Finite Group Databasebeta

← C22×#10622853 #15617238

Subgroups — C22×#10622853 #15617238

Order 2816.

5278 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C212yesmaximal, complemented
2C2×#10622853C2124yesmaximal, direct product factor
3C22×#66898C214yesmaximal, complemented
4C23×C11×#41C211yesmaximal, characteristic
5C22×C11×#41—22no—
6C22×C11×#41—22no—
7C22×C11×#41—212no—
8C22×C11×#41C4112yescomplemented
9C22×C11×#41C22112yes—
10C23×Q8×C11C411yescharacteristic, complemented
11C23×D4×C11C411yescharacteristic, complemented
12C23×D4×C11C2212yes—
13C24×C4×C11C412yescomplemented
14C24×C4×C11C2211yescharacteristic
15C22×C22⋊Dic11C2214yes—
16C2×#66979—212no—
17C2×#66979C22124yescomplemented
18C22×C4⋊Dic11—22no—
19C22×C4×Dic11—22no—
20#10622853C22164yesdirect product factor
21C2×#66898C22148yescomplemented
22C25×C11C2×C412yes—
23C25×C11C2311yescharacteristic
24C2×C11×#41—224no—
25C2×C11×#41—224no—
26C2×C11×#41—248no—
27C2×C11×#41—224no—
28C2×C11×#41—224no—
29C2×C11×#41—248no—
30C2×C11×#41C2×C4148yescomplemented
31C2×C11×#41C23116yes—
32C22×Q8×C11—26no—
33C22×Q8×C11—22no—
34C22×Q8×C11C2×C4112yescomplemented
35C22×D4×C11—24no—
36C22×D4×C11—212no—
37C22×D4×C11—26no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C4112yes—
40C22×D4×C11C2×C4112yescomplemented
41C22×D4×C11C23112yes—
42C23×C4×C11—212no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11C2×C412yes—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C416yes—
49C23×C4×C11C2×C4124yescomplemented
50C23×C4×C11D412yes—
51C23×C4×C11D412yes—
52C23×C4×C11D4112yes—
53C23×C4×C11C2316yes—
54C23×Dic11—24no—
55C2×C22⋊Dic11—212no—
56C2×C22⋊Dic11C23124yes—
57#66979—248no—
58#66979C23132yescomplemented
59C2×C4⋊Dic11—224no—
60C2×C4×Dic11—224no—
61#66898C23164yescomplemented
62C22×#410—111nomaximal, Sylow
63C24×C11—26no—
64C24×C11—22no—
65C24×C11—44no—
66C24×C11—48no—
67C24×C11C22×C411yescharacteristic
68C24×C11C22×C4112yes—
69C24×C11C22×C413yes—
70C24×C11C2×D412yes—
71C24×C11C2×D416yes—
72C24×C11C2413yes—
73C11×#41—296no—
74C11×#41—296no—
75C11×#41—232no—
76C11×#41—232no—
77C2×Q8×C11—224no—
78C2×Q8×C11—224no—
79C2×Q8×C11C22×C4116yescomplemented
80C2×D4×C11—224no—
81C2×D4×C11—224no—
82C2×D4×C11—224no—
83C2×D4×C11—224no—
84C2×D4×C11—224no—
85C2×D4×C11—224no—
86C2×D4×C11C22×C4124yes—
87C2×D4×C11C22×C4116yescomplemented
88C2×D4×C11C2418yes—
89C22×C4×C11—26no—
90C22×C4×C11—22no—
91C22×C4×C11—248no—
92C22×C4×C11—224no—
93C22×C4×C11—224no—
94C22×C4×C11C22⋊C416yes—
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22⋊C416yes—
