Finite Group Databasebeta

← #17962706

Subgroups — #17962706

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#14543924C214yesmaximal, complemented
3#14539187C211yesmaximal, characteristic
4#11763788—22no—
5#11763716—22no—
6#11763714C2214yes—
7#11763359C2211yescharacteristic
8#11763179C412yescomplemented
9#11763175C2212yes—
10#11763166—22no—
11#11762808—22no—
12C4×#63223C411yescharacteristic, complemented
13C2×C17×#125C411yescharacteristic, complemented
14C2×#63252D412yes—
15#10587677—42no—
16C17×#125—21no—
17C17×#125—41no—
18C17×#125C2×C412yes—
19C2×C4⋊C4×C17—21no—
20C2×C4⋊C4×C17—41no—
21C2×C42×C17C2×C411yescharacteristic
22#10587616—41no—
23C2×#63223—21no—
24#10587561D412yes—
25#10587560C2311yescharacteristic
26C4×D68—41no—
27#10587555C2×C411yescharacteristic
28#10587551—42no—
29#10587539—24no—
30#10587481—24no—
31#10587480—24no—
32#10587474C2×C412yes—
33C4×#3622—21no—
34C22×C4×C17—21no—
35C22×C4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C2×C22⋊D17—22no—
38#63252—42no—
39#63252—42no—
40C2×D68—41no—
41C2×D68C2×D412yes—
42C2×C4×D17—22no—
43C2×Dic34C22⋊C412yes—
44C22⋊#595—44no—
45C4⋊#595—82no—
46C4×#595—82no—
47C4⋊C4×C17—22no—
48C4⋊C4×C17—42no—
49C4⋊C4×C17—42no—
50C4⋊C4×C17—41no—
51C42×C17—21no—
52C42×C17C22⋊C411yescharacteristic
53C42×C17C22×C411yescharacteristic
54#63227—42no—
55C4⋊Dic17—41no—
56#63223—42no—
57C2×#3622—22no—
58#13596—171nomaximal, Sylow
59C23×C17#9911yescharacteristic
60C22×D17—22no—
61C2×#595—84no—
62C2×C4×C17—22no—
63C2×C4×C17—21no—
64C2×C4×C17—21no—
65C2×C4×C17—42no—
66C2×C4×C17—81no—
67C2×C4×C17—82no—
68C2×C4×C17#9911yescharacteristic
69C2×C4×C17C2×C22⋊C411yescharacteristic
70C22⋊D17—82no—
71C2×Dic17—22no—
72D68—42no—
73D68—82no—
74C4×D17—42no—
75C4×D17—42no—
76Dic34—42no—
77#3622—42no—
78#3142—171no—
79#2126—172no—
80#1412—174no—
81C22×C17—21no—
82C22×C17—41no—
83C22×C17C2×#9911yescharacteristic
84C2×D17—42no—
85C2×D17—82no—
86#595—164no—
87C4×C17—21no—
88C4×C17—41no—
89C4×C17—41no—
90C4×C17—82no—
91C4×C17#35412yes—
92Dic17—42no—
93#532—171no—
94C2×#125#59511yescharacteristic, complemented
95#491—172no—
96#490—172no—
97#488—342no—
98#417—342no—
99#410—342no—
100C4×M16—171no—
101#354—342no—
102#353—174no—
103C2×C17—21no—
104C2×C17—41no—
105C2×C17C2×#35411yescharacteristic
106D17—82no—
107C2×#41—172no—
108C2×M16—341no—
109C4⋊Q8—171no—
110#127—171no—
111#125—21no—
112#125—41no—
113#125C2×#59512yes—
114#124—172no—
115#121—681no—
116C4×D4—681no—
117#117—682no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C42C2×#59511yescharacteristic
121#103—344no—
122#102—344no—
123#99—344no—
124#99—682no—
125#97—172no—
126C4×C8—341no—
127C17#1359611yescharacteristic, complemented, Sylow
128#41—682no—
129#41—682no—
130C2×Q8—172no—
131C2×D4—172no—
132C2×D4—342no—
133C2×D4—681no—
134C22×C4—21no—
135C22×C4—41no—
136C22×C4—342no—
137C22×C4C22⋊#59511yescharacteristic
138M16—682no—
139C2×C8—342no—
140C4⋊C4—22no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—41no—
144C4⋊C4—681no—
145C4⋊C4—1362no—
146C22⋊C4—682no—
147C22⋊C4—684no—
148C42—21no—
149C42—1362no—
150C42C22⋊#59511yescharacteristic
151C42C22×#59511yescharacteristic
152C23—342no—
153C23#1058755111yescharacteristic
154Q8—682no—
155D4—682no—
156D4—1362no—
157D4—1362no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—342no—
165C2×C4—682no—
166C2×C4—682no—
167C2×C4—1364no—
168C2×C4#1058755111yescharacteristic
169C2×C4C2×C22⋊#59511yescharacteristic
170C8—682no—
171C22—21no—
172C22—41no—
173C22—682no—
174C22—1362no—
175C22C2×#1058755111yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—82no—
180C4—2724no—
181C4—682no—
182C4#1176371512yes—
183C2—21no—
184C2—41no—
185C2—1362no—
186C2C2×#1176371511yescharacteristic
subgroupG/H
centerC2C2×#11763715
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×#125C4
socleC2×C17C2×#354
prime radical#11763359C22
cosocle#10587560C23
hypercenterC2×#125#595
hypocenterC17#13596
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #14543924C2semidirect
8. #11763179C4semidirect
12. C4×#63223C4semidirect
13. C2×C17×#125C4semidirect
94. C2×#125#595semidirect
127. C17#13596semidirect

Maximal subgroups

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

subgroupindex
#145450572
#145439242
#145391872
#1359617