Finite Group Databasebeta

← C2×#13076754 #14960094

Subgroups — C2×#13076754 #14960094

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#13076754C2116yesmaximal, direct product factor
2C2×#10622605C211yesmaximal, characteristic, complemented
3C2×#10622287C211yesmaximal, characteristic, complemented
4C2×#10622606C211yesmaximal, characteristic, complemented
5C2×#10622607C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622604C211yesmaximal, characteristic, complemented
10C2×#10622604C211yesmaximal, characteristic, complemented
11C2×#10622604C211yesmaximal, characteristic, complemented
12C2×#10622284C211yesmaximal, characteristic
13C2×#10622601C211yesmaximal, characteristic, complemented
14C2×#10622282C211yesmaximal, characteristic, complemented
15C2×#10622265C211yesmaximal, characteristic, complemented
16C2×C11×#398C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#398C2218yescomplemented
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#10622607C2218yescomplemented
55#10622606C2218yescomplemented
56#10622605C2218yescomplemented
57#10622604C2218yescomplemented
58#10622604C2218yescomplemented
59#10622604C2218yescomplemented
60#10622601C2218yescomplemented
61#10622287C2218yescomplemented
62#10622285C2218yescomplemented
63#10622285C2218yescomplemented
64#10622284C2218yes—
65#10622282C2218yescomplemented
66#10622265C2218yescomplemented
67C24×D11C2311yescharacteristic
68C24×D11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C22×D44—24no—
83C22×D44—42no—
84C22×D44—42no—
85C22×D44—42no—
86C22×D44—42no—
87C22×D44—42no—
88C22×D44—42no—
89C22×D44—42no—
90C22×D44—42no—
91C22×D44C2314yes—
92C22×D44C2314yes—
93C22×D44C2314yes—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4—42no—
96C2×C11×C4⋊C4—42no—
97C2×C11×C4⋊C4—42no—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2314yes—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—42no—
104C2×(C2×D11)⋊C4—42no—
105C2×(C2×D11)⋊C4—42no—
106C2×(C2×D11)⋊C4—42no—
107C2×(C2×D11)⋊C4—42no—
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)⋊C4C2314yes—
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×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×C4⋊Dic11—42no—
133C2×C4⋊Dic11C2314yes—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—42no—
136C2×Dic11⋊C4—42no—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×C4×Dic11—42no—
141C2×C4×Dic11C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11×#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2829—111nomaximal, Sylow
151C24×C11C2411yescharacteristic
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—22no—
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×D11C2412yes—
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—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11#4114yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
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×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C2×D44—28no—
225C2×D44—44no—
226C2×D44—44no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44—44no—
230C2×D44—44no—
231C2×D44—44no—
232C2×D44—44no—
233C2×D44—416no—
234C2×D44—416no—
235C2×D44—416no—
236C11×C4⋊C4—44no—
237C11×C4⋊C4—44no—
238C11×C4⋊C4—44no—
239C11×C4⋊C4—44no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—44no—
242(C2×D11)⋊C4—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—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255C4⋊Dic11—44no—
256Dic11⋊C4—28no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—44no—
260#2829—1116no—
261C2×#399—111no—
262C2×#398D1111yescharacteristic, complemented
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×#388—111no—
275C2×#387—111no—
276C23×C11C2×#4112yes—
277C23×C11H(5,𝔽2)12yes—
278C23×C11H(5,𝔽2)12yes—
279C23×C11H(5,𝔽2)12yes—
280C23×C11H(5,𝔽2)12yes—
281C23×C11H(5,𝔽2)12yes—
282C23×C112−1+412yes—
283C23×C11C2511yescharacteristic
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11—44no—
308C22×D11—44no—
309C22×D11—44no—
310C22×D11—44no—
311C22×D11—44no—
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—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—44no—
348C2×C4×C11—44no—
349C2×C4×C11—44no—
350C2×C4×C11—44no—
351C2×C4×C11—44no—
352C2×C4×C11—44no—
353C2×C4×C11C2×#4114yes—
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—44no—
370C2×Dic11—44no—
371C2×Dic11—44no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374D44—416no—
375D44—416no—
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⋊C4C2×D1111yescharacteristic
385C22×C4⋊C4C2×D1111yescharacteristic
386C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
401C22×C22⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C42—111no—
404#399—118no—
405#398C2×D1118yescomplemented
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#388—118no—
418#387—118no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95C2×D1111yescharacteristic
425C2×#95C2×D1111yescharacteristic
426C2×#95C2×D1111yescharacteristic
427C22×C11#53814yes—
428C22×C11#54014yes—
429C22×C11#54214yes—
430C22×C11#56014yes—
431C22×C11#56014yes—
432C22×C11#56214yes—
433C22×C11#56214yes—
434C22×C11C22×#4111yescharacteristic
435C22×C11C2×H(5,𝔽2)11yescharacteristic
436C22×C11C2×H(5,𝔽2)11yescharacteristic
437C22×C11C2×H(5,𝔽2)11yescharacteristic
438C22×C11C2×H(5,𝔽2)11yescharacteristic
