Finite Group Databasebeta

← #14544155

Subgroups — #14544155

Order 2176.

238 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 60 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#11763828C211yesmaximal, characteristic, complemented
2#11763745C211yesmaximal, characteristic, complemented
3#11763662C212yesmaximal, complemented
4#11763660C212yesmaximal
5#11763341C211yesmaximal, characteristic
6C2×C4×#595—21no—
7C4×D4×C17C411yescharacteristic, complemented
8#10587624C2211yescharacteristic
9#10587622C411yescharacteristic, complemented
10C4×C22⋊D17—21no—
11#10587612—21no—
12#10587583C2211yescharacteristic
13#10587576C411yescharacteristic, complemented
14#10587569—21no—
15#10587565—21no—
16C42×D17C2211yescharacteristic
17C4×Dic34C411yescharacteristic, complemented
18(C2×#595)⋊C4—21no—
19(C2×#595)⋊C4C2212yes—
20#10587543C2212yes—
21C4⋊#3624—21no—
22C4×#3624—21no—
23C22×#595—22no—
24C2×D4×C17C2×C411yescharacteristic
25C22×C4×C17—21no—
26C2×C22⋊D17—21no—
27C2×C4×D17D411yescharacteristic
28C2×C4×D17D411yescharacteristic
29C2×C4×D17C2311yescharacteristic
30C2×Dic34C2×C411yescharacteristic
31C2×#3624—22no—
32C4×#595—24no—
33C4⋊C4×C17C2×C411yescharacteristic
34C22⋊C4×C17—21no—
35C42×C17C2×C411yescharacteristic
36C22⋊Dic17—21no—
37C22⋊Dic17—21no—
38C22⋊Dic17—21no—
39#63227—21no—
40C4⋊Dic17—21no—
41C4⋊Dic17—21no—
42C4⋊Dic17C2×C411yescharacteristic
43#63225—21no—
44#63225—21no—
45C4×Dic17—21no—
46C4×Dic17C2×C411yescharacteristic
47C4×Dic17D411yescharacteristic
48C4×Dic17D411yescharacteristic
49C23×C17—21no—
50C22×D17C2×D411yescharacteristic
51C2×#595—24no—
52C2×#595—42no—
53C2×#595—42no—
54D4×C17—41no—
55C2×C4×C17—21no—
56C2×C4×C17—42no—
57C2×C4×C17C22⋊C411yescharacteristic
58C2×C4×C17C22⋊C411yescharacteristic
59C2×C4×C17C22×C411yescharacteristic
60C22⋊D17—42no—
61C2×Dic17—21no—
62C2×Dic17—21no—
63C2×Dic17C22⋊C411yescharacteristic
64C2×Dic17C22⋊C411yescharacteristic
65C2×Dic17C2×D411yescharacteristic
66C4×D17—22no—
67C4×D17—22no—
68C4×D17—41no—
69Dic34—41no—
70#3624—42no—
71#1500—171nomaximal, Sylow
72C22×C17—41no—
73C22×C17—41no—
74C22×C17—41no—
75C22×C17C2×C22⋊C411yescharacteristic
76C2×D17—21no—
77C2×D17—21no—
78C2×D17#13512yes—
79#595—44no—
80C4×C17—21no—
81C4×C17—21no—
82C4×C17—41no—
83C4×C17#10412yes—
84Dic17—21no—
85Dic17—21no—
86Dic17—21no—
87Dic17—41no—
88Dic17—41no—
89#529—171no—
90#431—171no—
91#376—171no—
92#328—172no—
93#327—172no—
94C2×C17—81no—
95C2×C17#41011yescharacteristic
96C2×C17#41611yescharacteristic
97C2×C17C2×#10411yescharacteristic
98D17—22no—
99#126—341no—
100#125—171no—
101#124—171no—
102#123—341no—
103C22⋊Q8—171no—
104#121—171no—
105C4×Q8—171no—
106C4×D4—341no—
107C4×D4#59511yescharacteristic, complemented
108#117—341no—
109C2×C42—171no—
110C2×C42—341no—
111C4⋊C8—341no—
112C22⋊C8—172no—
113C4×C8—341no—
114#95—172no—
115#95—341no—
116C17#150011yescharacteristic, complemented, Sylow
117C2×Q8—171no—
118C2×D4—341no—
119C2×D4C2×#59511yescharacteristic
120C22×C4—21no—
121C22×C4—171no—
122C22×C4—171no—
123C22×C4—171no—
124C22×C4—342no—
125C2×C8—342no—
126C4⋊C4—171no—
127C4⋊C4—341no—
128C4⋊C4—341no—
129C4⋊C4—341no—
130C4⋊C4—341no—
131C4⋊C4C2×#59511yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—341no—
134C22⋊C4—341no—
135C22⋊C4—341no—
136C22⋊C4—341no—
137C42—171no—
138C42—171no—
139C42—171no—
140C42—344no—
141C42—341no—
142C42C2×#59511yescharacteristic
143C23—21no—
144C23—171no—
145Q8—681no—
146D4—41no—
147D4—682no—
148C2×C4—21no—
149C2×C4—42no—
150C2×C4—171no—
151C2×C4—171no—
152C2×C4—171no—
153C2×C4—342no—
154C2×C4—342no—
155C2×C4—344no—
156C2×C4—341no—
157C2×C4—341no—
158C2×C4—681no—
159C2×C4—682no—
160C2×C4—682no—
161C2×C4C22⋊#59511yescharacteristic
162C2×C4C22⋊#59511yescharacteristic
163C2×C4C22×#59511yescharacteristic
164C8—682no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—172no—
169C22—341no—
170C22—341no—
171C22C2×C22⋊#59511yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—341no—
176C4—341no—
177C4—341no—
178C4—684no—
179C4—681no—
180C4—681no—
181C4#1058754812yes—
182C2—81no—
183C2—342no—
184C2#1176378811yescharacteristic
185C2#1176379911yescharacteristic
186C2C2×#1058754811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC4×D4×C17C4
socleC22×C17C2×C22⋊C4
prime radical#10587624C22
cosocleC2×C4×D17C23
hypercenterC4×D4#595
hypocenterC17#1500
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11763828C2semidirect
2. #11763745C2semidirect
3. #11763662C2semidirect
7. C4×D4×C17C4semidirect
9. #10587622C4semidirect
13. #10587576C4semidirect
17. C4×Dic34C4semidirect
107. C4×D4#595semidirect
116. C17#1500semidirect

Maximal subgroups

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

subgroupindex
#117638282
#117637452
#117636622
#117636602
#117633412
#150017