Finite Group Databasebeta

← #261×#330 #16780684

Subgroups — #261×#330 #16780684

Order 3328.

532 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 116 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#125×#261C211yesmaximal, characteristic
2#97×#261C212yesmaximal
3D13⋊#330C211yesmaximal, characteristic
4#13129713C212yesmaximal
5D13×#330C211yesmaximal, characteristic
6D13×#125C2211yescharacteristic
7C2×#88100—22no—
8C2×C8×#261—22no—
9#11719083C412yes—
10#11719082—22no—
11C4⋊C4×#261—22no—
12C4⋊C4×#261C412yes—
13#11719060C2211yescharacteristic
14C42×#261C2211yescharacteristic
15#11719047C2212yes—
16D13×#97C2212yes—
17#11718242C414yescomplemented
18C13×#330C411yescharacteristic, complemented
19#11718135C411yescharacteristic, complemented
20#11718057C412yescomplemented
21C2×C4⋊#261—22no—
22C2×C4⋊#261C2×C412yes—
23C2×C4×#261—22no—
24C2×C4×#261C2×C411yescharacteristic
25C2×C4×#261C2×C411yescharacteristic
26C2×C4×#261D412yes—
27C2×C4×#261D412yes—
28C2×D13⋊C8—22no—
29C13×#125C2×C411yescharacteristic
30C2×C8×D13—22no—
31C4⋊C4×D13—22no—
32C4⋊C4×D13C2×C412yes—
33#88144C2×C412yes—
34#88143—22no—
35C42×D13C2311yescharacteristic
36#88124C2×C411yescharacteristic
37(C2×#261)⋊C4—22no—
38(C2×#261)⋊C4—22no—
39(C2×#261)⋊C4—22no—
40#88110—22no—
41#88110C2×C414yes—
42#88100—28no—
43C8×#261—28no—
44C13×#97C2×C412yes—
45#88055—22no—
46#88043C2×C412yes—
47C4×#330—131nomaximal, Sylow
48C22×#261—22no—
49C22×#261C22⋊C411yescharacteristic
50C22×#261C22⋊C412yes—
51C22×#261C22⋊C411yescharacteristic
52C2×C4×D13—22no—
53C2×C4×D13C22×C411yescharacteristic
54C2×C4×D13C2×D412yes—
55C2×#1057—24no—
56C4⋊#261—42no—
57C4⋊#261—44no—
58C4×#261—22no—
59C4×#261—24no—
60C4×#261—24no—
61C4×#261—41no—
62C4×#261—44no—
63D13⋊C8—24no—
64D13⋊C8—24no—
65C2×C8×C13—22no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4C4212yes—
68C42×C13C22×C411yescharacteristic
69C4⋊Dic13—22no—
70C4⋊Dic13C4212yes—
71#6101—22no—
72#6101—22no—
73#6101—22no—
74C4×Dic13C22×C411yescharacteristic
75C4×Dic13#4112yes—
76C2×#1055—22no—
77C8×D13—24no—
78C8×D13—24no—
79C4×#125—131no—
80C4×#97—132no—
81C2×#330—131no—
82C2×#330—131no—
83#1295—132no—
84C22×D13C2×C22⋊C411yescharacteristic
85C2×#261—22no—
86C2×#261—22no—
87C2×#261—21no—
88C2×#261—22no—
89C2×#261—42no—
90C2×#261—42no—
91C2×#261—42no—
92C2×#261#10112yes—
93C2×#261#10414yes—
94C2×#261#10414yes—
95C2×C4×C13—22no—
96C2×C4×C13C2×C4211yescharacteristic
97C2×C4×C13C4×D412yes—
98C2×Dic13—22no—
99C2×Dic13#11711yescharacteristic
100C2×Dic13C4×D412yes—
101C4×D13—21no—
102C4×D13—21no—
103C4×D13—22no—
104C4×D13—22no—
105C4×D13—42no—
106C4×D13—42no—
107#1057—28no—
108C8×C13—24no—
109#1055—24no—
110C2×#125—131no—
111C2×#97—132no—
112C2×#97—132no—
113C2×#97—262no—
114C2×C4×C8—262no—
115#389—132no—
116#387—262no—
117#382—131no—
118C4×C4⋊C4—132no—
119C4×C4⋊C4—262no—
120C43—131no—
