Finite Group Databasebeta

← C2×#13069414 #14757357

Subgroups — C2×#13069414 #14757357

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C22×(C2×D11)⋊C8C214yesmaximal, complemented
4#13069414C218yesmaximal, direct product factor
5C22×C11×#97C211yesmaximal, characteristic, complemented
6C23×D44C411yescharacteristic
7C23×C4×D11C2212yes—
8C23×C8×C11C2212yes—
9C22×C42×C11C2211yescharacteristic
10C22×(C2×D11)⋊C4C412yes—
11C22×C4⋊Dic11C411yescharacteristic
12C23×C11⋊C8C2212yes—
13C2×C4×D44—24no—
14C2×C4×D44—24no—
15C2×C4×D44C414yes—
16C2×C4×D44C2214yes—
17C2×C11×#97—24no—
18C2×C11×#97C2214yescomplemented
19C2×(C2×D11)⋊C8—216no—
20C2×(C2×D11)⋊C8C22116yescomplemented
21C2×C4⋊(C11⋊C8)—24no—
22C2×C4⋊(C11⋊C8)C2214yescomplemented
23C24×D11C2×C412yes—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2×C412yes—
28C22×D44—28no—
29C22×D44—24no—
30C22×D44C2×C414yes—
31C22×C4×D11—28no—
32C22×C4×D11—24no—
33C22×C4×D11—24no—
34C22×C4×D11—28no—
35C22×C4×D11C2×C414yes—
36C22×C4×D11C2314yes—
37C22×C8×C11—24no—
38C22×C8×C11—24no—
39C22×C8×C11D418yescomplemented
40C22×C8×C11C2314yes—
41C2×C42×C11C2×C412yes—
42C2×C42×C11D414yes—
43C2×C42×C11D414yes—
44C2×C42×C11C2312yes—
45C2×(C2×D11)⋊C4—28no—
46C2×(C2×D11)⋊C4C2×C418yes—
47C2×C4⋊Dic11—24no—
48C2×C4⋊Dic11C2×C414yes—
49C22×C11⋊C8—28no—
50C22×C11⋊C8—24no—
51C22×C11⋊C8C2314yes—
52C4×D44—216no—
53C4×D44—28no—
54C4×D44—28no—
55C11×#97—28no—
56(C2×D11)⋊C8—232no—
57C4⋊(C11⋊C8)—28no—
58C2×#1955—111nomaximal, Sylow
59C24×C11C22×C411yescharacteristic
60C23×D11—24no—
61C23×D11—28no—
62C23×D11—24no—
63C23×D11—28no—
64C23×D11M1618yes—
65C23×D11C22×C414yes—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11C22⋊C414yes—
69C22×C4×C11C22⋊C414yes—
70C22×C4×C11C22×C412yes—
71C22×C4×C11C22×C412yes—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D414yes—
76C22×C4×C11#4114yes—
77C22×C4×C11C2411yescharacteristic
78C22×Dic11—24no—
79C22×Dic11—28no—
80C22×Dic11C22×C414yes—
81C2×D44—232no—
82C2×D44—216no—
83C2×D44—28no—
84C2×C4×D11—28no—
85C2×C4×D11—216no—
86C2×C4×D11—28no—
87C2×C4×D11—24no—
88C2×C4×D11—24no—
89C2×C4×D11—28no—
90C2×C4×D11—416no—
91C2×C4×D11—48no—
92C2×C4×D11—48no—
93C2×C8×C11—216no—
94C2×C8×C11—24no—
95C2×C8×C11—24no—
96C2×C8×C11C2×D418yescomplemented
97C42×C11C22⋊C418yes—
98C42×C11C2×D414yes—
99C42×C11C2×D414yes—
100(C2×D11)⋊C4—216no—
101C4⋊Dic11—28no—
102C2×C11⋊C8—24no—
103C2×C11⋊C8—28no—
104C2×C11⋊C8—48no—
105C22×C4×D4—111no—
106C22×C4⋊C8—111no—
107C22×C22⋊C8—114no—
108C22×#97D1111yescharacteristic, complemented
109#1955—118no—
110C23×C11C2×C22⋊C412yes—
111C23×C11C4×D414yes—
112C23×C11C2×M1614yes—
113C23×C11#13114yes—
114C23×C11C23×C411yescharacteristic
115C22×D11—24no—
116C22×D11—28no—
117C22×D11—24no—
118C22×D11—28no—
119C22×D11—216no—
