Finite Group Databasebeta

← #16848650

Subgroups — #16848650

Order 3968.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758470C211yesmaximal, characteristic
2#14520941C211yesmaximal, characteristic, complemented
3#14520939C211yesmaximal, characteristic, complemented
4#14520935C211yesmaximal, characteristic, complemented
5#14520927C211yesmaximal, characteristic
6#14520927C211yesmaximal, characteristic
7#14520916C211yesmaximal, characteristic, complemented
8#14520911C211yesmaximal, characteristic, complemented
9#14520906C211yesmaximal, characteristic, complemented
10C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
11C4×(C2×D31)⋊C4C211yesmaximal, characteristic, complemented
12#14520896C211yesmaximal, characteristic, complemented
13#14520894C211yesmaximal, characteristic, complemented
14#95×D31C211yesmaximal, characteristic, complemented
15C31×#387C211yesmaximal, characteristic, complemented
16C22×D124C2211yescharacteristic
17C22×C4×D31C2211yescharacteristic
18C22×C4×D31C2211yescharacteristic
19C22×C4×D31C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic
21C2×C4⋊C4×C31C2211yescharacteristic
22C2×C4⋊C4×C31C2211yescharacteristic
23C2×C42×C31C2211yescharacteristic
24C2×(C2×D31)⋊C4C2211yescharacteristic
25C2×(C2×D31)⋊C4C2211yescharacteristic
26C2×(C2×D31)⋊C4C2211yescharacteristic
27C2×(C2×D31)⋊C4C2211yescharacteristic
28C2×(C2×D31)⋊C4C2211yescharacteristic
29C2×(C2×D31)⋊C4C2211yescharacteristic
30C2×(C2×D31)⋊C4C2211yescharacteristic
31C2×(C2×D31)⋊C4C2211yescharacteristic
32C2×C4⋊Dic31C2211yescharacteristic
33C2×C4×Dic31C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37#11758470C418yescomplemented
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
53C23×D31C2311yescharacteristic
54C22×C4×C31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×Dic31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C2×D124—22no—
68C2×D124—22no—
69C2×D124C2×C414yes—
70C2×C4×D31—22no—
71C2×C4×D31—22no—
72C2×C4×D31—22no—
73C2×C4×D31—22no—
74C2×C4×D31—41no—
75C2×C4×D31—41no—
76C2×C4×D31—41no—
77C2×C4×D31—41no—
78C2×C4×D31—41no—
79C2×C4×D31—41no—
80C2×C4×D31C2×C414yes—
81C2×C4×D31C2×C414yescomplemented
82C4⋊C4×C31—41no—
83C4⋊C4×C31C2×C414yescomplemented
84C42×C31—41no—
85(C2×D31)⋊C4—22no—
86(C2×D31)⋊C4—22no—
87(C2×D31)⋊C4—22no—
88(C2×D31)⋊C4—22no—
89(C2×D31)⋊C4—41no—
90(C2×D31)⋊C4—41no—
91(C2×D31)⋊C4C2×C414yes—
92(C2×D31)⋊C4C2×C414yescomplemented
93C4⋊Dic31—41no—
94C4×Dic31—22no—
95C4×Dic31—22no—
96C4×Dic31—41no—
97C4×Dic31C2×C414yescomplemented
98C23×C31C2411yescharacteristic
99C22×D31—21no—
100C22×D31—21no—
101C22×D31—21no—
102C22×D31—21no—
103C22×D31—21no—
104C22×D31—21no—
105C22×D31—21no—
106C22×D31—21no—
107C22×D31—21no—
108C22×D31—21no—
109C22×D31C22×C412yes—
110C22×D31C22×C412yes—
111C22×D31#4112yes—
112C22×D31#4112yes—
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×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31C22×C412yes—
