Finite Group Databasebeta

← #16943753

Subgroups — #16943753

Order 4352.

330 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 69 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#14537413C211yesmaximal, characteristic
2#14530593C212yesmaximal, complemented
3#14526734C212yesmaximal, complemented
4#14526720C211yesmaximal, characteristic
5C17×#1320C211yesmaximal, characteristic
6C22×C4×Dic17C411yescharacteristic
7#11762863—22no—
8#11762859—22no—
9#11762832C411yescharacteristic
10#11762832C2211yescharacteristic
11#11762773C411yescharacteristic
12M16×Dic17C411yescharacteristic
13M16×Dic17C2211yescharacteristic
14#11762629—22no—
15#11762591C2212yes—
16#11762586—22no—
17C17×#407C2211yescharacteristic
18C17×#349C2212yes—
19C23×C4×C17C2×C411yescharacteristic
20C23×Dic17—21no—
21C2×M16×C17C2×C411yescharacteristic
22C2×M16×C17C2311yescharacteristic
23C2×C4×Dic17—21no—
24C2×C4×Dic17—21no—
25C2×C4×Dic17—21no—
26C2×C4×Dic17—21no—
27C2×C4×Dic17—21no—
28C2×C4×Dic17C2×C411yescharacteristic
29C2×C4×Dic17C2×C411yescharacteristic
30C2×#63223C2×C411yescharacteristic
31C2×#63223C2×C411yescharacteristic
32C17×M32—22no—
33C17×C22⋊C8—22no—
34C22⋊#3622—22no—
35#10587486—21no—
36#10587486D412yes—
37#10587485—22no—
38#10587485—22no—
39C8×Dic17—21no—
40C8×Dic17D412yes—
41#10587483—22no—
42C24×C17M1611yescharacteristic
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17—41no—
46C22×C4×C17—41no—
47C22×C4×C17M1611yescharacteristic
48C22×C4×C17C22×C411yescharacteristic
49C22×Dic17—21no—
50C22×Dic17—21no—
51C22×Dic17—21no—
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17—21no—
55C22×Dic17—44no—
56M16×C17—41no—
57M16×C17—41no—
58C2×C8×C17—21no—
59C2×C8×C17C2×D412yes—
60C4×Dic17—21no—
61C4×Dic17—21no—
62C4×Dic17—21no—
63C4×Dic17—21no—
64C4×Dic17—21no—
65C4×Dic17—21no—
66C4×Dic17C22⋊C411yescharacteristic
67C4×Dic17C22⋊C411yescharacteristic
68C4×Dic17M1611yescharacteristic
69C4×Dic17M1611yescharacteristic
70#63223—41no—
71#63223—41no—
72C2×#3622—21no—
73C2×#3622C22⋊C412yes—
74C16×C17—42no—
75#63214—42no—
76#11521—171nomaximal, Sylow
77C23×C17—21no—
78C23×C17—42no—
79C23×C17—41no—
80C23×C17C2×M1611yescharacteristic
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—42no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17C2×C22⋊C411yescharacteristic
89C2×C4×C17C2×M1611yescharacteristic
90C2×Dic17—24no—
91C2×Dic17—21no—
92C2×Dic17—21no—
93C2×Dic17—21no—
94C2×Dic17—21no—
95C2×Dic17—42no—
96C2×Dic17—42no—
97C2×Dic17—42no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C8×C17—22no—
101C8×C17—41no—
102#3622—22no—
103#3622—41no—
104#2920—171no—
105#2165—172no—
106#1327—172no—
107#1320—171no—
108#1320D1711yescharacteristic
109C22×C17—22no—
110C22×C17—21no—
111C22×C17—41no—
112C22×C17—41no—
113C22×C17—42no—
114C22×C17—42no—
115C22×C17—41no—
116C22×C17#40711yescharacteristic
117C4×C17—21no—
118C4×C17—41no—
119C4×C17#41011yescharacteristic
120C4×C17#41311yescharacteristic
121Dic17—22no—
122Dic17—22no—
123Dic17—41no—
124Dic17—41no—
125C22×C42—171no—
126#432—342no—
127#431—342no—
128#423—171no—
129#423—171no—
130#407—171no—
131#407C2×D1711yescharacteristic
132C4×M16—171no—
133C4×M16—171no—
134#364—342no—
135#349—172no—
136#349C2×D1712yes—
137#347—342no—
138C2×C17—21no—
139C2×C17—42no—
140C2×C17—41no—
141C2×C17#146411yescharacteristic
142C23×C4—341no—
143C23×C4C4×D1711yescharacteristic
144C2×M16—171no—
145C2×M16—171no—
146C2×M16C4×D1711yescharacteristic
147C2×M16C22×D1711yescharacteristic
148C2×C42—171no—
149C2×C42—171no—
150C2×C42—341no—
151C2×C42—341no—
152C2×C42—341no—
153C2×C42—341no—
154C2×C42—341no—
155M32—22no—
156M32—342no—
157C4⋊C8—342no—
158C4⋊C8—342no—
159C22⋊C8—22no—
160C22⋊C8—342no—
161#97—172no—
162#97—341no—
163C4×C8—172no—
164C4×C8—341no—
165C17#1152111yescharacteristic, complemented, Sylow
166C24#6321811yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—341no—
172C22×C4—341no—
173C22×C4—341no—
174C22×C4—341no—
175C22×C4—341no—
176C22×C4—341no—
177C22×C4—684no—
178C22×C4#6321811yescharacteristic
179C22×C4C2×C4×D1711yescharacteristic
180M16—41no—
181M16—41no—
182M16—681no—
183M16—681no—
184C2×C8—21no—
185C2×C8—172no—
186C2×C8—341no—
187C2×C8D4×D1712yes—
188C42—171no—
189C42—171no—
190C42—171no—
191C42—171no—
192C42—341no—
193C42—341no—
194C42—341no—
195C42—341no—
196C42—341no—
197C42—341no—
198C16—42no—
199C16—682no—
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#6321811yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—344no—
212C2×C4—341no—
213C2×C4—341no—
214C2×C4—341no—
215C2×C4—341no—
216C2×C4—682no—
217C2×C4—682no—
218C2×C4—682no—
219C2×C4—682no—
220C2×C4—682no—
221C2×C4C22⋊C4×D1711yescharacteristic
222C2×C4M16×D1711yescharacteristic
223C8—22no—
224C8—41no—
225C8—342no—
226C8—681no—
227C22—22no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22#1176277111yescharacteristic
235C4—21no—
236C4—41no—
237C4—342no—
238C4—342no—
239C4—681no—
240C4—681no—
241C4#1176278111yescharacteristic
242C4#1176279011yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2#1452711511yescharacteristic
subgroupG/H
centerC4#11762781
commutatorC22×C4×C17C22×C4
FrattiniC2×M16C22×D17
FittingC17×#1320C2
socleC2×C17#1464
prime radicalC24×C17M16
cosocleC2×M16×C17C23
hypercenter#1320D17
hypocenterC17#11521
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #14530593C2semidirect
3. #14526734C2semidirect
165. C17#11521semidirect

Maximal subgroups

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

subgroupindex
#145374132
#145305932
#145267342
#145267202
C17×#13202
#1152117