Finite Group Databasebeta

← #16848585

Subgroups — #16848585

Order 3968.

548 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D31C211yesmaximal, characteristic
2#14520946C211yesmaximal, characteristic, complemented
3#14520944C211yesmaximal, characteristic, complemented
4#14520935C211yesmaximal, characteristic, complemented
5#14520934C211yesmaximal, characteristic, complemented
6#14520932C211yesmaximal, characteristic, complemented
7#14520908C211yesmaximal, characteristic
8#14520908C211yesmaximal, characteristic
9#14520906C211yesmaximal, characteristic
10C4×Dic31⋊C4C211yesmaximal, characteristic, complemented
11#14520900C211yesmaximal, characteristic, complemented
12C4×(C2×D31)⋊C4C211yesmaximal, characteristic
13#14520896C211yesmaximal, 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×Dic31⋊C4C2211yescharacteristic
33C2×Dic31⋊C4C2211yescharacteristic
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37C2×C4×Dic31C2211yescharacteristic
38C2×C4×Dic31C2211yescharacteristic
39C4⋊C4×D31C418yescomplemented
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)⋊C4Q814yes—
83C4⋊Dic31—41no—
84C4⋊Dic31C2×C414yes—
85Dic31⋊C4—22no—
86Dic31⋊C4—22no—
87Dic31⋊C4—41no—
88Dic31⋊C4—41no—
89Dic31⋊C4C2×C414yes—
90Dic31⋊C4C2×C414yes—
91C4×Dic31—22no—
92C4×Dic31—22no—
93C4×Dic31—41no—
94C4×Dic31—41no—
95C4×Dic31—41no—
96C23×C31C2411yescharacteristic
97C22×D31—21no—
98C22×D31—21no—
99C22×D31—21no—
100C22×D31—21no—
101C22×D31C22×C412yes—
102C22×D31C2×Q812yes—
103C22×D31#4112yes—
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×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31C22×C412yes—
122C2×C4×C31C22×C412yes—
123C2×C4×C31C22×C412yes—
124C2×C4×C31C2×Q812yes—
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×Dic31—21no—
140C2×Dic31C22×C412yes—
141C2×Dic31C22×C412yes—
142C2×Dic31C22×C412yes—
143C2×Dic31C2×Q812yes—
144C2×Dic31#4112yes—
145C2×Dic31#4112yes—
146C4×D31—28no—
147C4×D31—44no—
148C4×D31—44no—
149#2345—311nomaximal, Sylow
150C22×C31C23×C411yescharacteristic
151C22×C31C22×Q811yescharacteristic
152C22×C31C2×#4111yescharacteristic
153C22×C31C2×#4111yescharacteristic
154C22×C31C2×#4111yescharacteristic
155C22×C31H(5,𝔽2)11yescharacteristic
156C22×C31H(5,𝔽2)11yescharacteristic
157C2×D31—22no—
158C2×D31—22no—
159C2×D31—22no—
160C2×D31—22no—
161C2×D31—22no—
162C2×D31—22no—
163C2×D31C4×Q814yes—
164C4×C31—22no—
165C4×C31—22no—
166C4×C31—22no—
167C4×C31—22no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31—41no—
171Dic31—22no—
172Dic31—22no—
173Dic31—22no—
174Dic31—41no—
175Dic31—41no—
176Dic31—41no—
177Dic31#11714yes—
178C22×C4⋊C4—311no—
179#389—311no—
180#389—311no—
181#387—311no—
182#387—311no—
183#387—311no—
184#387D3111yescharacteristic, complemented
185#380—311no—
186#380—311no—
187#380—311no—
188C4×C4⋊C4—311no—
189C4×C4⋊C4—311no—
190C4×C22⋊C4—311no—
191C4×C22⋊C4—311no—
192C4×C22⋊C4—311no—
193C2×C31C2×#11711yescharacteristic
194C2×C31C2×C4×Q811yescharacteristic
195C2×C31#51811yescharacteristic
196C2×C31#55311yescharacteristic
197C2×C31#55311yescharacteristic
198C2×C31#55411yescharacteristic
199C2×C31#55411yescharacteristic
200D31—24no—
201C23×C4—311no—
202C23×C4—311no—
203C23×C4—311no—
204C2×C4⋊C4—311no—
205C2×C4⋊C4—311no—
206C2×C4⋊C4—311no—
207C2×C4⋊C4—318no—
208C2×C4⋊C4—311no—
209C2×C4⋊C4—311no—
210C2×C4⋊C4—311no—
211C2×C4⋊C4—311no—
212C2×C4⋊C4—311no—
