Finite Group Databasebeta

← #17949250

Subgroups — #17949250

Order 4352.

238 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 32 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#14543872C211yesmaximal, characteristic
2#14543719C211yesmaximal, characteristic
3#14529906C211yesmaximal, characteristic
4#11763788—21no—
5#11763705—21no—
6C2×#10587595—21no—
7C22×Dic68C411yescharacteristic, complemented
8C2×#10587495—21no—
9#11762775C2211yescharacteristic
10C17×#341C411yescharacteristic, complemented
11C2×#63252D411yescharacteristic
12C22×Dic34—21no—
13#10587677—41no—
14C2×M16×C17—21no—
15C22×C8×C17C2×C411yescharacteristic
16C2×#63223D411yescharacteristic
17#10587595—42no—
18#10587595—42no—
19C2×Dic68—41no—
20C2×Dic68—42no—
21C2×Dic68—41no—
22C2×#63219—41no—
23#10587551—22no—
24#10587539—41no—
25#10587538—41no—
26#10587495—42no—
27#10587491—41no—
28C22×C4×C17C22⋊C411yescharacteristic
29C2×C22⋊D17—21no—
30C22×Dic17—41no—
31#63252—41no—
32#63252—41no—
33C2×D68D811yescharacteristic
34C2×C4×D17—21no—
35C2×Dic34—22no—
36C2×Dic34—41no—
37C2×Dic34—41no—
38C2×Dic34—41no—
39C2×Dic34—41no—
40C2×Dic34—41no—
41C2×Dic34SD1611yescharacteristic
42C22⋊#595—42no—
43C4⋊#595—81no—
44C4×#595—81no—
45M16×C17—22no—
46M16×C17—41no—
47C2×C8×C17—21no—
48C2×C8×C17—41no—
49C2×C8×C17—41no—
50#63223—41no—
51C2×#3622—21no—
52Dic68—42no—
53Dic68—42no—
54Dic68—44no—
55#63219—44no—
56#63216—81no—
57#7399—171nomaximal, Sylow
58C23×C17#10411yescharacteristic
59C22×D17—21no—
60C2×#595—82no—
61C2×C4×C17—21no—
62C2×C4×C17—21no—
63C2×C4×C17#9911yescharacteristic
64C2×C4×C17#10211yescharacteristic
65C22⋊D17—81no—
66C2×Dic17—21no—
67C2×Dic17—42no—
68C2×Dic17—81no—
69C2×Dic17—81no—
70D68—41no—
71C4×D17—41no—
72C4×D17—41no—
73Dic34—41no—
74Dic34—42no—
75Dic34—42no—
76Dic34—81no—
77Dic34—81no—
78C8×C17—42no—
79C8×C17—41no—
80#3622—41no—
81#2020—171no—
82#1391—171no—
83#1321—171no—
84C22×C17—21no—
85C22×C17—41no—
86C22×C17#32711yescharacteristic
87C2×D17—41no—
88C2×D17—81no—
89#595—162no—
90C4×C17—21no—
91C4×C17AΣL(1,𝔽16)11yescharacteristic
92C4×C17#35311yescharacteristic
93Dic17—41no—
94Dic17—82no—
95C2×#137—341no—
96C22×Q16—171no—
97C2×#101—341no—
98#410—341no—
99#408—171no—
100#349—341no—
101#341#59511yescharacteristic, complemented
102C2×C17—21no—
103C2×C17—41no—
104C2×C17#134311yescharacteristic
105D17—81no—
106C2×#41—171no—
107C22×Q8—341no—
108#137—682no—
109#137—682no—
110C2×Q16—681no—
111C2×Q16—681no—
112C2×Q16—682no—
113C2×SD16—681no—
114C2×M16—21no—
115C2×M16—171no—
116C22×C8C2×#59511yescharacteristic
117#117—681no—
118M32—681no—
119#101—682no—
120#99—342no—
121#99—681no—
122C22⋊C8—681no—
123C17#739911yescharacteristic, complemented, Sylow
124#41—681no—
125#41—681no—
126C2×Q8—171no—
127C2×Q8—342no—
128C2×Q8—681no—
129C2×Q8—681no—
130C2×Q8—681no—
131C2×Q8—681no—
132C2×Q8—681no—
133C2×D4—171no—
134C2×D4—341no—
135C22×C4—341no—
136C22×C4—681no—
137C22×C4C22⋊#59511yescharacteristic
138Q16—682no—
139Q16—682no—
140Q16—684no—
141SD16—684no—
142M16—22no—
143M16—41no—
144M16—681no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—41no—
148C2×C8—341no—
149C4⋊C4—1361no—
150C22⋊C4—682no—
151C42—1361no—
152C16—1361no—
153C23—341no—
154C23#1058755011yescharacteristic
155Q8—681no—
156Q8—682no—
157Q8—682no—
158Q8—1361no—
159Q8—1361no—
160D4—681no—
161D4—1361no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—341no—
165C2×C4—681no—
166C2×C4—681no—
167C2×C4—682no—
168C2×C4—1362no—
169C2×C4—1361no—
170C2×C4—1361no—
171C2×C4#1058753911yescharacteristic
172C2×C4#1058754711yescharacteristic
173C8—42no—
174C8—41no—
175C8—681no—
176C22—21no—
177C22—41no—
178C22—681no—
179C22—1361no—
180C22#1176366111yescharacteristic
181C4—21no—
182C4—2722no—
183C4—681no—
184C4—1362no—
185C4#1176371011yescharacteristic
186C4#1176371411yescharacteristic
187C2—21no—
188C2—41no—
189C2—1361no—
190C2#1454376311yescharacteristic
subgroupG/H
centerC2#14543763
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC17×#341C4
socleC2×C17#1343
prime radicalC2×#63252D4
cosocle#11762775C22
hypercenter#341#595
hypocenterC17#7399
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
7. C22×Dic68C4semidirect
10. C17×#341C4semidirect
101. #341#595semidirect
123. C17#7399semidirect

Maximal subgroups

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

subgroupindex
#145438722
#145437192
#145299062
#739917