Finite Group Databasebeta

← #16846628

Subgroups — #16846628

Order 3968.

336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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
1#14521595C211yesmaximal, characteristic
2C2×#11758393C211yesmaximal, characteristic, complemented
3C2×#11758425C211yesmaximal, characteristic, complemented
4C2×#11758413C211yesmaximal, characteristic, complemented
5M16×Dic31C211yesmaximal, characteristic, complemented
6C4×Dic31⋊C4C211yesmaximal, characteristic, complemented
7C2×C31×#104C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C2×#92495C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×C42×C31C2211yescharacteristic
12#11758524C411yescharacteristic, complemented
13#11758521C411yescharacteristic, complemented
14#11758517C411yescharacteristic, complemented
15#11758516—21no—
16#11758516—21no—
17#11758513C411yescharacteristic, complemented
18C4×C22⋊D31—21no—
19C4×C22⋊D31—21no—
20C2×Dic31⋊C4—21no—
21C2×C4×Dic31C2211yescharacteristic
22C2×C4×Dic31C2211yescharacteristic
23C2×#92474C2211yescharacteristic
24C31×#104—22no—
25#11758425—22no—
26C31⋊#95—21no—
27#11758413—22no—
28#11758403—21no—
29C8×Dic31—21no—
30#11758393—22no—
31#41×C31—21no—
32#41×C31—21no—
33#41×C31—21no—
34#41×C31—21no—
35C2×Q8×C31C2×C411yescharacteristic
36C2×D4×C31—21no—
37C2×D4×C31C2×C411yescharacteristic
38C22×C4×C31—21no—
39C22×C4×C31—21no—
40C22×C4×C31C2311yescharacteristic
41C2×C22⋊D31—21no—
42C2×C22⋊D31—21no—
43C2×C22⋊D31—21no—
44C22×Dic31—21no—
45C22×Dic31D411yescharacteristic
46C22×Dic31D411yescharacteristic
47#92495—21no—
48#92495—21no—
49#92495—21no—
50#92495—21no—
51C2×D124C2×C411yescharacteristic
52C2×C4×D31—21no—
53C2×Dic62C2×C411yescharacteristic
54M16×C31—21no—
55M16×C31D412yescomplemented
56C2×C8×C31—21no—
57C42×C31—21no—
58C42×C31—21no—
59C22⋊Dic31—21no—
60C22⋊Dic31—21no—
61(C2×D31)⋊C4—21no—
62(C2×D31)⋊C4—21no—
63Dic31⋊C4—24no—
64Dic31⋊C4—21no—
65Dic31⋊C4—21no—
66C4×Dic31—21no—
67C4×Dic31—21no—
68C4×Dic31C2×C411yescharacteristic
69C4×Dic31C2×C411yescharacteristic
70C4×Dic31D411yescharacteristic
71C4×Dic31D411yescharacteristic
72#92474—21no—
73#92474D412yescomplemented
74C2×C31⋊C8—21no—
75C23×C31—21no—
76C23×C31C2×D411yescharacteristic
77C22×D31—21no—
78Q8×C31—21no—
79Q8×C31—21no—
80D4×C31—21no—
81D4×C31—21no—
82D4×C31—41no—
83D4×C31—41no—
84C2×C4×C31—22no—
85C2×C4×C31—21no—
86C2×C4×C31—41no—
87C2×C4×C31—41no—
88C2×C4×C31—41no—
89C2×C4×C31—41no—
90C2×C4×C31C22×C411yescharacteristic
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D411yescharacteristic
93C2×C4×C31C2×D411yescharacteristic
94C2×C4×C31#4111yescharacteristic
95C2×C4×C31#4111yescharacteristic
96C22⋊D31—42no—
97C22⋊D31—41no—
98C22⋊D31—41no—
99C22⋊D31—42no—
100C2×Dic31—22no—
101C2×Dic31—22no—
102C2×Dic31—21no—
103C2×Dic31—41no—
104C2×Dic31—41no—
105C2×Dic31—41no—
106C2×Dic31C22⋊C411yescharacteristic
107C2×Dic31C22⋊C411yescharacteristic
108C2×Dic31C22⋊C411yescharacteristic
109C2×Dic31C22⋊C411yescharacteristic
110D124—21no—
111D124—21no—
112C4×D31—41no—
113C4×D31—41no—
114Dic62—21no—
115Dic62—21no—
116C8×C31—22no—
117C31⋊C8—22no—
118#1980—311nomaximal, Sylow
119C22×C31—21no—
120C22×C31—21no—
121C22×C31—41no—
122C22×C31—41no—
123C22×C31—41no—
124C22×C31C2×C22⋊C411yescharacteristic
125C22×C31#12411yescharacteristic
126C22×C31#12711yescharacteristic
127C2×D31—41no—
128C2×D31—41no—
129C2×D31—41no—
130C4×C31—42no—
131C4×C31—41no—
132C4×C31C4×D411yescharacteristic
133C4×C31C4×D411yescharacteristic
134C4×C31#12111yescharacteristic
135C4×C31#12111yescharacteristic
136Dic31—21no—
137Dic31—21no—
138Dic31—21no—
139Dic31—42no—
140Dic31—41no—
