Finite Group Databasebeta

← #17948692

Subgroups — #17948692

Order 4352.

286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 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#14545012C211yesmaximal, characteristic
2#14544520C211yesmaximal, characteristic
3#14530394C211yesmaximal, characteristic
4C2×#10587530—21no—
5#11763777C411yescharacteristic
6C2×#10587532—21no—
7C4×C22⋊#595C411yescharacteristic
8#11763704—21no—
9C22⋊#63216C412yescomplemented
10#11763674—21no—
11C22×C8×D17C2211yescharacteristic
12C2×#10587483C411yescharacteristic, complemented
13#11762588—21no—
14#11762588—21no—
15C2×C17×M32C411yescharacteristic, complemented
16C22×C4×D17C2×C411yescharacteristic
17C2×C22⋊#595C812yes—
18C2×C4×#595—21no—
19C2×#63242—21no—
20C22×C8×C17C2×C411yescharacteristic
21C22×#3622C2×C411yescharacteristic
22C2×C8×D17—41no—
23C2×C8×D17—41no—
24C2×C8×D17D411yescharacteristic
25C2×C8×D17D411yescharacteristic
26C2×C8×D17D411yescharacteristic
27C2×C8×D17Q811yescharacteristic
28C22⋊#3624C812yes—
29(C2×#595)⋊C4—21no—
30#10587543—21no—
31C2×#63216—22no—
32#10587532—41no—
33#10587532—41no—
34#10587530—41no—
35#10587530—41no—
36C17×M32—41no—
37C2×C16×C17—21no—
38#10587483—41no—
39C2×#63214—21no—
40C23×D17C2×C811yescharacteristic
41C22×#595—22no—
42C22×C4×C17C4211yescharacteristic
43C22×Dic17C2×C811yescharacteristic
44C2×C4×D17—41no—
45C2×C4×D17—41no—
46C2×C4×D17C22⋊C411yescharacteristic
47C2×C4×D17C4⋊C411yescharacteristic
48C2×C4×D17M1611yescharacteristic
49C2×C4×D17M1611yescharacteristic
50C22⋊#595—42no—
51C2×#3624—22no—
52C4×#595—41no—
53C4×#595—41no—
54#63242—41no—
55#63242—41no—
56C2×C8×C17—21no—
57C2×C8×C17—21no—
58C2×C8×C17C22⋊C411yescharacteristic
59C2×C8×C17C4⋊C411yescharacteristic
60C2×#3622—41no—
61C2×#3622C22⋊C411yescharacteristic
62C2×#3622C4⋊C411yescharacteristic
63C8×D17—21no—
64C8×D17—21no—
65C8×D17—21no—
66C8×D17—21no—
67C8×D17—41no—
68C8×D17—41no—
69#63216—42no—
70C16×C17—41no—
71#63214—41no—
72#7201—171nomaximal, Sylow
73C23×C17C4×C811yescharacteristic
74C22×D17—22no—
75C22×D17—41no—
76C22×D17—41no—
77C22×D17C22⋊C811yescharacteristic
78C22×D17C4⋊C811yescharacteristic
79C2×#595—42no—
80C2×#595—42no—
81C2×#595—42no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17#9511yescharacteristic
85C2×C4×C17#9711yescharacteristic
86C2×Dic17—41no—
87C2×Dic17C22⋊C811yescharacteristic
88C2×Dic17C4⋊C811yescharacteristic
89C4×D17—21no—
90C4×D17—21no—
91C4×D17—21no—
92C4×D17—21no—
93C4×D17—41no—
94C4×D17—41no—
95#3624—42no—
96C8×C17—21no—
97C8×C17#9911yescharacteristic
98C8×C17#9911yescharacteristic
99#3622—21no—
100#3622—21no—
101#2112—171no—
102#2112—171no—
103#1752—171no—
104C22×C17—21no—
105C22×C17—21no—
106C22×C17—21no—
107C22×C17#33611yescharacteristic
108C2×D17—21no—
109C2×D17—21no—
110C2×D17—21no—
111C2×D17—21no—
112C2×D17—21no—
113C2×D17—44no—
114C2×D17#34912yes—
115#595—82no—
116C4×C17—21no—
117C4×C17#34211yescharacteristic
