Finite Group Databasebeta

← #14529232

Subgroups — #14529232

Order 2176.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#11763320C211yesmaximal, characteristic
2C2×#10587476C212yesmaximal, complemented
3#11762773C211yesmaximal, characteristic, complemented
4#11762569C212yesmaximal, complemented
5C2×C17×#117C211yesmaximal, characteristic, complemented
6C23×C4×C17C2211yescharacteristic
7C2×#63252C2211yescharacteristic
8C17×#117—24no—
9C2×C4⋊C4×C17—21no—
10C2×C22⋊C4×C17—21no—
11C2×C42×C17C2212yes—
12#10587639—21no—
13#10587616C412yescomplemented
14#10587615—21no—
15C4×C22⋊D17—22no—
16#10587612C2211yescharacteristic
17#10587610C412yescomplemented
18C2×#63223C2212yes—
19C22⋊#3622—22no—
20#10587476—24no—
21C24×C17D411yescharacteristic
22C22×C4×C17—22no—
23C22×C4×C17—22no—
24C22×C4×C17—22no—
25C22×C4×C17C2×C412yes—
26C22×C4×C17D412yes—
27C22×C4×C17D411yescharacteristic
28C22×C4×C17C2311yescharacteristic
29C2×C22⋊D17—22no—
30C2×C22⋊D17—21no—
31#63252—22no—
32#63252—22no—
33C2×D68C2×C411yescharacteristic
34C2×C4×D17—21no—
35C2×Dic34C2×C411yescharacteristic
36C4⋊C4×C17—24no—
37C22⋊C4×C17—24no—
38C42×C17—22no—
39C42×C17D414yescomplemented
40C22⋊Dic17—22no—
41C22⋊Dic17—21no—
42#63227—22no—
43C4⋊Dic17C2×C412yes—
44#63225—22no—
45C4×Dic17—21no—
46#63223—22no—
47#63223—22no—
48C2×#3622—22no—
49C23×C17—21no—
50C23×C17—21no—
51C23×C17—42no—
52C23×C17C22⋊C412yes—
53C23×C17C2×D411yescharacteristic
54C22×D17—21no—
55C2×C4×C17—21no—
56C2×C4×C17—21no—
57C2×C4×C17—24no—
58C2×C4×C17—24no—
59C2×C4×C17—24no—
60C2×C4×C17—44no—
61C2×C4×C17C22⋊C412yes—
62C2×C4×C17C22×C411yescharacteristic
63C2×C4×C17C2×D411yescharacteristic
64C2×C4×C17C2×D412yes—
65C2×C4×C17#4112yes—
66C22⋊D17—44no—
67C22⋊D17—41no—
68C22⋊D17—41no—
69C2×Dic17—21no—
70C2×Dic17—22no—
71D68—22no—
72C4×D17—42no—
73Dic34—22no—
74#3622—42no—
75#1897—171nomaximal, Sylow
76C22×C17—22no—
77C22×C17—22no—
78C22×C17—22no—
79C22×C17—22no—
80C22×C17—42no—
81C22×C17—42no—
82C22×C17C2×C22⋊C411yescharacteristic
83C22×C17#12011yescharacteristic
84C22×C17#12311yescharacteristic
85C2×D17—41no—
86C2×D17—42no—
87C4×C17—22no—
88C4×C17—44no—
89C4×C17C4×D412yes—
90C4×C17#12112yes—
91Dic17—41no—
92Dic17—42no—
93#525—171no—
94C2×#117D1711yescharacteristic, complemented
95C2×#104—172no—
96#407—171no—
97#339—172no—
98C2×C17—21no—
99C2×C17—21no—
100C2×C17—42no—
101C2×C17#38611yescharacteristic
102C2×C17#42112yes—
103D17—81no—
104C2×#41—171no—
105C23×C4C2×D1711yescharacteristic
106C2×M16—172no—
107#123—341no—
108C22⋊Q8—172no—
109#121—172no—
110#120—341no—
111C4×D4—342no—
112#117—24no—
113#117—171no—
114C2×C4⋊C4—21no—
115C2×C22⋊C4—21no—
116C2×C42C2×D1712yes—
117#104—344no—
118C22⋊C8—342no—
119C17#189711yescharacteristic, complemented, Sylow
120C24C22⋊D1711yescharacteristic
121#41—342no—
122#41—342no—
123C2×Q8—171no—
124C2×D4—171no—
125C2×D4—341no—
126C2×D4—342no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—341no—
131C22×C4C4×D1712yes—
132C22×C4D6812yes—
133C22×C4C22⋊D1711yescharacteristic
134C22×C4C22×D1711yescharacteristic
135M16—342no—
136M16—342no—
137C2×C8—342no—
138C4⋊C4—24no—
139C4⋊C4—172no—
140C4⋊C4—342no—
141C22⋊C4—24no—
142C22⋊C4—341no—
143C22⋊C4—342no—
144C22⋊C4—342no—
145C42—22no—
146C42—341no—
147C42C22⋊D1714yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—341no—
152C23#6322712yes—
153C23C2×C22⋊D1711yescharacteristic
154Q8—342no—
155D4—342no—
156D4—684no—
157D4—681no—
158D4—681no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—342no—
166C2×C4—341no—
167C2×C4—682no—
168C2×C4#6322712yes—
169C2×C4C2×C4×D1711yescharacteristic
170C2×C4C2×D6811yescharacteristic
171C2×C4#6325212yes—
172C2×C4C2×C22⋊D1712yes—
173C8—682no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—681no—
181C22—682no—
182C22C2×#6322711yescharacteristic
183C22#1058761511yescharacteristic
184C22#1058763911yescharacteristic
185C4—22no—
186C4—44no—
187C4—681no—
188C4—682no—
189C4C4×C22⋊D1712yes—
190C4#1058761612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—1361no—
195C2#1176268811yescharacteristic
196C2#1176282712yes—
subgroupG/H
centerC2×C4C2×D68
commutatorC2×C4×C17C22×C4
FrattiniC22×C4C22×D17
FittingC2×C17×#117C2
socleC22×C17C2×C22⋊C4
prime radical#11763320C2
cosocleC22×C4×C17C23
hypercenterC2×#117D17
hypocenterC17#1897
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#10587476C2semidirect
3. #11762773C2semidirect
4. #11762569C2semidirect
5. C2×C17×#117C2semidirect
13. #10587616C4semidirect
17. #10587610C4semidirect
39. C42×C17D4semidirect
94. C2×#117D17semidirect
119. C17#1897semidirect
147. C42C22⋊D17semidirect

Maximal subgroups

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

subgroupindex
#117633202
C2×#105874762
#117627732
#117625692
C2×C17×#1172
#189717