Finite Group Databasebeta

← #16848665

Subgroups — #16848665

Order 3968.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758464C211yesmaximal, characteristic
2#14520953C211yesmaximal, characteristic
3#14520953C211yesmaximal, characteristic
4#14520936C211yesmaximal, characteristic
5#14520935C211yesmaximal, characteristic
6#14520930C211yesmaximal, characteristic
7#14520918C211yesmaximal, characteristic
8#14520913C211yesmaximal, characteristic
9#14520913C211yesmaximal, characteristic
10C4×Dic31⋊C4C211yesmaximal, characteristic
11C4×Dic31⋊C4C211yesmaximal, characteristic
12#14520900C211yesmaximal, characteristic
13#14520900C211yesmaximal, characteristic
14#14520900C211yesmaximal, characteristic
15C31×#387C211yesmaximal, characteristic
16C22×Dic62C2211yescharacteristic
17C2×C4⋊C4×C31C2211yescharacteristic
18C2×C4⋊C4×C31C2211yescharacteristic
19C2×C42×C31C2211yescharacteristic
20C2×C4⋊Dic31C2211yescharacteristic
21C2×Dic31⋊C4C2211yescharacteristic
22C2×Dic31⋊C4C2211yescharacteristic
23C2×Dic31⋊C4C2211yescharacteristic
24C2×Dic31⋊C4C2211yescharacteristic
25C2×Dic31⋊C4C2211yescharacteristic
26C2×Dic31⋊C4C2211yescharacteristic
27C2×Dic31⋊C4C2211yescharacteristic
28C2×Dic31⋊C4C2211yescharacteristic
29C2×C4×Dic31C2211yescharacteristic
30C2×C4×Dic31C2211yescharacteristic
31C2×C4×Dic31C2211yescharacteristic
32C2×C4×Dic31C2211yescharacteristic
33C2×C4×Dic31C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37#11758464C418yescomplemented
38C31×#95C2211yescharacteristic
39C31×#95C2211yescharacteristic
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
67C2×Dic62—22no—
68C2×Dic62—22no—
69C2×Dic62C2×C414yes—
70C4⋊C4×C31—41no—
71C4⋊C4×C31C2×C414yes—
72C42×C31—41no—
73C4⋊Dic31—41no—
74Dic31⋊C4—22no—
75Dic31⋊C4—22no—
76Dic31⋊C4—22no—
77Dic31⋊C4—22no—
78Dic31⋊C4—22no—
79Dic31⋊C4C2×C414yes—
80Dic31⋊C4C2×C414yes—
81Dic31⋊C4Q814yescomplemented
82C4×Dic31—22no—
83C4×Dic31—22no—
84C4×Dic31—41no—
85C4×Dic31—41no—
86C4×Dic31—41no—
87C4×Dic31C2×C414yes—
88C4×Dic31C2×C414yes—
89C4×Dic31C2×C414yes—
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×Dic31C22×C412yes—
128C2×Dic31C22×C412yes—
129C2×Dic31C22×C412yes—
130C2×Dic31C22×C412yes—
131C2×Dic31C2×Q812yes—
132C2×Dic31C2×Q812yes—
133C2×Dic31#4112yes—
134C2×Dic31#4112yes—
135C2×Dic31#4112yes—
136Dic62—28no—
137#2355—311nomaximal, Sylow
138C22×C31C23×C411yescharacteristic
139C22×C31C22×Q811yescharacteristic
140C22×C31C2×#4111yescharacteristic
141C22×C31C2×#4111yescharacteristic
142C22×C31C2×#4111yescharacteristic
143C22×C31H(5,𝔽2)11yescharacteristic
144C22×C312−1+411yescharacteristic
145C4×C31—22no—
146C4×C31—22no—
147C4×C31—22no—
148C4×C31—22no—
149C4×C31—41no—
150C4×C31—41no—
151C4×C31—41no—
152Dic31—22no—
153Dic31—22no—
154Dic31—22no—
155Dic31—41no—
156Dic31—41no—
157Dic31—41no—
158Dic31#11714yes—
159Dic31C4×Q814yes—
160C2×C4×Q8—311no—
161#391—311no—
162#391—311no—
163#387—311no—
164#387—311no—
165#387—311no—
166#387D3111yescharacteristic
167#384—311no—
168#382—311no—
169#382—311no—
170C4×C4⋊C4—311no—
171C4×C4⋊C4—311no—
172C4×C4⋊C4—311no—
173C4×C4⋊C4—311no—
174C4×C4⋊C4—311no—
