Finite Group Databasebeta

← C22×#10622604 #14919959

Subgroups — C22×#10622604 #14919959

Order 2816.

8798 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×D44C211yesmaximal, characteristic
2C23×(C2×D11)⋊C4C212yesmaximal, complemented
3C23×(C2×D11)⋊C4C212yesmaximal, complemented
4C2×#10622604C2124yesmaximal, direct product factor
5C22×C11⋊#95C211yesmaximal, characteristic, complemented
6C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
7C25×D11C2212yes—
8C24×C4×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C23×D44—216no—
13C23×D44—28no—
14C23×D44C22112yes—
15C22×C11×C4⋊C4—28no—
16C22×C11×C4⋊C4C22112yescomplemented
17C22×(C2×D11)⋊C4—216no—
18C22×(C2×D11)⋊C4—216no—
19C22×(C2×D11)⋊C4C22124yescomplemented
20C22×(C2×D11)⋊C4C22124yescomplemented
21C2×C11⋊#95C22112yescomplemented
22#10622604C22164yesdirect product factor
23C25×C11C2311yescharacteristic
24C24×D11—28no—
25C24×D11—28no—
26C24×D11—28no—
27C24×D11—28no—
28C24×D11—28no—
29C24×D11—28no—
30C24×D11D4116yes—
31C24×D11C23112yes—
32C23×C4×C11—24no—
33C23×C4×C11—28no—
34C23×C4×C11—24no—
35C23×C4×C11—28no—
36C23×C4×C11—24no—
37C23×C4×C11D418yes—
38C23×C4×C11D418yescomplemented
39C23×C4×C11C2316yes—
40C23×C4×C11C2316yes—
41C23×C4×C11C2316yes—
42C23×Dic11—28no—
43C23×Dic11—28no—
44C23×Dic11—28no—
45C23×Dic11C23112yes—
46C22×D44—2128no—
47C22×D44—296no—
48C22×D44—248no—
49C22×D44C23116yes—
50C2×C11×C4⋊C4—248no—
51C2×C11×C4⋊C4C23116yescomplemented
52C2×(C2×D11)⋊C4—296no—
53C2×(C2×D11)⋊C4—296no—
54C2×(C2×D11)⋊C4C23132yescomplemented
55C2×(C2×D11)⋊C4C23132yescomplemented
56C11⋊#95C23116yescomplemented
57C22×#394—111nomaximal, Sylow
58C24×C11C2×D418yes—
59C24×C11C2×D414yes—
60C24×C11C2×D414yes—
61C24×C11#4114yes—
62C24×C11#4118yes—
63C24×C11C2413yes—
64C23×D11—264no—
65C23×D11—264no—
66C23×D11—264no—
67C23×D11—224no—
68C23×D11—224no—
69C23×D11—224no—
70C23×D11—224no—
71C23×D11—224no—
72C23×D11—224no—
73C23×D11—432no—
74C23×D11—432no—
75C23×D11—432no—
76C23×D11—432no—
77C23×D11C2×D4148yes—
78C23×D11C2418yes—
79C22×C4×C11—232no—
80C22×C4×C11—232no—
81C22×C4×C11—212no—
82C22×C4×C11—224no—
83C22×C4×C11—212no—
84C22×C4×C11—224no—
85C22×C4×C11—212no—
86C22×C4×C11—416no—
87C22×C4×C11C2×D4124yes—
88C22×C4×C11C2×D4124yescomplemented
89C22×C4×C11C2414yes—
90C22×C4×C11C2414yes—
91C22×C4×C11C2414yes—
92C22×Dic11—224no—
93C22×Dic11—224no—
94C22×Dic11—224no—
95C22×Dic11—432no—
96C22×Dic11C2418yes—
97C2×D44—2384no—
98C2×D44—264no—
99C2×D44—232no—
100C11×C4⋊C4—232no—
101(C2×D11)⋊C4—264no—
102(C2×D11)⋊C4—264no—
103C24×D4—111no—
104C23×C4⋊C4D1111yescharacteristic, complemented
105C23×C22⋊C4—112no—
106C23×C22⋊C4—112no—
107C2×#394—1124no—
108C22×#95—111no—
109C23×C11#120116yes—
110C23×C11#121132yes—
111C23×C11#121116yes—
112C23×C11#123132yes—
113C23×C11#124116yes—
114C23×C11C22×D416yes—
115C23×C11C22×D4112yes—
116C23×C11C22×D416yes—
117C23×C11C2×#4116yes—
118C23×C11C2×#41112yes—