213C2×C4⋊C4C2×D3111yescharacteristic
214C2×C4⋊C4C2×D3111yescharacteristic
215C2×C22⋊C4—311no—
216C2×C22⋊C4—311no—
217C2×C22⋊C4—311no—
218C2×C22⋊C4—311no—
219C2×C42—311no—
220C2×C42—311no—
221C2×C42—311no—
222C2×C42—311no—
223C2×C42—311no—
224C2×C42C2×D3111yescharacteristic
225#95—311no—
226#95—311no—
227#95—311no—
228#95—311no—
229#95—311no—
230#95—311no—
231#95—311no—
232#95—311no—
233#95C2×D3111yescharacteristic
234#95C2×D3111yescharacteristic
235#95C2×D3111yescharacteristic
236#95C2×D3111yescharacteristic
237C31#234511yescharacteristic, complemented, Sylow
238C24—311no—
239C22×C4—311no—
240C22×C4—311no—
241C22×C4—311no—
242C22×C4—311no—
243C22×C4—314no—
244C22×C4—314no—
245C22×C4—314no—
246C22×C4—311no—
247C22×C4—311no—
248C22×C4—311no—
249C22×C4—622no—
250C22×C4—622no—
251C22×C4—1241no—
252C22×C4—1241no—
253C22×C4—1241no—
254C22×C4—1241no—
255C22×C4C22×D3111yescharacteristic
256C22×C4C22×D3111yescharacteristic
257C22×C4C22×D3111yescharacteristic
258C22×C4C22×D3111yescharacteristic
259C22×C4C22×D3111yescharacteristic
260C22×C4C22×D3111yescharacteristic
261C22×C4C22×D3111yescharacteristic
262C4⋊C4—41no—
263C4⋊C4—314no—
264C4⋊C4—314no—
265C4⋊C4—314no—
266C4⋊C4—622no—
267C4⋊C4—622no—
268C4⋊C4—1241no—
269C4⋊C4—1241no—
270C4⋊C4—1241no—
271C4⋊C4C4×D3114yes—
272C22⋊C4—314no—
273C22⋊C4—622no—
274C22⋊C4—622no—
275C22⋊C4—622no—
276C42—41no—
277C42—622no—
278C42—622no—
279C42—1241no—
280C42—1241no—
281C42—1241no—
282C23—312no—
283C23—312no—
284C23—312no—
285C23—621no—
286C23—621no—
287C23—621no—
288C23—621no—
289C23C23×D3111yescharacteristic
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—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—312no—
308C2×C4—312no—
309C2×C4—312no—
310C2×C4—312no—
311C2×C4—312no—
312C2×C4—312no—
313C2×C4—628no—
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—621no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—1244no—
330C2×C4—1244no—
331C2×C4C2×C4×D3112yes—
332C2×C4C2×C4×D3112yes—
333C2×C4C2×C4×D3112yes—
334C2×C4Q8×D3112yes—
335C22—314no—
336C22—622no—
337C22—622no—
338C22—622no—
339C22—622no—
340C22—622no—
341C22—622no—
342C22C22×C4×D3111yescharacteristic
343C22#1175856111yescharacteristic
344C22C2×Q8×D3111yescharacteristic
345C22#41×D3111yescharacteristic
346C22#41×D3111yescharacteristic
347C22#41×D3111yescharacteristic
348C22#1175856611yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—314no—
357C4—622no—
358C4—622no—
359C4—622no—
360C4—1241no—
361C4—1241no—
362C4—1241no—
363C2—624no—
364C2#117×D3111yescharacteristic
365C2C4×Q8×D3111yescharacteristic
366C2#1452152111yescharacteristic
367C2#1452174411yescharacteristic
368C2#1452175011yescharacteristic
369C2#1452175311yescharacteristic
370C2#1452175511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#387C2
socle, cosocleC23×C31C24
prime radicalC23×D31C23
hypercenter#387D31
hypocenterC31#2345
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #14520946C2semidirect
3. #14520944C2semidirect
4. #14520935C2semidirect
5. #14520934C2semidirect
6. #14520932C2semidirect
10. C4×Dic31⋊C4C2semidirect
11. #14520900C2semidirect
15. C31×#387C2semidirect
39. C4⋊C4×D31C4semidirect
184. #387D31semidirect
237. C31#2345semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D312
#145209462
#145209442
#145209352
#145209342
#145209322
#145209082
#145209062
C4×Dic31⋊C42
#145209002
C4×(C2×D31)⋊C42
#145208962
C31×#3872
#234531