Finite Group Databasebeta

← C2×#13071627 #14913297

Subgroups — C2×#13071627 #14913297

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13071627C2116yesmaximal, direct product factor
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622260C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic, complemented
10C2×#10622282C211yesmaximal, characteristic, complemented
11C2×#10622571C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622559C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×#66992C4116yescomplemented
32C2×#66992C2218yes—
33C2×D4×Dic11—28no—
34C2×D4×Dic11C2218yescomplemented
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4—28no—
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2218yescomplemented
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C22×C4×Dic11C2211yescharacteristic
53C22×C4×Dic11C2211yescharacteristic
54C2×(C22⋊D11)⋊C4—28no—
55C2×(C22⋊D11)⋊C4C2218yescomplemented
56C11×#386C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63#10622571C2218yescomplemented
64#10622570C2218yescomplemented
65#10622559C2218yescomplemented
66#10622558C2218yescomplemented
67C22⋊C4×Dic11C2218yescomplemented
68#10622282C2218yescomplemented
69#10622281C2218yescomplemented
70#10622262C2218yescomplemented
71#10622260C2218yescomplemented
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11C2×C418yescomplemented
78C22×D4×C11C2314yes—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—42no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11C2×C418yescomplemented
93C22×C22⋊D11C2×C418yescomplemented
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C23×Dic11—24no—
97C23×Dic11—24no—
98C23×Dic11—24no—
99C23×Dic11—24no—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—42no—
103C23×Dic11—42no—
104C23×Dic11C2×C418yescomplemented
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2314yes—
107C23×Dic11C2314yes—
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2314yes—
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—42no—
118C22×C4×D11C2314yes—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—42no—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11C2×C418yescomplemented
127C2×C22⋊Dic11D418yescomplemented
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131#66992C2×C4164yescomplemented
132D4×Dic11—232no—
133C4×C22⋊D11—232no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—42no—
137C2×(C2×D11)⋊C4C2×C418yescomplemented
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11—24no—
143C2×C4⋊Dic11C2314yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—232no—
149C2×Dic11⋊C4C2×C418yescomplemented
150C2×Dic11⋊C4D418yescomplemented
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×Dic11⋊C4C2314yes—
157C2×C4×Dic11—24no—
158C2×C4×Dic11—24no—
159C2×C4×Dic11—24no—
160C2×C4×Dic11—24no—
161C2×C4×Dic11C2314yes—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165(C22⋊D11)⋊C4—232no—
166C11×#95C2314yes—
167C11×#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2361—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11C22×C414yes—
184C24×C11C22×C414yes—
185C24×C11C2×D414yes—
186C24×C11#4114yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11C22×C414yes—
197C23×D11C2412yes—
198C2×D4×C11—232no—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11C22×C4116yescomplemented
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—28no—
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—28no—
217C22×C4×C11—44no—
218C22×C4×C11—416no—
219C22×C4×C11C22×C414yes—
220C22×C4×C11C2×D414yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C2×C22⋊D11—232no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—232no—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11C22×C4116yescomplemented
233C2×C22⋊D11C22×C4116yescomplemented
234C22×Dic11—232no—
235C22×Dic11—28no—
236C22×Dic11—28no—
237C22×Dic11—28no—
238C22×Dic11—28no—
239C22×Dic11—28no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—28no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—44no—
255C22×Dic11—44no—
256C22×Dic11—416no—
257C22×Dic11—416no—
258C22×Dic11C22×C414yes—
259C22×Dic11C22×C414yes—
260C22×Dic11C22×C414yes—
