Finite Group Databasebeta

← #17949196

Subgroups — #17949196

Order 4352.

228 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 40 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#14543712C211yesmaximal, characteristic
2#14543600C211yesmaximal, characteristic
3#14528994C211yesmaximal, characteristic
4#11763675—21no—
5#11763654—21no—
6#11762852—21no—
7C2×#10587504C411yescharacteristic
8#11762712C2211yescharacteristic
9#11762568—21no—
10C17×#518C411yescharacteristic
11C22×D4×C17C2×C411yescharacteristic
12C22×#3624—41no—
13C4×D4×C17—41no—
14C4×D4×C17—41no—
15C17×#117—21no—
16C2×C22⋊C4×C17—41no—
17C2×C22⋊Dic17—41no—
18C2×C4⋊Dic17D411yescharacteristic
19C2×C4×Dic17D411yescharacteristic
20C2×#63223—21no—
21C22⋊#3624—41no—
22#10587504—21no—
23#10587504C812yescomplemented
24#10587479—41no—
25#10587478—41no—
26C24×C17—21no—
27C2×D4×C17—21no—
28C2×D4×C17—41no—
29C2×D4×C17—41no—
30C2×D4×C17C2×C811yescharacteristic
31C2×D4×C17M1611yescharacteristic
32C22×C4×C17—41no—
33C22×C4×C17—41no—
34C22×C4×C17C22⋊C411yescharacteristic
35C22×Dic17—21no—
36C22×Dic17—21no—
37C2×#3624—42no—
38C2×#3624—81no—
39C2×#3624—81no—
40C2×#3624—81no—
41C4⋊C4×C17—21no—
42C4⋊C4×C17—21no—
43C22⋊C4×C17—42no—
44C22⋊C4×C17—41no—
45C42×C17—41no—
46C22⋊Dic17—81no—
47C22⋊Dic17—81no—
48C4⋊Dic17—41no—
49C4×Dic17—41no—
50#63223—22no—
51#63223—41no—
52C2×#3622—41no—
53#7375—171nomaximal, Sylow
54C23×C17—21no—
55C23×C17—21no—
56C23×C17—41no—
57C23×C17—41no—
58C23×C17—81no—
59C23×C17—81no—
60C23×C17#9911yescharacteristic
61D4×C17—41no—
62D4×C17—41no—
63D4×C17—42no—
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—41no—
67C2×C4×C17—41no—
68C2×C4×C17—161no—
69C2×C4×C17—161no—
70C2×C4×C17C22⋊C811yescharacteristic
71C2×C4×C17#10111yescharacteristic
72C2×Dic17—21no—
73C2×Dic17—21no—
74C2×Dic17—41no—
75C2×Dic17—41no—
76C2×Dic17—41no—
77C2×Dic17—81no—
78#3624—82no—
79#3624—161no—
80#3622—42no—
81#1856—171no—
82#1318—171no—
83#1270—171no—
84C22×C17—21no—
85C22×C17—21no—
86C22×C17—41no—
87C22×C17—41no—
88C22×C17—81no—
89C22×C17—81no—
90C22×C17—81no—
91C22×C17—81no—
92C22×C17—161no—
93C22×C17#32411yescharacteristic
94C22×C17AΣL(1,𝔽16)11yescharacteristic
95C22×C17#35211yescharacteristic
96C4×C17—21no—
97C4×C17—21no—
98C4×C17—81no—
99C4×C17—81no—
100Dic17—41no—
101Dic17—41no—
102Dic17—81no—
103#518#59511yescharacteristic
104#428—341no—
105C2×#100—171no—
106#390—171no—
107#339—341no—
108#336—341no—
109#324—341no—
110C2×C17—21no—
111C2×C17—21no—
112C2×C17—81no—
113C2×C17—81no—
114C2×C17#132611yescharacteristic
115C2×C17#140211yescharacteristic
116C2×C17#140311yescharacteristic
117C22×D4C2×#59511yescharacteristic
118C2×M16—341no—
119C22×C8—681no—
120C4×D4—41no—
121C4×D4—41no—
122#117—21no—
123C2×C4⋊C4—171no—
124C2×C22⋊C4—41no—
125C2×C22⋊C4—681no—
126C2×C42—171no—
127#107—681no—
128#106—681no—
129#100—172no—
130#100—341no—
131C22⋊C8—681no—
132C17#737511yescharacteristic, complemented, Sylow
133C24—21no—
134C2×D4—21no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4#6324211yescharacteristic
138C2×D4#6324311yescharacteristic
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—341no—
142C22×C4—341no—
143C22×C4C22⋊#59511yescharacteristic
144M16—342no—
145M16—681no—
146C2×C8—681no—
147C2×C8—682no—
148C2×C8—1361no—
149C2×C8—1361no—
150C2×C8—1361no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—681no—
154C22⋊C4—42no—
155C22⋊C4—41no—
156C22⋊C4—1361no—
157C22⋊C4—1361no—
158C42—41no—
159C42—681no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—81no—
165C23—81no—
166C23#1058755111yescharacteristic
167D4—41no—
168D4—41no—
169D4—42no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—161no—
175C2×C4—161no—
176C2×C4—341no—
177C2×C4—341no—
178C2×C4—681no—
179C2×C4—681no—
180C2×C4—681no—
181C2×C4—1361no—
182C2×C4#1058754311yescharacteristic
183C2×C4#1058754511yescharacteristic
184C8—2721no—
185C8—682no—
186C8—1362no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—81no—
195C22—161no—
196C22#1176365511yescharacteristic
197C22#1176370911yescharacteristic
198C22#1176371111yescharacteristic
199C4—21no—
200C4—21no—
201C4—81no—
202C4—81no—
203C4—681no—
204C4—681no—
205C4—1361no—
206C2—21no—
207C2—21no—
208C2—81no—
209C2—81no—
210C2#1454372911yescharacteristic
211C2#1454390311yescharacteristic
212C2#1454390511yescharacteristic
subgroupG/H
centerC22#11763709
commutatorC2×D4×C17C2×C8
FrattiniC22×D4C2×#595
FittingC17×#518C4
socleC22×C17AΣL(1,𝔽16)
prime radicalC22×D4×C17C2×C4
cosocle#11762712C22
hypercenter#518#595
hypocenterC17#7375
LCSG ▷ C2×D4×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4 ◁ #518

Complements

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

NH ≅ G/Ntype
23. #10587504C8semidirect
132. C17#7375semidirect

Maximal subgroups

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

subgroupindex
#145437122
#145436002
#145289942
#737517