Finite Group Databasebeta

← #17958278

Subgroups — #17958278

Order 4352.

386 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 90 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#14545011C212yesmaximal, complemented
2#14543723C212yesmaximal, complemented
3#14543707C212yesmaximal, complemented
4#14537474C211yesmaximal, characteristic
5C2×#10587538—22no—
6C22⋊#63216—22no—
7C22⋊#63216C2214yes—
8C2×#10587593C411yescharacteristic
9C23×#3622C2211yescharacteristic
10#11763320C411yescharacteristic
11#11762877—22no—
12#11762872—22no—
13#11762837C2211yescharacteristic
14#11762777C2211yescharacteristic
15#11762767C411yescharacteristic
16C17×#407C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C2×#63252C2×C411yescharacteristic
19C2×M16×C17C2×C411yescharacteristic
20C2×M16×C17C2×C411yescharacteristic
21#10587639—21no—
22#10587616C812yes—
23#10587615—21no—
24C4×C22⋊D17—22no—
25#10587612C2×C411yescharacteristic
26#10587610C812yes—
27C22×#3622—42no—
28C22×#3622C2×C411yescharacteristic
29C22×#3622D412yes—
30C22×#3622D412yes—
31C22×#3622C2311yescharacteristic
32#10587593—42no—
33C2×#63218—21no—
34C2×C8×D17—21no—
35#10587538—44no—
36C2×#63216—24no—
37C17×C22⋊C8—22no—
38#10587491—22no—
39#10587486—21no—
40#10587485—22no—
41C8×Dic17—21no—
42C24×C17M1611yescharacteristic
43C22×C4×C17—41no—
44C22×C4×C17—41no—
45C22×C4×C17C22⋊C412yes—
46C22×C4×C17C2×C812yes—
47C22×C4×C17M1611yescharacteristic
48C22×C4×C17C22×C411yescharacteristic
49C2×C22⋊D17—22no—
50C2×C22⋊D17—21no—
51#63252—41no—
52#63252—41no—
53C2×D68C2×C811yescharacteristic
54C2×C4×D17—21no—
55C2×Dic34C2×C811yescharacteristic
56M16×C17—41no—
57M16×C17—41no—
58C2×C8×C17—21no—
59C2×C8×C17—21no—
60C22⋊Dic17—22no—
61C22⋊Dic17—21no—
62#63227—22no—
63C4⋊Dic17C2×C812yes—
64#63225—22no—
65C4×Dic17—21no—
66C2×#3622—24no—
67C2×#3622—22no—
68C2×#3622—42no—
69C2×#3622—41no—
70C2×#3622C22⋊C411yescharacteristic
71C2×#3622C22⋊C411yescharacteristic
72C2×#3622C2×D412yes—
73#63218—42no—
74C8×D17—42no—
75#63216—44no—
76#11469—171nomaximal, Sylow
77C23×C17—41no—
78C23×C17—42no—
79C23×C17C22⋊C812yes—
80C23×C17C2×M1611yescharacteristic
81C22×D17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—42no—
87C2×C4×C17—41no—
88C2×C4×C17C22⋊C812yes—
89C2×C4×C17C2×C22⋊C411yescharacteristic
90C2×C4×C17C22×C811yescharacteristic
91C22⋊D17—42no—
92C22⋊D17—44no—
93C2×Dic17—21no—
94C2×Dic17—22no—
95D68—41no—
96C4×D17—41no—
97C4×D17—41no—
98Dic34—41no—
99C8×C17—41no—
100C8×C17—41no—
101#3622—22no—
102#3622—21no—
103#3622#9912yes—
104#2929—171no—
105#2112—172no—
106#1323—172no—
107#1315—172no—
108C22×C17—22no—
109C22×C17—22no—
110C22×C17—22no—
111C22×C17—21no—
112C22×C17—22no—
113C22×C17—44no—
114C22×C17C2×C22⋊C811yescharacteristic
115C2×D17—42no—
116C2×D17—41no—
117C4×C17—21no—
118C4×C17—22no—
119C4×C17C2×#9911yescharacteristic
120C4×C17#41311yescharacteristic
121Dic17—42no—
122Dic17—41no—
123C2×#131—171no—
124C23×C8—171no—
125#525—171no—
126C2×M32—342no—
127#435—342no—
128C8×D4—342no—
129#424—171no—
130#408—171no—
131#407#59511yescharacteristic
132#405—171no—
133C22⋊C16—174no—
134C22⋊C16—342no—
135C2×C17—42no—
136C2×C17—41no—
137C2×C17#145911yescharacteristic
138C2×C17#211712yes—
139D17—81no—
140C2×#41—171no—
141C23×C4C2×#59511yescharacteristic
142#131—682no—
143C2×M16—341no—
144C2×M16C2×#59511yescharacteristic
145C2×M16C2×#59511yescharacteristic
146C22×C8—172no—
147C22×C8—171no—
148C22×C8—172no—
149C22×C8—171no—
150C22×C8—341no—
151C22×C8—682no—
152#123—341no—
153C22⋊Q8—172no—
154#121—172no—
155#120—341no—
156C4×D4—342no—
157#117—171no—
158M32—684no—
159C2×C16—344no—
160C4⋊C8—342no—
161C22⋊C8—22no—
162C22⋊C8—342no—
163#97—341no—
164C4×C8—341no—
165C17#1146911yescharacteristic, complemented, Sylow
166C24#6324311yescharacteristic
167#41—681no—
168#41—681no—
169C2×Q8—171no—
170C2×D4—171no—
171C2×D4—341no—
172C2×D4—342no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—341no—
176C22×C4#6324212yes—
177C22×C4#6324311yescharacteristic
178C22×C4C22⋊#59512yes—
179C22×C4C22×#59511yescharacteristic
180M16—41no—
181M16—41no—
182M16—682no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—171no—
186C2×C8—171no—
187C2×C8—172no—
188C2×C8—344no—
189C2×C8—342no—
190C2×C8—682no—
191C2×C8—681no—
192C2×C8—682no—
193C4⋊C4—172no—
194C4⋊C4—342no—
195C22⋊C4—341no—
196C22⋊C4—342no—
197C22⋊C4—342no—
198C42—341no—
199C16—684no—
200C23—41no—
201C23—42no—
202C23—341no—
203C23#1058754312yes—
204C23C2×#6324311yescharacteristic
205Q8—681no—
206D4—681no—
207D4—682no—
208D4—684no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—342no—
216C2×C4—341no—
217C2×C4—681no—
218C2×C4—681no—
219C2×C4#1058754312yes—
220C2×C4C2×#6324211yescharacteristic
221C2×C4C2×C22⋊#59511yescharacteristic
222C8—41no—
223C8—41no—
224C8—172no—
225C8—342no—
226C8—341no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—22no—
232C22—44no—
233C22—682no—
234C22—681no—
235C22C2×#1058754311yescharacteristic
236C4—21no—
237C4—22no—
238C4—682no—
239C4—681no—
240C4D17⋊#9911yescharacteristic
241C4#1176379611yescharacteristic
242C2—42no—
243C2—41no—
244C2—1361no—
245C2#1454402211yescharacteristic
246C2#1454502812yes—
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#407C4
socleC22×C17C2×C22⋊C8
prime radical#11763320C4
cosocleC22×#3622C23
hypercenter#407#595
hypocenterC17#11469
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #14545011C2semidirect
2. #14543723C2semidirect
3. #14543707C2semidirect
165. C17#11469semidirect

Maximal subgroups

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

subgroupindex
#145450112
#145437232
#145437072
#145374742
#1146917