Finite Group Databasebeta

← #15773662

Subgroups — #15773662

Order 3328.

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

normal subgroups only

This group has 388 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#13114919C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112866C212yesmaximal, complemented
4#13112863C212yesmaximal, complemented
5C13×#2396C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#400C2211yescharacteristic
9C13×#399C411yescharacteristic
10C13×#398—21no—
11C13×#396—21no—
12C13×#395C2211yescharacteristic
13C13×#393C411yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4C411yescharacteristic
16C4×C13×C22⋊C4—21no—
17#11718868—21no—
18#11718587—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120C2212yes—
22#11718117—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C13×#117—41no—
28C13×#117—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×#6099—22no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51C22⋊#1055—22no—
52C22⋊#1055—41no—
53C22⋊#1055—41no—
54C4⋊#1055—41no—
55#88043—41no—
56#11816—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C2×Q8×C13—42no—
59C2×Q8×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—42no—
90C42×C13—41no—
91C42×C13—41no—
92#6099—42no—
93#6099—42no—
94C2×#1055—42no—
95C2×#1055—42no—
96#2396D1311yescharacteristic
97#1822—131no—
98#1464—131no—
99#1354—132no—
100#1353—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13C2×C22⋊C411yescharacteristic
107Q8×C13—42no—
108Q8×C13—42no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
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—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×C13#13712yes—
138#1055—82no—
139#1055—82no—
140C2×C4×Q8Dic1311yescharacteristic
141C2×#117C2×D1311yescharacteristic
142#432—261no—
143#407—261no—
144#400C2×D1311yescharacteristic
145#399Dic1311yescharacteristic
146#398—21no—
147#396—21no—
148#395C2×D1311yescharacteristic
149#393Dic1311yescharacteristic
150C4×C4⋊C4—21no—
151C4×C4⋊C4Dic1311yescharacteristic
152C4×C22⋊C4—21no—
153#343—132no—
154#343—261no—
155#324—132no—
156#323—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—81no—
164C22×C13C2×#9911yescharacteristic
165C22×C13#41911yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—22no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—42no—
171C4×C13—41no—
172C4×C13—42no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—81no—
177C4×C13—81no—
178C22×Q8C2×Dic1311yescharacteristic
179C23×C4C22⋊D1311yescharacteristic
180C2×M16—262no—
181C4×Q8—41no—
182C4×Q8—41no—
183#117—41no—
184#117—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×Dic1311yescharacteristic
190C2×C4⋊C4C22⋊D1311yescharacteristic
191C2×C4⋊C4C22×D1311yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4C2×Dic1311yescharacteristic
195C2×C22⋊C4C22⋊D1311yescharacteristic
196C2×C42—21no—
197C2×C42—21no—
198C2×C42C2×Dic1311yescharacteristic
199C2×C42C22⋊D1311yescharacteristic
200C4⋊C8—521no—
201C22⋊C8—262no—
202C22⋊C8—521no—
203C22⋊C8—521no—
204#97—521no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95C2×Dic1311yescharacteristic
210#95C2×Dic1311yescharacteristic
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—81no—
214C2×C13#151111yescharacteristic
215C2×C13#212011yescharacteristic
216C2×C13#213211yescharacteristic
217C24C22⋊Dic1311yescharacteristic
218C2×Q8—42no—
219C2×Q8—41no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22⋊Dic1311yescharacteristic
230C22×C4C22⋊Dic1311yescharacteristic
231C22×C4C22×Dic1311yescharacteristic
232C22×C4C2×C22⋊D1311yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234M16—522no—
235M16—522no—
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—42no—
254C42—41no—
255C42—41no—
256C13#1181611yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23C2×C22⋊Dic1311yescharacteristic
263Q8—42no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
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—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4#8807411yescharacteristic
292C2×C4#8807411yescharacteristic
293C2×C4#8819612yes—
294C8—1042no—
295C8—1042no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#8807411yescharacteristic
304C22#1171888611yescharacteristic
305C22#1171889711yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—42no—
310C4—41no—
311C4—42no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1311336911yescharacteristic
321C2#1311647711yescharacteristic
322C2#1311652111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2396C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2396D13
hypocenterC13#11816
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2396

Complements

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

NH ≅ G/Ntype
3. #13112866C2semidirect
4. #13112863C2semidirect
256. C13#11816semidirect

Maximal subgroups

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

subgroupindex
#131149192
#131131702
#131128662
#131128632
C13×#23962
#1181613