Finite Group Databasebeta

← #16788069

Subgroups — #16788069

Order 3328.

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

normal subgroups only

This group has 382 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#13130733C211yesmaximal, characteristic
2#13130089C211yesmaximal, characteristic
3#13129833C214yesmaximal
4#13120658C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×#88126C2211yescharacteristic
7#11719135—21no—
8#11719128—21no—
9#11718892—21no—
10#11718890—21no—
11#11718653C2212yes—
12#11718648—21no—
13#11718643C412yescomplemented
14#11718634—21no—
15#11718597C411yescharacteristic, complemented
16#11718289—21no—
17#11718289C2212yes—
18#11718287C2212yes—
19#11718286—21no—
20C22×Q8×C13—21no—
21C22×C4×D13D411yescharacteristic
22C2×C22⋊#261—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×#6103D411yescharacteristic
30C2×#6103C2311yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×#6101—22no—
33C2×#6101C2×C411yescharacteristic
34C2×#6101D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36#88126—41no—
37#88126—41no—
38C22⋊#1057—22no—
39(C2×#261)⋊C4—41no—
40(C2×#261)⋊C4—41no—
41#88112—41no—
42#88110—41no—
43#88071—21no—
44#88071—22no—
45#88071—22no—
46#88071C2×C412yes—
47#11813—131nomaximal, Sylow
48C23×D13C2×D411yescharacteristic
49C22×#261—42no—
50C2×Q8×C13—42no—
51C2×Q8×C13—82no—
52C22×C4×C13—22no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C2×C4×D13—22no—
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—41no—
64C22⋊#261—42no—
65C22⋊#261—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#1820—131no—
83#1464—131no—
84#1352—134no—
85C23×C13C2×C22⋊C411yescharacteristic
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—41no—
89C22×D13—41no—
90C22×D13#13712yes—
91C2×#261—82no—
92C2×#261—82no—
93C2×#261—82no—
94Q8×C13—84no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13#9911yescharacteristic
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—41no—
112C2×Dic13—41no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C4×D13—42no—
117C4×D13—42no—
118#1057—82no—
119C2×C4⋊Q8#26111yescharacteristic, complemented
120C2×#117—131no—
121#432—261no—
122#400—132no—
123#399—132no—
124#395—261no—
125#393—261no—
126#389—261no—
127#382—131no—
128#381—261no—
129#380—261no—
130#342—132no—
131#342—261no—
132#324—261no—
133#323—132no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13C2×#9911yescharacteristic
137C22×C13#41911yescharacteristic
138C22×C13#42111yescharacteristic
139C2×D13—22no—
140C2×D13—41no—
141C2×D13—41no—
142C2×D13—42no—
143C2×D13—81no—
144#261—162no—
145C4×C13—21no—
146C4×C13—21no—
147C4×C13—41no—
148C4×C13—41no—
149C4×C13—82no—
150Dic13—41no—
151Dic13—41no—
152Dic13—41no—
153Dic13—82no—
154C22×Q8—21no—
155C23×C4—131no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158#117—521no—
159#117—521no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—261no—
164C2×C4⋊C4—262no—
165C2×C4⋊C4C2×#26112yes—
166C2×C22⋊C4—131no—
167C2×C22⋊C4—131no—
168C2×C22⋊C4—262no—
169C2×C22⋊C4—262no—
170C2×C42—131no—
171C2×C42C2×#26111yescharacteristic
172C4⋊C8—521no—
173C22⋊C8—262no—
174#97—521no—
175#95—132no—
176#95—262no—
177#95—262no—
178#95—261no—
179#95—521no—
180#95—521no—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13#151111yescharacteristic
184C2×C13#212311yescharacteristic
185C2×C13#212811yescharacteristic
186D13—42no—
187C24—131no—
188C2×Q8—42no—
189C2×Q8—82no—
190C22×C4—22no—
191C22×C4—131no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—262no—
195C22×C4—261no—
196C22×C4—261no—
197C22×C4—262no—
198C22×C4—521no—
199C22×C4—522no—
200C22×C4C22⋊#26111yescharacteristic
201C22×C4C22⋊#26111yescharacteristic
202C22×C4C22×#26111yescharacteristic
203C2×C8—522no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—521no—
208C4⋊C4—521no—
209C4⋊C4—522no—
210C4⋊C4—1042no—
211C22⋊C4—521no—
212C22⋊C4—521no—
213C22⋊C4—522no—
214C22⋊C4—522no—
215C22⋊C4—1042no—
216C42—21no—
217C42—21no—
218C42—261no—
219C42—261no—
220C13#1181311yescharacteristic, complemented, Sylow
221C23—132no—
222C23—261no—
223C23—261no—
224C23—521no—
225C23—521no—
226C23C2×C22⋊#26111yescharacteristic
227Q8—84no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—261no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—1042no—
250C2×C4—1042no—
251C2×C4—1042no—
252C2×C4#8811911yescharacteristic
253C2×C4#8811911yescharacteristic
254C8—1042no—
255C22—21no—
256C22—21no—
257C22—262no—
258C22—522no—
259C22—521no—
260C22—521no—
261C22—1041no—
262C22#1171915311yescharacteristic
263C22#1171915511yescharacteristic
264C22C2×#8811911yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—82no—
270C4—521no—
271C4—521no—
272C4—521no—
273C4—1042no—
274C4—2082no—
275C2—21no—
276C2—21no—
277C2—522no—
278C2#1313024611yescharacteristic
279C2#1313109811yescharacteristic
280C2#1313111511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×D13C2×D4
cosocleC2×#6103C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11813
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
5. C2×C13×C4⋊Q8C4semidirect
13. #11718643C4semidirect
15. #11718597C4semidirect
119. C2×C4⋊Q8#261semidirect
220. C13#11813semidirect

Maximal subgroups

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

subgroupindex
#131307332
#131300892
#131298332
#131206582
#1181313