Finite Group Databasebeta

← #17949259

Subgroups — #17949259

Order 4352.

304 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543881C211yesmaximal, characteristic, complemented
2#14543715C211yesmaximal, characteristic, complemented
3#14529872C211yesmaximal, characteristic
4C2×#10587545—21no—
5#11763654—21no—
6C22×#63229—21no—
7C2×#10587503—21no—
8#11762715C2211yescharacteristic
9#11762564C411yescharacteristic
10C2×C17×#127C411yescharacteristic
11C22×D4×C17—21no—
12C22×D4×C17—41no—
13C22×Dic34D411yescharacteristic
14C2×#63247—41no—
15C17×#127—42no—
16C2×C42×C17C2×C411yescharacteristic
17C2×#63229—42no—
18C2×#63229—42no—
19C2×#63229—41no—
20C2×#63229—41no—
21C2×C4⋊Dic17D411yescharacteristic
22C22×#3622—21no—
23C22⋊#3624—41no—
24#10587545—22no—
25#10587545—41no—
26#10587503—42no—
27#10587502—41no—
28C24×C17—41no—
29C2×D4×C17—22no—
30C2×D4×C17—41no—
31C2×D4×C17—41no—
32C2×D4×C17—41no—
33C2×D4×C17—42no—
34C2×D4×C17—42no—
35C2×D4×C17—41no—
36C2×D4×C17—41no—
37C2×D4×C17—82no—
38C2×D4×C17—82no—
39C22×C4×C17—21no—
40C22×C4×C17C22⋊C411yescharacteristic
41C22×Dic17—21no—
42C22×Dic17—21no—
43C2×Dic34—21no—
44C2×Dic34—41no—
45C2×Dic34—41no—
46C2×Dic34D811yescharacteristic
47C2×Dic34SD1611yescharacteristic
48#63247—42no—
49#63247—81no—
50C2×#3624—81no—
51C2×#3624—81no—
52C42×C17—41no—
53#63229—44no—
54#63229—44no—
55C4⋊Dic17—41no—
56C2×#3622—22no—
57C2×#3622—41no—
58C2×#3622—41no—
59#7404—171nomaximal, Sylow
60C23×C17—42no—
61C23×C17—82no—
62C23×C17—82no—
63C23×C17—81no—
64C23×C17—81no—
65C23×C17#9911yescharacteristic
66D4×C17—42no—
67D4×C17—42no—
68D4×C17—81no—
69D4×C17—81no—
70D4×C17—84no—
71D4×C17—84no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—22no—
75C2×C4×C17—41no—
76C2×C4×C17—41no—
77C2×C4×C17#10211yescharacteristic
78C2×C4×C17#10411yescharacteristic
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—41no—
82C2×Dic17—41no—
83C2×Dic17—41no—
84C2×Dic17—81no—
85Dic34—41no—
86Dic34—41no—
87Dic34—81no—
88#3624—82no—
89#3624—161no—
90#3622—42no—
91#2014—171no—
92#1394—171no—
93#1319—171no—
94C22×C17—21no—
95C22×C17—21no—
96C22×C17—84no—
97C22×C17—82no—
98C22×C17—162no—
99C22×C17—161no—
100C22×C17—161no—
101C22×C17#32711yescharacteristic
102C22×C17AΣL(1,𝔽16)11yescharacteristic
103C22×C17#35311yescharacteristic
104C4×C17—21no—
105C4×C17—21no—
106C4×C17—42no—
107Dic17—41no—
108Dic17—41no—
109Dic17—81no—
110C22×SD16—341no—
111C2×#127#59511yescharacteristic
112C2×#102—341no—
113C2×#101—341no—
114#391—171no—
115#336—171no—
116#324—341no—
117C2×C17—21no—
118C2×C17—21no—
119C2×C17—162no—
120C2×C17#134311yescharacteristic
121C2×C17#140611yescharacteristic
122C2×C17#141011yescharacteristic
123C22×Q8—171no—
124C22×D4—21no—
125C22×D4—41no—
126C2×SD16—682no—
127C2×SD16—682no—
128C2×SD16—681no—
129C2×SD16—681no—
130C2×M16—681no—
131C22×C8—341no—
132#127—42no—
133C2×C4⋊C4—171no—
134C2×C42C2×#59511yescharacteristic
135#102—682no—
136#101—342no—
137#101—681no—
138C22⋊C8—681no—
139#95—681no—
140C17#740411yescharacteristic, complemented, Sylow
141C24—41no—
142C2×Q8—171no—
143C2×Q8—171no—
144C2×Q8—341no—
145C2×Q8—681no—
146C2×Q8—681no—
147C2×D4—22no—
148C2×D4—41no—
149C2×D4—41no—
150C2×D4—41no—
151C2×D4—42no—
152C2×D4—42no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—82no—
156C2×D4—82no—
157C22×C4—21no—
158C22×C4—341no—
159C22×C4—341no—
160C22×C4C22⋊#59511yescharacteristic
161SD16—684no—
162SD16—684no—
163M16—682no—
164M16—1361no—
165C2×C8—342no—
166C2×C8—681no—
167C2×C8—681no—
168C2×C8—1361no—
169C2×C8—1361no—
170C4⋊C4—681no—
171C42—41no—
172C23—42no—
173C23—82no—
174C23—82no—
175C23—81no—
176C23—81no—
177C23#1058755111yescharacteristic
178Q8—681no—
179Q8—681no—
180Q8—1361no—
181D4—42no—
182D4—42no—
183D4—81no—
184D4—81no—
185D4—84no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—341no—
193C2×C4—341no—
194C2×C4—681no—
195C2×C4—681no—
196C2×C4—681no—
197C2×C4—1361no—
198C2×C4#1058754711yescharacteristic
199C2×C4#1058754811yescharacteristic
200C8—2721no—
201C8—682no—
202C8—1362no—
203C22—21no—
204C22—21no—
205C22—84no—
206C22—82no—
207C22—162no—
208C22—161no—
209C22—161no—
210C22#1176366011yescharacteristic
211C22#1176370911yescharacteristic
212C22#1176371311yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—681no—
217C4—681no—
218C4—1361no—
219C2—21no—
220C2—21no—
221C2—162no—
222C2#1454376211yescharacteristic
223C2#1454391111yescharacteristic
224C2#1454391911yescharacteristic
subgroupG/H
centerC22#11763713
commutatorC2×C42×C17C2×C4
FrattiniC2×C42C2×#595
Fitting, prime radicalC2×C17×#127C4
socleC22×C17#353
cosocle#11762715C22
hypercenterC2×#127#595
hypocenterC17#7404
LCSG ▷ C2×C42×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14543881C2semidirect
2. #14543715C2semidirect
140. C17#7404semidirect

Maximal subgroups

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

subgroupindex
#145438812
#145437152
#145298722
#740417