141Dic31#10412yescomplemented
142#532—311no—
143C2×#104—311no—
144C2×#104—311no—
145C2×#104—311no—
146C2×#104D3111yescharacteristic, complemented
147C4×M16—311no—
148C4×C4⋊C4—311no—
149C2×C31—21no—
150C2×C31—21no—
151C2×C31—81no—
152C2×C31#39011yescharacteristic
153C2×C31C2×#10411yescharacteristic
154C2×C31#42111yescharacteristic
155D31—81no—
156C2×#41—311no—
157C2×#41C2×D3111yescharacteristic
158C2×M16—311no—
159C2×M16C2×D3111yescharacteristic
160C4⋊Q8—311no—
161#127—311no—
162#124—311no—
163#124—311no—
164#121—621no—
165#121—621no—
166C4×D4—621no—
167C4×D4—621no—
168C2×C4⋊C4—621no—
169C2×C42—311no—
170C2×C42—311no—
171C2×C42C2×D3111yescharacteristic
172#104—22no—
173#104—622no—
174#104—622no—
175#104—622no—
176#97—621no—
177C4×C8—621no—
178#95—621no—
179C31#198011yescharacteristic, complemented, Sylow
180#41—21no—
181#41—21no—
182#41—21no—
183#41—21no—
184#41—621no—
185#41—621no—
186#41—621no—
187#41—621no—
188C2×Q8—311no—
189C2×Q8C4×D3111yescharacteristic
190C2×D4—21no—
191C2×D4—311no—
192C2×D4—621no—
193C2×D4—621no—
194C2×D4—621no—
195C2×D4C4×D3111yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—311no—
199C22×C4—311no—
200C22×C4—621no—
201C22×C4—621no—
202C22×C4C22×D3111yescharacteristic
203M16—21no—
204M16—312no—
205M16—621no—
206M16C22⋊D3112yescomplemented
207C2×C8—21no—
208C2×C8—621no—
209C4⋊C4—621no—
210C4⋊C4—621no—
211C4⋊C4—624no—
212C22⋊C4—621no—
213C22⋊C4—621no—
214C22⋊C4—621no—
215C22⋊C4—621no—
216C42—21no—
217C42—21no—
218C42—311no—
219C42—311no—
220C42—311no—
221C42—311no—
222C42—621no—
223C42—621no—
224C23—21no—
225C23—621no—
226C23D4×D3111yescharacteristic
227Q8—21no—
228Q8—21no—
229Q8—621no—
230Q8—621no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—621no—
236D4—621no—
237D4—1242no—
238D4—1242no—
239D4—1241no—
240D4—1241no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—311no—
248C2×C4—311no—
249C2×C4—311no—
250C2×C4—311no—
251C2×C4—622no—
252C2×C4—622no—
253C2×C4—621no—
254C2×C4—1241no—
255C2×C4—1241no—
256C2×C4—1241no—
257C2×C4—1241no—
258C2×C4—1241no—
259C2×C4C2×C4×D3111yescharacteristic
260C2×C4#9249511yescharacteristic
261C2×C4D4×D3111yescharacteristic
262C2×C4D4×D3111yescharacteristic
263C2×C4#9249711yescharacteristic
264C2×C4C2×C22⋊D3111yescharacteristic
265C8—22no—
266C8—622no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—1241no—
273C22—1241no—
274C22—1241no—
275C22C22⋊C4×D3111yescharacteristic
276C22#1175846211yescharacteristic
277C22#1175851711yescharacteristic
278C4—42no—
279C4—41no—
280C4—312no—
281C4—621no—
282C4—621no—
283C4—621no—
284C4—1242no—
285C4—1241no—
286C4(C22⋊D31)⋊C411yescharacteristic
287C4#1175846111yescharacteristic
288C4C4×C22⋊D3111yescharacteristic
289C4#1175851611yescharacteristic
290C2—21no—
291C2—21no—
292C2—81no—
293C2—2481no—
294C2#1452094911yescharacteristic
295C2#104×D3111yescharacteristic
296C2#1452106411yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#104C2
socleC22×C31C2×C22⋊C4
prime radical#14521595C2
cosocleC22×C4×C31C23
hypercenterC2×#104D31
hypocenterC31#1980
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11758393C2semidirect
3. C2×#11758425C2semidirect
4. C2×#11758413C2semidirect
5. M16×Dic31C2semidirect
6. C4×Dic31⋊C4C2semidirect
7. C2×C31×#104C2semidirect
12. #11758524C4semidirect
13. #11758521C4semidirect
14. #11758517C4semidirect
17. #11758513C4semidirect
55. M16×C31D4semidirect
73. #92474D4semidirect
141. Dic31#104semidirect
146. C2×#104D31semidirect
179. C31#1980semidirect
206. M16C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145215952
C2×#117583932
C2×#117584252
C2×#117584132
M16×Dic312
C4×Dic31⋊C42
C2×C31×#1042
#198031