Finite Group Databasebeta

← #16937571

Subgroups — #16937571

Order 4352.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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#14534454C211yesmaximal, characteristic
2#14528883C212yesmaximal
3#14526692C211yesmaximal, characteristic
4#14526636C212yesmaximal
5C17×#1820C211yesmaximal, characteristic
6#11762773C2212yes—
7#11762732—22no—
8#11762706—22no—
9#11762692—22no—
10C4×C22⋊Dic17C2212yes—
11#11762568—22no—
12#11762568—22no—
13C2×C17×#117C2211yescharacteristic
14C17×#381C2211yescharacteristic
15C17×#381C2211yescharacteristic
16C17×#342—22no—
17C23×C4×C17C2311yescharacteristic
18C17×#117—22no—
19C17×#117—22no—
20C2×C4⋊C4×C17Q812yes—
21C2×C22⋊C4×C17—21no—
22C2×C22⋊C4×C17—21no—
23C2×C22⋊C4×C17D412yes—
24C2×C42×C17—21no—
25C2×C22⋊Dic17—22no—
26C2×C4⋊Dic17—22no—
27C2×#63225—22no—
28C2×#63225—22no—
29C2×C4×Dic17D412yes—
30C2×C4×Dic17D412yes—
31C2×#63223—22no—
32C17×#95—22no—
33C17×#95—22no—
34#10587502—22no—
35#10587502—22no—
36C22⋊#3622—22no—
37C22⋊#3622—22no—
38C24×C17C2×D411yescharacteristic
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—42no—
42C22×C4×C17—41no—
43C22×C4×C17C2×D412yes—
44C22×C4×C17C2×Q811yescharacteristic
45C22×C4×C17#4111yescharacteristic
46C22×C4×C17#4112yes—
47C22×Dic17—22no—
48C22×Dic17—22no—
49C4⋊C4×C17—24no—
50C22⋊C4×C17—41no—
51C22⋊C4×C17—41no—
52C22⋊C4×C17—42no—
53C22⋊C4×C17—42no—
54C42×C17—42no—
55C22⋊Dic17—44no—
56C4⋊Dic17—44no—
57#63225—44no—
58#63225—82no—
59C4×Dic17—42no—
60C4×Dic17—42no—
61#63223—42no—
62#63223—42no—
63C2×#3622—42no—
64#10389—171nomaximal, Sylow
65C23×C17—22no—
66C23×C17—42no—
67C23×C17#12011yescharacteristic
68C23×C17C22⋊Q811yescharacteristic
69C23×C17#12411yescharacteristic
70C2×C4×C17—22no—
71C2×C4×C17—22no—
72C2×C4×C17—41no—
73C2×C4×C17—41no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—42no—
78C2×C4×C17—42no—
79C2×C4×C17—82no—
80C2×C4×C17—81no—
81C2×C4×C17—82no—
82C2×C4×C17C22⋊Q812yes—
83C2×C4×C17#12412yes—
84C2×Dic17—24no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90#3622—82no—
91#2608—171no—
92#1826—172no—
93#1820D1711yescharacteristic
94#1306—171no—
95#1284—172no—
96C22×C17—22no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17—22no—
100C22×C17—22no—
101C22×C17—82no—
102C22×C17#39311yescharacteristic
103C22×C17#45812yes—
104C4×C17—22no—
105C4×C17—22no—
106C4×C17—82no—
107C4×C17—82no—
108C4×C17—161no—
109Dic17—44no—
110Dic17—82no—
111C2×#117C2×D1711yescharacteristic
112#407—172no—
113#396—342no—
114#389—342no—
115#387—342no—
116#381C2×D1711yescharacteristic
117#381C2×D1711yescharacteristic
118C4×C22⋊C4—172no—
119#342—22no—
120#339—342no—
121#339—342no—
122C2×C17—22no—
123C2×C17—41no—
124C2×C17—41no—
125C2×C17#203011yescharacteristic
126C2×C17#203112yes—
127C23×C4C22×D1711yescharacteristic
128C2×M16—342no—
129#117—22no—
130#117—22no—
131C2×C4⋊C4—342no—
132C2×C4⋊C4—342no—
133C2×C4⋊C4—342no—
134C2×C4⋊C4Dic3412yes—
135C2×C22⋊C4—21no—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—342no—
138C2×C22⋊C4C22⋊D1712yes—
139C2×C42—21no—
140C2×C42—172no—
141C2×C42—172no—
142C22⋊C8—342no—
143C22⋊C8—342no—
144#95—22no—
145#95—22no—
146#95—342no—
147#95—342no—
148C17#1038911yescharacteristic, complemented, Sylow
149C24C2×C22⋊D1711yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—42no—
153C22×C4—41no—
154C22×C4—342no—
155C22×C4—342no—
156C22×C4C2×Dic3411yescharacteristic
157C22×C4#6325211yescharacteristic
158C22×C4D4×D1712yes—
159C22×C4#6325412yes—
160M16—682no—
161M16—682no—
162C2×C8—682no—
163C4⋊C4—24no—
164C4⋊C4—684no—
165C4⋊C4—684no—
166C4⋊C4—1362no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C22⋊C4—684no—
172C42—42no—
173C42—682no—
174C42—682no—
175C23—22no—
176C23—42no—
177C23#1058761011yescharacteristic
178C23#1058762211yescharacteristic
179C23#1058762311yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4—82no—
192C2×C4—344no—
193C2×C4—682no—
194C2×C4—682no—
195C2×C4—682no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4#1058756412yes—
199C2×C4#1058757112yes—
200C8—1362no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1176272111yescharacteristic
208C22#1176299812yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—82no—
213C4—161no—
214C4—684no—
215C4—1362no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#1452995111yescharacteristic
220C2#1452995812yes—
subgroupG/H
centerC22#11762721
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1820C2
socleC22×C17#393
prime radicalC24×C17C2×D4
hypercenter#1820D17
hypocenterC17#10389
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
148. C17#10389semidirect

Maximal subgroups

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

subgroupindex
#145344542
#145288832
#145266922
#145266362
C17×#18202
#1038917