Finite Group Databasebeta

← #17962701

Subgroups — #17962701

Order 4352.

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

normal subgroups only

This group has 326 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#14543925C214yesmaximal, complemented
3#14539130C211yesmaximal, characteristic
4#11763788—22no—
5#11763716—22no—
6#11763714C2214yes—
7#11763366C411yescharacteristic, complemented
8#11763359C2211yescharacteristic
9#11763178C412yescomplemented
10#11763174C2212yes—
11#11763169—22no—
12#11762806—22no—
13C2×C17×#97C411yescharacteristic, complemented
14C2×#63252D412yes—
15#10587677—42no—
16C22×C8×C17—21no—
17C2×C42×C17C2×C411yescharacteristic
18#10587616—41no—
19#10587612—21no—
20#10587610—41no—
21#10587561D412yes—
22#10587560C2311yescharacteristic
23C4×D68—41no—
24#10587556C2×C412yes—
25#10587555—21no—
26#10587555C2×C411yescharacteristic
27C4×Dic34—41no—
28#10587551—42no—
29#10587539—24no—
30C17×#97—21no—
31C17×#97C2×C412yes—
32#10587492—24no—
33#10587487—24no—
34C22×C4×C17—21no—
35C22×C4×C17C22⋊C411yescharacteristic
36C2×C22⋊D17—22no—
37#63252—42no—
38#63252—42no—
39C2×D68—41no—
40C2×D68C2×D412yes—
41C2×C4×D17—22no—
42C2×Dic34—41no—
43C2×Dic34C22⋊C412yes—
44C22⋊#595—44no—
45C4⋊#595—82no—
46C4×#595—82no—
47C2×C8×C17—22no—
48C2×C8×C17—41no—
49C2×C8×C17—41no—
50C42×C17—21no—
51C42×C17C22⋊C411yescharacteristic
52C42×C17C22×C411yescharacteristic
53C22⋊Dic17—41no—
54#63227—42no—
55C4⋊Dic17—22no—
56C4⋊Dic17—41no—
57C4⋊Dic17—41no—
58#63225—42no—
59C4×Dic17—41no—
60#13594—171nomaximal, Sylow
61C23×C17#9911yescharacteristic
62C22×D17—22no—
63C2×#595—84no—
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—81no—
69C2×C4×C17#9911yescharacteristic
70C2×C4×C17C2×C22⋊C411yescharacteristic
71C22⋊D17—82no—
72C2×Dic17—22no—
73C2×Dic17—42no—
74D68—42no—
75D68—82no—
76C4×D17—42no—
77C4×D17—42no—
78Dic34—42no—
79Dic34—82no—
80C8×C17—42no—
81#3135—171no—
82#2126—172no—
83#1412—174no—
84C22×C17—21no—
85C22×C17—41no—
86C22×C17C2×#9911yescharacteristic
87C2×D17—42no—
88C2×D17—82no—
89#595—164no—
90C4×C17—21no—
91C4×C17—41no—
92C4×C17—41no—
93C4×C17#35411yescharacteristic
94C4×C17#35411yescharacteristic
95Dic17—42no—
96Dic17—82no—
97#533—171no—
98#532—171no—
99#491—172no—
100#490—172no—
101#489—342no—
102#416—342no—
103#410—342no—
104C2×#97#59511yescharacteristic, complemented
105#354—342no—
106#353—174no—
107C2×C17—21no—
108C2×C17—41no—
109C2×C17C2×#35411yescharacteristic
110D17—82no—
111C2×#41—172no—
112C22×C8—21no—
113C4⋊Q8—171no—
114C4⋊Q8—341no—
115#127—171no—
116#125—172no—
117#124—172no—
118C22⋊Q8—681no—
119#121—681no—
120C4×Q8—681no—
121C4×D4—681no—
122#117—341no—
123#117—682no—
124C2×C42C2×#59511yescharacteristic
125#103—344no—
126#102—344no—
127#99—344no—
128#99—682no—
129#97—21no—
130#97C2×#59512yes—
131C17#1359411yescharacteristic, complemented, Sylow
132#41—682no—
133#41—682no—
134C2×Q8—172no—
135C2×Q8—681no—
136C2×D4—172no—
137C2×D4—342no—
138C2×D4—681no—
139C22×C4—21no—
140C22×C4—342no—
141C22×C4C22⋊#59511yescharacteristic
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C4⋊C4—342no—
146C4⋊C4—681no—
147C4⋊C4—682no—
148C4⋊C4—681no—
149C4⋊C4—1362no—
150C22⋊C4—682no—
151C22⋊C4—681no—
152C22⋊C4—684no—
153C42—21no—
154C42—681no—
155C42—1362no—
156C42C22⋊#59511yescharacteristic
157C42C22×#59511yescharacteristic
158C23—342no—
159C23#1058753911yescharacteristic
160Q8—682no—
161Q8—1362no—
162D4—682no—
163D4—1362no—
164D4—1362no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—81no—
170C2×C4—342no—
171C2×C4—682no—
172C2×C4—682no—
173C2×C4—682no—
174C2×C4—1364no—
175C2×C4#1058753911yescharacteristic
176C2×C4C2×C22⋊#59511yescharacteristic
177C8—42no—
178C22—21no—
179C22—41no—
180C22—682no—
181C22—1362no—
182C22C2×#1058753911yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—2724no—
187C4—682no—
188C4—1362no—
189C4#1176371611yescharacteristic
190C4#1176371611yescharacteristic
191C2—21no—
192C2—41no—
193C2—1362no—
194C2C2×#1176371611yescharacteristic
subgroupG/H
centerC4#11763716
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×#97C4
socleC2×C17C2×#354
prime radical#11763359C22
cosocle#10587560C23
hypercenterC2×#97#595
hypocenterC17#13594
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #14543925C2semidirect
7. #11763366C4semidirect
9. #11763178C4semidirect
13. C2×C17×#97C4semidirect
104. C2×#97#595semidirect
131. C17#13594semidirect

Maximal subgroups

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

subgroupindex
#145450572
#145439252
#145391302
#1359417