Finite Group Databasebeta

← C2×#13071635 #14913305

Subgroups — C2×#13071635 #14913305

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×#66937C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
6#13071635C2116yesmaximal, direct product factor
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622585C211yesmaximal, characteristic, complemented
9C2×#10622564C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×C4×C22⋊D11—28no—
32C2×C4×C22⋊D11—28no—
33C2×C4×C22⋊D11C2218yescomplemented
34C2×C4×C22⋊D11C2218yescomplemented
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×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66946—28no—
51C2×#66946C2218yescomplemented
52C2×C4⋊C4×D11—28no—
53C2×C4⋊C4×D11C2218yescomplemented
54C2×#66937C4116yescomplemented
55C2×#66937C2218yes—
56C11×#385C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63#10622603C2218yescomplemented
64#10622585C2218yescomplemented
65#10622570C2218yescomplemented
66#10622569C2218yescomplemented
67#10622564C2218yescomplemented
68#10622281C2218yescomplemented
69#10622279C2218yescomplemented
70#10622278C2218yescomplemented
71#10622262C2218yescomplemented
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11—42no—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11C2×C418yescomplemented
90C22×C22⋊D11C2×C418yescomplemented
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C22×D44—24no—
100C22×D44—24no—
101C22×D44C2×C418yescomplemented
102C22×D44C2314yes—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—24no—
111C22×C4×D11—42no—
112C22×C4×D11—42no—
113C22×C4×D11—42no—
114C22×C4×D11C2×C418yescomplemented
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yes—
117C22×C4×D11C2314yes—
118C22×C4×D11C2314yes—
119C2×C11×C4⋊C4—24no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4C2314yes—
122C2×C11×C4⋊C4C2314yes—
123C2×C11×C22⋊C4—42no—
124C2×C11×C22⋊C4C2×C418yescomplemented
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C4×C22⋊D11—232no—
132C4×C22⋊D11—232no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—42no—
137C2×(C2×D11)⋊C4C2×C418yescomplemented
138C2×(C2×D11)⋊C4D418yescomplemented
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×C4⋊Dic11—24no—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4C2×C418yescomplemented
150C2×Dic11⋊C4D418yescomplemented
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11—24no—
157C2×C4×Dic11—24no—
158C2×C4×Dic11—24no—
159C2×C4×Dic11C2314yes—
160C2×C4×Dic11C2314yes—
161C2×C4×Dic11C2314yes—
162C2×C4×Dic11C2314yes—
163#66946—232no—
164C4⋊C4×D11—232no—
165#66937C2×C4164yescomplemented
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×C11C22×C414yes—
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×D11C22×C414yes—
193C23×D11C22×C414yes—
194C23×D11C2×D414yes—
195C23×D11#4114yes—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
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—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—28no—
213C22×C4×C11—28no—
214C22×C4×C11—44no—
215C22×C4×C11—416no—
216C22×C4×C11C22×C414yes—
217C22×C4×C11C22×C414yes—
218C22×C4×C11C2×D414yes—
219C22×C4×C11C2×D414yes—
220C22×C4×C11C2412yes—
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—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11C22×C414yes—
247C22×Dic11C22×C414yes—
248C22×Dic11C2×D414yes—
249C22×Dic11C2×D414yes—
250C22×Dic11C2×D414yes—
251C22×Dic11#4114yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C2×D44—232no—
259C2×D44—28no—
260C2×D44—28no—
261C2×D44C22×C4116yescomplemented
262C2×C4×D11—232no—
263C2×C4×D11—28no—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11—416no—
275C2×C4×D11—416no—
276C2×C4×D11—416no—
277C2×C4×D11C22×C4116yescomplemented
278C11×C4⋊C4—28no—