97C22×C4×C11C22⋊C412yes—
98C22×C4×C11C22⋊C4112yes—
99C22×C4×C11C22⋊C4112yes—
100C22×C4×C11C22⋊C4124yes—
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22×C4112yes—
103C22×C4×C11C22×C416yes—
104C22×C4×C11C22×C416yes—
105C22×C4×C11C22×C4112yes—
106C22×C4×C11C22×C4132yescomplemented
107C22×C4×C11C2×D4112yes—
108C22×C4×C11C2×D4112yes—
109C22×C4×C11C2×D4124yes—
110C22×C4×C11C2414yes—
111C22×Dic11—224no—
112C22×Dic11—416no—
113C22⋊Dic11—224no—
114C22⋊Dic11C24116yes—
115C4⋊Dic11—232no—
116C4×Dic11—232no—
117C23×#41D1111yescharacteristic
118C22×#117—112no—
119C2×#410—1124no—
120C22×#99—114no—
121C23×C11—28no—
122C23×C11—24no—
123C23×C11—212no—
124C23×C11—212no—
125C23×C11—46no—
126C23×C11—412no—
127C23×C11—46no—
128C23×C11—424no—
129C23×C11—424no—
130C23×C11—48no—
131C23×C11C2×C22⋊C413yes—
132C23×C11C2×C22⋊C416yes—
133C23×C11C2×C22⋊C416yes—
134C23×C11C2×C22⋊C411yescharacteristic
135C23×C11C23×C413yes—
136C23×C11C23×C418yes—
137C23×C11C23×C413yes—
138C23×C11C22×D416yes—
139C23×C11C22×D416yes—
140C23×C11C2511yescharacteristic
141Q8×C11—232no—
142D4×C11—248no—
143D4×C11—216no—
144D4×C11—232no—
145C2×C4×C11—212no—
146C2×C4×C11—212no—
147C2×C4×C11—232no—
148C2×C4×C11—232no—
149C2×C4×C11C2×C22⋊C4112yes—
150C2×C4×C11C2×C22⋊C416yes—
151C2×C4×C11C2×C22⋊C416yes—
152C2×C4×C11C2×C22⋊C4112yes—
153C2×C4×C11C2×C22⋊C4112yes—
154C2×C4×C11C2×C22⋊C4124yes—
155C2×C4×C11C2×C22⋊C4124yes—
156C2×C4×C11C23×C418yes—
157C2×C4×C11C23×C414yes—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C22×D418yes—
160C2×C4×C11C22×D418yes—
161C2×Dic11—216no—
162C2×Dic11—448no—
163C22×#41—22no—
164C22×#41—212no—
165C22×#41—22no—
166C22×#41Dic11112yescomplemented
167C22×#41C2×D11112yes—
168C23×Q8Dic1111yescharacteristic, complemented
169C23×D4Dic1111yescharacteristic, complemented
170C23×D4C2×D1112yes—
171C24×C4Dic1112yescomplemented
172C24×C4C2×D1111yescharacteristic
173C2×#117—1124no—
174C2×#117—2212no—
175C22×C4⋊C4—222no—
176C22×C22⋊C4—114no—
177C22×C42—222no—
178#410—1164no—
179C2×#99—1148no—
180C22×C11—26no—
181C22×C11—26no—
182C22×C11—212no—
183C22×C11—212no—
184C22×C11—28no—
185C22×C11—46no—
186C22×C11—43no—
187C22×C11—46no—
188C22×C11—41no—
189C22×C11—48no—
190C22×C11—424no—
191C22×C11—424no—
192C22×C11#41014yescomplemented
193C22×C11C22×C22⋊C413yes—
194C22×C11C22×C22⋊C416yes—
195C22×C11C22×C22⋊C413yes—
196C22×C11C24×C411yescharacteristic
197C22×C11C23×D412yes—
198C4×C11—28no—
199C4×C11C22×C22⋊C414yes—
200C4×C11C22×C22⋊C414yes—
201C4×C11C22×C22⋊C418yes—
202Dic11—416no—
203C25C2×Dic1112yes—