439C22×C11C2×H(5,𝔽2)11yescharacteristic
440C22×C11C2×2−1+411yescharacteristic
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
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—88no—
463C2×D11—88no—
464C2×D11—88no—
465C4×C11—24no—
466C4×C11—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—
477C25—111no—
478C25—111no—
479C25—111no—
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×C4C22×D1111yescharacteristic
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—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
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⋊C4C22×D1114yes—
517C2×C4⋊C4C22×D1114yes—
518C2×C4⋊C4C22×D1114yes—
519C2×C4⋊C4C22×D1114yes—
520C2×C22⋊C4—114no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—114no—
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—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⋊C4—442no—
547C2×C22⋊C4—442no—
548C2×C22⋊C4—442no—
549C2×C22⋊C4—442no—
550C2×C42—114no—
551C2×C42—442no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—114no—
557#95C22×D1114yes—
558#95C22×D1114yes—
559#95C22×D1114yes—
560C2×C11#282918yescomplemented
561C2×C11C2×#53811yescharacteristic
562C2×C11C2×#54011yescharacteristic
563C2×C11C2×#54211yescharacteristic
564C2×C11C2×#56011yescharacteristic
565C2×C11C2×#56011yescharacteristic
566C2×C11C2×#56211yescharacteristic
567C2×C11C2×#56211yescharacteristic
568D11—82no—
569D11—82no—
570D11—82no—
571C24—112no—
572C24—112no—
573C24—112no—
574C24—222no—
575C24—222no—
576C24—222no—
577C24—222no—
578C24—222no—
579C24—222no—
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—
594C24—222no—
595C24C23×D1111yescharacteristic
596C2×D4—228no—
597C2×D4—444no—
598C2×D4—444no—
599C2×D4—444no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4—444no—
603C2×D4—444no—
604C2×D4—444no—
605C2×D4—4416no—
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—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—112no—
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#434314yes—
649C22×C4C23×D1112yes—
650C22×C4C23×D1112yes—
651C22×C4C23×D1112yes—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—228no—
661C4⋊C4—444no—
662C4⋊C4—444no—
663C4⋊C4—444no—
664C22⋊C4—228no—
665C22⋊C4—444no—
666C22⋊C4—444no—
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—444no—
680C11C2×#282911yescharacteristic, complemented, Sylow
681C23—222no—
682C23—222no—
683C23—222no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—444no—
703C23—444no—
704C23—444no—
705C23—444no—
706C23—444no—
707C23—444no—
708C23—444no—
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—
723C23#6703712yes—
724C23#6703712yes—
725C23C2×#434312yes—
726C23#6704012yes—
727C23#6704212yes—
728C23#6704212yes—
729C23#6704212yes—
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—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
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—444no—
777C2×C4—444no—
778C2×C4—444no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4C2×#434314yes—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—442no—
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—888no—
804C22—888no—
805C22—888no—
806C22#1062315114yes—
807C22#1062317514yes—
808C22#1062317814yes—
809C22#1062319714yes—
810C22#1062322914yes—
811C22#1062323114yes—
812C22#1062326414yes—
813C22C2×#6703711yescharacteristic
814C22C2×#6703711yescharacteristic
815C22C22×#434311yescharacteristic
816C22C2×#6704011yescharacteristic
817C22C2×#6704211yescharacteristic
818C22C2×#6704211yescharacteristic
819C22C2×#6704211yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—442no—
828C4—442no—
829C4—442no—
830C4—442no—
831C4—442no—
832C2—882no—
833C2—882no—
834C2—882no—
835C2#1307675418yesdirect product factor
836C2C2×#1062317511yescharacteristic
837C2C2×#1062322911yescharacteristic
838C2C2×#1062326411yescharacteristic
839C2C2×#1062315111yescharacteristic
840C2C2×#1062319711yescharacteristic
841C2C2×#1062317811yescharacteristic
842C2C2×#1062323111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×#398D11
hypocenterC11C2×#2829
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #13076754C2direct (N × H)
2. C2×#10622605C2semidirect
3. C2×#10622287C2semidirect
4. C2×#10622606C2semidirect
5. C2×#10622607C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622285C2semidirect
9. C2×#10622604C2semidirect
10. C2×#10622604C2semidirect
11. C2×#10622604C2semidirect
13. C2×#10622601C2semidirect
14. C2×#10622282C2semidirect
15. C2×#10622265C2semidirect
16. C2×C11×#398C2semidirect
44. C11×#398C22semidirect
53. #10622607C22semidirect
54. #10622607C22semidirect
55. #10622606C22semidirect
56. #10622605C22semidirect
57. #10622604C22semidirect
58. #10622604C22semidirect
59. #10622604C22semidirect
60. #10622601C22semidirect
61. #10622287C22semidirect
62. #10622285C22semidirect
63. #10622285C22semidirect
65. #10622282C22semidirect
66. #10622265C22semidirect
262. C2×#398D11semidirect
405. #398C2×D11semidirect
560. C2×C11#2829semidirect
680. C11C2×#2829semidirect
835. C2#13076754direct (N × H)

Maximal subgroups

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

subgroupindex
#130767542
C2×#106226052
C2×#106222872
C2×#106226062
C2×#106226072
C2×#106222852
C2×#106226042
C2×#106222842
C2×#106226012
C2×#106222822
C2×#106222652
C2×C11×#3982
C2×#282911