Finite Group Databasebeta

← #17949801

Subgroups — #17949801

Order 4352.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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#14544712C212yesmaximal
2#14543605C212yesmaximal
3#14543604C212yesmaximal
4C4×#10587630C211yesmaximal, characteristic
5#11763675—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#10587630C814yescomplemented
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#10587502—22no—
38#10587502—22no—
39C2×Q8×C17—21no—
40C2×Q8×C17—41no—
41C2×Q8×C17—41no—
42C2×Q8×C17C2×C812yes—
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C22×C411yescharacteristic
48C22×Dic17—21no—
49C22×Dic17—21no—
50C22×Dic17C22⋊C412yes—
51C22×Dic17C2×D412yes—
52C2×Dic34—21no—
53C2×Dic34—41no—
54C2×Dic34—41no—
55C2×Dic34C2×C812yes—
56C2×#3624—44no—
57C2×#3624—44no—
58C2×#3624—44no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—42no—
61C42×C17—22no—
62C42×C17—42no—
63C4⋊Dic17—41no—
64#63225—28no—
65#63225—44no—
66#63225—42no—
67C4×Dic17—24no—
68C4×Dic17—42no—
69C4×Dic17—41no—
70C4×Dic17—42no—
71C4×Dic17C2×C812yes—
72C4×Dic17M1612yes—
73#7605—171nomaximal, Sylow
74C23×C17C2×C22⋊C411yescharacteristic
75Q8×C17—42no—
76Q8×C17—42no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—22no—
80C2×C4×C17—22no—
81C2×C4×C17—21no—
82C2×C4×C17—22no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—42no—
87C2×C4×C17#10012yes—
88C2×C4×C17C22×C811yescharacteristic
89C2×C4×C17C2×M1611yescharacteristic
90C2×Dic17—22no—
91C2×Dic17—22no—
92C2×Dic17—22no—
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—41no—
96C2×Dic17—41no—
97C2×Dic17—41no—
98C2×Dic17—42no—
99C2×Dic17C22⋊C814yes—
100C2×Dic17#13714yes—
101Dic34—42no—
102Dic34—42no—
103#3624—84no—
104C4×C4⋊Q8—171no—
105#1839—172no—
106#1272—172no—
107#1272—172no—
108C22×C17C2×C22⋊C811yescharacteristic
109C22×C17#41011yescharacteristic
110C22×C17C2×#10011yescharacteristic
111C22×C17#41912yes—
112C22×C17#42112yes—
113C4×C17—22no—
114C4×C17—21no—
115C4×C17—21no—
116C4×C17—41no—
117C4×C17—42no—
118C4×C17—81no—
119Dic17—24no—
120Dic17—24no—
121Dic17—42no—
122Dic17—81no—
123C2×C4⋊Q8—171no—
124C2×C4×Q8—171no—
125C2×C4×Q8#59511yescharacteristic
126#391—171no—
127#391—171no—
128#389—342no—
129#384—171no—
130C4×C4⋊C4—342no—
131C43—171no—
132#336—174no—
133#336—342no—
134#336—342no—
135C2×C17#146011yescharacteristic
136C2×C17#147912yes—
137C2×C17#151512yes—
138C2×C17#153611yescharacteristic
139C2×C17#155811yescharacteristic
140C22×Q8—171no—
141C22×Q8C2×#59511yescharacteristic
142C22×C8—344no—
143C4⋊Q8—174no—
144C4⋊Q8—342no—
145C4×Q8—42no—
146C4×Q8—682no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—171no—
149C2×C4⋊C4—342no—
150C2×C4⋊C4—342no—
151C2×C4⋊C4—341no—
152C2×C4⋊C4C2×#59511yescharacteristic
153C2×C42—21no—
154C2×C42—171no—
155C2×C42—172no—
156C2×C42—172no—
157C2×C42—171no—
158C2×C42—341no—
159C2×C42C2×#59511yescharacteristic
160#95—342no—
161#95—342no—
162C17#760511yescharacteristic, complemented, Sylow
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—172no—
167C2×Q8—341no—
168C2×Q8—681no—
169C2×Q8—681no—
170C2×Q8#6324212yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—172no—
174C22×C4—172no—
175C22×C4—341no—
176C22×C4—341no—
177C22×C4C22⋊#59511yescharacteristic
178C22×C4C22⋊#59511yescharacteristic
179C22×C4C22×#59511yescharacteristic
180C2×C8—684no—
181C2×C8—684no—
182C2×C8—684no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—348no—
186C4⋊C4—681no—
187C4⋊C4—682no—
188C4⋊C4—684no—
189C42—22no—
190C42—42no—
191C42—172no—
192C42—172no—
193C42—344no—
194C42—681no—
195C42—682no—
196C42—682no—
197C23C2×C22⋊#59511yescharacteristic
198Q8—42no—
199Q8—42no—
200Q8—682no—
201Q8—682no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—174no—
213C2×C4—174no—
214C2×C4—342no—
215C2×C4—342no—
216C2×C4—342no—
217C2×C4—342no—
218C2×C4—342no—
219C2×C4—681no—
220C2×C4—681no—
221C2×C4—681no—
222C2×C4—682no—
223C2×C4#1058755312yes—
224C2×C4C2×#6324211yescharacteristic
225C2×C4D17⋊M1611yescharacteristic
226C8—1364no—
227C22#1176377711yescharacteristic
228C22#1176378811yescharacteristic
229C22C2×#1058755311yescharacteristic
230C22#1176380212yes—
231C22#1176380612yes—
232C4—21no—
233C4—21no—
234C4—22no—
235C4—41no—
236C4—42no—
237C4—81no—
238C4—344no—
239C4—344no—
240C4—682no—
241C4—1361no—
242C2#1454402311yescharacteristic
243C2#1454408712yes—
244C2#1454420612yes—
245C2#1454427211yescharacteristic
246C2#1454431711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×Q8#595
hypocenterC17#7605
LCSG ▷ C2×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
26. #10587630C8semidirect
162. C17#7605semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145436052
#145436042
C4×#105876302
#760517