Finite Group Databasebeta

← #16848449

Subgroups — #16848449

Order 3968.

444 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758466C211yesmaximal, characteristic
2#14520946C211yesmaximal, characteristic
3#14520945C211yesmaximal, characteristic
4#14520944C211yesmaximal, characteristic
5#14520944C211yesmaximal, characteristic
6#14520944C211yesmaximal, characteristic
7#14520935C211yesmaximal, characteristic
8#14520933C211yesmaximal, characteristic
9#14520932C211yesmaximal, characteristic
10#14520930C211yesmaximal, characteristic
11#14520918C211yesmaximal, characteristic
12C4×Dic31⋊C4C211yesmaximal, characteristic
13#14520900C211yesmaximal, characteristic
14#14520894C211yesmaximal, characteristic
15C31×#389C211yesmaximal, characteristic
16C2×C4⋊C4×C31C2211yescharacteristic
17C2×C4⋊C4×C31C2211yescharacteristic
18C2×C4⋊C4×C31C2211yescharacteristic
19C2×C4⋊C4×C31C2211yescharacteristic
20C2×C42×C31C2211yescharacteristic
21C2×C4⋊Dic31C2211yescharacteristic
22C2×C4⋊Dic31C2211yescharacteristic
23C2×Dic31⋊C4C2211yescharacteristic
24C2×Dic31⋊C4C2211yescharacteristic
25C2×Dic31⋊C4C2211yescharacteristic
26C2×Dic31⋊C4C2211yescharacteristic
27C2×Dic31⋊C4C2211yescharacteristic
28C2×Dic31⋊C4C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×Dic31⋊C4C2211yescharacteristic
31C2×Dic31⋊C4C2211yescharacteristic
32C2×Dic31⋊C4C2211yescharacteristic
33C2×C4×Dic31C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37C2×C4×Dic31C2211yescharacteristic
38C2×C4×Dic31C2211yescharacteristic
39#11758466C418yescomplemented
40C31×#95C2211yescharacteristic
41C31×#95C2211yescharacteristic
42C31⋊#95C2211yescharacteristic
43C31⋊#95C2211yescharacteristic
44C31⋊#95C2211yescharacteristic
45C31⋊#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C22×C4×C31C2311yescharacteristic
53C22×C4×C31C2311yescharacteristic
54C22×C4×C31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×Dic31C2311yescharacteristic
60C22×Dic31C2311yescharacteristic
61C22×Dic31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C4⋊C4×C31—41no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—41no—
70C4⋊C4×C31C2×C414yes—
71C42×C31—41no—
72C4⋊Dic31—41no—
73C4⋊Dic31C2×C414yes—
74Dic31⋊C4—22no—
75Dic31⋊C4—22no—
76Dic31⋊C4—41no—
77Dic31⋊C4—41no—
78Dic31⋊C4—41no—
79Dic31⋊C4—41no—
80Dic31⋊C4C2×C414yes—
81Dic31⋊C4C2×C414yes—
82Dic31⋊C4C2×C414yes—
83Dic31⋊C4C2×C414yes—
84C4×Dic31—22no—
85C4×Dic31—41no—
86C4×Dic31—41no—
87C4×Dic31—41no—
88C4×Dic31C2×C414yes—
89C4×Dic31Q814yes—
90C23×C31C2411yescharacteristic
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—21no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31C22×C412yes—
109C2×C4×C31C22×C412yes—
110C2×C4×C31C22×C412yes—
111C2×C4×C31C2×Q812yes—
112C2×Dic31—21no—
113C2×Dic31—21no—
114C2×Dic31—21no—
115C2×Dic31—21no—
116C2×Dic31—21no—
117C2×Dic31—21no—
118C2×Dic31—21no—
119C2×Dic31—21no—
120C2×Dic31—21no—
121C2×Dic31—21no—
122C2×Dic31—21no—
123C2×Dic31—21no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31C22×C412yes—
130C2×Dic31C22×C412yes—
131C2×Dic31C22×C412yes—
132C2×Dic31C22×C412yes—
133C2×Dic31C2×Q812yes—
134C2×Dic31C2×Q812yes—
135C2×Dic31#4112yes—
136#2330—311nomaximal, Sylow
137C22×C31C23×C411yescharacteristic
138C22×C31C22×Q811yescharacteristic
139C22×C31C2×#4111yescharacteristic
140C22×C31H(5,𝔽2)11yescharacteristic
141C22×C31H(5,𝔽2)11yescharacteristic
142C22×C312−1+411yescharacteristic
143C22×C312−1+411yescharacteristic
144C4×C31—22no—
145C4×C31—22no—
146C4×C31—22no—
147C4×C31—22no—
148C4×C31—41no—
149C4×C31—41no—
150C4×C31—41no—
151Dic31—22no—
152Dic31—22no—
153Dic31—22no—
154Dic31—22no—
155Dic31—41no—
156Dic31—41no—
157Dic31—41no—
158Dic31C4×Q814yes—
159C2×#125—311no—
160#389—311no—