261C22×Dic11C22×C4116yescomplemented
262C22×Dic11C2×D414yes—
263C22×Dic11C2×D414yes—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11#4114yes—
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—44no—
277C2×C4×D11—416no—
278C11×C22⋊C4—28no—
279C11×C22⋊C4—28no—
280C11×C22⋊C4—44no—
281C22⋊Dic11—28no—
282C22⋊Dic11C22×C4116yescomplemented
283C22⋊Dic11C2×D4116yescomplemented
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4C22×C4116yescomplemented
288C4⋊Dic11—28no—
289Dic11⋊C4—28no—
290Dic11⋊C4—28no—
291Dic11⋊C4—28no—
292Dic11⋊C4—28no—
293Dic11⋊C4C22×C4116yescomplemented
294Dic11⋊C4C2×D4116yescomplemented
295C4×Dic11—28no—
296C4×Dic11—28no—
297C4×Dic11—28no—
298C4×Dic11—28no—
299C22×#121—111no—
300C22×C4×D4—111no—
301C22×C4×D4—111no—
302C22×C4×D4—111no—
303C23×C4⋊C4—111no—
304#2361—1116no—
305C2×#390—111no—
306C2×#389—111no—
307C2×#388—111no—
308C2×#388—111no—
309C2×#386—111no—
310C2×#386D1111yescharacteristic, complemented
311C2×#385—111no—
312C2×#385—111no—
313C2×C4×C4⋊C4—111no—
314C2×C4×C22⋊C4—111no—
315C23×C11—28no—
316C23×C11—28no—
317C23×C11—28no—
318C23×C11—28no—
319C23×C11—28no—
320C23×C11—28no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11C4×D4116yescomplemented
339C23×C11C23×C414yes—
340C23×C11C23×C414yes—
341C23×C11C23×C412yes—
342C23×C11C22×D414yes—
343C23×C11C22×D412yes—
344C23×C11C22×D412yes—
345C23×C11C2×#4114yes—
346C23×C11C2×#4112yes—
347C23×C11C2×#4112yes—
348C23×C11H(5,𝔽2)12yes—
349C23×C112−1+412yes—
350C23×C11C2511yescharacteristic
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11C23×C414yes—
365D4×C11—232no—
366C2×C4×C11—28no—
367C2×C4×C11—28no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—416no—
382C2×C4×C11—44no—
383C2×C4×C11—44no—
384C2×C4×C11—44no—
385C2×C4×C11C23×C414yes—
386C2×C4×C11C22×D414yes—
387C22⋊D11—232no—
388C22⋊D11—232no—
389C2×Dic11—28no—
390C2×Dic11—28no—
391C2×Dic11—28no—
392C2×Dic11—28no—
393C2×Dic11—28no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—232no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—416no—
409C2×Dic11—416no—
410C2×Dic11—44no—
411C2×Dic11C4×D4116yescomplemented
412C2×Dic11C23×C414yes—
413C2×Dic11C23×C414yes—
414C2×Dic11C23×C414yes—
415C2×Dic11C22×D414yes—
416C2×Dic11C22×D414yes—
417C2×Dic11C22×D414yes—
418C2×Dic11C22×D414yes—
419C2×Dic11C2×#4114yes—
420C4×D11—416no—
421C23×D4—111no—
422C23×D4—111no—
423C23×D4C2×D1111yescharacteristic
424C24×C4—111no—
425C24×C4—111no—
426C24×C4—111no—
427C24×C4—111no—
428C24×C4C2×D1111yescharacteristic
429C2×#121—118no—
430C2×#121—1116no—
431C2×C4×D4—118no—
432C2×C4×D4—118no—
433C2×C4×D4—118no—
434C2×C4×D4—228no—
435C2×C4×D4—228no—
436C2×C4×D4—228no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—118no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4—228no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4C2×D1111yescharacteristic
456C22×C42—111no—
457C22×C42—111no—
458C22×C42—111no—
459C22×C42—111no—
460#390—118no—
461#389—118no—
462#388—118no—
463#388—118no—
464#386—118no—
465#386C2×D1118yescomplemented
466#385—118no—
467#385—118no—
468C4×C4⋊C4—118no—
469C4×C22⋊C4—118no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95C2×D1111yescharacteristic
475C2×#95C2×D1111yescharacteristic
476C22×C11—232no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—24no—
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—24no—
485C22×C11—24no—
486C22×C11—416no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11C2×C4×D414yes—
492C22×C11C2×C4×D414yes—
493C22×C11C2×C4×D418yescomplemented
494C22×C11#52014yes—
495C22×C11D4214yes—
496C22×C11#54714yes—
497C22×C11#54814yes—
498C22×C11#55314yes—
499C22×C11C24×C411yescharacteristic
500C22×C11C23×D411yescharacteristic
501C22×C11C23×D411yescharacteristic
502C22×C11C22×#4111yescharacteristic
503C22×C11C22×#4111yescharacteristic
504C22×C11C2×H(5,𝔽2)11yescharacteristic
505C22×C11C2×2−1+411yescharacteristic
506C2×D11—24no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—416no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C4×C11—24no—
515C4×C11—24no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—42no—
519Dic11—24no—
520Dic11—24no—