118C4×C17#34411yescharacteristic
119Dic17—21no—
120Dic17—21no—
121C23×C8—171no—
122C2×M32—171no—
123C2×M32—341no—
124C2×M32#59511yescharacteristic, complemented
125C2×C22⋊C8—171no—
126C2×#97—341no—
127C4×C22⋊C4—171no—
128C22⋊C16—172no—
129C22⋊C16—341no—
130C22⋊C16—341no—
131C22⋊C16—341no—
132#336—341no—
133C2×C17—41no—
134C2×C17#128211yescharacteristic
135C2×C17#137711yescharacteristic
136C2×C17#137811yescharacteristic
137D17—22no—
138D17—41no—
139C23×C4—171no—
140C22×C8—171no—
141C22×C8—171no—
142C22×C8—171no—
143C22×C8—171no—
144C22×C8—171no—
145C22×C8—341no—
146C22×C8—681no—
147C22×C8—681no—
148C22×C8C2×#59511yescharacteristic
149C2×C22⋊C4—172no—
150C2×C42—341no—
151M32—41no—
152M32—681no—
153M32—681no—
154M32—681no—
155C2×C16—21no—
156C2×C16—342no—
157C2×C16—341no—
158C22⋊C8—172no—
159C22⋊C8—341no—
160#97—681no—
161#97—681no—
162#95—341no—
163C17#720111yescharacteristic, complemented, Sylow
164C24—171no—
165C22×C4—171no—
166C22×C4—171no—
167C22×C4—171no—
168C22×C4—171no—
169C22×C4—171no—
170C22×C4—342no—
171C22×C4—681no—
172C22×C4—681no—
173C22×C4C4×#59511yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—171no—
177C2×C8—171no—
178C2×C8—341no—
179C2×C8—341no—
180C2×C8—341no—
181C2×C8—341no—
182C2×C8—342no—
183C2×C8—681no—
184C2×C8—681no—
185C2×C8—681no—
186C2×C8—681no—
187C2×C8—681no—
188C2×C8C4⋊#59511yescharacteristic
189C2×C8C22⋊#59511yescharacteristic
190C22⋊C4—682no—
191C42—681no—
192C42—681no—
193C16—41no—
194C16—682no—
195C16—681no—
196C23—171no—
197C23—171no—
198C23—342no—
199C23—681no—
200C23—681no—
201C23C8×#59511yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—171no—
205C2×C4—171no—
206C2×C4—341no—
207C2×C4—341no—
208C2×C4—341no—
209C2×C4—341no—
210C2×C4—681no—
211C2×C4—681no—
212C2×C4—681no—
213C2×C4—682no—
214C2×C4—682no—
215C2×C4—682no—
216C2×C4#1058753211yescharacteristic
217C2×C4(C2×#595)⋊C411yescharacteristic
218C8—21no—
219C8—341no—
220C8—341no—
221C8—682no—
222C8#1058753911yescharacteristic
223C8#1058755111yescharacteristic
224C22—21no—
225C22—21no—
226C22—21no—
227C22—172no—
228C22—341no—
229C22—341no—
230C22—341no—
231C22—341no—
232C22—341no—
233C22—684no—
234C22#1176367411yescharacteristic
235C4—21no—
236C4—341no—
237C4—341no—
238C4—1362no—
239C4#1176368711yescharacteristic
240C4#1176369111yescharacteristic
241C2—41no—
242C2—342no—
243C2—681no—
244C2#1454362611yescharacteristic
245C2#1454383011yescharacteristic
246C2#1454383611yescharacteristic
subgroupG/H
centerC2×C4(C2×#595)⋊C4
commutatorC23×C17C4×C8
FrattiniC22×C8C2×#595
FittingC2×C17×M32C4
socleC22×C17#336
prime radicalC23×D17C2×C8
cosocleC22×C8×D17C22
hypercenterC2×M32#595
hypocenterC17#7201
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
9. C22⋊#63216C4semidirect
12. C2×#10587483C4semidirect
15. C2×C17×M32C4semidirect
124. C2×M32#595semidirect
163. C17#7201semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145445202
#145303942
#720117