Finite Group Databasebeta

← #15779189

Subgroups — #15779189

Order 3328.

566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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#13117422C211yesmaximal, characteristic
2#13114760C211yesmaximal, characteristic
3#13112962C214yesmaximal, complemented
4C13×#1784C211yesmaximal, characteristic
5C23×Q8×C13C2211yescharacteristic
6C2×#88180C411yescharacteristic
7C2×#88180C411yescharacteristic
8C2×C13×#101—21no—
9C2×C13×#101C2212yes—
10C13×#407—21no—
11#11718891—21no—
12#11718891—21no—
13#11718891C412yes—
14#11718891C2212yes—
15C2×#88076—21no—
16C2×#88076C2212yes—
17#11718872—21no—
18#11718872—21no—
19#11718868—21no—
20C22×Q8×C13—24no—
21C22×Q8×C13—42no—
22C22×Q8×C13—42no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C22×Q8×C13D411yescharacteristic
26C22×Q8×C13C2311yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C2×C13×M16—22no—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33#88180—42no—
34#88180—42no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13C2×C412yes—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C412yes—
39C2×#6099—22no—
40C13×#101—24no—
41C13×#101—42no—
42C13×C22⋊C8—42no—
43#88076—24no—
44#88076—42no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071—22no—
49C22⋊#1055—42no—
50#12862—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13—416no—
64C2×Q8×C13#4114yes—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—22no—
81C22×Dic13—22no—
82C13×M16—42no—
83C13×M16—42no—
84C2×C8×C13—42no—
85C22⋊Dic13—42no—
86C22⋊Dic13—42no—
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4×Dic13—42no—
90C4×Dic13—42no—
91#6099—42no—
92#6099—42no—
93C2×#1055—42no—
94#2310—131no—
95#1784—131no—
96#1784D1311yescharacteristic
97#1394—134no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—42no—
101C23×C13#9912yes—
102C23×C13C2×C22⋊C411yescharacteristic
103Q8×C13—44no—
104Q8×C13—44no—
105Q8×C13—44no—
106Q8×C13—44no—
107C2×C4×C13—28no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—44no—
123C2×C4×C13—44no—
124C2×C4×C13#9912yes—
125C2×C4×C13#11712yes—
126C2×C4×C13#12312yes—
127C2×C4×C13#12312yes—
128C2×Dic13—44no—
129C2×Dic13—44no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C8×C13—82no—
133#1055—82no—
134C23×Q8C2×D1311yescharacteristic
135C2×#117—131no—
136C2×#117—131no—
137C2×#101—21no—
138C2×#101—132no—
139C2×#101—261no—
140C2×#101C2×D1312yes—
141#407—21no—
142#407—261no—
143#391—132no—
144#391—132no—
145#391—261no—
146#391—261no—
147#381—261no—
148#381—261no—
149C22×C13—22no—
150C22×C13—22no—
151C22×C13—24no—
152C22×C13—42no—
153C22×C13—42no—
154C22×C13#38111yescharacteristic
155C22×C13C2×#9911yescharacteristic
156C22×C13C2×#9911yescharacteristic
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—41no—
162C4×C13—41no—
163Dic13—82no—
164Dic13—82no—
165C22×Q8—24no—
166C22×Q8—42no—
167C22×Q8—42no—
168C22×Q8C4×D1311yescharacteristic
169C22×Q8D5211yescharacteristic
170C22×Q8C22⋊D1311yescharacteristic
171C22×Q8C22×D1311yescharacteristic
172C23×C4C4×D1311yescharacteristic
173C23×C4D5211yescharacteristic
174C23×C4C22⋊D1311yescharacteristic
175C2×M16—22no—
176C2×M16—262no—
177#117—522no—
178#117—522no—
179C2×C4⋊C4—132no—
180C2×C4⋊C4—261no—
181C2×C22⋊C4—261no—
182C2×C22⋊C4—261no—
183C2×C42—132no—
184C2×C42—261no—
185#101—24no—
186#101—42no—
187#101—264no—
188#101—522no—
189C22⋊C8—42no—
190C22⋊C8—522no—
191#95—262no—
192#95—262no—
193#95—262no—
194#95—262no—
195C2×C13—21no—
196C2×C13—21no—
197C2×C13—42no—
198C2×C13#181911yescharacteristic
199C2×C13#213312yes—
200C24#610311yescharacteristic
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—416no—
213C2×Q8#612914yes—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—262no—
224C22×C4—262no—
225C22×C4#610311yescharacteristic
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4C2×C4×D1311yescharacteristic
229C22×C4C2×D5211yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231M16—42no—
232M16—42no—
233M16—522no—
234M16—522no—
235C2×C8—42no—
236C2×C8—522no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C22⋊C4—522no—
240C22⋊C4—522no—
241C42—522no—
242C42—522no—
243C13#1286211yescharacteristic, complemented, Sylow
244C23—21no—
245C23—21no—
246C23—42no—
247C23#8804612yes—
248C23C2×#610311yescharacteristic
249Q8—44no—
250Q8—44no—
251Q8—44no—
252Q8—44no—
253C2×C4—28no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—524no—
271C2×C4—524no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4#8804612yes—
275C2×C4#8813112yes—
276C2×C4#8814012yes—
277C2×C4#8818912yes—
278C8—82no—
279C8—1042no—
280C22—22no—
281C22—22no—
282C22—24no—
283C22—42no—
284C22—42no—
285C22#1171860411yescharacteristic
286C22C2×#8804611yescharacteristic
287C22C2×#8804611yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—41no—
294C4—1042no—
295C4—1042no—
296C2—21no—
297C2—21no—
298C2—42no—
299C2#1311490811yescharacteristic
300C2#1311652312yes—
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1784C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1784D13
hypocenterC13#12862
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #1784

Complements

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

NH ≅ G/Ntype
3. #13112962C2semidirect
243. C13#12862semidirect

Maximal subgroups

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

subgroupindex
#131174222
#131147602
#131129622
C13×#17842
#1286213