Finite Group Databasebeta

← #15778930

Subgroups — #15778930

Order 3328.

432 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 119 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
2#13114832C212yesmaximal
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—
15#11718585—22no—
16#11718140—24no—
17#11718122—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×Q8×C13C2311yescharacteristic
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8D412yes—
22C13×C4⋊Q8Q812yes—
23C4×Q8×C13—42no—
24C4×Q8×C13—42no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C42×C13—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13D412yes—
35C2×#6099—24no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95—21no—
39C13×#95—21no—
40C13×#95—22no—
41#88076—24no—
42#88076—24no—
43C4⋊#1055—44no—
44#12804—131nomaximal, Sylow
45C2×Q8×C13—21no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13C4⋊C412yes—
51C2×Q8×C13C2×D411yescharacteristic
52C2×Q8×C13C2×Q811yescharacteristic
53C2×Q8×C13#4112yes—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D412yes—
63C13×C4⋊C4—24no—
64C13×C4⋊C4—24no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C42×C13—22no—
70C42×C13—24no—
71C42×C13—21no—
72C42×C13—41no—
73C42×C13—42no—
74C42×C13C4⋊C412yes—
75#6099—44no—
76#6099—44no—
77C2×#1055—44no—
78#2327D1311yescharacteristic
79C2×#356—132no—
80#1801—132no—
81#1394—132no—
82C23×C13C2×C22⋊C411yescharacteristic
83Q8×C13—41no—
84Q8×C13—41no—
85Q8×C13—42no—
86Q8×C13—42no—
87Q8×C13—42no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13#9912yes—
109C2×C4×C13C2×C4⋊C411yescharacteristic
110C2×C4×C13#11711yescharacteristic
111C2×C4×C13#12112yes—
112C2×C4×C13C22⋊Q812yes—
113#1055—84no—
114C2×C4⋊Q8C2×D1311yescharacteristic
115C2×C4×Q8Dic1311yescharacteristic
116C2×C4×Q8C2×D1311yescharacteristic
117#423—262no—
118C2×#101—134no—
119#391Dic1311yescharacteristic
120#391C2×D1311yescharacteristic
121#387—22no—
122#387—22no—
123#382Dic1311yescharacteristic
124#376Dic1311yescharacteristic
125#356—264no—
126#343—262no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13#38011yescharacteristic
130C22×C13C2×#9911yescharacteristic
131C22×C13#41011yescharacteristic
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—42no—
138C4×C13—42no—
139C4×C13—41no—
140C4×C13—42no—
141C4×C13—81no—
142C4×C13—81no—
143C22×Q8C2×Dic1311yescharacteristic
144C22×Q8C22×D1311yescharacteristic
145C2×M16—264no—
146C4⋊Q8—22no—
147C4⋊Q8Dic2612yes—
148C4⋊Q8D5212yes—
149C4×Q8—42no—
150C4×Q8—42no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×Dic1311yescharacteristic
154C2×C4⋊C4C2×Dic1311yescharacteristic
155C2×C4⋊C4C22⋊D1312yes—
156C2×C42—21no—
157C2×C42C2×Dic1311yescharacteristic
158C2×C42C2×Dic1311yescharacteristic
159C2×C42C2×Dic1311yescharacteristic
160C2×C42C22⋊D1312yes—
161C4⋊C8—524no—
162#101—264no—
163#101—264no—
164#95—21no—
165#95—22no—
166#95—22no—
167#95—21no—
168#95—22no—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13#179911yescharacteristic
172C2×C13#213311yescharacteristic
173C2×C13#213511yescharacteristic
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C4⋊Dic1312yes—
180C2×Q8C2×Dic2611yescharacteristic
181C2×Q8C2×D5211yescharacteristic
182C2×Q8#612712yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4C22⋊Dic1312yes—
188C22×C4C22⋊Dic1311yescharacteristic
189C22×C4C22⋊Dic1311yescharacteristic
190C22×C4C22×Dic1311yescharacteristic
191C22×C4C2×C22⋊D1312yes—
192M16—524no—
193M16—524no—
194C2×C8—524no—
195C4⋊C4—24no—
196C4⋊C4—24no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C42—24no—
202C42—22no—
203C42—21no—
204C42—41no—
205C42—42no—
206C42C4⋊Dic1312yes—
207C13#1280411yescharacteristic, complemented, Sylow
208C23C2×C22⋊Dic1311yescharacteristic
209Q8—41no—
210Q8—41no—
211Q8—42no—
212Q8—42no—
213Q8—42no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4#8807412yes—
235C2×C4#8817812yes—
236C2×C4C2×C4⋊Dic1311yescharacteristic
237C2×C4#8818011yescharacteristic
238C2×C4#8818412yes—
239C8—1044no—
240C22—21no—
241C22—21no—
242C22#1171887311yescharacteristic
243C22C2×#8807411yescharacteristic
244C22#1171890111yescharacteristic
245C4—22no—
246C4—22no—
247C4—22no—
248C4—21no—
249C4—21no—
250C4—42no—
251C4—41no—
252C4—42no—
253C4—42no—
254C4—81no—
255C4—81no—
256C2—21no—
257C2—21no—
258C2#1311482411yescharacteristic
259C2#1311652511yescharacteristic
260C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2327C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#2327D13
hypocenterC13#12804
LCSG ▷ C22×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
207. C13#12804semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131148322
#131129632
C13×#23272
#1280413