Finite Group Databasebeta

← #16776900

Subgroups — #16776900

Order 3328.

352 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 82 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#13130728C211yesmaximal, characteristic
2#13130691C211yesmaximal, characteristic
3#13114815C211yesmaximal, characteristic
4C2×C42×D13C2211yescharacteristic
5C2×#88111—21no—
6C2×#88111C412yes—
7C2×C4⋊#1057—21no—
8C2×#88060—21no—
9C2×#88054—21no—
10#11718290—21no—
11#11718290—21no—
12#11718290C412yes—
13C13×#336C411yescharacteristic
14#11718116C411yescharacteristic
15C22×C4×D13C2×C411yescharacteristic
16C22×C4×D13D411yescharacteristic
17C22×C4×D13Q811yescharacteristic
18C22×#1057—22no—
19C22×#1057—22no—
20C22×C8×C13—21no—
21C2×C42×C13C2×C411yescharacteristic
22C2×C4×Dic13C2×C411yescharacteristic
23C2×C4×Dic13D411yescharacteristic
24C2×C4×Dic13D411yescharacteristic
25C22×#1055—21no—
26C42×D13—42no—
27#88111—41no—
28#88111—41no—
29#88111—42no—
30C4⋊#1057—42no—
31#88060—41no—
32#88060—41no—
33#88054—42no—
34#7044—131nomaximal, Sylow
35C23×D13C4⋊C411yescharacteristic
36C22×C4×C13C4211yescharacteristic
37C22×C4×C13C22⋊C411yescharacteristic
38C22×C4×C13C4⋊C411yescharacteristic
39C22×Dic13C22⋊C411yescharacteristic
40C22×Dic13C22⋊C411yescharacteristic
41C22×Dic13C4⋊C411yescharacteristic
42C2×C4×D13—21no—
43C2×C4×D13—21no—
44C2×C4×D13—22no—
45C2×C4×D13—22no—
46C2×C4×D13—41no—
47C2×C4×D13—41no—
48C2×C4×D13—41no—
49C2×C4×D13—41no—
50C2×C4×D13—41no—
51C2×C4×D13D811yescharacteristic
52C2×C4×D13SD1611yescharacteristic
53C2×C4×D13SD1611yescharacteristic
54C2×C4×D13Q1611yescharacteristic
55C2×#1057—42no—
56C2×#1057—42no—
57C2×#1057—42no—
58C2×#1057—42no—
59C2×#1057—42no—
60C2×#1057—42no—
61C2×C8×C13—41no—
62C2×C8×C13—41no—
63C2×C8×C13—41no—
64C42×C13—41no—
65C4×Dic13—22no—
66C4×Dic13—22no—
67C4×Dic13—41no—
68C2×#1055—41no—
69C2×#1055—41no—
70C2×#1055—41no—
71#1817—131no—
72#1797—131no—
73#1797—131no—
74C23×C13#9511yescharacteristic
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—21no—
78C22×D13—21no—
79C22×D13—21no—
80C22×D13—21no—
81C22×D13#10611yescharacteristic
82C22×D13#10711yescharacteristic
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13#10211yescharacteristic
91C2×C4×C13#10311yescharacteristic
92C2×C4×C13#10811yescharacteristic
93C2×C4×C13#10811yescharacteristic
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13#9912yes—
101C2×Dic13#10211yescharacteristic
102C2×Dic13#10311yescharacteristic
103C2×Dic13#10812yes—
104C4×D13—41no—
105C4×D13—41no—
106C4×D13—41no—
107C4×D13—41no—
108C4×D13—42no—
109C4×D13—42no—
110C4×D13—44no—
111#1057—82no—
112#1057—82no—
113C8×C13—81no—
114#1055—81no—
115C22×C42—131no—
116C2×C4⋊C8—261no—
117C2×C4⋊C8—261no—
118C2×C22⋊C8—132no—
119C2×C22⋊C8—261no—
120C2×C22⋊C8—261no—
121#336—132no—
122#336—131no—
123#336—261no—
124#336—261no—
125#336#26111yescharacteristic
126C22×C13H(3,ℤ/4)11yescharacteristic
127C22×C13#34011yescharacteristic
128C22×C13#34111yescharacteristic
129C22×C13#34111yescharacteristic
130C22×C13#34211yescharacteristic
131C22×C13#34411yescharacteristic
132C22×C13#34411yescharacteristic
133C2×D13—21no—
134C2×D13—21no—
135C2×D13—21no—
136C2×D13—21no—
137C2×D13—21no—
