Finite Group Databasebeta

← #14544303

Subgroups — #14544303

Order 2176.

252 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 62 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
1#11763829C211yesmaximal, characteristic, complemented
2C2×#10587544C211yesmaximal, characteristic, complemented
3#11763669C212yesmaximal, complemented
4#11763667C212yesmaximal, complemented
5#11763355C211yesmaximal, characteristic
6C2×#41×C17C411yescharacteristic
7C2×#63252C411yescharacteristic
8C22×#3624—21no—
9#10587633C411yescharacteristic
10#10587630C2211yescharacteristic
11#10587626C2211yescharacteristic
12#10587625—21no—
13#10587625—21no—
14#10587622C411yescharacteristic
15C4×C22⋊D17—21no—
16C4×C22⋊D17—21no—
17C2×C4×Dic17C2211yescharacteristic
18C22⋊#3624—21no—
19#10587544—21no—
20#10587544C2212yes—
21#10587544C2212yes—
22#10587542—21no—
23#41×C17—42no—
24C2×Q8×C17C2×C411yescharacteristic
25C2×D4×C17—21no—
26C2×D4×C17C2×C411yescharacteristic
27C22×C4×C17—21no—
28C22×C4×C17C2×C411yescharacteristic
29C2×C22⋊D17—21no—
30C2×C22⋊D17—21no—
31C2×C22⋊D17—21no—
32C22×Dic17D411yescharacteristic
33C22×Dic17D411yescharacteristic
34#63252—42no—
35C2×D68C2×C411yescharacteristic
36C2×C4×D17—21no—
37C2×Dic34C2×C411yescharacteristic
38C2×#3624—22no—
39C2×#3624—22no—
40C2×#3624—42no—
41C22⋊Dic17—21no—
42C22⋊Dic17—21no—
43#63227—21no—
44#63227—21no—
45#63225—21no—
46#63225—21no—
47C4×Dic17C2×C411yescharacteristic
48C4×Dic17D411yescharacteristic
49C4×Dic17D411yescharacteristic
50C4×Dic17C2311yescharacteristic
51C23×C17—21no—
52C23×C17C22⋊C411yescharacteristic
53C22×D17—21no—
54Q8×C17—41no—
55D4×C17—41no—
56D4×C17—42no—
57C2×C4×C17—22no—
58C2×C4×C17—21no—
59C2×C4×C17—42no—
60C2×C4×C17C22⋊C411yescharacteristic
61C2×C4×C17C22×C411yescharacteristic
62C22⋊D17—42no—
63C22⋊D17—42no—
64C22⋊D17—41no—
65C22⋊D17—41no—
66C2×Dic17—22no—
67C2×Dic17—21no—
68C2×Dic17—21no—
69C2×Dic17—21no—
70C2×Dic17C22⋊C411yescharacteristic
71C2×Dic17C22⋊C411yescharacteristic
72C2×Dic17C2×D411yescharacteristic
73C2×Dic17C2×D411yescharacteristic
74D68—41no—
75C4×D17—42no—
76Dic34—41no—
77#3624—42no—
78#3624—42no—
79#1551—171nomaximal, Sylow
80C22×C17—21no—
81C22×C17—21no—
82C22×C17—41no—
83C22×C17—41no—
84C22×C17—41no—
85C22×C17#10012yes—
86C22×C17C2×C22⋊C411yescharacteristic
87C2×D17—41no—
88C2×D17—41no—
89C2×D17—41no—
90C4×C17—21no—
91C4×C17—21no—
92C4×C17—41no—
93Dic17—21no—
94Dic17—21no—
95Dic17—41no—
96Dic17#13512yes—
97Dic17AGL(1,ℤ/8)11yescharacteristic
98Dic17#13711yescharacteristic
99#532—171no—
100#432—171no—
101C2×C4⋊C8—171no—
102#333—172no—
103#331—172no—
104C2×C17—22no—
105C2×C17—81no—
106C2×C17C2×#10011yescharacteristic
107C2×C17#41611yescharacteristic
108C2×C17#41711yescharacteristic
109D17—81no—
110C2×#41—171no—
111C2×#41#59511yescharacteristic
112C22×C8—341no—
113C4⋊Q8—171no—
114#127—171no—
115#124—171no—
116#124—171no—
117#121—341no—
118#121—341no—
119C4×D4—341no—
120C4×D4—341no—
121C2×C42—171no—
122C4⋊C8—172no—
123C4⋊C8—172no—
124C4⋊C8—341no—
125C22⋊C8—341no—
126#97—341no—
127C17#155111yescharacteristic, complemented, Sylow
128#41—42no—
129#41—682no—
130C2×Q8—171no—
131C2×Q8C2×#59511yescharacteristic
132C2×D4—21no—
133C2×D4—171no—
134C2×D4—341no—
135C2×D4—341no—
136C2×D4—341no—
137C2×D4C2×#59511yescharacteristic
138C22×C4—21no—
139C22×C4—171no—
140C22×C4—171no—
141C22×C4—341no—
142C22×C4C2×#59511yescharacteristic
143C2×C8—342no—
144C2×C8—342no—
145C2×C8—682no—
146C4⋊C4—341no—
147C4⋊C4—341no—
148C22⋊C4—341no—
149C22⋊C4—341no—
150C22⋊C4—341no—
151C22⋊C4—341no—
152C42—171no—
153C42—171no—
154C42—171no—
155C42—171no—
156C23—21no—
157C23—341no—
158C23C22⋊#59511yescharacteristic
159Q8—41no—
160Q8—681no—
161D4—41no—
162D4—42no—
163D4—681no—
164D4—682no—
165D4—681no—
166D4—681no—
167D4—682no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—171no—
172C2×C4—171no—
173C2×C4—171no—
174C2×C4—171no—
175C2×C4—341no—
176C2×C4—342no—
177C2×C4—341no—
178C2×C4—341no—
179C2×C4—682no—
180C2×C4C22⋊#59511yescharacteristic
181C2×C4C22×#59511yescharacteristic
182C8—682no—
183C8—682no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—681no—
190C22—681no—
191C22—681no—
192C22#1058755312yes—
193C22C2×C22⋊#59511yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—172no—
198C4—171no—
199C4—171no—
200C4—341no—
201C4—341no—
202C4—681no—
203C2—22no—
204C2—81no—
205C2—1361no—
206C2C2×#1058755311yescharacteristic
207C2#1176379911yescharacteristic
208C2#1176380011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC2×#41×C17C4
socleC22×C17C2×C22⋊C4
prime radical#11763355C2
cosocleC4×Dic17C23
hypercenterC2×#41#595
hypocenterC17#1551
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11763829C2semidirect
2. C2×#10587544C2semidirect
3. #11763669C2semidirect
4. #11763667C2semidirect
127. C17#1551semidirect

Maximal subgroups

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

subgroupindex
#117638292
C2×#105875442
#117636692
#117636672
#117633552
#155117