204C25C22×D1111yescharacteristic
205C2×#41—224no—
206C2×#41—248no—
207C2×#41—224no—
208C2×#41—224no—
209C2×#41—224no—
210C2×#41—248no—
211C2×#41C2×Dic11148yescomplemented
212C2×#41C22×D11116yes—
213C22×Q8—26no—
214C22×Q8—22no—
215C22×Q8C2×Dic11112yescomplemented
216C22×D4—24no—
217C22×D4—212no—
218C22×D4—26no—
219C22×D4—22no—
220C22×D4C2×Dic11112yes—
221C22×D4C2×Dic11112yescomplemented
222C22×D4C22×D11112yes—
223C23×C4—212no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—224no—
227C23×C4C2×Dic1112yes—
228C23×C4C2×Dic1111yescharacteristic
229C23×C4C2×Dic1116yes—
230C23×C4C2×Dic1111yescharacteristic
231C23×C4C2×Dic11124yescomplemented
232C23×C4C22⋊D1112yes—
233C23×C4C22⋊D11112yes—
234C23×C4C22⋊D1112yes—
235C23×C4C22×D1116yes—
236#117—1132no—
237#117—2248no—
238C2×C4⋊C4—2224no—
239C2×C22⋊C4—1124no—
240C2×C22⋊C4—2212no—
241C2×C42—2224no—
242#99—1164no—
243C2×C11—22no—
244C2×C11—23no—
245C2×C11—21no—
246C2×C11—26no—
247C2×C11—48no—
248C2×C11C2×#41016yescomplemented
249C2×C11C23×C22⋊C411yescharacteristic
250C24—26no—
251C24—22no—
252C24—44no—
253C24—48no—
254C24C22×Dic1111yescharacteristic
255C24C22×Dic11112yes—
256C24C22×Dic1113yes—
257C24C2×C22⋊D1112yes—
258C24C2×C22⋊D1116yes—
259C24C23×D1113yes—
260#41—296no—
261#41—296no—
262#41—232no—
263#41—232no—
264C2×Q8—224no—
265C2×Q8—224no—
266C2×Q8C22×Dic11116yescomplemented
267C2×D4—224no—
268C2×D4—224no—
269C2×D4—224no—
270C2×D4—224no—
271C2×D4—224no—
272C2×D4—224no—
273C2×D4C22×Dic11124yes—
274C2×D4C22×Dic11116yescomplemented
275C2×D4C23×D1118yes—
276C22×C4—26no—
277C22×C4—22no—
278C22×C4—248no—
279C22×C4—224no—
280C22×C4—224no—
281C22×C4—2224no—
282C22×C4—4416no—
283C22×C4C22⋊Dic1111yescharacteristic
284C22×C4C22⋊Dic1116yes—
285C22×C4C22⋊Dic1116yes—
286C22×C4C22⋊Dic1112yes—
287C22×C4C22⋊Dic11112yes—
288C22×C4C22⋊Dic11124yes—
289C22×C4C22⋊Dic11112yes—
290C22×C4C22⋊Dic1111yescharacteristic
291C22×C4C22×Dic11112yes—
292C22×C4C22×Dic1116yes—
293C22×C4C22×Dic1116yes—
294C22×C4C22×Dic11112yes—
295C22×C4C22×Dic11132yescomplemented
296C22×C4C2×C22⋊D11112yes—
297C22×C4C2×C22⋊D11112yes—
298C22×C4C2×C22⋊D11124yes—
299C22×C4C23×D1114yes—
300C4⋊C4—2232no—
301C22⋊C4—1116no—
302C22⋊C4—2224no—
303C42—2232no—
304C11C22×#41011yescharacteristic, complemented, Sylow
305C23—28no—
306C23—24no—
307C23—212no—
308C23—212no—
309C23—46no—
310C23—412no—
311C23—46no—
312C23—424no—
313C23—424no—
314C23—48no—
315C23C2×C22⋊Dic1113yes—
316C23C2×C22⋊Dic1116yes—
317C23C2×C22⋊Dic1116yes—
318C23C2×C22⋊Dic1111yescharacteristic
319C23C23×Dic1113yes—
