Finite Group Databasebeta

← #16848243

Subgroups — #16848243

Order 3968.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758455C211yesmaximal, characteristic
2C2×#11758464C211yesmaximal, characteristic, complemented
3C22×C4×Dic31C211yesmaximal, characteristic
4#14520953C211yesmaximal, characteristic, complemented
5#14520944C211yesmaximal, characteristic, complemented
6#14520934C211yesmaximal, characteristic, complemented
7#14520930C211yesmaximal, characteristic, complemented
8#14520922C211yesmaximal, characteristic
9#14520907C211yesmaximal, characteristic
10C4⋊C4×Dic31C211yesmaximal, characteristic, complemented
11#14520900C211yesmaximal, characteristic, complemented
12#14520900C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic31C211yesmaximal, characteristic
14C22⋊C4×Dic31C211yesmaximal, characteristic
15C31×#385C211yesmaximal, characteristic
16C23×C4×C31C2211yescharacteristic
17C23×Dic31C2211yescharacteristic
18C23×Dic31C2211yescharacteristic
19C22×Dic62C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21C2×C4⋊C4×C31C2211yescharacteristic
22C2×C22⋊C4×C31C2211yescharacteristic
23C2×C22⋊C4×C31C2211yescharacteristic
24C2×C22⋊Dic31C2211yescharacteristic
25C2×C22⋊Dic31C2211yescharacteristic
26C2×C4⋊Dic31C2211yescharacteristic
27C2×Dic31⋊C4C2211yescharacteristic
28C2×Dic31⋊C4C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×Dic31⋊C4C2211yescharacteristic
31C2×Dic31⋊C4C2211yescharacteristic
32C2×Dic31⋊C4C2211yescharacteristic
33C2×C4×Dic31—24no—
34C2×C4×Dic31C2211yescharacteristic
35C2×C4×Dic31C2211yescharacteristic
36C2×C4×Dic31C2211yescharacteristic
37C2×C4×Dic31C2211yescharacteristic
38C2×C4×Dic31C2211yescharacteristic
39C2×C4×Dic31C2211yescharacteristic
40C2×C4×Dic31C2211yescharacteristic
41C2×C4×Dic31C2211yescharacteristic
42#11758464—24no—
43#11758455C418yescomplemented
44C31×#95C2211yescharacteristic
45C31×#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C31⋊#95C2211yescharacteristic
53C31⋊#95C2211yescharacteristic
54C24×C31C2311yescharacteristic
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×Dic31—22no—
65C22×Dic31—22no—
66C22×Dic31—22no—
67C22×Dic31—22no—
68C22×Dic31C2×C414yes—
69C22×Dic31Q814yescomplemented
70C22×Dic31C2311yescharacteristic
71C22×Dic31C2311yescharacteristic
72C22×Dic31C2311yescharacteristic
73C22×Dic31C2311yescharacteristic
74C22×Dic31C2311yescharacteristic
75C22×Dic31C2311yescharacteristic
76C22×Dic31C2311yescharacteristic
77C22×Dic31C2311yescharacteristic
78C2×Dic62—22no—
79C2×Dic62—22no—
80C2×Dic62C2×C414yescomplemented
81C4⋊C4×C31—22no—
82C4⋊C4×C31—22no—
83C22⋊C4×C31—22no—
84C22⋊C4×C31C2×C414yes—
85C22⋊Dic31—22no—
86C22⋊Dic31C2×C414yes—
87C4⋊Dic31C2×C414yescomplemented
88Dic31⋊C4—22no—
89Dic31⋊C4—22no—
90Dic31⋊C4—22no—
91Dic31⋊C4—22no—
92Dic31⋊C4C2×C414yescomplemented
93Dic31⋊C4C2×C414yescomplemented
94C4×Dic31—22no—
95C4×Dic31—22no—
96C4×Dic31—22no—
97C4×Dic31—22no—
98C4×Dic31—22no—
99C4×Dic31—22no—
100C4×Dic31—22no—
