Finite Group Databasebeta

← #14527933

Subgroups — #14527933

Order 2176.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#11763463C211yesmaximal, characteristic
2#11763159C211yesmaximal, characteristic, complemented
3#11763096C211yesmaximal, characteristic, complemented
4#11762556C211yesmaximal, characteristic, complemented
5D4⋊#3622C211yesmaximal, characteristic, complemented
6#11762536C211yesmaximal, characteristic, complemented
7C17×#476C211yesmaximal, characteristic, complemented
8C2×#63254—21no—
9C17×C4⋊Q8C2211yescharacteristic
10C4×D4×C17C2211yescharacteristic
11#10587616—21no—
12C2×C4⋊Dic17—21no—
13#10587583—21no—
14#10587572—22no—
15C4×D68C2211yescharacteristic
16#10587555C2211yescharacteristic
17C17×#106—21no—
18C17×C4⋊C8C2211yescharacteristic
19C17×#102—21no—
20#10587506—22no—
21#10587480—21no—
22#10587479—21no—
23C4⋊#3622C2211yescharacteristic
24C4×#3622C2211yescharacteristic
25C2×Q8×C17—21no—
26C2×D4×C17D411yescharacteristic
27C22×C4×C17—21no—
28C2×C22⋊D17—22no—
29C22×Dic17—22no—
30#63254—42no—
31#63254—42no—
32C2×D68D411yescharacteristic
33C2×C4×D17—21no—
34C2×Dic34—21no—
35C2×C8×C17—21no—
36C4⋊C4×C17—21no—
37C4⋊C4×C17—21no—
38C4⋊C4×C17D411yescharacteristic
39C22⋊C4×C17—21no—
40C42×C17C2311yescharacteristic
41#63227—22no—
42#63227—21no—
43C4⋊Dic17—22no—
44C4⋊Dic17—21no—
45C4⋊Dic17D411yescharacteristic
46C4⋊Dic17D412yes—
47C2×#3622—21no—
48C2×#3622—21no—
49C23×C17—21no—
50C22×D17—21no—
51Q8×C17—42no—
52D4×C17—21no—
53D4×C17SD1612yes—
54C2×C4×C17—21no—
55C2×C4×C17—41no—
56C2×C4×C17—41no—
57C2×C4×C17—41no—
58C2×C4×C17C2×D411yescharacteristic
59C2×C4×C17C2×D411yescharacteristic
60C2×C4×C17C2×D411yescharacteristic
61C22⋊D17—44no—
62C2×Dic17—22no—
63C2×Dic17—21no—
64C2×Dic17—44no—
65D68—21no—
66D68—21no—
67C4×D17—41no—
68C4×D17—41no—
69Dic34—41no—
70Dic34—41no—
71C8×C17—41no—
72#3622—41no—
73#3622—41no—
74#1635—171nomaximal, Sylow
75C22×C17—22no—
76C22×C17—41no—
77C22×C17—41no—
78C22×C17#12011yescharacteristic
79C2×D17—41no—
80C2×D17—41no—
81C2×D17—41no—
82C4×C17—21no—
83C4×C17—41no—
84C4×C17—81no—
85C4×C17C2×SD1611yescharacteristic
86C4×C17#13511yescharacteristic
87C4×C17AGL(1,ℤ/8)11yescharacteristic
88C4×C17#13711yescharacteristic
89Dic17—42no—
90Dic17—41no—
91#547—171no—
92#487—171no—
93#476—171no—
94#476D1711yescharacteristic, complemented
95#332—171no—
96D4⋊C8—171no—
97D4⋊C8—171no—
98C2×C17—42no—
99C2×C17#45011yescharacteristic
100C2×C17#45211yescharacteristic
101C2×C17#45411yescharacteristic
102D17—81no—
103C2×#41—341no—
104C4⋊Q8—171no—
105C4⋊Q8C2×D1711yescharacteristic
106#123—342no—
107C22⋊Q8—341no—
108#121—341no—
109C4×D4—171no—
110C4×D4C2×D1711yescharacteristic
111C2×C4⋊C4—341no—
112#106—21no—
113#106—341no—
114C4⋊C8—171no—
115C4⋊C8C2×D1711yescharacteristic
116#103—342no—
117#102—21no—
118#102—341no—
119C4×C8—171no—
120C17#163511yescharacteristic, complemented, Sylow
121#41—682no—
122#41—682no—
123C2×Q8—21no—
124C2×Q8—341no—
125C2×D4—171no—
126C2×D4—342no—
127C2×D4C22⋊D1711yescharacteristic
128C22×C4—21no—
129C22×C4—342no—
130C22×C4—341no—
131C2×C8—21no—
132C2×C8—341no—
133C2×C8—341no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—172no—
137C4⋊C4—171no—
138C4⋊C4—342no—
139C4⋊C4—341no—
140C4⋊C4C22⋊D1711yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—342no—
143C22⋊C4—341no—
144C42C22×D1711yescharacteristic
145C23—21no—
146C23—341no—
147Q8—42no—
148Q8—681no—
149Q8—681no—
150D4—21no—
151D4—341no—
152D4—341no—
153D4—684no—
154D4#6323012yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—341no—
160C2×C4—342no—
161C2×C4—684no—
162C2×C4—681no—
163C2×C4—681no—
164C2×C4D4×D1711yescharacteristic
165C2×C4D4×D1711yescharacteristic
166C2×C4C2×C22⋊D1711yescharacteristic
167C8—41no—
168C8—681no—
169C8—681no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—681no—
174C22—681no—
175C22—681no—
176C22#1058762311yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—681no—
181C4—682no—
182C4#1058760111yescharacteristic
183C4#1058760211yescharacteristic
184C4C2×#6323011yescharacteristic
185C4#1058763511yescharacteristic
186C2—42no—
187C2—1361no—
188C2#1176295911yescharacteristic
189C2#1176296811yescharacteristic
190C2#1176298011yescharacteristic
subgroupG/H
centerC22#10587623
commutator, cosocleC42×C17C23
FrattiniC42C22×D17
FittingC17×#476C2
socleC22×C17#120
prime radical#11763463C2
hypercenter#476D17
hypocenterC17#1635
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #11763159C2semidirect
3. #11763096C2semidirect
4. #11762556C2semidirect
5. D4⋊#3622C2semidirect
6. #11762536C2semidirect
7. C17×#476C2semidirect
94. #476D17semidirect
120. C17#1635semidirect

Maximal subgroups

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

subgroupindex
#117634632
#117631592
#117630962
#117625562
D4⋊#36222
#117625362
C17×#4762
#163517