Finite Group Databasebeta

← #15779760

Subgroups — #15779760

Order 3328.

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

normal subgroups only

This group has 460 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#13117926C211yesmaximal, characteristic
2#13115230C211yesmaximal, characteristic
3#13115053C212yesmaximal
4#13112962C212yesmaximal
5C2×C13×#356C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7#11719517C2211yescharacteristic
8C2×C13×#101C2212yes—
9#11718891—21no—
10#11718891C2212yes—
11C2×#88076C2211yescharacteristic
12#11718886—21no—
13#11718782—22no—
14#11718646—22no—
15C4⋊C4×Dic13—22no—
16C4×C4⋊Dic13—21no—
17C13×#356C414yescomplemented
18#11718147—22no—
19#11718115—21no—
20C22×Q8×C13D411yescharacteristic
21C22×Q8×C13C2311yescharacteristic
22C2×C13×M16—22no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8C2×C412yes—
25C13×C4⋊Q8Q812yes—
26C2×C13×C4⋊C4—22no—
27C2×C42×C13D411yescharacteristic
28Q8×Dic13—41no—
29Q8×Dic13—41no—
30#88180—22no—
31#88180—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13D412yes—
36C2×C4×Dic13—22no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13D412yes—
39C2×#6099—21no—
40C13×#101—22no—
41C13×#101C2×C414yes—
42#88076—22no—
43#88075—41no—
44#88075—41no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88058—42no—
49#88057—42no—
50#12973—131nomaximal, Sylow
51C2×Q8×C13—21no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13C4⋊C412yes—
57C2×Q8×C13C22×C411yescharacteristic
58C2×Q8×C13C2×Q811yescharacteristic
59C2×Q8×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D412yes—
64C22×Dic13—22no—
65C22×Dic13—22no—
66C13×M16—24no—
67C13×M16—42no—
68C2×C8×C13—42no—
69C13×C4⋊C4—24no—
70C13×C4⋊C4—24no—
71C42×C13—21no—
72C42×C13C4⋊C412yes—
73C22⋊Dic13—41no—
74C4⋊Dic13—24no—
75C4⋊Dic13—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13—22no—
78C4⋊Dic13—22no—
79C4⋊Dic13—42no—
80C4⋊Dic13—42no—
81C4⋊Dic13—81no—
82C4×Dic13—44no—
83C4×Dic13—41no—
84C4×Dic13—42no—
85C4×Dic13—42no—
86C4×Dic13—81no—
87#6099—41no—
88#6099—41no—
89C2×#1055—41no—
90#2369—131no—
91C2×#356D1311yescharacteristic
92#1886—131no—
93#1857—132no—
94#1394—132no—
95C23×C13#12011yescharacteristic
96Q8×C13—41no—
97Q8×C13—41no—
98Q8×C13—42no—
99Q8×C13—42no—
100Q8×C13—81no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13C2×C4⋊C411yescharacteristic
112C2×C4×C13C4×D412yes—
113C2×C4×C13C22⋊Q812yes—
114C2×C4×C13#12311yescharacteristic
115C2×Dic13—24no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—42no—
123C8×C13—44no—
124#1055—81no—
125C2×C4⋊Q8C2×D1311yescharacteristic
126#519—131no—
127#428—262no—
128#419—261no—
129C2×#101—131no—
130C2×#101C2×D1312yes—
131#391—132no—
132#391—261no—
133#389—262no—
134C4×C4⋊C4—262no—
135C4×C4⋊C4—261no—
136#356Dic1314yescomplemented
137#339—262no—
138#339—261no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13#38511yescharacteristic
142C22×C13B(4,𝔽2)11yescharacteristic
143C22×C13#45811yescharacteristic
144C4×C13—24no—
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—21no—
148C4×C13—22no—
149C4×C13—42no—
150Dic13—44no—
151Dic13—81no—
152Dic13—82no—
153Dic13—81no—
154C22×Q8D5211yescharacteristic
155C22×Q8C22×D1311yescharacteristic
156C2×M16—22no—
157C2×M16—261no—
158C4⋊Q8—22no—
159C4⋊Q8Dic2612yes—
160C4⋊Q8C2×Dic1312yes—
161C4×Q8—521no—
162C4×Q8—521no—
163#117—261no—
164#117—262no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C42—132no—
171C2×C42—262no—
172C2×C42—261no—
173C2×C42D5211yescharacteristic
174#107—522no—
175#106—522no—
176#103—521no—
177#103—521no—
178#101—22no—
179#101—262no—
180#101C2×Dic1314yes—
181#95—262no—
182#95—262no—
183#95—262no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#186711yescharacteristic
187C2×C13#220411yescharacteristic
188C2×C13#220511yescharacteristic
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8C4⋊Dic1312yes—
195C2×Q8C2×Dic2611yescharacteristic
196C2×Q8#612912yes—
197C2×Q8C22×Dic1311yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—262no—
201C22×C4—262no—
202C22×C4C2×D5211yescharacteristic
203C22×C4D4×D1312yes—
204M16—24no—
205M16—42no—
206M16—521no—
207M16—521no—
208C2×C8—42no—
209C2×C8—521no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—264no—
213C4⋊C4—261no—
214C4⋊C4—261no—
215C4⋊C4—262no—
216C4⋊C4—262no—
217C4⋊C4—522no—
218C4⋊C4—522no—
219C4⋊C4—1041no—
220C22⋊C4—521no—
221C42—21no—
222C42—522no—
223C42—524no—
224C42—522no—
225C42—521no—
226C42—1041no—
227C42C4⋊Dic1312yes—
228C13#1297311yescharacteristic, complemented, Sylow
229C23#8813611yescharacteristic
230Q8—41no—
231Q8—42no—
232Q8—41no—
233Q8—42no—
234Q8—81no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—264no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—522no—
253C2×C4#8813212yes—
254C2×C4#8814011yescharacteristic
255C2×C4C2×C4⋊Dic1311yescharacteristic
256C2×C4D4×Dic1312yes—
257C8—44no—
258C8—1041no—
259C22—21no—
260C22—21no—
261C22#1171840211yescharacteristic
262C22#1171840311yescharacteristic
263C22#1171861111yescharacteristic
264C4—24no—
265C4—22no—
266C4—21no—
267C4—22no—
268C4—21no—
269C4—42no—
270C4—524no—
271C4—1041no—
272C4—1042no—
273C4—1041no—
274C2—21no—
275C2—21no—
276C2#1311511911yescharacteristic
277C2#1311686411yescharacteristic
278C2#1311686711yescharacteristic
subgroupG/H
centerC22#11718402
commutatorC2×Q8×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC2×C13×#356C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
cosocleC22×Q8×C13C23
hypercenterC2×#356D13
hypocenterC13#12973
LCSG ▷ C2×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
17. C13×#356C4semidirect
136. #356Dic13semidirect
228. C13#12973semidirect

Maximal subgroups

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

subgroupindex
#131179262
#131152302
#131150532
#131129622
C2×C13×#3562
#1297313