Finite Group Databasebeta

← #15773735

Subgroups — #15773735

Order 3328.

384 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 91 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#13112866C212yesmaximal
4#13112842C212yesmaximal
5C13×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398—21no—
9C13×#398C411yescharacteristic
10C13×#398C2211yescharacteristic
11C13×#395—21no—
12C13×#395C411yescharacteristic
13C13×#395C2211yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4—21no—
16C13×#376C411yescharacteristic
17C2×#88076—21no—
18#11718587—21no—
19#11718585—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×C42×C13—21no—
39C2×C42×C13—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×#6099—22no—
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#11831—131nomaximal, Sylow
58C2×Q8×C13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13—42no—
63C2×Q8×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C42×C13—24no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—41no—
93C42×C13—41no—
94#6099—42no—
95#6099—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98#2399D1311yescharacteristic
99#1801—131no—
100#1467—131no—
101#1354—132no—
102#1346—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—42no—
105Q8×C13—42no—
106Q8×C13—42no—
107Q8×C13—42no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13#13711yescharacteristic
139#1055—82no—
140#1055—82no—
141C2×C4×Q8Dic1311yescharacteristic
142C2×C4×Q8C2×D1311yescharacteristic
143#432—261no—
144#423—261no—
145C2×#101—261no—
146#398—21no—
147#398Dic1311yescharacteristic
148#398C2×D1311yescharacteristic
149#395—21no—
150#395Dic1311yescharacteristic
151#395C2×D1311yescharacteristic
152C4×C4⋊C4—21no—
153C4×C4⋊C4—21no—
154#376Dic1311yescharacteristic
155#343—132no—
156#324—132no—
157#324—261no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13C2×#9911yescharacteristic
161C22×C13#41711yescharacteristic
162C22×C13#42111yescharacteristic
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—42no—
167C4×C13—42no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—42no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—81no—
175C4×C13#35612yes—
176C22×Q8C2×Dic1311yescharacteristic
177C22×Q8C22⋊D1311yescharacteristic
178C2×M16—262no—
179C4×Q8—41no—
180C4×Q8—41no—
181C4×Q8—41no—
182C4×Q8—41no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×Dic1311yescharacteristic
189C2×C4⋊C4C2×Dic1311yescharacteristic
190C2×C4⋊C4C22⋊D1311yescharacteristic
191C2×C4⋊C4C22×D1311yescharacteristic
192C2×C42—21no—
193C2×C42—21no—
194C2×C42C2×Dic1311yescharacteristic
195C2×C42C22⋊D1311yescharacteristic
196C2×C42C22⋊D1311yescharacteristic
197C4⋊C8—521no—
198C4⋊C8—521no—
199C4⋊C8—521no—
200#101—522no—
201C22⋊C8—262no—
202#97—521no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95C2×Dic1311yescharacteristic
209#95C2×Dic1311yescharacteristic
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#151311yescharacteristic
213C2×C13#212011yescharacteristic
214C2×C13C2×#35611yescharacteristic
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8—42no—
220C2×Q8—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C22⋊Dic1311yescharacteristic
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22×Dic1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232M16—522no—
233M16—522no—
234C2×C8—522no—
235C2×C8—522no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C42—24no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—41no—
254C42—41no—
255C13#1183111yescharacteristic, complemented, Sylow
256C23C2×C22⋊Dic1311yescharacteristic
257Q8—42no—
258Q8—42no—
259Q8—42no—
260Q8—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4#8807411yescharacteristic
289C2×C4#8807411yescharacteristic
290C2×C4#8820311yescharacteristic
291C2×C4#8820511yescharacteristic
292C8—1042no—
293C8—1042no—
294C22—21no—
295C22—21no—
296C22C2×#8807411yescharacteristic
297C22#1171889311yescharacteristic
298C22#1171889711yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—41no—
310C4—81no—
311C4#1171814012yes—
312C2—21no—
313C2—21no—
314C2#1311337911yescharacteristic
315C2#1311647711yescharacteristic
316C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2399C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2399D13
hypocenterC13#11831
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2399

Complements

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

NH ≅ G/Ntype
255. C13#11831semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131802
#131128662
#131128422
C13×#23992
#1183113