Finite Group Databasebeta

← #13125608

Subgroups — #13125608

Order 1664.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×#88178C211yesmaximal, characteristic
3#11718889C212yesmaximal, complemented
4C2×C22⋊#1055C211yesmaximal, characteristic
5#11718712C214yesmaximal, complemented
6#11718711C212yesmaximal, complemented
7#11718705C212yesmaximal, complemented
8#11718631C212yesmaximal, complemented
9C22×Q8×C13C2211yescharacteristic
10C23×C4×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C13×C22⋊Q8—21no—
13C13×C22⋊Q8—21no—
14C13×C22⋊Q8C2212yes—
15C13×C22⋊Q8C2212yes—
16C2×C13×C4⋊C4—21no—
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4—21no—
19C2×C22⋊Dic13—21no—
20C2×#6107C2214yescomplemented
21C2×C4⋊Dic13C2211yescharacteristic
22#88178—21no—
23#88178—21no—
24#88178C2212yes—
25#88178C2212yes—
26C2×#6101—21no—
27C22×#1055C2212yes—
28#88075C2214yescomplemented
29C22⋊#1055C2212yes—
30C22⋊#1055C2212yes—
31#88050C2214yescomplemented
32#88047C2214yescomplemented
33C24×C13D411yescharacteristic
34C2×Q8×C13—21no—
35C2×Q8×C13—42no—
36C2×Q8×C13C2312yes—
37C22×C4×C13—21no—
38C22×C4×C13—21no—
39C22×C4×C13—42no—
40C22×C4×C13D411yescharacteristic
41C22×C4×C13D411yescharacteristic
42C22×C4×C13D411yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C22×Dic13—21no—
47C22×Dic13—21no—
48C2×Dic26—21no—
49C2×Dic26—42no—
50C2×Dic26C2312yes—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C22⋊C4—22no—
56C13×C22⋊C4—22no—
57C22⋊Dic13—22no—
58C22⋊Dic13—22no—
59#6107—44no—
60C4⋊Dic13—21no—
61C4⋊Dic13C2312yes—
62#6101—22no—
63#6101—22no—
64C2×#1055—42no—
65C2×#1055C2314yes—
66#3189—131nomaximal, Sylow
67C23×C13—41no—
68C23×C13—41no—
69C23×C13Q1614yescomplemented
70C23×C13C2×D411yescharacteristic
71C23×C13C2×D411yescharacteristic
72C23×C13C2×D411yescharacteristic
73Q8×C13—24no—
74Q8×C13—42no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—41no—
81C2×C4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93Dic26—24no—
94Dic26—42no—
95#1055—24no—
96C2×C22⋊Q8—131no—
97C2×C22⋊Q8D1311yescharacteristic
98#484—132no—
99#484—132no—
100#467—134no—
101#451—132no—
102#451—132no—
103C2×C22⋊C8—131no—
104C22×C13—21no—
105C22×C13—21no—
106C22×C13—21no—
107C22×C13—21no—
108C22×C13—21no—
109C22×C13—21no—
110C22×C13—44no—
111C22×C13C2×Q1612yes—
112C22×C13C2×Q1612yes—
113C22×C13C2×Q1612yes—
114C22×C13C22×D411yescharacteristic
115C4×C13—21no—
116C4×C13—21no—
117C4×C13—21no—
118C4×C13—42no—
119C4×C13—42no—
120C4×C13H(5,𝔽2)12yes—
121Dic13—42no—
122Dic13—42no—
123C22×Q8—131no—
124C22×Q8C2×D1311yescharacteristic
125C23×C4C2×D1311yescharacteristic
126C2×Q16—134no—
127C22×C8—132no—
128C22⋊Q8—21no—
129C22⋊Q8—21no—
130C22⋊Q8—132no—
131C22⋊Q8—132no—
132C22⋊Q8—261no—
133C22⋊Q8—261no—
134C22⋊Q8C2×D1312yes—
135C22⋊Q8C2×D1312yes—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—261no—
139C2×C4⋊C4C2×D1311yescharacteristic
140C2×C22⋊C4—21no—
141C2×C22⋊C4—261no—
142#107—134no—
143#103—134no—
144#103—134no—
145C22⋊C8—132no—
146C22⋊C8—132no—
147C2×C13—22no—
148C2×C13—22no—
149C2×C13—22no—
150C2×C13#53411yescharacteristic
151C2×C13C22×Q1611yescharacteristic
152C2×C13#57511yescharacteristic
153C24C22⋊D1311yescharacteristic
154C2×Q8—21no—
155C2×Q8—42no—
156C2×Q8—132no—
157C2×Q8—261no—
158C2×Q8—522no—
159C2×Q8C22×D1312yes—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—42no—
163C22×C4—261no—
164C22×C4—261no—
165C22×C4C22⋊D1311yescharacteristic
166C22×C4C22⋊D1311yescharacteristic
167C22×C4C22⋊D1311yescharacteristic
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1311yescharacteristic
170C22×C4C22×D1311yescharacteristic
171Q16—524no—
172C2×C8—134no—
173C2×C8—522no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—132no—
178C4⋊C4—261no—
179C4⋊C4—262no—
180C4⋊C4—262no—
181C4⋊C4C22×D1312yes—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—262no—
185C22⋊C4—262no—
186C13#318911yescharacteristic, complemented, Sylow
187C23—41no—
188C23—41no—
189C23#610714yescomplemented
190C23C2×C22⋊D1311yescharacteristic
191C23C2×C22⋊D1311yescharacteristic
192C23C2×C22⋊D1311yescharacteristic
193Q8—24no—
194Q8—42no—
195Q8—264no—
196Q8—522no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4C2×C22⋊D1311yescharacteristic
212C2×C4C2×C22⋊D1311yescharacteristic
213C2×C4C2×C22⋊D1311yescharacteristic
214C2×C4C23×D1311yescharacteristic
215C8—264no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—44no—
223C22C2×#610712yes—
224C22C2×#610712yes—
225C22C2×#610712yes—
226C22C22×C22⋊D1311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—42no—
231C4—42no—
232C4—522no—
233C4—522no—
234C4#8825112yes—
235C2—22no—
236C2—22no—
237C2—22no—
238C2#1171950911yescharacteristic
239C2C22×#610711yescharacteristic
240C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×C22⋊Q8C2
socleC22×C13C22×D4
prime radicalC24×C13D4
hypercenterC2×C22⋊Q8D13
hypocenterC13#3189
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11718889C2semidirect
5. #11718712C2semidirect
6. #11718711C2semidirect
7. #11718705C2semidirect
8. #11718631C2semidirect
20. C2×#6107C22semidirect
28. #88075C22semidirect
31. #88050C22semidirect
32. #88047C22semidirect
69. C23×C13Q16semidirect
186. C13#3189semidirect
189. C23#6107semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×#881782
#117188892
C2×C22⋊#10552
#117187122
#117187112
#117187052
#117186312
#318913