Finite Group Databasebeta

← C2×#13076697 #14959957

Subgroups — C2×#13076697 #14959957

Order 2816.

2606 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076697C2116yesmaximal, direct product factor
2C2×#10622271C211yesmaximal, characteristic, complemented
3C2×#10622288C211yesmaximal, characteristic, complemented
4C2×#10622606C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622604C211yesmaximal, characteristic, complemented
9C2×#10622286C211yesmaximal, characteristic, complemented
10C2×#10622286C211yesmaximal, characteristic, complemented
11C2×#10622286C211yesmaximal, characteristic, complemented
12C2×#10622284C211yesmaximal, characteristic
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×#10622602C211yesmaximal, characteristic, complemented
16C2×C11×#400C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C11×#400C2218yescomplemented
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
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#10622606C2218yescomplemented
54#10622604C2218yescomplemented
55#10622604C2218yescomplemented
56#10622602C2218yescomplemented
57#10622288C2218yescomplemented
58#10622286C2218yescomplemented
59#10622286C2218yescomplemented
60#10622286C2218yescomplemented
61#10622285C2218yescomplemented
62#10622285C2218yescomplemented
63#10622284C2218yes—
64#10622278C2218yescomplemented
65#10622278C2218yescomplemented
66#10622271C2218yescomplemented
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—24no—
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—
94C22×C4×D11—42no—
95C22×C4×D11—42no—
96C22×C4×D11—42no—
97C22×C4×D11C2314yes—
98C22×Dic22—42no—
99C22×Dic22—42no—
100C22×Dic22—42no—
101C22×Dic22C2314yes—
102C2×C11×C4⋊C4—42no—
103C2×C11×C4⋊C4—42no—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
118C2×(C2×D11)⋊C4—42no—
119C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×Dic11⋊C4—42no—
135C2×Dic11⋊C4—42no—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2824—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#4114yes—
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—22no—
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—28no—
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—
236C2×C4×D11—44no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C2×C4×D11—416no—
240C2×Dic22—44no—
241C2×Dic22—44no—
242C2×Dic22—44no—
243C2×Dic22—416no—
244C11×C4⋊C4—44no—
245C11×C4⋊C4—44no—
246(C2×D11)⋊C4—28no—
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—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257(C2×D11)⋊C4—44no—
258(C2×D11)⋊C4—44no—
259(C2×D11)⋊C4—44no—
260Dic11⋊C4—44no—
261Dic11⋊C4—44no—
262#2824—1116no—
263C2×#400—111no—
264C2×#400D1111yescharacteristic, complemented
265C2×#397—111no—
266C2×#397—111no—
267C2×#394—111no—
268C2×#394—111no—
269C2×#394—111no—
270C2×#394—111no—
271C2×#393—111no—
272C2×#393—111no—
273C2×#393—111no—
274C2×#392—111no—
275C2×#386—111no—
276C2×#386—111no—
277C2×#385—111no—
278C23×C11C2×#4112yes—
279C23×C11H(5,𝔽2)12yes—
280C23×C11H(5,𝔽2)12yes—
281C23×C11H(5,𝔽2)12yes—
282C23×C11H(5,𝔽2)12yes—
283C23×C11H(5,𝔽2)12yes—
284C23×C112−1+412yes—
285C23×C11C2511yescharacteristic
286C22×D11—28no—
287C22×D11—28no—
288C22×D11—28no—
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—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
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—
326C22×D11—44no—
327C22×D11C2×#4114yes—
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—22no—
348C2×C4×C11—22no—
349C2×C4×C11—44no—
350C2×C4×C11—44no—
351C2×C4×C11—44no—
352C2×C4×C11—44no—
353C2×C4×C11—44no—
354C2×C4×C11—44no—
355C2×C4×C11—44no—