119C23×C11C2511yescharacteristic
120C22×D11—296no—
121C22×D11—296no—
122C22×D11—296no—
123C22×D11—28no—
124C22×D11—28no—
125C22×D11—28no—
126C22×D11—28no—
127C22×D11—28no—
128C22×D11—28no—
129C22×D11—448no—
130C22×D11—448no—
131C22×D11—448no—
132C22×D11—448no—
133C22×D11—4256no—
134C22×D11C22×D4116yes—
135C2×C4×C11—248no—
136C2×C4×C11—248no—
137C2×C4×C11—24no—
138C2×C4×C11—28no—
139C2×C4×C11—24no—
140C2×C4×C11—28no—
141C2×C4×C11—24no—
142C2×C4×C11—424no—
143C2×C4×C11C22×D418yes—
144C2×C4×C11C22×D418yescomplemented
145C2×Dic11—28no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—448no—
149D44—2128no—
150C26—112no—
151C23×D4—1112no—
152C23×D4—2216no—
153C23×D4—228no—
154C24×C4—112no—
155C24×C4C2×D1111yescharacteristic
156C24×C4C2×D1111yescharacteristic
157C24×C4C2×D1111yescharacteristic
158C22×C4⋊C4—28no—
159C22×C4⋊C4C2×D11112yescomplemented
160C22×C22⋊C4—1124no—
161C22×C22⋊C4—1124no—
162C22×C22⋊C4—2216no—
163C22×C22⋊C4—2216no—
164#394—1164no—
165C2×#95—1112no—
166C22×C11#394164yescomplemented
167C22×C11C2×#120112yes—
168C22×C11C2×#121124yes—
169C22×C11C2×#121112yes—
170C22×C11C2×#123124yes—
171C22×C11C2×#124112yes—
172C22×C11C23×D411yescharacteristic
173C22×C11C23×D412yes—
174C22×C11C23×D411yescharacteristic
175C22×C11C22×#4111yescharacteristic
176C22×C11C22×#4112yes—
177C2×D11—216no—
178C2×D11—216no—
179C2×D11—216no—
180C2×D11—4192no—
181C2×D11—48no—
182C2×D11—48no—
183C2×D11—48no—
184C2×D11—48no—
185C4×C11—28no—
186C4×C11—28no—
187C4×C11—44no—
188Dic11—48no—
189C25—1116no—
190C25—1112no—
191C25—228no—
192C25—228no—
193C25—228no—
194C25—228no—
195C25—228no—
196C25—228no—
197C25C22×D1111yescharacteristic
198C22×D4—1116no—
199C22×D4—2296no—
200C22×D4—22128no—
201C22×D4—2248no—
202C23×C4—24no—
203C23×C4—28no—
204C23×C4—24no—
205C23×C4—28no—
206C23×C4—24no—
207C23×C4—1112no—
208C23×C4—228no—
209C23×C4—228no—
210C23×C4—228no—
211C23×C4D4418yescomplemented
212C23×C4C22⋊D1118yes—
213C23×C4C22×D1116yes—
214C23×C4C22×D1116yes—
215C23×C4C22×D1116yes—
216C2×C4⋊C4—248no—
217C2×C4⋊C4C22×D11116yescomplemented
218C2×C22⋊C4—1132no—
219C2×C22⋊C4—1132no—
220C2×C22⋊C4—2296no—
221C2×C22⋊C4—2296no—
222#95—1116no—
223C2×C11C2×#394124yescomplemented
224C2×C11C22×#12011yescharacteristic
225C2×C11C22×#12111yescharacteristic
226C2×C11C22×#12112yes—
227C2×C11C22×#12312yes—
228C2×C11C22×#12411yescharacteristic
229D11—416no—
230C24—1148no—
231C24—118no—
232C24—2264no—
233C24—2264no—
234C24—2264no—
235C24—2224no—
236C24—2224no—
237C24—2224no—
238C24—2224no—
239C24—2224no—
240C24—2224no—
241C24—4432no—
242C24—4432no—
243C24—4432no—
244C24—4432no—
245C24C2×D4414yes—
246C24#433914yes—
247C24D4×D1118yes—
248C24#434318yes—
249C24C2×C22⋊D1114yes—
250C24C23×D1113yes—
251C2×D4—2264no—
252C2×D4—22384no—
253C2×D4—2232no—
254C22×C4—232no—
255C22×C4—232no—
256C22×C4—212no—
257C22×C4—224no—
258C22×C4—212no—
259C22×C4—224no—
260C22×C4—212no—
261C22×C4—416no—
262C22×C4—118no—
