Finite Group Databasebeta

← #15778105

Subgroups — #15778105

Order 3328.

464 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 135 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×#11718140C212yesmaximal
2C4×#88076C212yesmaximal
3#13112963C212yesmaximal
4C13×#2327C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C2211yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#391C411yescharacteristic
9C13×#391C2211yescharacteristic
10C13×#387—22no—
11C13×#387—22no—
12C13×#382C411yescharacteristic
13C13×#376C411yescharacteristic
14C2×#88076C2214yes—
15C4×#6099—22no—
16#11718140C418yescomplemented
17#11718122—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×Q8×C13C2311yescharacteristic
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8C2×C414yes—
22C4×Q8×C13—42no—
23C4×Q8×C13—42no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D412yes—
29C2×C42×C13—21no—
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D412yes—
34C2×#6099—24no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95—21no—
38C13×#95—21no—
39C13×#95—22no—
40#88076—24no—
41#88076C2×C418yes—
42#88043—42no—
43C4×#1055—42no—
44#12631—131nomaximal, Sylow
45C2×Q8×C13—21no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13C4212yes—
51C2×Q8×C13C22×C412yes—
52C2×Q8×C13#4112yes—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13C22⋊C412yes—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D412yes—
62C13×C4⋊C4—28no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C42×C13—22no—
68C42×C13—22no—
69C42×C13—22no—
70C42×C13—21no—
71C42×C13—41no—
72C42×C13—42no—
73C42×C13C4212yes—
74#6099—28no—
75#6099—44no—
76C2×#1055—44no—
77#2327D1311yescharacteristic
78C2×#356—132no—
79C4×#101—132no—
80#1394—132no—
81C23×C13C2×C22⋊C411yescharacteristic
82Q8×C13—42no—
83Q8×C13—42no—
84Q8×C13—42no—
85Q8×C13—42no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13#9912yes—
107C2×C4×C13C2×C4211yescharacteristic
108C2×C4×C13#11711yescharacteristic
109C2×C4×C13C4×D414yes—
110#1055—48no—
111C2×C4⋊Q8C2×D1311yescharacteristic
112C2×C4×Q8Dic1311yescharacteristic
113C2×C4×Q8C2×D1311yescharacteristic
114C2×#101—134no—
115C4×M16—262no—
116#391Dic1311yescharacteristic
117#391C2×D1311yescharacteristic
118#387—22no—
119#387—22no—
120#382Dic1311yescharacteristic
121#376Dic1311yescharacteristic
122#356—138no—
123#343—262no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13C4×C22⋊C411yescharacteristic
127C22×C13C2×#9911yescharacteristic
128C22×C13#41011yescharacteristic
129C4×C13—22no—
130C4×C13—24no—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13—42no—
134C4×C13—41no—
135C4×C13—42no—
136C4×C13—42no—
137C4×C13—81no—
138C4×C13—81no—
139C22×Q8C2×Dic1311yescharacteristic
140C22×Q8C22×D1311yescharacteristic
141C2×M16—264no—
142C4⋊Q8—22no—
143C4⋊Q8C4×D1314yes—
144C4×Q8—42no—
145C4×Q8—42no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4C2×Dic1311yescharacteristic
149C2×C4⋊C4C2×Dic1311yescharacteristic
150C2×C4⋊C4C22⋊D1312yes—
151C2×C42—21no—
152C2×C42C2×Dic1311yescharacteristic
153C2×C42C2×Dic1311yescharacteristic
154C2×C42C2×Dic1311yescharacteristic
155C2×C42C22⋊D1312yes—
156#101—138no—
157#101—264no—
158#97—522no—
159C4×C8—522no—
160#95—21no—
161#95—22no—
162#95—22no—
163#95—21no—
164#95—22no—
165C2×C13—21no—
166C2×C13—21no—
167C2×C13C4×#9911yescharacteristic
168C2×C13#213311yescharacteristic
169C2×C13#213511yescharacteristic
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8C4×Dic1312yes—
176C2×Q8C2×C4×D1312yes—
177C2×Q8#612712yes—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4C22⋊Dic1312yes—
183C22×C4C22⋊Dic1311yescharacteristic
184C22×C4C22⋊Dic1311yescharacteristic
185C22×C4C22×Dic1311yescharacteristic
186C22×C4C2×C22⋊D1312yes—
187M16—268no—
188M16—524no—
189C2×C8—524no—
190C4⋊C4—28no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C42—22no—
196C42—22no—
197C42—22no—
198C42—21no—
199C42—41no—
200C42—42no—
201C42C4×Dic1312yes—
202C13#1263111yescharacteristic, complemented, Sylow
203C23C2×C22⋊Dic1311yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—42no—
207Q8—42no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4#8807412yes—
229C2×C4C2×C4×Dic1311yescharacteristic
230C2×C4#8818011yescharacteristic
231C2×C4C4×C22⋊D1314yes—
232C8—528no—
233C22—21no—
234C22—21no—
235C22C4×C22⋊Dic1311yescharacteristic
236C22C2×#8807411yescharacteristic
237C22#1171890111yescharacteristic
238C4—24no—
239C4—21no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4—81no—
247C4—81no—
248C2—21no—
249C2—21no—
250C2C4×#8807411yescharacteristic
251C2#1311652511yescharacteristic
252C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC2×C4×C13C2×C42
FrattiniC22×Q8C22×D13
FittingC13×#2327C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#2327D13
hypocenterC13#12631
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2327

Complements

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

NH ≅ G/Ntype
16. #11718140C4semidirect
202. C13#12631semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
C4×#880762
#131129632
C13×#23272
#1263113