Finite Group Databasebeta

← #13127448

Subgroups — #13127448

Order 1664.

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

normal subgroups only

This group has 342 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#11719437C211yesmaximal, characteristic
2#11719284C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718740C211yesmaximal, characteristic, complemented
5C4×#6107C211yesmaximal, characteristic, complemented
6#11718523C212yesmaximal, complemented
7#11718522C212yesmaximal, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic
10#11718477C212yesmaximal, complemented
11#11718475C212yesmaximal, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C4×Q8×C13C2211yescharacteristic
14#88201—21no—
15#88200C2212yes—
16Q8×Dic13—21no—
17C2×#6107C2211yescharacteristic
18C2×#6094C2212yes—
19#88152—22no—
20#88151C2212yes—
21#88150—22no—
22#88146C2212yes—
23C4⋊C4×D13C2212yes—
24C4×D52—21no—
25C4×D52C2211yescharacteristic
26#88124—21no—
27#88123C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#103C2212yes—
32#88075C2211yescharacteristic
33#88060C2212yes—
34#88058C2212yes—
35#88056C2212yes—
36#88050C2211yescharacteristic
37#88048C2212yes—
38#88048C2212yes—
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43C2×D52D411yescharacteristic
44C2×C4×D13—22no—
45C2×C4×D13C2312yes—
46C2×Dic26—21no—
47C2×Dic26C2311yescharacteristic
48C2×C8×C13C2312yes—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C13×C4⋊C4C2311yescharacteristic
53C42×C13—21no—
54C42×C13C2311yescharacteristic
55#6107—22no—
56#6103—22no—
57#6103—22no—
58#6103—22no—
59#6103D412yes—
60C4⋊Dic13—21no—
61C4⋊Dic13—22no—
62C4⋊Dic13D411yescharacteristic
63C4⋊Dic13C2311yescharacteristic
64C4⋊Dic13C2312yes—
65#6101—21no—
66#6101—22no—
67#6101—22no—
68C4×Dic13—21no—
69C4×Dic13—22no—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72#6094—24no—
73#3356—131nomaximal, Sylow
74C22×D13C2×D412yes—
75Q8×C13—21no—
76Q8×C13—21no—
77Q8×C13—42no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2411yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13C2×D412yes—
88D52—22no—
89C4×D13—22no—
90C4×D13—22no—
91C4×D13—82no—
92Dic26—21no—
93Dic26—21no—
94Dic26—81no—
95C8×C13—22no—
96#1055—21no—
97#1055#4112yes—
98#556—131no—
99#554—131no—
100#498—131no—
101#485—132no—
102#483—132no—
103#477—131no—
104#475D1311yescharacteristic, complemented
105#470—132no—
106C4×Q16—131no—
107#436—131no—
108#428—132no—
109C22×C13C22×D411yescharacteristic
110C2×D13—22no—
111C2×D13—22no—
112C2×D13—22no—
113C4×C13—21no—
114C4×C13—41no—
115C4×C13—42no—
116C4×C13—41no—
117C4×C13#13712yes—
118C4×C13C2×#4111yescharacteristic
119C4×C132−1+411yescharacteristic
120Dic13—22no—
121Dic13—41no—
122Dic13—42no—
123Dic13—41no—
124C2×Q16—131no—
125C2×M16—132no—
126C4⋊Q8—131no—
127C4⋊Q8C2×D1311yescharacteristic
128#126—262no—
129#125—261no—
130#124—261no—
131C22⋊Q8—132no—
132C22⋊Q8—132no—
133C22⋊Q8—262no—
134C4×Q8—131no—
135C4×Q8—261no—
136C4×Q8C2×D1311yescharacteristic
137C4×D4—131no—
138C4×D4—261no—
139#117—132no—
140C2×C4⋊C4—132no—
141#107—132no—
142#107—131no—
143#106—132no—
144#106—132no—
145#106C2×D1312yes—
146C4⋊C8C2×D1311yescharacteristic
147#103—131no—
148#103—132no—
149#103—131no—
150#103C2×D1312yes—
151C22⋊C8—132no—
152C4×C8—131no—
153C2×C13#54711yescharacteristic
154C2×C13C2×#13711yescharacteristic
155C2×C13#57711yescharacteristic
156D13—42no—
157C2×Q8—21no—
158C2×Q8—131no—
159C2×Q8—261no—
160C2×Q8C22×D1311yescharacteristic
161C2×D4—131no—
162C22×C4—132no—
163C22×C4—262no—
164Q16—262no—
165M16—264no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8C22×D1312yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—131no—
172C4⋊C4—132no—
173C4⋊C4—131no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—261no—
178C4⋊C4—261no—
179C4⋊C4C22×D1311yescharacteristic
180C4⋊C4C22×D1312yes—
181C22⋊C4—132no—
182C22⋊C4—262no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C42—21no—
186C42—262no—
187C42—261no—
188C42C22×D1311yescharacteristic
189C13#335611yescharacteristic, complemented, Sylow
190C23—132no—
191Q8—21no—
192Q8—21no—
193Q8—42no—
194Q8—261no—
195Q8—261no—
196Q8—1041no—
197D4—262no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—132no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—262no—
207C2×C4—1042no—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1311yescharacteristic
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—132no—
213C8—261no—
214C22—262no—
215C22—262no—
216C22—262no—
217C22C2×D4×D1311yescharacteristic
218C4—21no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—262no—
223C4—521no—
224C4—522no—
225C4—521no—
226C4#8816912yes—
227C4#8825411yescharacteristic
228C4#41×D1311yescharacteristic
229C2—522no—
230C2#1171933611yescharacteristic
231C2C2×#8816911yescharacteristic
232C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#475D13
hypocenterC13#3356
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C13×#475C2semidirect
4. #11718740C2semidirect
5. C4×#6107C2semidirect
6. #11718523C2semidirect
7. #11718522C2semidirect
8. #11718511C2semidirect
10. #11718477C2semidirect
11. #11718475C2semidirect
104. #475D13semidirect
189. C13#3356semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117192842
C13×#4752
#117187402
C4×#61072
#117185232
#117185222
#117185112
#117184992
#117184772
#117184752
#335613