120C22×D11—232no—
121C22×D11—48no—
122C22×D11—48no—
123C22×D11—416no—
124C22×D11C2×M1618yes—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—28no—
128C2×C4×C11—28no—
129C2×C4×C11C2×C22⋊C414yes—
130C2×C4×C11C2×C22⋊C414yes—
131C2×C4×C11C2×C22⋊C412yes—
132C2×C4×C11C4×D414yes—
133C2×C4×C11#12118yes—
134C2×C4×C11#12414yes—
135C2×C4×C11#12714yes—
136C2×C4×C11C22×D412yes—
137C2×C4×C11C22×D411yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×C4×C11C2×#4112yes—
140C2×Dic11—24no—
141C2×Dic11—28no—
142C2×Dic11—48no—
143D44—232no—
144C4×D11—48no—
145C4×D11—44no—
146C4×D11—44no—
147C4×D11—416no—
148C8×C11—28no—
149C11⋊C8—44no—
150C23×D4—111no—
151C24×C4—112no—
152C23×C8—112no—
153C23×C8C2×D1112yes—
154C2×C4×D4—114no—
155C2×C4×D4—114no—
156C2×C4×D4—224no—
157C2×C4×D4—224no—
158C22×C4⋊C4—111no—
159C22×C22⋊C4—112no—
160C22×C42C2×D1111yescharacteristic
161C2×C4⋊C8—114no—
162C2×C4⋊C8—224no—
163C2×C22⋊C8—1116no—
164C2×C22⋊C8—2216no—
165C2×#97—24no—
166C2×#97C2×D1114yescomplemented
167C22×C11#39014yes—
168C22×C11#40714yes—
169C22×C11#40814yes—
170C22×C11#435116yes—
171C22×C11C22×C22⋊C411yescharacteristic
172C22×C11C2×C4×D412yes—
173C22×C11C22×M1612yes—
174C22×C11C2×#13112yes—
175C2×D11—28no—
176C2×D11—216no—
177C2×D11—44no—
178C2×D11—48no—
179C2×D11—432no—
180C2×D11—44no—
181C4×C11—24no—
182C4×C11—24no—
183C4×C11#39014yes—
184C4×C11C2×#12112yes—
185C4×C11C2×#12411yescharacteristic
186C4×C11C2×#12711yescharacteristic
187Dic11—44no—
188C25—112no—
189C22×D4—114no—
190C22×D4—228no—
191C22×D4—224no—
192C23×C4—112no—
193C23×C4—114no—
194C23×C4—114no—
195C23×C4—224no—
196C23×C4—228no—
197C23×C4—228no—
198C23×C4—224no—
199C23×C4C4×D1111yescharacteristic
200C23×C4C4×D1111yescharacteristic
201C23×C4C22×D1111yescharacteristic
202C22×C8—24no—
203C22×C8—24no—
204C22×C8—114no—
205C22×C8—228no—
206C22×C8—224no—
207C22×C8D4418yescomplemented
208C22×C8C22×D1114yes—
209C4×D4—2216no—
210C4×D4—228no—
211C4×D4—228no—
212C2×C4⋊C4—114no—
213C2×C4⋊C4—224no—
214C2×C22⋊C4—118no—
215C2×C22⋊C4—228no—
216C2×C42C4×D1112yes—
217C2×C42D4414yes—
218C2×C42C22⋊D1114yes—
219C2×C42C22×D1112yes—
220C4⋊C8—228no—
221C22⋊C8—2232no—
222#97—28no—
223C2×C11#195518yescomplemented
224C2×C11C2×#39011yescharacteristic
225C2×C11C2×#40711yescharacteristic
226C2×C11C2×#40811yescharacteristic
227C2×C11C2×#43514yes—
228D11—48no—
229C24—118no—
230C24—114no—
231C24—228no—
232C24—224no—
233C24—228no—
234C24—224no—
235C24C2×C4×D1111yescharacteristic
236C2×D4—2216no—
237C2×D4—2232no—
238C2×D4—228no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—114no—
242C22×C4—228no—
243C22×C4—224no—
244C22×C4—2216no—
245C22×C4—228no—
246C22×C4—228no—
247C22×C4—224no—
248C22×C4—228no—
249C22×C4—224no—
250C22×C4—448no—
251C22×C4—448no—
