Finite Group Databasebeta

← #16848439

Subgroups — #16848439

Order 3968.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758455C211yesmaximal, characteristic
2#14520955C211yesmaximal, characteristic, complemented
3#14520953C211yesmaximal, characteristic, complemented
4#14520947C211yesmaximal, characteristic, complemented
5#14520946C211yesmaximal, characteristic, complemented
6#14520936C211yesmaximal, characteristic, complemented
7#14520933C211yesmaximal, characteristic, complemented
8#14520933C211yesmaximal, characteristic, complemented
9#14520932C211yesmaximal, characteristic, complemented
10#14520924C211yesmaximal, characteristic
11#14520921C211yesmaximal, characteristic
12#14520907C211yesmaximal, characteristic
13C4×C22⋊Dic31C211yesmaximal, characteristic
14C2×C31⋊#95C211yesmaximal, characteristic
15C4×C22⋊C4×C31C211yesmaximal, characteristic
16C23×C4×C31C2211yescharacteristic
17C23×Dic31C2211yescharacteristic
18C23×Dic31C2211yescharacteristic
19C22×Dic62C2211yescharacteristic
20C2×C22⋊C4×C31C2211yescharacteristic
21C2×C22⋊C4×C31C2211yescharacteristic
22C2×C42×C31C2211yescharacteristic
23C2×C42×C31C2211yescharacteristic
24C2×C22⋊Dic31C2211yescharacteristic
25C2×C22⋊Dic31C2211yescharacteristic
26C2×C4⋊Dic31C2211yescharacteristic
27C2×C4⋊Dic31C2211yescharacteristic
28C2×C4⋊Dic31C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×Dic31⋊C4C2211yescharacteristic
31C2×Dic31⋊C4C2211yescharacteristic
32C2×Dic31⋊C4C2211yescharacteristic
33C2×Dic31⋊C4C2211yescharacteristic
34C2×Dic31⋊C4C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37#11758455C418yescomplemented
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
52C24×C31C2311yescharacteristic
53C22×C4×C31—41no—
54C22×C4×C31—41no—
55C22×C4×C31Q814yescomplemented
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×Dic31—22no—
63C22×Dic31—41no—
64C22×Dic31—41no—
65C22×Dic31—41no—
66C22×Dic31—41no—
67C22×Dic31C2×C414yes—
68C22×Dic31C2311yescharacteristic
69C22×Dic31C2311yescharacteristic
70C22×Dic31C2311yescharacteristic
71C22×Dic31C2311yescharacteristic
72C22×Dic31C2311yescharacteristic
73C22×Dic31C2311yescharacteristic
74C22×Dic31C2311yescharacteristic
75C22×Dic31C2311yescharacteristic
76C2×Dic62—41no—
77C2×Dic62—41no—
78C2×Dic62C2×C414yescomplemented
79C22⋊C4×C31—22no—
80C22⋊C4×C31C2×C414yes—
81C42×C31—41no—
82C42×C31—41no—
83C22⋊Dic31—22no—
84C22⋊Dic31C2×C414yes—
85C4⋊Dic31—41no—
86C4⋊Dic31—41no—
87C4⋊Dic31C2×C414yescomplemented
88Dic31⋊C4—41no—
89Dic31⋊C4—41no—
90Dic31⋊C4—41no—
91Dic31⋊C4—41no—
92Dic31⋊C4C2×C414yescomplemented
93Dic31⋊C4C2×C414yescomplemented
94C4×Dic31—41no—
95C4×Dic31—41no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31—21no—
99C23×C31—21no—
100C23×C31C22×C412yes—
101C23×C31C2×Q812yes—
102C23×C31#4112yes—
103C23×C31C2411yescharacteristic
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—44no—
119C2×C4×C31C22×C412yes—
120C2×C4×C31C22×C412yes—
121C2×C4×C31C2×Q812yes—
122C2×C4×C31C2×Q812yes—
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×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—21no—
142C2×Dic31—21no—
143C2×Dic31—44no—
144C2×Dic31—44no—
145C2×Dic31C22×C412yes—
146C2×Dic31C22×C412yes—
147C2×Dic31C22×C412yes—
148C2×Dic31C22×C412yes—
149Dic62—44no—
150#2329—311nomaximal, Sylow
151C22×C31—22no—
152C22×C31—22no—
153C22×C31—22no—
154C22×C31—22no—
155C22×C31—22no—
156C22×C31—22no—
157C22×C31C4×Q814yes—
158C22×C31C23×C411yescharacteristic
159C22×C31C22×Q811yescharacteristic
160C22×C31C2×#4111yescharacteristic
161C22×C31H(5,𝔽2)11yescharacteristic
162C22×C31H(5,𝔽2)11yescharacteristic
163C22×C31H(5,𝔽2)11yescharacteristic
164C22×C312−1+411yescharacteristic
165C4×C31—22no—
166C4×C31—22no—
167C4×C31—22no—
168C4×C31—22no—
169C4×C31—41no—
170C4×C31—41no—
171Dic31—22no—
172Dic31—22no—
173Dic31—22no—
174Dic31—22no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178Dic31—41no—
179C2×C22⋊Q8—311no—
180#391—311no—
181#391—311no—
182#389—311no—
183#389—311no—
184#387—311no—
185#387—311no—
186#387—311no—
187#387—311no—
188#385—311no—
189#385—311no—
