Finite Group Databasebeta

← #16848577

Subgroups — #16848577

Order 3968.

604 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758469C211yesmaximal, characteristic
2C2×#11758449C211yesmaximal, characteristic
3C2×C4⋊C4×D31C211yesmaximal, characteristic
4#14520946C211yesmaximal, characteristic, complemented
5#14520944C211yesmaximal, characteristic, complemented
6#14520935C211yesmaximal, characteristic, complemented
7#14520934C211yesmaximal, characteristic, complemented
8#14520932C211yesmaximal, characteristic, complemented
9#14520911C211yesmaximal, characteristic
10#14520911C211yesmaximal, characteristic
11#14520908C211yesmaximal, characteristic
12C4×Dic31⋊C4C211yesmaximal, characteristic, complemented
13#14520900C211yesmaximal, characteristic, complemented
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×Dic31⋊C4C2211yescharacteristic
33C2×Dic31⋊C4C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37C2×C4×Dic31C2211yescharacteristic
38C2×C4×Dic31C2211yescharacteristic
39#11758469—24no—
40C4⋊C4×D31C418yescomplemented
41#11758449—24no—
42C31×#95C2211yescharacteristic
43C31×#95C2211yescharacteristic
44C31×#95C2211yescharacteristic
45C31×#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C31⋊#95C2211yescharacteristic
53C31⋊#95C2211yescharacteristic
54C23×D31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C22×Dic31C2311yescharacteristic
68C22×Dic31C2311yescharacteristic
69C2×C4×D31—22no—
70C2×C4×D31—22no—
71C2×C4×D31—22no—
72C2×C4×D31—22no—
73C2×C4×D31—22no—
74C2×C4×D31—22no—
75C2×C4×D31C2×C414yes—
76C2×C4×D31C2×C414yes—
77C2×C4×D31C2×C414yes—
78C4⋊C4×C31—22no—
79C4⋊C4×C31C2×C414yes—
80C42×C31—22no—
81(C2×D31)⋊C4—22no—
82(C2×D31)⋊C4—22no—
83(C2×D31)⋊C4—22no—
84(C2×D31)⋊C4D414yes—
85C4⋊Dic31—22no—
86C4⋊Dic31C2×C414yes—
87Dic31⋊C4—22no—
88Dic31⋊C4—22no—
89Dic31⋊C4—22no—
90Dic31⋊C4—22no—
91Dic31⋊C4C2×C414yes—
92Dic31⋊C4C2×C414yes—
93C4×Dic31—22no—
94C4×Dic31—22no—
95C4×Dic31—22no—
96C4×Dic31—22no—
97C4×Dic31—22no—
98C23×C31C2411yescharacteristic
99C22×D31—21no—
100C22×D31—21no—
101C22×D31—21no—
102C22×D31—21no—
103C22×D31C22×C412yes—
104C22×D31C2×D412yes—
105C22×D31#4112yes—
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×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31C22×C412yes—
124C2×C4×C31C22×C412yes—
125C2×C4×C31C22×C412yes—
126C2×C4×C31C2×D412yes—
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×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—21no—
142C2×Dic31C22×C412yes—
143C2×Dic31C22×C412yes—
144C2×Dic31C22×C412yes—
145C2×Dic31C2×D412yes—
146C2×Dic31#4112yes—
147C2×Dic31#4112yes—
148C4×D31—28no—
149C4×D31—28no—
150C4×D31—28no—
151#2344—311nomaximal, Sylow
152C22×C31C23×C411yescharacteristic
153C22×C31C22×D411yescharacteristic
154C22×C31C2×#4111yescharacteristic
155C22×C31C2×#4111yescharacteristic
156C22×C31C2×#4111yescharacteristic
157C22×C312−1+411yescharacteristic
158C22×C312−1+411yescharacteristic
159C2×D31—22no—
160C2×D31—22no—
161C2×D31—22no—
162C2×D31—22no—
163C2×D31—22no—
164C2×D31—22no—
165C2×D31C4×D414yes—
166C4×C31—22no—
167C4×C31—22no—
168C4×C31—22no—
169C4×C31—22no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31—41no—
173Dic31—22no—
174Dic31—22no—
175Dic31—22no—
176Dic31—41no—
177Dic31—41no—
178Dic31—41no—
179Dic31#11714yescomplemented
180C2×#117—311no—
181C2×#117—311no—
182C22×C4⋊C4—311no—
183#389—311no—
184#389—311no—
185#387—311no—
186#387—311no—
187#387—311no—
188#387D3111yescharacteristic, complemented
189#381—311no—
190#381—311no—
191#380—311no—
192C4×C4⋊C4—311no—
193C4×C4⋊C4—311no—
194C4×C22⋊C4—311no—
195C2×C31C2×#11711yescharacteristic
196C2×C31C2×C4×D411yescharacteristic
197C2×C31#51911yescharacteristic
198C2×C31#54711yescharacteristic
199C2×C31#54711yescharacteristic
