Finite Group Databasebeta

← #14545077

Subgroups — #14545077

Order 2176.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#11763795C212yesmaximal, complemented
2#11763720C212yesmaximal, complemented
3#11763718C212yesmaximal, complemented
4#11763359C211yesmaximal, characteristic
5C2×#63252C411yescharacteristic
6C2×#63252C2211yescharacteristic
7D17⋊M16—22no—
8C2×C42×C17C411yescharacteristic
9#10587616—22no—
10#10587561C411yescharacteristic
11#10587561C2211yescharacteristic
12#10587560C411yescharacteristic
13C4×D68—22no—
14#10587555C2211yescharacteristic
15#10587553—22no—
16#10587545C2214yes—
17C22×C4×C17—21no—
18C22×C4×C17C2×C411yescharacteristic
19C2×C22⋊D17—21no—
20C2×C22⋊D17D412yes—
21#63252—41no—
22#63252—41no—
23#63252—41no—
24#63252—41no—
25C2×D68—22no—
26C2×D68C2×C411yescharacteristic
27C2×D68C2×C411yescharacteristic
28C2×C4×D17—21no—
29C2×C4×D17D412yes—
30C2×Dic34C2×C411yescharacteristic
31C2×Dic34C2311yescharacteristic
32#63247—24no—
33#63243—42no—
34#63242—42no—
35C42×C17—21no—
36C42×C17C2×C411yescharacteristic
37C42×C17C2×C411yescharacteristic
38#63227—22no—
39#63227—22no—
40C4⋊Dic17—22no—
41C23×C17C22⋊C411yescharacteristic
42C22×D17—21no—
43C22×D17C22⋊C412yes—
44C2×C4×C17—21no—
45C2×C4×C17—21no—
46C2×C4×C17—21no—
47C2×C4×C17—21no—
48C2×C4×C17—42no—
49C2×C4×C17C22⋊C411yescharacteristic
50C2×C4×C17C22×C411yescharacteristic
51C22⋊D17—42no—
52C22⋊D17—42no—
53C2×Dic17—21no—
54C2×Dic17C2×D412yes—
55D68—41no—
56D68—41no—
57D68—44no—
58C4×D17—22no—
59C4×D17—22no—
60C4×D17—41no—
61C4×D17—41no—
62Dic34—41no—
63Dic34—41no—
64#3624—44no—
65#2132—171nomaximal, Sylow
66C22×C17—21no—
67C22×C17—41no—
68C22×C17C2×C22⋊C411yescharacteristic
69C2×D17—22no—
70C2×D17—42no—
71C2×D17—42no—
72C2×D17—41no—
73C4×C17—22no—
74C4×C17—21no—
75C4×C17—41no—
76C4×C17#9911yescharacteristic
77C4×C17#9911yescharacteristic
78Dic17—22no—
79Dic17—41no—
80#532—171no—
81#413—172no—
82#356—172no—
83#355—172no—
84C2×C17—21no—
85C2×C17—41no—
86C2×C17C2×#9911yescharacteristic
87D17—42no—
88D17—81no—
89C2×#41—171no—
90C2×#41—171no—
91C2×M16—342no—
92C4⋊Q8—171no—
93#127—171no—
94#124—171no—
95#124—171no—
96#121—342no—
97C4×D4—342no—
98C2×C42#59511yescharacteristic
99#101—174no—
100#100—342no—
101C17#213211yescharacteristic, complemented, Sylow
102#41—681no—
103#41—681no—
104#41—681no—
105#41—681no—
106C2×Q8—171no—
107C2×Q8—171no—
108C2×D4—172no—
109C2×D4—171no—
110C2×D4—171no—
111C2×D4—342no—
112C2×D4—341no—
113C22×C4—21no—
114C22×C4—172no—
115C22×C4—341no—
116C22×C4C2×#59511yescharacteristic
117M16—344no—
118M16—682no—
119C2×C8—682no—
120C4⋊C4—342no—
121C22⋊C4—342no—
122C22⋊C4—342no—
123C42—21no—
124C42C2×#59511yescharacteristic
125C42C2×#59511yescharacteristic
126C23—172no—
127C23—341no—
128C23C22⋊#59511yescharacteristic
129Q8—681no—
130Q8—681no—
131D4—681no—
132D4—681no—
133D4—684no—
134D4—682no—
135D4—682no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—42no—
141C2×C4—172no—
142C2×C4—342no—
143C2×C4—342no—
144C2×C4—341no—
145C2×C4—681no—
146C2×C4—681no—
147C2×C4C22⋊#59511yescharacteristic
148C2×C4C22×#59511yescharacteristic
149C8—684no—
150C22—21no—
151C22—41no—
152C22—342no—
153C22—682no—
154C22—682no—
155C22—681no—
156C22C2×C22⋊#59511yescharacteristic
157C4—22no—
158C4—21no—
159C4—41no—
160C4—342no—
161C4—681no—
162C4#1058753911yescharacteristic
163C4#1058753911yescharacteristic
164C2—21no—
165C2—41no—
166C2—682no—
167C2—1361no—
168C2C2×#1058753911yescharacteristic
subgroupG/H
centerC4#10587539
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC2×C42×C17C4
socleC2×C17C2×#99
prime radical#11763359C2
cosocleC2×Dic34C23
hypercenterC2×C42#595
hypocenterC17#2132
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #11763795C2semidirect
2. #11763720C2semidirect
3. #11763718C2semidirect
101. C17#2132semidirect

Maximal subgroups

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

subgroupindex
#117637952
#117637202
#117637182
#117633592
#213217