Finite Group Databasebeta

← #17958250

Subgroups — #17958250

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#14543722C212yesmaximal, complemented
3#14543707C212yesmaximal
4#14537427C211yesmaximal, characteristic
5#11763730—22no—
6C22⋊#63216C2214yes—
7#11763695—22no—
8#11763277C411yescharacteristic
9#11762869—22no—
10#11762861—22no—
11#11762836C2211yescharacteristic
12#11762777C2211yescharacteristic
13#11762775C411yescharacteristic
14M16×Dic17C411yescharacteristic
15C2×C8×Dic17C2211yescharacteristic
16C17×#424C411yescharacteristic
17C2×#63252C2×C411yescharacteristic
18C2×M16×C17C2×C411yescharacteristic
19C22×C8×C17C2×C411yescharacteristic
20C17×#117C2×C411yescharacteristic
21C2×C4×Dic17C2×C411yescharacteristic
22C2×#63223C2×C411yescharacteristic
23C22×#3622C2311yescharacteristic
24#10587579C812yes—
25#10587573C812yes—
26#10587567—22no—
27#10587558—21no—
28C42×D17—21no—
29C2×#63216—24no—
30C17×C4⋊C8—22no—
31#10587491—22no—
32#10587491—22no—
33#10587486—21no—
34C8×Dic17—21no—
35C8×Dic17D412yes—
36C8×Dic17D412yes—
37C4⋊#3622—22no—
38C22×C4×C17C22×C411yescharacteristic
39C2×C22⋊D17—21no—
40C22×Dic17M1612yes—
41#63252—41no—
42#63252—41no—
43C2×D68C2×C811yescharacteristic
44C2×C4×D17—21no—
45C2×C4×D17—22no—
46C2×Dic34C2×C811yescharacteristic
47M16×C17—41no—
48C2×C8×C17—21no—
49C2×C8×C17—41no—
50C2×C8×C17C22⋊C412yes—
51C4⋊C4×C17C2×C812yes—
52C22⋊C4×C17—21no—
53C42×C17—21no—
54#63227—22no—
55#63225—22no—
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×C17C2×M1611yescharacteristic
67C22×D17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—22no—
71C2×C4×C17C2×C22⋊C411yescharacteristic
72C2×C4×C17C22×C811yescharacteristic
73C22⋊D17—42no—
74C2×Dic17—24no—
75C2×Dic17—21no—
76C2×Dic17C22⋊C812yes—
77C2×Dic17C22⋊C812yes—
78D68—41no—
79C4×D17—41no—
80C4×D17—41no—
81C4×D17—44no—
82Dic34—41no—
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×C17C2×C22⋊C811yescharacteristic
94C2×D17—42no—
95C2×D17—41no—
96C4×C17—21no—
97C4×C17—42no—
98C4×C17#41011yescharacteristic
99C4×C17#41311yescharacteristic
100Dic17—22no—
101Dic17—41no—
102Dic17#35014yes—
103C4×#41—171no—
104#433—342no—
105#431—342no—
106#424—171no—
107#424#59511yescharacteristic
108#408—171no—
109#408—171no—
110C4×M16—171no—
111C2×C4×C8—171no—
112C4⋊C16—342no—
113C22⋊C16—174no—
114C4×C16—342no—
115C2×C17—41no—
116C2×C17#145811yescharacteristic
117C2×C17C2×#35012yes—
118D17—81no—
119C2×#41—171no—
120C2×M16—171no—
121C2×M16C2×#59511yescharacteristic
122C22×C8—171no—
123C22×C8C2×#59511yescharacteristic
124C4×Q8—172no—
125C4×D4—172no—
126C4×D4—342no—
127#117—341no—
128#117C2×#59511yescharacteristic
129C2×C42—171no—
130C2×C42—341no—
131C2×C16—344no—
132C4⋊C8—22no—
133C4⋊C8—342no—
134C22⋊C8—342no—
135C22⋊C8—342no—
136#97—341no—
137C4×C8—172no—
138C4×C8—172no—
139C4×C8—341no—
140C17#1146211yescharacteristic, complemented, Sylow
141#41—681no—
142#41—681no—
143C2×Q8—171no—
144C2×D4—171no—
145C2×D4—341no—
146C22×C4—172no—
147C22×C4—342no—
148C22×C4—341no—
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—342no—
159C4⋊C4#6324212yes—
160C22⋊C4—21no—
161C22⋊C4—342no—
162C42—21no—
163C42—172no—
164C42—171no—
165C42—171no—
166C42—342no—
167C16—684no—
168C23—341no—
169C23D17⋊M1611yescharacteristic
170Q8—681no—
171D4—681no—
172D4—682no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—172no—
177C2×C4—172no—
178C2×C4—344no—
179C2×C4—341no—
180C2×C4—684no—
181C2×C4—681no—
182C2×C4—681no—
183C2×C4C2×#6324211yescharacteristic
184C2×C4C2×C22⋊#59511yescharacteristic
185C8—22no—
186C8—41no—
187C8—342no—
188C8—681no—
189C22—22no—
190C22—21no—
191C22—682no—
192C22—681no—
193C22#1176377711yescharacteristic
194C4—21no—
195C4—42no—
196C4—174no—
197C4—342no—
198C4—681no—
199C4#1176379011yescharacteristic
200C4#1176379611yescharacteristic
201C2—41no—
202C2—1361no—
203C2#1454401811yescharacteristic
204C2#1454502412yes—
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#424C4
socleC22×C17C2×C22⋊C8
prime radicalC2×#63252C2×C4
cosocleC22×#3622C23
hypercenter#424#595
hypocenterC17#11462
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14545142C2semidirect
2. #14543722C2semidirect
140. C17#11462semidirect

Maximal subgroups

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

subgroupindex
#145451422
#145437222
#145437072
#145374272
#1146217