Finite Group Databasebeta

← #14544089

Subgroups — #14544089

Order 2176.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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#11763826C211yesmaximal, characteristic, complemented
2C2×C4⋊#3624C211yesmaximal, characteristic, complemented
3#11763657C212yesmaximal, complemented
4D4⋊#3624C212yesmaximal, complemented
5#11763354C211yesmaximal, characteristic
6C2×#63254—21no—
7C22×#3624—21no—
8C17×#121C411yescharacteristic
9#10587626C411yescharacteristic
10#10587625—21no—
11D4×Dic17C2211yescharacteristic
12#10587616C411yescharacteristic
13C2×C4×Dic17C2211yescharacteristic
14#10587579C2211yescharacteristic
15#10587574C411yescharacteristic
16#10587571—21no—
17#10587567—21no—
18C22⋊#3624—21no—
19#10587544—21no—
20C4⋊#3624—21no—
21C4⋊#3624C2212yes—
22C4×#3624C2212yes—
23C2×D4×C17—21no—
24C2×D4×C17C2×C411yescharacteristic
25C22×C4×C17C2×C411yescharacteristic
26C2×C22⋊D17—21no—
27C2×C22⋊D17—21no—
28C2×C22⋊D17—21no—
29C22×Dic17—21no—
30C22×Dic17D411yescharacteristic
31C22×Dic17D411yescharacteristic
32#63254—42no—
33#63254—42no—
34C2×D68C2×C411yescharacteristic
35C2×C4×D17—21no—
36C2×Dic34—21no—
37C2×#3624—22no—
38C2×#3624—22no—
39C2×#3624—42no—
40C4⋊C4×C17C2×C411yescharacteristic
41C22⋊C4×C17—21no—
42C22⋊Dic17—21no—
43#63227—21no—
44#63227—21no—
45C4⋊Dic17C2×C411yescharacteristic
46#63225—21no—
47C4×Dic17C2×C411yescharacteristic
48C4×Dic17D411yescharacteristic
49C4×Dic17D411yescharacteristic
50C4×Dic17C2311yescharacteristic
51C23×C17—21no—
52C23×C17C22⋊C411yescharacteristic
53C22×D17—21no—
54D4×C17—22no—
55D4×C17—42no—
56C2×C4×C17—22no—
57C2×C4×C17—21no—
58C2×C4×C17C22⋊C411yescharacteristic
59C2×C4×C17C22×C411yescharacteristic
60C22⋊D17—42no—
61C22⋊D17—42no—
62C22⋊D17—42no—
63C2×Dic17—21no—
64C2×Dic17—41no—
65C2×Dic17—41no—
66C2×Dic17—41no—
67C2×Dic17C22⋊C411yescharacteristic
68C2×Dic17C22⋊C411yescharacteristic
69C2×Dic17D812yes—
70C2×Dic17SD1612yes—
71C2×Dic17C2×D411yescharacteristic
72C2×Dic17C2×D411yescharacteristic
73D68—22no—
74C4×D17—41no—
75C4×D17—41no—
76Dic34—42no—
77#3624—42no—
78#3624—42no—
79#1480—171nomaximal, Sylow
80C22×C17—21no—
81C22×C17—21no—
82C22×C17—41no—
83C22×C17—41no—
84C22×C17—41no—
85C22×C17#10212yes—
86C22×C17C2×C22⋊C411yescharacteristic
87C2×D17—41no—
88C2×D17—41no—
89C2×D17—41no—
90C4×C17—21no—
91C4×C17—41no—
92C4×C17#13112yes—
93Dic17—21no—
94Dic17—21no—
95Dic17—41no—
96Dic17#10212yes—
97Dic17C2×D811yescharacteristic
98Dic17C2×SD1611yescharacteristic
99#532—171no—
100#431—171no—
101C2×C4⋊C8—171no—
102D4⋊C8—172no—
103D4⋊C8—172no—
104C2×C17—22no—
105C2×C17—81no—
106C2×C17#40811yescharacteristic
107C2×C17C2×#10211yescharacteristic
108C2×C17#42111yescharacteristic
109D17—81no—
110C2×#41—341no—
111C22×C8—341no—
112C4⋊Q8—171no—
113#127—171no—
114#124—341no—
115#121—171no—
116#121—341no—
117#121#59511yescharacteristic
118C4×D4—171no—
119C4×D4—171no—
120C4×D4—341no—
121C2×C42—171no—
122C4⋊C8—172no—
123C4⋊C8—341no—
124C4⋊C8—341no—
125C22⋊C8—341no—
126C4×C8—172no—
127C17#148011yescharacteristic, complemented, Sylow
128#41—682no—
129#41—682no—
130C2×Q8—341no—
131C2×D4—21no—
132C2×D4—171no—
133C2×D4—341no—
134C2×D4—341no—
135C2×D4—341no—
136C2×D4C2×#59511yescharacteristic
137C22×C4—171no—
138C22×C4—171no—
139C22×C4—341no—
140C22×C4—341no—
141C22×C4C2×#59511yescharacteristic
142C2×C8—342no—
143C2×C8—342no—
144C2×C8—682no—
145C4⋊C4—171no—
146C4⋊C4—341no—
147C4⋊C4C2×#59511yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—341no—
150C22⋊C4—341no—
151C22⋊C4—341no—
152C42—171no—
153C42—171no—
154C42—171no—
155C42—171no—
156C23—21no—
157C23—341no—
158C23C22⋊#59511yescharacteristic
159Q8—682no—
160D4—22no—
161D4—42no—
162D4—342no—
163D4—682no—
164D4—682no—
165D4—682no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—171no—
169C2×C4—171no—
170C2×C4—172no—
171C2×C4—172no—
172C2×C4—171no—
173C2×C4—171no—
174C2×C4—341no—
175C2×C4—681no—
176C2×C4—681no—
177C2×C4—681no—
178C2×C4—681no—
179C2×C4—681no—
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#1058754712yes—
193C22C2×C22⋊#59511yescharacteristic
194C4—21no—
195C4—41no—
196C4—171no—
197C4—171no—
198C4—172no—
199C4—341no—
200C4—341no—
201C4—681no—
202C4#1058767812yes—
203C2—22no—
204C2—81no—
205C2—1361no—
206C2#1176378211yescharacteristic
207C2C2×#1058754711yescharacteristic
208C2#1176380611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#121C4
socleC22×C17C2×C22⋊C4
prime radical#11763354C2
cosocleC4×Dic17C23
hypercenter#121#595
hypocenterC17#1480
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #11763826C2semidirect
2. C2×C4⋊#3624C2semidirect
3. #11763657C2semidirect
4. D4⋊#3624C2semidirect
127. C17#1480semidirect

Maximal subgroups

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

subgroupindex
#117638262
C2×C4⋊#36242
#117636572
D4⋊#36242
#117633542
#148017