Finite Group Databasebeta

← #13120606

Subgroups — #13120606

Order 1664.

528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88198C211yesmaximal, characteristic, complemented
3C2×#88180C211yesmaximal, characteristic
4C2×#88178C211yesmaximal, characteristic
5#11718891C211yesmaximal, characteristic, complemented
6#11718645C214yesmaximal, complemented
7#11718638C211yesmaximal, characteristic, complemented
8#11718635C211yesmaximal, characteristic, complemented
9#11718613C214yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C13×C22⋊Q8—24no—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19#88198—24no—
20#88180—24no—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2212yes—
23#88178—24no—
24C2×#6101C2212yes—
25C2×#6101C2214yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28#88071C2214yes—
29#88071C2214yes—
30#88071C2214yes—
31C24×C13C2311yescharacteristic
32C2×Q8×C13—22no—
33C2×Q8×C13—22no—
34C2×Q8×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—22no—
37C22×C4×C13D414yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×Dic26—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—24no—
51C13×C22⋊C4—24no—
52C22⋊Dic13—24no—
53C22⋊Dic13—24no—
54C4⋊Dic13—22no—
55C4⋊Dic13—24no—
56#6101—24no—
57#6101—28no—
58C4×Dic13—22no—
59C4×Dic13D414yes—
60#2621—131nomaximal, Sylow
61C23×C13—21no—
62C23×C13—21no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13C2×D412yes—
66C23×C13C2411yescharacteristic
67Q8×C13—44no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—28no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×D412yes—
79C2×C4×C13#4112yes—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—24no—
89C2×Dic13—22no—
90C2×Dic13C2×D414yes—
91Dic26—44no—
92C2×C4⋊Q8—131no—
93C2×C22⋊Q8—131no—
94C2×C22⋊Q8D1311yescharacteristic
95C2×#117—131no—
96#398—134no—
97#397—134no—
98#391—131no—
99#391—131no—
100#382—131no—
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—22no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13C22×D411yescharacteristic
107C22×C13C22×D411yescharacteristic
108C22×C13C2×#4111yescharacteristic
109C22×C132−1+412yes—
110C22×C132−1+412yes—
111C4×C13—22no—
112C4×C13—42no—
113C4×C13—42no—
114C4×C13#12114yes—
115Dic13—24no—
116Dic13—42no—
117Dic13—42no—
118Dic13—42no—
119C22×Q8—131no—
120C22×Q8C2×D1311yescharacteristic
121C23×C4C2×D1311yescharacteristic
122C4⋊Q8—264no—
123C22⋊Q8—24no—
124C22⋊Q8—264no—
125#117—264no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—134no—
130C2×C4⋊C4C2×D1311yescharacteristic
131C2×C4⋊C4C2×D1312yes—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—132no—
134C2×C22⋊C4C2×D1312yes—
135C2×C42—131no—
136C2×C42—131no—
137#95—134no—
138#95—134no—
139#95—134no—
140C2×C13—42no—
141C2×C13C2×#12111yescharacteristic
142C2×C13#53611yescharacteristic
143C2×C13#53611yescharacteristic
144C2×C13#53612yes—
145C2×C13#54112yes—
146C24C22×D1311yescharacteristic
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—262no—
151C2×Q8—262no—
152C2×Q8—262no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—132no—
156C22×C4—132no—
157C22×C4—132no—
158C22×C4—132no—
159C22×C4C22⋊D1314yes—
160C22×C4C22×D1312yes—
161C22×C4C22×D1312yes—
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—24no—
166C4⋊C4—264no—
167C4⋊C4—268no—
168C4⋊C4—264no—
169C4⋊C4—262no—
170C22⋊C4—24no—
171C22⋊C4—264no—
172C22⋊C4—264no—
173C42—134no—
174C42—262no—
175C13#262111yescharacteristic, complemented, Sylow
176C23—21no—
177C23—21no—
178C23—22no—
179C23—22no—
180C23C2×C22⋊D1312yes—
181C23C23×D1311yescharacteristic
182Q8—44no—
183Q8—524no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—134no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—264no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4D4×D1312yes—
204C2×C4#612912yes—
205C2×C4C2×C22⋊D1312yes—
206C2×C4C2×C22⋊D1312yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C2×D4×D1311yescharacteristic
213C22C2×#612911yescharacteristic
214C22#8825412yes—
215C22#8825712yes—
216C22C22×C22⋊D1311yescharacteristic
217C4—22no—
218C4—42no—
219C4—42no—
220C4—264no—
221C4—522no—
222C4—522no—
223C4—522no—
224C4#8819314yes—
225C2—42no—
226C2#1171933012yes—
227C2#1171933312yes—
228C2C2×#8819311yescharacteristic
229C2#1171952111yescharacteristic
230C2#1171953011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC24×C13C23
hypercenterC2×C22⋊Q8D13
hypocenterC13#2621
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#88198C2semidirect
5. #11718891C2semidirect
6. #11718645C2semidirect
7. #11718638C2semidirect
8. #11718635C2semidirect
175. C13#2621semidirect

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×#881982
C2×#881802
C2×#881782
#117188912
#117186452
#117186382
#117186352
#117186132
#262113