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—
376D44—416no—
377D44—416no—
378D44—416no—
379C4×D11—416no—
380Dic22—416no—
381C23×Q8—111no—
382C23×D4—111no—
383C23×D4—111no—
384C23×D4—111no—
385C24×C4—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
401C22×C22⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C22⋊C4—111no—
404#400—118no—
405#400C2×D1118yescomplemented
406#397—118no—
407#397—118no—
408#394—118no—
409#394—118no—
410#394—118no—
411#394—118no—
412#393—118no—
413#393—118no—
414#393—118no—
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×#95C2×D1111yescharacteristic
427C2×#95C2×D1111yescharacteristic
428C2×#95C2×D1111yescharacteristic
429C2×#95C2×D1111yescharacteristic
430C2×#95C2×D1111yescharacteristic
431C22×C11#53814yes—
432C22×C11#53814yes—
433C22×C11#53914yes—
434C22×C11#56014yes—
435C22×C11H(3,𝔽4)14yes—
436C22×C11#56214yes—
437C22×C11#56214yes—
438C22×C11C22×#4111yescharacteristic
439C22×C11C2×H(5,𝔽2)11yescharacteristic
440C22×C11C2×H(5,𝔽2)11yescharacteristic
441C22×C11C2×H(5,𝔽2)11yescharacteristic
442C22×C11C2×H(5,𝔽2)11yescharacteristic
443C22×C11C2×H(5,𝔽2)11yescharacteristic
444C22×C11C2×2−1+411yescharacteristic
445C2×D11—24no—
446C2×D11—24no—
447C2×D11—24no—
448C2×D11—416no—
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—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—88no—
468C2×D11—88no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—42no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480Dic11—42no—
481C25—111no—
482C25—111no—
483C25—111no—
484C22×Q8—114no—
485C22×Q8—442no—
486C22×Q8—442no—
487C22×Q8—442no—
488C22×D4—114no—
489C22×D4—114no—
490C22×D4—114no—
491C22×D4—224no—
492C22×D4—224no—
493C22×D4—442no—
494C22×D4—442no—
495C22×D4—442no—
496C22×D4—442no—
497C22×D4—442no—
498C22×D4—442no—
499C22×D4—442no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—114no—
506C23×C4—442no—
507C23×C4—442no—
508C23×C4—442no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C23×C4C22×D1111yescharacteristic
513C23×C4C22×D1111yescharacteristic
514C23×C4C22×D1111yescharacteristic
515C23×C4C22×D1111yescharacteristic
516C2×C4⋊C4—42no—
517C2×C4⋊C4—42no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—114no—
520C2×C4⋊C4—442no—
521C2×C4⋊C4—442no—
522C2×C4⋊C4C22×D1114yes—
523C2×C4⋊C4C22×D1114yes—
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—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⋊C4—442no—
549C2×C22⋊C4—442no—
550C2×C22⋊C4—442no—
551C2×C22⋊C4—442no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95C22×D1114yes—
560#95C22×D1114yes—
561#95C22×D1114yes—
562#95C22×D1114yes—
563#95C22×D1114yes—
564C2×C11#282418yescomplemented
565C2×C11C2×#53811yescharacteristic
566C2×C11C2×#53811yescharacteristic
567C2×C11C2×#53911yescharacteristic
568C2×C11C2×#56011yescharacteristic
569C2×C11C2×H(3,𝔽4)11yescharacteristic
570C2×C11C2×#56211yescharacteristic
571C2×C11C2×#56211yescharacteristic
572D11—44no—
573D11—82no—
574D11—82no—
575C24—114no—
576C24—112no—
577C24—112no—
578C24—112no—
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—
595C24—222no—
596C24—222no—
597C24—222no—
598C24—222no—
599C24C23×D1111yescharacteristic
600C2×Q8—444no—
601C2×Q8—444no—
602C2×Q8—444no—
603C2×Q8—4416no—
604C2×D4—228no—
605C2×D4—228no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4—444no—
611C2×D4—444no—
612C2×D4—444no—
613C2×D4—4416no—
614C2×D4—4416no—
615C2×D4—4416no—
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—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
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—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—444no—
658C22×C4—444no—
