Finite Group Databasebeta

← #17949326

Subgroups — #17949326

Order 4352.

206 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543882C211yesmaximal, characteristic
2#14543605C211yesmaximal, characteristic
3#14529942C211yesmaximal, characteristic
4C2×#10587545—21no—
5#11763675—21no—
6#11762817—21no—
7#11762714C2211yescharacteristic
8#11762578C411yescharacteristic
9#11762568—21no—
10C17×#544C411yescharacteristic
11C22×Dic34D411yescharacteristic
12C2×#63247—41no—
13C22×#3624—41no—
14C17×C4⋊Q8—41no—
15C17×#125—41no—
16C17×C22⋊Q8—41no—
17C17×#117—21no—
18C2×C4⋊C4×C17C2×C411yescharacteristic
19C2×C4×Dic17D411yescharacteristic
20C2×#63223—21no—
21#10587545—22no—
22#10587545—41no—
23#10587502—41no—
24#10587481—41no—
25#10587481—41no—
26C2×Q8×C17—41no—
27C22×C4×C17—21no—
28C22×C4×C17C22⋊C411yescharacteristic
29C22×Dic17—21no—
30C22×Dic17—21no—
31C2×Dic34—21no—
32C2×Dic34—41no—
33C2×Dic34—41no—
34C2×Dic34SD1611yescharacteristic
35C2×Dic34Q1611yescharacteristic
36#63247—42no—
37#63247—81no—
38C2×#3624—42no—
39C2×#3624—81no—
40C2×#3624—81no—
41C2×#3624—81no—
42C4⋊C4×C17—21no—
43C4⋊C4×C17—21no—
44C4⋊C4×C17—41no—
45C4⋊C4×C17—41no—
46C4⋊C4×C17—42no—
47C22⋊C4×C17—41no—
48C42×C17—41no—
49C4×Dic17—41no—
50#63223—41no—
51#63223—41no—
52C2×#3622—41no—
53#7431—171nomaximal, Sylow
54C23×C17#9911yescharacteristic
55Q8×C17—161no—
56C2×C4×C17—21no—
57C2×C4×C17—21no—
58C2×C4×C17—41no—
59C2×C4×C17—41no—
60C2×C4×C17—41no—
61C2×C4×C17—81no—
62C2×C4×C17#10311yescharacteristic
63C2×C4×C17#10411yescharacteristic
64C2×Dic17—21no—
65C2×Dic17—21no—
66C2×Dic17—21no—
67C2×Dic17—21no—
68C2×Dic17—41no—
69C2×Dic17—41no—
70C2×Dic17—41no—
71C2×Dic17—41no—
72Dic34—41no—
73Dic34—41no—
74Dic34—81no—
75#3624—82no—
76#3624—82no—
77#3622—81no—
78#2028—171no—
79#1394—171no—
80#1272—171no—
81C22×C17—21no—
82C22×C17—21no—
83C22×C17#32811yescharacteristic
84C22×C17AΣL(1,𝔽16)11yescharacteristic
85C22×C17#35411yescharacteristic
86C4×C17—21no—
87C4×C17—21no—
88C4×C17—81no—
89C4×C17—81no—
90C4×C17—81no—
91Dic17—41no—
92Dic17—41no—
93Dic17—41no—
94Dic17—41no—
95#544#59511yescharacteristic
96#419—341no—
97C2×#101—341no—
98#391—171no—
99#343—171no—
100#339—341no—
101#336—341no—
102C2×C17—21no—
103C2×C17—21no—
104C2×C17#135111yescharacteristic
105C2×C17#140311yescharacteristic
106C2×C17#140511yescharacteristic
107C22×Q8—171no—
108C2×M16—341no—
109C2×M16—681no—
110C22×C8—681no—
111C4⋊Q8—41no—
112#125—41no—
113C22⋊Q8—41no—
114#117—21no—
115C2×C4⋊C4C2×#59511yescharacteristic
116C2×C42—171no—
117#103—681no—
118#103—681no—
119#101—342no—
120#101—681no—
121#95—681no—
122C17#743111yescharacteristic, complemented, Sylow
123C2×Q8—41no—
124C2×Q8—171no—
125C2×Q8—171no—
126C2×Q8—341no—
127C2×Q8—681no—
128C2×Q8—681no—
129C22×C4—21no—
130C22×C4—341no—
131C22×C4—341no—
132C22×C4C22⋊#59511yescharacteristic
133M16—681no—
134M16—682no—
135M16—681no—
136M16—1361no—
137C2×C8—681no—
138C2×C8—682no—
139C2×C8—1361no—
140C2×C8—1361no—
141C2×C8—1361no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—42no—
147C22⋊C4—41no—
148C42—41no—
149C42—681no—
150C23#1058755111yescharacteristic
151Q8—161no—
152Q8—681no—
153Q8—681no—
154Q8—1361no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—341no—
162C2×C4—341no—
163C2×C4—341no—
164C2×C4—341no—
165C2×C4—681no—
166C2×C4—681no—
167C2×C4—681no—
168C2×C4—681no—
169C2×C4#1058754911yescharacteristic
170C2×C4#1058755011yescharacteristic
171C8—1361no—
172C8—1362no—
173C8—1362no—
174C22—21no—
175C22—21no—
176C22#1176366311yescharacteristic
177C22#1176370911yescharacteristic
178C22#1176371511yescharacteristic
179C4—21no—
180C4—21no—
181C4—81no—
182C4—81no—
183C4—81no—
184C4—681no—
185C4—681no—
186C4—681no—
187C4—681no—
188C2—21no—
189C2—21no—
190C2#1454377911yescharacteristic
191C2#1454390511yescharacteristic
192C2#1454390911yescharacteristic
subgroupG/H
centerC22#11763709
commutatorC2×C4⋊C4×C17C2×C4
FrattiniC2×C4⋊C4C2×#595
FittingC17×#544C4
socleC22×C17AΣL(1,𝔽16)
prime radicalC23×C17#99
cosocle#11762714C22
hypercenter#544#595
hypocenterC17#7431
LCSG ▷ C2×C4⋊C4×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #544

Complements

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

NH ≅ G/Ntype
122. C17#7431semidirect

Maximal subgroups

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

subgroupindex
#145438822
#145436052
#145299422
#743117