175C2×C31C2×#11711yescharacteristic
176C2×C31C2×C4×Q811yescharacteristic
177C2×C31#52011yescharacteristic
178C2×C31#55411yescharacteristic
179C2×C31#55611yescharacteristic
180C2×C31#55711yescharacteristic
181C2×C31#55911yescharacteristic
182C22×Q8—311no—
183C4×Q8—318no—
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⋊C4C2×D3111yescharacteristic
194C2×C4⋊C4C2×D3111yescharacteristic
195C2×C42—311no—
196C2×C42—311no—
197C2×C42—311no—
198C2×C42—311no—
199C2×C42—311no—
200C2×C42—311no—
201C2×C42—311no—
202C2×C42—311no—
203C2×C42C2×D3111yescharacteristic
204#95—311no—
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#95C2×D3111yescharacteristic
215#95C2×D3111yescharacteristic
216#95C2×D3111yescharacteristic
217#95C2×D3111yescharacteristic
218C31#235511yescharacteristic, complemented, Sylow
219C2×Q8—314no—
220C2×Q8—622no—
221C2×Q8—622no—
222C22×C4—311no—
223C22×C4—311no—
224C22×C4—311no—
225C22×C4—311no—
226C22×C4—311no—
227C22×C4—311no—
228C22×C4—311no—
229C22×C4—311no—
230C22×C4C22×D3111yescharacteristic
231C22×C4C22×D3111yescharacteristic
232C22×C4C22×D3111yescharacteristic
233C22×C4C22×D3111yescharacteristic
234C22×C4C22×D3111yescharacteristic
235C22×C4C22×D3111yescharacteristic
236C22×C4C22×D3111yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—314no—
239C4⋊C4—314no—
240C4⋊C4—314no—
241C4⋊C4—622no—
242C4⋊C4—622no—
243C4⋊C4—622no—
244C4⋊C4—622no—
245C4⋊C4—622no—
246C4⋊C4—1241no—
247C4⋊C4C4×D3114yes—
248C42—41no—
249C42—314no—
250C42—314no—
251C42—314no—
252C42—622no—
253C42—622no—
254C42—1241no—
255C42—1241no—
256C42—1241no—
257C23C23×D3111yescharacteristic
258Q8—628no—
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—21no—
275C2×C4—21no—
276C2×C4—312no—
277C2×C4—312no—
278C2×C4—312no—
279C2×C4—312no—
280C2×C4—312no—
281C2×C4—312no—
282C2×C4—312no—
283C2×C4—312no—
284C2×C4—312no—
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×C4—621no—
299C2×C4—621no—
300C2×C4C2×C4×D3112yes—
301C2×C4C2×C4×D3112yes—
302C2×C4C2×C4×D3112yes—
303C2×C4Q8×D3112yes—
304C22C22×C4×D3111yescharacteristic
305C22#1175856111yescharacteristic
306C22C2×Q8×D3111yescharacteristic
307C22#41×D3111yescharacteristic
308C22#41×D3111yescharacteristic
309C22#41×D3111yescharacteristic
310C22#1175856711yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—314no—
319C4—314no—
320C4—622no—
321C4—622no—
322C4—622no—
323C4—1241no—
324C4—1241no—
325C4—1241no—
326C2#117×D3111yescharacteristic
327C2C4×Q8×D3111yescharacteristic
328C2#1452152811yescharacteristic
329C2#1452175311yescharacteristic
330C2#1452176611yescharacteristic
331C2#1452177611yescharacteristic
332C2#1452178311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#387C2
socle, prime radical, cosocleC23×C31C24
hypercenter#387D31
hypocenterC31#2355
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
37. #11758464C4semidirect
81. Dic31⋊C4Q8semidirect
218. C31#2355semidirect

Maximal subgroups

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

subgroupindex
C2×#117584642
#145209532
#145209362
#145209352
#145209302
#145209182
#145209132
C4×Dic31⋊C42
#145209002
C31×#3872
#235531