138C2×D13—21no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—41no—
142C2×D13—41no—
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—21no—
147C4×C13—41no—
148Dic13—21no—
149Dic13—21no—
150Dic13—22no—
151Dic13—22no—
152C23×C4—131no—
153C23×C4—131no—
154C23×C4—131no—
155C22×C8—21no—
156C22×C8—262no—
157C22×C8—262no—
158C22×C8—261no—
159C2×C42—131no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—522no—
163C2×C42C2×#26111yescharacteristic
164C4⋊C8—522no—
165C4⋊C8—522no—
166C22⋊C8—521no—
167C22⋊C8—521no—
168C22⋊C8—521no—
169C22⋊C8—521no—
170C22⋊C8—522no—
171C2×C13#128711yescharacteristic
172C2×C13#128711yescharacteristic
173C2×C13#128911yescharacteristic
174C2×C13#129811yescharacteristic
175C2×C13#130111yescharacteristic
176C2×C13#130111yescharacteristic
177C2×C13#130611yescharacteristic
178D13—41no—
179D13—41no—
180C24—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—131no—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—261no—
191C22×C4—261no—
192C22×C4—521no—
193C22×C4—521no—
194C22×C4—521no—
195C22×C4—521no—
196C22×C4—521no—
197C22×C4C4×#26111yescharacteristic
198C22×C4C4⋊#26111yescharacteristic
199C22×C4C22⋊#26111yescharacteristic
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—521no—
204C2×C8—521no—
205C2×C8—522no—
206C2×C8—522no—
207C2×C8—522no—
208C2×C8—522no—
209C2×C8—522no—
210C2×C8—522no—
211C2×C8—521no—
212C42—41no—
213C42—262no—
214C42—262no—
215C42—521no—
216C13#704411yescharacteristic, complemented, Sylow
217C23—131no—
218C23—131no—
219C23—261no—
220C23—261no—
221C23—261no—
222C23—261no—
223C23—261no—
224C23—261no—
225C23(C2×#261)⋊C411yescharacteristic
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—132no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—132no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—524no—
250C2×C4#8810311yescharacteristic
251C2×C4#8810411yescharacteristic
252C2×C4#8811511yescharacteristic
253C2×C4#8811711yescharacteristic
254C8—81no—
255C8—1041no—
256C8—1042no—
257C8—1042no—
258C22—261no—
259C22—261no—
260C22—261no—
261C22—261no—
262C22—261no—
263C22—261no—
264C22—521no—
265C22—521no—
266C22—521no—
267C22—521no—
268C22#1171823511yescharacteristic
269C22#1171823811yescharacteristic
270C22#1171824611yescharacteristic
271C22#1171826611yescharacteristic
272C22#1171826811yescharacteristic
273C22#1171827311yescharacteristic
274C22#1171827411yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—41no—
280C4—262no—
281C4—261no—
282C4—261no—
283C4—262no—
284C2—521no—
285C2—521no—
286C2#1312969211yescharacteristic
287C2#1312969311yescharacteristic
288C2#1312969811yescharacteristic
289C2#1312971911yescharacteristic
290C2#1312972611yescharacteristic
291C2#1312972811yescharacteristic
292C2#1312974011yescharacteristic
subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC22×C4×C13C42
FrattiniC2×C42C2×#261
FittingC13×#336C4
socleC23×C13#95
prime radicalC23×D13C4⋊C4
cosocleC2×C42×D13C22
hypercenter#336#261
hypocenterC13#7044
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
216. C13#7044semidirect

Maximal subgroups

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

subgroupindex
#131307282
#131306912
#131148152
#704413