Finite Group Databasebeta

← #16937406

Subgroups — #16937406

Order 4352.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#14529757C212yesmaximal
3#14529603C211yesmaximal, characteristic
4#14526666C212yesmaximal
5C17×#1295C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7C2×#10587481—22no—
8C2×#10587474C2211yescharacteristic
9#11762743—22no—
10#11762742—22no—
11#11762741—22no—
12#11762675C2212yes—
13#11762572—22no—
14#11762572—22no—
15C2×C17×#97C2212yes—
16C17×#382C2211yescharacteristic
17C22×Dic34—21no—
18C22×C8×C17—22no—
19C2×C4⋊C4×C17D412yes—
20C2×C42×C17C2311yescharacteristic
21C2×C4⋊Dic17—22no—
22C2×C4⋊Dic17—22no—
23C2×C4⋊Dic17D412yes—
24C2×C4⋊Dic17D412yes—
25C2×#63225—22no—
26C2×#63225—22no—
27C22×#3622—21no—
28#10587555—21no—
29#10587555—22no—
30#10587555Q812yes—
31C17×#97—22no—
32C17×#97—22no—
33C17×#95—22no—
34#10587502—22no—
35#10587502—22no—
36#10587502—22no—
37#10587481—44no—
38#10587474—22no—
39C22×C4×C17—22no—
40C22×C4×C17C2×D411yescharacteristic
41C22×C4×C17C2×D412yes—
42C22×Dic17—22no—
43C22×Dic17—22no—
44C22×Dic17—41no—
45C2×Dic34—22no—
46C2×Dic34—42no—
47C2×Dic34—42no—
48C2×Dic34—41no—
49C2×C8×C17—24no—
50C2×C8×C17—42no—
51C2×C8×C17—42no—
52C4⋊C4×C17—42no—
53C42×C17C2×Q811yescharacteristic
54C42×C17#4112yes—
55C42×C17#4111yescharacteristic
56C4⋊Dic17—24no—
57C4⋊Dic17—42no—
58C4⋊Dic17—42no—
59C4⋊Dic17—42no—
60C4⋊Dic17—82no—
61#63225—82no—
62#63225—82no—
63C2×#3622—22no—
64C2×#3622—41no—
65C2×#3622—41no—
66#10361—171nomaximal, Sylow
67C23×C17#12011yescharacteristic
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—22no—
71C2×C4×C17—22no—
72C2×C4×C17—42no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17C22⋊Q812yes—
76C2×C4×C17C22⋊Q811yescharacteristic
77C2×C4×C17#12411yescharacteristic
78C2×C4×C17#12412yes—
79C2×Dic17—42no—
80C2×Dic17—42no—
81C2×Dic17—42no—
82C2×Dic17—42no—
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17—81no—
87C2×Dic17—81no—
88Dic34—44no—
89Dic34—82no—
90C8×C17—44no—
91#3622—42no—
92#2845—171no—
93#1993—172no—
94#1960—171no—
95#1295—172no—
96#1295D1711yescharacteristic
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—
107Dic17—82no—
108Dic17—82no—
109Dic17—82no—
110C2×C4⋊Q8—171no—
111C2×#103—342no—
112C2×#97—171no—
113C2×#97C2×D1712yes—
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—341no—
127C22×C8—22no—
128C22×C8—341no—
129C4⋊Q8—172no—
130C4⋊Q8—342no—
131C4⋊Q8—341no—
132C2×C4⋊C4—172no—
133C2×C4⋊C4—172no—
134C2×C4⋊C4—342no—
135C2×C4⋊C4—342no—
136C2×C4⋊C4—342no—
137C2×C4⋊C4—342no—
138C2×C4⋊C4D6812yes—
139C2×C42C22×D1711yescharacteristic
140#103—684no—
141#97—22no—
142#97—22no—
143#97—342no—
144#95—22no—
145#95—342no—
146#95—342no—
147#95—342no—
148C17#1036111yescharacteristic, complemented, Sylow
149C2×Q8—342no—
150C2×Q8—682no—
151C2×Q8—682no—
152C2×Q8—681no—
153C22×C4—22no—
154C22×C4—342no—
155C22×C4—342no—
156C22×C4—681no—
157C22×C4C2×D6811yescharacteristic
158C22×C4D4×D1712yes—
159C2×C8—24no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—342no—
163C2×C8—681no—
164C2×C8—681no—
165C4⋊C4—42no—
166C4⋊C4—344no—
167C4⋊C4—682no—
168C4⋊C4—682no—
169C4⋊C4—682no—
170C4⋊C4—1362no—
171C4⋊C4—1362no—
172C4⋊C4—1362no—
173C42#6325212yes—
174C42#6325411yescharacteristic
175C42Q8×D1711yescharacteristic
176C23#1058756811yescharacteristic
177Q8—684no—
178Q8—1362no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4—682no—
189C2×C4—682no—
190C2×C4—682no—
191C2×C4—682no—
192C2×C4—682no—
193C2×C4—1361no—
194C2×C4—1361no—
195C2×C4#1058756111yescharacteristic
196C2×C4#1058757112yes—
197C2×C4#1058758212yes—
198C2×C4#1058758311yescharacteristic
199C8—44no—
200C8—682no—
201C22#1176272211yescharacteristic
202C22#1176297911yescharacteristic
203C22#1176298411yescharacteristic
204C22#1176298812yes—
205C22#1176299312yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—1362no—
212C4—1362no—
213C4—1362no—
214C2#1452810212yes—
215C2#1452810811yescharacteristic
216C2#1452811311yescharacteristic
217C2#1452994111yescharacteristic
218C2#1452994412yes—
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1295C2
socle, prime radicalC23×C17#120
hypercenter#1295D17
hypocenterC17#10361
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

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
#145297572
#145296032
#145266662
C17×#12952
#1036117