161#389—311no—
162#389—311no—
163#389—311no—
164#389—311no—
165#389D3111yescharacteristic
166#387—311no—
167#387—311no—
168#387—311no—
169#387—311no—
170#384—311no—
171C4×C4⋊C4—311no—
172C4×C4⋊C4—311no—
173#376—311no—
174C2×C31C2×C4×Q811yescharacteristic
175C2×C31#52011yescharacteristic
176C2×C31#52011yescharacteristic
177C2×C31#54011yescharacteristic
178C2×C31#54111yescharacteristic
179C2×C31#54411yescharacteristic
180C2×C31#54411yescharacteristic
181#125—318no—
182C2×C4⋊C4—311no—
183C2×C4⋊C4—311no—
184C2×C4⋊C4—311no—
185C2×C4⋊C4—311no—
186C2×C4⋊C4—311no—
187C2×C4⋊C4—311no—
188C2×C4⋊C4—311no—
189C2×C4⋊C4—311no—
190C2×C4⋊C4—311no—
191C2×C4⋊C4—311no—
192C2×C4⋊C4—311no—
193C2×C4⋊C4—311no—
194C2×C4⋊C4C2×D3111yescharacteristic
195C2×C4⋊C4C2×D3111yescharacteristic
196C2×C4⋊C4C2×D3111yescharacteristic
197C2×C4⋊C4C2×D3111yescharacteristic
198C2×C42—311no—
199C2×C42—311no—
200C2×C42—311no—
201C2×C42—311no—
202C2×C42—311no—
203C2×C42—311no—
204C2×C42C2×D3111yescharacteristic
205#95—311no—
206#95—311no—
207#95—311no—
208#95—311no—
209#95—311no—
210#95—311no—
211#95—311no—
212#95—311no—
213#95—311no—
214#95—311no—
215#95C2×D3111yescharacteristic
216#95C2×D3111yescharacteristic
217C31#233011yescharacteristic, complemented, Sylow
218C22×C4—311no—
219C22×C4—311no—
220C22×C4—311no—
221C22×C4—311no—
222C22×C4—311no—
223C22×C4—311no—
224C22×C4—311no—
225C22×C4—311no—
226C22×C4C22×D3111yescharacteristic
227C22×C4C22×D3111yescharacteristic
228C22×C4C22×D3111yescharacteristic
229C22×C4C22×D3111yescharacteristic
230C22×C4C22×D3111yescharacteristic
231C22×C4C22×D3111yescharacteristic
232C22×C4C22×D3111yescharacteristic
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—314no—
237C4⋊C4—314no—
238C4⋊C4—314no—
239C4⋊C4—314no—
240C4⋊C4—314no—
241C4⋊C4—622no—
242C4⋊C4—622no—
243C4⋊C4—1241no—
244C4⋊C4—1241no—
245C4⋊C4—1241no—
246C4⋊C4—1241no—
247C4⋊C4—1241no—
248C4⋊C4C4×D3114yes—
249C42—41no—
250C42—314no—
251C42—314no—
252C42—622no—
253C42—1241no—
254C42—1241no—
255C42—1241no—
256C23C23×D3111yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
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—312no—
275C2×C4—312no—
276C2×C4—312no—
277C2×C4—312no—
278C2×C4—312no—
279C2×C4—312no—
280C2×C4—312no—
281C2×C4—621no—
282C2×C4—621no—
283C2×C4—621no—
284C2×C4—621no—
285C2×C4—621no—
286C2×C4—621no—
287C2×C4—621no—
288C2×C4—621no—
289C2×C4—621no—
290C2×C4—621no—
291C2×C4—621no—
292C2×C4—621no—
293C2×C4—621no—
294C2×C4—621no—
295C2×C4—621no—
296C2×C4—621no—
297C2×C4—621no—
298C2×C4C2×C4×D3112yes—
299C2×C4C2×C4×D3112yes—
300C2×C4C2×C4×D3112yes—
301C2×C4Q8×D3112yes—
302C22C22×C4×D3111yescharacteristic
303C22#1175856111yescharacteristic
304C22#1175856111yescharacteristic
305C22C2×Q8×D3111yescharacteristic
306C22#1175856411yescharacteristic
307C22#41×D3111yescharacteristic
308C22#1175856711yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—314no—
317C4—622no—
318C4—622no—
319C4—622no—
320C4—622no—
321C4—1241no—
322C4—1241no—
323C4—1241no—
324C2C4×Q8×D3111yescharacteristic
325C2#1452152811yescharacteristic
326C2#1452153011yescharacteristic
327C2#1452164911yescharacteristic
328C2#1452165811yescharacteristic
329C2#1452167611yescharacteristic
330C2#1452167811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#389C2
socle, prime radical, cosocleC23×C31C24
hypercenter#389D31
hypocenterC31#2330
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
39. #11758466C4semidirect
217. C31#2330semidirect

Maximal subgroups

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

subgroupindex
C2×#117584662
#145209462
#145209452
#145209442
#145209352
#145209332
#145209322
#145209302
#145209182
C4×Dic31⋊C42
#145209002
#145208942
C31×#3892
#233031