Finite Group Databasebeta

← #17958248

Subgroups — #17958248

Order 4352.

314 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 86 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#14545142C212yesmaximal, complemented
2#14543723C212yesmaximal, complemented
3#14543706C212yesmaximal
4#14537424C211yesmaximal, characteristic
5#11763730—22no—
6C22⋊#63216C2214yes—
7#11763695—22no—
8#41×Dic17C411yescharacteristic
9#11762867—22no—
10#11762859—22no—
11#11762837C2211yescharacteristic
12#11762835C411yescharacteristic
13#11762776C2211yescharacteristic
14M16×Dic17C411yescharacteristic
15C2×C8×Dic17C2211yescharacteristic
16C17×#408C411yescharacteristic
17C2×#41×C17C2×C411yescharacteristic
18C2×M16×C17C2×C411yescharacteristic
19C22×C8×C17C2×C411yescharacteristic
20Q8×Dic17C812yes—
21D4×Dic17—22no—
22D4×Dic17C812yes—
23#10587612—21no—
24#10587612C2×C411yescharacteristic
25C2×C4×Dic17—21no—
26C2×C4×Dic17C2×C411yescharacteristic
27C2×#63223C2×C411yescharacteristic
28C22×#3622C2311yescharacteristic
29C2×#63216—24no—
30C17×C22⋊C8—22no—
31C22⋊#3622—22no—
32#10587486—21no—
33#10587485—22no—
34#10587485—22no—
35C8×Dic17—21no—
36C8×Dic17D412yes—
37C8×Dic17D412yes—
38#41×C17—41no—
39#41×C17—41no—
40C2×Q8×C17C2×C811yescharacteristic
41C2×D4×C17—21no—
42C2×D4×C17C2×C811yescharacteristic
43C22×C4×C17—21no—
44C22×C4×C17C22×C411yescharacteristic
45C22×Dic17—22no—
46C22×Dic17M1612yes—
47M16×C17—41no—
48C2×C8×C17—21no—
49C2×C8×C17—41no—
50C2×C8×C17C22⋊C412yes—
51C22⋊Dic17—21no—
52C22⋊Dic17—22no—
53C4⋊Dic17—22no—
54C4⋊Dic17C2×C812yes—
55C4×Dic17—21no—
56C4×Dic17—22no—
57C4×Dic17C22⋊C411yescharacteristic
58C4×Dic17C22⋊C411yescharacteristic
59C4×Dic17C2×C812yes—
60#63223—41no—
61C2×#3622—21no—
62C2×#3622—41no—
63C2×#3622C2×D412yes—
64#63216—44no—
65#11462—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—41no—
75C2×C4×C17—41no—
76C2×C4×C17C2×C22⋊C411yescharacteristic
77C2×C4×C17C22×C811yescharacteristic
78C2×Dic17—24no—
79C2×Dic17—22no—
80C2×Dic17—44no—
81C2×Dic17C22⋊C812yes—
82C2×Dic17C22⋊C812yes—
83C8×C17—22no—
84C8×C17—41no—
85#3622—22no—
86#3622—41no—
87#2922—171no—
88#2162—172no—
89#1323—172no—
90#1315—172no—
91C22×C17—22no—
92C22×C17—21no—
93C22×C17—42no—
94C22×C17—41no—
95C22×C17C2×C22⋊C811yescharacteristic
96C4×C17—21no—
97C4×C17—41no—
98C4×C17#41011yescharacteristic
99C4×C17#41311yescharacteristic
100Dic17—22no—
101Dic17—42no—
102Dic17#35014yes—
103C4×#41—171no—
104#433—342no—
105#431—342no—
106#424—171no—
107#424—171no—
108#408—171no—
109#408#59511yescharacteristic
110C4×M16—171no—
111C2×C4×C8—171no—
112C4⋊C16—342no—
113C22⋊C16—174no—
114C4×C16—342no—
115C2×C17—41no—
116C2×C17—81no—
117C2×C17#145811yescharacteristic
118C2×C17C2×#35012yes—
119C2×#41C2×#59511yescharacteristic
120C2×M16—171no—
121C2×M16C2×#59511yescharacteristic
122C22×C8—171no—
123C22×C8C2×#59511yescharacteristic
124C4×Q8—172no—
125C4×D4—172no—
126C4×D4—342no—
127#117—171no—
128#117—341no—
129C2×C42—171no—
130C2×C42—341no—
131C2×C16—344no—
132C4⋊C8—342no—
133C4⋊C8—342no—
134C22⋊C8—22no—
135C22⋊C8—342no—
136#97—341no—
137C4×C8—172no—
138C4×C8—172no—
139C4×C8—341no—
140C17#1146211yescharacteristic, complemented, Sylow
141#41—41no—
142#41—41no—
143C2×Q8#6324211yescharacteristic
144C2×D4—21no—
145C2×D4#6324211yescharacteristic
146C22×C4—21no—
147C22×C4—172no—
148C22×C4—342no—
149C22×C4C22×#59511yescharacteristic
150M16—41no—
151M16—681no—
152C2×C8—21no—
153C2×C8—41no—
154C2×C8—172no—
155C2×C8—341no—
156C2×C8—681no—
157C2×C8C22⋊#59512yes—
158C4⋊C4—172no—
159C4⋊C4—342no—
160C22⋊C4—342no—
161C22⋊C4—341no—
162C42—172no—
163C42—171no—
164C42—171no—
165C42—342no—
166C42—341no—
167C16—684no—
168C23—21no—
169C23D17⋊M1611yescharacteristic
170Q8—41no—
171D4—41no—
172D4—42no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—172no—
179C2×C4—172no—
180C2×C4—344no—
181C2×C4—342no—
182C2×C4—684no—
183C2×C4C2×#6324211yescharacteristic
184C2×C4C2×C22⋊#59511yescharacteristic
185C8—22no—
186C8—41no—
187C8—342no—
188C8—681no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—41no—
193C22#1176377711yescharacteristic
194C4—21no—
195C4—41no—
196C4—174no—
197C4—342no—
198C4—682no—
199C4#1176378911yescharacteristic
200C4#1176379611yescharacteristic
201C2—41no—
202C2—81no—
203C2#1454401611yescharacteristic
204C2#1454502412yes—
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#408C4
socleC22×C17C2×C22⋊C8
prime radicalC2×#41×C17C2×C4
cosocleC22×#3622C23
hypercenter#408#595
hypocenterC17#11462
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14545142C2semidirect
2. #14543723C2semidirect
140. C17#11462semidirect

Maximal subgroups

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

subgroupindex
#145451422
#145437232
#145437062
#145374242
#1146217