279C11×C4⋊C4—28no—
280C11×C22⋊C4—44no—
281C11×C22⋊C4C22×C4116yescomplemented
282C22⋊Dic11—28no—
283C22⋊Dic11—28no—
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—44no—
288(C2×D11)⋊C4C22×C4116yescomplemented
289(C2×D11)⋊C4C2×D4116yescomplemented
290C4⋊Dic11—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×#386—111no—
311C2×#385—111no—
312C2×#385D1111yescharacteristic, complemented
313C2×C4×C4⋊C4—111no—
314C2×C4×C22⋊C4—111no—
315C23×C11—28no—
316C23×C11—28no—
317C23×C11—28no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11C23×C414yes—
329C23×C11C23×C412yes—
330C23×C11C22×D412yes—
331C23×C11C22×D412yes—
332C23×C11C2×#4112yes—
333C23×C11C2×#4112yes—
334C23×C11H(5,𝔽2)12yes—
335C23×C112−1+412yes—
336C23×C11C2511yescharacteristic
337C22×D11—28no—
338C22×D11—28no—
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
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—44no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11—44no—
360C22×D11C4×D4116yescomplemented
361C22×D11C23×C414yes—
362C22×D11C23×C414yes—
363C22×D11C22×D414yes—
364C22×D11C2×#4114yes—
365C2×C4×C11—28no—
366C2×C4×C11—28no—
367C2×C4×C11—28no—
368C2×C4×C11—28no—
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—22no—
382C2×C4×C11—22no—
383C2×C4×C11—416no—
384C2×C4×C11—44no—
385C2×C4×C11—44no—
386C2×C4×C11C23×C414yes—
387C2×C4×C11C23×C414yes—
388C2×C4×C11C22×D414yes—
389C2×C4×C11C22×D414yes—
390C22⋊D11—232no—
391C22⋊D11—232no—
392C2×Dic11—28no—
393C2×Dic11—28no—
394C2×Dic11—28no—
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—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—44no—
408C2×Dic11—44no—
409C2×Dic11C4×D4116yescomplemented
410C2×Dic11C23×C414yes—
411C2×Dic11C23×C414yes—
412C2×Dic11C22×D414yes—
413C2×Dic11C22×D414yes—
414C2×Dic11C22×D414yes—
415C2×Dic11C2×#4114yes—
416D44—232no—
417C4×D11—232no—
418C4×D11—416no—
419C4×D11—416no—
420C4×D11—416no—
421C23×D4—111no—
422C23×D4—111no—
423C23×D4—111no—
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—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—118no—
443C22×C4⋊C4—228no—
444C22×C4⋊C4C2×D1111yescharacteristic
445C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
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#386—118no—
466#385—118no—
467#385C2×D1118yescomplemented
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—24no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—416no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11C2×C4×D414yes—
485C22×C11C2×C4×D414yes—
486C22×C11#52014yes—
487C22×C11D4214yes—
488C22×C11#54714yes—
489C22×C11#54814yes—
490C22×C11#55314yes—
491C22×C11C24×C411yescharacteristic
492C22×C11C23×D411yescharacteristic
493C22×C11C23×D411yescharacteristic
494C22×C11C22×#4111yescharacteristic
495C22×C11C22×#4111yescharacteristic
496C22×C11C2×H(5,𝔽2)11yescharacteristic
497C22×C11C2×2−1+411yescharacteristic
498C2×D11—232no—
499C2×D11—24no—
500C2×D11—24no—
501C2×D11—24no—
502C2×D11—24no—
503C2×D11—24no—
504C2×D11—24no—
505C2×D11—24no—
506C2×D11—24no—
507C2×D11—24no—
508C2×D11—416no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11C2×C4×D418yescomplemented
514C4×C11—24no—
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—24no—
518C4×C11—42no—
519C4×C11—42no—
520Dic11—24no—
521Dic11—24no—
522Dic11—24no—
523Dic11—42no—
524Dic11—42no—
525Dic11C2×C4×D418yescomplemented
526C25—111no—
527C25—111no—
528C25C22×D1111yescharacteristic
529C22×D4—118no—
530C22×D4—118no—
531C22×D4—114no—
532C22×D4—114no—
533C22×D4—118no—
534C22×D4—114no—
535C22×D4—224no—
536C22×D4—224no—
537C22×D4—224no—
538C22×D4—224no—
539C22×D4—224no—
540C22×D4—224no—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—42no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—118no—
