Finite Group Databasebeta

← #15778926

Subgroups — #15778926

Order 3328.

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

normal subgroups only

This group has 480 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×#11718134C212yesmaximal
2#13114832C212yesmaximal, complemented
3#13112963C212yesmaximal, complemented
4C13×#2326C211yesmaximal, characteristic
5C2×C13×#124C2211yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C411yescharacteristic
8C13×#391C2211yescharacteristic
9C13×#390C411yescharacteristic
10C13×#388—22no—
11C13×#385—22no—
12C13×#384C411yescharacteristic
13C13×#376C411yescharacteristic
14C2×#88076C2214yes—
15#11718585—22no—
16#11718134—24no—
17#11718122—22no—
18C22×Q8×C13C2311yescharacteristic
19C22×D4×C13C2×C411yescharacteristic
20C23×C4×C13—21no—
21C13×#124—22no—
22C13×#124D412yes—
23C13×#124Q812yes—
24C4×Q8×C13—42no—
25C4×D4×C13—42no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—22no—
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D412yes—
37C2×#6099—24no—
38C13×#95—21no—
39C13×#95—21no—
40C13×#95—22no—
41#88076—24no—
42#88076—24no—
43C4⋊#1055—44no—
44#12803—131nomaximal, Sylow
45C24×C13—21no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13C2×D411yescharacteristic
49C2×Q8×C13C2×Q811yescharacteristic
50C2×Q8×C13#4112yes—
51C2×D4×C13—21no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13C4⋊C412yes—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—42no—
59C22×C4×C13—82no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D412yes—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—82no—
69C13×C22⋊C4—24no—
70C13×C22⋊C4—24no—
71C13×C22⋊C4—42no—
72C13×C22⋊C4—82no—
73C42×C13—22no—
74C42×C13—24no—
75C42×C13—21no—
76C42×C13—41no—
77C42×C13C4⋊C412yes—
78#6099—44no—
79#6099—44no—
80C2×#1055—44no—
81#2326D1311yescharacteristic
82C2×#355—132no—
83#1801—132no—
84#1394—132no—
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—42no—
88C23×C13—41no—
89C23×C13—41no—
90C23×C13C2×C22⋊C411yescharacteristic
91Q8×C13—41no—
92Q8×C13—41no—
93Q8×C13—42no—
94D4×C13—42no—
95D4×C13—42no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—84no—
114C2×C4×C13#9912yes—
115C2×C4×C13C2×C4⋊C411yescharacteristic
116C2×C4×C13#11711yescharacteristic
117C2×C4×C13#12112yes—
118C2×C4×C13C22⋊Q812yes—
119#1055—84no—
120C2×#124C2×D1311yescharacteristic
121C2×C4×Q8C2×D1311yescharacteristic
122C2×C4×D4Dic1311yescharacteristic
123#423—262no—
124C2×#101—134no—
125#391C2×D1311yescharacteristic
126#390Dic1311yescharacteristic
127#388—22no—
128#385—22no—
129#384Dic1311yescharacteristic
130#376Dic1311yescharacteristic
131#355—264no—
132#343—262no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—44no—
136C22×C13—42no—
137C22×C13—82no—
138C22×C13—81no—
139C22×C13—81no—
140C22×C13#38011yescharacteristic
141C22×C13C2×#9911yescharacteristic
142C22×C13#41011yescharacteristic
143C4×C13—22no—
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—22no—
148C4×C13—42no—
149C4×C13—42no—
150C4×C13—41no—
151C4×C13—81no—
152C4×C13—81no—
153C22×Q8C22×D1311yescharacteristic
154C22×D4C2×Dic1311yescharacteristic
155C23×C4—21no—
156C2×M16—264no—
157#124—22no—
158#124Dic2612yes—
159#124D5212yes—
160C4×Q8—42no—
161C4×D4—42no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4C2×Dic1311yescharacteristic
164C2×C4⋊C4C2×Dic1311yescharacteristic
165C2×C4⋊C4C22⋊D1312yes—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—22no—
169C2×C42C2×Dic1311yescharacteristic
170C2×C42C2×Dic1311yescharacteristic
171C2×C42C2×Dic1311yescharacteristic
172C2×C42C22⋊D1312yes—
173C4⋊C8—524no—
174#101—264no—
175#101—264no—
176#95—21no—
177#95—21no—
178#95—22no—
179C2×C13—21no—
180C2×C13—21no—
181C2×C13—82no—
182C2×C13#179911yescharacteristic
183C2×C13#213311yescharacteristic
184C2×C13#213411yescharacteristic
185C24—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8C2×Dic2611yescharacteristic
189C2×Q8C2×D5211yescharacteristic
190C2×Q8#612712yes—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C4⋊Dic1312yes—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—82no—
200C22×C4C22⋊Dic1311yescharacteristic
201C22×C4C22⋊Dic1312yes—
202C22×C4C22⋊Dic1311yescharacteristic
203C22×C4C22×Dic1311yescharacteristic
204C22×C4C2×C22⋊D1312yes—
205M16—524no—
206M16—524no—
207C2×C8—524no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C4⋊C4—41no—
211C4⋊C4—82no—
212C22⋊C4—24no—
213C22⋊C4—24no—
214C22⋊C4—42no—
215C22⋊C4—82no—
216C42—24no—
217C42—22no—
218C42—21no—
219C42—41no—
220C42C4⋊Dic1312yes—
221C13#1280311yescharacteristic, complemented, Sylow
222C23—22no—
223C23—42no—
224C23—42no—
225C23—41no—
226C23—41no—
227C23C2×C22⋊Dic1311yescharacteristic
228Q8—41no—
229Q8—41no—
230Q8—42no—
231D4—42no—
232D4—42no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—84no—
251C2×C4#8807412yes—
252C2×C4#8817812yes—
253C2×C4C2×C4⋊Dic1311yescharacteristic
254C2×C4#8818011yescharacteristic
255C2×C4#8818412yes—
256C8—1044no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—82no—
262C22—81no—
263C22—81no—
264C22#1171887311yescharacteristic
265C22C2×#8807411yescharacteristic
266C22#1171890111yescharacteristic
267C4—22no—
268C4—22no—
269C4—22no—
270C4—21no—
271C4—21no—
272C4—42no—
273C4—42no—
274C4—41no—
275C4—81no—
276C4—81no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2#1311482411yescharacteristic
281C2#1311652511yescharacteristic
282C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2326C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC22×Q8×C13C23
hypercenter#2326D13
hypocenterC13#12803
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #13114832C2semidirect
3. #13112963C2semidirect
221. C13#12803semidirect

Maximal subgroups

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

subgroupindex
C2×#117181342
#131148322
#131129632
C13×#23262
#1280313