Finite Group Databasebeta

← #16943967

Subgroups — #16943967

Order 4352.

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

normal subgroups only

This group has 394 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#14526718C214yesmaximal
4C17×#2546C211yesmaximal, characteristic
5#11762866—21no—
6#11762862—21no—
7#11762535—21no—
8#11762535—21no—
9#11762535C2212yes—
10#11762535C2212yes—
11C2×C17×C4⋊Q8C411yescharacteristic
12C2×C17×C4⋊Q8C412yes—
13C2×C4×Q8×C17C2211yescharacteristic
14C17×#398—21no—
15C17×#398—21no—
16C17×#391C2212yes—
17C17×#389—21no—
18C17×#389—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Q8×C17C2×C412yes—
21C22×Q8×C17C2×C411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—44no—
25C4×Q8×C17—41no—
26C4×Q8×C17—41no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17—22no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C4⋊C4×C17C2311yescharacteristic
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17C2×C412yes—
37C2×C42×C17D411yescharacteristic
38C2×C42×C17D411yescharacteristic
39C17×#95—21no—
40C17×#95—22no—
41C17×#95—22no—
42C22⋊#3622—22no—
43C22⋊#3622—22no—
44C4⋊#3622—41no—
45C4⋊#3622—41no—
46#10587474—41no—
47C4×#3622—41no—
48C2×Q8×C17—22no—
49C2×Q8×C17—22no—
50C2×Q8×C17—24no—
51C2×Q8×C17—41no—
52C2×Q8×C17—42no—
53C2×Q8×C17—42no—
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—24no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—44no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—44no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—42no—
79C2×#3622—42no—
80C2×#3622—42no—
81#11568—171nomaximal, Sylow
82C23×C17C2×C22⋊C411yescharacteristic
83Q8×C17—44no—
84Q8×C17—84no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—24no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17#9911yescharacteristic
106C2×C4×C17#9911yescharacteristic
107C2×C4×C17#10012yes—
108C2×C4×C17#13112yes—
109#3622—82no—
110#3622—82no—
111#2546D1711yescharacteristic
112#1467—171no—
113#1461—171no—
114#1319—174no—
115C22×C17—21no—
116C22×C17—21no—
117C22×C17#40811yescharacteristic
118C22×C17C2×#9911yescharacteristic
119C22×C17C2×#10011yescharacteristic
120C4×C17—21no—
121C4×C17—22no—
122C4×C17—22no—
123C4×C17—44no—
124C4×C17—41no—
125C4×C17—41no—
126C4×C17—41no—
127C4×C17—41no—
128C4×C17—82no—
129C4×C17#35612yes—
130C2×C4⋊Q8Dic1711yescharacteristic
131C2×C4⋊Q8Dic1712yes—
132C2×C4×Q8C2×D1711yescharacteristic
133#432—341no—
134#431—341no—
135#398—21no—
136#398—21no—
137#391C2×D1712yes—
138#389—21no—
139#389—21no—
140C4×C4⋊C4Dic1711yescharacteristic
141#324—172no—
142#324—172no—
143#324—341no—
144#324—341no—
145C2×C17—21no—
146C2×C17—21no—
147C2×C17#147111yescharacteristic
148C2×C17#212911yescharacteristic
149C2×C17C2×#35611yescharacteristic
150C22×Q8C2×Dic1712yes—
151C22×Q8C2×Dic1711yescharacteristic
152C4⋊Q8—41no—
153C4⋊Q8—41no—
154C4⋊Q8—44no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C22⋊D1711yescharacteristic
163C2×C4⋊C4C22⋊D1711yescharacteristic
164C2×C4⋊C4C22×D1711yescharacteristic
165C2×C42C2×Dic1711yescharacteristic
166C2×C42C2×Dic1712yes—
167C2×C42C22⋊D1711yescharacteristic
168C2×C42C22⋊D1711yescharacteristic
169C4⋊C8—681no—
170C4⋊C8—681no—
171C22⋊C8—342no—
172C22⋊C8—342no—
173#97—681no—
174C4×C8—681no—
175#95—21no—
176#95—22no—
177#95—22no—
178C17#1156811yescharacteristic, complemented, Sylow
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—24no—
182C2×Q8—41no—
183C2×Q8—42no—
184C2×Q8—42no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C22⋊Dic1711yescharacteristic
188C22×C4C22⋊Dic1711yescharacteristic
189C22×C4C22⋊Dic1711yescharacteristic
190C22×C4C22⋊Dic1711yescharacteristic
191C22×C4C22×Dic1711yescharacteristic
192C22×C4C2×C22⋊D1711yescharacteristic
193C22×C4C2×C22⋊D1711yescharacteristic
194C2×C8—682no—
195C2×C8—682no—
196C4⋊C4—24no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—44no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—42no—
212C23C2×C22⋊Dic1711yescharacteristic
213Q8—44no—
214Q8—84no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4#1058750412yes—
236C2×C4#1058750511yescharacteristic
237C2×C4#1058750511yescharacteristic
238C2×C4#1058763412yes—
239C8—1362no—
240C8—1362no—
241C22—21no—
242C22—21no—
243C22#1176277611yescharacteristic
244C22C2×#1058750511yescharacteristic
245C22C2×#1058750411yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—44no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4#1176260812yes—
256C2—21no—
257C2—21no—
258C2#1452714411yescharacteristic
259C2#1453045911yescharacteristic
260C2C2×#1176260811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2546C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2546D17
hypocenterC17#11568
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
178. C17#11568semidirect

Maximal subgroups

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

subgroupindex
#145271282
#145271082
#145267182
C17×#25462
#1156817