Finite Group Databasebeta

← #16938824

Subgroups — #16938824

Order 4352.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#14528919C212yesmaximal
3#14526666C212yesmaximal
4#14526665C211yesmaximal, characteristic
5C17×#1847C211yesmaximal, characteristic
6C2×#10587474C2212yes—
7#11762751—22no—
8#11762748—21no—
9#11762730—22no—
10#11762729—21no—
11#11762675C2212yes—
12#11762571—22no—
13#11762571—22no—
14C2×C17×#107—21no—
15C2×C17×#106—21no—
16C2×C17×#97C2211yescharacteristic
17C17×#384C2211yescharacteristic
18C17×#382C2211yescharacteristic
19C22×Dic34—21no—
20C22×C8×C17—21no—
21C2×C4⋊C4×C17—22no—
22C2×C4⋊C4×C17—21no—
23C2×C4⋊C4×C17D411yescharacteristic
24C2×C4⋊C4×C17D411yescharacteristic
25C2×C42×C17C2311yescharacteristic
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17D412yes—
28C2×C4⋊Dic17D412yes—
29C2×#63225—22no—
30C22×#3622—22no—
31C17×#107—42no—
32C17×#106—42no—
33C17×#97—21no—
34C17×#97Q812yescomplemented
35C17×#95—22no—
36#10587502—21no—
37#10587502—22no—
38#10587502—21no—
39#10587502—22no—
40#10587502—22no—
41#10587474—22no—
42#10587474Q814yescomplemented
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17—41no—
46C22×C4×C17C2×D412yes—
47C22×C4×C17C2×D411yescharacteristic
48C22×Dic17—22no—
49C22×Dic17—22no—
50C2×Dic34—81no—
51C2×Dic34—82no—
52C2×C8×C17—22no—
53C2×C8×C17—22no—
54C2×C8×C17—22no—
55C4⋊C4×C17—41no—
56C4⋊C4×C17—41no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—41no—
59C4⋊C4×C17—44no—
60C42×C17C2×Q811yescharacteristic
61C42×C17C2×Q812yes—
62C42×C17#4111yescharacteristic
63C4⋊Dic17—42no—
64C4⋊Dic17—42no—
65C4⋊Dic17—81no—
66#63225—82no—
67C2×#3622—24no—
68C2×#3622—42no—
69C2×#3622—42no—
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×C17—81no—
81C2×C4×C17—82no—
82C2×C4×C17C22⋊Q812yes—
83C2×C4×C17C22⋊Q811yescharacteristic
84C2×C4×C17C4⋊Q812yes—
85C2×C4×C17C4⋊Q811yescharacteristic
86C2×Dic17—42no—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—42no—
92Dic34—84no—
93C8×C17—24no—
94#3622—44no—
95#2844—171no—
96#1847D1711yescharacteristic
97#1836—172no—
98#1295—172no—
99#1295—171no—
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—
111C4×C17—161no—
112Dic17—82no—
113Dic17—82no—
114C2×#107—21no—
115C2×#106—21no—
116C2×#97—172no—
117C2×#97C2×D1711yescharacteristic
118#400—342no—
119#400—341no—
120#395—342no—
121#395—341no—
122#384C2×D1711yescharacteristic
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—21no—
134C22×C8—342no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—172no—
138C2×C4⋊C4—172no—
139C2×C4⋊C4—342no—
140C2×C4⋊C4—341no—
141C2×C4⋊C4C22⋊D1711yescharacteristic
142C2×C4⋊C4C22⋊D1711yescharacteristic
143C2×C42C22×D1711yescharacteristic
144#107—42no—
145#106—42no—
146#97—21no—
147#97—174no—
148#97—342no—
149#97Dic3412yescomplemented
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—41no—
162C22×C4—342no—
163C22×C4—342no—
164C22×C4D4×D1712yes—
165C22×C4C2×C22⋊D1711yescharacteristic
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—344no—
170C2×C8—682no—
171C2×C8—682no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—44no—
177C4⋊C4—682no—
178C4⋊C4—682no—
179C4⋊C4—1362no—
180C4⋊C4—1361no—
181C42C2×Dic3411yescharacteristic
182C42#6325211yescharacteristic
183C42Q8×D1712yes—
184C23#1058762311yescharacteristic
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—81no—
195C2×C4—82no—
196C2×C4—682no—
197C2×C4—682no—
198C2×C4—682no—
199C2×C4—682no—
200C2×C4—682no—
201C2×C4—682no—
202C2×C4#1058757412yes—
203C2×C4#1058758212yes—
204C2×C4#1058761011yescharacteristic
205C2×C4#1058763011yescharacteristic
206C8—24no—
207C8—684no—
208C22#1176272911yescharacteristic
209C22#1176297611yescharacteristic
210C22#1176298012yes—
211C22#1176298512yes—
212C22#1176299111yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—161no—
220C4—1362no—
221C4—1362no—
222C2#1452808011yescharacteristic
223C2#1452808811yescharacteristic
224C2#1452811612yes—
225C2#1453012911yescharacteristic
226C2#1453013212yes—
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1847C2
socle, prime radicalC23×C17#120
hypercenter#1847D17
hypocenterC17#10584
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
34. 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
#145289192
#145266662
#145266652
C17×#18472
#1058417