Finite Group Databasebeta

← #16938835

Subgroups — #16938835

Order 4352.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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#14528918C212yesmaximal
3#14528917C211yesmaximal, characteristic
4#14526666C212yesmaximal
5C17×#1295C211yesmaximal, characteristic
6C2×#10587474C2211yescharacteristic
7#11762743—22no—
8#11762742—22no—
9#11762741—22no—
10#11762679C2211yescharacteristic
11#11762675C2212yes—
12#11762572—22no—
13#11762572—22no—
14#11762571—22no—
15C2×C17×#97C2212yes—
16C17×#382C2211yescharacteristic
17C22×C8×C17—22no—
18C2×C4⋊C4×C17D412yes—
19C2×C42×C17C2311yescharacteristic
20C2×C4⋊Dic17—22no—
21C2×C4⋊Dic17—21no—
22C2×C4⋊Dic17—22no—
23C2×C4⋊Dic17D412yes—
24C2×C4⋊Dic17D412yes—
25C2×#63225—22no—
26C2×#63225—22no—
27C22×#3622—21no—
28C17×#97—22no—
29C17×#97Q814yes—
30C17×#95—22no—
31#10587502—22no—
32#10587502—22no—
33#10587502—22no—
34#10587474—21no—
35#10587474Q812yes—
36C22×C4×C17—22no—
37C22×C4×C17C2×D411yescharacteristic
38C22×C4×C17C2×D412yes—
39C22×Dic17—22no—
40C22×Dic17—22no—
41C22×Dic17—41no—
42C2×C8×C17—24no—
43C2×C8×C17—42no—
44C2×C8×C17—42no—
45C4⋊C4×C17—42no—
46C42×C17C2×Q812yes—
47C42×C17C2×Q811yescharacteristic
48C42×C17#4111yescharacteristic
49C4⋊Dic17—42no—
50C4⋊Dic17—42no—
51C4⋊Dic17—44no—
52C4⋊Dic17—42no—
53C4⋊Dic17—82no—
54#63225—82no—
55#63225—82no—
56C2×#3622—22no—
57C2×#3622—41no—
58C2×#3622—41no—
59#10586—171nomaximal, Sylow
60C23×C17#12011yescharacteristic
61C2×C4×C17—22no—
62C2×C4×C17—21no—
63C2×C4×C17—21no—
64C2×C4×C17—22no—
65C2×C4×C17—42no—
66C2×C4×C17—42no—
67C2×C4×C17—42no—
68C2×C4×C17C22⋊Q812yes—
69C2×C4×C17C22⋊Q811yescharacteristic
70C2×C4×C17C4⋊Q811yescharacteristic
71C2×C4×C17C4⋊Q812yes—
72C2×Dic17—42no—
73C2×Dic17—42no—
74C2×Dic17—42no—
75C2×Dic17—42no—
76C2×Dic17—42no—
77C2×Dic17—42no—
78C2×Dic17—82no—
79C2×Dic17—81no—
80C8×C17—44no—
81#3622—42no—
82#2845—171no—
83#1836—172no—
84#1836—171no—
85#1295—172no—
86#1295D1711yescharacteristic
87C22×C17#39511yescharacteristic
88C22×C17#45412yes—
89C22×C17#45411yescharacteristic
90C22×C17#45512yes—
91C22×C17#45511yescharacteristic
92C4×C17—21no—
93C4×C17—22no—
94C4×C17—22no—
95C4×C17—21no—
96C4×C17—82no—
97Dic17—82no—
98Dic17—82no—
99Dic17—161no—
100C2×#97—171no—
101C2×#97C2×D1712yes—
102#398—342no—
103#398—342no—
104#398—342no—
105#384—171no—
106#382—172no—
107#382C2×D1711yescharacteristic
108#340—342no—
109#340—342no—
110#340—342no—
111C2×C17#165811yescharacteristic
112C2×C17#166211yescharacteristic
113C2×C17#166212yes—
114C2×C17#206112yes—
115C2×C17#206111yescharacteristic
116C22×C8—22no—
117C22×C8—341no—
118C2×C4⋊C4—172no—
119C2×C4⋊C4—172no—
120C2×C4⋊C4—341no—
121C2×C4⋊C4—342no—
122C2×C4⋊C4—342no—
123C2×C4⋊C4—342no—
124C2×C4⋊C4—342no—
125C2×C4⋊C4D6812yes—
126C2×C42C22×D1711yescharacteristic
127#97—22no—
128#97—172no—
129#97—341no—
130#97Dic3414yes—
131#95—22no—
132#95—342no—
133#95—342no—
134#95—342no—
135C17#1058611yescharacteristic, complemented, Sylow
136C22×C4—22no—
137C22×C4—342no—
138C22×C4—342no—
139C22×C4—681no—
140C22×C4C2×D6811yescharacteristic
141C22×C4D4×D1712yes—
142C2×C8—24no—
143C2×C8—42no—
144C2×C8—42no—
145C2×C8—342no—
146C2×C8—681no—
147C2×C8—681no—
148C4⋊C4—42no—
149C4⋊C4—682no—
150C4⋊C4—682no—
151C4⋊C4—684no—
152C4⋊C4—682no—
153C4⋊C4—1362no—
154C4⋊C4—1362no—
155C4⋊C4—1362no—
156C42C2×Dic3412yes—
157C42#6325411yescharacteristic
158C42Q8×D1711yescharacteristic
159C23#1058756811yescharacteristic
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—682no—
168C2×C4—682no—
169C2×C4—682no—
170C2×C4—682no—
171C2×C4—682no—
172C2×C4—682no—
173C2×C4—1362no—
174C2×C4—1361no—
175C2×C4#1058755511yescharacteristic
176C2×C4#1058756412yes—
177C2×C4#1058757412yes—
178C2×C4#1058758311yescharacteristic
179C8—44no—
180C8—682no—
181C22#1176273011yescharacteristic
182C22#1176298312yes—
183C22#1176298411yescharacteristic
184C22#1176298812yes—
185C22#1176298911yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—2721no—
192C4—1362no—
193C4—1362no—
194C2#1452808711yescharacteristic
195C2#1452810811yescharacteristic
196C2#1452810912yes—
197C2#1453013312yes—
198C2#1453013511yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1295C2
socle, prime radicalC23×C17#120
hypercenter#1295D17
hypocenterC17#10586
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
135. C17#10586semidirect

Maximal subgroups

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

subgroupindex
#145370592
#145289182
#145289172
#145266662
C17×#12952
#1058617