Finite Group Databasebeta

← C2×#11763712 #14545034

Subgroups — C2×#11763712 #14545034

Order 2176.

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

normal subgroups only

This group has 278 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
2C2×#10587551C211yesmaximal, characteristic
3#11763712C214yesmaximal, direct product factor
4C2×#10587572C211yesmaximal, characteristic
5C22×C22⋊D17C2211yescharacteristic
6C23×Dic17C411yescharacteristic, complemented
7C2×C22⋊#595—21no—
8C2×#63247—21no—
9C2×C22⋊C4×C17C411yescharacteristic, complemented
10C2×#63227—21no—
11C2×C4⋊Dic17—21no—
12#10587572—21no—
13#10587572—21no—
14#10587572C412yescomplemented
15#10587572C2212yes—
16#10587553—21no—
17#10587553C2212yes—
18#10587551—21no—
19#10587551C2212yes—
20C24×C17C2×C411yescharacteristic
21C23×D17D411yescharacteristic
22C22×#595—41no—
23C22×C4×C17—21no—
24C2×C22⋊D17—41no—
25C2×C22⋊D17—41no—
26C2×C22⋊D17C2×C411yescharacteristic
27C2×C22⋊D17D411yescharacteristic
28C2×C22⋊D17D411yescharacteristic
29C2×C22⋊D17C2311yescharacteristic
30C22×Dic17—21no—
31C22×Dic17—21no—
32C22×Dic17—41no—
33C22×Dic17—41no—
34C22×Dic17C2×C412yescomplemented
35C22×Dic17D411yescharacteristic
36C22⋊#595—22no—
37C22⋊#595—41no—
38#63247—22no—
39#63247—41no—
40C2×#3624—41no—
41C22⋊C4×C17—21no—
42C22⋊C4×C17C2×C412yescomplemented
43#63227—22no—
44#63227—22no—
45C4⋊Dic17—22no—
46C4⋊Dic17—22no—
47C23×C17—21no—
48C23×C17—21no—
49C23×C17—42no—
50C23×C17C22⋊C411yescharacteristic
51C23×C17C22⋊C411yescharacteristic
52C23×C17C22×C411yescharacteristic
53C22×D17—21no—
54C22×D17—21no—
55C22×D17—42no—
56C22×D17C22⋊C411yescharacteristic
57C22×D17C2×D411yescharacteristic
58C2×#595—42no—
59C2×#595—82no—
60C2×C4×C17—22no—
61C2×C4×C17—42no—
62C22⋊D17—41no—
63C22⋊D17—41no—
64C22⋊D17—41no—
65C22⋊D17—41no—
66C2×Dic17—21no—
67C2×Dic17—21no—
68C2×Dic17—22no—
69C2×Dic17—42no—
70C2×Dic17—41no—
71C2×Dic17—41no—
72C2×Dic17—42no—
73C2×Dic17C22⋊C411yescharacteristic
74C2×Dic17C2×D411yescharacteristic
75#3624—42no—
76C2×#352—171nomaximal, Sylow
77C22×C17—22no—
78C22×C17—21no—
79C22×C17—21no—
80C22×C17—41no—
81C22×C17—41no—
82C22×C17—42no—
83C22×C17—42no—
84C22×C17#9911yescharacteristic
85C22×C17#9911yescharacteristic
86C22×C17C2×C22⋊C411yescharacteristic
87C2×D17—21no—
88C2×D17—21no—
89C2×D17—42no—
90C2×D17—41no—
91C2×D17—41no—
92C2×D17—81no—
93#595—82no—
94C4×C17—42no—
95Dic17—21no—
96Dic17—21no—
97Dic17—42no—
98C2×#123—171no—
99C2×#100—171no—
100C2×#99—171no—
101#352—174no—
102C2×C17—21no—
103C2×C17—21no—
104C2×C17—41no—
105C2×C17—41no—
106C2×C17#35212yescomplemented
107C2×C17C2×#9911yescharacteristic
108D17—41no—
109D17—41no—
110C22×D4—171no—
111C23×C4—171no—
112C2×M16—341no—
113#123—172no—
114#123—172no—
115#123—341no—
116#123—341no—
117C2×C4⋊C4—341no—
118C2×C22⋊C4—341no—
119C2×C22⋊C4—341no—
120C2×C22⋊C4#59511yescharacteristic, complemented
121#100—172no—
122#100—341no—
123#99—172no—
124#99—341no—
125C17C2×#35211yescharacteristic, complemented, Sylow
126C24—171no—
127C24C2×#59511yescharacteristic
128C2×D4—171no—
129C2×D4—171no—
130C2×D4—171no—
131C2×D4—171no—
132C2×D4—681no—
133C2×D4—681no—
134C22×C4—21no—
135C22×C4—171no—
136C22×C4—172no—
137C22×C4—341no—
138C22×C4—341no—
139C22×C4—681no—
140C22×C4—681no—
141C22×C4—681no—
142M16—342no—
143M16—681no—
144C2×C8—681no—
145C4⋊C4—342no—
146C4⋊C4—342no—
147C22⋊C4—21no—
148C22⋊C4—342no—
149C22⋊C4—342no—
150C22⋊C4—342no—
151C22⋊C4—681no—
152C22⋊C4C2×#59512yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—171no—
157C23—171no—
158C23—341no—
159C23—341no—
160C23—682no—
161C23C22⋊#59511yescharacteristic
162C23C22⋊#59511yescharacteristic
163C23C22×#59511yescharacteristic
164D4—681no—
165D4—681no—
166D4—681no—
167D4—681no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—171no—
171C2×C4—171no—
172C2×C4—341no—
173C2×C4—341no—
174C2×C4—342no—
175C2×C4—682no—
176C2×C4—681no—
177C2×C4—681no—
178C2×C4—682no—
179C2×C4—682no—
180C2×C4—1362no—
181C8—682no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—341no—
190C22—341no—
191C22—681no—
192C22—681no—
193C22—682no—
194C22—1361no—
195C22#1058753911yescharacteristic
196C22#1058753911yescharacteristic
197C22C2×C22⋊#59511yescharacteristic
198C4—42no—
199C4—341no—
200C4—341no—
201C4—682no—
202C4—1362no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—681no—
208C2—681no—
209C2#1176371212yesdirect product factor
210C2C2×#1058753911yescharacteristic
subgroupG/H
centerC22#10587539
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC2×C22⋊C4×C17C4
socleC22×C17#99
prime radicalC22×C22⋊D17C22
cosocleC2×C22⋊D17C23
hypercenterC2×C22⋊C4#595
hypocenterC17C2×#352
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11763712C2direct (N × H)
6. C23×Dic17C4semidirect
9. C2×C22⋊C4×C17C4semidirect
14. #10587572C4semidirect
34. C22×Dic17C2×C4semidirect
42. C22⋊C4×C17C2×C4semidirect
106. C2×C17#352semidirect
120. C2×C22⋊C4#595semidirect
125. C17C2×#352semidirect
152. C22⋊C4C2×#595semidirect
209. C2#11763712direct (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
#117637122
C2×#105875722
C2×#35217