521Dic11—24no—
522Dic11—24no—
523Dic11—24no—
524Dic11—42no—
525Dic11C2×C4×D418yescomplemented
526C25—111no—
527C25C22×D1111yescharacteristic
528C25C22×D1111yescharacteristic
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—118no—
532C22×D4—118no—
533C22×D4—114no—
534C22×D4—114no—
535C22×D4—224no—
536C22×D4—224no—
537C22×D4—224no—
538C22×D4—224no—
539C22×D4C4×D1118yescomplemented
540C22×D4C22×D1114yes—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—42no—
544C23×C4—111no—
545C23×C4—118no—
546C23×C4—114no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—114no—
554C23×C4—114no—
555C23×C4—114no—
556C23×C4—224no—
557C23×C4—224no—
558C23×C4—224no—
559C23×C4—224no—
560C23×C4—224no—
561C23×C4—224no—
562C23×C4—224no—
563C23×C4—224no—
564C23×C4—442no—
565C23×C4—442no—
566C23×C4—442no—
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1114yes—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573#121—1164no—
574C4×D4—2232no—
575C4×D4—2232no—
576C4×D4—2232no—
577C2×C4⋊C4—118no—
578C2×C4⋊C4—118no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—2232no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—224no—
589C2×C4⋊C4—224no—
590C2×C4⋊C4—224no—
591C2×C4⋊C4—224no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—118no—
596C2×C22⋊C4—118no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—118no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—442no—
609C2×C22⋊C4C22×D1114yes—
610C2×C22⋊C4C22×D1114yes—
611C2×C22⋊C4C22×D1114yes—
612C2×C42—114no—
613C2×C42—114no—
614C2×C42—114no—
615C2×C42—114no—
616C2×C42—224no—
617C2×C42—224no—
618C2×C42—224no—
619C2×C42—224no—
620#95—114no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95C22×D1114yes—
625#95C22×D1114yes—
626C2×C11—28no—
627C2×C11—44no—
628C2×C11#236118yescomplemented
629C2×C11C22×C4×D411yescharacteristic
630C2×C11C22×C4×D411yescharacteristic
631C2×C11C2×#52011yescharacteristic
632C2×C11C2×D4211yescharacteristic
633C2×C11C2×#54711yescharacteristic
634C2×C11C2×#54811yescharacteristic
635C2×C11C2×#55311yescharacteristic
636D11—44no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—114no—
648C24—112no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24C2×C4×D1114yes—
656C24C2×C4×D1114yes—
657C24D4×D1114yes—
658C24#434114yes—
659C24C23×D1112yes—
660C24C23×D1112yes—
661C24C23×D1111yescharacteristic
662C2×D4—232no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—1116no—
666C2×D4—1116no—
667C2×D4—228no—
668C2×D4—2232no—
669C2×D4—228no—
670C2×D4—2232no—
671C2×D4—228no—
672C2×D4—228no—
673C2×D4C2×C4×D11116yescomplemented
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—28no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—28no—
689C22×C4—44no—
690C22×C4—416no—
691C22×C4—114no—
692C22×C4—114no—
693C22×C4—114no—
694C22×C4—112no—
695C22×C4—114no—
696C22×C4—114no—
697C22×C4—1116no—
698C22×C4—114no—
699C22×C4—114no—
700C22×C4—114no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—228no—
708C22×C4—228no—
709C22×C4—2232no—
710C22×C4—228no—
711C22×C4—228no—
712C22×C4—228no—
713C22×C4—228no—
714C22×C4—222no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—228no—
727C22×C4—222no—
728C22×C4—228no—
729C22×C4—444no—
730C22×C4—4416no—
731C22×C4—444no—
732C22×C4—444no—
733C22×C4—4416no—
734C22×C4—4416no—
735C22×C4C2×C4×D1114yes—
736C22×C4D4×D1114yes—
737C22×C4C23×D1112yes—
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C4⋊C4—1116no—
743C4⋊C4—1116no—
744C4⋊C4—228no—
745C4⋊C4—228no—
746C4⋊C4—228no—
747C4⋊C4—228no—
748C4⋊C4—228no—
749C22⋊C4—28no—
750C22⋊C4—28no—
751C22⋊C4—44no—
752C22⋊C4—1116no—
753C22⋊C4—1116no—
754C22⋊C4—1116no—
755C22⋊C4—228no—
756C22⋊C4—228no—
757C22⋊C4—228no—
758C22⋊C4—444no—
759C42—228no—
760C42—228no—
761C42—228no—
762C42—228no—
763C11C2×#236111yescharacteristic, complemented, Sylow
764C23—28no—
765C23—28no—
766C23—28no—
767C23—28no—
768C23—28no—
769C23—28no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—114no—
788C23—228no—
789C23—228no—
790C23—228no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—444no—
798C23—444no—
799C23—444no—
800C23—444no—
801C23(C22⋊D11)⋊C4116yescomplemented
802C23C22×C4×D1114yes—
803C23C22×C4×D1114yes—