549C23×C4—114no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—114no—
553C23×C4—114no—
554C23×C4—114no—
555C23×C4—224no—
556C23×C4—224no—
557C23×C4—224no—
558C23×C4—224no—
559C23×C4—224no—
560C23×C4—224no—
561C23×C4—224no—
562C23×C4—224no—
563C23×C4—442no—
564C23×C4—442no—
565C23×C4—442no—
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1114yes—
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573#121—1164no—
574C4×D4—2232no—
575C4×D4—2232no—
576C4×D4—2232no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—118no—
580C2×C4⋊C4—118no—
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⋊C4C22×D1114yes—
591C2×C4⋊C4C22×D1114yes—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—118no—
594C2×C22⋊C4—118no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—224no—
604C2×C22⋊C4—224no—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—442no—
609C2×C22⋊C4C4×D1118yescomplemented
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—44no—
627C2×C11#236118yescomplemented
628C2×C11C22×C4×D411yescharacteristic
629C2×C11C22×C4×D411yescharacteristic
630C2×C11C2×#52011yescharacteristic
631C2×C11C2×D4211yescharacteristic
632C2×C11C2×#54711yescharacteristic
633C2×C11C2×#54811yescharacteristic
634C2×C11C2×#55311yescharacteristic
635D11—28no—
636D11—44no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—114no—
644C24—114no—
645C24—114no—
646C24—112no—
647C24—114no—
648C24—112no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24—222no—
656C24—222no—
657C24—222no—
658C24—222no—
659C24C2×C4×D1114yes—
660C24C23×D1112yes—
661C24C23×D1111yescharacteristic
662C2×D4—1116no—
663C2×D4—1116no—
664C2×D4—1116no—
665C2×D4—228no—
666C2×D4—2232no—
667C2×D4—228no—
668C2×D4—228no—
669C2×D4—2232no—
670C2×D4—228no—
671C2×D4—228no—
672C2×D4—2232no—
673C2×D4—228no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—44no—
691C22×C4—416no—
692C22×C4—114no—
693C22×C4—114no—
694C22×C4—114no—
695C22×C4—112no—
696C22×C4—114no—
697C22×C4—114no—
698C22×C4—114no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—1116no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—228no—
706C22×C4—2232no—
707C22×C4—228no—
708C22×C4—228no—
709C22×C4—228no—
710C22×C4—228no—
711C22×C4—228no—
712C22×C4—222no—
713C22×C4—222no—
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—228no—
725C22×C4—228no—
726C22×C4—444no—
727C22×C4—444no—
728C22×C4—444no—
729C22×C4—4416no—
730C22×C4—4416no—
731C22×C4—4416no—
732C22×C4C2×C4×D1114yes—
733C22×C4C2×C4×D1114yes—
734C22×C4D4×D1114yes—
735C22×C4D4×D1114yes—
736C22×C4C23×D1112yes—
737C22×C4C23×D1112yes—
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—1116no—
745C4⋊C4—1116no—
746C4⋊C4—228no—
747C4⋊C4—228no—
748C4⋊C4—228no—
749C22⋊C4—44no—
750C22⋊C4—1116no—
751C22⋊C4—1116no—
752C22⋊C4—228no—
753C22⋊C4—228no—
754C22⋊C4—228no—
755C22⋊C4—228no—
756C22⋊C4—228no—
757C22⋊C4—444no—
758C22⋊C4C2×C4×D11116yescomplemented
759C42—228no—
760C42—228no—
761C42—228no—
762C42—228no—
763C11C2×#236111yescharacteristic, complemented, Sylow
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—1116no—
778C23—114no—
779C23—114no—
780C23—114no—
781C23—114no—
782C23—228no—
783C23—228no—
784C23—228no—
785C23—228no—
786C23—228no—
787C23—222no—
788C23—222no—
789C23—228no—
790C23—222no—
791C23—222no—
792C23—228no—
793C23—228no—
794C23—228no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—444no—
802C23—444no—
803C23—444no—
804C23—444no—
805C23C22×C4×D1114yes—
806C23C22×C4×D1112yes—
807C23C2×D4×D1112yes—
808C23C2×D4×D1112yes—
809C23#6703712yes—
810C23#6704012yes—
811C23#41×D1112yes—
812C23#41×D1112yes—
813C23C24×D1111yescharacteristic
814D4—2232no—
815D4—2232no—
816D4—2232no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
