Finite Group Databasebeta

← #15779755

Subgroups — #15779755

Order 3328.

492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117948C211yesmaximal, characteristic
2#13115240C211yesmaximal, characteristic
3#13115053C212yesmaximal, complemented
4#13112962C212yesmaximal, complemented
5C2×C13×#355C211yesmaximal, characteristic
6C2×C13×#124C2211yescharacteristic
7#11719517C2211yescharacteristic
8C2×C13×#101C2212yes—
9#11718891C2212yes—
10C2×#88076C2211yescharacteristic
11#11718881—21no—
12#11718876—21no—
13#11718782—22no—
14#11718612—22no—
15C22⋊C4×Dic13—22no—
16#11718593—21no—
17C13×#355C414yescomplemented
18#11718147—22no—
19#11718115—21no—
20C22×Q8×C13C2311yescharacteristic
21C22×D4×C13D411yescharacteristic
22C23×Dic13—21no—
23C2×C13×M16—22no—
24C13×#124—22no—
25C13×#124C2×C412yes—
26C13×#124Q812yes—
27C2×C13×C22⋊C4—22no—
28C2×C42×C13D411yescharacteristic
29C2×C22⋊Dic13—22no—
30C2×C22⋊Dic13—21no—
31Q8×Dic13—42no—
32#88180—22no—
33#88180—21no—
34C2×C4⋊Dic13D412yes—
35C2×C4×Dic13—22no—
36C2×C4×Dic13D412yes—
37C2×#6099—21no—
38C13×#101—22no—
39C13×#101C2×C414yescomplemented
40#88076—22no—
41#88072—42no—
42#88071—21no—
43#88071—21no—
44#88071—22no—
45#88071—22no—
46#88058—42no—
47#88057—42no—
48#12972—131nomaximal, Sylow
49C24×C13—21no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13C22×C411yescharacteristic
53C2×Q8×C13C2×Q811yescharacteristic
54C2×Q8×C13#4112yes—
55C2×D4×C13—21no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13C4⋊C412yes—
59C22×C4×C13—21no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—44no—
65C22×Dic13—81no—
66C13×M16—24no—
67C13×M16—42no—
68C2×C8×C13—42no—
69C13×C22⋊C4—24no—
70C13×C22⋊C4—24no—
71C42×C13—21no—
72C42×C13C4⋊C412yes—
73C22⋊Dic13—44no—
74C22⋊Dic13—41no—
75C22⋊Dic13—81no—
76C4⋊Dic13—22no—
77C4⋊Dic13—22no—
78C4⋊Dic13—22no—
79C4⋊Dic13—42no—
80C4×Dic13—44no—
81C4×Dic13—41no—
82C4×Dic13—42no—
83C4×Dic13—42no—
84#6099—41no—
85#6099—41no—
86C2×#1055—41no—
87#2372—131no—
88C2×#355D1311yescharacteristic
89#1888—131no—
90#1857—132no—
91#1394—132no—
92C23×C13—22no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13#12011yescharacteristic
98Q8×C13—41no—
99Q8×C13—41no—
100Q8×C13—42no—
101D4×C13—42no—
102D4×C13—81no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—42no—
109C2×C4×C13C2×C4⋊C411yescharacteristic
110C2×C4×C13C4×D412yes—
111C2×C4×C13C22⋊Q812yes—
112C2×C4×C13#12311yescharacteristic
113C2×Dic13—24no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—84no—
121C8×C13—44no—
122#1055—81no—
123C2×#124C2×D1311yescharacteristic
124#519—131no—
125#428—262no—
126#418—261no—
127C2×#101—131no—
128C2×#101C2×D1312yes—
129#391—132no—
130#388—262no—
131#386—261no—
132C4×C22⋊C4—262no—
133#376—261no—
134#355Dic1314yescomplemented
135#339—262no—
136#339—261no—
137C22×C13—22no—
138C22×C13—44no—
139C22×C13—42no—
140C22×C13—81no—
141C22×C13—81no—
142C22×C13—82no—
143C22×C13#38511yescharacteristic
144C22×C13B(4,𝔽2)11yescharacteristic
145C22×C13#45811yescharacteristic
