Finite Group Databasebeta

← C2×#13067694 #14729643

Subgroups — C2×#13067694 #14729643

Order 2816.

1126 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622698C211yesmaximal, characteristic
2C2×#10622640C212yesmaximal
3#13067694C218yesmaximal, direct product factor
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×Q8⋊(C11⋊C8)C212yesmaximal, complemented
6C2×Q82×C11C211yesmaximal, characteristic, complemented
7Q82×C11—22no—
8Q82×C11—24no—
9Q82×C11C2214yescomplemented
10C2×C11×C4⋊Q8—22no—
11C2×C11×C4⋊Q8—22no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—22no—
14C2×C4×Q8×C11C2212yes—
15C22×#4325—22no—
16C22×#4325—22no—
17C2×#66927C2211yescharacteristic
18#10622698—22no—
19#10622698C2214yes—
20#10622640—24no—
21#10622640C2218yes—
22C2×#66873—22no—
23C2×C4⋊(C11⋊C8)C2212yes—
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622184C2214yescomplemented
26Q8⋊(C11⋊C8)C2218yescomplemented
27C22×Q8×C11—22no—
28C22×Q8×C11D412yes—
29C22×Q8×C11D412yes—
30C22×D44—21no—
31C22×D44—22no—
32C11×C4⋊Q8—28no—
33C11×C4⋊Q8—28no—
34C11×C4⋊Q8—28no—
35C11×C4⋊Q8—28no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8C2312yes—
39C4×Q8×C11—28no—
40C4×Q8×C11—28no—
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C4×Q8×C11D414yes—
44C4×Q8×C11C2314yes—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4D412yes—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11C2311yescharacteristic
52C2×#4325—28no—
53C2×#4325—28no—
54C2×#4325—48no—
55C2×#4325—48no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8—22no—
58#66927—22no—
59#66927—21no—
60#66927C2312yes—
61#66873—28no—
62C4⋊(C11⋊C8)—22no—
63C4⋊(C11⋊C8)C2314yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8C2312yes—
66C2×#1623—111nomaximal, Sylow
67C23×D11—41no—
68C2×Q8×C11—28no—
69C2×Q8×C11—22no—
70C2×Q8×C11—22no—
71C2×Q8×C11—24no—
72C2×Q8×C11—44no—
73C2×Q8×C11—84no—
74C2×Q8×C11SD1618yescomplemented
75C2×Q8×C11C2×D414yes—
76C2×Q8×C11C2×D414yes—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×D44—24no—
83C2×D44—22no—
84C2×D44—44no—
85C2×D44—41no—
86C2×D44—42no—
87C2×D44—44no—
88C2×D44—44no—
89C11×C4⋊C4—216no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4C2×D414yes—
96C42×C11—28no—
97C42×C11—24no—
98C42×C11—24no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D412yes—
101C42×C11C2411yescharacteristic
102#4325—416no—
103#4325—416no—
104C2×C11⋊C8—24no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—44no—
108C2×Q82D1111yescharacteristic, complemented
109C2×#492—111no—
110C2×#460—112no—
111#1623—118no—
112C2×#333—111no—
113C2×Q8⋊C8—112no—
114C23×C11#12011yescharacteristic
115C22×D11—42no—
116C22×D11—84no—
117C22×D11—82no—
118Q8×C11—24no—
119Q8×C11—28no—
120Q8×C11—44no—
121Q8×C11—82no—
122Q8×C11—88no—
123Q8×C11C2×SD1618yescomplemented
124C2×C4×C11—24no—
125C2×C4×C11—28no—
126C2×C4×C11—22no—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12012yes—
133C2×C4×C11C2×SD1614yes—
134C2×C4×C11#13714yes—
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C22×D412yes—
137D44—44no—
138D44—44no—
139D44—44no—
140D44—82no—
141D44—84no—
142C11⋊C8—24no—
143C11⋊C8—44no—
144C22×SD16—222no—
145C22×SD16—222no—
146Q82—22no—
147Q82—24no—
148Q82C2×D1114yescomplemented
149C2×C4⋊Q8—22no—
150C2×C4⋊Q8—22no—
151C2×C4⋊Q8C2×D1111yescharacteristic
152C2×#127—111no—
153C2×C4×Q8—22no—
154C2×C4×Q8C2×D1112yes—
155#492—114no—
156#492—222no—
157#460—118no—
158#460—224no—
159C2×C4⋊C8—112no—
160C2×#102—222no—
161C2×C4×C8—111no—
162#333—114no—
163Q8⋊C8—118no—
