Finite Group Databasebeta

← #14543877

Subgroups — #14543877

Order 2176.

232 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D17⋊#99C211yesmaximal, characteristic
2#11763761C211yesmaximal, characteristic
3#99×D17C211yesmaximal, characteristic
4C2×D4×D17C2211yescharacteristic
5C2×C22⋊#595—21no—
6C2×C22⋊#595—21no—
7C2×C22⋊#595—21no—
8C2×C4⋊#595C411yescharacteristic, complemented
9C2×C4×#595C411yescharacteristic, complemented
10C22⋊C4×D17—21no—
11#10587551—21no—
12#10587539C412yescomplemented
13C17×#99C411yescharacteristic, complemented
14#10587505C411yescharacteristic, complemented
15#10587477—21no—
16C23×D17D411yescharacteristic
17C23×D17D411yescharacteristic
18C22×#595—21no—
19C22×#595—21no—
20C22×#595—41no—
21C2×D4×C17C2×C411yescharacteristic
22C2×C22⋊D17D411yescharacteristic
23C2×C22⋊D17Q811yescharacteristic
24D4×D17—41no—
25D4×D17—41no—
26C2×D68C2×C411yescharacteristic
27C2×C4×D17—41no—
28C2×C4×D17C2×C411yescharacteristic
29C22⋊#595—22no—
30C22⋊#595—42no—
31C22⋊#595—42no—
32C22⋊#595—41no—
33C4⋊#595—41no—
34C4×#595—41no—
35C22⋊C4×C17—21no—
36C22⋊Dic17—21no—
37#63227—41no—
38C23×C17C22⋊C411yescharacteristic
39C23×C17C4⋊C411yescharacteristic
40C22×D17—21no—
41C22×D17—21no—
42C22×D17—21no—
43C22×D17—21no—
44C22×D17—41no—
45C22×D17—41no—
46C22×D17—41no—
47C22×D17—41no—
48C22×D17C22⋊C411yescharacteristic
49C22×D17C22⋊C411yescharacteristic
50C22×D17C4⋊C411yescharacteristic
51C2×#595—22no—
52C2×#595—41no—
53C2×#595—41no—
54C2×#595—42no—
55C2×#595—41no—
56C2×#595—41no—
57C2×#595—41no—
58C2×#595—81no—
59C2×#595—81no—
60D4×C17—41no—
61C2×C4×C17—41no—
62C2×C4×C17C4211yescharacteristic
63C22⋊D17—41no—
64C22⋊D17—41no—
65C2×Dic17—41no—
66C2×Dic17C4⋊C411yescharacteristic
67D68—41no—
68C4×D17—21no—
69C4×D17—21no—
70C4×D17—81no—
71C4×D17—81no—
72#1393—171nomaximal, Sylow
73C22×C17—21no—
74C22×C17—21no—
75C22×C17—41no—
76C22×C17—41no—
77C22×C17#9511yescharacteristic
78C2×D17—21no—
79C2×D17—21no—
80C2×D17—21no—
81C2×D17—21no—
82C2×D17—41no—
83C2×D17—41no—
84C2×D17—41no—
85C2×D17—41no—
86C2×D17—41no—
87C2×D17—41no—
88C2×D17—81no—
89C2×D17—81no—
90C2×D17#9911yescharacteristic
91C2×D17#9911yescharacteristic
92#595—42no—
93#595—82no—
94#595—81no—
95C4×C17—21no—
96C4×C17—81no—
97Dic17—21no—
98Dic17—81no—
99C2×#99—171no—
100C2×#99—171no—
101#390—171no—
102C2×C17—21no—
103C2×C17—41no—
104C2×C17—41no—
105C2×C17#34211yescharacteristic
106D17—21no—
107D17—41no—
108D17—41no—
109D17#35311yescharacteristic
110D17#35411yescharacteristic
111C22×D4—171no—
112C2×C4⋊C4—171no—
113C2×C22⋊C4—341no—
114C2×C22⋊C4—341no—
115C2×C22⋊C4—341no—
116C2×C22⋊C4—341no—
117C2×C42—171no—
118#99—172no—
119#99—171no—
120#99—341no—
121#99—341no—
122#99#59511yescharacteristic, complemented
123C17#139311yescharacteristic, complemented, Sylow
124C24—171no—
125C24—171no—
126C2×D4—171no—
127C2×D4—171no—
128C2×D4—171no—
129C2×D4—681no—
130C2×D4—681no—
131C2×D4C2×#59511yescharacteristic
132C22×C4—171no—
133C22×C4—341no—
134C22×C4—341no—
135C22×C4—681no—
136C22×C4—681no—
137C4⋊C4—681no—
138C22⋊C4—21no—
139C22⋊C4—342no—
140C22⋊C4—341no—
141C22⋊C4—681no—
142C22⋊C4—682no—
143C22⋊C4—682no—
144C22⋊C4—681no—
145C42—681no—
146C23—171no—
147C23—171no—
148C23—171no—
149C23—341no—
150C23—341no—
151C23—341no—
152C23—341no—
153C23—681no—
154C23—681no—
155C23—681no—
156C23—681no—
157C23C4⋊#59511yescharacteristic
158C23C22⋊#59511yescharacteristic
159D4—41no—
160D4—681no—
161D4—681no—
162D4—681no—
163C2×C4—41no—
164C2×C4—171no—
165C2×C4—341no—
166C2×C4—341no—
167C2×C4—342no—
168C2×C4—681no—
169C2×C4—681no—
170C2×C4—681no—
171C2×C4—681no—
172C2×C4—682no—
173C2×C4—681no—
174C2×C4—681no—
175C2×C4—1361no—
176C2×C4—1361no—
177C2×C4—1361no—
178C2×C4—1361no—
179C2×C4C4×#59511yescharacteristic
180C22—21no—
181C22—21no—
182C22—41no—
183C22—41no—
184C22—171no—
185C22—171no—
186C22—341no—
187C22—341no—
188C22—341no—
189C22—341no—
190C22—681no—
191C22—681no—
192C22—681no—
193C22—681no—
194C22—681no—
195C22—681no—
196C22—1361no—
197C22—1361no—
198C22(C2×#595)⋊C411yescharacteristic
199C4—21no—
200C4—81no—
201C4—341no—
202C4—682no—
203C4—1361no—
204C4—1361no—
205C4—1362no—
206C2—21no—
207C2—41no—
208C2—41no—
209C2—171no—
210C2—171no—
211C2—341no—
212C2—681no—
213C2—681no—
214C2#1176368611yescharacteristic
subgroupG/H
centerC2#11763686
commutatorC2×C4×C17C42
FrattiniC2×D4C2×#595
FittingC17×#99C4
socleC2×C17#342
prime radical, cosocleC2×D4×D17C22
hypercenter#99#595
hypocenterC17#1393
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
8. C2×C4⋊#595C4semidirect
9. C2×C4×#595C4semidirect
12. #10587539C4semidirect
13. C17×#99C4semidirect
14. #10587505C4semidirect
122. #99#595semidirect
123. C17#1393semidirect

Maximal subgroups

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

subgroupindex
D17⋊#992
#117637612
#99×D172
#139317