Finite Group Databasebeta

← #16846756

Subgroups — #16846756

Order 3968.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#11758519C211yesmaximal, characteristic, complemented
2#14521627C211yesmaximal, characteristic
3C2×#11758425C211yesmaximal, characteristic, complemented
4C2×#11758413C211yesmaximal, characteristic, complemented
5#14520956C211yesmaximal, characteristic, complemented
6#14520817C211yesmaximal, characteristic, complemented
7C2×C31×#137C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C22×Q8×C31C2211yescharacteristic
10C2×#92495C2211yescharacteristic
11C31×#137—22no—
12C31×#137—22no—
13C2×Q16×C31—21no—
14C2×SD16×C31—21no—
15C2×M16×C31C2211yescharacteristic
16#11758523—21no—
17C2×#92482—21no—
18#11758519—22no—
19#11758519—22no—
20C2×#92481—21no—
21#11758516—22no—
22#11758515—21no—
23#11758507—21no—
24C2×C4⋊Dic31C2211yescharacteristic
25#11758501—21no—
26C2×C4×Dic31C2211yescharacteristic
27C2×#92474C2211yescharacteristic
28#11758425—22no—
29C31⋊#95—22no—
30#11758413—22no—
31#41×C31—21no—
32#41×C31—21no—
33#41×C31—21no—
34#41×C31—21no—
35C2×Q8×C31—21no—
36C2×Q8×C31—21no—
37C2×Q8×C31—21no—
38C2×Q8×C31—21no—
39C2×Q8×C31—21no—
40C2×Q8×C31D411yescharacteristic
41C2×Q8×C31D412yescomplemented
42C2×D4×C31—21no—
43C2×D4×C31D411yescharacteristic
44C22×C4×C31—21no—
45C22×C4×C31—21no—
46C22×C4×C31C2311yescharacteristic
47C2×C22⋊D31—21no—
48C2×C22⋊D31—22no—
49C22×Dic31—21no—
50C22×Dic31D412yes—
51#92495—21no—
52#92495—21no—
53#92495—21no—
54#92495—21no—
55C2×D124D411yescharacteristic
56C2×C4×D31—21no—
57C2×Dic62D411yescharacteristic
58Q16×C31—24no—
59SD16×C31—24no—
60M16×C31—21no—
61M16×C31D412yescomplemented
62C2×C8×C31—21no—
63C22⋊Dic31—22no—
64#92482—24no—
65#92481—24no—
66(C2×D31)⋊C4—22no—
67C4⋊Dic31—21no—
68C4⋊Dic31—21no—
69Dic31⋊C4—22no—
70C4×Dic31—21no—
71C4×Dic31—21no—
72#92474—21no—
73#92474D412yescomplemented
74C2×C31⋊C8—21no—
75C23×C31—21no—
76C23×C31C2×D411yescharacteristic
77C22×D31—21no—
78Q8×C31—22no—
79Q8×C31—22no—
80Q8×C31—21no—
81Q8×C31—21no—
82Q8×C31—41no—
83Q8×C31—41no—
84D4×C31—21no—
85D4×C31—21no—
86D4×C31—41no—
87D4×C31—41no—
88C2×C4×C31—21no—
89C2×C4×C31—22no—
90C2×C4×C31—41no—
91C2×C4×C31—41no—
92C2×C4×C31—41no—
93C2×C4×C31—41no—
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31C2×D411yescharacteristic
96C2×C4×C31C2×D411yescharacteristic
97C2×C4×C31C2×D411yescharacteristic
98C2×C4×C31C2×D411yescharacteristic
99C2×C4×C31#4111yescharacteristic
100C22⋊D31—41no—
101C22⋊D31—41no—
102C22⋊D31—82no—
103C2×Dic31—22no—
104C2×Dic31—21no—
105C2×Dic31—22no—
106C2×Dic31—41no—
107C2×Dic31—41no—
108C2×Dic31—42no—
109D124—21no—
110D124—21no—
111C4×D31—41no—
112C4×D31—41no—
113Dic62—21no—
114Dic62—21no—
115C8×C31—22no—
116C31⋊C8—22no—
117#2007—311nomaximal, Sylow
118C22×C31—21no—
119C22×C31—21no—
120C22×C31—41no—
121C22×C31—41no—
122C22×C31—41no—
123C22×C31#12011yescharacteristic
124C22×C31#12111yescharacteristic
125C22×C31#12711yescharacteristic
126C2×D31—41no—
127C2×D31—41no—
128C2×D31—41no—
129C4×C31—41no—
130C4×C31—42no—
131C4×C31#12011yescharacteristic
132C4×C31#12011yescharacteristic
133C4×C31#12111yescharacteristic
134C4×C31#12111yescharacteristic
135Dic31—42no—
136Dic31—41no—
137Dic31—42no—
138C2×#137—311no—
139C2×#137D3111yescharacteristic, complemented
140#537—311no—
141C2×#104—311no—
142C2×#104—311no—
