Finite Group Databasebeta

← #16846715

Subgroups — #16846715

Order 3968.

444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#92480C211yesmaximal, characteristic, complemented
2C2×#11758474C211yesmaximal, characteristic, complemented
3C2×#11758515C211yesmaximal, characteristic
4C2×#11758404C211yesmaximal, characteristic, complemented
5C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
6#14520811C211yesmaximal, characteristic, complemented
7C2×C31×#102C211yesmaximal, characteristic, complemented
8C22×D4×C31C2211yescharacteristic
9C22×C22⋊D31—21no—
10C22×C4×D31C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C22×C8×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C22⋊Dic31—21no—
15#11758515—22no—
16#11758515—22no—
17C2×#92480—22no—
18C2×#92480—22no—
19C2×#92480—22no—
20C2×(C2×D31)⋊C4—21no—
21C2×C4⋊Dic31—21no—
22C2×C4⋊Dic31C2211yescharacteristic
23C22×C31⋊C8C2211yescharacteristic
24#11758474—22no—
25#11758474—22no—
26C31×#102—22no—
27(C2×D31)⋊C8—22no—
28#11758404—22no—
29C24×C31—21no—
30C23×D31D411yescharacteristic
31C2×D4×C31—21no—
32C2×D4×C31—21no—
33C2×D4×C31—21no—
34C2×D4×C31—21no—
35C2×D4×C31—21no—
36C2×D4×C31D412yes—
37C22×C4×C31—21no—
38C22×C4×C31C2311yescharacteristic
39C2×C22⋊D31—24no—
40C2×C22⋊D31—42no—
41C2×C22⋊D31—42no—
42C22×Dic31—21no—
43C22×Dic31—21no—
44C22×Dic31D411yescharacteristic
45C2×C4×D31—21no—
46C2×C4×D31—21no—
47C2×C4×D31—21no—
48C2×C4×D31—21no—
49C2×C4×D31—21no—
50C2×C4×D31—21no—
51C2×Dic62—21no—
52C2×Dic62—21no—
53C2×Dic62—21no—
54C2×Dic62—21no—
55C2×Dic62—21no—
56C2×Dic62D412yescomplemented
57C2×C8×C31—21no—
58C2×C8×C31—21no—
59C2×C8×C31—21no—
60C4⋊C4×C31—21no—
61C4⋊C4×C31D412yescomplemented
62C22⋊Dic31—24no—
63#92480—28no—
64(C2×D31)⋊C4—24no—
65C4⋊Dic31—24no—
66C4⋊Dic31—21no—
67C4⋊Dic31D412yes—
68C2×C31⋊C8—21no—
69C2×C31⋊C8—21no—
70C2×C31⋊C8D412yescomplemented
71C23×C31—22no—
72C23×C31—41no—
73C23×C31—41no—
74C23×C31—41no—
75C23×C31—41no—
76C23×C31—41no—
77C23×C31—41no—
78C23×C31C2×D411yescharacteristic
79C22×D31—21no—
80C22×D31—21no—
81C22×D31—21no—
82C22×D31—21no—
83C22×D31—21no—
84C22×D31—21no—
85C22×D31SD1612yescomplemented
86D4×C31—22no—
87D4×C31—22no—
88D4×C31—41no—
89D4×C31—41no—
90C2×C4×C31—22no—
91C2×C4×C31—41no—
92C2×C4×C31—41no—
93C2×C4×C31C2×D411yescharacteristic
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31C2×D411yescharacteristic
96C2×C4×C31C2×D411yescharacteristic
97C2×C4×C31C2×D411yescharacteristic
98C2×C4×C31#4111yescharacteristic
99C22⋊D31—48no—
100C2×Dic31—21no—
101C2×Dic31—22no—
102C2×Dic31—22no—
103C2×Dic31—21no—
104C2×Dic31—21no—
105C2×Dic31—41no—
106C2×Dic31—41no—
107C2×Dic31—41no—
108C2×Dic31—41no—
109C4×D31—41no—
110C4×D31—41no—
111C4×D31—41no—
112C4×D31—41no—
113Dic62—22no—
114Dic62—22no—
115Dic62—41no—
116Dic62—41no—
117C8×C31—41no—
118C31⋊C8—22no—
119#2000—311nomaximal, Sylow
120C22×C31—42no—
121C22×C31—42no—
122C22×C31—42no—
123C22×C31—81no—
124C22×C31—81no—
125C22×C31—81no—
126C22×C31—81no—
127C22×C31#12011yescharacteristic
128C22×C31#12011yescharacteristic
129C22×C31#12111yescharacteristic
130C22×C31C2×SD1611yescharacteristic
131C22×C31#13511yescharacteristic
132C22×C31AGL(1,ℤ/8)11yescharacteristic
133C22×C31#13711yescharacteristic
134C2×D31—22no—
135C2×D31—22no—
136C2×D31—22no—
137C2×D31—41no—
138C2×D31—41no—
139C2×D31—41no—
140C2×D31—41no—
141C4×C31—42no—
142C4×C31#12011yescharacteristic
143C4×C31#12111yescharacteristic
144C4×C31#12111yescharacteristic
145C4×C31#12711yescharacteristic
146Dic31—42no—
147Dic31—41no—
148Dic31—42no—
149C22×SD16—311no—
150C2×C22⋊Q8—311no—
151C2×#121—311no—
152C2×#103—311no—
153C2×#102D3111yescharacteristic, complemented
154C2×C22⋊C8—311no—
155#340—311no—
156C2×C31—82no—
157C2×C31#39211yescharacteristic
