Finite Group Databasebeta

← #16790416

Subgroups — #16790416

Order 3328.

488 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C22×#88098C211yesmaximal, characteristic, complemented
2C2×#11718304C212yesmaximal, complemented
3#13131065C211yesmaximal, characteristic, complemented
4#13129891C212yesmaximal, complemented
5#13123533C211yesmaximal, characteristic
6#11719533C411yescharacteristic
7C2×#88202C2211yescharacteristic
8C22×C8×D13C2211yescharacteristic
9C2×#88106C2212yes—
10C22×#6092C2212yes—
11C2×#88098—22no—
12C2×#88098—24no—
13C13×#408C411yescharacteristic
14#11718787C411yescharacteristic
15#11718783C2211yescharacteristic
16#11718763C411yescharacteristic
17#11718389—22no—
18#11718386—22no—
19#11718304—24no—
20#11718259—22no—
21C2×C13×#41C2×C411yescharacteristic
22C22×C4×D13C2×C411yescharacteristic
23C2×C13×M16C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25#88202—22no—
26#88202—22no—
27#88200C812yes—
28#88192C812yes—
29#88191—21no—
30#88189—21no—
31C4×C22⋊D13—22no—
32#88180C2×C411yescharacteristic
33C2×#6099—21no—
34C2×#6099C2×C411yescharacteristic
35C22×#1055—21no—
36C22×#1055C2311yescharacteristic
37C2×C8×D13—22no—
38C2×C8×D13—22no—
39C2×C8×D13D412yes—
40C2×C8×D13D412yes—
41#88106—22no—
42#88106—22no—
43C2×#6092—22no—
44C2×#6092—22no—
45C2×#6092—22no—
46C2×#6092D414yescomplemented
47#88098—28no—
48C13×C22⋊C8—22no—
49#88060—22no—
50#88055—21no—
51#88054—22no—
52C8×Dic13—21no—
53#12984—131nomaximal, Sylow
54C23×D13M1611yescharacteristic
55C13×#41—22no—
56C13×#41—22no—
57C2×Q8×C13C2×C811yescharacteristic
58C2×D4×C13—21no—
59C2×D4×C13C2×C811yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C22×C411yescharacteristic
62C2×C22⋊D13—22no—
63C22×Dic13M1611yescharacteristic
64C2×C4×D13—22no—
65C2×C4×D13—22no—
66C2×C4×D13C22⋊C412yes—
67C2×C4×D13C2×C812yes—
68C13×M16—22no—
69C2×C8×C13—22no—
70C2×C8×C13—21no—
71C2×C8×C13C22⋊C412yes—
72C22⋊Dic13—21no—
73C22⋊Dic13—22no—
74#6103—22no—
75C4⋊Dic13C2×C812yes—
76#6101—22no—
77C4×Dic13—21no—
78#6099—22no—
79#6099—41no—
80#6099—41no—
81C2×#1055—21no—
82C2×#1055—42no—
83C2×#1055C2×D412yes—
84C2×#1055C2×D411yescharacteristic
85C2×#1055C2×D411yescharacteristic
86C2×#1055#4112yes—
87C8×D13—22no—
88C8×D13—24no—
89C8×D13—22no—
90#6092—24no—
91#6092—42no—
92C22×M32—131no—
93#2929—131no—
94C2×#350—132no—
95#2112—131no—
96#1379—132no—
97C23×C13—21no—
98C23×C13C2×M1611yescharacteristic
99C22×D13—22no—
100C22×D13—42no—
101C22×D13C22⋊C812yes—
102Q8×C13—22no—
103D4×C13—22no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13C4×D412yes—
110C2×C4×C13C22×C811yescharacteristic
111C2×C4×C13#13112yes—
112C22⋊D13—44no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13C22⋊C812yes—
116C4×D13—22no—
117C4×D13—22no—
118C4×D13—24no—
119C8×C13—22no—
120C8×C13—41no—
121#1055—41no—
122#1055#12011yescharacteristic
123#1055#12112yes—
124#1055#12311yescharacteristic
125C2×#131—131no—
126C23×C8—131no—
127#525—131no—
128C2×M32—132no—
129C2×M32—264no—
130C2×M32—262no—
131C22×C16—132no—
132#435—262no—
133C8×D4—262no—
134#424—131no—
135#408#26111yescharacteristic
136#407—131no—
137#405—131no—
138#350—264no—