143#391—311no—
144#343—311no—
145C2×C31—21no—
146C2×C31—21no—
147C2×C31—81no—
148C2×C31#39211yescharacteristic
149C2×C31#45511yescharacteristic
150C2×C31#45611yescharacteristic
151D31—81no—
152C2×#41—311no—
153C2×#41C2×D3111yescharacteristic
154C22×Q8C2×D3111yescharacteristic
155#137—22no—
156#137—22no—
157#137—622no—
158#137—622no—
159C2×Q16—21no—
160C2×Q16—621no—
161C2×SD16—21no—
162C2×SD16—621no—
163C2×M16—311no—
164C2×M16C2×D3111yescharacteristic
165C22⋊Q8—621no—
166C22⋊Q8—621no—
167#121—621no—
168#121—622no—
169#121—621no—
170C2×C4⋊C4—311no—
171C2×C42—311no—
172#104—622no—
173#104—622no—
174#95—622no—
175C31#200711yescharacteristic, complemented, Sylow
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—621no—
181#41—621no—
182#41—621no—
183#41—621no—
184C2×Q8—21no—
185C2×Q8—21no—
186C2×Q8—21no—
187C2×Q8—21no—
188C2×Q8—21no—
189C2×Q8—311no—
190C2×Q8C22⋊D3111yescharacteristic
191C2×Q8C22⋊D3112yescomplemented
192C2×D4—21no—
193C2×D4—311no—
194C2×D4—621no—
195C2×D4—622no—
196C2×D4C22⋊D3111yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—312no—
200C22×C4—621no—
201C22×C4—621no—
202C22×C4C22×D3111yescharacteristic
203Q16—24no—
204Q16—624no—
205SD16—24no—
206SD16—624no—
207M16—21no—
208M16—312no—
209M16—621no—
210M16C22⋊D3112yescomplemented
211C2×C8—21no—
212C2×C8—621no—
213C4⋊C4—622no—
214C4⋊C4—621no—
215C4⋊C4—621no—
216C22⋊C4—622no—
217C22⋊C4—622no—
218C42—621no—
219C42—621no—
220C23—21no—
221C23—621no—
222C23D4×D3111yescharacteristic
223Q8—22no—
224Q8—21no—
225Q8—22no—
226Q8—21no—
227Q8—41no—
228Q8—41no—
229Q8—621no—
230Q8—621no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—621no—
236D4—621no—
237D4—1241no—
238D4—1241no—
239D4—2482no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—622no—
247C2×C4—622no—
248C2×C4—621no—
249C2×C4—1241no—
250C2×C4—1241no—
251C2×C4—1241no—
252C2×C4—1241no—
253C2×C4—1242no—
254C2×C4D4×D3111yescharacteristic
255C2×C4D4×D3111yescharacteristic
256C2×C4#9249711yescharacteristic
257C2×C4C2×C22⋊D3111yescharacteristic
258C2×C4C2×C22⋊D3111yescharacteristic
259C2×C4C2×C22⋊D3111yescharacteristic
260C8—22no—
261C8—622no—
262C22—21no—
263C22—21no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—1241no—
268C22—1241no—
269C22—1241no—
270C22#1175851411yescharacteristic
271C22#1175851611yescharacteristic
272C22#1175851711yescharacteristic
273C4—41no—
274C4—42no—
275C4—1242no—
276C4—1241no—
277C4—1242no—
278C4#1175851411yescharacteristic
279C4#1175851511yescharacteristic
280C4#1175851611yescharacteristic
281C4#1175853011yescharacteristic
282C2—21no—
283C2—21no—
284C2—81no—
285C2—2481no—
286C2#1452095711yescharacteristic
287C2#1452122511yescharacteristic
288C2#1452123011yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#137C2
socleC22×C31#120
prime radical#14521627C2
hypercenterC2×#137D31
hypocenterC31#2007
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#11758519C2semidirect
3. C2×#11758425C2semidirect
4. C2×#11758413C2semidirect
5. #14520956C2semidirect
6. #14520817C2semidirect
7. C2×C31×#137C2semidirect
41. C2×Q8×C31D4semidirect
61. M16×C31D4semidirect
73. #92474D4semidirect
139. C2×#137D31semidirect
175. C31#2007semidirect
191. C2×Q8C22⋊D31semidirect
210. M16C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585192
#145216272
C2×#117584252
C2×#117584132
#145209562
#145208172
C2×C31×#1372
#200731