Finite Group Databasebeta

← #15775694

Subgroups — #15775694

Order 3328.

460 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 63 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#13115997C211yesmaximal, characteristic, complemented
2#13113775C212yesmaximal, complemented
3#13112839C212yesmaximal, complemented
4#13112770C211yesmaximal, characteristic, complemented
5C13×#2733C211yesmaximal, characteristic
6C2×C13×#124—21no—
7#11719205C2211yescharacteristic
8C13×#394C2212yes—
9C13×#392—22no—
10C13×#391C2211yescharacteristic
11C13×#390—21no—
12C13×#388—22no—
13#11718886—21no—
14#11718879—22no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13D411yescharacteristic
20C22×D4×C13—21no—
21C22×D4×C13—21no—
22C22×D4×C13D412yes—
23C13×#124—42no—
24C13×#124—42no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—21no—
32C2×C42×C13D411yescharacteristic
33C2×#6105—42no—
34#88180—21no—
35#88178—22no—
36C2×#6099—21no—
37#88144—41no—
38#88142—41no—
39C13×#95—22no—
40C13×#95D412yes—
41#88075—41no—
42#88075—41no—
43#88072—42no—
44C22⋊#1055—22no—
45#12212—131nomaximal, Sylow
46C24×C13—22no—
47C2×Q8×C13—21no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13SD1612yescomplemented
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—42no—
54C2×D4×C13—82no—
55C2×D4×C13—81no—
56C2×D4×C13—81no—
57C2×D4×C13—81no—
58C2×D4×C13—81no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D412yes—
64C2×Dic26—22no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—81no—
67C13×C22⋊C4—44no—
68C13×C22⋊C4—44no—
69C13×C22⋊C4—42no—
70C13×C22⋊C4—42no—
71C13×C22⋊C4—82no—
72C42×C13—41no—
73C42×C13—42no—
74C22⋊Dic13—41no—
75#6105—84no—
76C4⋊Dic13—22no—
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79#6101—42no—
80C4×Dic13—41no—
81#6099—41no—
82#6099—41no—
83C2×#1055—42no—
84C2×#1055—41no—
85#2733D1311yescharacteristic
86#2028—131no—
87#1599—132no—
88#1345—132no—
89#1319—131no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13#12011yescharacteristic
98Q8×C13—42no—
99Q8×C13—81no—
100D4×C13—44no—
101D4×C13—84no—
102D4×C13—84no—
103D4×C13—82no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13C2×SD1611yescharacteristic
118C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
119C2×Dic13—41no—
120C2×Dic13—41no—
121Dic26—82no—
122#1055—81no—
123#1055—82no—
124#544—131no—
125C2×#124—21no—
126#450—262no—
127#419—261no—
128#394C2×D1312yes—
129#392—22no—
130#391C2×D1311yescharacteristic
131#390—21no—
132#388—22no—
133#343—131no—
134#339—261no—
135#328—262no—
136#324—132no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—82no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13—82no—
143C22×C13—82no—
144C22×C13—82no—
145C22×C13—82no—
146C22×C13#45011yescharacteristic
147C22×C13#45511yescharacteristic
148C22×C13B(4,𝔽2)11yescharacteristic
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—42no—
152C4×C13—42no—
153C4×C13—42no—
154C4×C13—82no—
155Dic13—81no—
156Dic13—81no—
157C22×Q8C22⋊D1311yescharacteristic
158C22×D4—21no—
159C22×D4—21no—
160C22×D4C22⋊D1312yes—
161C2×SD16—522no—
162C2×M16—261no—
163C4⋊Q8—521no—
164#125—521no—
165#124—42no—
166#124—42no—
167C22⋊Q8—262no—
168#117—261no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4C22×D1311yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C42—21no—
176C2×C42C22⋊D1311yescharacteristic
177#103—521no—
178#103—521no—
179#102—522no—
180C22⋊C8—262no—
181#95—22no—
182#95C22⋊D1312yes—
183C2×C13—21no—
184C2×C13—21no—
185C2×C13—162no—
186C2×C13#160111yescharacteristic
187C2×C13#219911yescharacteristic
188C2×C13#220411yescharacteristic
189C24—22no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—262no—
194C2×Q8#610512yescomplemented
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—42no—
198C2×D4—82no—
199C2×D4—81no—
200C2×D4—81no—
201C2×D4—81no—
202C2×D4—81no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4C2×C22⋊D1311yescharacteristic
207C22×C4C2×C22⋊D1312yes—
208SD16—1044no—
209M16—521no—
210M16—521no—
211C2×C8—522no—
212C2×C8—521no—
213C4⋊C4—41no—
214C4⋊C4—81no—
215C4⋊C4—262no—
216C4⋊C4—261no—
217C4⋊C4—261no—
218C4⋊C4—522no—
219C22⋊C4—44no—
220C22⋊C4—44no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—82no—
224C22⋊C4—521no—
225C42—41no—
226C42—42no—
227C42—521no—
228C13#1221211yescharacteristic, complemented, Sylow
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23—42no—
235C23—42no—
236C23#8820711yescharacteristic
237Q8—42no—
238Q8—81no—
239Q8—1042no—
240D4—44no—
241D4—82no—
242D4—84no—
243D4—84no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4#8818611yescharacteristic
260C2×C4C2×#610511yescharacteristic
261C8—1041no—
262C8—1042no—
263C22—21no—
264C22—21no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22—82no—
269C22—82no—
270C22—82no—
271C22—82no—
272C22#1171887911yescharacteristic
273C22#1171890311yescharacteristic
274C22#1171890511yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—42no—
280C4—82no—
281C4—1041no—
282C4—1041no—
283C2—21no—
284C2—21no—
285C2—162no—
286C2#1311378811yescharacteristic
287C2#1311683711yescharacteristic
288C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
Fitting, prime radicalC13×#2733C2
socleC22×C13B(4,𝔽2)
hypercenter#2733D13
hypocenterC13#12212
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #13115997C2semidirect
2. #13113775C2semidirect
3. #13112839C2semidirect
4. #13112770C2semidirect
50. C2×Q8×C13SD16semidirect
194. C2×Q8#6105semidirect
228. C13#12212semidirect

Maximal subgroups

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

subgroupindex
#131159972
#131137752
#131128392
#131127702
C13×#27332
#1221213