252C22×C4—4416no—
253C22×C4(C2×D11)⋊C414yes—
254C22×C4(C2×D11)⋊C414yes—
255C22×C4C2×C4×D1112yes—
256C22×C4C2×C4×D1112yes—
257C22×C4C2×C4×D1111yescharacteristic
258C22×C4C2×D4414yes—
259C22×C4C2×D4412yes—
260C22×C4#433914yes—
261C22×C4C2×C22⋊D1112yes—
262C22×C4C23×D1111yescharacteristic
263C2×C8—216no—
264C2×C8—24no—
265C2×C8—24no—
266C2×C8—228no—
267C2×C8—224no—
268C2×C8—448no—
269C2×C8C2×D4418yescomplemented
270C4⋊C4—228no—
271C22⋊C4—2216no—
272C42(C2×D11)⋊C418yes—
273C42C2×D4414yes—
274C42C2×C22⋊D1114yes—
275C11C2×#195511yescharacteristic, complemented, Sylow
276C23—118no—
277C23—2216no—
278C23—228no—
279C23—224no—
280C23—228no—
281C23—224no—
282C23—2232no—
283C23—448no—
284C23—448no—
285C23—4416no—
286C23C4×D4414yes—
287C23M16×D1114yes—
288C23#6696014yes—
289C23C2×(C2×D11)⋊C412yes—
290C23C22×C4×D1111yescharacteristic
291D4—2232no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—228no—
297C2×C4—224no—
298C2×C4—448no—
299C2×C4—444no—
300C2×C4—444no—
301C2×C4—4416no—
302C2×C4—448no—
303C2×C4C4×D4414yes—
304C2×C4#6692714yes—
305C2×C4#6692814yes—
306C2×C4C2×(C2×D11)⋊C414yes—
307C2×C4C2×(C2×D11)⋊C414yes—
308C2×C4C2×(C2×D11)⋊C412yes—
309C2×C4#6698318yes—
310C2×C4C22×D4411yescharacteristic
311C2×C4C22×D4412yes—
312C2×C4C2×#433912yes—
313C2×C4C22×C22⋊D1111yescharacteristic
314C8—28no—
315C8—444no—
316C22—2216no—
317C22—228no—
318C22—448no—
319C22—444no—
320C22—4432no—
321C22—444no—
322C22#10622319116yes—
323C22#1062255214yes—
324C22#1062273914yes—
325C22#1062274214yes—
326C22C2×C4×D4412yes—
327C22C2×M16×D1112yes—
328C22C2×#6696012yes—
329C22C22×(C2×D11)⋊C411yescharacteristic
330C4—24no—
331C4—24no—
332C4—444no—
333C4#1062255214yes—
334C4C2×#6692711yescharacteristic
335C4C2×#6692811yescharacteristic
336C4C2×#6698312yes—
337C2—448no—
338C2#1306941418yesdirect product factor
339C2C2×#1062255211yescharacteristic
340C2C2×#1062273911yescharacteristic
341C2C2×#1062274211yescharacteristic
342C2C2×#1062231914yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#97C2
socleC24×C11C22×C4
prime radicalC23×D44C4
cosocleC22×C4×C11C24
hypercenterC22×#97D11
hypocenterC11C2×#1955
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊(C11⋊C8)C2semidirect
3. C22×(C2×D11)⋊C8C2semidirect
4. #13069414C2direct (N × H)
5. C22×C11×#97C2semidirect
18. C2×C11×#97C22semidirect
20. C2×(C2×D11)⋊C8C22semidirect
22. C2×C4⋊(C11⋊C8)C22semidirect
39. C22×C8×C11D4semidirect
96. C2×C8×C11C2×D4semidirect
108. C22×#97D11semidirect
166. C2×#97C2×D11semidirect
207. C22×C8D44semidirect
223. C2×C11#1955semidirect
269. C2×C8C2×D44semidirect
275. C11C2×#1955semidirect
338. C2#13069414direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D442
C22×C4⋊(C11⋊C8)2
C22×(C2×D11)⋊C82
#130694142
C22×C11×#972
C2×#195511