Finite Group Databasebeta

← C2×#13072511 #14921282

Subgroups — C2×#13072511 #14921282

Order 2816.

4282 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66948C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072511C2116yesmaximal, direct product factor
6C2×#10622573C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622601C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622282C211yesmaximal, characteristic, complemented
12C2×#10622591C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C2×#10622602C211yesmaximal, characteristic, complemented
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊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×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66948—28no—
47C2×#66948C2218yescomplemented
48C2×#66947—28no—
49C2×#66947C2218yescomplemented
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4—28no—
52C2×(C22⋊D11)⋊C4C2218yescomplemented
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C11×#396C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622603C2218yescomplemented
62#10622602C2218yescomplemented
63#10622601C2218yescomplemented
64#10622591C2218yescomplemented
65#10622573C2218yescomplemented
66#10622573C2218yescomplemented
67#10622573C2218yescomplemented
68#10622571C2218yescomplemented
69#10622282C2218yescomplemented
70#10622278C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11—24no—
94C23×Dic11—24no—
95C23×Dic11—42no—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×D44—24no—
103C22×D44—24no—
104C22×D44—24no—
105C22×D44—24no—
106C22×D44—24no—
107C22×D44—24no—
108C22×D44—42no—
109C22×D44—42no—
110C22×D44—42no—
111C22×D44C2314yes—
112C22×D44C2314yes—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—42no—
119C22×C4×D11—42no—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C2×C11×C4⋊C4—24no—
123C2×C11×C4⋊C4—24no—
124C2×C11×C4⋊C4—42no—
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C4⋊C4C2314yes—
127C2×C11×C4⋊C4C2314yes—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4—42no—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4—42no—
143C2×(C2×D11)⋊C4D418yescomplemented
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4D418yescomplemented
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C2×C4×Dic11—24no—
159C2×C4×Dic11—24no—
160C2×C4×Dic11C2314yes—
161C2×C4×Dic11C2314yes—
162#66948—232no—
163#66947—232no—
164(C22⋊D11)⋊C4—232no—
165(C22⋊D11)⋊C4—232no—
166C11×#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2456—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11C2×D414yes—
202C23×D11#4114yes—
203C23×D11C2412yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11C2×D414yes—
223C22×C4×C11C2×D414yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—232no—
231C2×C22⋊D11—232no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—416no—
242C22×Dic11—28no—
243C22×Dic11—28no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—44no—
256C22×Dic11—416no—
257C22×Dic11C2×D414yes—
258C22×Dic11C2×D414yes—
259C22×Dic11C2×D414yes—
260C22×Dic11#4114yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×D44—28no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—28no—
270C2×D44—28no—
271C2×D44—28no—
272C2×D44—44no—
273C2×D44—44no—
274C2×D44—44no—
275C2×D44—416no—
276C2×D44—416no—
277C2×D44—416no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—416no—
285C2×C4×D11—416no—
286C11×C4⋊C4—28no—
287C11×C4⋊C4—28no—
288C11×C4⋊C4—44no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—44no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4C2×D4116yescomplemented
302Dic11⋊C4—28no—
303Dic11⋊C4C2×D4116yescomplemented
304C4×Dic11—28no—
305C4×Dic11—28no—
306C22×#123—111no—
307C22×#121—111no—
308C22×C4×D4—111no—
309C22×C4×D4—111no—
310#2456—1116no—
311C2×#396D1111yescharacteristic, complemented
312C2×#392—111no—
313C2×#392—111no—
314C2×#392—111no—
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#387—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#385—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11C22×D412yes—
336C23×C11C22×D412yes—
337C23×C11C2×#4114yes—
338C23×C11C2×#4112yes—
339C23×C11C2×#4112yes—
340C23×C11C2×#4112yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11C2511yescharacteristic
344C22×D11—28no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11—44no—
