Finite Group Databasebeta

← #16943820

Subgroups — #16943820

Order 4352.

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

normal subgroups only

This group has 376 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#14527128C212yesmaximal
2#14526728C212yesmaximal
3#14526718C212yesmaximal
4C17×#2327C211yesmaximal, characteristic
5#11762866—22no—
6#11762535—22no—
7#11762535C2214yes—
8C2×C17×C4⋊Q8C411yescharacteristic
9C2×C4×Q8×C17C411yescharacteristic
10C2×C4×Q8×C17C2211yescharacteristic
11C17×#391C411yescharacteristic
12C17×#391C2211yescharacteristic
13C17×#387—22no—
14C17×#387—22no—
15C17×#382C2211yescharacteristic
16C17×#376C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×Q8×C17C2×C411yescharacteristic
19C17×C4⋊Q8—22no—
20C17×C4⋊Q8—22no—
21C4×Q8×C17—42no—
22C4×Q8×C17—42no—
23C2×C4⋊C4×C17—22no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17C2×C411yescharacteristic
26C2×C4⋊C4×C17D412yes—
27C2×C4⋊C4×C17C2311yescharacteristic
28C2×C42×C17—21no—
29C2×C42×C17C2×C411yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17D412yes—
33C17×#95—21no—
34C17×#95—21no—
35C17×#95—22no—
36C17×#95—22no—
37C17×#95—22no—
38C22⋊#3622—24no—
39C4⋊#3622—42no—
40#10587474—42no—
41C2×Q8×C17—21no—
42C2×Q8×C17—21no—
43C2×Q8×C17—21no—
44C2×Q8×C17—41no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17—41no—
48C2×Q8×C17M1612yes—
49C22×C4×C17—21no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17C22⋊C412yes—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×C4×C17C2×D412yes—
58C4⋊C4×C17—28no—
59C4⋊C4×C17—42no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—42no—
63C42×C17—22no—
64C42×C17—22no—
65C42×C17—22no—
66C42×C17—21no—
67C42×C17—41no—
68C42×C17—42no—
69C42×C17M1612yes—
70C2×#3622—44no—
71#11536—171nomaximal, Sylow
72C23×C17C2×C22⋊C411yescharacteristic
73Q8×C17—42no—
74Q8×C17—42no—
75Q8×C17—42no—
76Q8×C17—42no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—22no—
80C2×C4×C17—22no—
81C2×C4×C17—22no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—22no—
85C2×C4×C17—22no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17#9912yes—
99C2×C4×C17C2×M1611yescharacteristic
100C2×C4×C17C2×M1611yescharacteristic
101#3622—84no—
102#2327D1711yescharacteristic
103#1467—172no—
104#1324—172no—
105#1319—172no—
106C22×C17—21no—
107C22×C17—21no—
108C22×C17#40711yescharacteristic
109C22×C17C2×#9911yescharacteristic
110C22×C17#41311yescharacteristic
111C4×C17—22no—
112C4×C17—21no—
113C4×C17—21no—
114C4×C17—42no—
115C4×C17—42no—
116C4×C17—41no—
117C4×C17—42no—
118C4×C17—42no—
119C4×C17—81no—
120C4×C17—81no—
121C2×C4⋊Q8Dic1711yescharacteristic
122C2×C4×Q8Dic1711yescharacteristic
123C2×C4×Q8C2×D1711yescharacteristic
124#432—342no—
125#391Dic1711yescharacteristic
126#391C2×D1711yescharacteristic
127#387—22no—
128#387—22no—
129#382C2×D1711yescharacteristic
130#376Dic1711yescharacteristic
131#324—174no—
132#324—342no—
133C2×C17—21no—
134C2×C17—21no—
135C2×C17#146511yescharacteristic
136C2×C17#212911yescharacteristic
137C2×C17#213311yescharacteristic
138C22×Q8C2×Dic1711yescharacteristic
139C22×Q8C2×Dic1711yescharacteristic
140C4⋊Q8—22no—
141C4⋊Q8—22no—
142C4×Q8—42no—
143C4×Q8—42no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4C2×Dic1711yescharacteristic
147C2×C4⋊C4C22⋊D1712yes—
148C2×C4⋊C4C22×D1711yescharacteristic
149C2×C42—21no—
150C2×C42C2×Dic1711yescharacteristic
151C2×C42C2×Dic1711yescharacteristic
152C2×C42C2×Dic1711yescharacteristic
153C2×C42C22⋊D1712yes—
154C4⋊C8—682no—
155C22⋊C8—344no—
156#97—682no—
157#95—21no—
158#95—22no—
159#95—21no—
160#95—22no—
161#95—22no—
162C17#1153611yescharacteristic, complemented, Sylow
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8#6322312yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4C22⋊Dic1712yes—
176C22×C4C22⋊Dic1711yescharacteristic
177C22×C4C22⋊Dic1711yescharacteristic
178C22×C4C22×Dic1711yescharacteristic
179C22×C4C2×C22⋊D1712yes—
180C2×C8—684no—
181C4⋊C4—28no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C42—22no—
187C42—22no—
188C42—22no—
189C42—21no—
190C42—41no—
191C42—42no—
192C42#6322312yes—
193C23C2×C22⋊Dic1711yescharacteristic
194Q8—42no—
195Q8—42no—
196Q8—42no—
197Q8—42no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4#1058750512yes—
220C2×C4C2×#6322311yescharacteristic
221C2×C4C2×#6322311yescharacteristic
222C8—1364no—
223C22—21no—
224C22—21no—
225C22#1176277311yescharacteristic
226C22C2×#1058750511yescharacteristic
227C22#1176279311yescharacteristic
228C4—21no—
229C4—21no—
230C4—22no—
231C4—42no—
232C4—42no—
233C4—42no—
234C4—42no—
235C4—41no—
236C4—81no—
237C4—81no—
238C2—21no—
239C2—21no—
240C2#1452712211yescharacteristic
241C2#1453045911yescharacteristic
242C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2327C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2327D17
hypocenterC17#11536
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2327

Complements

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

NH ≅ G/Ntype
162. C17#11536semidirect

Maximal subgroups

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

subgroupindex
#145271282
#145267282
#145267182
C17×#23272
#1153617