Finite Group Databasebeta

← #14530765

Subgroups — #14530765

Order 2176.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#11763622C211yesmaximal, characteristic
2#11763252C211yesmaximal, characteristic, complemented
3C2×#10587500C211yesmaximal, characteristic, complemented
4#11763085C211yesmaximal, characteristic, complemented
5#11762615C211yesmaximal, characteristic, complemented
6#11762594C211yesmaximal, characteristic, complemented
7C17×#362C211yesmaximal, characteristic, complemented
8#10587694—21no—
9C2×Q16×C17C2211yescharacteristic
10#10587628—21no—
11#10587605—21no—
12#10587604—22no—
13Q16×D17—21no—
14#10587595—21no—
15C2×Dic68C2211yescharacteristic
16#10587590C2211yescharacteristic
17#10587587C2211yescharacteristic
18C17×M32C2211yescharacteristic
19C17×#108C2211yescharacteristic
20#10587500—22no—
21#10587495—21no—
22C2×#63214C2211yescharacteristic
23Dic136—21no—
24#10587471—21no—
25C2×Q8×C17—21no—
26#63256—22no—
27#63256—41no—
28Q8×D17—22no—
29Q8×D17—41no—
30#63252—21no—
31#63252—42no—
32#63252D411yescharacteristic
33C2×Dic34—21no—
34Q16×C17—21no—
35Q16×C17D412yes—
36M16×C17—21no—
37C2×C8×C17C2311yescharacteristic
38#63231—22no—
39#63230—22no—
40#63223D411yescharacteristic
41Dic68—21no—
42Dic68—21no—
43Dic68—41no—
44Dic68D411yescharacteristic
45D136D411yescharacteristic
46#63219—21no—
47#63219—41no—
48#63218—21no—
49C8×D17—21no—
50C16×C17—21no—
51#63214—21no—
52Q8×C17—22no—
53Q8×C17—41no—
54C2×C4×C17—41no—
55C2×C4×C17C2×D411yescharacteristic
56C22⋊D17—21no—
57C22⋊D17—41no—
58C2×Dic17—41no—
59D68—21no—
60D68—42no—
61D68D811yescharacteristic
62C4×D17—21no—
63C4×D17—42no—
64C4×D17—42no—
65C4×D17—41no—
66Dic34—21no—
67Dic34—42no—
68Dic34—41no—
69Dic34—41no—
70Dic34D811yescharacteristic
71C8×C17—41no—
72C8×C17C2×D411yescharacteristic
73C8×C17C2×D411yescharacteristic
74#3622—21no—
75#2195—171nomaximal, Sylow
76C22×C17AGL(1,ℤ/8)11yescharacteristic
77C2×D17—21no—
78C2×D17—41no—
79C4×C17—42no—
80C4×C17#12011yescharacteristic
81C4×C17C2×D811yescharacteristic
82Dic17—21no—
83Dic17—41no—
84Dic17—81no—
85#578—171no—
86#510—171no—
87C2×Q32—171no—
88#473—171no—
89#362D1711yescharacteristic, complemented
90#359—171no—
91#350—171no—
92C2×C17—21no—
93C2×C17#44711yescharacteristic
94D17—41no—
95D17—81no—
962−1+4—341no—
97#137—341no—
98#137—341no—
99#137—342no—
100#135—171no—
101#135—341no—
102C2×Q16—171no—
103C2×Q16—341no—
104C2×Q16C2×D1711yescharacteristic
105#131—171no—
106Q32—341no—
107Q32—342no—
108SD32—341no—
109M32C2×D1711yescharacteristic
110C2×C16—171no—
111#108C2×D1711yescharacteristic
112#101—341no—
113C17#219511yescharacteristic, complemented, Sylow
114#41—171no—
115#41—342no—
116#41—341no—
117#41—682no—
118#41—681no—
119C2×Q8—21no—
120C2×Q8—342no—
121C2×Q8—341no—
122C2×Q8—681no—
123Q16—21no—
124Q16—171no—
125Q16—342no—
126Q16—341no—
127Q16—341no—
128Q16—681no—
129Q16D6812yes—
130SD16—342no—
131SD16—341no—
132SD16—681no—
133D8—171no—
134M16—21no—
135M16—171no—
136M16—341no—
137C2×C8—341no—
138C2×C8C22×D1711yescharacteristic
139C16—21no—
140C16—341no—
141Q8—22no—
142Q8—41no—
143Q8—171no—
144Q8—341no—
145Q8—682no—
146Q8—681no—
147Q8—681no—
148D4—171no—
149D4—341no—
150D4—341no—
151D4—682no—
152D4—681no—
153C2×C4—41no—
154C2×C4—341no—
155C2×C4—682no—
156C2×C4—682no—
157C2×C4—681no—
158C2×C4—681no—
159C2×C4D4×D1711yescharacteristic
160C8—41no—
161C8—341no—
162C8C2×D6811yescharacteristic
163C8D4×D1711yescharacteristic
164C22—341no—
165C22—681no—
166C22#1058760011yescharacteristic
167C4—42no—
168C4—341no—
169C4—681no—
170C4—1361no—
171C4#1058756811yescharacteristic
172C4D8×D1711yescharacteristic
173C2—21no—
174C2—681no—
175C2—1361no—
176C2#1176294411yescharacteristic
subgroupG/H
centerC2#11762944
commutator, cosocleC2×C8×C17C23
FrattiniC2×C8C22×D17
FittingC17×#362C2
socleC2×C17#447
prime radical#11763622C2
hypercenter#362D17
hypocenterC17#2195
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
2. #11763252C2semidirect
3. C2×#10587500C2semidirect
4. #11763085C2semidirect
5. #11762615C2semidirect
6. #11762594C2semidirect
7. C17×#362C2semidirect
89. #362D17semidirect
113. C17#2195semidirect

Maximal subgroups

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

subgroupindex
#117636222
#117632522
C2×#105875002
#117630852
#117626152
#117625942
C17×#3622
#219517