Finite Group Databasebeta

← #13125491

Subgroups — #13125491

Order 1664.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719288C212yesmaximal
2C4×C13×Q16C211yesmaximal, characteristic, complemented
3#11718849C211yesmaximal, characteristic
4#11718842C211yesmaximal, characteristic, complemented
5#11718691C212yesmaximal, complemented
6#11718548C211yesmaximal, characteristic
7#11718539C211yesmaximal, characteristic, complemented
8#11718477C212yesmaximal
9#11718458C212yesmaximal, complemented
10C4×Dic52C211yesmaximal, characteristic, complemented
11#11718350C211yesmaximal, characteristic
12C2×C13×Q16C2211yescharacteristic
13C4×Q8×C13C2212yes—
14#88200C2212yes—
15#88198C2212yes—
16C2×#6107C2212yes—
17C2×Dic52C2211yescharacteristic
18C2×#6094C2211yescharacteristic
19C2×C8×D13C2211yescharacteristic
20#88152—22no—
21#88151C2212yes—
22#88144C2212yes—
23#88143—22no—
24#88130—22no—
25#88126C2211yescharacteristic
26#88124—22no—
27C4×Dic26C2212yes—
28C13×#107C2211yescharacteristic
29C13×#103C2212yes—
30C4×C8×C13C2211yescharacteristic
31#88075C2212yes—
32#88058C2211yescharacteristic
33#88056C2212yes—
34#88055C2211yescharacteristic
35C8×Dic13C2211yescharacteristic
36#88050C2212yes—
37#88048C2212yes—
38#88043C2211yescharacteristic
39C2×Q8×C13C2312yes—
40C2×C4×D13C2311yescharacteristic
41C2×Dic26C2312yes—
42C13×Q16—22no—
43C2×C8×C13C2311yescharacteristic
44C2×C8×C13C2311yescharacteristic
45C13×C4⋊C4—22no—
46C13×C4⋊C4C2312yes—
47C42×C13—22no—
48C42×C13C2311yescharacteristic
49#6107—24no—
50#6103—22no—
51#6103—22no—
52#6103D411yescharacteristic
53#6103D411yescharacteristic
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13C2312yes—
57#6101—22no—
58#6101—22no—
59#6101—22no—
60#6101—22no—
61#6101—22no—
62#6101D411yescharacteristic
63#6101D411yescharacteristic
64C4×Dic13—22no—
65C4×Dic13C2311yescharacteristic
66C2×#1055C2311yescharacteristic
67C2×#1055C2311yescharacteristic
68Dic52—22no—
69#6094—22no—
70C8×D13—22no—
71#3177—131nomaximal, Sylow
72C22×D13C2×D411yescharacteristic
73Q8×C13—22no—
74Q8×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2411yescharacteristic
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13C2×D411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13C2×D411yescharacteristic
85C4×D13—21no—
86C4×D13—21no—
87Dic26—22no—
88Dic26—22no—
89C8×C13—21no—
90C8×C13#4112yes—
91#1055—21no—
92#1055#4112yes—
93#541—132no—
94#499—131no—
95#494—131no—
96#491—132no—
97#470—132no—
98#467—131no—
99#467—131no—
100#441—132no—
101C4×Q16—131no—
102C4×Q16D1311yescharacteristic, complemented
103#405—131no—
104C22×C13C22×D411yescharacteristic
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—42no—
111C4×C13—42no—
112C4×C13C2×#4111yescharacteristic
113C4×C13C2×#4111yescharacteristic
114Dic13—21no—
115Dic13—21no—
116Dic13—21no—
117Dic13—42no—
118Dic13—42no—
119C2×Q16—132no—
120C2×Q16—131no—
121C2×Q16C2×D1311yescharacteristic
122C2×M16—131no—
123C22×C8—131no—
124C4⋊Q8—132no—
125#126—262no—
126#126—262no—
127#125—132no—
128#125—262no—
129#125—262no—
130C22⋊Q8—132no—
131C22⋊Q8—132no—
132C4×Q8—132no—
133C4×Q8C2×D1312yes—
134#117—131no—
135#107—131no—
136#107C2×D1311yescharacteristic
137#106—132no—
138#103—132no—
139#103—132no—
140#103—132no—
141#103C2×D1312yes—
142#97—131no—
143#97—131no—
144C4×C8—131no—
145C4×C8C2×D1311yescharacteristic
146C2×C13#53211yescharacteristic
147C2×C13#57811yescharacteristic
148C2×C13#57811yescharacteristic
149D13—41no—
150C2×Q8—132no—
151C2×Q8C22×D1312yes—
152C22×C4—131no—
153Q16—22no—
154Q16—264no—
155Q16—262no—
156M16—262no—
157C2×C8—131no—
158C2×C8—131no—
159C2×C8—262no—
160C2×C8C22×D1311yescharacteristic
161C2×C8C22×D1311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—131no—
164C4⋊C4—131no—
165C4⋊C4—132no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4C22×D1312yes—
174C22⋊C4—131no—
175C22⋊C4—131no—
176C22⋊C4—262no—
177C22⋊C4—262no—
178C42—22no—
179C42—131no—
180C42—262no—
181C42C22×D1311yescharacteristic
182C13#317711yescharacteristic, complemented, Sylow
183C23—131no—
184Q8—22no—
185Q8—22no—
186Q8—262no—
187Q8—262no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—261no—
194C2×C4—261no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4D4×D1311yescharacteristic
198C2×C4D4×D1311yescharacteristic
199C2×C4C23×D1311yescharacteristic
200C8—21no—
201C8—132no—
202C8—261no—
203C8#612712yes—
204C22—261no—
205C22—261no—
206C22—261no—
207C22C2×D4×D1311yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—261no—
213C4—261no—
214C4—261no—
215C4—522no—
216C4—522no—
217C4C2×#612711yescharacteristic
218C4#41×D1311yescharacteristic
219C2—521no—
220C2#1171925311yescharacteristic
221C2#1171947111yescharacteristic
222C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×Q16C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenterC4×Q16D13
hypocenterC13#3177
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. C4×C13×Q16C2semidirect
4. #11718842C2semidirect
5. #11718691C2semidirect
7. #11718539C2semidirect
9. #11718458C2semidirect
10. C4×Dic52C2semidirect
102. C4×Q16D13semidirect
182. C13#3177semidirect

Maximal subgroups

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

subgroupindex
#117192882
C4×C13×Q162
#117188492
#117188422
#117186912
#117185482
#117185392
#117184772
#117184582
C4×Dic522
#117183502
#317713