Finite Group Databasebeta

← #17949913

Subgroups — #17949913

Order 4352.

436 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 102 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#14544569C212yesmaximal
2#14543602C214yesmaximal
3#125×Dic17C211yesmaximal, characteristic
4C2×#10587544—22no—
5C2×#10587542—22no—
6#11763675C2214yes—
7#11762708C2212yes—
8#11762695—22no—
9#11762675C411yescharacteristic
10C4⋊C4×Dic17—22no—
11C4⋊C4×Dic17C412yes—
12C42×Dic17C2211yescharacteristic
13C2×C17×#125C411yescharacteristic
14C22×#3624—24no—
15C17×#125—24no—
16C2×C4⋊C4×C17—22no—
17C2×C4⋊C4×C17C2×C412yes—
18C2×C42×C17C2×C411yescharacteristic
19C2×C4⋊Dic17—22no—
20C2×C4⋊Dic17C2×C412yes—
21C2×C4×Dic17—22no—
22C2×C4×Dic17C2×C411yescharacteristic
23C2×C4×Dic17D412yes—
24C2×C4×Dic17D412yes—
25C2×C4×Dic17C2311yescharacteristic
26#10587544—28no—
27#10587542—44no—
28#10587502—22no—
29#10587502—22no—
30#10587502—22no—
31C22×C4×C17—22no—
32C22×C4×C17C22⋊C412yes—
33C22×C4×C17C22×C411yescharacteristic
34C22×Dic17—22no—
35C22×Dic17C22⋊C411yescharacteristic
36C22×Dic17C22⋊C411yescharacteristic
37C22×Dic17C2×D412yes—
38C2×#3624—28no—
39C2×#3624—44no—
40C2×#3624—44no—
41C4⋊C4×C17—28no—
42C4⋊C4×C17—22no—
43C4⋊C4×C17M1614yes—
44C42×C17—22no—
45C4⋊Dic17—42no—
46C4⋊Dic17—42no—
47C4⋊Dic17—42no—
48C4×Dic17—22no—
49C4×Dic17—24no—
50C4×Dic17—22no—
51C4×Dic17—22no—
52C4×Dic17—41no—
53C4×Dic17—44no—
54#7636—171nomaximal, Sylow
55C23×C17C2×C22⋊C411yescharacteristic
56C2×C4×C17—21no—
57C2×C4×C17—21no—
58C2×C4×C17—22no—
59C2×C4×C17—24no—
60C2×C4×C17—22no—
61C2×C4×C17—22no—
62C2×C4×C17—42no—
63C2×C4×C17—42no—
64C2×C4×C17C2×M1612yes—
65C2×Dic17—22no—
66C2×Dic17—22no—
67C2×Dic17—21no—
68C2×Dic17—22no—
69C2×Dic17—42no—
70C2×Dic17—42no—
71C2×Dic17—42no—
72C2×Dic17#10112yes—
73C2×Dic17#10414yes—
74C2×Dic17AGL(1,ℤ/8)12yes—
75C2×Dic17#13712yes—
76#3624—48no—
77C4×#125—171no—
78#1767—172no—
79#1271—174no—
80C22×C17#40711yescharacteristic
81C22×C17#41011yescharacteristic
82C22×C17C2×#10111yescharacteristic
83C22×C17#41712yes—
84C22×C17C2×#10412yes—
85C4×C17—22no—
86C4×C17—42no—
87C4×C17—44no—
88Dic17—22no—
89Dic17—22no—
90Dic17—41no—
91Dic17—82no—
92Dic17#33014yes—
93C2×#125#59511yescharacteristic
94C2×C4⋊C8—342no—
95C2×#97—342no—
96#389—172no—
97#387—342no—
98#382—171no—
99C4×C4⋊C4—172no—
100C4×C4⋊C4—342no—
101C43—171no—
102#336—174no—
103C2×C17#146711yescharacteristic
104C2×C17#148912yes—
105C2×C17#150912yes—
106C2×C17C2×#33011yescharacteristic
107C2×C17#156111yescharacteristic
108C22×C8—344no—
109#125—24no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—172no—
112C2×C4⋊C4—342no—
113C2×C4⋊C4C2×#59512yes—
114C2×C42—172no—
115C2×C42—172no—
116C2×C42—171no—
117C2×C42—171no—
118C2×C42—342no—
119C2×C42C2×#59511yescharacteristic
120C4⋊C8—348no—
121#97—684no—
122#95—342no—
123#95—342no—
124#95—342no—
125C17#763611yescharacteristic, complemented, Sylow
126C22×C4—22no—
127C22×C4—171no—
128C22×C4—172no—
129C22×C4—171no—
130C22×C4—342no—
131C22×C4C22⋊#59512yes—
132C22×C4C22×#59511yescharacteristic
133C2×C8—348no—
134C2×C8—684no—
135C2×C8—684no—
136C4⋊C4—28no—
137C4⋊C4—22no—
138C4⋊C4—682no—
139C4⋊C4—682no—
140C4⋊C4—682no—
141C4⋊C4#6324714yes—
142C42—22no—
143C42—342no—
144C42—344no—
145C42—342no—
146C42—342no—
147C42—681no—
148C42—684no—
149C23C2×C22⋊#59511yescharacteristic
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—172no—
159C2×C4—174no—
160C2×C4—172no—
161C2×C4—172no—
162C2×C4—342no—
163C2×C4—342no—
164C2×C4—341no—
165C2×C4—342no—
166C2×C4—682no—
167C2×C4—682no—
168C2×C4—682no—
169C2×C4C2×#6324712yes—
170C8—688no—
171C22#1176377911yescharacteristic
172C22#1176379011yescharacteristic
173C22D17⋊#10111yescharacteristic
174C22#1176380012yes—
175C22D17⋊#10412yes—
176C4—22no—
177C4—42no—
178C4—44no—
179C4—174no—
180C4—342no—
181C4—342no—
182C4—681no—
183C4—1362no—
184C2#1454404711yescharacteristic
185C2#1454411912yes—
186C2#1454418712yes—
187C2D17⋊#33011yescharacteristic
188C2#1454432411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#125C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#125#595
hypocenterC17#7636
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
125. C17#7636semidirect

Maximal subgroups

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

subgroupindex
#145445692
#145436022
#125×Dic172
#763617