263C22×C4—2224no—
264C22×C4—2224no—
265C22×C4—2224no—
266C22×C4—4432no—
267C22×C4C2×D44124yescomplemented
268C22×C4C2×C22⋊D11124yes—
269C22×C4C23×D1114yes—
270C22×C4C23×D1114yes—
271C22×C4C23×D1114yes—
272C4⋊C4—232no—
273C22⋊C4—2264no—
274C22⋊C4—2264no—
275C11C22×#39411yescharacteristic, complemented, Sylow
276C23—1116no—
277C23—2296no—
278C23—2296no—
279C23—2296no—
280C23—228no—
281C23—228no—
282C23—228no—
283C23—228no—
284C23—228no—
285C23—228no—
286C23—4448no—
287C23—4448no—
288C23—4448no—
289C23—4448no—
290C23—44256no—
291C23#66947132yes—
292C23#66948132yes—
293C23#66983116yes—
294C23#66990116yes—
295C23#67000116yes—
296C23C22×D4416yes—
297C23C2×#433916yes—
298C23C2×D4×D11112yes—
299C23C2×#4343112yes—
300C23C22×C22⋊D1116yes—
301C23C24×D1111yescharacteristic
302D4—22128no—
303C2×C4—248no—
304C2×C4—248no—
305C2×C4—24no—
306C2×C4—28no—
307C2×C4—24no—
308C2×C4—28no—
309C2×C4—24no—
310C2×C4—424no—
311C2×C4—228no—
312C2×C4—228no—
313C2×C4—228no—
314C2×C4—4448no—
315C2×C4C22×D4418yescomplemented
316C2×C4C22×C22⋊D1118yes—
317C22—2216no—
318C22—2216no—
319C22—2216no—
320C22—448no—
321C22—44192no—
322C22—448no—
323C22—448no—
324C22—448no—
325C22#10622604164yesdirect product factor
326C22C2×#66947124yes—
327C22C2×#66948124yes—
328C22C2×#66983112yes—
329C22C2×#66990112yes—
330C22C2×#67000112yes—
331C22C23×D4411yescharacteristic
332C22C22×#433911yescharacteristic
333C22C22×D4×D1112yes—
334C22C22×#434312yes—
335C22C23×C22⋊D1111yescharacteristic
336C4—28no—
337C4—28no—
338C4—44no—
339C4—448no—
340C2—4416no—
341C2C2×#10622604124yesdirect product factor
342C2C22×#6699011yescharacteristic
343C2C22×#6698311yescharacteristic
344C2C22×#6694812yes—
345C2C22×#6694712yes—
346C2C22×#6700011yescharacteristic
subgroupG/H
centerC25C22×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC23×C11×C4⋊C4C2
socleC25×C11C23
prime radicalC24×D44C2
hypercenterC23×C4⋊C4D11
hypocenterC11C22×#394
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×(C2×D11)⋊C4C2semidirect
3. C23×(C2×D11)⋊C4C2semidirect
4. C2×#10622604C2direct (N × H)
5. C22×C11⋊#95C2semidirect
6. C23×C11×C4⋊C4C2semidirect
16. C22×C11×C4⋊C4C22semidirect
19. C22×(C2×D11)⋊C4C22semidirect
20. C22×(C2×D11)⋊C4C22semidirect
21. C2×C11⋊#95C22semidirect
22. #10622604C22direct (N × H)
38. C23×C4×C11D4semidirect
51. C2×C11×C4⋊C4C23semidirect
54. C2×(C2×D11)⋊C4C23semidirect
55. C2×(C2×D11)⋊C4C23semidirect
56. C11⋊#95C23semidirect
88. C22×C4×C11C2×D4semidirect
104. C23×C4⋊C4D11semidirect
144. C2×C4×C11C22×D4semidirect
159. C22×C4⋊C4C2×D11semidirect
166. C22×C11#394semidirect
211. C23×C4D44semidirect
217. C2×C4⋊C4C22×D11semidirect
223. C2×C11C2×#394semidirect
267. C22×C4C2×D44semidirect
275. C11C22×#394semidirect
315. C2×C4C22×D44semidirect
325. C22#10622604direct (N × H)
341. C2C2×#10622604direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D442
C23×(C2×D11)⋊C42
C2×#106226042
C22×C11⋊#952
C23×C11×C4⋊C42
C22×#39411