372C22×D11—44no—
373C22×D11—44no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11C22×D414yes—
385C22×D11C2×#4114yes—
386C2×C4×C11—28no—
387C2×C4×C11—28no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11—44no—
407C2×C4×C11—44no—
408C2×C4×C11C22×D414yes—
409C2×C4×C11C22×D414yes—
410C22⋊D11—232no—
411C22⋊D11—232no—
412C22⋊D11—416no—
413C2×Dic11—28no—
414C2×Dic11—28no—
415C2×Dic11—28no—
416C2×Dic11—28no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—416no—
429C2×Dic11—44no—
430C2×Dic11C22×D414yes—
431C2×Dic11C22×D414yes—
432C2×Dic11C22×D414yes—
433C2×Dic11C2×#4114yes—
434D44—416no—
435D44—416no—
436D44—416no—
437C4×D11—416no—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4—111no—
445C24×C4—111no—
446C24×C4—111no—
447C24×C4—111no—
448C2×#123—118no—
449C2×#123—228no—
450C2×#121—118no—
451C2×#121—228no—
452C2×C4×D4—118no—
453C2×C4×D4—118no—
454C2×C4×D4—228no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4C2×D1111yescharacteristic
459C22×C4⋊C4C2×D1111yescharacteristic
460C22×C4⋊C4C2×D1111yescharacteristic
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C42—111no—
475C22×C42—111no—
476#396C2×D1118yescomplemented
477#392—118no—
478#392—118no—
479#392—118no—
480#390—118no—
481#388—118no—
482#388—118no—
483#387—118no—
484#386—118no—
485#386—118no—
486#385—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95C2×D1111yescharacteristic
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11#52514yes—
502C22×C11#52514yes—
503C22×C11#53814yes—
504C22×C11D4214yes—
505C22×C11#54614yes—
506C22×C11#55014yes—
507C22×C11#55314yes—
508C22×C11C23×D411yescharacteristic
509C22×C11C23×D411yescharacteristic
510C22×C11C22×#4111yescharacteristic
511C22×C11C22×#4111yescharacteristic
512C22×C11C22×#4111yescharacteristic
513C22×C11C2×H(5,𝔽2)11yescharacteristic
514C22×C11C2×H(5,𝔽2)11yescharacteristic
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—416no—
530C2×D11—416no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—88no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545Dic11—24no—
546Dic11—24no—
547Dic11—24no—
548Dic11—24no—
549Dic11—42no—
550C25—111no—
551C25—111no—
552C25—111no—
553C25C22×D1111yescharacteristic
554C22×D4—114no—
555C22×D4—114no—
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—114no—
560C22×D4—224no—
561C22×D4—224no—
562C22×D4—224no—
563C22×D4—224no—
564C22×D4—224no—
565C22×D4—224no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4—442no—
576C22×D4—442no—
577C22×D4—442no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—114no—
584C23×C4—114no—
585C23×C4—114no—
586C23×C4—224no—
587C23×C4—224no—
588C23×C4—224no—
589C23×C4—224no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—442no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4C22×D1111yescharacteristic
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#121—2232no—
603C4×D4—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—42no—
608C2×C4⋊C4—118no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4C22×D1114yes—
613C2×C4⋊C4C22×D1114yes—
614C2×C4⋊C4C22×D1114yes—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—42no—
618C2×C22⋊C4—118no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4—442no—
637C2×C22⋊C4—442no—
638C2×C22⋊C4C22×D1114yes—
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1114yes—
641C2×C42—114no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95C22×D1114yes—
651C2×C11—44no—
652C2×C11#245618yescomplemented
653C2×C11C2×#52511yescharacteristic
654C2×C11C2×#52511yescharacteristic
655C2×C11C2×#53811yescharacteristic
656C2×C11C2×D4211yescharacteristic
657C2×C11C2×#54611yescharacteristic
658C2×C11C2×#55011yescharacteristic
659C2×C11C2×#55311yescharacteristic
660D11—44no—
661D11—44no—
662D11—82no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—114no—
670C24—114no—
671C24—112no—
672C24—112no—
673C24—112no—
674C24—222no—
675C24—222no—
676C24—222no—
677C24—222no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—222no—
693C24#434314yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×D4—228no—
697C2×D4—228no—
698C2×D4—228no—
699C2×D4—228no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—2232no—
705C2×D4—2232no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—444no—
712C2×D4—444no—
