Finite Group Databasebeta

← #15773755

Subgroups — #15773755

Order 3328.

340 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114832C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112863C212yesmaximal
4#13112842C212yesmaximal
5C13×#2634C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#400—21no—
9C13×#400C411yescharacteristic
10C13×#400C2211yescharacteristic
11C13×#398C411yescharacteristic
12C13×#398C2211yescharacteristic
13C13×#395—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#383C411yescharacteristic
17C2×#88076—21no—
18#11718587—21no—
19#11718585—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C13×#125—41no—
25C13×#125—41no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4C2311yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×#6099—22no—
41C13×#95—21no—
42C13×#95—21no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88076—42no—
52C22⋊#1055—22no—
53C4⋊#1055—41no—
54C4⋊#1055—41no—
55C4⋊#1055—41no—
56#88043—41no—
57#11835—131nomaximal, Sylow
58C2×Q8×C13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90#6099—42no—
91#6099—42no—
92C2×#1055—42no—
93C2×#1055—42no—
94#2634D1311yescharacteristic
95#1801—131no—
96#1467—131no—
97#1353—132no—
98#1346—132no—
99C23×C13C2×C22⋊C411yescharacteristic
100Q8×C13—42no—
101Q8×C13—42no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C13#13711yescharacteristic
132#1055—82no—
133#1055—82no—
134C2×#125Dic1311yescharacteristic
135C2×C4×Q8C2×D1311yescharacteristic
136#432—261no—
137#423—261no—
138C2×#101—261no—
139#400—21no—
140#400Dic1311yescharacteristic
141#400C2×D1311yescharacteristic
142#398Dic1311yescharacteristic
143#398C2×D1311yescharacteristic
144#395—21no—
145#387—21no—
146#387—21no—
147#383Dic1311yescharacteristic
148#343—132no—
149#324—132no—
150#324—261no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13C2×#9911yescharacteristic
154C22×C13#41711yescharacteristic
155C22×C13#42111yescharacteristic
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—81no—
166C4×C13—81no—
167C4×C13—81no—
168C4×C13—81no—
169C22×Q8C22⋊D1311yescharacteristic
170C2×M16—262no—
171#125—41no—
172#125—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C2×Dic1311yescharacteristic
180C2×C4⋊C4C2×Dic1311yescharacteristic
181C2×C4⋊C4C2×Dic1311yescharacteristic
182C2×C4⋊C4C22⋊D1311yescharacteristic
183C2×C4⋊C4C22×D1311yescharacteristic
184C2×C42C2×Dic1311yescharacteristic
185C2×C42C22⋊D1311yescharacteristic
186C2×C42C22⋊D1311yescharacteristic
187C4⋊C8—521no—
188C4⋊C8—521no—
189C4⋊C8—521no—
190#101—522no—
191C22⋊C8—262no—
192#97—521no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95C2×Dic1311yescharacteristic
202#95C2×Dic1311yescharacteristic
203C2×C13—21no—
204C2×C13—21no—
205C2×C13#151311yescharacteristic
206C2×C13#212311yescharacteristic
207C2×C13#213311yescharacteristic
208C2×Q8—21no—
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—41no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4C22⋊Dic1311yescharacteristic
217C22×C4C22⋊Dic1311yescharacteristic
218C22×C4C22⋊Dic1311yescharacteristic
219C22×C4C22⋊Dic1311yescharacteristic
220C22×C4C22×Dic1311yescharacteristic
221C22×C4C2×C22⋊D1311yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223M16—522no—
224M16—522no—
225C2×C8—522no—
226C2×C8—522no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C13#1183511yescharacteristic, complemented, Sylow
245C23C2×C22⋊Dic1311yescharacteristic
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4#8807411yescharacteristic
275C2×C4#8807411yescharacteristic
276C2×C4#8820311yescharacteristic
277C2×C4#8820511yescharacteristic
278C8—1042no—
279C8—1042no—
280C22—21no—
281C22—21no—
282C22C2×#8807411yescharacteristic
283C22#1171889311yescharacteristic
284C22#1171889711yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4—81no—
298C2—21no—
299C2—21no—
300C2#1311337911yescharacteristic
301C2#1311649011yescharacteristic
302C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2634C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2634D13
hypocenterC13#11835
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2634

Complements

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

NH ≅ G/Ntype
244. C13#11835semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131802
#131128632
#131128422
C13×#26342
#1183513