Finite Group Databasebeta

← #16944920

Subgroups — #16944920

Order 4352.

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

normal subgroups only

This group has 414 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
2C4×#10587507C211yesmaximal, characteristic
3#14526791C214yesmaximal
4C17×#1467C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic
6C2×#10587630—21no—
7C2×#10587507—21no—
8C4×#63223—21no—
9#11762739C412yes—
10#11762739C2212yes—
11#11762714—21no—
12#11762707—21no—
13#11762707—21no—
14C4×C4⋊Dic17C411yescharacteristic
15#11762578C2212yes—
16C2×C4×Q8×C17C2211yescharacteristic
17C17×#432—21no—
18C17×#324—21no—
19C17×#324C2212yes—
20C22×Q8×C17D411yescharacteristic
21C22×Dic34—21no—
22C4×Q8×C17—41no—
23C4×Q8×C17—41no—
24C2×C4⋊C4×C17C2×C411yescharacteristic
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⋊Dic17C2×C412yes—
34C2×#63225—22no—
35C2×#63225—22no—
36C2×C4×Dic17—21no—
37C2×#63223—22no—
38#10587555—41no—
39#10587555—41no—
40C17×C4⋊C8—41no—
41C17×C22⋊C8—22no—
42C17×#97—41no—
43#10587507—24no—
44#10587502—22no—
45#10587502—22no—
46#10587502C2×C412yes—
47#10587474—41no—
48C4×#3622—41no—
49C2×Q8×C17—22no—
50C2×Q8×C17—22no—
51C2×Q8×C17—41no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—22no—
60C22×Dic17—22no—
61C2×Dic34—42no—
62C2×Dic34—42no—
63C2×Dic34—42no—
64C2×C8×C17—42no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—41no—
68C42×C17—21no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—21no—
72C42×C17—21no—
73C42×C17—21no—
74C4⋊Dic17—24no—
75C4⋊Dic17—41no—
76C4⋊Dic17—41no—
77C4⋊Dic17—42no—
78#63225—44no—
79#63225—44no—
80C4×Dic17—42no—
81#63223—24no—
82#63223—42no—
83C2×#3622—42no—
84#11782—171nomaximal, Sylow
85C23×C17C2×C22⋊C411yescharacteristic
86Q8×C17—44no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—22no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17#9911yescharacteristic
102C2×C4×C17#9911yescharacteristic
103C2×C4×C17#10412yes—
104C2×C4×C17AGL(1,ℤ/8)12yes—
105C2×Dic17—24no—
106C2×Dic17—42no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111Dic34—84no—
112C8×C17—82no—
113#3622—44no—
114#2546—171no—
115C4×#101—171no—
116#1467D1711yescharacteristic
117#1346—174no—
118C22×C17—21no—
119C22×C17—21no—
120C22×C17C2×#9911yescharacteristic
121C22×C17#41811yescharacteristic
122C22×C17C2×#10411yescharacteristic
123C4×C17—21no—
124C4×C17—22no—
125C4×C17—22no—
126C4×C17—41no—
127C4×C17—41no—
128C4×C17—41no—
129C4×C17—41no—
130C4×C17#35612yes—
131Dic17—44no—
132Dic17—82no—
133C2×C4⋊Q8—171no—
134C2×C4⋊Q8—341no—
135C2×C4×Q8C2×D1711yescharacteristic
136#432—21no—
137C2×#101—341no—
138C4×M16—341no—
139#398—172no—
140#398—172no—
141#391—341no—
142#389—341no—
143#389—341no—
144C4×C4⋊C4—171no—
145#343—172no—
146#324—21no—
147#324C2×D1712yes—
148C2×C17—21no—
149C2×C17—21no—
150C2×C17#150711yescharacteristic
151C2×C17#212311yescharacteristic
152C2×C17C2×#35611yescharacteristic
153C22×Q8—341no—
154C22×Q8D6811yescharacteristic
155C2×M16—342no—
156C4⋊Q8—681no—
157C4⋊Q8—681no—
158C4⋊Q8—684no—
159C4×Q8—41no—
160C4×Q8—41no—
161C2×C4⋊C4—172no—
162C2×C4⋊C4—341no—
163C2×C4⋊C4—342no—
164C2×C4⋊C4—342no—
165C2×C4⋊C4—341no—
166C2×C4⋊C4C4×D1711yescharacteristic
167C2×C4⋊C4C22⋊D1711yescharacteristic
168C2×C4⋊C4C22×D1711yescharacteristic
169C2×C42—341no—
170C2×C42C4×D1711yescharacteristic
171C2×C42D6811yescharacteristic
172C2×C42C22⋊D1711yescharacteristic
173C4⋊C8—41no—
174#101—344no—
175C22⋊C8—22no—
176#97—41no—
177#97—681no—
178C4×C8—681no—
179#95—172no—
180#95—342no—
181#95—342no—
182C17#1178211yescharacteristic, complemented, Sylow
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—682no—
187C2×Q8—682no—
188C2×Q8—682no—
189C22×C4—342no—
190C22×C4—342no—
191C22×C4#6322711yescharacteristic
192C22×C4#6322711yescharacteristic
193C22×C4#6322711yescharacteristic
194C22×C4#6322711yescharacteristic
195C22×C4C2×C4×D1711yescharacteristic
196C22×C4C2×D6811yescharacteristic
197C22×C4C2×C22⋊D1711yescharacteristic
198M16—344no—
199M16—682no—
200C2×C8—42no—
201C2×C8—682no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—344no—
206C4⋊C4—682no—
207C4⋊C4—684no—
208C4⋊C4—681no—
209C4⋊C4—681no—
210C4⋊C4—684no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—682no—
218C23C2×#6322711yescharacteristic
219Q8—44no—
220Q8—1364no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—344no—
236C2×C4—682no—
237C2×C4—682no—
238C2×C4—682no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4#1058747711yescharacteristic
242C2×C4#1058747711yescharacteristic
243C2×C4#1058749612yes—
244C2×C4#1058759412yes—
245C8—82no—
246C8—684no—
247C22—21no—
248C22—21no—
249C22C2×#1058747711yescharacteristic
250C22#1176281511yescharacteristic
251C22C2×#1058749611yescharacteristic
252C4—22no—
253C4—22no—
254C4—21no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—684no—
260C4—1362no—
261C4#1176260712yes—
262C2—21no—
263C2—21no—
264C2#1452730111yescharacteristic
265C2#1453043711yescharacteristic
266C2C2×#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#11782
LCSG ▷ C22×C4×C17 ▷ C23×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
182. C17#11782semidirect

Maximal subgroups

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

subgroupindex
#145337692
C4×#105875072
#145267912
C17×#14672
#1178217