121#330—134no—
122#330—131no—
123#330—132no—
124#330#26111yescharacteristic, direct product factor
125C22×C13C4×C22⋊C411yescharacteristic
126C2×D13C2×#10111yescharacteristic
127C2×D13#41311yescharacteristic
128C2×D13C2×#10412yes—
129C2×D13C2×#10412yes—
130#261—24no—
131#261—41no—
132#261—82no—
133#261#33014yesdirect product factor
134C4×C13—21no—
135C4×C13—22no—
136C4×C13—42no—
137Dic13—21no—
138Dic13—22no—
139Dic13—42no—
140C22×C8—262no—
141C22×C8—262no—
142#125—132no—
143#125—131no—
144#125—262no—
145#125C2×#26111yescharacteristic
146C2×C4⋊C4—132no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4—262no—
150C2×C42—131no—
151C2×C42—131no—
152C2×C42—132no—
153C2×C42—132no—
154C2×C42—131no—
155C2×C42—262no—
156#97—134no—
157#97—132no—
158#97—262no—
159#97—262no—
160#97—268no—
161#97C2×#26112yes—
162C4×C8—268no—
163#95—262no—
164#95—262no—
165#95—262no—
166C2×C13C4×#10111yescharacteristic
167C2×C13C4×#10412yes—
168D13C2×#33011yescharacteristic
169D13#152412yes—
170D13#152611yescharacteristic
171C22×C4—131no—
172C22×C4—132no—
173C22×C4—131no—
174C22×C4—132no—
175C22×C4—131no—
176C22×C4—262no—
177C22×C4—262no—
178C2×C8—22no—
179C2×C8—264no—
180C2×C8—264no—
181C2×C8—264no—
182C2×C8—264no—
183C2×C8—264no—
184C2×C8—262no—
185C4⋊C4—22no—
186C4⋊C4—132no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—524no—
192C4⋊C4—522no—
193C4⋊C4C4×#26112yes—
194C42—131no—
195C42—132no—
196C42—264no—
197C42—264no—
198C42—262no—
199C42—524no—
200C42—521no—
201C42C22×#26111yescharacteristic
202C13C4×#33011yescharacteristic, complemented, Sylow
203C23—131no—
204C2×C4—22no—
205C2×C4—134no—
206C2×C4—132no—
207C2×C4—134no—
208C2×C4—132no—
209C2×C4—131no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—522no—
220C2×C4—522no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4C2×C4×#26111yescharacteristic
225C2×C4D4×#26112yes—
226C8—24no—
227C8—264no—
228C8—268no—
229C22—131no—
230C22—131no—
231C22—132no—
232C22—132no—
233C22C22⋊C4×#26111yescharacteristic
234C4—21no—
235C4—22no—
236C4—42no—
237C4—134no—
238C4—264no—
239C4—261no—
240C4—262no—
241C4—521no—
242C4—522no—
243C4—1042no—
244C2—131no—
245C2—132no—
246C2—131no—
247C2#101×#26111yescharacteristic
248C2#104×#26112yes—
subgroupG/H
centerC22C22⋊C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC42C22×#261
FittingC13×#330C4
socleC22×C13C4×C22⋊C4
prime radicalC22×D13C2×C22⋊C4
cosocleC42×D13C23
hypercenter#330#261
hypocenterC13C4×#330
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
17. #11718242C4semidirect
18. C13×#330C4semidirect
19. #11718135C4semidirect
20. #11718057C4semidirect
124. #330#261direct (N × H)
133. #261#330direct (N × H)
202. C13C4×#330semidirect

Maximal subgroups

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

subgroupindex
#125×#2612
#97×#2612
D13⋊#3302
#131297132
D13×#3302
C4×#33013