Finite Group Databasebeta

← #15781607

Subgroups — #15781607

Order 3328.

420 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 111 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#13114832C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13112963C214yesmaximal
4C13×#2567C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#395—21no—
8C13×#395—21no—
9C13×#391C2212yes—
10C13×#389—21no—
11C13×#389—21no—
12C13×#384C412yes—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076C2212yes—
15C2×#88076C2212yes—
16#11718585—21no—
17C4×#6099—21no—
18#11718122—21no—
19#11718122—21no—
20C22×Q8×C13—21no—
21C22×Q8×C13C2311yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C412yes—
36C2×C42×C13D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×#6099—22no—
39C2×#6099—22no—
40C13×#95—21no—
41C13×#95—22no—
42C13×#95—22no—
43#88076—22no—
44#88076—24no—
45#88076Q814yescomplemented
46C4⋊#1055—41no—
47C4⋊#1055—41no—
48#88043—41no—
49C4×#1055—41no—
50#13302—131nomaximal, Sylow
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13—42no—
54C2×Q8×C13—82no—
55C2×Q8×C13C2×Q812yes—
56C2×Q8×C13#4112yes—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C13×C4⋊C4—24no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—82no—
74C13×C4⋊C4—82no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—42no—
82#6099—24no—
83#6099—42no—
84#6099—42no—
85#6099—42no—
86C2×#1055—42no—
87C2×#1055—42no—
88#2567D1311yescharacteristic
89#1801—131no—
90C4×#101—131no—
91#1394—134no—
92C23×C13C2×C22⋊C411yescharacteristic
93Q8×C13—42no—
94Q8×C13—42no—
95Q8×C13—84no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—24no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13C4×Q812yes—
118C2×C4×C13C22⋊Q812yes—
119C2×C4×C13#12411yescharacteristic
120C2×C4×C13C4⋊Q811yescharacteristic
121#1055—44no—
122#1055—82no—
123C2×C4⋊Q8Dic1311yescharacteristic
124C2×C4×Q8C2×D1311yescharacteristic
125#423—261no—
126C2×#101—132no—
127C2×#101—132no—
128C4×M16—261no—
129#395—21no—
130#395—21no—
131#391C2×D1312yes—
132#389—21no—
133#389—21no—
134#384Dic1312yes—
135C4×C4⋊C4Dic1311yescharacteristic
136#343—261no—
137#343—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#39111yescharacteristic
141C22×C13C2×#9911yescharacteristic
142C22×C13#41011yescharacteristic
143C4×C13—21no—
144C4×C13—22no—
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—21no—
148C4×C13—44no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13—82no—
153C4×C13#35612yes—
154C22×Q8—21no—
155C22×Q8C22×D1311yescharacteristic
156C2×M16—262no—
157C2×M16—262no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×Dic1312yes—
167C2×C4⋊C4C2×Dic1311yescharacteristic
168C2×C4⋊C4C22⋊D1311yescharacteristic
169C2×C4⋊C4C22⋊D1311yescharacteristic
170C2×C42C2×Dic1311yescharacteristic
171C2×C42C2×Dic1312yes—
172C2×C42C22⋊D1311yescharacteristic
173C2×C42C22⋊D1311yescharacteristic
174C4⋊C8—521no—
175C4⋊C8—521no—
176#101—134no—
177#101—262no—
178#101—264no—
179#97—521no—
180C4×C8—521no—
181#95—21no—
182#95—22no—
183#95—22no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#199611yescharacteristic
187C2×C13C2×#35611yescharacteristic
188C2×C13#213411yescharacteristic
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—42no—
192C2×Q8—82no—
193C2×Q8Q8×D1312yes—
194C2×Q8#613112yes—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4C22⋊Dic1311yescharacteristic
198C22×C4C22⋊Dic1311yescharacteristic
199C22×C4C22⋊Dic1311yescharacteristic
200C22×C4C22⋊Dic1311yescharacteristic
201C22×C4C22×Dic1311yescharacteristic
202C22×C4C2×C22⋊D1311yescharacteristic
203C22×C4C2×C22⋊D1311yescharacteristic
204M16—264no—
205M16—522no—
206M16—522no—
207M16—522no—
208C2×C8—522no—
209C2×C8—522no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—82no—
218C4⋊C4—82no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—42no—
226C13#1330211yescharacteristic, complemented, Sylow
227C23C2×C22⋊Dic1311yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4#8807411yescharacteristic
251C2×C4#8807411yescharacteristic
252C2×C4#8819811yescharacteristic
253C2×C4Q8×Dic1312yes—
254C2×C4#8820012yes—
255C2×C4#8820111yescharacteristic
256C8—524no—
257C8—1042no—
258C22—21no—
259C22—21no—
260C22C2×#8807411yescharacteristic
261C22#1171889111yescharacteristic
262C22#1171890111yescharacteristic
263C4—21no—
264C4—22no—
265C4—21no—
266C4—21no—
267C4—22no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4#1171814012yes—
274C2—21no—
275C2—21no—
276C2#1311582211yescharacteristic
277C2C2×#1171814011yescharacteristic
278C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2567C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#2567D13
hypocenterC13#13302
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
45. #88076Q8semidirect
226. C13#13302semidirect

Maximal subgroups

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

subgroupindex
#131148322
C4×#880762
#131129632
C13×#25672
#1330213