Finite Group Databasebeta

← #16943968

Subgroups — #16943968

Order 4352.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#14533769C211yesmaximal, characteristic
2#14527108C211yesmaximal, characteristic
3#14526717C214yesmaximal
4C17×#1467C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic
6C2×#10587630C412yes—
7#11762862—21no—
8#11762739—21no—
9#11762739—21no—
10#11762714C2212yes—
11#11762707—21no—
12#11762707—21no—
13C4×C4⋊Dic17C411yescharacteristic
14#11762535—21no—
15#11762535C2212yes—
16C2×C4×Q8×C17C2211yescharacteristic
17C17×#432—21no—
18C17×#324—21no—
19C17×#324C2212yes—
20C22×Q8×C17C2×C411yescharacteristic
21C22×Dic34C2×C412yes—
22C4×Q8×C17—41no—
23C4×Q8×C17—41no—
24C2×C4⋊C4×C17D411yescharacteristic
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C4⋊C4×C17C2311yescharacteristic
27C2×C42×C17C2×C411yescharacteristic
28C2×C42×C17D411yescharacteristic
29C2×C42×C17D411yescharacteristic
30#10587630—44no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×#63225—22no—
35C2×#63225—22no—
36C2×C4×Dic17C2×C412yes—
37#10587555—41no—
38#10587555—41no—
39C17×C4⋊C8—41no—
40C17×C22⋊C8—22no—
41C17×#97—41no—
42#10587502—21no—
43#10587502—22no—
44#10587502—22no—
45C22⋊#3622—22no—
46C4⋊#3622—41no—
47C4×#3622—41no—
48C2×Q8×C17—22no—
49C2×Q8×C17—22no—
50C2×Q8×C17—41no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×C4×C17C2×D411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×Dic17—22no—
59C22×Dic17—22no—
60C2×Dic34—24no—
61C2×Dic34—42no—
62C2×Dic34—42no—
63C2×C8×C17—42no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C42×C17—21no—
68C42×C17—21no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—21no—
72C42×C17—21no—
73C4⋊Dic17—24no—
74C4⋊Dic17—42no—
75C4⋊Dic17—41no—
76C4⋊Dic17—41no—
77#63225—44no—
78#63225—44no—
79C4×Dic17—42no—
80C2×#3622—42no—
81#11568—171nomaximal, Sylow
82C23×C17C2×C22⋊C411yescharacteristic
83Q8×C17—44no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
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—41no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17#9911yescharacteristic
99C2×C4×C17#9911yescharacteristic
100C2×C4×C17#10012yes—
101C2×C4×C17#13112yes—
102C2×Dic17—24no—
103C2×Dic17—42no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17—42no—
107C2×Dic17—42no—
108Dic34—84no—
109C8×C17—82no—
110#3622—82no—
111#2546—171no—
112#1467D1711yescharacteristic
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—41no—
124C4×C17—41no—
125C4×C17—41no—
126C4×C17—41no—
127C4×C17#35612yes—
128Dic17—44no—
129Dic17—82no—
130C2×C4⋊Q8—172no—
131C2×C4⋊Q8—171no—
132C2×C4×Q8C2×D1711yescharacteristic
133#432—21no—
134#431—341no—
135#398—341no—
136#398—341no—
137#391—172no—
138#389—341no—
139#389—341no—
140C4×C4⋊C4—171no—
141#324—21no—
142#324—172no—
143#324—341no—
144#324C2×D1712yes—
145C2×C17—21no—
146C2×C17—21no—
147C2×C17#147111yescharacteristic
148C2×C17#212911yescharacteristic
149C2×C17C2×#35611yescharacteristic
150C22×Q8—172no—
151C22×Q8C4×D1711yescharacteristic
152C4⋊Q8—681no—
153C4⋊Q8—681no—
154C4⋊Q8—684no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—341no—
158C2×C4⋊C4—342no—
159C2×C4⋊C4—342no—
160C2×C4⋊C4—341no—
161C2×C4⋊C4—341no—
162C2×C4⋊C4D6811yescharacteristic
163C2×C4⋊C4C22⋊D1711yescharacteristic
164C2×C4⋊C4C22×D1711yescharacteristic
165C2×C42—172no—
166C2×C42C4×D1711yescharacteristic
167C2×C42D6811yescharacteristic
168C2×C42C22⋊D1711yescharacteristic
169C4⋊C8—41no—
170C4⋊C8—681no—
171C22⋊C8—22no—
172C22⋊C8—342no—
173#97—41no—
174C4×C8—681no—
175#95—342no—
176#95—342no—
177#95—341no—
178C17#1156811yescharacteristic, complemented, Sylow
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—344no—
183C2×Q8—682no—
184C2×Q8—682no—
185C22×C4—342no—
186C22×C4—342no—
187C22×C4#6322711yescharacteristic
188C22×C4#6322711yescharacteristic
189C22×C4#6322711yescharacteristic
190C22×C4#6322711yescharacteristic
191C22×C4C2×C4×D1711yescharacteristic
192C22×C4C2×D6811yescharacteristic
193C22×C4C2×C22⋊D1711yescharacteristic
194C2×C8—42no—
195C2×C8—682no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—344no—
200C4⋊C4—684no—
201C4⋊C4—682no—
202C4⋊C4—681no—
203C4⋊C4—681no—
204C4⋊C4—684no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—682no—
212C23C2×#6322711yescharacteristic
213Q8—44no—
214Q8—1364no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—344no—
230C2×C4—682no—
231C2×C4—682no—
232C2×C4—682no—
233C2×C4—682no—
234C2×C4—682no—
235C2×C4#1058747711yescharacteristic
236C2×C4#1058747711yescharacteristic
237C2×C4#1058749412yes—
238C2×C4#1058759312yes—
239C8—82no—
240C8—1362no—
241C22—21no—
242C22—21no—
243C22#1176277711yescharacteristic
244C22C2×#1058747711yescharacteristic
245C22C2×#1058749411yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—684no—
254C4—1362no—
255C4#1176260712yes—
256C2—21no—
257C2—21no—
258C2#1452714511yescharacteristic
259C2#1453045811yescharacteristic
260C2C2×#1176260711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1467C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1467D17
hypocenterC17#11568
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

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
#145337692
#145271082
#145267172
C17×#14672
#1156817