Finite Group Databasebeta

← #16950335

Subgroups — #16950335

Order 4352.

432 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#11762608C212yesmaximal
2#14528780C212yesmaximal
3#14526911C212yesmaximal
4C17×#2327C211yesmaximal, characteristic
5#11762833—22no—
6C2×#10587507C2214yes—
7#11762608—24no—
8#11762578—22no—
9C2×C17×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C17C411yescharacteristic
11C2×C4×Q8×C17C2211yescharacteristic
12C17×#391C411yescharacteristic
13C17×#391C2211yescharacteristic
14C17×#387—22no—
15C17×#387—22no—
16C17×#382C411yescharacteristic
17C17×#376C411yescharacteristic
18C22×Q8×C17C2×C411yescharacteristic
19C22×Q8×C17C2311yescharacteristic
20C17×C4⋊Q8—22no—
21C17×C4⋊Q8D412yes—
22C17×C4⋊Q8Q812yes—
23C4×Q8×C17—42no—
24C4×Q8×C17—42no—
25C2×C4⋊C4×C17—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17D412yes—
30C2×C42×C17—21no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17C2×C411yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×C42×C17D412yes—
35C2×#63223—24no—
36C17×#95—21no—
37C17×#95—21no—
38C17×#95—22no—
39C17×#95—22no—
40C17×#95—22no—
41#10587507—24no—
42#10587507—24no—
43C4⋊#3622—44no—
44C2×Q8×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17—41no—
48C2×Q8×C17—41no—
49C2×Q8×C17C4⋊C412yes—
50C2×Q8×C17C2×D411yescharacteristic
51C2×Q8×C17C2×Q811yescharacteristic
52C2×Q8×C17#4112yes—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17C22⋊C412yes—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×C4×C17C2×D412yes—
62C4⋊C4×C17—24no—
63C4⋊C4×C17—24no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—42no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—42no—
68C42×C17—24no—
69C42×C17—22no—
70C42×C17—21no—
71C42×C17—41no—
72C42×C17—42no—
73C42×C17C4⋊C412yes—
74#63223—44no—
75#63223—44no—
76C2×#3622—44no—
77#12804—171nomaximal, Sylow
78C23×C17C2×C22⋊C411yescharacteristic
79Q8×C17—41no—
80Q8×C17—41no—
81Q8×C17—42no—
82Q8×C17—42no—
83Q8×C17—42no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—21no—
91C2×C4×C17—22no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—42no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—42no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17#9912yes—
105C2×C4×C17C2×C4⋊C411yescharacteristic
106C2×C4×C17#11711yescharacteristic
107C2×C4×C17#12112yes—
108C2×C4×C17C22⋊Q812yes—
109#3622—84no—
110#2327D1711yescharacteristic
111C2×#356—172no—
112#1801—172no—
113#1394—172no—
114C22×C17—21no—
115C22×C17—21no—
116C22×C17#38011yescharacteristic
117C22×C17C2×#9911yescharacteristic
118C22×C17#41011yescharacteristic
119C4×C17—22no—
120C4×C17—21no—
121C4×C17—21no—
122C4×C17—22no—
123C4×C17—22no—
124C4×C17—42no—
125C4×C17—42no—
126C4×C17—41no—
127C4×C17—42no—
128C4×C17—81no—
129C4×C17—81no—
130C2×C4⋊Q8C2×D1711yescharacteristic
131C2×C4×Q8Dic1711yescharacteristic
132C2×C4×Q8C2×D1711yescharacteristic
133#423—342no—
134C2×#101—174no—
135#391Dic1711yescharacteristic
136#391C2×D1711yescharacteristic
137#387—22no—
138#387—22no—
139#382Dic1711yescharacteristic
140#376Dic1711yescharacteristic
141#356—344no—
142#343—342no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17#179911yescharacteristic
146C2×C17#213311yescharacteristic
147C2×C17#213511yescharacteristic
148C22×Q8C2×Dic1711yescharacteristic
149C22×Q8C22×D1711yescharacteristic
150C2×M16—344no—
151C4⋊Q8—22no—
152C4⋊Q8Dic3412yes—
153C4⋊Q8D6812yes—
154C4×Q8—42no—
155C4×Q8—42no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4C2×Dic1711yescharacteristic
159C2×C4⋊C4C2×Dic1711yescharacteristic
160C2×C4⋊C4C22⋊D1712yes—
161C2×C42—21no—
162C2×C42C2×Dic1711yescharacteristic
163C2×C42C2×Dic1711yescharacteristic
164C2×C42C2×Dic1711yescharacteristic
165C2×C42C22⋊D1712yes—
166C4⋊C8—684no—
167#101—344no—
168#101—344no—
169#95—21no—
170#95—22no—
171#95—22no—
172#95—21no—
173#95—22no—
174C17#1280411yescharacteristic, complemented, Sylow
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8C4⋊Dic1712yes—
181C2×Q8C2×Dic3411yescharacteristic
182C2×Q8C2×D6811yescharacteristic
183C2×Q8#6325212yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4C22⋊Dic1712yes—
189C22×C4C22⋊Dic1711yescharacteristic
190C22×C4C22⋊Dic1711yescharacteristic
191C22×C4C22×Dic1711yescharacteristic
192C22×C4C2×C22⋊D1712yes—
193M16—684no—
194M16—684no—
195C2×C8—684no—
196C4⋊C4—24no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C42—24no—
203C42—22no—
204C42—21no—
205C42—41no—
206C42—42no—
207C42C4⋊Dic1712yes—
208C23C2×C22⋊Dic1711yescharacteristic
209Q8—41no—
210Q8—41no—
211Q8—42no—
212Q8—42no—
213Q8—42no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4#1058750512yes—
235C2×C4#1058761012yes—
236C2×C4C2×C4⋊Dic1711yescharacteristic
237C2×C4#1058761211yescharacteristic
238C2×C4#1058761612yes—
239C8—1364no—
240C22—21no—
241C22—21no—
242C22#1176266911yescharacteristic
243C22C2×#1058750511yescharacteristic
244C22#1176278311yescharacteristic
245C4—22no—
246C4—22no—
247C4—21no—
248C4—21no—
249C4—22no—
250C4—42no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4—81no—
256C2—21no—
257C2—21no—
258C2#1452877211yescharacteristic
259C2#1453047311yescharacteristic
260C2#1453047911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC22×Q8C22×D17
FittingC17×#2327C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Q8×C17C23
hypercenter#2327D17
hypocenterC17#12804
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
174. C17#12804semidirect

Maximal subgroups

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

subgroupindex
C2×#117626082
#145287802
#145269112
C17×#23272
#1280417