Finite Group Databasebeta

← #16848310

Subgroups — #16848310

Order 3968.

512 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D31C211yesmaximal, characteristic
2#14520936C211yesmaximal, characteristic, complemented
3#14520935C211yesmaximal, characteristic, complemented
4#14520934C211yesmaximal, characteristic, complemented
5#14520933C211yesmaximal, characteristic, complemented
6#14520932C211yesmaximal, characteristic, complemented
7#14520931C211yesmaximal, characteristic, complemented
8#14520930C211yesmaximal, characteristic, complemented
9#14520911C211yesmaximal, characteristic
10#14520911C211yesmaximal, characteristic
11#14520908C211yesmaximal, characteristic
12#14520906C211yesmaximal, characteristic
13C4×(C2×D31)⋊C4C211yesmaximal, characteristic
14#14520896C211yesmaximal, characteristic
15C31×#387C211yesmaximal, characteristic, complemented
16C22×C4×D31C2211yescharacteristic
17C22×C4×D31C2211yescharacteristic
18C22×C4×D31C2211yescharacteristic
19C2×C4⋊C4×C31C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21C2×C42×C31C2211yescharacteristic
22C2×(C2×D31)⋊C4C2211yescharacteristic
23C2×(C2×D31)⋊C4C2211yescharacteristic
24C2×(C2×D31)⋊C4C2211yescharacteristic
25C2×(C2×D31)⋊C4C2211yescharacteristic
26C2×C4⋊Dic31C2211yescharacteristic
27C2×C4⋊Dic31C2211yescharacteristic
28C2×Dic31⋊C4C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×Dic31⋊C4C2211yescharacteristic
31C2×Dic31⋊C4C2211yescharacteristic
32C2×C4×Dic31C2211yescharacteristic
33C2×C4×Dic31C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C4⋊C4×D31C418yescomplemented
36C31×#95C2211yescharacteristic
37C31×#95C2211yescharacteristic
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
52C23×D31C2311yescharacteristic
53C22×C4×C31C2311yescharacteristic
54C22×C4×C31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×Dic31C2311yescharacteristic
61C22×Dic31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C2×C4×D31—22no—
68C2×C4×D31—22no—
69C2×C4×D31—41no—
70C2×C4×D31—41no—
71C2×C4×D31—41no—
72C2×C4×D31—41no—
73C2×C4×D31C2×C414yes—
74C2×C4×D31C2×C414yes—
75C2×C4×D31C2×C414yes—
76C4⋊C4×C31—41no—
77C4⋊C4×C31C2×C414yes—
78C42×C31—41no—
79(C2×D31)⋊C4—22no—
80(C2×D31)⋊C4—22no—
81(C2×D31)⋊C4—22no—
82(C2×D31)⋊C4—22no—
83C4⋊Dic31—41no—
84C4⋊Dic31C2×C414yes—
85Dic31⋊C4—41no—
86Dic31⋊C4—41no—
87Dic31⋊C4C2×C414yes—
88Dic31⋊C4C2×C414yes—
89C4×Dic31—41no—
90C4×Dic31—41no—
91C4×Dic31—41no—
92C23×C31C2411yescharacteristic
93C22×D31—21no—
94C22×D31—21no—
95C22×D31—21no—
96C22×D31—21no—
97C22×D31C22×C412yes—
98C22×D31#4112yes—
99C22×D31#4112yes—
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×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31C22×C412yes—
119C2×C4×C31C22×C412yes—
120C2×C4×C31C22×C412yes—
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×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138C2×Dic31—21no—
139C2×Dic31C22×C412yes—
140C2×Dic31C22×C412yes—
141C2×Dic31C22×C412yes—
142C4×D31—28no—
143C4×D31—44no—
144C4×D31—44no—
145#2313—311nomaximal, Sylow
146C22×C31C23×C411yescharacteristic
147C22×C31C2×#4111yescharacteristic
148C22×C31C2×#4111yescharacteristic
149C22×C31H(5,𝔽2)11yescharacteristic
150C22×C31H(5,𝔽2)11yescharacteristic
151C22×C312−1+411yescharacteristic
152C22×C312−1+411yescharacteristic
153C2×D31—22no—
154C2×D31—22no—
155C2×D31—22no—
156C2×D31—22no—
157C2×D31—22no—
158C2×D31—22no—
159C2×D31#11714yes—
160C4×C31—22no—
161C4×C31—22no—
162C4×C31—22no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167Dic31—22no—
168Dic31—22no—
169Dic31—22no—
170Dic31—41no—
171Dic31—41no—
172Dic31—41no—
173Dic31—41no—
174C22×C4⋊C4—311no—
175#387—311no—
176#387—311no—
177#387—311no—
178#387—311no—
179#387—311no—
180#387—311no—
181#387—311no—
182#387D3111yescharacteristic, complemented
