Finite Group Databasebeta

← #16944972

Subgroups — #16944972

Order 4352.

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

normal subgroups only

This group has 378 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
1C4×#10587507C211yesmaximal, characteristic
2#14527128C211yesmaximal, characteristic
3#14526811C214yesmaximal
4C17×#2568C211yesmaximal, characteristic
5#11762866—21no—
6C2×#10587507—21no—
7C4×#63223—21no—
8#11762578C2212yes—
9#11762535—21no—
10#11762535C2212yes—
11C2×C17×C4⋊Q8C411yescharacteristic
12C2×C4×Q8×C17C2211yescharacteristic
13C17×#400C412yes—
14C17×#400C2212yes—
15C17×#391—21no—
16C17×#391—21no—
17C17×#391—21no—
18C17×#382—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Q8×C17D411yescharacteristic
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×C17C2×C412yes—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17C2311yescharacteristic
32C2×C42×C17—21no—
33C2×C42×C17C2×C411yescharacteristic
34C2×C42×C17D411yescharacteristic
35C2×C42×C17D411yescharacteristic
36C2×#63223—22no—
37C17×#95—22no—
38C17×#95—22no—
39C17×#95—22no—
40C17×#95—22no—
41C17×#95C2×C412yes—
42#10587507—24no—
43C22⋊#3622—22no—
44C4⋊#3622—41no—
45#10587474—41no—
46#10587474—41no—
47C4×#3622—41no—
48C2×Q8×C17—22no—
49C2×Q8×C17—22no—
50C2×Q8×C17—41no—
51C2×Q8×C17—44no—
52C2×Q8×C17—41no—
53C2×Q8×C17—41no—
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C4⋊C4×C17—41no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—42no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—42no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—21no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—42no—
76#63223—24no—
77#63223—42no—
78C2×#3622—42no—
79C2×#3622—42no—
80#11794—171nomaximal, Sylow
81C23×C17C2×C22⋊C411yescharacteristic
82Q8×C17—44no—
83Q8×C17—82no—
84Q8×C17—82no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—42no—
100C2×C4×C17—42no—
101C2×C4×C17—44no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#9911yescharacteristic
106C2×C4×C17#10412yes—
107C2×C4×C17#13712yes—
108#3622—44no—
109#3622—82no—
110#2568D1711yescharacteristic
111C4×#101—171no—
112#1467—171no—
113#1353—174no—
114C22×C17—21no—
115C22×C17—21no—
116C22×C17C2×#9911yescharacteristic
117C22×C17#41911yescharacteristic
118C22×C17C2×#10411yescharacteristic
119C4×C17—21no—
120C4×C17—22no—
121C4×C17—22no—
122C4×C17—41no—
123C4×C17—41no—
124C4×C17—41no—
125C4×C17—41no—
126C4×C17—82no—
127C4×C17—82no—
128C4×C17#35512yes—
129C2×C4⋊Q8Dic1711yescharacteristic
130C2×C4×Q8C2×D1711yescharacteristic
131#432—341no—
132C2×#101—341no—
133C4×M16—341no—
134#400Dic1712yes—
135#400C2×D1712yes—
136#391—21no—
137#391—21no—
138#391—21no—
139#382—21no—
140C4×C4⋊C4Dic1711yescharacteristic
141#343—172no—
142#324—172no—
143#324—341no—
144C2×C17—21no—
145C2×C17—21no—
146C2×C17#150811yescharacteristic
147C2×C17#212311yescharacteristic
148C2×C17C2×#35511yescharacteristic
149C22×Q8—21no—
150C22×Q8C22⋊D1711yescharacteristic
151C2×M16—342no—
152C4⋊Q8—41no—
153C4⋊Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4C2×Dic1712yes—
159C2×C4⋊C4C2×Dic1711yescharacteristic
160C2×C4⋊C4C22⋊D1711yescharacteristic
161C2×C4⋊C4C22×D1711yescharacteristic
162C2×C42—21no—
163C2×C42C2×Dic1711yescharacteristic
164C2×C42C22⋊D1711yescharacteristic
165C2×C42C22⋊D1711yescharacteristic
166C4⋊C8—681no—
167#101—344no—
168C22⋊C8—342no—
169#97—681no—
170#97—681no—
171C4×C8—681no—
172#95—22no—
173#95—22no—
174#95—22no—
175#95—22no—
176#95C2×Dic1712yes—
177C17#1179411yescharacteristic, complemented, Sylow
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—44no—
182C2×Q8—41no—
183C2×Q8—41no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊Dic1711yescharacteristic
187C22×C4C22⋊Dic1711yescharacteristic
188C22×C4C22⋊Dic1711yescharacteristic
189C22×C4C22⋊Dic1711yescharacteristic
190C22×C4C22×Dic1711yescharacteristic
191C22×C4C2×C22⋊D1711yescharacteristic
192C22×C4C2×C22⋊D1711yescharacteristic
193M16—344no—
194M16—682no—
195C2×C8—682no—
196C2×C8—682no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—42no—
210C23C2×C22⋊Dic1711yescharacteristic
211Q8—44no—
212Q8—82no—
213Q8—82no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4#1058750511yescharacteristic
234C2×C4#1058750511yescharacteristic
235C2×C4#1058750812yes—
236C2×C4#1058762812yes—
237C8—684no—
238C8—1362no—
239C22—21no—
240C22—21no—
241C22C2×#1058750511yescharacteristic
242C22#1176281811yescharacteristic
243C22C2×#1058750811yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—82no—
252C4—82no—
253C4#1176260612yes—
254C2—21no—
255C2—21no—
256C2#1452730411yescharacteristic
257C2#1453043811yescharacteristic
258C2C2×#1176260611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2568C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2568D17
hypocenterC17#11794
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2568

Complements

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

NH ≅ G/Ntype
177. C17#11794semidirect

Maximal subgroups

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

subgroupindex
C4×#105875072
#145271282
#145268112
C17×#25682
#1179417