659C22×C4—444no—
660C22×C4—4416no—
661C22×C4C23×D1112yes—
662C22×C4C23×D1112yes—
663C22×C4C23×D1112yes—
664C22×C4C23×D1112yes—
665C22×C4C23×D1112yes—
666C22×C4C23×D1112yes—
667C22×C4C23×D1112yes—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—444no—
671C4⋊C4—444no—
672C22⋊C4—228no—
673C22⋊C4—444no—
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—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C11C2×#282411yescharacteristic, complemented, Sylow
687C23—114no—
688C23—228no—
689C23—228no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—228no—
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—222no—
710C23—222no—
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—444no—
724C23—444no—
725C23—444no—
726C23—444no—
727C23—444no—
728C23—444no—
729C23#6703712yes—
730C23#6704012yes—
731C23#41×D1112yes—
732C23#6704212yes—
733C23#6704212yes—
734C23#6704212yes—
735C23#6704212yes—
736C23C24×D1111yescharacteristic
737Q8—4416no—
738D4—4416no—
739D4—4416no—
740D4—4416no—
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—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
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—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—4416no—
785C2×C4—444no—
786C2×C4—444no—
787C2×C4—444no—
788C2×C4—444no—
789C2×C4—444no—
790C22—224no—
791C22—224no—
792C22—224no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—4416no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—888no—
813C22—888no—
814C22#1062317814yes—
815C22#1062318814yes—
816C22#1062321414yes—
817C22#1062322314yes—
818C22#1062323114yes—
819C22#1062323514yes—
820C22#1062324214yes—
821C22C2×#6703711yescharacteristic
822C22C2×#6704011yescharacteristic
823C22C2×#41×D1111yescharacteristic
824C22C2×#6704211yescharacteristic
825C22C2×#6704211yescharacteristic
826C22C2×#6704211yescharacteristic
827C22C2×#6704211yescharacteristic
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—442no—
836C4—442no—
837C4—442no—
838C4—442no—
839C4—442no—
840C2—444no—
841C2—882no—
842C2—882no—
843C2#1307669718yesdirect product factor
844C2C2×#1062318811yescharacteristic
845C2C2×#1062323511yescharacteristic
846C2C2×#1062322311yescharacteristic
847C2C2×#1062324211yescharacteristic
848C2C2×#1062321411yescharacteristic
849C2C2×#1062317811yescharacteristic
850C2C2×#1062323111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×#400D11
hypocenterC11C2×#2824
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #13076697C2direct (N × H)
2. C2×#10622271C2semidirect
3. C2×#10622288C2semidirect
4. C2×#10622606C2semidirect
5. C2×#10622285C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622604C2semidirect
9. C2×#10622286C2semidirect
10. C2×#10622286C2semidirect
11. C2×#10622286C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622278C2semidirect
15. C2×#10622602C2semidirect
16. C2×C11×#400C2semidirect
40. C11×#400C22semidirect
53. #10622606C22semidirect
54. #10622604C22semidirect
55. #10622604C22semidirect
56. #10622602C22semidirect
57. #10622288C22semidirect
58. #10622286C22semidirect
59. #10622286C22semidirect
60. #10622286C22semidirect
61. #10622285C22semidirect
62. #10622285C22semidirect
64. #10622278C22semidirect
65. #10622278C22semidirect
66. #10622271C22semidirect
264. C2×#400D11semidirect
405. #400C2×D11semidirect
564. C2×C11#2824semidirect
686. C11C2×#2824semidirect
843. C2#13076697direct (N × H)

Maximal subgroups

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

subgroupindex
#130766972
C2×#106222712
C2×#106222882
C2×#106226062
C2×#106222852
C2×#106226042
C2×#106222862
C2×#106222842
C2×#106222782
C2×#106226022
C2×C11×#4002
C2×#282411