Finite Group Databasebeta

← C2×#11763709 #14545029

Subgroups — C2×#11763709 #14545029

Order 2176.

438 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 58 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×#10587553C211yesmaximal, characteristic, complemented
2C2×#10587551C211yesmaximal, characteristic, complemented
3#11763709C214yesmaximal, direct product factor
4C2×#10587639C211yesmaximal, characteristic
5C25×C17C411yescharacteristic, complemented
6C22×C22⋊D17—21no—
7C22×C22⋊D17C2211yescharacteristic
8C2×C22⋊#595—21no—
9C2×#63247—21no—
10#10587639—21no—
11#10587639—21no—
12#10587639C412yescomplemented
13#10587639C2212yes—
14C2×C22⋊Dic17—21no—
15C2×C22⋊Dic17C411yescharacteristic, complemented
16#10587553—21no—
17#10587553C2212yescomplemented
18#10587551—21no—
19#10587551C2212yescomplemented
20C24×C17—21no—
21C24×C17—21no—
22C24×C17—44no—
23C24×C17—41no—
24C24×C17—41no—
25C24×C17C2×C411yescharacteristic
26C24×C17C2×C412yescomplemented
27C23×D17D411yescharacteristic
28C22×#595—41no—
29C2×C22⋊D17—22no—
30C2×C22⋊D17—22no—
31C2×C22⋊D17—41no—
32C2×C22⋊D17—41no—
33C2×C22⋊D17—44no—
34C2×C22⋊D17C2×C411yescharacteristic
35C2×C22⋊D17D411yescharacteristic
36C2×C22⋊D17D411yescharacteristic
37C2×C22⋊D17C2311yescharacteristic
38C22×Dic17—21no—
39C22×Dic17D411yescharacteristic
40C22⋊#595—22no—
41C22⋊#595—41no—
42#63247—22no—
43#63247—41no—
44C2×#3624—41no—
45C22⋊Dic17—21no—
46C22⋊Dic17—22no—
47C22⋊Dic17—22no—
48C22⋊Dic17C2×C412yescomplemented
49C23×C17—24no—
50C23×C17—21no—
51C23×C17—21no—
52C23×C17—22no—
53C23×C17—42no—
54C23×C17—44no—
55C23×C17—42no—
56C23×C17—42no—
57C23×C17—44no—
58C23×C17—42no—
59C23×C17—44no—
60C23×C17—48no—
61C23×C17—44no—
62C23×C17—41no—
63C23×C17—41no—
64C23×C17C22⋊C411yescharacteristic
65C23×C17C22⋊C411yescharacteristic
66C23×C17C22×C411yescharacteristic
67C22×D17—21no—
68C22×D17—21no—
69C22×D17—42no—
70C22×D17C22⋊C411yescharacteristic
71C22×D17C2×D411yescharacteristic
72C2×#595—42no—
73C2×#595—82no—
74C22⋊D17—41no—
75C22⋊D17—41no—
76C22⋊D17—41no—
77C22⋊D17—41no—
78C22⋊D17—44no—
79C22⋊D17—44no—
80C2×Dic17—21no—
81C2×Dic17—21no—
82C2×Dic17—22no—
83C2×Dic17—42no—
84C2×Dic17C22⋊C411yescharacteristic
85C2×Dic17C2×D411yescharacteristic
86#3624—42no—
87C2×AΣL(1,𝔽16)—171nomaximal, Sylow
88C22×C17—22no—
89C22×C17—24no—
90C22×C17—21no—
91C22×C17—21no—
92C22×C17—41no—
93C22×C17—41no—
94C22×C17—42no—
95C22×C17—44no—
96C22×C17—42no—
97C22×C17—44no—
98C22×C17—44no—
99C22×C17—48no—
100C22×C17—44no—
101C22×C17—42no—
102C22×C17—42no—
103C22×C17#9911yescharacteristic
104C22×C17#9911yescharacteristic
105C22×C17C2×C22⋊C411yescharacteristic
106C2×D17—21no—
107C2×D17—21no—
108C2×D17—42no—
109C2×D17—41no—
110C2×D17—41no—
111C2×D17—81no—
112#595—82no—
113Dic17—21no—
114Dic17—21no—
115Dic17—42no—
116C2×#120—171no—
117C2×#100—171no—
118C2×#99—171no—
119AΣL(1,𝔽16)—174no—
120C2×C17—21no—
121C2×C17—21no—
122C2×C17—44no—
123C2×C17—41no—
124C2×C17—41no—
