Finite Group Databasebeta

← C2×#13066786 #14674117

Subgroups — C2×#13066786 #14674117

Order 2816.

390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10622684C211yesmaximal, characteristic
2C2×#10622183C211yesmaximal, characteristic
3#13066786C214yesmaximal, direct product factor
4C2×C11×#353C211yesmaximal, characteristic
5C2×C11×#127C2211yescharacteristic
6C2×#66923C411yescharacteristic, complemented
7C2×C11×#99—21no—
8C2×#66898—21no—
9C2×#66896—21no—
10C2×#66896—21no—
11#10622684—21no—
12#10622684—21no—
13#10622684C412yescomplemented
14#10622684C2212yes—
15C2×#66867C411yescharacteristic, complemented
16C11×#353—21no—
17C11×#353C2212yes—
18#10622183—21no—
19#10622183C2212yes—
20C22×D4×C11—41no—
21C22×D4×C11D411yescharacteristic
22C22×D4×C11D411yescharacteristic
23C11×#127—41no—
24C11×#127C2×C411yescharacteristic
25C11×#127D411yescharacteristic
26C11×#127D411yescharacteristic
27C11×#127C2311yescharacteristic
28C2×C11×C22⋊C4—41no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C22⋊Dic11—41no—
31C2×C4⋊Dic11—21no—
32C2×Dic11⋊C4—41no—
33C22×C11⋊C8—21no—
34#66923—21no—
35#66923—41no—
36#66923C2×C412yescomplemented
37C11×#99—22no—
38C11×#99—41no—
39#66898—22no—
40#66898—41no—
41#66896—22no—
42#66896—22no—
43#66896—22no—
44#66896—22no—
45#66867—21no—
46#66867C2×C412yescomplemented
47C2×#1412—111nomaximal, Sylow
48C24×C11—21no—
49C24×C11—21no—
50C2×D4×C11—21no—
51C2×D4×C11—21no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—84no—
61C2×D4×C11C22⋊C411yescharacteristic
62C2×D4×C11C22⋊C411yescharacteristic
63C2×D4×C11C2×D411yescharacteristic
64C2×D4×C11C2×D411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—81no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×Dic11—41no—
69C22×Dic11—81no—
70C11×C22⋊C4—42no—
71C11×C22⋊C4—81no—
72C42×C11—21no—
73C42×C11C22⋊C411yescharacteristic
74C42×C11C22×C411yescharacteristic
75C22⋊Dic11—42no—
76C22⋊Dic11—81no—
77C4⋊Dic11—22no—
78C4⋊Dic11—41no—
79Dic11⋊C4—42no—
80Dic11⋊C4—42no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84C2×#490—111no—
85C2×#353—111no—
86C2×#353D1111yescharacteristic
87#1412—114no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—82no—
97C23×C11—82no—
98C23×C11#9911yescharacteristic
99D4×C11—41no—
100D4×C11—41no—
101D4×C11—41no—
102D4×C11—41no—
103D4×C11—81no—
104D4×C11—81no—
105D4×C11—82no—
106D4×C11—82no—
107D4×C11—82no—
108D4×C11—82no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—82no—
115C2×C4×C11—162no—
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×Dic11—42no—
119C2×Dic11—82no—
120C2×Dic11—82no—
121C2×Dic11—162no—
122C11⋊C8—42no—
123C2×#127C2×D1111yescharacteristic
124C2×#125—111no—
125#490—112no—
126#490—112no—
127#490—221no—
128#490—221no—
129C2×#102—221no—
130C2×#102—221no—
131C2×#99—21no—
132C2×#99—221no—
133C2×#97—111no—
134#353—21no—
135#353—112no—
136#353—221no—
137#353C2×D1112yes—
138C22×C11—22no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11—81no—
144C22×C11—81no—
145C22×C11—81no—
146C22×C11—81no—
147C22×C11—82no—
148C22×C11—82no—
149C22×C11—161no—
150C22×C11—161no—
151C22×C11#35411yescharacteristic
152C22×C11#35411yescharacteristic
153C22×C11C2×#9911yescharacteristic