158C2×C31#44811yescharacteristic
159C2×C31#44911yescharacteristic
160C2×C31#45011yescharacteristic
161C2×C31#45211yescharacteristic
162C2×C31#46511yescharacteristic
163C2×C31#46811yescharacteristic
164D31—42no—
165C22×Q8—311no—
166C22×D4—621no—
167C22×D4C2×D3111yescharacteristic
168C23×C4—311no—
169C2×SD16—622no—
170C2×SD16—622no—
171C2×SD16—622no—
172C22×C8—311no—
173C22×C8C2×D3111yescharacteristic
174C22⋊Q8—622no—
175C22⋊Q8—622no—
176#121—622no—
177#121—622no—
178C2×C4⋊C4—311no—
179C2×C4⋊C4—621no—
180C2×C4⋊C4C2×D3111yescharacteristic
181C2×C22⋊C4—621no—
182C2×C22⋊C4—621no—
183#103—622no—
184#102—22no—
185C22⋊C8—622no—
186C31#200011yescharacteristic, complemented, Sylow
187C24—21no—
188C24—311no—
189C2×Q8—312no—
190C2×Q8—621no—
191C2×Q8—621no—
192C2×Q8—621no—
193C2×Q8—621no—
194C2×Q8—621no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—624no—
201C2×D4—1242no—
202C2×D4—1242no—
203C2×D4D12412yes—
204C22×C4—21no—
205C22×C4—311no—
206C22×C4—621no—
207C22×C4—621no—
208C22×C4—621no—
209C22×C4—621no—
210C22×C4—621no—
211C22×C4—621no—
212C22×C4—621no—
213C22×C4—621no—
214C22×C4C22×D3111yescharacteristic
215SD16—628no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—312no—
220C2×C8—621no—
221C2×C8—621no—
222C4⋊C4—21no—
223C4⋊C4—312no—
224C4⋊C4—624no—
225C4⋊C4—621no—
226C4⋊C4C22⋊D3112yescomplemented
227C22⋊C4—624no—
228C22⋊C4—624no—
229C23—22no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—312no—
237C23—621no—
238C23—621no—
239C23—621no—
240C23—621no—
241C23—621no—
242C23—621no—
243C23D4×D3111yescharacteristic
244Q8—622no—
245Q8—622no—
246Q8—1241no—
247Q8—1241no—
248D4—22no—
249D4—22no—
250D4—41no—
251D4—41no—
252D4—1248no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—621no—
257C2×C4—622no—
258C2×C4—621no—
259C2×C4—622no—
260C2×C4—621no—
261C2×C4—1241no—
262C2×C4—1241no—
263C2×C4—1241no—
264C2×C4—1241no—
265C2×C4—1241no—
266C2×C4—1241no—
267C2×C4—1241no—
268C2×C4—1241no—
269C2×C4C2×D12411yescharacteristic
270C2×C4#9249511yescharacteristic
271C2×C4D4×D3111yescharacteristic
272C2×C4D4×D3111yescharacteristic
273C2×C4D4×D3111yescharacteristic
274C2×C4C2×C22⋊D3111yescharacteristic
275C8—41no—
276C8—622no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—81no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22—622no—
285C22—622no—
286C22—622no—
287C22—1241no—
288C22—1241no—
289C22—1241no—
290C22—1241no—
291C22#1175845911yescharacteristic
292C22#1175846111yescharacteristic
293C22#1175848811yescharacteristic
294C22#1175848911yescharacteristic
295C22SD16×D3111yescharacteristic
296C22#1175849211yescharacteristic
297C22#1175851411yescharacteristic
298C4—42no—
299C4—1242no—
300C4—1241no—
301C4—1242no—
302C4#1175845911yescharacteristic
303C4#1175846111yescharacteristic
304C4#1175850711yescharacteristic
305C4#1175851711yescharacteristic
306C2—82no—
307C2—1242no—
308C2#1452095811yescharacteristic
309C2#1452118611yescharacteristic
310C2#1452119111yescharacteristic
311C2#1452120111yescharacteristic
312C2#1452121211yescharacteristic
313C2#1452127711yescharacteristic
314C2#1452129411yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
prime radicalC2×#11758515C2
hypercenterC2×#102D31
hypocenterC31#2000
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#92480C2semidirect
2. C2×#11758474C2semidirect
4. C2×#11758404C2semidirect
5. C2×(C2×D31)⋊C8C2semidirect
6. #14520811C2semidirect
7. C2×C31×#102C2semidirect
56. C2×Dic62D4semidirect
61. C4⋊C4×C31D4semidirect
70. C2×C31⋊C8D4semidirect
85. C22×D31SD16semidirect
153. C2×#102D31semidirect
186. C31#2000semidirect
226. C4⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C22×#924802
C2×#117584742
C2×#117585152
C2×#117584042
C2×(C2×D31)⋊C82
#145208112
C2×C31×#1022
#200031