101C4×Dic31D414yes—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31C22×C412yes—
107C23×C31C2×Q812yes—
108C23×C31#4112yes—
109C23×C31C2411yescharacteristic
110C2×C4×C31—28no—
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×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31C22×C412yes—
126C2×C4×C31C22×C412yes—
127C2×C4×C31C2×D412yes—
128C2×C4×C31#4112yes—
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—28no—
138C2×Dic31—28no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—21no—
142C2×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—21no—
145C2×Dic31C22×C412yes—
146C2×Dic31C22×C412yes—
147C2×Dic31C22×C412yes—
148C2×Dic31C22×C412yes—
149C2×Dic31C2×D412yes—
150C2×Dic31C2×D412yes—
151C2×Dic31C2×Q812yes—
152C2×Dic31C2×Q812yes—
153C2×Dic31#4112yes—
154C2×Dic31#4112yes—
155Dic62—28no—
156C4×C22⋊Q8—311nomaximal, Sylow
157C22×C31—22no—
158C22×C31—22no—
159C22×C31—22no—
160C22×C31—22no—
161C22×C31—22no—
162C22×C31—22no—
163C22×C31C4×Q814yescomplemented
164C22×C31C23×C411yescharacteristic
165C22×C31C22×D411yescharacteristic
166C22×C31C22×Q811yescharacteristic
167C22×C31C2×#4111yescharacteristic
168C22×C31C2×#4111yescharacteristic
169C22×C31C2×#4111yescharacteristic
170C22×C31C2×#4111yescharacteristic
171C4×C31—22no—
172C4×C31—22no—
173C4×C31—22no—
174C4×C31—22no—
175C4×C31—41no—
176C4×C31—41no—
177Dic31—22no—
178Dic31—22no—
179Dic31—22no—
180Dic31—22no—
181Dic31—41no—
182Dic31—41no—
183Dic31C4×D414yes—
184Dic31C22⋊Q814yescomplemented
185C2×C22⋊Q8—311no—
186C2×C4×Q8—311no—
187C22×C42—311no—
188#391—311no—
189#389—311no—
190#387—311no—
191#387—311no—
192#385—311no—
193#385D3111yescharacteristic
194#380—311no—
195C4×C4⋊C4—311no—
196C4×C4⋊C4—311no—
197C4×C4⋊C4—311no—
198C4×C22⋊C4—311no—
199C4×C22⋊C4—311no—
200C2×C31—24no—
201C2×C31C2×C4×D411yescharacteristic
202C2×C31C2×C4×Q811yescharacteristic
203C2×C31C4×#4111yescharacteristic
204C2×C31C2×C22⋊Q811yescharacteristic
205C2×C31#52511yescharacteristic
206C2×C31#52911yescharacteristic
207C2×C31#53311yescharacteristic
208C22×Q8—311no—
209C23×C4—311no—
210C23×C4—311no—
211C23×C4C2×D3111yescharacteristic
212C22⋊Q8—318no—
213C4×Q8—624no—
214C2×C4⋊C4—311no—
215C2×C4⋊C4—311no—
216C2×C4⋊C4—311no—
217C2×C4⋊C4—311no—
218C2×C4⋊C4—311no—
219C2×C4⋊C4—311no—
220C2×C4⋊C4—311no—
221C2×C4⋊C4C2×D3111yescharacteristic
222C2×C4⋊C4C2×D3111yescharacteristic
223C2×C22⋊C4—311no—
224C2×C22⋊C4—311no—
225C2×C22⋊C4C2×D3111yescharacteristic
226C2×C22⋊C4C2×D3111yescharacteristic
227C2×C42—311no—
228C2×C42—311no—
229C2×C42—311no—
230C2×C42—311no—
231C2×C42—311no—
232C2×C42—311no—
233C2×C42—311no—
234C2×C42—311no—
235C2×C42—624no—
236#95—311no—
237#95—311no—
238#95—311no—
239#95—311no—
240#95—311no—
241#95—311no—
242#95—311no—
243#95—311no—
244#95C2×D3111yescharacteristic
245#95C2×D3111yescharacteristic
246C31C4×C22⋊Q811yescharacteristic, complemented, Sylow
247C24C22×D3111yescharacteristic
248C2×Q8—314no—
249C2×Q8—622no—
250C2×Q8—622no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—311no—
255C22×C4—311no—