146C4×C13—21no—
147C4×C13—22no—
148C4×C13—21no—
149C4×C13—22no—
150C4×C13—42no—
151Dic13—44no—
152Dic13—82no—
153Dic13—82no—
154C22×Q8C22×D1311yescharacteristic
155C22×D4D5211yescharacteristic
156C23×C4—261no—
157C2×M16—22no—
158C2×M16—261no—
159#124—22no—
160#124Dic2612yes—
161#124C2×Dic1312yes—
162C4×Q8—522no—
163#117—261no—
164#117—262no—
165C2×C4⋊C4—132no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—262no—
168C2×C22⋊C4—261no—
169C2×C42—132no—
170C2×C42—262no—
171C2×C42D5211yescharacteristic
172#107—522no—
173#106—522no—
174#102—522no—
175#101—22no—
176#101—262no—
177#101C2×Dic1314yescomplemented
178#95—261no—
179#95—261no—
180#95—262no—
181#95—262no—
182C2×C13—21no—
183C2×C13—21no—
184C2×C13—82no—
185C2×C13#186711yescharacteristic
186C2×C13#220412yes—
187C24—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C2×Dic2611yescharacteristic
191C2×Q8#612912yes—
192C2×Q8C22×Dic1311yescharacteristic
193C2×D4—21no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4C4⋊Dic1312yes—
197C22×C4—21no—
198C22×C4—262no—
199C22×C4—262no—
200C22×C4—524no—
201C22×C4—1041no—
202C22×C4C2×D5211yescharacteristic
203C22×C4D4×D1312yes—
204M16—24no—
205M16—42no—
206M16—521no—
207M16—521no—
208C2×C8—42no—
209C2×C8—521no—
210C4⋊C4—262no—
211C4⋊C4—262no—
212C4⋊C4—262no—
213C4⋊C4—522no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—524no—
217C22⋊C4—521no—
218C22⋊C4—1041no—
219C42—21no—
220C42—522no—
221C42—522no—
222C42—521no—
223C42—524no—
224C42C4⋊Dic1312yes—
225C13#1297211yescharacteristic, complemented, Sylow
226C23—22no—
227C23—42no—
228C23—42no—
229C23—41no—
230C23—41no—
231C23#8813611yescharacteristic
232Q8—41no—
233Q8—42no—
234Q8—41no—
235D4—42no—
236D4—81no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—264no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—1044no—
251C2×C4#8813212yes—
252C2×C4#8814011yescharacteristic
253C2×C4C2×C4⋊Dic1311yescharacteristic
254C2×C4D4×Dic1312yes—
255C8—44no—
256C8—1041no—
257C22—22no—
258C22—44no—
259C22—42no—
260C22—81no—
261C22—81no—
262C22—82no—
263C22#1171840211yescharacteristic
264C22#1171840311yescharacteristic
265C22#1171861111yescharacteristic
266C4—22no—
267C4—21no—
268C4—22no—
269C4—21no—
270C4—42no—
271C4—524no—
272C4—1042no—
273C4—1042no—
274C2—21no—
275C2—21no—
276C2—82no—
277C2#1311511911yescharacteristic
278C2#1311686312yes—
subgroupG/H
centerC22#11718402
commutatorC2×Q8×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC2×C13×#355C2
socleC22×C13B(4,𝔽2)
prime radicalC22×D4×C13D4
cosocleC22×Q8×C13C23
hypercenterC2×#355D13
hypocenterC13#12972
LCSG ▷ C2×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
3. #13115053C2semidirect
4. #13112962C2semidirect
17. C13×#355C4semidirect
39. C13×#101C2×C4semidirect
134. #355Dic13semidirect
177. #101C2×Dic13semidirect
225. C13#12972semidirect

Maximal subgroups

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

subgroupindex
#131179482
#131152402
#131150532
#131129622
C2×C13×#3552
#1297213