713C2×D4—444no—
714C2×D4—4416no—
715C2×D4—4416no—
716C2×D4—4416no—
717C2×D4—444no—
718C2×D4—444no—
719C2×D4—4416no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—114no—
737C22×C4—114no—
738C22×C4—114no—
739C22×C4—114no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—228no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—228no—
749C22×C4—228no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—228no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4—4416no—
765C22×C4—4416no—
766C22×C4—444no—
767C22×C4—4416no—
768C22×C4D4×D1114yes—
769C22×C4D4×D1114yes—
770C22×C4C23×D1112yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—1116no—
780C4⋊C4—228no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—1116no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—444no—
793C22⋊C4—444no—
794C42—228no—
795C42—228no—
796C11C2×#245611yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—114no—
811C23—114no—
812C23—228no—
813C23—228no—
814C23—228no—
815C23—228no—
816C23—228no—
817C23—228no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—444no—
838C23—444no—
839C23—444no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×D4×D1112yes—
853C23C2×D4×D1112yes—
854C23#6703712yes—
855C23C2×#434314yes—
856C23C2×#434312yes—
857C23#41×D1112yes—
858C23#41×D1112yes—
859C23#6704212yes—
860C23C24×D1111yescharacteristic
861D4—2232no—
862D4—2232no—
863D4—4416no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—114no—
890C2×C4—114no—
891C2×C4—114no—
892C2×C4—114no—
893C2×C4—228no—
894C2×C4—228no—
895C2×C4—228no—
896C2×C4—228no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—4416no—
909C2×C4—4416no—
910C2×C4—4416no—
911C2×C4—444no—
912C2×C4C2×D4×D1114yes—
913C2×C4C2×D4×D1114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—416no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—224no—
923C22—224no—
924C22—224no—
925C22—224no—
926C22—224no—
927C22—224no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—4416no—
934C22—4416no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—888no—
946C22#1062313014yes—
947C22#1062314014yes—
948C22#1062314114yes—
949C22#1062315814yes—
950C22#1062315814yes—
951C22#1062317514yes—
952C22#1062324014yes—
953C22C22×D4×D1111yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C2×#6703711yescharacteristic
956C22C22×#434311yescharacteristic
957C22C2×#41×D1111yescharacteristic
958C22C2×#41×D1111yescharacteristic
959C22C2×#6704211yescharacteristic
960C4—24no—
961C4—24no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—224no—
967C4—224no—
968C4—224no—
969C4—224no—
970C4—442no—
971C2—44no—
972C2—444no—
973C2—444no—
974C2—882no—
975C2#1307251118yesdirect product factor
976C2C2×#1062315811yescharacteristic
977C2C2×#1062315811yescharacteristic
978C2C2×#1062317511yescharacteristic
979C2C2×#1062314011yescharacteristic
980C2C2×#1062314111yescharacteristic
981C2C2×#1062313011yescharacteristic
982C2C2×#1062324011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
hypercenterC2×#396D11
hypocenterC11C2×#2456
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×#66948C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072511C2direct (N × H)
6. C2×#10622573C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622282C2semidirect
12. C2×#10622591C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622571C2semidirect
15. C2×#10622602C2semidirect
16. C2×C11×#396C2semidirect
47. C2×#66948C22semidirect
49. C2×#66947C22semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C11×#396C22semidirect
61. #10622603C22semidirect
62. #10622602C22semidirect
63. #10622601C22semidirect
64. #10622591C22semidirect
65. #10622573C22semidirect
66. #10622573C22semidirect
67. #10622573C22semidirect
68. #10622571C22semidirect
69. #10622282C22semidirect
70. #10622278C22semidirect
143. C2×(C2×D11)⋊C4D4semidirect
155. C2×Dic11⋊C4D4semidirect
301. (C2×D11)⋊C4C2×D4semidirect
303. Dic11⋊C4C2×D4semidirect
311. C2×#396D11semidirect
476. #396C2×D11semidirect
652. C2×C11#2456semidirect
796. C11C2×#2456semidirect
975. C2#13072511direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669482
C22×(C22⋊D11)⋊C42
#130725112
C2×#106225732
C2×#106226012
C2×#106226032
C2×#106222822
C2×#106225912
C2×#106222782
C2×#106225712
C2×#106226022
C2×C11×#3962
C2×#245611