Finite Group Databasebeta

← #17958463

Subgroups — #17958463

Order 4352.

280 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 68 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#14545153C212yesmaximal, complemented
2#14543732C212yesmaximal, complemented
3#14543718C212yesmaximal
4#14537435C211yesmaximal, characteristic
5#11763732—22no—
6#11763705C2214yes—
7#11763701—22no—
8#11762870—22no—
9#11762866—22no—
10#11762836C411yescharacteristic
11#11762836C2211yescharacteristic
12#11762776C411yescharacteristic
13#11762776C2211yescharacteristic
14C4×#63223C2211yescharacteristic
15C2×#10587474C411yescharacteristic
16C4×#41×C17C411yescharacteristic
17C2×#41×C17C2×C411yescharacteristic
18C4×Q8×C17—21no—
19C4×D4×C17—21no—
20C4×D4×C17—22no—
21C17×#117—21no—
22C17×#117C2×C411yescharacteristic
23C2×C42×C17—21no—
24C2×C42×C17C2×C411yescharacteristic
25C2×#63223C2×C411yescharacteristic
26C2×#63223C2311yescharacteristic
27C22×#3622C2×C411yescharacteristic
28C22×#3622C2×C411yescharacteristic
29#10587538—24no—
30C22⋊#3622—22no—
31C22⋊#3622—22no—
32C4⋊#3622—22no—
33C4⋊#3622—22no—
34#10587474—21no—
35#10587474—21no—
36#10587474D412yes—
37C4×#3622D412yes—
38#41×C17—41no—
39#41×C17—41no—
40C2×Q8×C17M1611yescharacteristic
41C2×D4×C17—21no—
42C2×D4×C17M1611yescharacteristic
43C22×C4×C17—22no—
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17C22×C411yescharacteristic
47C4⋊C4×C17—22no—
48C4⋊C4×C17—21no—
49C22⋊C4×C17—22no—
50C22⋊C4×C17M1612yes—
51C42×C17—22no—
52C42×C17—21no—
53C42×C17—21no—
54C42×C17C22⋊C411yescharacteristic
55C42×C17C22⋊C411yescharacteristic
56#63223—41no—
57#63223—41no—
58C2×#3622—21no—
59C2×#3622—21no—
60C2×#3622—41no—
61C2×#3622—41no—
62C2×#3622C22⋊C412yes—
63C2×#3622C2×D412yes—
64#63216—44no—
65#11523—171nomaximal, Sylow
66C23×C17—21no—
67C23×C17C2×M1611yescharacteristic
68Q8×C17—41no—
69D4×C17—41no—
70D4×C17—42no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—22no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—41no—
78C2×C4×C17—41no—
79C2×C4×C17—81no—
80C2×C4×C17—82no—
81C2×C4×C17C2×C22⋊C411yescharacteristic
82C2×C4×C17C2×M1611yescharacteristic
83#3622—22no—
84#3622—22no—
85#3622—41no—
86#3622—41no—
87#2923—171no—
88#2165—172no—
89#1328—172no—
90#1321—172no—
91C22×C17—21no—
92C22×C17—41no—
93C22×C17—42no—
94C22×C17—41no—
95C22×C17#40711yescharacteristic
96C4×C17—21no—
97C4×C17—42no—
98C4×C17—41no—
99C4×C17—41no—
100C4×C17—41no—
101C4×C17#41011yescharacteristic
102C4×C17#41311yescharacteristic
103C4×#41#59511yescharacteristic
104#433—342no—
105#432—342no—
106#424—171no—
107#424—171no—
108#408—171no—
109#408—171no—
110C4×M16—171no—
111C2×#97—171no—
112#364—342no—
113#349—174no—
114#347—342no—
115C2×C17—21no—
116C2×C17—41no—
117C2×C17—81no—
118C2×C17#146411yescharacteristic
119C2×#41C2×#59511yescharacteristic
120C2×M16—171no—
121C2×M16—171no—
122C22×C8—171no—
123C22×C8—171no—
124C4×Q8—21no—
125C4×D4—21no—
126C4×D4—22no—
127#117—21no—
128#117C2×#59511yescharacteristic
129C2×C42—21no—
130C2×C42C2×#59511yescharacteristic
131M32—344no—
132C4⋊C8—342no—
133C4⋊C8—342no—
134C22⋊C8—342no—
135C22⋊C8—342no—
136#97—172no—
137#97—341no—
138#97—341no—
139C4×C8—172no—
140C17#1152311yescharacteristic, complemented, Sylow
141#41—41no—
142#41—41no—
143C2×Q8#6324711yescharacteristic
144C2×D4—21no—
145C2×D4#6324711yescharacteristic
146C22×C4—22no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4C22×#59511yescharacteristic
150M16—681no—
151M16—681no—
152C2×C8—172no—
153C2×C8—172no—
154C2×C8—341no—
155C2×C8—341no—
156C2×C8—681no—
157C2×C8—681no—
158C4⋊C4—22no—
159C4⋊C4—21no—
160C22⋊C4—22no—
161C22⋊C4#6324712yes—
162C42—22no—
163C42—21no—
164C42—21no—
165C42C22⋊#59511yescharacteristic
166C42C22⋊#59511yescharacteristic
167C16—684no—
168C23—21no—
169C23C2×#6324711yescharacteristic
170Q8—41no—
171D4—41no—
172D4—42no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4—82no—
183C2×C4C2×#6324711yescharacteristic
184C2×C4C2×C22⋊#59511yescharacteristic
185C8—342no—
186C8—342no—
187C8—681no—
188C8—681no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—41no—
193C22#1176377911yescharacteristic
194C4—21no—
195C4—41no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4#1176378811yescharacteristic
200C4#1176379511yescharacteristic
201C2—21no—
202C2—41no—
203C2—81no—
204C2#1454403511yescharacteristic
subgroupG/H
centerC4#11763788
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×#41×C17C4
socleC2×C17#1464
prime radicalC2×#41×C17C2×C4
cosocleC2×#63223C23
hypercenterC4×#41#595
hypocenterC17#11523
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #14545153C2semidirect
2. #14543732C2semidirect
140. C17#11523semidirect

Maximal subgroups

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

subgroupindex
#145451532
#145437322
#145437182
#145374352
#1152317