Finite Group Databasebeta

← #15782000

Subgroups — #15782000

Order 3328.

406 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 101 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#13116551C212yesmaximal
2#13115712C211yesmaximal, characteristic
3#13112941C212yesmaximal, complemented
4#13112920C211yesmaximal, characteristic, complemented
5C13×#3162C211yesmaximal, characteristic, complemented
6C13×#533—21no—
7C22×D104C2211yescharacteristic
8C13×#501—24no—
9C13×#427—21no—
10C13×#427C2212yes—
11C2×C13×#97C2211yescharacteristic
12C2×#88061—21no—
13C2×#88057C2211yescharacteristic
14C2×#88052C2212yes—
15#11718600—21no—
16#11718083—24no—
17C22×D52—21no—
18C22×C8×C13D411yescharacteristic
19C22×C8×C13C2311yescharacteristic
20C13×C4⋊Q8—22no—
21C13×#125—22no—
22C13×C22⋊Q8—42no—
23C4×Q8×C13—42no—
24C13×#117—22no—
25C2×C42×C13D411yescharacteristic
26C2×#6103—42no—
27C2×C4⋊Dic13—21no—
28C2×D104—22no—
29C2×D104—22no—
30C2×D104—21no—
31C2×D104Q812yescomplemented
32C13×#107—22no—
33C13×#107D414yes—
34C13×#106—22no—
35C13×#106—22no—
36C13×#97—22no—
37#88061—42no—
38#88057—22no—
39#88052—22no—
40#88052—22no—
41C2×#6090—22no—
42#13367—131nomaximal, Sylow
43C23×D13—41no—
44C2×Q8×C13—42no—
45C22×C4×C13D812yes—
46C22×C4×C13C2×D411yescharacteristic
47C22×Dic13—41no—
48C2×D52—22no—
49C2×D52—41no—
50C2×D52—41no—
51C2×D52—41no—
52C2×D52—41no—
53C2×D52—41no—
54C2×C8×C13—21no—
55C2×C8×C13—21no—
56C2×C8×C13SD1612yes—
57C2×C8×C13C2×D412yes—
58C2×C8×C13C2×Q811yescharacteristic
59C2×C8×C13#4112yes—
60C2×C8×C13#4111yescharacteristic
61C13×C4⋊C4—24no—
62C13×C4⋊C4—44no—
63C13×C4⋊C4—42no—
64C13×C22⋊C4—42no—
65C42×C13—21no—
66C42×C13—21no—
67C42×C13—42no—
68#6103—84no—
69C4⋊Dic13—41no—
70C4⋊Dic13—41no—
71D104—24no—
72D104—42no—
73#6090—42no—
74#3162D1311yescharacteristic, complemented
75#2140—132no—
76#1972—131no—
77#1386—132no—
78#1377—131no—
79C23×C13C2×D811yescharacteristic
80C22×D13—42no—
81C22×D13—82no—
82C22×D13—82no—
83C22×D13—81no—
84C22×D13—81no—
85Q8×C13—84no—
86C2×C4×C13—22no—
87C2×C4×C13—42no—
88C2×C4×C13—44no—
89C2×C4×C13#12011yescharacteristic
90C2×C4×C13C22⋊Q811yescharacteristic
91C2×C4×C13#12411yescharacteristic
92C2×C4×C13C2×SD1611yescharacteristic
93C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
94C2×C4×C13#13711yescharacteristic
95C2×Dic13—82no—
96C2×Dic13—81no—
97D52—42no—
98D52—42no—
99D52—81no—
100D52—81no—
101C8×C13—22no—
102C8×C13C22⋊Q812yes—
103C8×C13#12412yes—
104C22×D8—131no—
105#533—21no—
106C2×M32—132no—
107#501—24no—
108#427—21no—
109#427C2×D1312yes—
110C2×#106—131no—
111C2×#102—261no—
112C2×#97C2×D1311yescharacteristic
113#390—261no—
114#357—264no—
115C22×C13—22no—
116C22×C13#44711yescharacteristic
117C22×C13#47411yescharacteristic
118C22×C13#48611yescharacteristic
119C2×D13—84no—
120C2×D13—82no—
121C2×D13—161no—
122C2×D13—161no—
123C2×D13—162no—
124C4×C13—42no—
125C4×C13—84no—
126C4×C13#39311yescharacteristic
