Finite Group Databasebeta

← #17962718

Subgroups — #17962718

Order 4352.

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

normal subgroups only

This group has 312 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
1C2×#11763720C212yesmaximal
2#14543928C214yesmaximal, complemented
3#14539165C211yesmaximal, characteristic
4C2×#10587545—22no—
5#11763720—22no—
6#11763720C2214yes—
7#11763366C411yescharacteristic
8C2×#10587555C2211yescharacteristic
9#11763178C412yes—
10#11763178C2212yes—
11#11763160—22no—
12#11762819—22no—
13C4×M16×C17C411yescharacteristic
14C22×Dic34D412yes—
15C2×#63247—42no—
16C2×M16×C17—21no—
17C2×C42×C17C2×C411yescharacteristic
18#10587612—21no—
19C2×C4⋊Dic17—41no—
20#10587610—41no—
21#10587556C2×C412yes—
22#10587555—21no—
23#10587555—41no—
24#10587555C2×C411yescharacteristic
25#10587555D412yes—
26#10587555C2311yescharacteristic
27C4×Dic34—41no—
28#10587545—24no—
29#10587545—42no—
30C17×#97C2×C412yes—
31C4×C8×C17—21no—
32#10587487—24no—
33#10587487—24no—
34C22×C4×C17—21no—
35C22×C4×C17C22⋊C411yescharacteristic
36C22×Dic17—22no—
37C2×Dic34—22no—
38C2×Dic34—42no—
39C2×Dic34—42no—
40C2×Dic34—41no—
41C2×Dic34C22⋊C412yes—
42C2×Dic34C2×D412yes—
43#63247—44no—
44#63247—82no—
45C2×#3624—82no—
46M16×C17—42no—
47C2×C8×C17—22no—
48C42×C17—21no—
49C42×C17C22⋊C411yescharacteristic
50C42×C17C22×C411yescharacteristic
51C22⋊Dic17—41no—
52C4⋊Dic17—22no—
53C4⋊Dic17—41no—
54C4⋊Dic17—42no—
55C4⋊Dic17—41no—
56C4⋊Dic17—41no—
57#63225—42no—
58C4×Dic17—41no—
59#13599—171nomaximal, Sylow
60C23×C17#9911yescharacteristic
61C2×C4×C17—22no—
62C2×C4×C17—21no—
63C2×C4×C17—21no—
64C2×C4×C17—42no—
65C2×C4×C17#9911yescharacteristic
66C2×C4×C17C2×C22⋊C411yescharacteristic
67C2×Dic17—22no—
68C2×Dic17—22no—
69C2×Dic17—42no—
70C2×Dic17—42no—
71C2×Dic17—42no—
72Dic34—42no—
73Dic34—42no—
74Dic34—82no—
75Dic34—82no—
76#3624—84no—
77C8×C17—42no—
78#3139—171no—
79C2×#356—172no—
80#1413—174no—
81C22×C17—41no—
82C22×C17#35412yes—
83C22×C17C2×#9911yescharacteristic
84C4×C17—22no—
85C4×C17—21no—
86C4×C17—21no—
87C4×C17—41no—
88Dic17—42no—
89Dic17—42no—
90Dic17—82no—
91#533—171no—
92C2×C4⋊Q8—171no—
93#491—172no—
94#491—172no—
95#487—342no—
96#419—342no—
97C2×#101—342no—
98C4×M16#59511yescharacteristic
99#356—174no—
100#356—342no—
101C2×C17—21no—
102C2×C17—22no—
103C2×C17C2×#35411yescharacteristic
104C22×Q8—172no—
105C2×M16—21no—
106C2×M16—682no—
107C4⋊Q8—172no—
108C4⋊Q8—171no—
109C4⋊Q8—171no—
110C4⋊Q8—341no—
111C4⋊Q8—681no—
112#125—172no—
113C22⋊Q8—681no—
114C4×Q8—681no—
115#117—341no—
116C2×C4⋊C4—681no—
117C2×C42C2×#59511yescharacteristic
118#103—344no—
119#103—344no—
120#101—344no—
121#101—682no—
122#97C2×#59512yes—
123C4×C8—21no—
124C17#1359911yescharacteristic, complemented, Sylow
125C2×Q8—172no—
126C2×Q8—172no—
127C2×Q8—342no—
128C2×Q8—681no—
129C2×Q8—682no—
130C2×Q8—682no—
131C22×C4—21no—
132C22×C4—342no—
133C22×C4C22⋊#59511yescharacteristic
134M16—42no—
135M16—684no—
136M16—1362no—
137C2×C8—22no—
138C2×C8—1362no—
139C4⋊C4—342no—
140C4⋊C4—682no—
141C4⋊C4—681no—
142C4⋊C4—681no—
143C4⋊C4—682no—
144C4⋊C4—681no—
145C22⋊C4—681no—
146C42—21no—
147C42—681no—
148C42C22⋊#59511yescharacteristic
149C42C22×#59511yescharacteristic
150C23#1058753911yescharacteristic
151Q8—682no—
152Q8—682no—
153Q8—1362no—
154Q8—1362no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—342no—
160C2×C4—342no—
161C2×C4—682no—
162C2×C4—682no—
163C2×C4—682no—
164C2×C4#1058753911yescharacteristic
165C2×C4C2×C22⋊#59511yescharacteristic
166C8—42no—
167C8—1364no—
168C22—41no—
169C22#1176371612yes—
170C22C2×#1058753911yescharacteristic
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—682no—
176C4—682no—
177C4—1362no—
178C2—21no—
179C2—22no—
180C2C2×#1176371611yescharacteristic
subgroupG/H
centerC2C2×#11763716
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC4×M16×C17C4
socleC2×C17C2×#354
prime radicalC23×C17#99
cosocle#10587555C23
hypercenterC4×M16#595
hypocenterC17#13599
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #14543928C2semidirect
124. C17#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#117637202
#145439282
#145391652
#1359917