Finite Group Databasebeta

← #14544156

Subgroups — #14544156

Order 2176.

238 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 58 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#11763827C211yesmaximal, characteristic, complemented
2#11763745C211yesmaximal, characteristic, complemented
3#11763663C212yesmaximal, complemented
4#11763660C212yesmaximal
5#11763338C211yesmaximal, characteristic
6C2×C4×#595—21no—
7C17×#124C411yescharacteristic, complemented
8#10587632C2211yescharacteristic
9Q8×Dic17C411yescharacteristic, complemented
10#10587624C2211yescharacteristic
11D4×Dic17C411yescharacteristic, complemented
12#10587569—21no—
13#10587567—21no—
14#10587565—21no—
15#10587563—21no—
16C42×D17C2211yescharacteristic
17#10587556C411yescharacteristic, complemented
18(C2×#595)⋊C4—21no—
19(C2×#595)⋊C4C2212yes—
20#10587544—21no—
21#10587543C2212yes—
22C4×#3624—21no—
23C22×#595—22no—
24C2×Q8×C17C2×C411yescharacteristic
25C2×D4×C17C2×C411yescharacteristic
26C2×C22⋊D17—21no—
27C22×Dic17—21no—
28C2×C4×D17D411yescharacteristic
29C2×C4×D17D411yescharacteristic
30C2×C4×D17C2311yescharacteristic
31C2×#3624—22no—
32C4×#595—24no—
33C22⋊C4×C17—21no—
34C22⋊C4×C17—21no—
35C42×C17C2×C411yescharacteristic
36C22⋊Dic17—21no—
37C22⋊Dic17—21no—
38#63227—21no—
39C4⋊Dic17—21no—
40C4⋊Dic17C2×C411yescharacteristic
41C4⋊Dic17C2×C411yescharacteristic
42#63225—21no—
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—
54Q8×C17—41no—
55D4×C17—41no—
56C2×C4×C17—21no—
57C2×C4×C17C22⋊C411yescharacteristic
58C2×C4×C17C22⋊C411yescharacteristic
59C2×C4×C17C22×C411yescharacteristic
60C22⋊D17—42no—
61C2×Dic17—21no—
62C2×Dic17—21no—
63C2×Dic17—42no—
64C2×Dic17C22⋊C411yescharacteristic
65C2×Dic17C22⋊C411yescharacteristic
66C2×Dic17C2×D411yescharacteristic
67C4×D17—22no—
68C4×D17—22no—
69C4×D17—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—21no—
83C4×C17—41no—
84Dic17—21no—
85Dic17—21no—
86Dic17—41no—
87Dic17—41no—
88Dic17#10412yes—
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#59511yescharacteristic, complemented
102#123—341no—
103C22⋊Q8—171no—
104#121—171no—
105C4×Q8—171no—
106C4×D4—171no—
107C4×D4—341no—
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×Q8C2×#59511yescharacteristic
118C2×D4—341no—
119C2×D4C2×#59511yescharacteristic
120C22×C4—171no—
121C22×C4—171no—
122C22×C4—171no—
123C22×C4—341no—
124C22×C4—342no—
125C2×C8—342no—
126C4⋊C4—171no—
127C4⋊C4—171no—
128C4⋊C4—341no—
129C4⋊C4—341no—
130C4⋊C4—341no—
131C4⋊C4—341no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—341no—
135C22⋊C4—341no—
136C22⋊C4—341no—
137C42—171no—
138C42—171no—
139C42—171no—
140C42—341no—
141C42—344no—
142C42C2×#59511yescharacteristic
143C23—21no—
144C23—171no—
145Q8—41no—
146D4—41no—
147D4—682no—
148C2×C4—21no—
149C2×C4—171no—
150C2×C4—171no—
151C2×C4—171no—
152C2×C4—342no—
153C2×C4—342no—
154C2×C4—344no—
155C2×C4—341no—
156C2×C4—341no—
157C2×C4—681no—
158C2×C4—682no—
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—21no—
175C4—41no—
176C4—172no—
177C4—341no—
178C4—341no—
179C4—684no—
180C4—681no—
181C4—681no—
182C2—81no—
183C2—342no—
184C2#1176378911yescharacteristic
185C2#1176379911yescharacteristic
186C2D17⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#124C4
socleC22×C17C2×C22⋊C4
prime radical#10587624C22
cosocleC2×C4×D17C23
hypercenter#124#595
hypocenterC17#1500
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #11763827C2semidirect
2. #11763745C2semidirect
3. #11763663C2semidirect
7. C17×#124C4semidirect
9. Q8×Dic17C4semidirect
11. D4×Dic17C4semidirect
17. #10587556C4semidirect
101. #124#595semidirect
116. C17#1500semidirect

Maximal subgroups

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

subgroupindex
#117638272
#117637452
#117636632
#117636602
#117633382
#150017