Finite Group Databasebeta

← #13116027

Subgroups — #13116027

Order 1664.

368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#88149C211yesmaximal, characteristic
2C2×C13×#106C211yesmaximal, characteristic, complemented
3C2×#88061C211yesmaximal, characteristic, complemented
4C2×#88060C211yesmaximal, characteristic, complemented
5#11718648C211yesmaximal, characteristic, complemented
6C2×#88049C211yesmaximal, characteristic, complemented
7#11718121C211yesmaximal, characteristic, complemented
8C22×D52—21no—
9C22×D52C2211yescharacteristic
10C22×C4×D13C2211yescharacteristic
11C22×C8×C13C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×#6103—21no—
15C2×#6103—21no—
16C2×C4⋊Dic13C2211yescharacteristic
17C22×#1055C2211yescharacteristic
18#88149—22no—
19#88149—22no—
20C13×#106—22no—
21#88071—21no—
22#88061—22no—
23#88060—22no—
24#88049—22no—
25C23×D13—21no—
26C23×D13D411yescharacteristic
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13C2311yescharacteristic
30C22×Dic13—21no—
31C22×Dic13D411yescharacteristic
32C2×D52—21no—
33C2×D52—21no—
34C2×D52—21no—
35C2×D52—21no—
36C2×D52—24no—
37C2×D52—21no—
38C2×D52—42no—
39C2×D52—42no—
40C2×D52D412yes—
41C2×C4×D13—21no—
42C2×C4×D13—21no—
43C2×C4×D13—21no—
44C2×C4×D13—21no—
45C2×C4×D13—21no—
46C2×C4×D13—21no—
47C2×C8×C13—21no—
48C2×C8×C13—21no—
49C2×C8×C13D412yescomplemented
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4D412yes—
54#6103—24no—
55#6103—42no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C2×#1055—21no—
59C2×#1055—21no—
60C2×#1055—21no—
61#2034—131nomaximal, Sylow
62C23×C13C2×D411yescharacteristic
63C22×D13—21no—
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—21no—
68C22×D13—21no—
69C22×D13—22no—
70C22×D13—41no—
71C22×D13—41no—
72C22×D13—41no—
73C22×D13—41no—
74C22×D13—41no—
75C22×D13—41no—
76C22×D13SD1612yes—
77C2×C4×C13—22no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13#4111yescharacteristic
87C2×C4×C13#4111yescharacteristic
88C2×C4×C13#4111yescharacteristic
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—41no—
93C2×Dic13—41no—
94C2×Dic13—41no—
95D52—22no—
96D52—22no—
97D52—48no—
98D52—41no—
99D52—41no—
100C4×D13—41no—
101C4×D13—41no—
102C4×D13—41no—
103C4×D13—41no—
104C8×C13—22no—
105#1055—41no—
106C2×#121—131no—
107C2×#106D1311yescharacteristic, complemented
108C2×#102—131no—
109C2×#102—131no—
110C2×C22⋊C8—131no—
111#380—131no—
112#340—131no—
113C22×C13#12011yescharacteristic
114C22×C13#12111yescharacteristic
115C22×C13#12311yescharacteristic
116C22×C13C2×SD1611yescharacteristic
117C22×C13#13511yescharacteristic
118C22×C13AGL(1,ℤ/8)11yescharacteristic
119C22×C13AGL(1,ℤ/8)11yescharacteristic
120C2×D13—22no—
121C2×D13—22no—
122C2×D13—22no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—41no—
126C2×D13—41no—
127C2×D13—42no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—81no—
131C2×D13—81no—
132C2×D13—81no—
133C2×D13—81no—
134C4×C13—42no—
135C4×C13—81no—
136C4×C13#12111yescharacteristic
137C4×C13#12111yescharacteristic
138C4×C13#12311yescharacteristic
139C4×C13#12411yescharacteristic
140Dic13—41no—
141Dic13—81no—
142C22×D4—131no—
143C22×D4—261no—
144C23×C4—131no—
145C22×C8—131no—
146C22×C8C2×D1311yescharacteristic
147#121—262no—
