Finite Group Databasebeta

← #17959811

Subgroups — #17959811

Order 4352.

388 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544650C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14543784C214yesmaximal
4#14533992C211yesmaximal, characteristic
5#11763826—21no—
6#11763812—21no—
7C2×#10587545—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×#10587555C411yescharacteristic
12C2×C4×Dic34C2211yescharacteristic
13#11762730C412yes—
14#11762730C2212yes—
15#11762715—21no—
16#11762708—21no—
17#11762708—21no—
18#11762679—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Dic34C2×C412yes—
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—21no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17—22no—
30C2×C4⋊Dic17D411yescharacteristic
31C2×#63225C2×C411yescharacteristic
32C2×#63225C2311yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35#10587555—41no—
36#10587555—41no—
37C4×Dic34—41no—
38C4×Dic34—41no—
39C22⋊#3624—22no—
40#10587545—42no—
41#10587544—41no—
42#10587544—41no—
43C4⋊#3624—41no—
44C4×#3624—41no—
45C17×#95C2×C412yes—
46#10587502—22no—
47#10587502—22no—
48C22×C4×C17—22no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—22no—
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C2×Dic34—41no—
58C2×Dic34—41no—
59C2×Dic34—42no—
60C2×Dic34—82no—
61C2×Dic34SD1612yes—
62C2×Dic34Q1612yes—
63#63247—42no—
64#63247—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C4⋊C4×C17—24no—
68C42×C17—21no—
69C42×C17—21no—
70C42×C17—42no—
71C4⋊Dic17—41no—
72C4⋊Dic17—42no—
73C4⋊Dic17—41no—
74C4⋊Dic17—41no—
75C4⋊Dic17—82no—
76C4⋊Dic17—82no—
77#63225—41no—
78#63225—41no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82C4×Dic17—21no—
83#11908—171nomaximal, Sylow
84C23×C17C2×C22⋊C411yescharacteristic
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—24no—
89C2×C4×C17—21no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17—41no—
93C2×C4×C17#9911yescharacteristic
94C2×C4×C17#9911yescharacteristic
95C2×C4×C17#10312yes—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17—42no—
107C2×Dic17#10312yes—
108C2×Dic17C2×SD1611yescharacteristic
109C2×Dic17C2×Q1611yescharacteristic
110Dic34—42no—
111Dic34—42no—
112Dic34—84no—
113#3624—82no—
114#3624—82no—
115#2567—171no—
116#1801—171no—
117#1461—171no—
118#1354—174no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17C2×#9911yescharacteristic
122C22×C17C2×#10311yescharacteristic
123C22×C17#42111yescharacteristic
124C4×C17—21no—
125C4×C17—22no—
126C4×C17—44no—
127C4×C17—41no—
128C4×C17#35612yes—
129Dic17—21no—
130Dic17—22no—
131Dic17—21no—
132Dic17—41no—
133Dic17—41no—
134Dic17—82no—
135C2×C4⋊Q8—171no—
136C2×C4×Q8—171no—
137#431—341no—
138#423—341no—
139C2×#101—341no—
140#395—172no—
141#395—172no—
142#391—341no—
143#389—341no—
144#389—341no—
145#384—341no—
146C4×C4⋊C4#59511yescharacteristic
147#343—172no—
148#324—172no—
149#324—341no—
150C2×C17—21no—
151C2×C17—21no—
152C2×C17#152011yescharacteristic
153C2×C17#212211yescharacteristic
154C2×C17C2×#35611yescharacteristic
155C22×Q8—171no—
156C22×Q8—172no—
157C2×M16—342no—
158C4⋊Q8—681no—
159C4⋊Q8—681no—
160C4×Q8—681no—
161C4×Q8—681no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—171no—
164C2×C4⋊C4—171no—
165C2×C4⋊C4—171no—
166C2×C4⋊C4—341no—
167C2×C4⋊C4—341no—
168C2×C4⋊C4—342no—
169C2×C4⋊C4—342no—
170C2×C42—21no—
171C2×C42—171no—
172C2×C42—171no—
173C2×C42C2×#59511yescharacteristic
174C4⋊C8—681no—
175C4⋊C8—681no—
176C4⋊C8—681no—
177#101—682no—
178C22⋊C8—342no—
179C4×C8—681no—
180#95—342no—
181#95—342no—
182#95C2×#59512yes—
183C17#1190811yescharacteristic, complemented, Sylow
184C2×Q8—172no—
185C2×Q8—172no—
186C2×Q8—681no—
187C2×Q8—681no—
188C2×Q8—682no—
189C2×Q8—1362no—
190C22×C4—22no—
191C22×C4—171no—
192C22×C4—171no—
193C22×C4—171no—
194C22×C4—171no—
195C22×C4—342no—
196C22×C4C22⋊#59511yescharacteristic
197C22×C4C22⋊#59511yescharacteristic
198C22×C4C22×#59511yescharacteristic
199M16—682no—
200M16—682no—
201C2×C8—682no—
202C2×C8—682no—
203C4⋊C4—24no—
204C4⋊C4—681no—
205C4⋊C4—681no—
206C4⋊C4—681no—
207C4⋊C4—682no—
208C4⋊C4—681no—
209C4⋊C4—681no—
210C4⋊C4—1362no—
211C4⋊C4—1362no—
212C42—21no—
213C42—21no—
214C42—42no—
215C42—341no—
216C42—341no—
217C42—341no—
218C42—341no—
219C23C2×C22⋊#59511yescharacteristic
220Q8—682no—
221Q8—682no—
222Q8—1364no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—171no—
232C2×C4—172no—
233C2×C4—171no—
234C2×C4—341no—
235C2×C4—341no—
236C2×C4—341no—
237C2×C4—341no—
238C2×C4—341no—
239C2×C4—341no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4—682no—
243C2×C4—682no—
244C2×C4—682no—
245C2×C4#1058753911yescharacteristic
246C2×C4#1058753911yescharacteristic
247C2×C4#1058754912yes—
248C8—1362no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22C2×#1058753911yescharacteristic
253C22C2×#1058754911yescharacteristic
254C22#1176380711yescharacteristic
255C4—22no—
256C4—21no—
257C4—44no—
258C4—41no—
259C4—341no—
260C4—342no—
261C4—341no—
262C4—681no—
263C4—681no—
264C4—1362no—
265C4#1176372012yes—
266C2—21no—
267C2—21no—
268C2#1454422311yescharacteristic
269C2#1454504511yescharacteristic
270C2C2×#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#11908
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
183. C17#11908semidirect

Maximal subgroups

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

subgroupindex
#145446502
#145440262
#145437842
#145339922
#1190817