Finite Group Databasebeta

← #14528261

Subgroups — #14528261

Order 2176.

198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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#11763185C211yesmaximal, characteristic, complemented
2#11763004C211yesmaximal, characteristic, complemented
3#11762887C211yesmaximal, characteristic, complemented
4#11762559C211yesmaximal, characteristic, complemented
5#11762553C211yesmaximal, characteristic, complemented
6#11762552C211yesmaximal, characteristic, complemented
7C17×#459C211yesmaximal, characteristic, complemented
8C2×D8×C17—21no—
9C17×#127C2211yescharacteristic
10C4×D4×C17C2211yescharacteristic
11C2×#63228—21no—
12C2×#63228—21no—
13C2×#63228—21no—
14C2×#63223—21no—
15#10587560C2211yescharacteristic
16C17×C4⋊C8C2211yescharacteristic
17C17×#102—21no—
18C22⋊#3622—21no—
19#10587480—21no—
20C4⋊#3622C2211yescharacteristic
21C4⋊#3622C2211yescharacteristic
22C4×#3622C2211yescharacteristic
23C2×D4×C17—21no—
24C2×D4×C17—21no—
25C2×D4×C17—21no—
26C2×D4×C17D411yescharacteristic
27C22×C4×C17—21no—
28C2×D68—21no—
29C2×D68—21no—
30C2×D68—21no—
31D8×C17—42no—
32C2×C8×C17—21no—
33C4⋊C4×C17D411yescharacteristic
34C22⋊C4×C17—21no—
35C42×C17C2311yescharacteristic
36#63228—42no—
37#63228—42no—
38#63228—42no—
39#63223—42no—
40C2×#3622—21no—
41C2×#3622—21no—
42C2×#3622D411yescharacteristic
43C2×#3622D411yescharacteristic
44C23×C17—21no—
45C23×C17—41no—
46C22×D17—41no—
47D4×C17—21no—
48D4×C17—21no—
49D4×C17—41no—
50D4×C17—41no—
51D4×C17—41no—
52D4×C17—41no—
53D4×C17—81no—
54C2×C4×C17—21no—
55C2×C4×C17—41no—
56C2×C4×C17—41no—
57C2×C4×C17C2×D411yescharacteristic
58C2×C4×C17C2×D411yescharacteristic
59C2×C4×C17#4111yescharacteristic
60D68—41no—
61D68—41no—
62D68—41no—
63D68—41no—
64D68—81no—
65C8×C17—41no—
66#3622—21no—
67#3622—41no—
68#3622—41no—
69#3622D812yescomplemented
70#1687—171nomaximal, Sylow
71C22×C17—41no—
72C22×C17—41no—
73C22×C17—41no—
74C22×C17—81no—
75C22×C17—81no—
76C22×C17—81no—
77C22×C17#12111yescharacteristic
78C2×D17—81no—
79C2×D17—81no—
80C2×D17—81no—
81C4×C17—21no—
82C4×C17—41no—
83C4×C17C2×D811yescharacteristic
84C4×C17AGL(1,ℤ/8)11yescharacteristic
85C4×C17AGL(1,ℤ/8)11yescharacteristic
86C4×C17AGL(1,ℤ/8)11yescharacteristic
87#493—171no—
88#459—171no—
89#459D1711yescharacteristic, complemented
90#436—171no—
91#334—171no—
92#331—171no—
93#331—171no—
94C2×C17—81no—
95C2×C17—161no—
96C2×C17#45911yescharacteristic
97C2×C17#46911yescharacteristic
98C2×C17#47211yescharacteristic
99D17—161no—
100C2×D8—21no—
101C2×D8—341no—
102C2×D8—341no—
103C2×D8—341no—
104C2×M16—341no—
105#127—171no—
106#127C2×D1711yescharacteristic
107C4×D4C2×D1711yescharacteristic
108C4⋊C8—171no—
109C4⋊C8—171no—
110C4⋊C8C2×D1711yescharacteristic
111#102—21no—
112#102—341no—
113C22⋊C8—341no—
114C4×C8—171no—
115C17#168711yescharacteristic, complemented, Sylow
116C2×D4—21no—
117C2×D4—21no—
118C2×D4—21no—
119C2×D4—341no—
120C2×D4—341no—
121C2×D4—341no—
122C2×D4C22⋊D1711yescharacteristic
123C22×C4—21no—
124D8—42no—
125D8—682no—
126D8—682no—
127D8—682no—
128M16—682no—
129C2×C8—21no—
130C2×C8—171no—
131C2×C8—171no—
132C2×C8—341no—
133C2×C8—341no—
134C4⋊C4C22⋊D1711yescharacteristic
135C22⋊C4—21no—
136C42C22×D1711yescharacteristic
137C23—21no—
138C23—41no—
139C23—681no—
140D4—21no—
141D4—21no—
142D4—41no—
143D4—41no—
144D4—41no—
145D4—41no—
146D4—81no—
147D4—681no—
148D4—681no—
149D4—681no—
150D4—681no—
151D4—1361no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4D4×D1711yescharacteristic
156C2×C4#6325411yescharacteristic
157C2×C4C2×C22⋊D1711yescharacteristic
158C8—41no—
159C8—172no—
160C8—341no—
161C8—681no—
162C8—681no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—81no—
167C22—81no—
168C22—81no—
169C22—1361no—
170C22—1361no—
171C22—1361no—
172C22#1058762511yescharacteristic
173C4—21no—
174C4—41no—
175C4D8×D1711yescharacteristic
176C4#1058759711yescharacteristic
177C4#1058761811yescharacteristic
178C4#1058763511yescharacteristic
179C2—81no—
180C2—161no—
181C2—2721no—
182C2#1176300211yescharacteristic
183C2#1176306011yescharacteristic
184C2#1176307711yescharacteristic
subgroupG/H
centerC22#10587625
commutator, cosocleC42×C17C23
FrattiniC42C22×D17
FittingC17×#459C2
socleC22×C17#121
hypercenter#459D17
hypocenterC17#1687
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #11763185C2semidirect
2. #11763004C2semidirect
3. #11762887C2semidirect
4. #11762559C2semidirect
5. #11762553C2semidirect
6. #11762552C2semidirect
7. C17×#459C2semidirect
69. #3622D8semidirect
89. #459D17semidirect
115. C17#1687semidirect

Maximal subgroups

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

subgroupindex
#117631852
#117630042
#117628872
#117625592
#117625532
#117625522
C17×#4592
#168717