256C22×C4—314no—
257C22×C4—314no—
258C22×C4—311no—
259C22×C4—311no—
260C22×C4—311no—
261C22×C4—311no—
262C22×C4—311no—
263C22×C4—311no—
264C22×C4—622no—
265C22×C4—622no—
266C22×C4—622no—
267C22×C4—622no—
268C22×C4C22×D3111yescharacteristic
269C22×C4C22×D3111yescharacteristic
270C22×C4C22×D3111yescharacteristic
271C22×C4C22×D3111yescharacteristic
272C22×C4C22×D3111yescharacteristic
273C22×C4C22×D3111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—314no—
277C4⋊C4—314no—
278C4⋊C4—314no—
279C4⋊C4—622no—
280C4⋊C4—622no—
281C4⋊C4—622no—
282C4⋊C4—622no—
283C22⋊C4—22no—
284C22⋊C4—314no—
285C22⋊C4—622no—
286C22⋊C4C4×D3114yes—
287C42—314no—
288C42—622no—
289C42—622no—
290C42—622no—
291C42—622no—
292C42—622no—
293C42—622no—
294C42—622no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×C4×D3112yes—
300C23#9249712yes—
301C23Q8×D3112yes—
302C23C23×D3111yescharacteristic
303Q8—628no—
304C2×C4—28no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—312no—
320C2×C4—312no—
321C2×C4—312no—
322C2×C4—312no—
323C2×C4—312no—
324C2×C4—312no—
325C2×C4—312no—
326C2×C4—312no—
327C2×C4—312no—
328C2×C4—312no—
329C2×C4—628no—
330C2×C4—628no—
331C2×C4—621no—
332C2×C4—621no—
333C2×C4—621no—
334C2×C4—621no—
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×C4C2×C4×D3112yes—
346C2×C4C2×C4×D3112yes—
347C2×C4D4×D3112yes—
348C2×C4#9249712yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22#1175846414yescomplemented
356C22C22×C4×D3111yescharacteristic
357C22C2×D4×D3111yescharacteristic
358C22C2×#9249711yescharacteristic
359C22C2×#9249711yescharacteristic
360C22C2×Q8×D3111yescharacteristic
361C22#41×D3111yescharacteristic
362C22#41×D3111yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—314no—
370C4—314no—
371C4—622no—
372C4—622no—
373C4—622no—
374C4—622no—
375C4—1241no—
376C4—1241no—
377C2—24no—
378C2C4×D4×D3111yescharacteristic
379C2C2×#1175846411yescharacteristic
380C2C4×#9249711yescharacteristic
381C2C22⋊Q8×D3111yescharacteristic
382C2#1452155511yescharacteristic
383C2#1452157611yescharacteristic
384C2#1452160111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#385C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenter#385D31
hypocenterC31C4×C22⋊Q8
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#11758464C2semidirect
4. #14520953C2semidirect
5. #14520944C2semidirect
6. #14520934C2semidirect
7. #14520930C2semidirect
10. C4⋊C4×Dic31C2semidirect
11. #14520900C2semidirect
12. #14520900C2semidirect
43. #11758455C4semidirect
69. C22×Dic31Q8semidirect
80. C2×Dic62C2×C4semidirect
87. C4⋊Dic31C2×C4semidirect
92. Dic31⋊C4C2×C4semidirect
93. Dic31⋊C4C2×C4semidirect
163. C22×C31C4×Q8semidirect
184. Dic31C22⋊Q8semidirect
246. C31C4×C22⋊Q8semidirect
355. C22#11758464semidirect

Maximal subgroups

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

subgroupindex
C2×#117584552
C2×#117584642
C22×C4×Dic312
#145209532
#145209442
#145209342
#145209302
#145209222
#145209072
C4⋊C4×Dic312
#145209002
C22⋊C4×Dic312
C31×#3852
C4×C22⋊Q831