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—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—416no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—1116no—
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—222no—
850C2×C4—222no—
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—4416no—
862C2×C4—4416no—
863C2×C4—4416no—
864C2×C4—444no—
865C2×C4—444no—
866C2×C4C22×C4×D1114yes—
867C2×C4C22×C4×D1114yes—
868C2×C4C2×D4×D1114yes—
869C2×C4C2×D4×D1114yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—416no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—118no—
879C22—2232no—
880C22—224no—
881C22—224no—
882C22—224no—
883C22—224no—
884C22—224no—
885C22—224no—
886C22—224no—
887C22—224no—
888C22—224no—
889C22—4416no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—442no—
894C22#1062303514yes—
895C22C4×D4×D1114yes—
896C22C4×D4×D1114yes—
897C22#1062312114yes—
898C22#1062316214yes—
899C22#1062316414yes—
900C22#1062319214yes—
901C22C23×C4×D1111yescharacteristic
902C22C22×D4×D1111yescharacteristic
903C22C22×D4×D1111yescharacteristic
904C22C2×#6703711yescharacteristic
905C22C2×#6704011yescharacteristic
906C22C2×#41×D1111yescharacteristic
907C22C2×#41×D1111yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—118no—
915C4—224no—
916C4—224no—
917C4—224no—
918C4—442no—
919C4—442no—
920C2—44no—
921C2—228no—
922C2—444no—
923C2#1307163518yesdirect product factor
924C2C2×C4×D4×D1111yescharacteristic
925C2C2×C4×D4×D1111yescharacteristic
926C2C2×#1062303511yescharacteristic
927C2C2×#1062312111yescharacteristic
928C2C2×#1062316211yescharacteristic
929C2C2×#1062316411yescharacteristic
930C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC22×#66937C2
cosocleC23×C11C25
hypercenterC2×#385D11
hypocenterC11C2×#2361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#66946C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. C22×C4×C22⋊D11C2semidirect
5. C22×C4⋊C4×D11C2semidirect
6. #13071635C2direct (N × H)
7. C2×#10622570C2semidirect
8. C2×#10622585C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622262C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#385C2semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
51. C2×#66946C22semidirect
53. C2×C4⋊C4×D11C22semidirect
54. C2×#66937C4semidirect
56. C11×#385C22semidirect
63. #10622603C22semidirect
64. #10622585C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622564C22semidirect
68. #10622281C22semidirect
69. #10622279C22semidirect
70. #10622278C22semidirect
71. #10622262C22semidirect
89. C22×C22⋊D11C2×C4semidirect
90. C22×C22⋊D11C2×C4semidirect
101. C22×D44C2×C4semidirect
114. C22×C4×D11C2×C4semidirect
124. C2×C11×C22⋊C4C2×C4semidirect
137. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×(C2×D11)⋊C4D4semidirect
149. C2×Dic11⋊C4C2×C4semidirect
150. C2×Dic11⋊C4D4semidirect
165. #66937C2×C4semidirect
232. C2×C22⋊D11C22×C4semidirect
233. C2×C22⋊D11C22×C4semidirect
261. C2×D44C22×C4semidirect
277. C2×C4×D11C22×C4semidirect
281. C11×C22⋊C4C22×C4semidirect
288. (C2×D11)⋊C4C22×C4semidirect
289. (C2×D11)⋊C4C2×D4semidirect
293. Dic11⋊C4C22×C4semidirect
294. Dic11⋊C4C2×D4semidirect
312. C2×#385D11semidirect
360. C22×D11C4×D4semidirect
409. C2×Dic11C4×D4semidirect
467. #385C2×D11semidirect
513. C2×D11C2×C4×D4semidirect
525. Dic11C2×C4×D4semidirect
609. C2×C22⋊C4C4×D11semidirect
627. C2×C11#2361semidirect
758. C22⋊C4C2×C4×D11semidirect
763. C11C2×#2361semidirect
923. C2#13071635direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×#669462
C22×C4×C22⋊D112
C22×C4⋊C4×D112
#130716352
C2×#106225702
C2×#106225852
C2×#106225642
C2×#106226032
C2×#106222782
C2×#106225692
C2×#106222812
C2×#106222622
C2×#106222792
C2×C11×#3852
C2×#236111