190#380—311no—
191C4×C22⋊C4—311no—
192C4×C22⋊C4D3111yescharacteristic
193C2×#95—311no—
194C2×C31—24no—
195C2×C31C2×C4×Q811yescharacteristic
196C2×C31#51811yescharacteristic
197C2×C31#52011yescharacteristic
198C2×C31#53811yescharacteristic
199C2×C31#53911yescharacteristic
200C2×C31#54311yescharacteristic
201C2×C31#54411yescharacteristic
202C22×Q8—311no—
203C23×C4—311no—
204C23×C4—311no—
205C23×C4C2×D3111yescharacteristic
206C22⋊Q8—318no—
207C2×C4⋊C4—311no—
208C2×C4⋊C4—311no—
209C2×C4⋊C4—311no—
210C2×C4⋊C4—311no—
211C2×C4⋊C4—311no—
212C2×C4⋊C4—311no—
213C2×C4⋊C4—311no—
214C2×C4⋊C4—311no—
215C2×C4⋊C4—311no—
216C2×C22⋊C4—311no—
217C2×C22⋊C4—311no—
218C2×C22⋊C4C2×D3111yescharacteristic
219C2×C22⋊C4C2×D3111yescharacteristic
220C2×C42—311no—
221C2×C42—311no—
222C2×C42C2×D3111yescharacteristic
223C2×C42C2×D3111yescharacteristic
224#95—311no—
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#95—311no—
234#95—311no—
235#95—311no—
236#95C2×D3111yescharacteristic
237#95C2×D3111yescharacteristic
238C31#232911yescharacteristic, complemented, Sylow
239C24C22×D3111yescharacteristic
240C2×Q8—314no—
241C2×Q8—1241no—
242C2×Q8—1241no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—311no—
246C22×C4—311no—
247C22×C4—311no—
248C22×C4—311no—
249C22×C4—314no—
250C22×C4—311no—
251C22×C4—311no—
252C22×C4—311no—
253C22×C4—311no—
254C22×C4—622no—
255C22×C4—1241no—
256C22×C4—1241no—
257C22×C4—1241no—
258C22×C4—1241no—
259C22×C4Dic6214yescomplemented
260C22×C4C22×D3111yescharacteristic
261C22×C4C22×D3111yescharacteristic
262C22×C4C22×D3111yescharacteristic
263C22×C4C22×D3111yescharacteristic
264C22×C4C22×D3111yescharacteristic
265C22×C4C22×D3111yescharacteristic
266C4⋊C4—314no—
267C4⋊C4—314no—
268C4⋊C4—314no—
269C4⋊C4—1241no—
270C4⋊C4—1241no—
271C4⋊C4—1241no—
272C4⋊C4—1241no—
273C4⋊C4—1241no—
274C4⋊C4—1241no—
275C22⋊C4—22no—
276C22⋊C4—314no—
277C22⋊C4—622no—
278C22⋊C4C4×D3114yes—
279C42—41no—
280C42—41no—
281C42—1241no—
282C42—1241no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×Dic6212yes—
288C23C2×C4×D3112yes—
289C23#9249512yes—
290C23C23×D3111yescharacteristic
291Q8—1244no—
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—44no—
307C2×C4—312no—
308C2×C4—312no—
309C2×C4—312no—
310C2×C4—312no—
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—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—1244no—
332C2×C4—1244no—
333C2×C4C2×Dic6212yes—
334C2×C4C2×Dic6212yes—
335C2×C4C2×C4×D3112yes—
336C2×C4C2×C4×D3112yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22C4×Dic6214yes—
344C22C22×Dic6211yescharacteristic
345C22C22×C4×D3111yescharacteristic
346C22C2×#9249511yescharacteristic
347C22#1175856111yescharacteristic
348C22#1175856111yescharacteristic
349C22#1175856611yescharacteristic
350C22#1175856711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—622no—
358C4—622no—
359C4—622no—
360C4—622no—
361C4—1241no—
362C4—1241no—
363C4—1241no—
364C4—1241no—
365C2—24no—
366C2C2×C4×Dic6211yescharacteristic
367C2#1452152111yescharacteristic
368C2#1452152811yescharacteristic
369C2#1452163211yescharacteristic
370C2#1452164111yescharacteristic
371C2#1452167511yescharacteristic
372C2#1452167711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC4×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenterC4×C22⋊C4D31
hypocenterC31#2329
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14520955C2semidirect
3. #14520953C2semidirect
4. #14520947C2semidirect
5. #14520946C2semidirect
6. #14520936C2semidirect
7. #14520933C2semidirect
8. #14520933C2semidirect
9. #14520932C2semidirect
37. #11758455C4semidirect
55. C22×C4×C31Q8semidirect
78. C2×Dic62C2×C4semidirect
87. C4⋊Dic31C2×C4semidirect
92. Dic31⋊C4C2×C4semidirect
93. Dic31⋊C4C2×C4semidirect
238. C31#2329semidirect
259. C22×C4Dic62semidirect

Maximal subgroups

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

subgroupindex
C2×#117584552
#145209552
#145209532
#145209472
#145209462
#145209362
#145209332
#145209322
#145209242
#145209212
#145209072
C4×C22⋊Dic312
C2×C31⋊#952
C4×C22⋊C4×C312
#232931