Finite Group Databasebeta

← #15773832

Subgroups — #15773832

Order 3328.

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

normal subgroups only

This group has 396 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#13114916C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic
3#13112863C212yesmaximal, complemented
4#13112842C212yesmaximal, complemented
5C13×#2484C211yesmaximal, characteristic
6C2×C13×#117C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#400C411yescharacteristic
9C13×#400C2211yescharacteristic
10C13×#398C411yescharacteristic
11C13×#398C2211yescharacteristic
12C13×#387—21no—
13C13×#387—21no—
14C13×#385—21no—
15C13×#381—21no—
16C13×#381C411yescharacteristic
17#11718868—21no—
18C2×C22⋊#1055—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—21no—
41C2×#6099—22no—
42C22×#1055—41no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52C22⋊#1055—22no—
53C22⋊#1055—41no—
54C22⋊#1055—41no—
55C22⋊#1055—41no—
56#11850—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
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—21no—
68C22×C4×C13—21no—
69C22×C4×C13—41no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C42×C13—42no—
90#6099—42no—
91#6099—42no—
92C2×#1055—42no—
93C2×#1055—42no—
94C2×#1055—82no—
95#2484D1311yescharacteristic
96#1821—131no—
97C2×#324—131no—
98#1353—132no—
99#1346—132no—
100C23×C13—22no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13#9911yescharacteristic
105C23×C13#9911yescharacteristic
106C23×C13C2×C22⋊C411yescharacteristic
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—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
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—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—81no—
137C2×C4×C13#13512yes—
138#1055—82no—
139#1055—82no—
140C2×#117Dic1311yescharacteristic
141C22×C4⋊C4C2×D1311yescharacteristic
142#407—261no—
143C2×C22⋊C8—261no—
144#400Dic1311yescharacteristic
145#400C2×D1311yescharacteristic
146#398Dic1311yescharacteristic
147#398C2×D1311yescharacteristic
148#387—21no—
149#387—21no—
150#385—21no—
151#381—21no—
152#381Dic1311yescharacteristic
153#343—132no—
154#343—261no—
155#324—132no—
156#324—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—42no—
165C22×C13—42no—
166C22×C13#35212yes—
167C22×C13C2×#9911yescharacteristic
168C22×C13#41611yescharacteristic
169C22×C13#42111yescharacteristic
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—81no—
180C23×C4C2×Dic1311yescharacteristic
181C23×C4C22⋊D1311yescharacteristic
182C23×C4C22⋊D1311yescharacteristic
183C2×M16—262no—
184C22×C8—521no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×Dic1311yescharacteristic
192C2×C4⋊C4C2×Dic1311yescharacteristic
193C2×C4⋊C4C2×Dic1311yescharacteristic
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C4⋊C4C22×D1311yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C42—21no—
200C22⋊C8—262no—
201C22⋊C8—521no—
202C22⋊C8—521no—
203C22⋊C8—521no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95C2×Dic1311yescharacteristic
212#95C2×Dic1311yescharacteristic
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—22no—
216C2×C13—41no—
217C2×C13#151611yescharacteristic
218C2×C13C2×#35211yescharacteristic
219C2×C13#213311yescharacteristic
220C24C22⋊Dic1311yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C22⋊Dic1311yescharacteristic
236C22×C4C22⋊Dic1311yescharacteristic
237C22×C4C22⋊Dic1311yescharacteristic
238C22×C4C22×Dic1311yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—522no—
242M16—522no—
243C2×C8—522no—
244C2×C8—522no—
245C2×C8—1042no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C42—42no—
258C13#1185011yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—22no—
262C23—41no—
263C23#8807411yescharacteristic
264C23#8807411yescharacteristic
265C23C2×C22⋊Dic1311yescharacteristic
266C2×C4—21no—
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—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
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—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4#8820412yes—
297C8—1042no—
298C8—1042no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22#1171813112yes—
309C22C2×#8807411yescharacteristic
310C22#1171889411yescharacteristic
311C22#1171889711yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2#1311339211yescharacteristic
327C2C2×#1171813111yescharacteristic
328C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2484C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2484D13
hypocenterC13#11850
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
3. #13112863C2semidirect
4. #13112842C2semidirect
258. C13#11850semidirect

Maximal subgroups

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

subgroupindex
#131149162
C2×#117181202
#131128632
#131128422
C13×#24842
#1185013