Finite Group Databasebeta

← #13115293

Subgroups — #13115293

Order 1664.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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×#88140C211yesmaximal, characteristic
2C2×#88131C211yesmaximal, characteristic, complemented
3C2×#88046C211yesmaximal, characteristic
4C2×#88046C211yesmaximal, characteristic
5#11718604C211yesmaximal, characteristic, complemented
6C13×#342C211yesmaximal, characteristic, complemented
7#11718118C211yesmaximal, characteristic, complemented
8C22×C22⋊D13C2211yescharacteristic
9C23×Dic13C2211yescharacteristic
10C2×C13×C22⋊C4C2211yescharacteristic
11C2×C13×C22⋊C4C2211yescharacteristic
12C2×C13×C22⋊C4C2211yescharacteristic
13C2×C22⋊Dic13C2211yescharacteristic
14C2×C22⋊Dic13C2211yescharacteristic
15C2×#6103C412yescomplemented
16C2×C4⋊Dic13C412yescomplemented
17C2×#6101—21no—
18C2×C4×Dic13—21no—
19#88140—22no—
20#88140—21no—
21#88140—21no—
22#88131—22no—
23#88131—22no—
24#88071—22no—
25#88046—22no—
26#88046—22no—
27C24×C13C2311yescharacteristic
28C23×D13C2×C411yescharacteristic
29C22×C4×C13—21no—
30C22×C4×C13—21no—
31C22×C4×C13C2×C412yes—
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C2×C22⋊D13—21no—
35C2×C22⋊D13—21no—
36C2×C22⋊D13—21no—
37C2×C22⋊D13—21no—
38C22×Dic13—21no—
39C22×Dic13—21no—
40C22×Dic13—21no—
41C22×Dic13—21no—
42C22×Dic13—21no—
43C22×Dic13—21no—
44C22×Dic13C2×C411yescharacteristic
45C22×Dic13C2×C412yes—
46C22×Dic13D412yes—
47C22×Dic13D411yescharacteristic
48C22×Dic13D411yescharacteristic
49C13×C22⋊C4—21no—
50C13×C22⋊C4—21no—
51C13×C22⋊C4—21no—
52C13×C22⋊C4—21no—
53C13×C22⋊C4—21no—
54C13×C22⋊C4D412yes—
55C22⋊Dic13—21no—
56C22⋊Dic13—21no—
57C22⋊Dic13—21no—
58C22⋊Dic13D412yes—
59#6103—22no—
60#6103—22no—
61C4⋊Dic13—22no—
62C4⋊Dic13—22no—
63#6101—24no—
64C4×Dic13—24no—
65#1899—131nomaximal, Sylow
66C23×C13—42no—
67C23×C13C22×C411yescharacteristic
68C23×C13C2×D411yescharacteristic
69C23×C13C2×D411yescharacteristic
70C23×C13C2×D411yescharacteristic
71C23×C13C2×D411yescharacteristic
72C23×C13#4111yescharacteristic
73C23×C13#4111yescharacteristic
74C22×D13—21no—
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—42no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—41no—
84C22⋊D13—41no—
85C22⋊D13—41no—
86C22⋊D13—41no—
87C22⋊D13—41no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—22no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—41no—
103C2×Dic13C22⋊C412yes—
104C2×Dic13C22⋊C412yes—
105C2×#123—131no—
106C2×#117—131no—
107C2×#99—131no—
108C2×#99—131no—
109#381—131no—
110#342—131no—
111#342D1311yescharacteristic, complemented
112C22×C13—22no—
113C22×C13—22no—
114C22×C13—22no—
115C22×C13—41no—
116C22×C13—41no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13C2×C22⋊C411yescharacteristic
120C22×C13C4×D411yescharacteristic
121C22×C13C4×D411yescharacteristic
122C22×C13#12011yescharacteristic
123C22×C13#12111yescharacteristic
124C22×C13#12111yescharacteristic
125C22×C13#12311yescharacteristic
126C2×D13—41no—
127C2×D13—42no—
128C2×D13—81no—
129C2×D13—81no—
130C4×C13—42no—
131C4×C13—42no—
132C4×C13—81no—
133Dic13—22no—
134Dic13—22no—
135Dic13—42no—
136Dic13—41no—
137Dic13—81no—
138C22×D4—131no—
139C23×C4—131no—
140#123—262no—
141#123—261no—
142#123—261no—
143#117—262no—
144#117—262no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—261no—
147C2×C22⋊C4—131no—
148C2×C22⋊C4—132no—
149C2×C22⋊C4—131no—
150C2×C22⋊C4C2×D1311yescharacteristic
151C2×C22⋊C4C2×D1311yescharacteristic
152C2×C22⋊C4C2×D1311yescharacteristic
153C2×C42—261no—
154#99—262no—
155#99—262no—
156#95—262no—
157C2×C13—21no—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—21no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#38611yescharacteristic
164C2×C13#41012yes—
165D13—81no—
166C24—131no—
167C24C22×D1311yescharacteristic
168C2×D4—261no—
169C2×D4—261no—
170C2×D4—261no—
171C2×D4—261no—
172C2×D4—261no—
173C2×D4—261no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—132no—
177C22×C4—132no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—131no—
181C22×C4—261no—
182C22×C4—261no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4—261no—
186C22×C4—261no—
187C22×C4C4×D1312yes—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—264no—
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—132no—
197C22⋊C4—262no—
198C22⋊C4—262no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C22⋊C4—261no—
202C22⋊C4D5212yes—
203C42—264no—
204C13#189911yescharacteristic, complemented, Sylow
205C23—42no—
206C23—261no—
207C23—261no—
208C23—261no—
209C23—522no—
210C23C2×C4×D1311yescharacteristic
211C23C2×D5211yescharacteristic
212C23#612711yescharacteristic
213C23D4×D1311yescharacteristic
214C23D4×D1311yescharacteristic
215C23D4×D1311yescharacteristic
216C23#613111yescharacteristic
217D4—521no—
218D4—521no—
219D4—521no—
220D4—521no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—132no—
228C2×C4—132no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—262no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—262no—
240C2×C4—261no—
241C2×C4—522no—
242C2×C4—522no—
243C2×C4—521no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—522no—
252C22—521no—
253C22—1041no—
254C22—1041no—
255C22C4×D5211yescharacteristic
256C22C22⋊C4×D1311yescharacteristic
257C22#8813611yescharacteristic
258C22#8813811yescharacteristic
259C22#8814711yescharacteristic
260C22#8814811yescharacteristic
261C22#8814911yescharacteristic
262C4—42no—
263C4—42no—
264C4—81no—
265C4—262no—
266C4—262no—
267C4—522no—
268C4—521no—
269C4—1041no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—1041no—
277C2#1171832611yescharacteristic
278C2#1171840112yes—
subgroupG/H
centerC22C22⋊C4×D13
commutatorC23×C13C22×C4
FrattiniC24C22×D13
FittingC13×#342C2
socleC22×C13C2×C22⋊C4
prime radicalC22×C22⋊D13C22
cosocleC24×C13C23
hypercenter#342D13
hypocenterC13#1899
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#88131C2semidirect
5. #11718604C2semidirect
6. C13×#342C2semidirect
7. #11718118C2semidirect
15. C2×#6103C4semidirect
16. C2×C4⋊Dic13C4semidirect
111. #342D13semidirect
204. C13#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#881402
C2×#881312
C2×#880462
#117186042
C13×#3422
#117181182
#189913