Finite Group Databasebeta

← #15773645

Subgroups — #15773645

Order 3328.

382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114913C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112857C214yesmaximal
4C13×#2628C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×#117C2211yescharacteristic
7C13×#400—21no—
8C13×#399—21no—
9C13×#395C412yescomplemented
10C13×#393C2212yes—
11C13×#389—21no—
12C13×#382C411yescharacteristic, complemented
13C13×#380—21no—
14#11718872—21no—
15#11718587—21no—
16#11718120—21no—
17#11718118—21no—
18#11718118C2212yes—
19#11718117C2212yes—
20C22×Q8×C13C2×C412yes—
21C23×C4×C13D411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C13×#117—41no—
25C13×#117—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2311yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C22⋊Dic13—22no—
38C13×#95—22no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95C2×C412yes—
42#88071—41no—
43#88071—41no—
44C22⋊#1055—22no—
45C4⋊#1055—41no—
46#88043—41no—
47#11812—131nomaximal, Sylow
48C24×C13C2×D411yescharacteristic
49C2×Q8×C13—42no—
50C2×Q8×C13—82no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—41no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—42no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—82no—
71C13×C22⋊C4—41no—
72C13×C22⋊C4—41no—
73C13×C22⋊C4—82no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C22⋊Dic13—42no—
79C22⋊Dic13—42no—
80C2×#1055—42no—
81#2628D1311yescharacteristic
82#1820—131no—
83#1464—131no—
84#1351—134no—
85C23×C13—21no—
86C23×C13—21no—
87C23×C13—41no—
88C23×C13—41no—
89C23×C13C2×C22⋊C411yescharacteristic
90C23×C13#13712yes—
91Q8×C13—84no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×Dic13—82no—
116C2×Dic13—82no—
117C2×Dic13—82no—
118#1055—82no—
119C2×C4⋊Q8Dic1311yescharacteristic, complemented
120C2×#117C2×D1311yescharacteristic
121#432—261no—
122#400—21no—
123#399—21no—
124#395Dic1312yescomplemented
125#393C2×D1312yes—
126#389—21no—
127#382Dic1311yescharacteristic, complemented
128#381—261no—
129#380—21no—
130#342—132no—
131#342—261no—
132#324—261no—
133#323—132no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—22no—
137C22×C13—42no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—81no—
141C22×C13C2×#9911yescharacteristic
142C22×C13#41911yescharacteristic
143C22×C13#42111yescharacteristic
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—41no—
147C4×C13—41no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—82no—
152C4×C13—82no—
153Dic13—162no—
154C22×Q8C2×Dic1312yes—
155C23×C4C22⋊D1311yescharacteristic
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158#117—41no—
159#117—41no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C2×Dic1311yescharacteristic
165C2×C4⋊C4C22⋊D1311yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—262no—
168C2×C22⋊C4C22⋊D1311yescharacteristic
169C2×C22⋊C4C22×D1311yescharacteristic
170C2×C42C2×Dic1311yescharacteristic
171C2×C42C22⋊D1311yescharacteristic
172C4⋊C8—521no—
173C22⋊C8—262no—
174#97—521no—
175#95—22no—
176#95—21no—
177#95—22no—
178#95—521no—
179#95—521no—
180#95C2×Dic1312yes—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13—42no—
184C2×C13#151111yescharacteristic
185C2×C13#212211yescharacteristic
186C2×C13#212911yescharacteristic
187C24C2×C22⋊D1311yescharacteristic
188C2×Q8—42no—
189C2×Q8—82no—
190C22×C4—22no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—41no—
196C22×C4—522no—
197C22×C4C22⋊Dic1311yescharacteristic
198C22×C4C22⋊Dic1311yescharacteristic
199C22×C4C22⋊Dic1311yescharacteristic
200C22×C4C22⋊Dic1311yescharacteristic
201C22×C4C22×Dic1311yescharacteristic
202C22×C4C2×C22⋊D1311yescharacteristic
203C2×C8—522no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—82no—
214C22⋊C4—522no—
215C22⋊C4—522no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C13#1181211yescharacteristic, complemented, Sylow
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23#8819612yes—
226C23C2×C22⋊Dic1311yescharacteristic
227Q8—84no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—1042no—
250C2×C4—1042no—
251C2×C4—1042no—
252C2×C4#8807411yescharacteristic
253C2×C4#8807411yescharacteristic
254C8—1042no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×#8807411yescharacteristic
263C22#1171888611yescharacteristic
264C22#1171889711yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4—82no—
274C4—2082no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2#1311336911yescharacteristic
279C2#1311648611yescharacteristic
280C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2628C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2628D13
hypocenterC13#11812
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
5. C2×C13×C4⋊Q8C4semidirect
9. C13×#395C4semidirect
12. C13×#382C4semidirect
119. C2×C4⋊Q8Dic13semidirect
124. #395Dic13semidirect
127. #382Dic13semidirect
220. C13#11812semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131131702
#131128572
C13×#26282
#1181213