Finite Group Databasebeta

← #17958466

Subgroups — #17958466

Order 4352.

280 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 66 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#14545154C212yesmaximal, complemented
2#14543732C212yesmaximal, complemented
3#14543719C212yesmaximal
4#14537434C211yesmaximal, characteristic
5#11763731—22no—
6#11763705C2214yes—
7#11763702—22no—
8#11763277C411yescharacteristic
9#11762869—22no—
10#11762865—22no—
11#11762836C2211yescharacteristic
12#11762777C411yescharacteristic
13#11762775C2211yescharacteristic
14M16×Dic17C2211yescharacteristic
15C2×#10587486C411yescharacteristic
16C17×#424C411yescharacteristic
17C2×#63252C2×C411yescharacteristic
18C2×M16×C17C2×C411yescharacteristic
19C22×C8×C17C2×C411yescharacteristic
20C17×#117C2×C411yescharacteristic
21C2×C4×Dic17C2×C411yescharacteristic
22C2×#63223C2311yescharacteristic
23C22×#3622C2×C411yescharacteristic
24#10587579—21no—
25#10587573—21no—
26#10587567—22no—
27#10587558—21no—
28C42×D17—21no—
29#10587538—24no—
30C17×C4⋊C8—22no—
31#10587491—22no—
32#10587491—22no—
33#10587486—21no—
34#10587486—21no—
35#10587486D412yes—
36C8×Dic17D412yes—
37C4⋊#3622—22no—
38C22×C4×C17C22×C411yescharacteristic
39C2×C22⋊D17—21no—
40C22×Dic17—21no—
41#63252—41no—
42#63252—41no—
43C2×D68M1611yescharacteristic
44C2×C4×D17—21no—
45C2×C4×D17—22no—
46C2×Dic34M1611yescharacteristic
47M16×C17—41no—
48C2×C8×C17—21no—
49C2×C8×C17—41no—
50C2×C8×C17C22⋊C412yes—
51C4⋊C4×C17—21no—
52C22⋊C4×C17M1612yes—
53C42×C17—21no—
54#63227—22no—
55#63225—22no—
56C4×Dic17—22no—
57C4×Dic17—21no—
58C4×Dic17C22⋊C411yescharacteristic
59C4×Dic17C22⋊C411yescharacteristic
60#63223—41no—
61C2×#3622—21no—
62C2×#3622—41no—
63C2×#3622C2×D412yes—
64#63216—44no—
65#11523—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×C17C2×M1611yescharacteristic
73C22⋊D17—42no—
74C2×Dic17—21no—
75C2×Dic17—21no—
76C2×Dic17—21no—
77C2×Dic17—81no—
78D68—41no—
79C4×D17—41no—
80C4×D17—41no—
81C4×D17—82no—
82Dic34—41no—
83C8×C17—22no—
84C8×C17—41no—
85#3622—22no—
86#3622—41no—
87#2923—171no—
88#2165—172no—
89#1328—172no—
90#1321—172no—
91C22×C17—21no—
92C22×C17—41no—
93C22×C17#40711yescharacteristic
94C2×D17—42no—
95C2×D17—41no—
96C4×C17—21no—
97C4×C17—42no—
98C4×C17#41011yescharacteristic
99C4×C17#41311yescharacteristic
100Dic17—41no—
101Dic17—41no—
102Dic17—41no—
103C4×#41—171no—
104#433—342no—
105#432—342no—
106#424—171no—
107#424#59511yescharacteristic
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#146411yescharacteristic
118D17—81no—
119C2×#41—171no—
120C2×M16—171no—
121C2×M16C2×#59511yescharacteristic
122C22×C8—171no—
123C22×C8C2×#59511yescharacteristic
124C4×Q8—341no—
125C4×D4—341no—
126C4×D4—342no—
127#117—341no—
128#117C2×#59511yescharacteristic
129C2×C42—171no—
130C2×C42—341no—
131M32—344no—
132C4⋊C8—22no—
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—681no—
142#41—681no—
143C2×Q8—171no—
144C2×D4—171no—
145C2×D4—341no—
146C22×C4—342no—
147C22×C4—341no—
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—21no—
159C4⋊C4—342no—
160C22⋊C4—342no—
161C22⋊C4#6324312yes—
162C42—21no—
163C42—171no—
164C42—171no—
165C42—342no—
166C42—341no—
167C16—684no—
168C23—341no—
169C23C2×#6324311yescharacteristic
170Q8—681no—
171D4—681no—
172D4—682no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—341no—
177C2×C4—341no—
178C2×C4—341no—
179C2×C4—681no—
180C2×C4—681no—
181C2×C4—1362no—
182C2×C4—1361no—
183C2×C4D17⋊M1611yescharacteristic
184C2×C4C2×C22⋊#59511yescharacteristic
185C8—22no—
186C8—41no—
187C8—342no—
188C8—681no—
189C22—21no—
190C22—41no—
191C22—682no—
192C22—681no—
193C22#1176378011yescharacteristic
194C4—21no—
195C4—42no—
196C4—681no—
197C4—681no—
198C4—681no—
199C4#1176379011yescharacteristic
200C4#1176379611yescharacteristic
201C2—21no—
202C2—41no—
203C2—1361no—
204C2#1454403811yescharacteristic
subgroupG/H
centerC4#11763790
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#424C4
socleC2×C17#1464
prime radicalC2×#63252C2×C4
cosocleC2×#63223C23
hypercenter#424#595
hypocenterC17#11523
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14545154C2semidirect
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
#145451542
#145437322
#145437192
#145374342
#1152317