Finite Group Databasebeta

← #13127576

Subgroups — #13127576

Order 1664.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q82×C13C211yesmaximal, characteristic, complemented
2#11719289C211yesmaximal, characteristic
3#11718755C212yesmaximal, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718750C212yesmaximal
6#11718745C211yesmaximal, characteristic
7#11718692C211yesmaximal, characteristic, complemented
8#11718691C212yesmaximal, complemented
9#11718689C212yesmaximal
10C4×#6106C211yesmaximal, characteristic
11#11718685C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8—21no—
13C13×C4⋊Q8—22no—
14C13×C4⋊Q8C2211yescharacteristic
15C13×C4⋊Q8C2212yes—
16C4×Q8×C13—21no—
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2212yes—
19C4×Q8×C13C2211yescharacteristic
20#88200—21no—
21C2×#6107C2212yes—
22C2×#6106C2211yescharacteristic
23#88152—22no—
24#88146—21no—
25#88129C2212yes—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26C2212yes—
29#88075C2211yescharacteristic
30#88050C2212yes—
31#88050C2212yes—
32#88050C2212yes—
33#88049C2211yescharacteristic
34#88049C2212yes—
35#88048C2211yescharacteristic
36#88048C2212yes—
37C4⋊#1055C2212yes—
38C4⋊#1055C2211yescharacteristic
39#88043C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—21no—
43C2×Q8×C13D411yescharacteristic
44C2×Q8×C13C2311yescharacteristic
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×Dic26C2312yes—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4D411yescharacteristic
53C13×C4⋊C4D412yes—
54C13×C4⋊C4C2311yescharacteristic
55C13×C4⋊C4C2312yes—
56C42×C13—22no—
57C42×C13—21no—
58C42×C13C2312yes—
59C42×C13C2311yescharacteristic
60#6107—24no—
61#6106—22no—
62#6103—21no—
63#6103—22no—
64#6103—22no—
65C4⋊Dic13—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13C2311yescharacteristic
68#6101—22no—
69C4×Dic13—22no—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72C2×#1055C2312yes—
73#3369—131nomaximal, Sylow
74C22×D13—21no—
75Q8×C13—22no—
76Q8×C13—21no—
77Q8×C13—82no—
78Q8×C13—81no—
79Q8×C13#4112yes—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13C2×D412yes—
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—22no—
90D52—21no—
91D52—21no—
92C4×D13—42no—
93Dic26—22no—
94Dic26—22no—
95#1055—21no—
96#1055—22no—
97#1055—21no—
98Q82D1311yescharacteristic, complemented
99#556—131no—
100#489—132no—
101#487—131no—
102#476—131no—
103#475—132no—
104#464—132no—
105#462—131no—
106#446—131no—
107#441—132no—
108C4×SD16—131no—
109C22×C13C22×D411yescharacteristic
110C2×D13—41no—
111C2×D13—41no—
112C2×D13—41no—
113C4×C13—22no—
114C4×C13—22no—
115C4×C13—22no—
116C4×C13—21no—
117C4×C13—42no—
118C4×C13—41no—
119C4×C13#13712yes—
120C4×C13C2×#4111yescharacteristic
121C4×C132−1+411yescharacteristic
122Dic13—42no—
123Dic13—41no—
124C2×Q16—132no—
125C2×SD16—131no—
126C4⋊Q8—21no—
127C4⋊Q8—22no—
128C4⋊Q8—131no—
129C4⋊Q8C2×D1312yes—
130C4⋊Q8C2×D1311yescharacteristic
131#126—262no—
132#124—132no—
133C22⋊Q8—261no—
134C4×Q8—21no—
135C4×Q8—132no—
136C4×Q8C2×D1311yescharacteristic
137C4×Q8C2×D1312yes—
138C4×Q8C2×D1311yescharacteristic
139C4×D4—131no—
140#117—261no—
141#106—131no—
142#106—132no—
143C4⋊C8—131no—
144C4⋊C8—132no—
145#103—131no—
146#103—132no—
147#103—132no—
148#103—132no—
149#102—131no—
150#102—132no—
151#97—132no—
152C4×C8—131no—
153C2×C13#54811yescharacteristic
154C2×C13C2×#13711yescharacteristic
155C2×C13#57711yescharacteristic
156D13—81no—
157C2×Q8—22no—
158C2×Q8—21no—
159C2×Q8—132no—
160C2×Q8C22⋊D1311yescharacteristic
161C2×Q8C22×D1311yescharacteristic
162C2×D4—131no—
163C22×C4—261no—
164Q16—264no—
165SD16—262no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—132no—
169C4⋊C4—22no—
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—21no—
173C4⋊C4—131no—
174C4⋊C4—261no—
175C4⋊C4—262no—
176C4⋊C4—261no—
177C4⋊C4C22⋊D1311yescharacteristic
178C4⋊C4C22⋊D1312yes—
179C4⋊C4C22×D1311yescharacteristic
180C4⋊C4C22×D1312yes—
181C22⋊C4—262no—
182C22⋊C4—261no—
183C22⋊C4—262no—
184C42—22no—
185C42—21no—
186C42—262no—
187C42C22×D1311yescharacteristic
188C42C22×D1312yes—
189C13#336911yescharacteristic, complemented, Sylow
190C23—261no—
191Q8—22no—
192Q8—21no—
193Q8—82no—
194Q8—81no—
195Q8—262no—
196Q8—262no—
197Q8#613112yes—
198D4—261no—
199D4—261no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—261no—
204C2×C4—262no—
205C2×C4—522no—
206C2×C4C2×C22⋊D1312yes—
207C2×C4C2×C22⋊D1312yes—
208C2×C4C2×C22⋊D1311yescharacteristic
209C2×C4C2×C22⋊D1311yescharacteristic
210C2×C4C23×D1311yescharacteristic
211C8—261no—
212C8—262no—
213C8—261no—
214C22—521no—
215C22—521no—
216C22—521no—
217C22C22×C22⋊D1311yescharacteristic
218C4—22no—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—42no—
223C4—41no—
224C4—521no—
225C4—522no—
226C4#8819612yes—
227C4C2×#613111yescharacteristic
228C4#8825411yescharacteristic
229C2—1041no—
230C2C2×#8819611yescharacteristic
231C2#1171952211yescharacteristic
232C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingQ82×C13C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenterQ82D13
hypocenterC13#3369
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
1. Q82×C13C2semidirect
3. #11718755C2semidirect
4. #11718754C2semidirect
7. #11718692C2semidirect
8. #11718691C2semidirect
11. #11718685C2semidirect
98. Q82D13semidirect
189. C13#3369semidirect

Maximal subgroups

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

subgroupindex
Q82×C132
#117192892
#117187552
#117187542
#117187502
#117187452
#117186922
#117186912
#117186892
C4×#61062
#117186852
#336913