Finite Group Databasebeta

← C2×#13074604 #14920232

Subgroups — C2×#13074604 #14920232

Order 2816.

2654 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#13074604C2116yesmaximal, direct product factor
2C2×#10622271C211yesmaximal, characteristic, complemented
3C2×#10622287C211yesmaximal, characteristic, complemented
4C2×#10622566C211yesmaximal, characteristic, complemented
5C2×#10622561C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622282C211yesmaximal, characteristic, complemented
13C2×#10622268C211yesmaximal, characteristic, complemented
14C2×#10622826C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C11×#386C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45#10622836C2218yes—
46#10622835C2218yescomplemented
47#10622826C2218yescomplemented
48C4×C22⋊Dic11C2218yescomplemented
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622574C2218yescomplemented
58#10622572C2218yescomplemented
59#10622570C2218yescomplemented
60#10622566C2218yescomplemented
61#10622564C2218yescomplemented
62#10622561C2218yescomplemented
63#10622287C2218yescomplemented
64#10622282C2218yescomplemented
65#10622271C2218yescomplemented
66#10622268C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C22×D4×C11—24no—
71C22×D4×C11—42no—
72C22×D4×C11—42no—
73C22×D4×C11C2314yes—
74C23×C4×C11—24no—
75C23×C4×C11—42no—
76C23×C4×C11—42no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2314yes—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C2×C11×C22⋊C4—24no—
99C2×C11×C22⋊C4—42no—
100C2×C11×C22⋊C4—42no—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—42no—
107C2×C22⋊Dic11—42no—
108C2×C22⋊Dic11—42no—
109C2×C22⋊Dic11—42no—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—42no—
118C2×(C2×D11)⋊C4—42no—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×C4⋊Dic11—42no—
127C2×C4⋊Dic11—42no—
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2314yes—
130C2×Dic11⋊C4—24no—
131C2×Dic11⋊C4—42no—
132C2×Dic11⋊C4—42no—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×C4×Dic11—42no—
137C2×C4×Dic11—42no—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2648—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#4114yes—
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—28no—
195C22×C4×C11—44no—
196C22×C4×C11—44no—
197C22×C4×C11—416no—
198C22×C4×C11#4114yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—28no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—44no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—416no—
211C2×C22⋊D11—416no—
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×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11#4114yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C11×C22⋊C4—28no—
241C11×C22⋊C4—44no—
242C11×C22⋊C4—44no—
243C22⋊Dic11—28no—
244C22⋊Dic11—28no—
245C22⋊Dic11—44no—
246C22⋊Dic11—44no—
247C22⋊Dic11—44no—
248C22⋊Dic11—44no—
249(C2×D11)⋊C4—28no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254C4⋊Dic11—44no—
255C4⋊Dic11—44no—
256Dic11⋊C4—28no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—44no—
260C4×Dic11—44no—
261#2648—1116no—
262C2×#400—111no—
263C2×#397—111no—
264C2×#397—111no—
265C2×#396—111no—
266C2×#394—111no—
267C2×#394—111no—
268C2×#394—111no—
269C2×#392—111no—
270C2×#390—111no—
271C2×#388—111no—
272C2×#388—111no—
273C2×#387—111no—
274C2×#386—111no—
275C2×#386D1111yescharacteristic, complemented
276C2×C4×C22⋊C4—111no—
277C23×C11—28no—
278C23×C11—28no—
279C23×C11—28no—
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—22no—
292C23×C11—22no—
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×#4114yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C11H(5,𝔽2)12yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11C2511yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—44no—
321C22×D11—44no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—44no—
327D4×C11—416no—
328C2×C4×C11—28no—
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—416no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—44no—
348C2×C4×C11C2×#4114yes—
349C22⋊D11—416no—
350C22⋊D11—416no—
351C2×Dic11—28no—
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—22no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11—44no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C2×Dic11—44no—
378C2×Dic11C2×#4114yes—
379C23×D4—111no—
380C23×D4—111no—
381C23×D4C2×D1111yescharacteristic
382C24×C4C2×D1111yescharacteristic
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
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×C42—111no—
403C22×C42—111no—
404#400—118no—
405#397—118no—
406#397—118no—
407#396—118no—
408#394—118no—
409#394—118no—
410#394—118no—
411#392—118no—
412#390—118no—
413#388—118no—
414#388—118no—
415#387—118no—
416#386—118no—
417#386C2×D1118yescomplemented
418C4×C22⋊C4—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×#95C2×D1111yescharacteristic
428C2×#95C2×D1111yescharacteristic
429C22×C11—24no—
430C22×C11—24no—
431C22×C11—24no—
432C22×C11—416no—
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—42no—
444C22×C11—88no—
445C22×C11#52914yes—
446C22×C11#53814yes—
447C22×C11#53814yes—
448C22×C11#53814yes—
449C22×C11#53814yes—
450C22×C11#54014yes—
451C22×C11#54014yes—
452C22×C11C22×#4111yescharacteristic
453C22×C11C22×#4111yescharacteristic
454C22×C11C22×#4111yescharacteristic
455C22×C11C2×H(5,𝔽2)11yescharacteristic
456C22×C11C2×H(5,𝔽2)11yescharacteristic
457C22×C11C2×H(5,𝔽2)11yescharacteristic
458C22×C11C2×H(5,𝔽2)11yescharacteristic
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—88no—