183#381—311no—
184#381—311no—
185#380—311no—
186#380—311no—
187C4×C22⋊C4—311no—
188C4×C22⋊C4—311no—
189C2×C31C2×#11711yescharacteristic
190C2×C31#51811yescharacteristic
191C2×C31#51911yescharacteristic
192C2×C31#53911yescharacteristic
193C2×C31#53911yescharacteristic
194C2×C31#53911yescharacteristic
195C2×C31#53911yescharacteristic
196D31—24no—
197C23×C4—311no—
198C23×C4—311no—
199C23×C4—311no—
200C2×C4⋊C4—311no—
201C2×C4⋊C4—311no—
202C2×C4⋊C4—311no—
203C2×C4⋊C4—318no—
204C2×C4⋊C4—311no—
205C2×C4⋊C4—311no—
206C2×C4⋊C4—311no—
207C2×C4⋊C4C2×D3111yescharacteristic
208C2×C4⋊C4C2×D3111yescharacteristic
209C2×C22⋊C4—311no—
210C2×C22⋊C4—311no—
211C2×C22⋊C4—311no—
212C2×C22⋊C4—311no—
213C2×C42—311no—
214C2×C42—311no—
215C2×C42—311no—
216C2×C42C2×D3111yescharacteristic
217#95—311no—
218#95—311no—
219#95—311no—
220#95—311no—
221#95—311no—
222#95—311no—
223#95—311no—
224#95—311no—
225#95—311no—
226#95—311no—
227#95—311no—
228#95—311no—
229#95C2×D3111yescharacteristic
230#95C2×D3111yescharacteristic
231#95C2×D3111yescharacteristic
232#95C2×D3111yescharacteristic
233C31#231311yescharacteristic, complemented, Sylow
234C24—311no—
235C22×C4—311no—
236C22×C4—311no—
237C22×C4—311no—
238C22×C4—314no—
239C22×C4—314no—
240C22×C4—314no—
241C22×C4—311no—
242C22×C4—311no—
243C22×C4—311no—
244C22×C4—311no—
245C22×C4—622no—
246C22×C4—622no—
247C22×C4—1241no—
248C22×C4—1241no—
249C22×C4—1241no—
250C22×C4—1241no—
251C22×C4C22×D3111yescharacteristic
252C22×C4C22×D3111yescharacteristic
253C22×C4C22×D3111yescharacteristic
254C22×C4C22×D3111yescharacteristic
255C22×C4C22×D3111yescharacteristic
256C22×C4C22×D3111yescharacteristic
257C22×C4C22×D3111yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—314no—
260C4⋊C4—314no—
261C4⋊C4—314no—
262C4⋊C4—1241no—
263C4⋊C4—1241no—
264C4⋊C4—1241no—
265C4⋊C4C4×D3114yes—
266C22⋊C4—622no—
267C22⋊C4—622no—
268C22⋊C4—622no—
269C22⋊C4—622no—
270C42—41no—
271C42—1241no—
272C42—1241no—
273C42—1241no—
274C23—312no—
275C23—312no—
276C23—312no—
277C23—621no—
278C23—621no—
279C23—621no—
280C23—621no—
281C23C23×D3111yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—312no—
301C2×C4—312no—
302C2×C4—312no—
303C2×C4—628no—
304C2×C4—621no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—1244no—
323C2×C4—1244no—
324C2×C4C2×C4×D3112yes—
325C2×C4C2×C4×D3112yes—
326C2×C4C2×C4×D3112yes—
327C22—314no—
328C22—622no—
329C22—622no—
330C22—622no—
331C22—622no—
332C22—622no—
333C22—622no—
334C22C22×C4×D3111yescharacteristic
335C22#1175856111yescharacteristic
336C22#1175856411yescharacteristic
337C22#41×D3111yescharacteristic
338C22#41×D3111yescharacteristic
339C22#1175856611yescharacteristic
340C22#1175856711yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—622no—
349C4—622no—
350C4—622no—
351C4—1241no—
352C4—1241no—
353C4—1241no—
354C4—1241no—
355C2—624no—
356C2#117×D3111yescharacteristic
357C2#1452152111yescharacteristic
358C2#1452152511yescharacteristic
359C2#1452164011yescharacteristic
360C2#1452164211yescharacteristic
361C2#1452164511yescharacteristic
362C2#1452164711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#387C2
socle, cosocleC23×C31C24
prime radicalC23×D31C23
hypercenter#387D31
hypocenterC31#2313
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #14520936C2semidirect
3. #14520935C2semidirect
4. #14520934C2semidirect
5. #14520933C2semidirect
6. #14520932C2semidirect
7. #14520931C2semidirect
8. #14520930C2semidirect
15. C31×#387C2semidirect
35. C4⋊C4×D31C4semidirect
182. #387D31semidirect
233. C31#2313semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D312
#145209362
#145209352
#145209342
#145209332
#145209322
#145209312
#145209302
#145209112
#145209082
#145209062
C4×(C2×D31)⋊C42
#145208962
C31×#3872
#231331