Finite Group Databasebeta

← #14544129

Subgroups — #14544129

Order 2176.

276 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 72 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#11763812C211yesmaximal, characteristic, complemented
2C2×C4×#3624C211yesmaximal, characteristic, complemented
3#11763657C212yesmaximal, complemented
4D4⋊#3624C212yesmaximal, complemented
5#11763354C211yesmaximal, characteristic
6C2×#63254—21no—
7C2×#63247—21no—
8C22×#3624—21no—
9C17×#121C411yescharacteristic
10#10587626C411yescharacteristic
11#10587625—21no—
12D4×Dic17C2211yescharacteristic
13#10587616C411yescharacteristic
14C2×C4×Dic17C2211yescharacteristic
15#10587579C2211yescharacteristic
16#10587574C411yescharacteristic
17#10587571—21no—
18#10587567—21no—
19#10587544—21no—
20C4⋊#3624C2212yes—
21C4×#3624—21no—
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—
37#63247—42no—
38C2×#3624—24no—
39C2×#3624—22no—
40C2×#3624—22no—
41C4⋊C4×C17C2×C411yescharacteristic
42C22⋊C4×C17—21no—
43C22⋊Dic17—21no—
44#63227—21no—
45#63227—21no—
46C4⋊Dic17C2×C411yescharacteristic
47#63225—21no—
48C4×Dic17C2×C411yescharacteristic
49C4×Dic17D411yescharacteristic
50C4×Dic17D411yescharacteristic
51C4×Dic17C2311yescharacteristic
52C23×C17—21no—
53C23×C17C22⋊C411yescharacteristic
54C22×D17—21no—
55D4×C17—22no—
56D4×C17—42no—
57C2×C4×C17—22no—
58C2×C4×C17—21no—
59C2×C4×C17C22⋊C411yescharacteristic
60C2×C4×C17C22×C411yescharacteristic
61C22⋊D17—42no—
62C22⋊D17—42no—
63C22⋊D17—42no—
64C2×Dic17—22no—
65C2×Dic17—21no—
66C2×Dic17—41no—
67C2×Dic17—41no—
68C2×Dic17C22⋊C411yescharacteristic
69C2×Dic17C22⋊C411yescharacteristic
70C2×Dic17D812yes—
71C2×Dic17SD1612yes—
72C2×Dic17C2×D411yescharacteristic
73C2×Dic17C2×D411yescharacteristic
74D68—22no—
75C4×D17—41no—
76C4×D17—41no—
77Dic34—42no—
78#3624—24no—
79#3624—42no—
80#1492—171nomaximal, Sylow
81C22×C17—21no—
82C22×C17—21no—
83C22×C17—41no—
84C22×C17—41no—
85C22×C17—41no—
86C22×C17#10212yes—
87C22×C17C2×C22⋊C411yescharacteristic
88C2×D17—41no—
89C2×D17—41no—
90C2×D17—41no—
91C4×C17—21no—
92C4×C17—41no—
93C4×C17#13112yes—
94Dic17—21no—
95Dic17—41no—
96Dic17#10212yes—
97Dic17#10412yes—
98Dic17C2×D811yescharacteristic
99Dic17C2×SD1611yescharacteristic
100#532—171no—
101#423—171no—
102C2×C4×C8—171no—
103D4⋊C8—172no—
104D4⋊C8—172no—
105C2×C17—22no—
106C2×C17—81no—
107C2×C17#40811yescharacteristic
108C2×C17C2×#10211yescharacteristic
109C2×C17C2×#10411yescharacteristic
110D17—81no—
111C2×#41—341no—
112C2×M16—341no—
113C22×C8—341no—
114C4⋊Q8—171no—
115#127—171no—
116#124—341no—
117#121—171no—
118#121—341no—
119#121#59511yescharacteristic
120C4×D4—171no—
121C4×D4—171no—
122C4×D4—341no—
123C2×C42—171no—
124C4⋊C8—172no—
125C4⋊C8—341no—
126C4×C8—172no—
127C4×C8—341no—
128C17#149211yescharacteristic, complemented, Sylow
129#41—682no—
130#41—682no—
131C2×Q8—341no—
132C2×D4—21no—
133C2×D4—171no—
134C2×D4—341no—
135C2×D4—341no—
136C2×D4—341no—
137C2×D4C2×#59511yescharacteristic
138C22×C4—171no—
139C22×C4—171no—
140C22×C4—341no—
141C22×C4—341no—
142C22×C4C2×#59511yescharacteristic
143M16—682no—
144C2×C8—342no—
145C2×C8—344no—
146C2×C8—342no—
147C4⋊C4—171no—
148C4⋊C4—341no—
149C4⋊C4C2×#59511yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—341no—
152C22⋊C4—341no—
153C22⋊C4—341no—
154C42—171no—
155C42—171no—
156C42—171no—
157C42—171no—
158C23—21no—
159C23—341no—
160C23C22⋊#59511yescharacteristic
161Q8—682no—
162D4—22no—
163D4—42no—
164D4—342no—
165D4—682no—
166D4—682no—
167D4—682no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—171no—
171C2×C4—171no—
172C2×C4—171no—
173C2×C4—172no—
174C2×C4—172no—
175C2×C4—171no—
176C2×C4—342no—
177C2×C4—341no—
178C2×C4—681no—
179C2×C4—681no—
180C2×C4—681no—
181C2×C4—681no—
182C2×C4C22⋊#59511yescharacteristic
183C2×C4C22×#59511yescharacteristic
184C8—344no—
185C8—682no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—681no—
192C22—681no—
193C22—681no—
194C22#1058754712yes—
195C22C2×C22⋊#59511yescharacteristic
196C4—21no—
197C4—41no—
198C4—171no—
199C4—171no—
200C4—172no—
201C4—172no—
202C4—341no—
203C4—681no—
204C4#1058767812yes—
205C2—22no—
206C2—81no—
207C2—1361no—
208C2#1176378211yescharacteristic
209C2C2×#1058754711yescharacteristic
210C2D17⋊#10411yescharacteristic
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#1492
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. #11763812C2semidirect
2. C2×C4×#3624C2semidirect
3. #11763657C2semidirect
4. D4⋊#3624C2semidirect
128. C17#1492semidirect

Maximal subgroups

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

subgroupindex
#117638122
C2×C4×#36242
#117636572
D4⋊#36242
#117633542
#149217