Finite Group Databasebeta

← #16785046

Subgroups — #16785046

Order 3328.

512 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 138 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#13130622C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3#13129672C214yesmaximal
4C4⋊Q8×Dic13C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×Q8×Dic13—21no—
7C2×#88112—21no—
8C2×#88110—21no—
9C2×C4⋊#1057C2212yes—
10C2×C4×#1057C2212yes—
11#11718891—21no—
12#11718646—21no—
13#11718646C412yes—
14C4⋊C4×Dic13—21no—
15C4⋊C4×Dic13C2212yes—
16#11718596C411yescharacteristic
17C42×Dic13C2211yescharacteristic
18#11718290—21no—
19#11718290—21no—
20C22×Q8×C13—21no—
21C22×#1057—22no—
22C22×#1057—22no—
23C13×C4⋊Q8—24no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27Q8×Dic13—42no—
28Q8×Dic13—42no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—22no—
32C2×C4⋊Dic13C2×C412yes—
33C2×C4×Dic13—22no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13C2311yescharacteristic
40#88112—24no—
41#88110—42no—
42C4⋊#1057—22no—
43C4⋊#1057Q814yescomplemented
44C4×#1057—24no—
45#88071—22no—
46#88071—22no—
47#9869—131nomaximal, Sylow
48C2×Q8×C13—24no—
49C2×Q8×C13—42no—
50C2×Q8×C13—42no—
51C22×C4×C13—22no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—22no—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C2×D411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C2×#1057—24no—
61C2×#1057—24no—
62C2×#1057—42no—
63C2×#1057—42no—
64C2×#1057—42no—
65C2×#1057—42no—
66C13×C4⋊C4—24no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4M1614yes—
69C42×C13—22no—
70C4⋊Dic13—24no—
71C4⋊Dic13—42no—
72C4⋊Dic13—42no—
73C4⋊Dic13—44no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13—22no—
77C4×Dic13—41no—
78C4×Dic13—42no—
79C4×Dic13—42no—
80C4×Dic13D812yes—
81C4×Dic13SD1612yes—
82C4×Dic13C2×Q812yes—
83C4×Dic13#4112yes—
84C4×C4⋊Q8—131no—
85#1767—131no—
86C4×C4⋊C8—131no—
87#1279—134no—
88C23×C13C2×C22⋊C411yescharacteristic
89Q8×C13—48no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—24no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13#10212yes—
98C2×C4×C13#10412yes—
99C2×C4×C13C4×Q812yes—
100C2×C4×C13C2×M1612yes—
101C2×C4×C13#13112yes—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13#10212yes—
113C2×Dic13C22⋊Q812yes—
114C2×Dic13#12411yescharacteristic
115C2×Dic13C4⋊Q811yescharacteristic
116C2×Dic13C2×D811yescharacteristic
117C2×Dic13C2×SD1611yescharacteristic
118C2×Dic13#13712yes—
119#1057—44no—
120#1057—44no—
121C2×C4⋊Q8#26111yescharacteristic
122C2×C4×Q8—261no—
123C2×C4⋊C8—132no—
124C2×C4⋊C8—261no—
125C2×#97—261no—
126C2×C4×C8—132no—
127#391—261no—
128#389—132no—
129#389—261no—
130#384—131no—
131C4×C4⋊C4—132no—
132C4×C4⋊C4—261no—
133C43—131no—
134#336—261no—
135#336—261no—
136C22×C13#39111yescharacteristic
137C22×C13#40711yescharacteristic
138C22×C13#40811yescharacteristic
139C22×C13C2×#10211yescharacteristic
140C22×C13#41911yescharacteristic
141C22×C13C2×#10411yescharacteristic
142C22×C13#42111yescharacteristic
143C4×C13—22no—
144C4×C13—22no—
145C4×C13—44no—
146C4×C13#44614yes—
147Dic13—21no—
148Dic13—21no—
149Dic13—22no—
150Dic13—41no—
151Dic13—82no—
152Dic13#47412yes—
153Dic13#47512yes—
154C22×Q8—21no—
155C22×C8—262no—
156C22×C8—262no—
157C4⋊Q8—24no—
158C4×Q8—522no—
159C4×Q8—522no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—132no—
162C2×C4⋊C4—262no—
163C2×C4⋊C4—261no—
164C2×C4⋊C4—261no—
165C2×C4⋊C4C2×#26112yes—
166C2×C42—131no—
167C2×C42—131no—
168C2×C42—131no—
169C2×C42—131no—
170C2×C42—131no—
171C2×C42—131no—
172C2×C42—262no—
173C2×C42C2×#26111yescharacteristic
174C4⋊C8—134no—
175C4⋊C8—262no—
176C4⋊C8—264no—
177#97—522no—
178C4×C8—264no—
179#95—262no—
180#95—262no—
181C2×C13#148611yescharacteristic
182C2×C13#149111yescharacteristic
183C2×C13#149211yescharacteristic
184C2×C13#149711yescharacteristic
185C2×C13#198511yescharacteristic
186C2×C13#198611yescharacteristic
187C2×C13#198811yescharacteristic
188C2×Q8—24no—
189C2×Q8—42no—
190C2×Q8—42no—
191C22×C4—22no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—262no—
197C22×C4C22⋊#26111yescharacteristic
198C22×C4C22⋊#26111yescharacteristic
199C22×C4C22×#26111yescharacteristic
200C2×C8—264no—
201C2×C8—264no—
202C2×C8—522no—
203C2×C8—522no—
204C2×C8—522no—
205C2×C8—522no—
206C4⋊C4—24no—
207C4⋊C4—22no—
208C4⋊C4—264no—
209C4⋊C4—524no—
210C4⋊C4—522no—
211C4⋊C4—522no—
212C4⋊C4#612214yes—
213C42—22no—
214C42—132no—
215C42—132no—
216C42—132no—
217C42—132no—
218C42—262no—
219C42—262no—
220C42—262no—
221C42—521no—
222C42—522no—
223C42—522no—
224C13#986911yescharacteristic, complemented, Sylow
225C23C2×C22⋊#26111yescharacteristic
226Q8—48no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—24no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—132no—
237C2×C4—132no—
238C2×C4—132no—
239C2×C4—131no—
240C2×C4—131no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4#8811512yes—
252C2×C4#8811812yes—
253C2×C4#8824012yes—
254C2×C4Q8×#26112yes—
255C2×C4C2×#612212yes—
256C8—524no—
257C8—524no—
258C22C2×#8811511yescharacteristic
259C22#1171914011yescharacteristic
260C22#1171915311yescharacteristic
261C22C2×#8811811yescharacteristic
262C22#1171915911yescharacteristic
263C22(C2×#261)⋊Q811yescharacteristic
264C22#1171916911yescharacteristic
265C4—22no—
266C4—22no—
267C4—44no—
268C4—132no—
269C4—132no—
270C4—261no—
271C4—261no—
272C4—262no—
273C4—521no—
274C4—1042no—
275C4#1171915814yes—
276C2#1313016111yescharacteristic
277C2#1313017811yescharacteristic
278C2#1313018311yescharacteristic
279C2#1313020011yescharacteristic
280C2#1313101011yescharacteristic
281C2#1313101111yescharacteristic
282C2#1313101511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#9869
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
43. C4⋊#1057Q8semidirect
224. C13#9869semidirect

Maximal subgroups

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

subgroupindex
#131306222
C4×#881122
#131296722
C4⋊Q8×Dic132
#986913