Finite Group Databasebeta

← #15773514

Subgroups — #15773514

Order 3328.

414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#88076C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112842C214yesmaximal
4C13×#2546C211yesmaximal, characteristic
5C2×C13×C4⋊Q8—21no—
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398C412yes—
9C13×#398C2212yes—
10C13×#391—21no—
11C13×#389—21no—
12C13×#389—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076—21no—
15#11718587—21no—
16C4×#6099—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13—21no—
21C22×Q8×C13D411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C13×C4⋊Q8—44no—
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×#6099—22no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43#88076—24no—
44C22⋊#1055—22no—
45C4⋊#1055—41no—
46#88043—41no—
47#88043—41no—
48C4×#1055—41no—
49#11782—131nomaximal, Sylow
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—41no—
53C2×Q8×C13—42no—
54C2×Q8×C13—42no—
55C2×Q8×C13—42no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C13×C4⋊C4—24no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—44no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—44no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—42no—
81#6099—24no—
82#6099—42no—
83C2×#1055—42no—
84C2×#1055—42no—
85#2546D1311yescharacteristic
86C4×#101—131no—
87#1467—131no—
88#1346—134no—
89C23×C13C2×C22⋊C411yescharacteristic
90Q8×C13—44no—
91Q8×C13—84no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—24no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13#9911yescharacteristic
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#10412yes—
115C2×C4×C13AGL(1,ℤ/8)12yes—
116#1055—44no—
117#1055—82no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8Dic1311yescharacteristic
120C2×C4×Q8C2×D1311yescharacteristic
121#432—261no—
122C2×#101—261no—
123C4×M16—261no—
124#398Dic1312yes—
125#398C2×D1312yes—
126#391—21no—
127#389—21no—
128#389—21no—
129C4×C4⋊C4Dic1311yescharacteristic
130#343—132no—
131#324—132no—
132#324—261no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13C2×#9911yescharacteristic
136C22×C13#41811yescharacteristic
137C22×C13C2×#10411yescharacteristic
138C4×C13—21no—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—44no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13—41no—
145C4×C13—41no—
146C4×C13—82no—
147C4×C13#35612yes—
148C22×Q8—21no—
149C22×Q8C22⋊D1311yescharacteristic
150C2×M16—262no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4⋊Q8—44no—
154C4×Q8—41no—
155C4×Q8—41no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4C2×Dic1312yes—
161C2×C4⋊C4C2×Dic1311yescharacteristic
162C2×C4⋊C4C22⋊D1311yescharacteristic
163C2×C4⋊C4C22×D1311yescharacteristic
164C2×C42—21no—
165C2×C42C2×Dic1311yescharacteristic
166C2×C42C22⋊D1311yescharacteristic
167C2×C42C22⋊D1311yescharacteristic
168C4⋊C8—521no—
169#101—264no—
170C22⋊C8—262no—
171#97—521no—
172#97—521no—
173C4×C8—521no—
174#95—22no—
175#95—22no—
176#95C2×Dic1312yes—
177C2×C13—21no—
178C2×C13—21no—
179C2×C13#150711yescharacteristic
180C2×C13#212311yescharacteristic
181C2×C13C2×#35611yescharacteristic
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—41no—
185C2×Q8—42no—
186C2×Q8—42no—
187C2×Q8—42no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4C22⋊Dic1311yescharacteristic
191C22×C4C22⋊Dic1311yescharacteristic
192C22×C4C22⋊Dic1311yescharacteristic
193C22×C4C22⋊Dic1311yescharacteristic
194C22×C4C22×Dic1311yescharacteristic
195C22×C4C2×C22⋊D1311yescharacteristic
196C22×C4C2×C22⋊D1311yescharacteristic
197M16—264no—
198M16—522no—
199C2×C8—522no—
200C2×C8—522no—
201C4⋊C4—24no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—44no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—44no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—42no—
217C13#1178211yescharacteristic, complemented, Sylow
218C23C2×C22⋊Dic1311yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4#8807411yescharacteristic
242C2×C4#8807411yescharacteristic
243C2×C4#8807712yes—
244C2×C4#8818612yes—
245C8—524no—
246C8—1042no—
247C22—21no—
248C22—21no—
249C22#1171887611yescharacteristic
250C22C2×#8807411yescharacteristic
251C22C2×#8807711yescharacteristic
252C4—22no—
253C4—22no—
254C4—21no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4#1171814012yes—
262C2—21no—
263C2—21no—
264C2#1311335211yescharacteristic
265C2#1311649011yescharacteristic
266C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2546C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2546D13
hypocenterC13#11782
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
217. C13#11782semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131131802
#131128422
C13×#25462
#1178213