Finite Group Databasebeta

← #17962672

Subgroups — #17962672

Order 4352.

406 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 60 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#14545057C212yesmaximal
2#14543917C214yesmaximal, complemented
3#14539241C211yesmaximal, characteristic
4#11763788—22no—
5#11763716—22no—
6#11763714C2214yes—
7C2×#10587628—22no—
8#11763359C2211yescharacteristic
9#11763201—22no—
10#11763188C412yescomplemented
11#11763183C2212yes—
12C4×#63223C411yescharacteristic, complemented
13C2×C17×C4⋊Q8C411yescharacteristic, complemented
14C22×Q8×C17—21no—
15C2×#63252D412yes—
16#10587677—42no—
17C17×C4⋊Q8—21no—
18C17×C4⋊Q8—41no—
19C17×C4⋊Q8C2×C412yes—
20C2×C4⋊C4×C17—41no—
21C2×C42×C17C2×C411yescharacteristic
22C2×#63231—24no—
23#10587628—44no—
24#10587628—44no—
25C2×#63230—24no—
26#10587616—41no—
27C2×#63223—21no—
28#10587561D412yes—
29#10587560C2311yescharacteristic
30C4×D68—41no—
31#10587555C2×C411yescharacteristic
32#10587551—42no—
33#10587539—24no—
34#10587474—21no—
35C4×#3622C2×C412yes—
36C2×Q8×C17—22no—
37C2×Q8×C17—42no—
38C2×Q8×C17—42no—
39C2×Q8×C17—41no—
40C22×C4×C17—21no—
41C22×C4×C17—41no—
42C22×C4×C17C22⋊C411yescharacteristic
43C2×C22⋊D17—22no—
44#63252—42no—
45#63252—42no—
46C2×D68—41no—
47C2×D68C2×D412yes—
48C2×C4×D17—22no—
49C2×Dic34C22⋊C412yes—
50C22⋊#595—44no—
51C4⋊#595—82no—
52C4×#595—82no—
53C4⋊C4×C17—42no—
54C4⋊C4×C17—42no—
55C42×C17—21no—
56C42×C17C22⋊C411yescharacteristic
57C42×C17C22×C411yescharacteristic
58#63231—48no—
59#63230—48no—
60#63227—42no—
61C4⋊Dic17—41no—
62#63223—24no—
63C2×#3622—22no—
64#13586—171nomaximal, Sylow
65C23×C17#9911yescharacteristic
66C22×D17—22no—
67C2×#595—84no—
68Q8×C17—44no—
69Q8×C17—82no—
70C2×C4×C17—21no—
71C2×C4×C17—22no—
72C2×C4×C17—21no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—81no—
76C2×C4×C17—81no—
77C2×C4×C17#9911yescharacteristic
78C2×C4×C17C2×C22⋊C411yescharacteristic
79C22⋊D17—82no—
80C2×Dic17—22no—
81D68—42no—
82D68—82no—
83C4×D17—42no—
84C4×D17—42no—
85Dic34—42no—
86#3622—24no—
87#3152—171no—
88#2126—172no—
89#1409—174no—
90C22×C17—21no—
91C22×C17—41no—
92C22×C17C2×#9911yescharacteristic
93C2×D17—42no—
94C2×D17—82no—
95#595—164no—
96C4×C17—22no—
97C4×C17—21no—
98C4×C17—41no—
99C4×C17—82no—
100C4×C17#35312yes—
101Dic17—42no—
102C2×#137—342no—
103#532—171no—
104C2×C4⋊Q8#59511yescharacteristic, complemented
105#497—342no—
106#494—172no—
107#492—172no—
108#410—342no—
109C4×M16—171no—
110#354—342no—
111#353—174no—
112C2×C17—21no—
113C2×C17—41no—
114C2×C17C2×#35311yescharacteristic
115D17—82no—
116C2×#41—172no—
117C22×Q8—21no—
118#137—684no—
119#137—684no—
120C2×Q16—344no—
121C2×SD16—344no—
122C2×M16—341no—
123C4⋊Q8—21no—
124C4⋊Q8—41no—
125C4⋊Q8—171no—
126C4⋊Q8C2×#59512yes—
127#127—171no—
128#124—172no—
129#121—681no—
130C4×D4—681no—
131#117—682no—
132C2×C4⋊C4—41no—
133C2×C42C2×#59511yescharacteristic
134#99—344no—
135#99—682no—
136#97—341no—
137C4×C8—172no—
138C17#1358611yescharacteristic, complemented, Sylow
139#41—682no—
140#41—682no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—41no—
145C2×Q8—172no—
146C2×D4—172no—
147C2×D4—342no—
148C2×D4—681no—
149C22×C4—21no—
150C22×C4—41no—
151C22×C4—342no—
152C22×C4C22⋊#59511yescharacteristic
153Q16—688no—
154SD16—688no—
155M16—344no—
156C2×C8—342no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—681no—
160C4⋊C4—1362no—
161C22⋊C4—682no—
162C22⋊C4—684no—
163C42—21no—
164C42—1362no—
165C42C22⋊#59511yescharacteristic
166C42C22×#59511yescharacteristic
167C23—342no—
168C23#1058755111yescharacteristic
169Q8—44no—
170Q8—82no—
171Q8—682no—
172D4—682no—
173D4—1362no—
174D4—1362no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—342no—
183C2×C4—682no—
184C2×C4—682no—
185C2×C4—1364no—
186C2×C4#1058755111yescharacteristic
187C2×C4C2×C22⋊#59511yescharacteristic
188C8—344no—
189C22—21no—
190C22—41no—
191C22—682no—
192C22—1362no—
193C22C2×#1058755111yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—82no—
198C4—2724no—
199C4—682no—
200C4#1176371312yes—
201C2—21no—
202C2—41no—
203C2—1362no—
204C2C2×#1176371311yescharacteristic
subgroupG/H
centerC2C2×#11763713
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×C4⋊Q8C4
socleC2×C17C2×#353
prime radical#11763359C22
cosocle#10587560C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#13586
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14543917C2semidirect
10. #11763188C4semidirect
12. C4×#63223C4semidirect
13. C2×C17×C4⋊Q8C4semidirect
104. C2×C4⋊Q8#595semidirect
138. C17#13586semidirect

Maximal subgroups

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

subgroupindex
#145450572
#145439172
#145392412
#1358617