Finite Group Databasebeta

← #13116014

Subgroups — #13116014

Order 1664.

278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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#11719188C211yesmaximal, characteristic, complemented
2C2×#88046C211yesmaximal, characteristic
3C2×#88046C211yesmaximal, characteristic
4C2×#88046C211yesmaximal, characteristic
5C13×#342C211yesmaximal, characteristic, complemented
6#11718119C211yesmaximal, characteristic, complemented
7#11718118C211yesmaximal, characteristic, complemented
8C22×C22⋊D13C2211yescharacteristic
9C2×C13×C22⋊C4C2211yescharacteristic
10C2×C13×C22⋊C4C2211yescharacteristic
11C2×C13×C22⋊C4C2211yescharacteristic
12C2×C22⋊Dic13C2211yescharacteristic
13C2×C22⋊Dic13C2211yescharacteristic
14C2×C22⋊Dic13C2211yescharacteristic
15#88178—22no—
16#88132—22no—
17#88132—22no—
18#88046—22no—
19#88046—22no—
20#88046—22no—
21C24×C13C2311yescharacteristic
22C23×D13Q811yescharacteristic, complemented
23C22×C4×C13—21no—
24C22×C4×C13—21no—
25C22×C4×C13—21no—
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28C2×C22⋊D13—21no—
29C2×C22⋊D13—21no—
30C2×C22⋊D13—21no—
31C2×C22⋊D13—21no—
32C22×Dic13—21no—
33C22×Dic13—21no—
34C22×Dic13—21no—
35C22×Dic13Q811yescharacteristic, complemented
36C2×Dic26—22no—
37C13×C22⋊C4—21no—
38C13×C22⋊C4—21no—
39C13×C22⋊C4—21no—
40C13×C22⋊C4—21no—
41C13×C22⋊C4—21no—
42C13×C22⋊C4D412yes—
43C22⋊Dic13—21no—
44C22⋊Dic13—21no—
45C22⋊Dic13—21no—
46C22⋊Dic13—21no—
47C22⋊Dic13D412yes—
48C22⋊Dic13D412yes—
49C4⋊Dic13—22no—
50#6101—24no—
51#2032—131nomaximal, Sylow
52C23×C13—81no—
53C23×C13C2×D411yescharacteristic
54C23×C13C2×D411yescharacteristic
55C23×C13C2×D411yescharacteristic
56C23×C13C2×Q811yescharacteristic
57C23×C13#4111yescharacteristic
58C23×C13#4111yescharacteristic
59C23×C13#4111yescharacteristic
60C22×D13—21no—
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—81no—
64C2×C4×C13—22no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—81no—
68C2×C4×C13—81no—
69C2×C4×C13—81no—
70C22⋊D13—41no—
71C22⋊D13—41no—
72C22⋊D13—41no—
73C22⋊D13—41no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—41no—
80C2×Dic13—81no—
81C2×Dic13—81no—
82C2×Dic13—81no—
83Dic26—82no—
84#543—131no—
85C2×#99—131no—
86C2×#99—131no—
87C2×#99—131no—
88#342—131no—
89#342—131no—
90#342D1311yescharacteristic, complemented
91C22×C13—41no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13—41no—
95C22×C13—41no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13#12011yescharacteristic
99C22×C13C22⋊Q811yescharacteristic
100C22×C13C22⋊Q811yescharacteristic
101C22×C13C22⋊Q811yescharacteristic
102C22×C13#12411yescharacteristic
103C22×C13#12411yescharacteristic
104C22×C13#12411yescharacteristic
105C2×D13—41no—
106C2×D13—81no—
107C2×D13—81no—
108C2×D13—81no—
109C4×C13—42no—
110C4×C13—81no—
111C4×C13—81no—
112Dic13—42no—
113Dic13—42no—
114Dic13—41no—
115Dic13—81no—
116C22×D4—131no—
117C22⋊Q8—262no—
118C22⋊Q8—262no—
119C22⋊Q8—262no—
120C2×C22⋊C4—131no—
121C2×C22⋊C4—131no—
122C2×C22⋊C4—131no—
123C2×C22⋊C4C2×D1311yescharacteristic
124C2×C22⋊C4C2×D1311yescharacteristic
125C2×C22⋊C4C2×D1311yescharacteristic
126#99—262no—
127#99—262no—
128#99—262no—
129C2×C13—21no—
130C2×C13—21no—
131C2×C13—21no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13—21no—
135C2×C13—21no—
136C2×C13#39311yescharacteristic
137D13—81no—
138C24—131no—
139C24C22×D1311yescharacteristic
140C2×Q8—262no—
141C2×D4—261no—
142C2×D4—261no—
143C2×D4—261no—
144C2×D4—261no—
145C2×D4—261no—
146C2×D4—261no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—131no—
151C22×C4—261no—
152C22×C4—261no—
153C22×C4—261no—
154C4⋊C4—264no—
155C4⋊C4—262no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—132no—
162C22⋊C4—132no—
163C22⋊C4—261no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—261no—
167C22⋊C4D5212yes—
168C13#203211yescharacteristic, complemented, Sylow
169C23—81no—
170C23—261no—
171C23—261no—
172C23—261no—
173C23—1041no—
174C23C2×D5211yescharacteristic
175C23#612711yescharacteristic
176C23#612711yescharacteristic
177C23D4×D1311yescharacteristic
178C23D4×D1311yescharacteristic
179C23#612911yescharacteristic
180C23Q8×D1311yescharacteristic
181Q8—1042no—
182D4—521no—
183D4—521no—
184D4—521no—
185D4—521no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—521no—
198C2×C4—1041no—
199C2×C4—1041no—
200C2×C4—1041no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—521no—
209C22—1041no—
210C22—1041no—
211C22—1041no—
212C22#8812911yescharacteristic
213C22#8813611yescharacteristic
214C22#8813911yescharacteristic
215C22#8813911yescharacteristic
216C22#8815011yescharacteristic
217C22#8815011yescharacteristic
218C22#8815111yescharacteristic
219C4—42no—
220C4—81no—
221C4—81no—
222C4—522no—
223C4—522no—
224C4—521no—
225C4—1041no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—1041no—
234C2#1171833411yescharacteristic
subgroupG/H
centerC2#11718334
commutator, cosocleC24×C13C23
FrattiniC24C22×D13
FittingC13×#342C2
socleC2×C13#393
prime radicalC22×C22⋊D13C22
hypercenter#342D13
hypocenterC13#2032
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #11719188C2semidirect
5. C13×#342C2semidirect
6. #11718119C2semidirect
7. #11718118C2semidirect
22. C23×D13Q8semidirect
35. C22×Dic13Q8semidirect
90. #342D13semidirect
168. C13#2032semidirect

Maximal subgroups

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

subgroupindex
#117191882
C2×#880462
C13×#3422
#117181192
#117181182
#203213