Finite Group Databasebeta

← #16937405

Subgroups — #16937405

Order 4352.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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#14537059C211yesmaximal, characteristic
2#14529758C212yesmaximal
3#14526666C212yesmaximal
4#14526665C211yesmaximal, characteristic
5C17×#1960C211yesmaximal, characteristic
6C2×#10587474C2212yes—
7#11762743—22no—
8#11762742—22no—
9#11762741—22no—
10#11762675C2212yes—
11#11762571—22no—
12#11762571—22no—
13C2×C17×C4⋊Q8C2211yescharacteristic
14C2×C17×#103—22no—
15C2×C17×#97C2211yescharacteristic
16C17×#382C2211yescharacteristic
17C22×Q8×C17—21no—
18C22×C8×C17—21no—
19C17×C4⋊Q8—22no—
20C17×C4⋊Q8—21no—
21C17×C4⋊Q8Q812yes—
22C2×C4⋊C4×C17—22no—
23C2×C4⋊C4×C17D412yes—
24C2×C42×C17C2311yescharacteristic
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17D412yes—
27C2×C4⋊Dic17D412yes—
28C2×#63225—22no—
29C2×#63225—22no—
30C22×#3622—22no—
31C17×#103—44no—
32C17×#97—22no—
33C17×#95—22no—
34#10587502—22no—
35#10587502—22no—
36#10587502—22no—
37#10587474—22no—
38#10587474—22no—
39C2×Q8×C17—22no—
40C2×Q8×C17—42no—
41C2×Q8×C17—42no—
42C2×Q8×C17—41no—
43C22×C4×C17—22no—
44C22×C4×C17—41no—
45C22×C4×C17C2×D412yes—
46C22×C4×C17C2×D411yescharacteristic
47C22×Dic17—22no—
48C22×Dic17—22no—
49C2×C8×C17—22no—
50C2×C8×C17—41no—
51C2×C8×C17—41no—
52C4⋊C4×C17—24no—
53C4⋊C4×C17—42no—
54C4⋊C4×C17—42no—
55C42×C17C2×Q811yescharacteristic
56C42×C17#4111yescharacteristic
57C42×C17#4112yes—
58C4⋊Dic17—42no—
59C4⋊Dic17—42no—
60C4⋊Dic17—82no—
61#63225—82no—
62#63225—82no—
63C2×#3622—24no—
64C2×#3622—42no—
65C2×#3622—42no—
66#10361—171nomaximal, Sylow
67C23×C17#12011yescharacteristic
68Q8×C17—44no—
69Q8×C17—82no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—22no—
73C2×C4×C17—22no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—42no—
78C2×C4×C17—81no—
79C2×C4×C17—81no—
80C2×C4×C17C22⋊Q812yes—
81C2×C4×C17C22⋊Q811yescharacteristic
82C2×C4×C17#12412yes—
83C2×C4×C17#12411yescharacteristic
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C8×C17—42no—
91#3622—44no—
92#2845—171no—
93#1993—172no—
94#1960D1711yescharacteristic
95#1295—172no—
96#1295—171no—
97C22×C17#39311yescharacteristic
98C22×C17#45311yescharacteristic
99C22×C17#45411yescharacteristic
100C22×C17#45512yes—
101C22×C17#45612yes—
102C4×C17—21no—
103C4×C17—21no—
104C4×C17—22no—
105C4×C17—22no—
106C4×C17—82no—
107C4×C17—82no—
108Dic17—82no—
109Dic17—82no—
110C2×C4⋊Q8C2×D1711yescharacteristic
111C2×#103—22no—
112C2×#97—172no—
113C2×#97C2×D1711yescharacteristic
114#398—342no—
115#398—342no—
116#398—342no—
117#382—172no—
118#382C2×D1711yescharacteristic
119#340—342no—
120#340—342no—
121C2×C17#166112yes—
122C2×C17#166211yescharacteristic
123C2×C17#166311yescharacteristic
124C2×C17#202711yescharacteristic
125C2×C17#202812yes—
126C22×Q8—21no—
127C22×C8—21no—
128C22×C8—342no—
129C4⋊Q8—21no—
130C4⋊Q8—22no—
131C4⋊Q8Dic3412yes—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—172no—
134C2×C4⋊C4—172no—
135C2×C4⋊C4—342no—
136C2×C4⋊C4—342no—
137C2×C4⋊C4—342no—
138C2×C4⋊C4C22⋊D1712yes—
139C2×C42C22×D1711yescharacteristic
140#103—44no—
141#97—22no—
142#97—342no—
143#97—342no—
144#95—22no—
145#95—342no—
146#95—342no—
147#95—342no—
148C17#1036111yescharacteristic, complemented, Sylow
149C2×Q8—22no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—41no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—342no—
156C22×C4—342no—
157C22×C4D4×D1712yes—
158C22×C4C2×C22⋊D1711yescharacteristic
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—344no—
163C2×C8—682no—
164C2×C8—682no—
165C4⋊C4—24no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—682no—
169C4⋊C4—682no—
170C4⋊C4—1362no—
171C4⋊C4—1362no—
172C4⋊C4—1362no—
173C42C2×Dic3411yescharacteristic
174C42#6325211yescharacteristic
175C42#6325412yes—
176C23#1058762311yescharacteristic
177Q8—44no—
178Q8—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—682no—
190C2×C4—682no—
191C2×C4—682no—
192C2×C4—682no—
193C2×C4—682no—
194C2×C4—682no—
195C2×C4#1058756412yes—
196C2×C4#1058757112yes—
197C2×C4#1058761011yescharacteristic
198C2×C4#1058762211yescharacteristic
199C8—42no—
200C8—684no—
201C22#1176272111yescharacteristic
202C22#1176297611yescharacteristic
203C22#1176298111yescharacteristic
204C22#1176298512yes—
205C22#1176299012yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—1362no—
213C4—1362no—
214C2#1452809812yes—
215C2#1452810511yescharacteristic
216C2#1452811011yescharacteristic
217C2#1452994011yescharacteristic
218C2#1452994312yes—
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1960C2
socle, prime radicalC23×C17#120
hypercenter#1960D17
hypocenterC17#10361
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
148. C17#10361semidirect

Maximal subgroups

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

subgroupindex
#145370592
#145297582
#145266662
#145266652
C17×#19602
#1036117