131C2×C4×C31C22×C412yes—
132C2×C4×C31C22×C412yes—
133C2×C4×C31#4112yes—
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×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—21no—
145C2×Dic31—21no—
146C2×Dic31—21no—
147C2×Dic31—21no—
148C2×Dic31—21no—
149C2×Dic31C22×C412yes—
150C2×Dic31C22×C412yes—
151C2×Dic31#4112yes—
152D124—28no—
153C4×D31—44no—
154C4×D31—44no—
155C4×D31—44no—
156C4×D31—44no—
157#2353—311nomaximal, Sylow
158C22×C31C23×C411yescharacteristic
159C22×C31C2×#4111yescharacteristic
160C22×C31C2×#4111yescharacteristic
161C22×C31C2×#4111yescharacteristic
162C22×C31C2×#4111yescharacteristic
163C22×C31H(5,𝔽2)11yescharacteristic
164C22×C31H(5,𝔽2)11yescharacteristic
165C2×D31—22no—
166C2×D31—22no—
167C2×D31—22no—
168C2×D31—22no—
169C2×D31—22no—
170C2×D31—22no—
171C2×D31—22no—
172C2×D31—22no—
173C2×D31—22no—
174C2×D31—41no—
175C2×D31—41no—
176C2×D31—41no—
177C2×D31—41no—
178C2×D31#11714yes—
179C4×C31—22no—
180C4×C31—22no—
181C4×C31—22no—
182C4×C31—22no—
183C4×C31—41no—
184C4×C31—41no—
185C4×C31—41no—
186Dic31—22no—
187Dic31—22no—
188Dic31—22no—
189Dic31—41no—
190Dic31—41no—
191Dic31—41no—
192C2×C4×D4—311no—
193#388—311no—
194#388—311no—
195#387—311no—
196#387D3111yescharacteristic, complemented
197#386—311no—
198#386—311no—
199#383—311no—
200#381—311no—
201#380—311no—
202C4×C22⋊C4—311no—
203C4×C22⋊C4—311no—
204C4×C22⋊C4—311no—
205#376—311no—
206C2×#95—311no—
207C2×C31C2×#11711yescharacteristic
208C2×C31C4×#4111yescharacteristic
209C2×C31#51811yescharacteristic
210C2×C31#55111yescharacteristic
211C2×C31#55111yescharacteristic
212C2×C31#55311yescharacteristic
213C2×C31#55311yescharacteristic
214D31—24no—
215D31—42no—
216C22×D4—311no—
217C23×C4—311no—
218C23×C4—311no—
219C23×C4—311no—
220C23×C4—311no—
221C4×D4—318no—
222C2×C4⋊C4—311no—
223C2×C4⋊C4C2×D3111yescharacteristic
224C2×C4⋊C4C2×D3111yescharacteristic
225C2×C22⋊C4—311no—
226C2×C22⋊C4—311no—
227C2×C22⋊C4—311no—
228C2×C22⋊C4—311no—
229C2×C22⋊C4—311no—
230C2×C22⋊C4—311no—
231C2×C22⋊C4—311no—
232C2×C22⋊C4—311no—
233C2×C42—311no—
234C2×C42—311no—
235C2×C42—311no—
236C2×C42—311no—
237C2×C42C2×D3111yescharacteristic
238#95—311no—
239#95—311no—
240#95—311no—
241#95—311no—
242#95—311no—
243#95—311no—
244#95—311no—
245#95—311no—
246#95—311no—
247#95—311no—
248#95C2×D3111yescharacteristic
249#95C2×D3111yescharacteristic
250#95C2×D3111yescharacteristic
251#95C2×D3111yescharacteristic
252C31#235311yescharacteristic, complemented, Sylow
253C24—311no—
254C24—311no—
255C2×D4—314no—
256C2×D4—622no—
257C2×D4—622no—
258C22×C4—311no—
259C22×C4—311no—
260C22×C4—311no—
261C22×C4—314no—
262C22×C4—314no—
263C22×C4—311no—
264C22×C4—311no—
265C22×C4—311no—
266C22×C4—622no—
267C22×C4—622no—
268C22×C4—622no—
269C22×C4—622no—
270C22×C4—1241no—
271C22×C4—1241no—
272C22×C4—1241no—
273C22×C4—1241no—
274C22×C4—1241no—
275C22×C4—1241no—
276C22×C4C22×D3111yescharacteristic
277C22×C4C22×D3111yescharacteristic