467C4×C11—24no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472Dic11—24no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479C25—111no—
480C25C22×D1111yescharacteristic
481C25C22×D1111yescharacteristic
482C22×D4—24no—
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—24no—
495C23×C4—42no—
496C23×C4—42no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4C22×D1111yescharacteristic
505C23×C4C22×D1111yescharacteristic
506C23×C4C22×D1111yescharacteristic
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1114yes—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—224no—
516C2×C4⋊C4—442no—
517C2×C4⋊C4—442no—
518C2×C4⋊C4—442no—
519C2×C4⋊C4—442no—
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—224no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4—224no—
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⋊C4C22×D1114yes—
546C2×C22⋊C4C22×D1114yes—
547C2×C22⋊C4C22×D1114yes—
548C2×C42—114no—
549C2×C42—114no—
550C2×C42—442no—
551C2×C42—442no—
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#95C22×D1114yes—
561#95C22×D1114yes—
562C2×C11—44no—
563C2×C11—82no—
564C2×C11#264818yescomplemented
565C2×C11C2×#52911yescharacteristic
566C2×C11C2×#53811yescharacteristic
567C2×C11C2×#53811yescharacteristic
568C2×C11C2×#53811yescharacteristic
569C2×C11C2×#53811yescharacteristic
570C2×C11C2×#54011yescharacteristic
571C2×C11C2×#54011yescharacteristic
572D11—82no—
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—112no—
587C24—222no—
588C24—222no—
589C24—222no—
590C24—222no—
591C24—222no—
592C24—222no—
593C24—222no—
594C24#433914yes—
595C24C23×D1112yes—
596C24C23×D1112yes—
597C24C23×D1111yescharacteristic
598C2×D4—28no—
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—28no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—416no—
628C22×C4—114no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
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—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4#434114yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C22×C4C23×D1112yes—
661C22×C4C23×D1112yes—
662C4⋊C4—228no—
663C4⋊C4—444no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C4⋊C4—444no—
667C22⋊C4—28no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—228no—
671C22⋊C4—228no—
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—
681C42—444no—
682C42—444no—
683C11C2×#264811yescharacteristic, complemented, Sylow
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—444no—
719C23—444no—
720C23—444no—
721C23—444no—
722C23—444no—
723C23—444no—
724C23—444no—
725C23C2×#433914yes—
726C23C2×#433912yes—
727C23C2×#434112yes—
728C23#6703712yes—
729C23#6703712yes—
730C23#6703712yes—
731C23#41×D1112yes—
732C23#6704212yes—
733C23C24×D1111yescharacteristic
734D4—416no—
735D4—4416no—
736D4—4416no—
737C2×C4—28no—
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—416no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—114no—
758C2×C4—228no—
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—222no—
779C2×C4—444no—
780C2×C4—444no—
781C2×C4—444no—
782C2×C4—444no—
783C2×C4—444no—
784C2×C4—444no—
785C2×C4C2×#434114yes—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—416no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—88no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—888no—
810C22#1062302514yes—
811C22#1062306914yes—
812C22#1062309114yes—
813C22#1062312414yes—
814C22#1062314414yes—
815C22#1062315014yes—
816C22#1062319414yes—
817C22C22×#433911yescharacteristic
818C22C22×#434111yescharacteristic
819C22C2×#6703711yescharacteristic
820C22C2×#6703711yescharacteristic
821C22C2×#6703711yescharacteristic
822C22C2×#41×D1111yescharacteristic
823C22C2×#6704211yescharacteristic
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—224no—
830C4—442no—
831C4—442no—
832C4—442no—
833C4—442no—
834C4—442no—
835C4—442no—
836C2—44no—
837C2—82no—
838C2—882no—
839C2#1307460418yesdirect product factor
840C2C2×#1062306911yescharacteristic
841C2C2×#1062314411yescharacteristic
842C2C2×#1062309111yescharacteristic
843C2C2×#1062312411yescharacteristic
844C2C2×#1062302511yescharacteristic
845C2C2×#1062319411yescharacteristic
846C2C2×#1062315011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11C2×#2648
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #13074604C2direct (N × H)
2. C2×#10622271C2semidirect
3. C2×#10622287C2semidirect
4. C2×#10622566C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622835C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622282C2semidirect
13. C2×#10622268C2semidirect
14. C2×#10622826C2semidirect
15. C2×C4×C22⋊Dic11C2semidirect
16. C2×C11×#386C2semidirect
42. C11×#386C22semidirect
46. #10622835C22semidirect
47. #10622826C22semidirect
48. C4×C22⋊Dic11C22semidirect
57. #10622574C22semidirect
58. #10622572C22semidirect
59. #10622570C22semidirect
60. #10622566C22semidirect
61. #10622564C22semidirect
62. #10622561C22semidirect
63. #10622287C22semidirect
64. #10622282C22semidirect
65. #10622271C22semidirect
66. #10622268C22semidirect
275. C2×#386D11semidirect
417. #386C2×D11semidirect
564. C2×C11#2648semidirect
683. C11C2×#2648semidirect
839. C2#13074604direct (N × H)

Maximal subgroups

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

subgroupindex
#130746042
C2×#106222712
C2×#106222872
C2×#106225662
C2×#106225612
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225702
C2×#106225642
C2×#106222822
C2×#106222682
C2×#106228262
C2×C4×C22⋊Dic112
C2×C11×#3862
C2×#264811