Finite Group Databasebeta

← #16786722

Subgroups — #16786722

Order 3328.

678 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130067C212yesmaximal, complemented
2#13129762C212yesmaximal, complemented
3#13129760C212yesmaximal
4#13117219C211yesmaximal, characteristic
5C24×C4×C13C411yescharacteristic
6C2×#88180C411yescharacteristic
7C2×#88180C2211yescharacteristic
8#11719119—22no—
9#11718908C411yescharacteristic
10#11718908C2211yescharacteristic
11#11718873—22no—
12#11718872C411yescharacteristic
13#11718872C2211yescharacteristic
14C4×C22⋊Dic13—22no—
15#11718305C2214yes—
16#11718285—22no—
17C25×C13C2×C411yescharacteristic
18C23×C4×C13—21no—
19C23×C4×C13—21no—
20C23×C4×C13—22no—
21C23×C4×C13—41no—
22C23×C4×C13—41no—
23C23×C4×C13—42no—
24C23×C4×C13C814yescomplemented
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13C2×C411yescharacteristic
30C2×C22⋊Dic13C2×C411yescharacteristic
31C2×C22⋊Dic13C2×C411yescharacteristic
32C2×C22⋊Dic13C2311yescharacteristic
33#88180—41no—
34#88180—41no—
35#88180—42no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D412yes—
38C2×C4×Dic13—21no—
39C2×C4×Dic13D412yes—
40C22⋊#1057—24no—
41C4⋊#1057—42no—
42C4×#1057—42no—
43#88071—22no—
44#88071—22no—
45#11425—131nomaximal, Sylow
46C24×C13—21no—
47C24×C13—21no—
48C24×C13—41no—
49C24×C13—41no—
50C24×C13—44no—
51C24×C13C2×C812yes—
52C24×C13C22×C411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—24no—
59C22×C4×C13—24no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—44no—
63C22×C4×C13—44no—
64C22×C4×C13—44no—
65C22×C4×C13—44no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C2×C812yes—
74C22×C4×C13C2×C812yes—
75C22×C4×C13M1612yes—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13C22⋊C412yes—
79C22×Dic13C2×D412yes—
80C2×#1057—44no—
81C22⋊Dic13—41no—
82C22⋊Dic13—41no—
83C22⋊Dic13—44no—
84C22⋊Dic13—44no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—42no—
92#2280—131no—
93#1458—132no—
94#1317—132no—
95#1316—132no—
96C23×C13—24no—
97C23×C13—22no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—44no—
103C23×C13—42no—
104C23×C13—44no—
105C23×C13—42no—
106C23×C13—48no—
107C23×C13—44no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—44no—
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13C22×C811yescharacteristic
113C23×C13C2×M1611yescharacteristic
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—48no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—44no—
126C2×C4×C13—44no—
127C2×C4×C13—42no—
128C2×C4×C13C22⋊C812yes—
129C2×C4×C13C22⋊C812yes—
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#10012yes—
133C2×Dic13—22no—
134C2×Dic13—22no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141#1057—84no—
142C24×C4#26111yescharacteristic
143C2×#117—131no—
144C2×#117—131no—
145#431—262no—
146#381—131no—
147#381—131no—
148#380—262no—
149#379—131no—
150#379—131no—
151C4×C22⋊C4—262no—
152#324—262no—
153#323—134no—
154C22×C13—22no—
155C22×C13—24no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—44no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—44no—
164C22×C13—48no—
165C22×C13—44no—
166C22×C13—44no—
167C22×C13—42no—
168C22×C13—42no—
169C22×C13C2×C22⋊C811yescharacteristic
170C22×C13C2×#9911yescharacteristic
171C22×C13C2×#10011yescharacteristic
172C4×C13—22no—
173C4×C13—42no—
174C4×C13#32312yes—
175C4×C13#32312yes—
176Dic13—42no—
177Dic13—42no—
178Dic13—81no—
179Dic13—81no—
180C25C2×#26111yescharacteristic
181C23×C4—22no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—41no—
185C23×C4—41no—
186C23×C4—42no—
187C23×C4#105714yescomplemented
188C23×C4C2×#26111yescharacteristic
189C23×C4C2×#26111yescharacteristic
190#117—521no—
191#117—521no—
192#117—522no—
193C2×C4⋊C4—132no—
194C2×C4⋊C4—261no—
195C2×C22⋊C4—131no—
196C2×C22⋊C4—131no—
197C2×C22⋊C4—131no—
198C2×C22⋊C4—131no—
199C2×C22⋊C4—262no—
200C2×C22⋊C4—262no—
201C2×C42—132no—
202C2×C42—261no—
203C4⋊C8—522no—
204C22⋊C8—264no—
205C4×C8—522no—
206#95—262no—
207#95—262no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—44no—
211C2×C13—41no—
212C2×C13—41no—
213C2×C13C2×#32311yescharacteristic
214C2×C13#212012yes—
215C24—21no—
216C24—21no—
217C24—41no—
218C24—41no—
219C24—44no—
220C24C2×#105712yes—
221C24C22×#26111yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—42no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—132no—
241C22×C4—132no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4C2×#105712yes—
245C22×C4C2×#105712yes—
246C22×C4#612212yes—
247C22×C4C22⋊#26111yescharacteristic
248C22×C4C22⋊#26111yescharacteristic
249C2×C8—524no—
250C4⋊C4—522no—
251C4⋊C4—522no—
252C22⋊C4—521no—
253C22⋊C4—521no—
254C22⋊C4—524no—
255C22⋊C4—524no—
256C22⋊C4—521no—
257C22⋊C4—521no—
258C42—262no—
259C42—262no—
260C42—522no—
261C13#1142511yescharacteristic, complemented, Sylow
262C23—24no—
263C23—22no—
264C23—21no—
265C23—21no—
266C23—42no—
267C23—44no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—44no—
272C23—44no—
273C23—48no—
274C23—44no—
275C23—41no—
276C23—41no—
277C23C22×#105711yescharacteristic
278C23C2×#612211yescharacteristic
279C23C2×C22⋊#26111yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—48no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—262no—
295C2×C4—262no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4#8811911yescharacteristic
303C2×C4#8811911yescharacteristic
304C2×C4C22⋊#105712yes—
305C2×C4C22⋊#105712yes—
306C2×C4#8812112yes—
307C8—1044no—
308C22—22no—
309C22—24no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—44no—
318C22—44no—
319C22—48no—
320C22—42no—
321C22—44no—
322C22—42no—
323C22C2×#8811911yescharacteristic
324C22C2×C22⋊#105711yescharacteristic
325C22C2×#8812111yescharacteristic
326C4—22no—
327C4—42no—
328C4—522no—
329C4—522no—
330C4—1041no—
331C4—1041no—
332C4#1171830512yes—
333C4#1171830512yes—
334C2—21no—
335C2—21no—
336C2—44no—
337C2—41no—
338C2—41no—
339C2C2×#1171830511yescharacteristic
340C2#1313108712yes—
subgroupG/H
centerC2×C4#88119
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC24×C4×C13C4
socleC22×C13C2×#99
prime radicalC25×C13C2×C4
cosocleC2×C22⋊Dic13C23
hypercenterC24×C4#261
hypocenterC13#11425
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #13130067C2semidirect
2. #13129762C2semidirect
24. C23×C4×C13C8semidirect
187. C23×C4#1057semidirect
261. C13#11425semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297622
#131297602
#131172192
#1142513