Finite Group Databasebeta

← #17949921

Subgroups — #17949921

Order 4352.

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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#14544501C212yesmaximal
2#14543605C212yesmaximal
3#14543604C212yesmaximal
4C4×#10587630C211yesmaximal, characteristic
5C2×#10587542—22no—
6#11763675—22no—
7#11763675C2214yes—
8C2×#10587630C411yescharacteristic
9C2×C4×Dic34C411yescharacteristic
10#11762716C2211yescharacteristic
11#11762714C2211yescharacteristic
12#11762704—22no—
13#11762678C411yescharacteristic
14C4×#63225—22no—
15C42×Dic17C2211yescharacteristic
16C2×C4×Q8×C17C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×Dic34C2×C411yescharacteristic
19C22×#3624—24no—
20C4×Q8×C17—42no—
21C2×C4⋊C4×C17—21no—
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C42×C17—21no—
24C2×C42×C17C2×C411yescharacteristic
25#10587630—22no—
26#10587630—22no—
27C2×C4⋊Dic17C2×C411yescharacteristic
28C2×#63225—21no—
29C2×#63225—22no—
30C2×#63225—22no—
31C2×C4×Dic17—21no—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34C2×C4×Dic17D412yes—
35C2×C4×Dic17C2311yescharacteristic
36C4×Dic34—42no—
37#10587542—28no—
38#10587502—22no—
39#10587502—22no—
40C2×Q8×C17—21no—
41C2×Q8×C17—41no—
42C2×Q8×C17—41no—
43C2×Q8×C17M1612yes—
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C22⋊C411yescharacteristic
48C22×C4×C17C22×C411yescharacteristic
49C22×Dic17—21no—
50C22×Dic17—21no—
51C22×Dic17C22⋊C412yes—
52C22×Dic17C2×D412yes—
53C2×Dic34—21no—
54C2×Dic34—41no—
55C2×Dic34—41no—
56C2×Dic34M1612yes—
57C2×#3624—28no—
58C2×#3624—44no—
59C2×#3624—44no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—42no—
62C42×C17—22no—
63C42×C17—42no—
64C4⋊Dic17—41no—
65#63225—28no—
66#63225—42no—
67#63225—44no—
68C4×Dic17—21no—
69C4×Dic17—21no—
70C4×Dic17—24no—
71C4×Dic17—24no—
72C4×Dic17—41no—
73C4×Dic17—42no—
74#7639—171nomaximal, Sylow
75C23×C17C2×C22⋊C411yescharacteristic
76Q8×C17—42no—
77Q8×C17—42no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—22no—
81C2×C4×C17—22no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—42no—
88C2×C4×C17#10012yes—
89C2×C4×C17C2×M1611yescharacteristic
90C2×C4×C17C2×M1611yescharacteristic
91C2×Dic17—22no—
92C2×Dic17—22no—
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—22no—
96C2×Dic17—41no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17—42no—
100C2×Dic17#10414yes—
101C2×Dic17#13714yes—
102Dic34—42no—
103Dic34—42no—
104#3624—48no—
105C4×C4⋊Q8—171no—
106#1745—172no—
107#1272—172no—
108#1272—172no—
109C22×C17#40711yescharacteristic
110C22×C17#41011yescharacteristic
111C22×C17C2×#10011yescharacteristic
112C22×C17#41912yes—
113C22×C17C2×#10412yes—
114C4×C17—22no—
115C4×C17—21no—
116C4×C17—21no—
117C4×C17—42no—
118C4×C17—41no—
119C4×C17—81no—
120Dic17—24no—
121Dic17—24no—
122Dic17—42no—
123Dic17—81no—
124C2×C4⋊Q8—171no—
125C2×C4×Q8—171no—
126C2×C4×Q8#59511yescharacteristic
127C2×#97—342no—
128#391—171no—
129#391—171no—
130#389—342no—
131#384—171no—
132C4×C4⋊C4—342no—
133C43—171no—
134#336—174no—
135#336—342no—
136C2×C17#146611yescharacteristic
137C2×C17#149112yes—
138C2×C17#150612yes—
139C2×C17#152511yescharacteristic
140C2×C17#155811yescharacteristic
141C22×Q8—171no—
142C22×Q8C2×#59511yescharacteristic
143C22×C8—344no—
144C4⋊Q8—342no—
145C4⋊Q8—342no—
146C4×Q8—42no—
147C4×Q8—682no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—171no—
150C2×C4⋊C4—342no—
151C2×C4⋊C4—342no—
152C2×C4⋊C4—341no—
153C2×C4⋊C4C2×#59511yescharacteristic
154C2×C42—21no—
155C2×C42—172no—
156C2×C42—172no—
157C2×C42—171no—
158C2×C42—171no—
159C2×C42—341no—
160C2×C42C2×#59511yescharacteristic
161#97—348no—
162#95—342no—
163#95—342no—
164C17#763911yescharacteristic, complemented, Sylow
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—172no—
169C2×Q8—341no—
170C2×Q8—681no—
171C2×Q8—681no—
172C2×Q8#6324312yes—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—172no—
176C22×C4—172no—
177C22×C4—341no—
178C22×C4—341no—
179C22×C4C22⋊#59511yescharacteristic
180C22×C4C22⋊#59511yescharacteristic
181C22×C4C22×#59511yescharacteristic
182C2×C8—348no—
183C2×C8—684no—
184C2×C8—684no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—348no—
188C4⋊C4—681no—
189C4⋊C4—682no—
190C4⋊C4—684no—
191C42—22no—
192C42—42no—
193C42—344no—
194C42—344no—
195C42—341no—
196C42—341no—
197C42—681no—
198C42—682no—
199C23C2×C22⋊#59511yescharacteristic
200Q8—42no—
201Q8—42no—
202Q8—682no—
203Q8—682no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—174no—
215C2×C4—174no—
216C2×C4—342no—
217C2×C4—342no—
218C2×C4—342no—
219C2×C4—342no—
220C2×C4—342no—
221C2×C4—681no—
222C2×C4—681no—
223C2×C4—681no—
224C2×C4—682no—
225C2×C4#1058755312yes—
226C2×C4C2×#6324311yescharacteristic
227C2×C4D17⋊M1611yescharacteristic
228C8—688no—
229C22#1176378011yescharacteristic
230C22#1176378811yescharacteristic
231C22C2×#1058755311yescharacteristic
232C22#1176380212yes—
233C22D17⋊#10412yes—
234C4—21no—
235C4—21no—
236C4—22no—
237C4—41no—
238C4—42no—
239C4—81no—
240C4—344no—
241C4—344no—
242C4—682no—
243C4—1361no—
244C2#1454404311yescharacteristic
245C2#1454412712yes—
246C2#1454417712yes—
247C2#1454423811yescharacteristic
248C2#1454431711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×Q8#595
hypocenterC17#7639
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
164. C17#7639semidirect

Maximal subgroups

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

subgroupindex
#145445012
#145436052
#145436042
C4×#105876302
#763917