Finite Group Databasebeta

← #15750135

Subgroups — #15750135

Order 3328.

324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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#13113157C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3C13×#1870C211yesmaximal, characteristic
4C22×C13×M16C411yescharacteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×C13×C22⋊C8—21no—
7C2×C13×C22⋊C8C411yescharacteristic
8C2×C22⋊#1055—21no—
9#11718586—21no—
10C13×#336—21no—
11#11718120C412yes—
12#11718117—21no—
13#11718117—21no—
14#11718117C412yes—
15C22×D4×C13Q811yescharacteristic
16C23×C4×C13C2×C411yescharacteristic
17C23×C4×C13D411yescharacteristic
18C2×C13×M16—42no—
19C2×C13×M16—41no—
20C22×C8×C13—21no—
21C22×C8×C13—21no—
22C4×D4×C13—41no—
23C4×D4×C13—41no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C22⋊C4C2×C411yescharacteristic
26C2×C13×C22⋊C4D411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C22×#1055—41no—
29C13×C22⋊C8—42no—
30C13×C22⋊C8—41no—
31C22⋊#1055—22no—
32C22⋊#1055—22no—
33C22⋊#1055—41no—
34C4⋊#1055—41no—
35C4×#1055—41no—
36#7285—131nomaximal, Sylow
37C24×C13C4⋊C411yescharacteristic
38C24×C13C4⋊C411yescharacteristic
39C2×D4×C13—22no—
40C2×D4×C13—22no—
41C2×D4×C13—41no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—41no—
47C22×C4×C13—41no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13C4211yescharacteristic
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C4⋊C411yescharacteristic
55C13×M16—42no—
56C13×M16—42no—
57C2×C8×C13—22no—
58C2×C8×C13—41no—
59C2×C8×C13—41no—
60C2×C8×C13—41no—
61C2×C8×C13—41no—
62C2×C8×C13—41no—
63C13×C4⋊C4—41no—
64C13×C22⋊C4—41no—
65C13×C22⋊C4—41no—
66C42×C13—21no—
67C42×C13—21no—
68C2×#1055—42no—
69C2×#1055—42no—
70C2×#1055—81no—
71C2×#1055—81no—
72#1870D1311yescharacteristic
73#1460—131no—
74#1459—131no—
75C23×C13—21no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—41no—
81C23×C13—41no—
82C23×C13—41no—
83C23×C13—41no—
84C23×C13#9511yescharacteristic
85C23×C13#10812yes—
86D4×C13—44no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—81no—
103C2×C4×C13#9911yescharacteristic
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13#10812yes—
106C8×C13—42no—
107C8×C13—81no—
108#1055—82no—
109#1055—82no—
110C22×M16Dic1311yescharacteristic
111C2×C4×D4C2×D1311yescharacteristic
112#431—261no—
113C2×C22⋊C8—21no—
114C2×C22⋊C8—261no—
115C2×C22⋊C8Dic1311yescharacteristic
116#336—21no—
117#324—132no—
118#323—132no—
119#323—261no—
120#323—261no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—22no—
124C22×C13—42no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13—81no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13#34111yescharacteristic
134C22×C13#34111yescharacteristic
135C22×C13#34211yescharacteristic
136C4×C13—22no—
137C4×C13—21no—
138C4×C13—41no—
139C4×C13—41no—
140C4×C13—41no—
141C4×C13AΣL(1,𝔽16)11yescharacteristic
142C4×C13#35211yescharacteristic
143C22×D4Dic2611yescharacteristic
144C23×C4C2×Dic1311yescharacteristic
145C23×C4C22⋊D1311yescharacteristic
146C2×M16—42no—
147C2×M16—41no—
148C22×C8—21no—
149C22×C8—21no—
150C22×C8—521no—
151C4×D4—41no—
152C4×D4—41no—
153C2×C4⋊C4C4×D1311yescharacteristic
154C2×C22⋊C4C4×D1311yescharacteristic
155C2×C22⋊C4D5211yescharacteristic
156C2×C42C22⋊D1311yescharacteristic
157C4⋊C8—521no—
158C22⋊C8—42no—
159C22⋊C8—41no—
160C22⋊C8—262no—
161C22⋊C8—262no—
162C22⋊C8—521no—
163C4×C8—521no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13—42no—
167C2×C13—81no—
168C2×C13#129811yescharacteristic
169C2×C13#139011yescharacteristic
170C2×C13#139511yescharacteristic
171C24#610111yescharacteristic
172C24C4⋊Dic1311yescharacteristic
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—41no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4C4×Dic1311yescharacteristic
185C22×C4#610111yescharacteristic
186C22×C4#610311yescharacteristic
187C22×C4#610311yescharacteristic
188C22×C4C22⋊Dic1311yescharacteristic
189M16—42no—
190M16—42no—
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—522no—
198C2×C8—522no—
199C2×C8—1041no—
200C2×C8—1041no—
201C4⋊C4—41no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C42—21no—
205C42—21no—
206C13#728511yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23#8806212yes—
217C23#8807111yescharacteristic
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4#8806212yes—
236C2×C4#8807411yescharacteristic
237C2×C4#8807411yescharacteristic
238C8—42no—
239C8—81no—
240C8—1042no—
241C8—1042no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#1171811811yescharacteristic
255C22#1171815011yescharacteristic
256C22#1171815011yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4#1171812811yescharacteristic
263C4#1171813111yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—81no—
268C2#1311272311yescharacteristic
269C2#1311295411yescharacteristic
270C2#1311296511yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C42
FrattiniC2×C4×D4C2×D13
FittingC13×#1870C2
socleC22×C13#342
prime radicalC22×D4×C13Q8
cosocleC2×C4×D4×C13C22
hypercenter#1870D13
hypocenterC13#7285
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
206. C13#7285semidirect

Maximal subgroups

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

subgroupindex
#131131572
#131131542
C13×#18702
#728513