Finite Group Databasebeta

← #16788086

Subgroups — #16788086

Order 3328.

368 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 66 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#13130737C211yesmaximal, characteristic
2#13130089C211yesmaximal, characteristic
3#13129835C214yesmaximal, complemented
4#13120658C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×#88126C2211yescharacteristic
7#11719128—21no—
8#11719126—21no—
9#11718892—21no—
10#11718890—21no—
11#11718653C412yes—
12#11718648—21no—
13#11718643C2212yes—
14#11718634—21no—
15#11718597C411yescharacteristic
16#11718291—21no—
17#11718291C2212yes—
18#11718287—21no—
19#11718286C2212yes—
20C22×Q8×C13—21no—
21C22×C4×D13D411yescharacteristic
22C2×#6122—22no—
23C13×C4⋊Q8—41no—
24C13×C4⋊Q8—41no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C412yes—
27C2×C42×C13C2×C411yescharacteristic
28C2×#6103—22no—
29C2×#6103C2×C411yescharacteristic
30C2×#6103D411yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×#6101—22no—
33C2×#6101D411yescharacteristic
34C2×#6101C2311yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36#88126—41no—
37#88126—41no—
38C22⋊#1057—22no—
39#88112—41no—
40#88111—41no—
41#88111—41no—
42#88110—41no—
43#88071—21no—
44#88071—22no—
45#88071—22no—
46#88071C2×C412yes—
47#11818—131nomaximal, Sylow
48C23×D13C22⋊C411yescharacteristic
49C2×Q8×C13—42no—
50C2×Q8×C13—82no—
51C22×C4×C13—22no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—22no—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C2×D411yescharacteristic
58C22×Dic13C2×D411yescharacteristic
59C2×C4×D13—21no—
60C2×C4×D13—21no—
61C2×C4×D13—22no—
62C2×C4×D13—41no—
63#6122—42no—
64#6122—42no—
65C2×#1057—42no—
66C2×#1057—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C42×C13—21no—
71C42×C13—21no—
72#6103—41no—
73#6103—41no—
74#6103—82no—
75C4⋊Dic13—42no—
76#6101—41no—
77#6101—41no—
78#6101—82no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81#2628—131no—
82#1822—131no—
83#1464—131no—
84#1353—134no—
85C23×C13C2×C22⋊C411yescharacteristic
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—21no—
89C22×D13—41no—
90C22×D13—41no—
91Q8×C13—84no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13#9911yescharacteristic
102C2×C4×C13#9911yescharacteristic
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13#13712yes—
113C4×D13—42no—
114C4×D13—42no—
115#1057—82no—
116#1057—82no—
117C2×C4⋊Q8#26111yescharacteristic
118C2×#117—131no—
119#432—261no—
120#407—261no—
121#400—132no—
122#399—132no—
123#395—261no—
124#393—261no—
125#389—261no—
126#382—131no—
127#380—261no—
128#343—132no—
129#343—261no—
130#324—132no—
131#323—261no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13C2×#9911yescharacteristic
135C22×C13#41911yescharacteristic
136C22×C13#42111yescharacteristic
137C2×D13—42no—
138C2×D13—41no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—81no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13—41no—
146C4×C13—82no—
147Dic13—22no—
148Dic13—41no—
149Dic13—41no—
150Dic13—82no—
151C22×Q8—21no—
152C23×C4—131no—
153C2×M16—262no—
154C4⋊Q8—41no—
155C4⋊Q8—41no—
156#117—521no—
157#117—521no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—131no—
160C2×C4⋊C4—131no—
161C2×C4⋊C4—261no—
162C2×C4⋊C4—262no—
163C2×C4⋊C4C2×#26112yes—
164C2×C22⋊C4—131no—
165C2×C22⋊C4—131no—
166C2×C22⋊C4—262no—
167C2×C42—131no—
168C2×C42C2×#26111yescharacteristic
169C4⋊C8—521no—
170C22⋊C8—262no—
171C22⋊C8—521no—
172C22⋊C8—521no—
173#97—521no—
174#95—132no—
175#95—262no—
176#95—262no—
177#95—261no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13#151111yescharacteristic
181C2×C13#212311yescharacteristic
182C2×C13#213411yescharacteristic
183D13—81no—
184C24—131no—
185C2×Q8—42no—
186C2×Q8—82no—
187C22×C4—22no—
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—262no—
192C22×C4—261no—
193C22×C4—261no—
194C22×C4—262no—
195C22×C4—521no—
196C22×C4C22⋊#26111yescharacteristic
197C22×C4C22⋊#26111yescharacteristic
198C22×C4C22×#26111yescharacteristic
199M16—522no—
200M16—522no—
201C2×C8—522no—
202C2×C8—522no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—521no—
207C4⋊C4—521no—
208C4⋊C4—522no—
209C4⋊C4—1042no—
210C22⋊C4—521no—
211C22⋊C4—521no—
212C22⋊C4—1042no—
213C42—21no—
214C42—21no—
215C42—261no—
216C42—261no—
217C13#1181811yescharacteristic, complemented, Sylow
218C23—261no—
219C23—261no—
220C23—261no—
221C23—521no—
222C23—521no—
223C23C2×C22⋊#26111yescharacteristic
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—132no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—521no—
242C2×C4—521no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4#8811911yescharacteristic
247C2×C4#8811911yescharacteristic
248C8—1042no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22—522no—
253C22—521no—
254C22—521no—
255C22—521no—
256C22—1041no—
257C22#1171915311yescharacteristic
258C22#1171915511yescharacteristic
259C22C2×#8811911yescharacteristic
260C4—21no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4—262no—
266C4—521no—
267C4—521no—
268C4—1042no—
269C2—21no—
270C2—21no—
271C2—1041no—
272C2#1313024611yescharacteristic
273C2#1313109811yescharacteristic
274C2#1313113511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×#6101C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11818
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13129835C2semidirect
217. C13#11818semidirect

Maximal subgroups

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

subgroupindex
#131307372
#131300892
#131298352
#131206582
#1181813