062309311yescharacteristic
838C2C2×#1062306511yescharacteristic
839C2C2×#1062315111yescharacteristic
840C2C2×#1062324211yescharacteristic
841C2C2×#1062321511yescharacteristic
842C2C2×#1062319811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11C2×#2829
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #13076742C2direct (N × H)
2. C2×#10622605C2semidirect
3. C2×#10622274C2semidirect
4. C2×#10622288C2semidirect
5. C2×#10622287C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622285C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622574C2semidirect
11. C2×#10622572C2semidirect
12. C2×#10622572C2semidirect
14. C2×#10622552C2semidirect
15. C2×#10622546C2semidirect
16. C2×C11×#388C2semidirect
44. C11×#388C22semidirect
53. #10622607C22semidirect
54. #10622605C22semidirect
55. #10622574C22semidirect
56. #10622574C22semidirect
58. #10622572C22semidirect
59. #10622572C22semidirect
60. #10622561C22semidirect
61. #10622552C22semidirect
62. #10622546C22semidirect
63. #10622288C22semidirect
64. #10622287C22semidirect
65. #10622285C22semidirect
66. #10622274C22semidirect
274. C2×#388D11semidirect
417. #388C2×D11semidirect
561. C2×C11#2829semidirect
680. C11C2×#2829semidirect
835. C2#13076742direct (N × H)

Maximal subgroups

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

subgroupindex
#130767422
C2×#106226052
C2×#106222742
C2×#106222882
C2×#106222872
C2×#106225612
C2×#106226072
C2×#106222852
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106225522
C2×#106225462
C2×C11×#3882
C2×#282911