278C22×C4C22×D3111yescharacteristic
279C22×C4C22×D3111yescharacteristic
280C22×C4C22×D3111yescharacteristic
281C22×C4C22×D3111yescharacteristic
282C22×C4C22×D3111yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—1241no—
285C4⋊C4C4×D3114yescomplemented
286C22⋊C4—314no—
287C22⋊C4—314no—
288C22⋊C4—622no—
289C22⋊C4—622no—
290C22⋊C4—622no—
291C22⋊C4—622no—
292C22⋊C4—1241no—
293C22⋊C4—1241no—
294C42—41no—
295C42—314no—
296C42—622no—
297C42—622no—
298C42—1241no—
299C23—312no—
300C23—312no—
301C23—312no—
302C23—312no—
303C23—621no—
304C23—621no—
305C23—621no—
306C23—621no—
307C23—621no—
308C23—621no—
309C23—621no—
310C23—621no—
311C23—621no—
312C23—621no—
313C23C23×D3111yescharacteristic
314D4—628no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—312no—
333C2×C4—312no—
334C2×C4—312no—
335C2×C4—621no—
336C2×C4—621no—
337C2×C4—621no—
338C2×C4—621no—
339C2×C4—621no—
340C2×C4—621no—
341C2×C4—621no—
342C2×C4—621no—
343C2×C4—621no—
344C2×C4—621no—
345C2×C4—621no—
346C2×C4—621no—
347C2×C4—621no—
348C2×C4—621no—
349C2×C4—621no—
350C2×C4—1244no—
351C2×C4—1244no—
352C2×C4—1244no—
353C2×C4—1244no—
354C2×C4C2×C4×D3112yes—
355C2×C4C2×C4×D3112yes—
356C2×C4C2×C4×D3112yes—
357C2×C4#9249912yes—
358C22—314no—
359C22—622no—
360C22—622no—
361C22—622no—
362C22—622no—
363C22—622no—
364C22—622no—
365C22—622no—
366C22—622no—
367C22—622no—
368C22—1241no—
369C22—1241no—
370C22—1241no—
371C22—1241no—
372C22C22×C4×D3111yescharacteristic
373C22#1175856111yescharacteristic
374C22C2×#9249911yescharacteristic
375C22#41×D3111yescharacteristic
376C22#41×D3111yescharacteristic
377C22#41×D3111yescharacteristic
378C22#1175856611yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—622no—
387C4—622no—
388C4—622no—
389C4—1241no—
390C4—1241no—
391C4—1241no—
392C2—624no—
393C2—1242no—
394C2#117×D3111yescharacteristic
395C2C4×#9249911yescharacteristic
396C2#1452152111yescharacteristic
397C2#1452172411yescharacteristic
398C2#1452172611yescharacteristic
399C2#1452174411yescharacteristic
400C2#1452175211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#387C2
socle, cosocleC23×C31C24
prime radicalC22×D124C22
hypercenter#387D31
hypocenterC31#2353
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #14520941C2semidirect
3. #14520939C2semidirect
4. #14520935C2semidirect
7. #14520916C2semidirect
8. #14520911C2semidirect
9. #14520906C2semidirect
10. C4×(C2×D31)⋊C4C2semidirect
11. C4×(C2×D31)⋊C4C2semidirect
12. #14520896C2semidirect
13. #14520894C2semidirect
14. #95×D31C2semidirect
15. C31×#387C2semidirect
37. #11758470C4semidirect
81. C2×C4×D31C2×C4semidirect
83. C4⋊C4×C31C2×C4semidirect
92. (C2×D31)⋊C4C2×C4semidirect
97. C4×Dic31C2×C4semidirect
196. #387D31semidirect
252. C31#2353semidirect
285. C4⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584702
#145209412
#145209392
#145209352
#145209272
#145209162
#145209112
#145209062
C4×(C2×D31)⋊C42
#145208962
#145208942
#95×D312
C31×#3872
#235331