804C23C22×C4×D1112yes—
805C23C2×D4×D1114yes—
806C23C2×D4×D1112yes—
807C23C2×D4×D1112yes—
808C23C2×#434114yes—
809C23C2×#434112yes—
810C23#6703712yes—
811C23#41×D1112yes—
812C23#6704312yes—
813C23C24×D1111yescharacteristic
814D4—232no—
815D4—2232no—
816D4—2232no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—416no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—1116no—
837C2×C4—114no—
838C2×C4—114no—
839C2×C4—114no—
840C2×C4—114no—
841C2×C4—114no—
842C2×C4—114no—
843C2×C4—114no—
844C2×C4—114no—
845C2×C4—2232no—
846C2×C4—228no—
847C2×C4—228no—
848C2×C4—228no—
849C2×C4—228no—
850C2×C4—228no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—4416no—
865C2×C4—4416no—
866C2×C4—4416no—
867C2×C4—444no—
868C2×C4C22×C4×D1114yes—
869C2×C4C2×D4×D1114yes—
870C22—232no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—416no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—224no—
886C22—224no—
887C22—224no—
888C22—4416no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22C2×(C22⋊D11)⋊C414yes—
894C22C2×(C22⋊D11)⋊C418yescomplemented
895C22C4×D4×D1114yes—
896C22#1062307714yes—
897C22#1062312114yes—
898C22#1062312914yes—
899C22#1062313214yes—
900C22#1062318614yes—
901C22C23×C4×D1111yescharacteristic
902C22C22×D4×D1111yescharacteristic
903C22C22×D4×D1111yescharacteristic
904C22C22×#434111yescharacteristic
905C22C2×#6703711yescharacteristic
906C22C2×#41×D1111yescharacteristic
907C22C2×#6704311yescharacteristic
908C4—24no—
909C4—24no—
910C4—42no—
911C4—42no—
912C4—42no—
913C4—118no—
914C4—224no—
915C4—224no—
916C4—224no—
917C4—224no—
918C4—224no—
919C4—442no—
920C2—28no—
921C2—44no—
922C2—444no—
923C2#1307162718yesdirect product factor
924C2C2×C4×D4×D1111yescharacteristic
925C2C22×(C22⋊D11)⋊C411yescharacteristic
926C2C2×#1062307711yescharacteristic
927C2C2×#1062312111yescharacteristic
928C2C2×#1062318611yescharacteristic
929C2C2×#1062312911yescharacteristic
930C2C2×#1062313211yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66992C2
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic11C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. C23×Dic11⋊C4C2semidirect
6. #13071627C2direct (N × H)
7. C2×#10622570C2semidirect
8. C2×#10622260C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622282C2semidirect
11. C2×#10622571C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622559C2semidirect
14. C2×#10622262C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#386C2semidirect
31. C2×#66992C4semidirect
34. C2×D4×Dic11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
49. C22×Dic11⋊C4C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
56. C11×#386C22semidirect
63. #10622571C22semidirect
64. #10622570C22semidirect
65. #10622559C22semidirect
66. #10622558C22semidirect
67. C22⋊C4×Dic11C22semidirect
68. #10622282C22semidirect
69. #10622281C22semidirect
70. #10622262C22semidirect
71. #10622260C22semidirect
77. C22×D4×C11C2×C4semidirect
92. C22×C22⋊D11C2×C4semidirect
93. C22×C22⋊D11C2×C4semidirect
104. C23×Dic11C2×C4semidirect
126. C2×C22⋊Dic11C2×C4semidirect
127. C2×C22⋊Dic11D4semidirect
131. #66992C2×C4semidirect
137. C2×(C2×D11)⋊C4C2×C4semidirect
149. C2×Dic11⋊C4C2×C4semidirect
150. C2×Dic11⋊C4D4semidirect
201. C2×D4×C11C22×C4semidirect
232. C2×C22⋊D11C22×C4semidirect
233. C2×C22⋊D11C22×C4semidirect
261. C22×Dic11C22×C4semidirect
282. C22⋊Dic11C22×C4semidirect
283. C22⋊Dic11C2×D4semidirect
287. (C2×D11)⋊C4C22×C4semidirect
293. Dic11⋊C4C22×C4semidirect
294. Dic11⋊C4C2×D4semidirect
310. C2×#386D11semidirect
338. C23×C11C4×D4semidirect
411. C2×Dic11C4×D4semidirect
465. #386C2×D11semidirect
493. C22×C11C2×C4×D4semidirect
525. Dic11C2×C4×D4semidirect
539. C22×D4C4×D11semidirect
628. C2×C11#2361semidirect
673. C2×D4C2×C4×D11semidirect
763. C11C2×#2361semidirect
801. C23(C22⋊D11)⋊C4semidirect
894. C22C2×(C22⋊D11)⋊C4semidirect
923. C2#13071627direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×D4×Dic112
C22×C4×C22⋊D112
C22×(C22⋊D11)⋊C42
C23×Dic11⋊C42
#130716272
C2×#106225702
C2×#106222602
C2×#106225582
C2×#106222822
C2×#106225712
C2×#106222812
C2×#106225592
C2×#106222622
C2×C22⋊C4×Dic112
C2×C11×#3862
C2×#236111