127C4×C13#44811yescharacteristic
128C4×C13#47611yescharacteristic
129C4×C13#48911yescharacteristic
130Dic13—161no—
131C22×D4—261no—
132C2×D8—132no—
133C2×D8—262no—
134C2×D8—261no—
135C2×D8—262no—
136C22×C8C22⋊D1311yescharacteristic
137C22×C8C22×D1311yescharacteristic
138C4⋊Q8—22no—
139#125—22no—
140C22⋊Q8—42no—
141C4×Q8—42no—
142#117—22no—
143C2×C4⋊C4—261no—
144C2×C22⋊C4—522no—
145C2×C42C22⋊D1311yescharacteristic
146M32—262no—
147M32—262no—
148C2×C16—262no—
149#107—22no—
150#107C22⋊D1314yes—
151#106—22no—
152#106—22no—
153#106—262no—
154#102—522no—
155#97—22no—
156C2×C13—21no—
157C2×C13—21no—
158C2×C13#202311yescharacteristic
159C2×C13#219012yes—
160D13—162no—
161C24—521no—
162C2×Q8—42no—
163C2×D4—262no—
164C2×D4—521no—
165C2×D4—521no—
166C2×D4—521no—
167C2×D4—521no—
168C2×D4—521no—
169C22×C4—521no—
170C22×C4#610412yes—
171C22×C4C2×C22⋊D1311yescharacteristic
172D8—264no—
173D8—522no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8#610612yes—
177C2×C8Q8×D1311yescharacteristic
178C2×C8#613112yes—
179C2×C8#613111yescharacteristic
180C2×C8C2×C22⋊D1312yes—
181C4⋊C4—24no—
182C4⋊C4—44no—
183C4⋊C4—42no—
184C4⋊C4—521no—
185C4⋊C4—521no—
186C22⋊C4—42no—
187C22⋊C4—1044no—
188C42—21no—
189C42—21no—
190C42—42no—
191C16—522no—
192C13#1336711yescharacteristic, complemented, Sylow
193C23—522no—
194C23—1042no—
195C23—1042no—
196C23—1041no—
197C23—1041no—
198C23C2×#610411yescharacteristic
199Q8—84no—
200D4—522no—
201D4—522no—
202D4—1041no—
203D4—1041no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—1042no—
208C2×C4—1041no—
209C2×C4#8818611yescharacteristic
210C2×C4C2×#610611yescharacteristic
211C2×C4#8819611yescharacteristic
212C2×C4#8820011yescharacteristic
213C2×C4#8820111yescharacteristic
214C2×C4#8820711yescharacteristic
215C8—22no—
216C8#8820012yes—
217C8#8820112yes—
218C22—22no—
219C22—1044no—
220C22—1042no—
221C22—2081no—
222C22—2081no—
223C22—2082no—
224C22#1171874811yescharacteristic
225C22#1171874911yescharacteristic
226C22#1171887811yescharacteristic
227C4—42no—
228C4—84no—
229C4—2081no—
230C4#1171874511yescharacteristic
231C4#1171875011yescharacteristic
232C4#1171888811yescharacteristic
233C4#1171889211yescharacteristic
234C2—21no—
235C2—21no—
236C2—2082no—
237C2#1311596911yescharacteristic
238C2#1311678212yes—
subgroupG/H
centerC22#11718878
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#3162C2
socleC22×C13#447
prime radicalC22×D104C22
hypercenter#3162D13
hypocenterC13#13367
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #3162

Complements

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

NH ≅ G/Ntype
3. #13112941C2semidirect
4. #13112920C2semidirect
5. C13×#3162C2semidirect
31. C2×D104Q8semidirect
74. #3162D13semidirect
192. C13#13367semidirect

Maximal subgroups

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

subgroupindex
#131165512
#131157122
#131129412
#131129202
C13×#31622
#1336713