Finite Group Databasebeta

← #17958523

Subgroups — #17958523

Order 4352.

334 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 70 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#14545158C212yesmaximal, complemented
2#14543719C212yesmaximal, complemented
3#14543716C212yesmaximal, complemented
4#14537487C211yesmaximal, characteristic
5#11763731—22no—
6#11763705C2214yes—
7#11763702—22no—
8C2×#10587587C411yescharacteristic
9#11763320C411yescharacteristic
10#11762885—22no—
11#11762878—22no—
12#11762835C411yescharacteristic
13#11762775C2211yescharacteristic
14#11762773C2211yescharacteristic
15#11762764C2211yescharacteristic
16C22×M16×C17C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C2×#63252C2×C411yescharacteristic
19C2×M16×C17—21no—
20C2×M16×C17—21no—
21C2×M16×C17—42no—
22C22×C8×C17C2×C411yescharacteristic
23C22×C8×C17C2×C411yescharacteristic
24#10587639—21no—
25#10587616—21no—
26#10587615—21no—
27C4×C22⋊D17—22no—
28#10587612C2×C411yescharacteristic
29#10587610—21no—
30C2×#63223C2×C411yescharacteristic
31C2×#63223C2311yescharacteristic
32#10587587—42no—
33C2×#63218—21no—
34C2×C8×D17—21no—
35#10587538—24no—
36C22⋊#3622—22no—
37#10587491—22no—
38#10587486D412yes—
39#10587485—22no—
40C8×Dic17D412yes—
41C24×C17M1611yescharacteristic
42C22×C4×C17—21no—
43C22×C4×C17—21no—
44C22×C4×C17—41no—
45C22×C4×C17—41no—
46C22×C4×C17M1611yescharacteristic
47C22×C4×C17C22×C411yescharacteristic
48C2×C22⋊D17—21no—
49C2×C22⋊D17—22no—
50#63252—41no—
51#63252—41no—
52C2×D68M1611yescharacteristic
53C2×C4×D17—21no—
54C2×Dic34M1611yescharacteristic
55M16×C17—42no—
56M16×C17—42no—
57C2×C8×C17—22no—
58C2×C8×C17—21no—
59C2×C8×C17—41no—
60C2×C8×C17C22⋊C411yescharacteristic
61C2×C8×C17C22⋊C411yescharacteristic
62C22⋊Dic17—22no—
63C22⋊Dic17—21no—
64#63227—22no—
65C4⋊Dic17—21no—
66#63225—22no—
67C4×Dic17C22⋊C412yes—
68#63223—41no—
69#63223—41no—
70C2×#3622—21no—
71C2×#3622C2×D412yes—
72#63218—42no—
73C8×D17—42no—
74#63216—44no—
75#11538—171nomaximal, Sylow
76C23×C17—21no—
77C23×C17—41no—
78C23×C17—81no—
79C23×C17C2×M1611yescharacteristic
80C22×D17—21no—
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
90C22⋊D17—42no—
91C22⋊D17—82no—
92C2×Dic17—21no—
93C2×Dic17—22no—
94D68—41no—
95C4×D17—41no—
96C4×D17—41no—
97Dic34—41no—
98C8×C17—21no—
99C8×C17—41no—
100C8×C17#10012yes—
101#3622—22no—
102#3622—41no—
103#2930—171no—
104#2166—172no—
105#1321—172no—
106#1320—172no—
107C22×C17—21no—
108C22×C17—41no—
109C22×C17—41no—
110C22×C17—41no—
111C22×C17—41no—
112C22×C17—82no—
113C22×C17#40711yescharacteristic
114C2×D17—42no—
115C2×D17—41no—
116C4×C17—21no—
117C4×C17—41no—
118C4×C17#41011yescharacteristic
119C4×C17C2×#10011yescharacteristic
120Dic17—42no—
121Dic17—41no—
122C2×#131—171no—
123C22×M16#59511yescharacteristic
124#525—171no—
125#436—342no—
126#435—342no—
127#424—171no—
128#408—171no—
129#407—171no—
130#405—171no—
131#364—342no—
132#349—174no—
133#347—342no—
134C2×C17—21no—
135C2×C17—41no—
136C2×C17—81no—
137C2×C17#146611yescharacteristic
138D17—81no—
139C2×#41—171no—
140C23×C4C2×#59511yescharacteristic
141#131—682no—
142C2×M16—21no—
143C2×M16—21no—
144C2×M16—42no—
145C2×M16—171no—
146C2×M16—171no—
147C2×M16—341no—
148C22×C8—341no—
149C22×C8C2×#59511yescharacteristic
150C22×C8C2×#59511yescharacteristic
151#123—341no—
152C22⋊Q8—341no—
153#121—341no—
154#120—341no—
155C4×D4—342no—
156#117—171no—
157M32—344no—
158C4⋊C8—342no—
159C22⋊C8—342no—
160C22⋊C8—342no—
161#97—172no—
162C4×C8—172no—
163C17#1153811yescharacteristic, complemented, Sylow
164C24#6324311yescharacteristic
165#41—681no—
166#41—681no—
167C2×Q8—171no—
168C2×D4—171no—
169C2×D4—341no—
170C2×D4—342no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—341no—
176C22×C4#6324311yescharacteristic
177C22×C4C22×#59511yescharacteristic
178M16—42no—
179M16—42no—
180M16—681no—
181M16—682no—
182M16—681no—
183C2×C8—22no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—172no—
187C2×C8—341no—
188C2×C8—682no—
189C2×C8C22⋊#59511yescharacteristic
190C2×C8C22⋊#59511yescharacteristic
191C4⋊C4—342no—
192C4⋊C4—341no—
193C22⋊C4—342no—
194C22⋊C4—342no—
195C22⋊C4—341no—
196C42—172no—
197C16—684no—
198C23—21no—
199C23—41no—
200C23—81no—
201C23—341no—
202C23C2×#6324311yescharacteristic
203Q8—681no—
204D4—681no—
205D4—682no—
206D4—1362no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—342no—
215C2×C4—341no—
216C2×C4—681no—
217C2×C4—681no—
218C2×C4D17⋊M1611yescharacteristic
219C2×C4C2×C22⋊#59511yescharacteristic
220C8—21no—
221C8—41no—
222C8—342no—
223C8—681no—
224C8#1058755312yes—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—82no—
231C22—682no—
232C22—681no—
233C22#1176378011yescharacteristic
234C4—21no—
235C4—41no—
236C4—682no—
237C4—681no—
238C4#1176378811yescharacteristic
239C4C2×#1058755311yescharacteristic
240C2—21no—
241C2—41no—
242C2—81no—
243C2—1361no—
244C2#1454404311yescharacteristic
subgroupG/H
centerC4#11763788
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC2×C17#1466
prime radical#11763320C4
cosocleC2×#63223C23
hypercenterC22×M16#595
hypocenterC17#11538
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #14545158C2semidirect
2. #14543719C2semidirect
3. #14543716C2semidirect
163. C17#11538semidirect

Maximal subgroups

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

subgroupindex
#145451582
#145437192
#145437162
#145374872
#1153817