Finite Group Databasebeta

← #17948388

Subgroups — #17948388

Order 4352.

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

normal subgroups only

This group has 264 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
1#14543705C211yesmaximal, characteristic
2#14543656C211yesmaximal, characteristic
3#14529791C211yesmaximal, characteristic
4#11763780—21no—
5C22⋊#63216—21no—
6C2×#10587632—21no—
7C2×#10587506—21no—
8C2×#10587491C2211yescharacteristic
9#11762572C411yescharacteristic
10C22×Q16×C17C411yescharacteristic
11C22×Q8×C17—21no—
12C22×C4×D17D411yescharacteristic
13C2×#63243—41no—
14C2×Q16×C17—41no—
15C2×Q16×C17—42no—
16C22×C8×C17C2×C411yescharacteristic
17#10587632—42no—
18#10587632—42no—
19C2×#63227—41no—
20C2×C4⋊Dic17—21no—
21C2×#63225—41no—
22C22×#3622D411yescharacteristic
23C22⋊#3624—41no—
24#10587543—22no—
25C2×#63216—41no—
26#10587506—42no—
27#10587491—41no—
28C23×D17SD1611yescharacteristic
29C2×Q8×C17—22no—
30C2×Q8×C17—41no—
31C2×Q8×C17—41no—
32C2×Q8×C17—41no—
33C2×Q8×C17—41no—
34C2×Q8×C17—41no—
35C22×C4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C22×Dic17—41no—
38C22×Dic17D811yescharacteristic
39C2×C4×D17—21no—
40C2×C4×D17—21no—
41C2×C4×D17—41no—
42C2×C4×D17—41no—
43C2×#3624—42no—
44#63243—81no—
45#63243—81no—
46Q16×C17—42no—
47Q16×C17—42no—
48C2×C8×C17—21no—
49C2×C8×C17—41no—
50#63227—44no—
51C4⋊Dic17—22no—
52C4⋊Dic17—41no—
53#63225—44no—
54C2×#3622—21no—
55C2×#3622—41no—
56#63216—81no—
57#7086—171nomaximal, Sylow
58C23×C17#10211yescharacteristic
59C22×D17—21no—
60C22×D17—21no—
61C22×D17—21no—
62C22×D17—41no—
63C22×D17—41no—
64Q8×C17—42no—
65Q8×C17—42no—
66Q8×C17—81no—
67Q8×C17—81no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—42no—
71C2×C4×C17—81no—
72C2×C4×C17—81no—
73C2×C4×C17#9911yescharacteristic
74C2×C4×C17#10411yescharacteristic
75C2×Dic17—21no—
76C2×Dic17—41no—
77C2×Dic17—42no—
78C2×Dic17—81no—
79C2×Dic17—81no—
80C4×D17—41no—
81C4×D17—41no—
82C4×D17—81no—
83#3624—82no—
84C8×C17—41no—
85#3622—41no—
86#2001—171no—
87#1314—171no—
88#1293—171no—
89C22×C17—21no—
90C22×C17—21no—
91C22×C17#32711yescharacteristic
92C22×C17#35911yescharacteristic
93C22×C17#36211yescharacteristic
94C2×D17—42no—
95C2×D17—41no—
96C2×D17—41no—
97C2×D17—41no—
98C2×D17—81no—
99C4×C17—21no—
100C4×C17—82no—
101C4×C17AΣL(1,𝔽16)11yescharacteristic
102C4×C17#35311yescharacteristic
103Dic17—41no—
104Dic17—82no—
105C22×Q16#59511yescharacteristic
106C2×C22⋊Q8—341no—
107C2×#103—341no—
108#407—341no—
109C2×C22⋊C8—171no—
110C22⋊C16—341no—
111#340—171no—
112C2×C17—21no—
113C2×C17—21no—
114C2×C17#134211yescharacteristic
115C2×C17#134311yescharacteristic
116C2×C17#135011yescharacteristic
117D17—81no—
118C22×Q8—21no—
119C23×C4—171no—
120C2×Q16—41no—
121C2×Q16—42no—
122C2×M16—681no—
123C22×C8—171no—
124C22×C8C2×#59511yescharacteristic
125C22⋊Q8—682no—
126C22⋊Q8—682no—
127C2×C4⋊C4—341no—
128C2×C4⋊C4—681no—
129C2×C22⋊C4—681no—
130C2×C16—681no—
131#103—682no—
132C22⋊C8—342no—
133C22⋊C8—681no—
134C22⋊C8—681no—
135C17#708611yescharacteristic, complemented, Sylow
136C24—171no—
137C2×Q8—22no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C22×C4—41no—
144C22×C4—171no—
145C22×C4—341no—
146C22×C4—341no—
147C22×C4—681no—
148C22×C4—681no—
149C22×C4—681no—
150C22×C4C22⋊#59511yescharacteristic
151Q16—42no—
152Q16—42no—
153M16—1361no—
154M16—1361no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8—341no—
158C2×C8—681no—
159C2×C8—682no—
160C4⋊C4—342no—
161C4⋊C4—681no—
162C4⋊C4—684no—
163C22⋊C4—684no—
164C16—1361no—
165C23—341no—
166C23—341no—
167C23—341no—
168C23—681no—
169C23—681no—
170C23#1058754711yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—81no—
174Q8—81no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—341no—
181C2×C4—681no—
182C2×C4—681no—
183C2×C4—681no—
184C2×C4—682no—
185C2×C4—1361no—
186C2×C4—1361no—
187C2×C4—1361no—
188C2×C4#1058754811yescharacteristic
189C2×C4#1058755111yescharacteristic
190C8—41no—
191C8—681no—
192C8—1362no—
193C22—21no—
194C22—21no—
195C22—682no—
196C22—681no—
197C22—681no—
198C22—681no—
199C22—1361no—
200C22#1176366011yescharacteristic
201C22#1176372411yescharacteristic
202C22#1176372811yescharacteristic
203C4—21no—
204C4—82no—
205C4—681no—
206C4—1362no—
207C4#1176370911yescharacteristic
208C4#1176371311yescharacteristic
209C2—21no—
210C2—21no—
211C2—1361no—
212C2#1454376011yescharacteristic
213C2#1454376211yescharacteristic
214C2#1454377611yescharacteristic
subgroupG/H
centerC22#11763660
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC22×Q16×C17C4
socleC22×C17#327
prime radicalC23×D17SD16
cosocleC2×#10587491C22
hypercenterC22×Q16#595
hypocenterC17#7086
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
135. C17#7086semidirect

Maximal subgroups

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

subgroupindex
#145437052
#145436562
#145297912
#708617