139C22⋊C16—262no—
140C22×C13—22no—
141C22×C13—42no—
142C22×C13—41no—
143C22×C13C2×C22⋊C811yescharacteristic
144C22×C13#43512yes—
145C2×D13—22no—
146C2×D13—22no—
147C2×D13—22no—
148C2×D13—44no—
149C4×C13—41no—
150C4×C13#38611yescharacteristic
151C4×C13#40811yescharacteristic
152C4×C13C8×D412yes—
153Dic13—22no—
154Dic13—42no—
155C2×#41C2×#26111yescharacteristic
156C23×C4—131no—
157#131—262no—
158#131—262no—
159C2×M16—131no—
160C2×M16—261no—
161C2×M16C2×#26111yescharacteristic
162C22×C8—131no—
163C22×C8—132no—
164C22×C8—132no—
165C22×C8—262no—
166C22×C8—262no—
167C22×C8—261no—
168C22×C8C2×#26111yescharacteristic
169#123—261no—
170C22⋊Q8—132no—
171#121—132no—
172#120—261no—
173C4×D4—262no—
174#117—131no—
175M32—268no—
176M32—262no—
177M32—262no—
178C2×C16—134no—
179C2×C16—262no—
180C2×C16—262no—
181C2×C16—262no—
182C4⋊C8—262no—
183C22⋊C8—22no—
184C22⋊C8—262no—
185#97—261no—
186C4×C8—261no—
187C2×C13—22no—
188C2×C13—81no—
189C2×C13#186911yescharacteristic
190C2×C13#211712yes—
191D13—42no—
192C24—131no—
193#41—22no—
194#41—22no—
195C2×Q8D13⋊C811yescharacteristic
196C2×D4—21no—
197C2×D4—262no—
198C2×D4D13⋊C811yescharacteristic
199C22×C4—21no—
200C22×C4—131no—
201C22×C4—132no—
202C22×C4—132no—
203C22×C4—262no—
204C22×C4—262no—
205C22×C4C22×#26111yescharacteristic
206M16—22no—
207M16—262no—
208M16—521no—
209M16—521no—
210C2×C8—22no—
211C2×C8—21no—
212C2×C8—132no—
213C2×C8—132no—
214C2×C8—131no—
215C2×C8—131no—
216C2×C8—262no—
217C2×C8—264no—
218C2×C8—262no—
219C2×C8—261no—
220C2×C8—522no—
221C2×C8C22⋊#26112yes—
222C4⋊C4—132no—
223C4⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C22⋊C4—261no—
227C42—261no—
228C16—264no—
229C16—522no—
230C13#1298411yescharacteristic, complemented, Sylow
231C23—21no—
232C23—132no—
233C23—262no—
234C23—522no—
235C23D13⋊M1611yescharacteristic
236Q8—22no—
237D4—22no—
238D4—42no—
239D4—524no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—132no—
244C2×C4—262no—
245C2×C4—264no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4C2×D13⋊C811yescharacteristic
250C2×C4#8823812yes—
251C2×C4D4×#26112yes—
252C2×C4C2×C22⋊#26111yescharacteristic
253C8—22no—
254C8—41no—
255C8—131no—
256C8—132no—
257C8—131no—
258C8—521no—
259C22—22no—
260C22—41no—
261C22—42no—
262C22—262no—
263C22—262no—
264C22—262no—
265C22—524no—
266C22#1171906512yes—
267C22D13⋊(C22⋊C8)11yescharacteristic
268C4—41no—
269C4—262no—
270C4—522no—
271C4#1171906312yes—
272C4#1171914711yescharacteristic
273C4#1171915011yescharacteristic
274C2—22no—
275C2—81no—
276C2—522no—
277C2#1313081011yescharacteristic
278C2#1313107912yes—
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#408C4
socleC22×C13C2×C22⋊C8
prime radical#11719533C4
cosocleC22×#1055C23
hypercenter#408#261
hypocenterC13#12984
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C22×#88098C2semidirect
2. C2×#11718304C2semidirect
3. #13131065C2semidirect
4. #13129891C2semidirect
46. C2×#6092D4semidirect
230. C13#12984semidirect

Maximal subgroups

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

subgroupindex
C22×#880982
C2×#117183042
#131310652
#131298912
#131235332
#1298413