Finite Group Databasebeta

← #16929271

Subgroups — #16929271

Order 4352.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#14539129C211yesmaximal, characteristic
2#14537855C211yesmaximal, characteristic
3#14527258C212yesmaximal, complemented
4#14526684C212yesmaximal, complemented
5C17×#1543C211yesmaximal, characteristic
6#11763366C2211yescharacteristic
7#11763177—21no—
8#11763173—21no—
9#11763168C414yes—
10#11762881—24no—
11#11762866C2212yes—
12#11762805—22no—
13#11762776—22no—
14C2×#10587474C2211yescharacteristic
15#11762541—24no—
16C17×#532C2211yescharacteristic
17C17×#431C2212yes—
18C17×#333—21no—
19C17×#331—21no—
20C2×#41×C17D412yes—
21C17×C4⋊Q8D411yescharacteristic
22C17×#127D411yescharacteristic
23C17×#124C2×C412yes—
24C17×#121—22no—
25C4×D4×C17—22no—
26C2×C42×C17C2311yescharacteristic
27#10587612—21no—
28#10587610—22no—
29C2×#63223—22no—
30C22×#3622—22no—
31C22×#3622—21no—
32#10587556—21no—
33#10587555C2×C412yes—
34C4×Dic34—22no—
35C17×C4⋊C8—22no—
36C17×C22⋊C8—22no—
37C4×C8×C17—22no—
38#10587506—24no—
39#10587503—24no—
40C22⋊#3622—24no—
41C22⋊#3622—22no—
42C4⋊#3622D414yes—
43#10587474—21no—
44#10587474—22no—
45#10587474C2×C412yes—
46#41×C17—42no—
47#41×C17—42no—
48C2×Q8×C17C22⋊C412yes—
49C2×D4×C17—22no—
50C2×D4×C17—22no—
51C2×D4×C17C22⋊C412yes—
52C22×C4×C17—22no—
53C22×C4×C17C2×D411yescharacteristic
54C22×C4×C17#4112yes—
55C2×Dic34—22no—
56C2×C8×C17—42no—
57C4⋊C4×C17—22no—
58C22⋊C4×C17—24no—
59C42×C17C22×C411yescharacteristic
60C42×C17C2×D412yes—
61C42×C17C2×D411yescharacteristic
62C22⋊Dic17—41no—
63C4⋊Dic17—22no—
64C4⋊Dic17—22no—
65#63225—42no—
66C4×Dic17—41no—
67#63223—82no—
68C2×#3622—22no—
69C2×#3622—24no—
70C2×#3622—42no—
71C2×#3622—82no—
72#9005—171nomaximal, Sylow
73C23×C17—22no—
74C23×C17#12311yescharacteristic
75Q8×C17—42no—
76D4×C17—42no—
77D4×C17—82no—
78D4×C17—82no—
79C2×C4×C17—22no—
80C2×C4×C17—22no—
81C2×C4×C17—42no—
82C2×C4×C17—42no—
83C2×C4×C17—42no—
84C2×C4×C17C2×C22⋊C411yescharacteristic
85C2×C4×C17C4×D412yes—
86C2×C4×C17#12011yescharacteristic
87C2×C4×C17#12112yes—
88C2×Dic17—42no—
89Dic34—44no—
90C8×C17—82no—
91#3622—42no—
92#3622—44no—
93#3135—171no—
94#2980—171no—
95#1543D1711yescharacteristic
96#1497—172no—
97#1302—172no—
98C22×C17—22no—
99C22×C17—21no—
100C22×C17—44no—
101C22×C17—42no—
102C22×C17#38611yescharacteristic
103C4×C17—22no—
104C4×C17—22no—
105C4×C17—21no—
106C4×C17—42no—
107C4×C17#45512yes—
108Dic17—82no—
109#533—171no—
110#532C2×D1711yescharacteristic
111#491—341no—
112#490—341no—
113#489—174no—
114#435—344no—
115#432—172no—
116#431C2×D1712yes—
117#416—342no—
118#408—342no—
119C2×#97—171no—
120#333—21no—
121#331—21no—
122Q8⋊C8—344no—
123C2×C17—41no—
124C2×C17—82no—
125C2×C17#188112yes—
126C2×C17#188511yescharacteristic
127C2×#41D6812yes—
128C2×M16—342no—
129C22×C8—341no—
130C22×C8—342no—
131C4⋊Q8—172no—
132C4⋊Q8C22⋊D1711yescharacteristic
133#127C22⋊D1711yescharacteristic
134#125—341no—
135#124C4×D1712yes—
136C22⋊Q8—342no—
137#121—22no—
138C4×Q8—342no—
139C4×D4—22no—
140#117—341no—
141C2×C42C22×D1711yescharacteristic
142C4⋊C8—22no—
143C4⋊C8—174no—
144#103—344no—
145#102—344no—
146C22⋊C8—22no—
147C22⋊C8—344no—
148C22⋊C8—342no—
149#97—172no—
150#97—342no—
151#97—341no—
152C4×C8—22no—
153C17#900511yescharacteristic, complemented, Sylow
154#41—42no—
155#41—42no—
156C2×Q8—342no—
157C2×Q8#6322712yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4#6322712yes—
161C22×C4—22no—
162C22×C4C2×D6811yescharacteristic
163C22×C4#6325412yes—
164M16—1362no—
165C2×C8—42no—
166C2×C8—344no—
167C2×C8—342no—
168C2×C8—682no—
169C2×C8—1362no—
170C4⋊C4—22no—
171C4⋊C4—342no—
172C4⋊C4—342no—
173C4⋊C4—682no—
174C22⋊C4—24no—
175C22⋊C4—681no—
176C42—681no—
177C42C2×C4×D1711yescharacteristic
178C42D4×D1712yes—
179C42C2×C22⋊D1711yescharacteristic
180C23—22no—
181C23#1058757211yescharacteristic
182Q8—42no—
183Q8—684no—
184D4—42no—
185D4—82no—
186D4—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—682no—
193C2×C4#1058756712yes—
194C2×C4#1058756811yescharacteristic
195C2×C4C2×#6322711yescharacteristic
196C2×C4#1058762512yes—
197C8—82no—
198C8—682no—
199C8—684no—
200C22—22no—
201C22—21no—
202C22—44no—
203C22—42no—
204C22#1176268611yescharacteristic
205C4—22no—
206C4—22no—
207C4—21no—
208C4—42no—
209C4—1362no—
210C4#1176298912yes—
211C2—41no—
212C2—82no—
213C2#1452914412yes—
214C2#1452917011yescharacteristic
subgroupG/H
centerC2×C4#10587568
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1543C2
socleC22×C17#386
prime radicalC17×#532C22
cosocleC2×C42×C17C23
hypercenter#1543D17
hypocenterC17#9005
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
3. #14527258C2semidirect
4. #14526684C2semidirect
153. C17#9005semidirect

Maximal subgroups

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

subgroupindex
#145391292
#145378552
#145272582
#145266842
C17×#15432
#900517