Finite Group Databasebeta

← #14544163

Subgroups — #14544163

Order 2176.

284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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#11763827C211yesmaximal, characteristic, complemented
2C4×C4⋊#595C211yesmaximal, characteristic, complemented
3#11763661C212yesmaximal, complemented
4#11763660C212yesmaximal, complemented
5#11763356C211yesmaximal, characteristic
6C2×#63252—21no—
7C2×C4⋊#595—21no—
8C2×C4×#595—21no—
9C4×D4×C17C411yescharacteristic, complemented
10#10587626C411yescharacteristic, complemented
11#10587624C2211yescharacteristic
12C4×C22⋊D17—21no—
13#10587581C2211yescharacteristic
14#10587574C411yescharacteristic, complemented
15#10587571—21no—
16#10587570—21no—
17C4×D68C411yescharacteristic, complemented
18C42×D17C2211yescharacteristic
19(C2×#595)⋊C4C2212yes—
20#10587544—21no—
21#10587543C2212yes—
22C4×#3624—21no—
23C22×#595—22no—
24C2×D4×C17C2×C411yescharacteristic
25C22×C4×C17—21no—
26C2×C22⋊D17—21no—
27C2×C22⋊D17—21no—
28C2×C22⋊D17—21no—
29#63252—42no—
30#63252—42no—
31C2×D68—21no—
32C2×D68C2×C411yescharacteristic
33C2×C4×D17—21no—
34C2×C4×D17D411yescharacteristic
35C2×C4×D17D411yescharacteristic
36C2×C4×D17C2311yescharacteristic
37C2×Dic34—21no—
38C2×#3624—22no—
39C4⋊#595—24no—
40C4×#595—42no—
41C4⋊C4×C17C2×C411yescharacteristic
42C22⋊C4×C17—21no—
43C42×C17C2×C411yescharacteristic
44C22⋊Dic17—21no—
45#63227—21no—
46#63227—21no—
47C4⋊Dic17C2×C411yescharacteristic
48#63225—21no—
49C4×Dic17C2×C411yescharacteristic
50C4×Dic17D411yescharacteristic
51C4×Dic17D411yescharacteristic
52C23×C17—21no—
53C22×D17—21no—
54C22×D17C2×D411yescharacteristic
55C2×#595—24no—
56C2×#595—42no—
57C2×#595—42no—
58D4×C17—41no—
59C2×C4×C17—21no—
60C2×C4×C17—42no—
61C2×C4×C17C22⋊C411yescharacteristic
62C2×C4×C17C22⋊C411yescharacteristic
63C2×C4×C17C22×C411yescharacteristic
64C22⋊D17—41no—
65C22⋊D17—41no—
66C22⋊D17—42no—
67C22⋊D17—42no—
68C2×Dic17—21no—
69C2×Dic17C22⋊C411yescharacteristic
70C2×Dic17C22⋊C411yescharacteristic
71C2×Dic17C2×D411yescharacteristic
72D68—41no—
73D68—41no—
74D68—41no—
75C4×D17—22no—
76C4×D17—41no—
77C4×D17—42no—
78C4×D17D812yes—
79C4×D17SD1612yes—
80Dic34—42no—
81#3624—42no—
82#1502—171nomaximal, Sylow
83C22×C17—41no—
84C22×C17—41no—
85C22×C17—41no—
86C22×C17C2×C22⋊C411yescharacteristic
87C2×D17—21no—
88C2×D17—21no—
89C2×D17—41no—
90C2×D17—41no—
91C2×D17—41no—
92C2×D17C2×D811yescharacteristic
93C2×D17C2×SD1611yescharacteristic
94#595—44no—
95C4×C17—21no—
96C4×C17—21no—
97C4×C17—41no—
98C4×C17#10212yes—
99Dic17—21no—
100Dic17—41no—
101Dic17#10212yes—
102Dic17#10412yes—
103#532—171no—
104#431—171no—
105C4×C4⋊C4—171no—
106#327—172no—
107#327—172no—
108C2×C17—81no—
109C2×C17#41011yescharacteristic
110C2×C17C2×#10211yescharacteristic
111C2×C17C2×#10411yescharacteristic
112D17—21no—
113D17—21no—
114D17—81no—
115C2×#41—341no—
116C4⋊Q8—171no—
117#127—171no—
118#124—341no—
119#121—171no—
120#121—171no—
121#121—341no—
122C4×D4—171no—
123C4×D4—341no—
124C4×D4#59511yescharacteristic, complemented
125C2×C4⋊C4—341no—
126C2×C42—171no—
127C2×C42—341no—
128C4⋊C8—341no—
129C22⋊C8—172no—
130C4×C8—341no—
131#95—172no—
132C17#150211yescharacteristic, complemented, Sylow
133#41—682no—
134#41—682no—
135C2×Q8—341no—
136C2×D4—171no—
137C2×D4—341no—
138C2×D4—341no—
139C2×D4—341no—
140C2×D4—341no—
141C2×D4C2×#59511yescharacteristic
142C22×C4—21no—
143C22×C4—171no—
144C22×C4—171no—
145C22×C4—171no—
146C22×C4—342no—
147C22×C4—341no—
148C2×C8—342no—
149C4⋊C4—171no—
150C4⋊C4—341no—
151C4⋊C4—344no—
152C4⋊C4C2×#59511yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—341no—
155C22⋊C4—341no—
156C22⋊C4—341no—
157C42—171no—
158C42—171no—
159C42—171no—
160C42—682no—
161C42C2×#59511yescharacteristic
162C23—21no—
163C23—171no—
164C23—341no—
165Q8—682no—
166D4—41no—
167D4—681no—
168D4—681no—
169D4—681no—
170D4—682no—
171D4—682no—
172D4—681no—
173D4—681no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—171no—
177C2×C4—171no—
178C2×C4—172no—
179C2×C4—172no—
180C2×C4—171no—
181C2×C4—342no—
182C2×C4—344no—
183C2×C4—341no—
184C2×C4—681no—
185C2×C4—682no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4C22⋊#59511yescharacteristic
189C2×C4C22⋊#59511yescharacteristic
190C2×C4C22×#59511yescharacteristic
191C8—682no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—171no—
196C22—171no—
197C22—341no—
198C22—341no—
199C22—681no—
200C22—681no—
201C22—681no—
202C22C2×C22⋊#59511yescharacteristic
203C4—21no—
204C4—21no—
205C4—41no—
206C4—172no—
207C4—172no—
208C4—341no—
209C4—684no—
210C4—681no—
211C4#1058754712yes—
212C2—81no—
213C2—341no—
214C2—341no—
215C2—1361no—
216C2#1176378811yescharacteristic
217C2C2×#1058754711yescharacteristic
218C2D17⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC4×D4×C17C4
socleC22×C17C2×C22⋊C4
prime radical#11763356C2
cosocleC2×C4×D17C23
hypercenterC4×D4#595
hypocenterC17#1502
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11763827C2semidirect
2. C4×C4⋊#595C2semidirect
3. #11763661C2semidirect
4. #11763660C2semidirect
9. C4×D4×C17C4semidirect
10. #10587626C4semidirect
14. #10587574C4semidirect
17. C4×D68C4semidirect
124. C4×D4#595semidirect
132. C17#1502semidirect

Maximal subgroups

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

subgroupindex
#117638272
C4×C4⋊#5952
#117636612
#117636602
#117633562
#150217