200C2×C31#55211yescharacteristic
201C2×C31#55211yescharacteristic
202D31—24no—
203C23×C4—311no—
204C23×C4—311no—
205C23×C4—311no—
206#117—624no—
207#117—624no—
208C2×C4⋊C4—311no—
209C2×C4⋊C4—311no—
210C2×C4⋊C4—311no—
211C2×C4⋊C4—318no—
212C2×C4⋊C4—311no—
213C2×C4⋊C4—311no—
214C2×C4⋊C4—311no—
215C2×C4⋊C4—311no—
216C2×C4⋊C4—311no—
217C2×C4⋊C4C2×D3111yescharacteristic
218C2×C4⋊C4C2×D3111yescharacteristic
219C2×C22⋊C4—311no—
220C2×C22⋊C4—311no—
221C2×C22⋊C4—311no—
222C2×C22⋊C4—311no—
223C2×C42—311no—
224C2×C42—311no—
225C2×C42—311no—
226C2×C42—311no—
227C2×C42—311no—
228C2×C42C2×D3111yescharacteristic
229#95—311no—
230#95—311no—
231#95—311no—
232#95—311no—
233#95—311no—
234#95—311no—
235#95—311no—
236#95—311no—
237#95C2×D3111yescharacteristic
238#95C2×D3111yescharacteristic
239#95C2×D3111yescharacteristic
240#95C2×D3111yescharacteristic
241C31#234411yescharacteristic, complemented, Sylow
242C24—311no—
243C22×C4—311no—
244C22×C4—311no—
245C22×C4—311no—
246C22×C4—311no—
247C22×C4—314no—
248C22×C4—314no—
249C22×C4—314no—
250C22×C4—311no—
251C22×C4—311no—
252C22×C4—311no—
253C22×C4—622no—
254C22×C4—622no—
255C22×C4—622no—
256C22×C4—622no—
257C22×C4—622no—
258C22×C4—622no—
259C22×C4C22×D3111yescharacteristic
260C22×C4C22×D3111yescharacteristic
261C22×C4C22×D3111yescharacteristic
262C22×C4C22×D3111yescharacteristic
263C22×C4C22×D3111yescharacteristic
264C22×C4C22×D3111yescharacteristic
265C22×C4C22×D3111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—314no—
268C4⋊C4—314no—
269C4⋊C4—314no—
270C4⋊C4—622no—
271C4⋊C4—622no—
272C4⋊C4—622no—
273C4⋊C4—622no—
274C4⋊C4—622no—
275C4⋊C4C4×D3114yes—
276C22⋊C4—314no—
277C22⋊C4—622no—
278C22⋊C4—622no—
279C22⋊C4—622no—
280C42—22no—
281C42—622no—
282C42—622no—
283C42—622no—
284C42—622no—
285C42—622no—
286C23—312no—
287C23—312no—
288C23—312no—
289C23—621no—
290C23—621no—
291C23—621no—
292C23—621no—
293C23C23×D3111yescharacteristic
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—312no—
312C2×C4—312no—
313C2×C4—312no—
314C2×C4—312no—
315C2×C4—312no—
316C2×C4—312no—
317C2×C4—628no—
318C2×C4—628no—
319C2×C4—628no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—621no—
332C2×C4—621no—
333C2×C4—621no—
334C2×C4—621no—
335C2×C4C2×C4×D3112yes—
336C2×C4C2×C4×D3112yes—
337C2×C4C2×C4×D3112yes—
338C2×C4D4×D3112yes—
339C22—314no—
340C22—622no—
341C22—622no—
342C22—622no—
343C22—622no—
344C22—622no—
345C22—622no—
346C22C22×C4×D3111yescharacteristic
347C22C2×D4×D3111yescharacteristic
348C22#1175856411yescharacteristic
349C22#41×D3111yescharacteristic
350C22#41×D3111yescharacteristic
351C22#41×D3111yescharacteristic
352C22#1175856711yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—314no—
361C4—622no—
362C4—622no—
363C4—622no—
364C4—1241no—
365C4—1241no—
366C4—1241no—
367C2—624no—
368C2#117×D3111yescharacteristic
369C2C4×D4×D3111yescharacteristic
370C2#1452152511yescharacteristic
371C2#1452169711yescharacteristic
372C2#1452170111yescharacteristic
373C2#1452173111yescharacteristic
374C2#1452173511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#387C2
socle, cosocleC23×C31C24
prime radicalC23×D31C23
hypercenter#387D31
hypocenterC31#2344
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. #14520946C2semidirect
5. #14520944C2semidirect
6. #14520935C2semidirect
7. #14520934C2semidirect
8. #14520932C2semidirect
12. C4×Dic31⋊C4C2semidirect
13. #14520900C2semidirect
15. C31×#387C2semidirect
40. C4⋊C4×D31C4semidirect
179. Dic31#117semidirect
188. #387D31semidirect
241. C31#2344semidirect

Maximal subgroups

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

subgroupindex
C2×#117584692
C2×#117584492
C2×C4⋊C4×D312
#145209462
#145209442
#145209352
#145209342
#145209322
#145209112
#145209082
C4×Dic31⋊C42
#145209002
#145208962
C31×#3872
#234431