320C23C23×Dic1118yes—
321C23C23×Dic1113yes—
322C23C22×C22⋊D1116yes—
323C23C22×C22⋊D1116yes—
324C23C24×D1111yescharacteristic
325Q8—232no—
326D4—248no—
327D4—216no—
328D4—232no—
329C2×C4—212no—
330C2×C4—212no—
331C2×C4—232no—
332C2×C4—232no—
333C2×C4—2216no—
334C2×C4—4448no—
335C2×C4C2×C22⋊Dic11112yes—
336C2×C4C2×C22⋊Dic1116yes—
337C2×C4C2×C22⋊Dic1116yes—
338C2×C4C2×C22⋊Dic11112yes—
339C2×C4C2×C22⋊Dic11112yes—
340C2×C4C2×C22⋊Dic11124yes—
341C2×C4C2×C22⋊Dic11124yes—
342C2×C4C23×Dic1118yes—
343C2×C4C23×Dic1114yes—
344C2×C4C23×Dic1114yes—
345C2×C4C22×C22⋊D1118yes—
346C2×C4C22×C22⋊D1118yes—
347C22—212no—
348C22—26no—
349C22—26no—
350C22—212no—
351C22—28no—
352C22—46no—
353C22—43no—
354C22—46no—
355C22—41no—
356C22—48no—
357C22—424no—
358C22—424no—
359C22#1062285314yesdirect product factor
360C22C22×C22⋊Dic1113yes—
361C22C22×C22⋊Dic1116yes—
362C22C22×C22⋊Dic1113yes—
363C22C24×Dic1111yescharacteristic
364C22C23×C22⋊D1112yes—
365C4—28no—
366C4—4416no—
367C4C22×C22⋊Dic1114yes—
368C4C22×C22⋊Dic1114yes—
369C4C22×C22⋊Dic1118yes—
370C2—22no—
371C2—23no—
372C2—21no—
373C2—26no—
374C2—48no—
375C2C2×#1062285316yesdirect product factor
376C2C23×C22⋊Dic1111yescharacteristic
subgroupG/H
centerC22×C4C22⋊Dic11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
Fitting, prime radicalC23×C11×#41C2
socleC23×C11C2×C22⋊C4
cosocleC23×C11C25
hypercenterC23×#41D11
hypocenterC11C22×#410
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#66979C2semidirect
2. C2×#10622853C2direct (N × H)
3. C22×#66898C2semidirect
8. C22×C11×#41C4semidirect
10. C23×Q8×C11C4semidirect
11. C23×D4×C11C4semidirect
13. C24×C4×C11C4semidirect
17. C2×#66979C22semidirect
20. #10622853C22direct (N × H)
21. C2×#66898C22semidirect
30. C2×C11×#41C2×C4semidirect
34. C22×Q8×C11C2×C4semidirect
40. C22×D4×C11C2×C4semidirect
49. C23×C4×C11C2×C4semidirect
58. #66979C23semidirect
61. #66898C23semidirect
79. C2×Q8×C11C22×C4semidirect
87. C2×D4×C11C22×C4semidirect
106. C22×C4×C11C22×C4semidirect
166. C22×#41Dic11semidirect
168. C23×Q8Dic11semidirect
169. C23×D4Dic11semidirect
171. C24×C4Dic11semidirect
192. C22×C11#410semidirect
211. C2×#41C2×Dic11semidirect
215. C22×Q8C2×Dic11semidirect
221. C22×D4C2×Dic11semidirect
231. C23×C4C2×Dic11semidirect
248. C2×C11C2×#410semidirect
266. C2×Q8C22×Dic11semidirect
274. C2×D4C22×Dic11semidirect
295. C22×C4C22×Dic11semidirect
304. C11C22×#410semidirect
359. C22#10622853direct (N × H)
375. C2C2×#10622853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106228532
C22×#668982
C23×C11×#412
C22×#41011