148#121—262no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4C2×D1311yescharacteristic
151C2×C4⋊C4C2×D1311yescharacteristic
152C2×C22⋊C4—261no—
153C2×C22⋊C4—261no—
154#106—22no—
155#102—262no—
156#102—262no—
157C22⋊C8—262no—
158#95—261no—
159C2×C13#39411yescharacteristic
160C2×C13#44911yescharacteristic
161C2×C13#45011yescharacteristic
162C2×C13#46511yescharacteristic
163C2×C13#46911yescharacteristic
164C2×C13#48111yescharacteristic
165C2×C13#48211yescharacteristic
166D13—42no—
167D13—82no—
168C24—131no—
169C24—261no—
170C2×D4—132no—
171C2×D4—264no—
172C2×D4—261no—
173C2×D4—261no—
174C2×D4—261no—
175C2×D4—261no—
176C2×D4—261no—
177C2×D4—522no—
178C2×D4—522no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—131no—
182C22×C4—261no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4—261no—
186C22×C4—261no—
187C22×C4—261no—
188C22×C4—261no—
189C22×C4C22×D1311yescharacteristic
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—261no—
193C2×C8—261no—
194C2×C8—261no—
195C2×C8D5212yescomplemented
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—261no—
200C4⋊C4—261no—
201C4⋊C4C22⋊D1312yes—
202C22⋊C4—264no—
203C22⋊C4—522no—
204C13#203411yescharacteristic, complemented, Sylow
205C23—132no—
206C23—261no—
207C23—261no—
208C23—261no—
209C23—261no—
210C23—261no—
211C23—261no—
212C23—262no—
213C23—521no—
214C23—521no—
215C23—521no—
216C23—521no—
217C23—521no—
218C23—521no—
219C23D4×D1311yescharacteristic
220D4—262no—
221D4—262no—
222D4—528no—
223D4—521no—
224D4—521no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—521no—
237C2×C4—521no—
238C2×C4—521no—
239C2×C4—521no—
240C2×C4—521no—
241C2×C4C2×D5211yescharacteristic
242C2×C4#612711yescharacteristic
243C2×C4D4×D1311yescharacteristic
244C2×C4#613111yescharacteristic
245C2×C4#613111yescharacteristic
246C2×C4C2×C22⋊D1311yescharacteristic
247C8—22no—
248C8—521no—
249C22—262no—
250C22—262no—
251C22—262no—
252C22—521no—
253C22—521no—
254C22—521no—
255C22—521no—
256C22—522no—
257C22—522no—
258C22—522no—
259C22—1041no—
260C22—1041no—
261C22—1041no—
262C22—1041no—
263C22#8814811yescharacteristic
264C22#8814911yescharacteristic
265C22SD16×D1311yescharacteristic
266C22#8816811yescharacteristic
267C22#8816811yescharacteristic
268C22#8817011yescharacteristic
269C22#8819111yescharacteristic
270C4—42no—
271C4—81no—
272C4—521no—
273C4—1041no—
274C4#8814811yescharacteristic
275C4#8814911yescharacteristic
276C4#8818411yescharacteristic
277C4#8820111yescharacteristic
278C2—522no—
279C2—1042no—
280C2#1171852411yescharacteristic
281C2#1171852511yescharacteristic
282C2#1171852611yescharacteristic
283C2#1171852711yescharacteristic
284C2#1171865211yescharacteristic
285C2#1171883011yescharacteristic
286C2#1171883311yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#106C2
socleC23×C13C2×D4
prime radicalC2×#88149C2
hypercenterC2×#106D13
hypocenterC13#2034
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C13×#106C2semidirect
3. C2×#88061C2semidirect
4. C2×#88060C2semidirect
5. #11718648C2semidirect
6. C2×#88049C2semidirect
7. #11718121C2semidirect
49. C2×C8×C13D4semidirect
107. C2×#106D13semidirect
195. C2×C8D52semidirect
204. C13#2034semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C2×C13×#1062
C2×#880612
C2×#880602
#117186482
C2×#880492
#117181212
#203413