Finite Group Databasebeta

← #17959411

Subgroups — #17959411

Order 4352.

378 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 74 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×#10587545C211yesmaximal, characteristic
2#14544046C211yesmaximal, characteristic
3#14543783C214yesmaximal
4#14534000C211yesmaximal, characteristic
5#11763830—21no—
6C2×#10587545—21no—
7C4×#63247—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×C4×Dic34C2211yescharacteristic
12#11762747C412yes—
13#11762747C2212yes—
14#11762716—21no—
15#11762716—21no—
16#11762714—21no—
17#11762674—21no—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Dic34D411yescharacteristic
22C2×#63247—22no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—41no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17C2×C412yes—
27C2×C42×C17C2×C411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17D411yescharacteristic
30C2×#63225C2×C411yescharacteristic
31C2×#63225C2311yescharacteristic
32C2×C4×Dic17—21no—
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C4×Dic34—41no—
36C4×Dic34—41no—
37C22⋊#3624—22no—
38#10587545—24no—
39#10587542—41no—
40#10587542—41no—
41C4⋊#3624—41no—
42C4×#3624—41no—
43#10587502—22no—
44#10587502—22no—
45#10587502—22no—
46#10587502—22no—
47#10587502C2×C412yes—
48C2×Q8×C17—44no—
49C2×Q8×C17—41no—
50C2×Q8×C17—41no—
51C22×C4×C17—22no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—22no—
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C2×Dic34—22no—
61C2×Dic34—22no—
62C2×Dic34—41no—
63#63247—24no—
64#63247—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—42no—
69C42×C17—21no—
70C42×C17—21no—
71C4⋊Dic17—41no—
72C4⋊Dic17—42no—
73#63225—41no—
74#63225—41no—
75C4×Dic17—21no—
76C4×Dic17—21no—
77C4×Dic17—21no—
78C4×Dic17—21no—
79C4×Dic17—42no—
80#11794—171nomaximal, Sylow
81C23×C17C2×C22⋊C411yescharacteristic
82Q8×C17—82no—
83Q8×C17—82no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17—21no—
88C2×C4×C17—41no—
89C2×C4×C17—44no—
90C2×C4×C17—42no—
91C2×C4×C17#9911yescharacteristic
92C2×C4×C17#9911yescharacteristic
93C2×C4×C17#10412yes—
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—42no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17#13712yes—
107Dic34—44no—
108#3624—44no—
109#3624—82no—
110#2568—171no—
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—41no—
122C4×C17—82no—
123C4×C17#35512yes—
124Dic17—22no—
125Dic17—41no—
126Dic17—41no—
127Dic17—41no—
128Dic17—82no—
129C2×C4⋊Q8#59511yescharacteristic
130C2×C4×Q8—171no—
131#432—341no—
132C2×#101—341no—
133C4×M16—341no—
134#400—172no—
135#400—172no—
136#391—341no—
137#391—341no—
138#391—341no—
139#382—341no—
140C4×C4⋊C4—171no—
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×Q8—171no—
151C2×M16—342no—
152C4⋊Q8—41no—
153C4⋊Q8—41no—
154C4×Q8—681no—
155C4×Q8—681no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—171no—
159C2×C4⋊C4—171no—
160C2×C4⋊C4—341no—
161C2×C4⋊C4C2×#59512yes—
162C2×C42—171no—
163C2×C42—171no—
164C2×C42—341no—
165C2×C42C2×#59511yescharacteristic
166C4⋊C8—681no—
167#101—344no—
168C22⋊C8—342no—
169#97—681no—
170#97—681no—
171C4×C8—681no—
172#95—172no—
173#95—342no—
174#95—342no—
175#95—342no—
176#95—342no—
177C17#1179411yescharacteristic, complemented, Sylow
178C2×Q8—44no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—342no—
182C2×Q8—342no—
183C2×Q8—681no—
184C22×C4—22no—
185C22×C4—171no—
186C22×C4—171no—
187C22×C4—171no—
188C22×C4—171no—
189C22×C4—342no—
190C22×C4C22⋊#59511yescharacteristic
191C22×C4C22⋊#59511yescharacteristic
192C22×C4C22×#59511yescharacteristic
193M16—344no—
194M16—682no—
195C2×C8—682no—
196C2×C8—682no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—681no—
200C4⋊C4—681no—
201C4⋊C4—681no—
202C4⋊C4—682no—
203C42—21no—
204C42—21no—
205C42—341no—
206C42—341no—
207C42—341no—
208C42—341no—
209C42—682no—
210C23C2×C22⋊#59511yescharacteristic
211Q8—82no—
212Q8—82no—
213Q8—684no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—172no—
222C2×C4—341no—
223C2×C4—341no—
224C2×C4—341no—
225C2×C4—341no—
226C2×C4—341no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—681no—
230C2×C4—681no—
231C2×C4—682no—
232C2×C4—682no—
233C2×C4—682no—
234C2×C4#1058755012yes—
235C2×C4#1058755111yescharacteristic
236C2×C4#1058755111yescharacteristic
237C8—684no—
238C8—1362no—
239C22—21no—
240C22—21no—
241C22C2×#1058755111yescharacteristic
242C22#1176380211yescharacteristic
243C22C2×#1058755011yescharacteristic
244C4—22no—
245C4—21no—
246C4—41no—
247C4—82no—
248C4—342no—
249C4—681no—
250C4—681no—
251C4—681no—
252C4—1362no—
253C4#1176371712yes—
254C2—21no—
255C2—21no—
256C2#1454418411yescharacteristic
257C2#1454504611yescharacteristic
258C2C2×#1176371711yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#11794
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

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×#105875452
#145440462
#145437832
#145340002
#1179417