Finite Group Databasebeta

← #16938825

Subgroups — #16938825

Order 4352.

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

normal subgroups only

This group has 374 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#14537056C211yesmaximal, characteristic
2#14528953C211yesmaximal, characteristic
3#14528918C212yesmaximal
4#14526666C212yesmaximal
5C17×#1295C211yesmaximal, characteristic
6C2×#10587478—21no—
7C2×#10587479—21no—
8C2×#10587474C2211yescharacteristic
9#11762751—22no—
10#11762748—21no—
11#11762730—22no—
12#11762729—21no—
13#11762679C2211yescharacteristic
14#11762675C2212yes—
15#11762572—22no—
16#11762572—22no—
17C2×C17×#97C2212yes—
18C17×#382C2211yescharacteristic
19C22×Dic34—21no—
20C22×C8×C17—22no—
21C2×C4⋊C4×C17D411yescharacteristic
22C2×C4⋊C4×C17D411yescharacteristic
23C2×C42×C17C2311yescharacteristic
24C2×C4⋊Dic17—21no—
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17D412yes—
28C2×C4⋊Dic17D412yes—
29C2×#63225—22no—
30C22×#3622—21no—
31C17×#97—22no—
32C17×#97Q814yescomplemented
33C17×#95—22no—
34#10587502—21no—
35#10587502—22no—
36#10587502—21no—
37#10587502—22no—
38#10587502—22no—
39#10587479—42no—
40#10587478—42no—
41#10587474—21no—
42#10587474Q812yescomplemented
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17C2×D411yescharacteristic
46C22×C4×C17C2×D412yes—
47C22×Dic17—22no—
48C22×Dic17—22no—
49C22×Dic17—41no—
50C2×Dic34—81no—
51C2×Dic34—82no—
52C2×C8×C17—24no—
53C2×C8×C17—42no—
54C2×C8×C17—42no—
55C4⋊C4×C17—41no—
56C4⋊C4×C17—41no—
57C42×C17C2×Q812yes—
58C42×C17C2×Q811yescharacteristic
59C42×C17#4111yescharacteristic
60C4⋊Dic17—42no—
61C4⋊Dic17—42no—
62C4⋊Dic17—41no—
63C4⋊Dic17—41no—
64C4⋊Dic17—44no—
65C4⋊Dic17—81no—
66#63225—82no—
67C2×#3622—22no—
68C2×#3622—22no—
69C2×#3622—22no—
70#10584—171nomaximal, Sylow
71C23×C17#12011yescharacteristic
72C2×C4×C17—21no—
73C2×C4×C17—22no—
74C2×C4×C17—22no—
75C2×C4×C17—21no—
76C2×C4×C17—41no—
77C2×C4×C17—41no—
78C2×C4×C17—42no—
79C2×C4×C17—42no—
80C2×C4×C17C22⋊Q812yes—
81C2×C4×C17C22⋊Q811yescharacteristic
82C2×C4×C17C4⋊Q811yescharacteristic
83C2×C4×C17C4⋊Q812yes—
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—81no—
91C2×Dic17—82no—
92Dic34—84no—
93C8×C17—44no—
94#3622—24no—
95#2844—171no—
96#1847—171no—
97#1836—172no—
98#1295—172no—
99#1295D1711yescharacteristic
100C22×C17#39511yescharacteristic
101C22×C17#45311yescharacteristic
102C22×C17#45412yes—
103C22×C17#45512yes—
104C22×C17#45611yescharacteristic
105C4×C17—21no—
106C4×C17—21no—
107C4×C17—22no—
108C4×C17—22no—
109C4×C17—81no—
110C4×C17—81no—
111Dic17—82no—
112Dic17—82no—
113Dic17—161no—
114C2×#107—341no—
115C2×#106—341no—
116C2×#97—171no—
117C2×#97C2×D1712yes—
118#400—342no—
119#400—341no—
120#395—342no—
121#395—341no—
122#384—171no—
123#382—172no—
124#382C2×D1711yescharacteristic
125#340—342no—
126#340—342no—
127C2×C17#165711yescharacteristic
128C2×C17#165911yescharacteristic
129C2×C17#166412yes—
130C2×C17#206011yescharacteristic
131C2×C17#206112yes—
132C22×Q8—341no—
133C22×C8—22no—
134C22×C8—341no—
135C2×C4⋊C4—172no—
136C2×C4⋊C4—172no—
137C2×C4⋊C4—341no—
138C2×C4⋊C4—342no—
139C2×C4⋊C4—342no—
140C2×C4⋊C4—341no—
141C2×C4⋊C4D6811yescharacteristic
142C2×C4⋊C4D6811yescharacteristic
143C2×C42C22×D1711yescharacteristic
144#107—682no—
145#106—682no—
146#97—22no—
147#97—172no—
148#97—341no—
149#97Dic3414yescomplemented
150#95—22no—
151#95—342no—
152#95—341no—
153#95—341no—
154#95—342no—
155#95—342no—
156C17#1058411yescharacteristic, complemented, Sylow
157C2×Q8—1361no—
158C2×Q8—1362no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—342no—
162C22×C4—342no—
163C22×C4—681no—
164C22×C4C2×D6811yescharacteristic
165C22×C4D4×D1712yes—
166C2×C8—24no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—342no—
170C2×C8—342no—
171C2×C8—342no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—682no—
175C4⋊C4—682no—
176C4⋊C4—681no—
177C4⋊C4—681no—
178C4⋊C4—684no—
179C4⋊C4—1362no—
180C4⋊C4—1361no—
181C42C2×Dic3412yes—
182C42#6325411yescharacteristic
183C42Q8×D1711yescharacteristic
184C23#1058756811yescharacteristic
185Q8—1364no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—682no—
195C2×C4—682no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4—682no—
199C2×C4—682no—
200C2×C4—1361no—
201C2×C4—1362no—
202C2×C4#1058755511yescharacteristic
203C2×C4#1058756412yes—
204C2×C4#1058757412yes—
205C2×C4#1058758311yescharacteristic
206C8—44no—
207C8—344no—
208C22#1176273011yescharacteristic
209C22#1176297911yescharacteristic
210C22#1176298312yes—
211C22#1176298812yes—
212C22#1176299411yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—2721no—
220C4—1362no—
221C4—1362no—
222C2#1452808311yescharacteristic
223C2#1452809111yescharacteristic
224C2#1452812012yes—
225C2#1453013011yescharacteristic
226C2#1453013312yes—
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1295C2
socle, prime radicalC23×C17#120
hypercenter#1295D17
hypocenterC17#10584
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
32. C17×#97Q8semidirect
42. #10587474Q8semidirect
149. #97Dic34semidirect
156. C17#10584semidirect

Maximal subgroups

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

subgroupindex
#145370562
#145289532
#145289182
#145266662
C17×#12952
#1058417