125C2×C17AΣL(1,𝔽16)12yescomplemented
126C2×C17C2×#9911yescharacteristic
127D17—41no—
128D17—41no—
129C25#59511yescharacteristic, complemented
130C22×D4—171no—
131C22×D4—341no—
132C2×M16—341no—
133#120—172no—
134#120—172no—
135#120—341no—
136#120—341no—
137C2×C22⋊C4—171no—
138C2×C22⋊C4—341no—
139C2×C22⋊C4—341no—
140#100—172no—
141#100—341no—
142#99—172no—
143#99—341no—
144C17C2×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
145C24—21no—
146C24—21no—
147C24—44no—
148C24—41no—
149C24—41no—
150C24—171no—
151C24C2×#59511yescharacteristic
152C24C2×#59512yescomplemented
153C2×D4—171no—
154C2×D4—171no—
155C2×D4—171no—
156C2×D4—171no—
157C2×D4—342no—
158C2×D4—342no—
159C2×D4—681no—
160C2×D4—681no—
161C2×D4—684no—
162C22×C4—171no—
163C22×C4—341no—
164C22×C4—681no—
165M16—342no—
166M16—681no—
167C2×C8—681no—
168C22⋊C4—172no—
169C22⋊C4—342no—
170C22⋊C4—342no—
171C22⋊C4—341no—
172C22⋊C4—342no—
173C22⋊C4—681no—
174C23—24no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—42no—
179C23—44no—
180C23—42no—
181C23—42no—
182C23—44no—
183C23—42no—
184C23—44no—
185C23—48no—
186C23—44no—
187C23—41no—
188C23—41no—
189C23—171no—
190C23—171no—
191C23—341no—
192C23—341no—
193C23—682no—
194C23C22⋊#59511yescharacteristic
195C23C22⋊#59511yescharacteristic
196C23C22×#59511yescharacteristic
197D4—681no—
198D4—681no—
199D4—681no—
200D4—681no—
201D4—684no—
202D4—684no—
203C2×C4—171no—
204C2×C4—171no—
205C2×C4—341no—
206C2×C4—341no—
207C2×C4—342no—
208C2×C4—682no—
209C2×C4—682no—
210C2×C4—1362no—
211C8—682no—
212C22—22no—
213C22—24no—
214C22—21no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22—44no—
220C22—42no—
221C22—44no—
222C22—44no—
223C22—48no—
224C22—42no—
225C22—44no—
226C22—42no—
227C22—341no—
228C22—341no—
229C22—681no—
230C22—681no—
231C22—682no—
232C22—1361no—
233C22#1058755111yescharacteristic
234C22#1058755111yescharacteristic
235C22C2×C22⋊#59511yescharacteristic
236C4—341no—
237C4—341no—
238C4—682no—
239C4—1362no—
240C2—21no—
241C2—21no—
242C2—44no—
243C2—41no—
244C2—41no—
245C2—681no—
246C2—681no—
247C2#1176370912yesdirect product factor
248C2C2×#1058755111yescharacteristic
subgroupG/H
centerC22#10587551
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC25×C17C4
socleC22×C17#99
prime radicalC2×#10587639C2
cosocleC2×C22⋊D17C23
hypercenterC25#595
hypocenterC17C2×AΣL(1,𝔽16)
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C2×#10587553C2semidirect
2. C2×#10587551C2semidirect
3. #11763709C2direct (N × H)
5. C25×C17C4semidirect
12. #10587639C4semidirect
15. C2×C22⋊Dic17C4semidirect
17. #10587553C22semidirect
19. #10587551C22semidirect
26. C24×C17C2×C4semidirect
48. C22⋊Dic17C2×C4semidirect
125. C2×C17AΣL(1,𝔽16)semidirect
129. C25#595semidirect
144. C17C2×AΣL(1,𝔽16)semidirect
152. C24C2×#595semidirect
247. C2#11763709direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105875532
C2×#105875512
#117637092
C2×#105876392
C2×AΣL(1,𝔽16)17