Finite Group Databasebeta

← #17959370

Subgroups — #17959370

Order 4352.

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

normal subgroups only

This group has 414 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#14543769C214yesmaximal
4#14533772C211yesmaximal, characteristic
5#11763830—21no—
6C2×#10587545—21no—
7C4×#63247—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×#10587555—21no—
12C2×#10587555C411yescharacteristic
13C2×C4×Dic34C2211yescharacteristic
14#11762741C412yes—
15#11762741C2212yes—
16#11762715—21no—
17#11762708—21no—
18#11762708—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Dic34—21no—
21C22×Dic34D411yescharacteristic
22C2×#63247—22no—
23C2×C4⋊C4×C17—21no—
24C2×C42×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17—22no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17C2×C412yes—
30C2×C4⋊Dic17D411yescharacteristic
31C2×#63225C2×C411yescharacteristic
32C2×#63225C2311yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35#10587555—41no—
36#10587555—41no—
37#10587555—44no—
38C4×Dic34—41no—
39C4×Dic34—41no—
40C22⋊#3624—22no—
41#10587545—24no—
42#10587542—41no—
43#10587542—41no—
44C4⋊#3624—41no—
45C4×#3624—41no—
46C17×#95C2×C412yes—
47#10587502—22no—
48#10587502—22no—
49C22×C4×C17—22no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—22no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C2×Dic34—22no—
59C2×Dic34—22no—
60C2×Dic34—41no—
61C2×Dic34—42no—
62C2×Dic34—42no—
63C2×Dic34—42no—
64#63247—24no—
65#63247—42no—
66C2×#3624—42no—
67C2×#3624—42no—
68C4⋊C4×C17—24no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—42no—
72C4⋊Dic17—41no—
73C4⋊Dic17—44no—
74C4⋊Dic17—41no—
75C4⋊Dic17—41no—
76C4⋊Dic17—44no—
77C4⋊Dic17—42no—
78#63225—41no—
79#63225—41no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82C4×Dic17—21no—
83C4×Dic17—21no—
84#11782—171nomaximal, Sylow
85C23×C17C2×C22⋊C411yescharacteristic
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—24no—
90C2×C4×C17—21no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17#9911yescharacteristic
95C2×C4×C17#9911yescharacteristic
96C2×C4×C17#10412yes—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—41no—
105C2×Dic17—41no—
106C2×Dic17—42no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17AGL(1,ℤ/8)12yes—
110Dic34—44no—
111Dic34—84no—
112#3624—44no—
113#3624—82no—
114#2546—171no—
115C4×#101—171no—
116#1467—171no—
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—44no—
126C4×C17—41no—
127C4×C17#35612yes—
128Dic17—22no—
129Dic17—41no—
130Dic17—41no—
131Dic17—41no—
132Dic17—82no—
133C2×C4⋊Q8—171no—
134C2×C4⋊Q8—341no—
135C2×C4×Q8—171no—
136#432—341no—
137C2×#101—341no—
138C4×M16—341no—
139#398—172no—
140#398—172no—
141#391—341no—
142#389—341no—
143#389—341no—
144C4×C4⋊C4#59511yescharacteristic
145#343—172no—
146#324—172no—
147#324—341no—
148C2×C17—21no—
149C2×C17—21no—
150C2×C17#150711yescharacteristic
151C2×C17#212311yescharacteristic
152C2×C17C2×#35611yescharacteristic
153C22×Q8—171no—
154C22×Q8—341no—
155C2×M16—342no—
156C4⋊Q8—681no—
157C4⋊Q8—681no—
158C4⋊Q8—684no—
159C4×Q8—681no—
160C4×Q8—681no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—171no—
163C2×C4⋊C4—171no—
164C2×C4⋊C4—171no—
165C2×C4⋊C4—172no—
166C2×C4⋊C4—342no—
167C2×C4⋊C4—342no—
168C2×C4⋊C4—341no—
169C2×C42—21no—
170C2×C42—171no—
171C2×C42—171no—
172C2×C42C2×#59511yescharacteristic
173C4⋊C8—681no—
174#101—344no—
175C22⋊C8—342no—
176#97—681no—
177#97—681no—
178C4×C8—681no—
179#95—342no—
180#95—342no—
181#95C2×#59512yes—
182C17#1178211yescharacteristic, complemented, Sylow
183C2×Q8—342no—
184C2×Q8—342no—
185C2×Q8—681no—
186C2×Q8—682no—
187C2×Q8—682no—
188C2×Q8—682no—
189C22×C4—22no—
190C22×C4—171no—
191C22×C4—171no—
192C22×C4—171no—
193C22×C4—171no—
194C22×C4—342no—
195C22×C4C22⋊#59511yescharacteristic
196C22×C4C22⋊#59511yescharacteristic
197C22×C4C22×#59511yescharacteristic
198M16—344no—
199M16—682no—
200C2×C8—682no—
201C2×C8—682no—
202C4⋊C4—24no—
203C4⋊C4—681no—
204C4⋊C4—681no—
205C4⋊C4—681no—
206C4⋊C4—682no—
207C4⋊C4—684no—
208C4⋊C4—684no—
209C4⋊C4—681no—
210C4⋊C4—681no—
211C42—21no—
212C42—21no—
213C42—42no—
214C42—341no—
215C42—341no—
216C42—341no—
217C42—341no—
218C23C2×C22⋊#59511yescharacteristic
219Q8—684no—
220Q8—1364no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—24no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—172no—
230C2×C4—341no—
231C2×C4—341no—
232C2×C4—341no—
233C2×C4—341no—
234C2×C4—341no—
235C2×C4—341no—
236C2×C4—341no—
237C2×C4—681no—
238C2×C4—681no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4—682no—
242C2×C4#1058753911yescharacteristic
243C2×C4#1058753911yescharacteristic
244C2×C4#1058755012yes—
245C8—684no—
246C8—1362no—
247C22—21no—
248C22—21no—
249C22C2×#1058753911yescharacteristic
250C22#1176380111yescharacteristic
251C22C2×#1058755011yescharacteristic
252C4—22no—
253C4—21no—
254C4—44no—
255C4—41no—
256C4—342no—
257C4—681no—
258C4—681no—
259C4—681no—
260C4—1362no—
261C4#1176372012yes—
262C2—21no—
263C2—21no—
264C2#1454418111yescharacteristic
265C2#1454504811yescharacteristic
266C2C2×#1176372011yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenterC4×C4⋊C4#595
hypocenterC17#11782
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

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
C4×#105875452
#145440462
#145437692
#145337722
#1178217