Finite Group Databasebeta

← #17959809

Subgroups — #17959809

Order 4352.

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

normal subgroups only

This group has 372 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#14543783C214yesmaximal
4#14534000C211yesmaximal, characteristic
5#11763826—21no—
6#11763812—21no—
7C2×#10587545—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×C4×Dic34C2211yescharacteristic
12#11762747C412yes—
13#11762747C2212yes—
14#11762716—21no—
15#11762716—21no—
16#11762714—21no—
17#11762674—21no—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Dic34D411yescharacteristic
22C2×#63247—22no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—41no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17C2×C412yes—
27C2×C42×C17C2×C411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17D411yescharacteristic
30C2×#63225C2×C411yescharacteristic
31C2×#63225C2311yescharacteristic
32C2×C4×Dic17—21no—
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C4×Dic34—41no—
36C4×Dic34—41no—
37C22⋊#3624—22no—
38#10587545—42no—
39#10587544—41no—
40#10587544—41no—
41C4⋊#3624—41no—
42C4×#3624—41no—
43#10587502—22no—
44#10587502—22no—
45#10587502—22no—
46#10587502—22no—
47#10587502C2×C412yes—
48C2×Q8×C17—44no—
49C2×Q8×C17—41no—
50C2×Q8×C17—41no—
51C22×C4×C17—22no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—22no—
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C2×Dic34—41no—
61C2×Dic34—41no—
62C2×Dic34SD1612yes—
63C2×Dic34Q1612yes—
64#63247—42no—
65#63247—42no—
66C2×#3624—42no—
67C2×#3624—42no—
68C4⋊C4×C17—42no—
69C4⋊C4×C17—42no—
70C42×C17—21no—
71C42×C17—21no—
72C4⋊Dic17—41no—
73C4⋊Dic17—42no—
74#63225—41no—
75#63225—41no—
76C4×Dic17—21no—
77C4×Dic17—21no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80C4×Dic17—42no—
81#11907—171nomaximal, Sylow
82C23×C17C2×C22⋊C411yescharacteristic
83Q8×C17—82no—
84Q8×C17—82no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—21no—
89C2×C4×C17—41no—
90C2×C4×C17—44no—
91C2×C4×C17—42no—
92C2×C4×C17#9911yescharacteristic
93C2×C4×C17#9911yescharacteristic
94C2×C4×C17#10312yes—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—42no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17#10312yes—
107C2×Dic17C2×SD1611yescharacteristic
108C2×Dic17C2×Q1611yescharacteristic
109Dic34—42no—
110Dic34—42no—
111#3624—82no—
112#3624—82no—
113#2568—171no—
114#1801—171no—
115#1461—171no—
116#1353—174no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17C2×#9911yescharacteristic
120C22×C17C2×#10311yescharacteristic
121C22×C17#42111yescharacteristic
122C4×C17—21no—
123C4×C17—22no—
124C4×C17—41no—
125C4×C17—82no—
126C4×C17#35512yes—
127Dic17—21no—
128Dic17—22no—
129Dic17—21no—
130Dic17—41no—
131Dic17—41no—
132Dic17—82no—
133C2×C4⋊Q8#59511yescharacteristic
134C2×C4×Q8—171no—
135#431—341no—
136#423—341no—
137C2×#101—341no—
138#400—172no—
139#400—172no—
140#391—341no—
141#391—341no—
142#391—341no—
143#382—341no—
144C4×C4⋊C4—171no—
145#343—172no—
146#324—172no—
147#324—341no—
148C2×C17—21no—
149C2×C17—21no—
150C2×C17#152011yescharacteristic
151C2×C17#212311yescharacteristic
152C2×C17C2×#35511yescharacteristic
153C22×Q8—21no—
154C22×Q8—171no—
155C2×M16—342no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158C4×Q8—681no—
159C4×Q8—681no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—171no—
162C2×C4⋊C4—171no—
163C2×C4⋊C4—171no—
164C2×C4⋊C4—341no—
165C2×C4⋊C4C2×#59512yes—
166C2×C42—171no—
167C2×C42—171no—
168C2×C42—341no—
169C2×C42C2×#59511yescharacteristic
170C4⋊C8—681no—
171C4⋊C8—681no—
172C4⋊C8—681no—
173#101—682no—
174C22⋊C8—342no—
175C4×C8—681no—
176#95—172no—
177#95—342no—
178#95—342no—
179#95—342no—
180#95—342no—
181C17#1190711yescharacteristic, complemented, Sylow
182C2×Q8—44no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—172no—
186C2×Q8—172no—
187C2×Q8—681no—
188C2×Q8—681no—
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—682no—
199M16—682no—
200C2×C8—682no—
201C2×C8—682no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—681no—
205C4⋊C4—681no—
206C4⋊C4—681no—
207C4⋊C4—682no—
208C42—21no—
209C42—21no—
210C42—341no—
211C42—341no—
212C42—341no—
213C42—341no—
214C42—682no—
215C23C2×C22⋊#59511yescharacteristic
216Q8—82no—
217Q8—82no—
218Q8—682no—
219Q8—682no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—171no—
228C2×C4—172no—
229C2×C4—171no—
230C2×C4—341no—
231C2×C4—341no—
232C2×C4—341no—
233C2×C4—341no—
234C2×C4—341no—
235C2×C4—341no—
236C2×C4—681no—
237C2×C4—681no—
238C2×C4—682no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4#1058754912yes—
242C2×C4#1058755111yescharacteristic
243C2×C4#1058755111yescharacteristic
244C8—1362no—
245C8—1362no—
246C22—21no—
247C22—21no—
248C22C2×#1058755111yescharacteristic
249C22C2×#1058754911yescharacteristic
250C22#1176380811yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—82no—
255C4—341no—
256C4—342no—
257C4—341no—
258C4—681no—
259C4—681no—
260C4—1362no—
261C4#1176371712yes—
262C2—21no—
263C2—21no—
264C2#1454422411yescharacteristic
265C2#1454504611yescharacteristic
266C2C2×#1176371711yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#11907
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
181. C17#11907semidirect

Maximal subgroups

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

subgroupindex
#145446502
#145440262
#145437832
#145340002
#1190717