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—162no—
159Dic11—82no—
160Dic11—162no—
161C22×D4—41no—
162C22×D4D4411yescharacteristic
163C22×D4C22⋊D1111yescharacteristic
164C22×C8—221no—
165#127—41no—
166#127C4×D1111yescharacteristic
167#127D4411yescharacteristic
168#127C22⋊D1111yescharacteristic
169#127C22×D1111yescharacteristic
170#125—112no—
171#125—221no—
172#125—441no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—441no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—441no—
177C2×C42C4×D1111yescharacteristic
178#102—222no—
179#102—222no—
180#102—222no—
181#102—222no—
182#99—22no—
183#99—41no—
184#99—222no—
185#99—441no—
186#97—112no—
187#97—221no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—81no—
191C2×C11—81no—
192C2×C11—81no—
193C2×C11—81no—
194C2×C11#141212yescomplemented
195C2×C11C2×#35411yescharacteristic
196C24—21no—
197C24—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—84no—
209C2×D4(C2×D11)⋊C411yescharacteristic
210C2×D4(C2×D11)⋊C411yescharacteristic
211C2×D4C2×D4411yescharacteristic
212C2×D4C2×C22⋊D1111yescharacteristic
213C22×C4—21no—
214C22×C4—81no—
215C22×C4—441no—
216C22×C4—881no—
217C22×C4(C2×D11)⋊C411yescharacteristic
218C2×C8—222no—
219C2×C8—441no—
220C2×C8—441no—
221C4⋊C4—222no—
222C4⋊C4—442no—
223C4⋊C4—442no—
224C4⋊C4—441no—
225C22⋊C4—42no—
226C22⋊C4—81no—
227C22⋊C4—442no—
228C22⋊C4—881no—
229C42—21no—
230C42(C2×D11)⋊C411yescharacteristic
231C42C2×C4×D1111yescharacteristic
232C11C2×#141211yescharacteristic, complemented, Sylow
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—82no—
242C23—82no—
243C23#6687011yescharacteristic
244D4—41no—
245D4—41no—
246D4—41no—
247D4—41no—
248D4—81no—
249D4—81no—
250D4—82no—
251D4—82no—
252D4—82no—
253D4—82no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—82no—
260C2×C4—162no—
261C2×C4—442no—
262C2×C4—882no—
263C2×C4—882no—
264C2×C4—1762no—
265C2×C4#6687011yescharacteristic
266C2×C4C2×(C2×D11)⋊C411yescharacteristic
267C8—442no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22—81no—
275C22—81no—
276C22—81no—
277C22—82no—
278C22—82no—
279C22—161no—
280C22—161no—
281C22#1062211111yescharacteristic
282C22#1062211111yescharacteristic
283C22C2×#6687011yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—162no—
289C4—882no—
290C4—1762no—
291C2—21no—
292C2—21no—
293C2—81no—
294C2—81no—
295C2—81no—
296C2—81no—
297C2#1306678612yesdirect product factor
298C2C2×#1062211111yescharacteristic
subgroupG/H
centerC22#10622111
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC2×C11×#353C2
socleC22×C11#354
prime radicalC2×C11×#127C22
cosocleC11×#127C23
hypercenterC2×#353D11
hypocenterC11C2×#1412
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ C2×#353

Complements

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

NH ≅ G/Ntype
3. #13066786C2direct (N × H)
6. C2×#66923C4semidirect
13. #10622684C4semidirect
15. C2×#66867C4semidirect
36. #66923C2×C4semidirect
46. #66867C2×C4semidirect
194. C2×C11#1412semidirect
232. C11C2×#1412semidirect
297. C2#13066786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226842
C2×#106221832
#130667862
C2×C11×#3532
C2×#141211