164C22×C11#44814yes—
165C22×C11#45312yes—
166C22×C11C2×#12011yescharacteristic
167C2×D11—84no—
168C2×D11—82no—
169C2×D11—164no—
170C4×C11—28no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—44no—
174C4×C11—44no—
175C4×C11#44814yes—
176C4×C11C22×SD1612yes—
177C4×C11C2×#13712yes—
178C22×Q8—22no—
179C22×Q8C22⋊D1112yes—
180C22×Q8C22⋊D1112yes—
181C22×D4—221no—
182C22×D4—222no—
183C2×SD16—228no—
184C2×SD16—228no—
185C2×SD16—448no—
186C2×SD16—448no—
187C22×C8—221no—
188C22×C8—222no—
189C4⋊Q8—28no—
190C4⋊Q8—28no—
191C4⋊Q8—28no—
192C4⋊Q8—28no—
193C4⋊Q8—22no—
194C4⋊Q8C22⋊D1112yes—
195C4⋊Q8C22×D1112yes—
196#127—112no—
197#127—222no—
198#127—221no—
199C4×Q8—28no—
200C4×Q8—28no—
201C4×Q8—22no—
202C4×Q8—22no—
203C4×Q8C22⋊D1114yes—
204C4×Q8C22×D1114yes—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4C22⋊D1112yes—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—114no—
213C4⋊C8—222no—
214#102—228no—
215C4×C8—112no—
216C4×C8—221no—
217C2×C11#162314yescomplemented
218C2×C11C2×#44812yes—
219C2×C11C2×#45311yescharacteristic
220D11—162no—
221C24—441no—
222C2×Q8—28no—
223C2×Q8—24no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—44no—
227C2×Q8—84no—
228C2×Q8#432518yescomplemented
229C2×Q8C2×C22⋊D1114yes—
230C2×Q8C2×C22⋊D1114yes—
231C2×D4—224no—
232C2×D4—222no—
233C2×D4—444no—
234C2×D4—444no—
235C2×D4—444no—
236C2×D4—441no—
237C2×D4—442no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4C2×C22⋊D1111yescharacteristic
242C22×C4C2×C22⋊D1112yes—
243SD16—4416no—
244SD16—4416no—
245C2×C8—224no—
246C2×C8—222no—
247C2×C8—224no—
248C2×C8—444no—
249C4⋊C4—216no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—22no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4C2×C22⋊D1114yes—
256C42—28no—
257C42—24no—
258C42—24no—
259C42C2×C22⋊D1111yescharacteristic
260C42C2×C22⋊D1112yes—
261C42C23×D1111yescharacteristic
262C11C2×#162311yescharacteristic, complemented, Sylow
263C23—442no—
264C23—884no—
265C23—882no—
266C23#6700611yescharacteristic
267Q8—24no—
268Q8—28no—
269Q8—44no—
270Q8—82no—
271Q8—88no—
272Q8C2×#432518yescomplemented
273D4—444no—
274D4—444no—
275D4—444no—
276D4—882no—
277D4—884no—
278C2×C4—28no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4C2×#432514yes—
286C2×C4#6699514yes—
287C2×C4#6700611yescharacteristic
288C2×C4#6700612yes—
289C2×C4C22×C22⋊D1111yescharacteristic
290C2×C4C22×C22⋊D1112yes—
291C8—224no—
292C8—444no—
293C22—884no—
294C22—882no—
295C22—1764no—
296C22#1062284014yes—
297C22#1062285412yes—
298C22C2×#6700611yescharacteristic
299C4—28no—
300C4—21no—
301C4—21no—
302C4—44no—
303C4—44no—
304C4#1062284014yes—
305C4C22×#432512yes—
306C4C2×#6699512yes—
307C2—1762no—
308C2#1306769414yesdirect product factor
309C2C2×#1062284012yes—
310C2C2×#1062285411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×Q82×C11C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenterC2×Q82D11
hypocenterC11C2×#1623
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
3. #13067694C2direct (N × H)
4. C2×#10622184C2semidirect
5. C2×Q8⋊(C11⋊C8)C2semidirect
6. C2×Q82×C11C2semidirect
9. Q82×C11C22semidirect
25. #10622184C22semidirect
26. Q8⋊(C11⋊C8)C22semidirect
74. C2×Q8×C11SD16semidirect
108. C2×Q82D11semidirect
123. Q8×C11C2×SD16semidirect
148. Q82C2×D11semidirect
217. C2×C11#1623semidirect
228. C2×Q8#4325semidirect
262. C11C2×#1623semidirect
272. Q8C2×#4325semidirect
308. C2#13067694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226402
#130676942
C2×#106221842
C2×Q8⋊(C11⋊C8)2
C2×Q82×C112
C2×#162311