Finite Group Databasebeta

← #17949249

Subgroups — #17949249

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#14529903C211yesmaximal, characteristic
4#11763788—21no—
5#11763705—21no—
6C2×#10587628—21no—
7C2×#10587507—21no—
8#11762775C2211yescharacteristic
9#11762574C411yescharacteristic, complemented
10C22×Q16×C17C411yescharacteristic, complemented
11C22×Q8×C17—21no—
12C2×#63252D411yescharacteristic
13#10587677—41no—
14C2×Q16×C17—41no—
15C2×Q16×C17—42no—
16C22×C8×C17C2×C411yescharacteristic
17C2×#63231—41no—
18#10587628—42no—
19#10587628—42no—
20C2×#63230—41no—
21C2×#63223—21no—
22C2×#63223D411yescharacteristic
23#10587551—22no—
24#10587539—41no—
25#10587538—41no—
26#10587507—42no—
27#10587491—41no—
28C2×Q8×C17—22no—
29C2×Q8×C17—41no—
30C2×Q8×C17—41no—
31C2×Q8×C17—41no—
32C2×Q8×C17—41no—
33C2×Q8×C17—41no—
34C22×C4×C17—41no—
35C22×C4×C17C22⋊C411yescharacteristic
36C2×C22⋊D17—21no—
37#63252—41no—
38#63252—41no—
39C2×D68D811yescharacteristic
40C2×C4×D17—21no—
41C2×Dic34SD1611yescharacteristic
42C22⋊#595—42no—
43C4⋊#595—81no—
44C4×#595—81no—
45Q16×C17—42no—
46Q16×C17—42no—
47C2×C8×C17—21no—
48C2×C8×C17—41no—
49#63231—44no—
50#63230—44no—
51#63223—22no—
52#63223—41no—
53#63223—41no—
54C2×#3622—21no—
55C2×#3622—41no—
56#63216—81no—
57#7399—171nomaximal, Sylow
58C23×C17#10411yescharacteristic
59C22×D17—21no—
60C2×#595—82no—
61Q8×C17—42no—
62Q8×C17—42no—
63Q8×C17—81no—
64Q8×C17—81no—
65C2×C4×C17—21no—
66C2×C4×C17—21no—
67C2×C4×C17—42no—
68C2×C4×C17—81no—
69C2×C4×C17—81no—
70C2×C4×C17#9911yescharacteristic
71C2×C4×C17#10211yescharacteristic
72C22⋊D17—81no—
73C2×Dic17—21no—
74D68—41no—
75C4×D17—41no—
76C4×D17—41no—
77Dic34—41no—
78C8×C17—41no—
79#3622—42no—
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×C17—82no—
92C4×C17AΣL(1,𝔽16)11yescharacteristic
93C4×C17#35311yescharacteristic
94Dic17—41no—
95C2×#137—341no—
96C22×Q16#59511yescharacteristic, complemented
97C2×#101—341no—
98#410—341no—
99#408—171no—
100#349—341no—
101#341—171no—
102C2×C17—21no—
103C2×C17—41no—
104C2×C17#134311yescharacteristic
105D17—81no—
106C2×#41—171no—
107C22×Q8—21no—
108#137—682no—
109#137—682no—
110C2×Q16—41no—
111C2×Q16—42no—
112C2×Q16—681no—
113C2×SD16—681no—
114C2×M16—171no—
115C2×M16—341no—
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—22no—
127C2×Q8—41no—
128C2×Q8—41no—
129C2×Q8—41no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—171no—
133C2×D4—171no—
134C2×D4—341no—
135C22×C4—41no—
136C22×C4—341no—
137C22×C4C22⋊#59511yescharacteristic
138Q16—42no—
139Q16—42no—
140Q16—684no—
141SD16—684no—
142M16—342no—
143M16—681no—
144M16—681no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—341no—
148C2×C8—681no—
149C4⋊C4—1361no—
150C22⋊C4—682no—
151C42—1361no—
152C16—1361no—
153C23—341no—
154C23#1058754811yescharacteristic
155Q8—42no—
156Q8—42no—
157Q8—81no—
158Q8—81no—
159Q8—681no—
160D4—681no—
161D4—1361no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—341no—
168C2×C4—681no—
169C2×C4—681no—
170C2×C4—1362no—
171C2×C4#1058754711yescharacteristic
172C2×C4#1058755111yescharacteristic
173C8—41no—
174C8—682no—
175C8—681no—
176C22—21no—
177C22—41no—
178C22—681no—
179C22—1361no—
180C22#1176366011yescharacteristic
181C4—21no—
182C4—82no—
183C4—2722no—
184C4—681no—
185C4#1176370911yescharacteristic
186C4#1176371311yescharacteristic
187C2—21no—
188C2—41no—
189C2—1361no—
190C2#1454376211yescharacteristic
subgroupG/H
centerC2#14543762
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC22×Q16×C17C4
socleC2×C17#1343
prime radicalC2×#63252D4
cosocle#11762775C22
hypercenterC22×Q16#595
hypocenterC17#7399
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
9. #11762574C4semidirect
10. C22×Q16×C17C4semidirect
96. C22×Q16#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
#145299032
#739917