Finite Group Databasebeta

← #16943993

Subgroups — #16943993

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#14527128C211yesmaximal, characteristic
2#14527108C211yesmaximal, characteristic
3#14526730C214yesmaximal
4C17×#2567C211yesmaximal, characteristic
5#11762866—21no—
6#11762862—21no—
7#11762535—21no—
8#11762535—21no—
9#11762535C2212yes—
10#11762535C2212yes—
11C2×C17×C4⋊Q8C411yescharacteristic
12C2×C4×Q8×C17C2211yescharacteristic
13C17×#395—21no—
14C17×#395—21no—
15C17×#391C412yes—
16C17×#389—21no—
17C17×#389—21no—
18C17×#384C2212yes—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Q8×C17C2×C411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C4×Q8×C17—41no—
25C4×Q8×C17—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—22no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17C2×C412yes—
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17C2311yescharacteristic
34C2×C42×C17C2×C412yes—
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17D411yescharacteristic
37C2×C42×C17D411yescharacteristic
38C17×#95—21no—
39C17×#95—22no—
40C17×#95—22no—
41C22⋊#3622—22no—
42C22⋊#3622—22no—
43C4⋊#3622—41no—
44C4⋊#3622—41no—
45#10587474—41no—
46C4×#3622—41no—
47C2×Q8×C17—22no—
48C2×Q8×C17—22no—
49C2×Q8×C17—41no—
50C2×Q8×C17—42no—
51C2×Q8×C17—82no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C4⋊C4×C17—24no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—42no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—82no—
69C4⋊C4×C17—82no—
70C42×C17—21no—
71C42×C17—21no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—24no—
77C2×#3622—42no—
78C2×#3622—42no—
79#11574—171nomaximal, Sylow
80C23×C17C2×C22⋊C411yescharacteristic
81Q8×C17—44no—
82Q8×C17—84no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—24no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17#9911yescharacteristic
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#10112yes—
106C2×C4×C17#13112yes—
107#3622—82no—
108#3622—82no—
109#2567D1711yescharacteristic
110#1467—171no—
111#1461—171no—
112#1325—174no—
113C22×C17—21no—
114C22×C17—21no—
115C22×C17#40811yescharacteristic
116C22×C17C2×#9911yescharacteristic
117C22×C17C2×#10111yescharacteristic
118C4×C17—21no—
119C4×C17—22no—
120C4×C17—22no—
121C4×C17—44no—
122C4×C17—41no—
123C4×C17—41no—
124C4×C17—41no—
125C4×C17—41no—
126C4×C17—82no—
127C4×C17#35612yes—
128C2×C4⋊Q8Dic1711yescharacteristic
129C2×C4×Q8C2×D1711yescharacteristic
130#432—341no—
131#431—341no—
132#395—21no—
133#395—21no—
134#391Dic1712yes—
135#389—21no—
136#389—21no—
137#384C2×D1712yes—
138C4×C4⋊C4Dic1711yescharacteristic
139#324—172no—
140#324—172no—
141#324—341no—
142#324—341no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17#147211yescharacteristic
146C2×C17#212811yescharacteristic
147C2×C17C2×#35611yescharacteristic
148C22×Q8—21no—
149C22×Q8C2×Dic1711yescharacteristic
150C4⋊Q8—41no—
151C4⋊Q8—41no—
152C4×Q8—41no—
153C4×Q8—41no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4C2×Dic1712yes—
159C2×C4⋊C4C22⋊D1711yescharacteristic
160C2×C4⋊C4C22⋊D1711yescharacteristic
161C2×C4⋊C4C22×D1711yescharacteristic
162C2×C42C2×Dic1712yes—
163C2×C42C2×Dic1711yescharacteristic
164C2×C42C22⋊D1711yescharacteristic
165C2×C42C22⋊D1711yescharacteristic
166C4⋊C8—681no—
167C4⋊C8—681no—
168C22⋊C8—342no—
169C22⋊C8—342no—
170#97—681no—
171C4×C8—681no—
172#95—21no—
173#95—22no—
174#95—22no—
175C17#1157411yescharacteristic, complemented, Sylow
176C2×Q8—22no—
177C2×Q8—22no—
178C2×Q8—41no—
179C2×Q8—42no—
180C2×Q8—82no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4C22⋊Dic1711yescharacteristic
184C22×C4C22⋊Dic1711yescharacteristic
185C22×C4C22⋊Dic1711yescharacteristic
186C22×C4C22⋊Dic1711yescharacteristic
187C22×C4C22×Dic1711yescharacteristic
188C22×C4C2×C22⋊D1711yescharacteristic
189C22×C4C2×C22⋊D1711yescharacteristic
190C2×C8—682no—
191C2×C8—682no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—24no—
208C23C2×C22⋊Dic1711yescharacteristic
209Q8—44no—
210Q8—84no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#1058750511yescharacteristic
232C2×C4#1058750511yescharacteristic
233C2×C4#1058750712yes—
234C2×C4#1058763412yes—
235C8—1362no—
236C8—1362no—
237C22—21no—
238C22—21no—
239C22#1176277611yescharacteristic
240C22C2×#1058750511yescharacteristic
241C22C2×#1058750711yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—44no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4#1176260812yes—
252C2—21no—
253C2—21no—
254C2#1452714811yescharacteristic
255C2#1453045611yescharacteristic
256C2C2×#1176260811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2567C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2567D17
hypocenterC17#11574
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
175. C17#11574semidirect

Maximal subgroups

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

subgroupindex
#145271282
#145271082
#145267302
C17×#25672
#1157417