Finite Group Databasebeta

← #16846759

Subgroups — #16846759

Order 3968.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11758486C211yesmaximal, characteristic, complemented
2C2×#11758528C211yesmaximal, characteristic, complemented
3#14521627C211yesmaximal, characteristic
4C2×#11758393C211yesmaximal, characteristic, complemented
5#14520955C211yesmaximal, characteristic, complemented
6#14520817C211yesmaximal, characteristic, complemented
7C2×C31×#104C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C2×#92495C2211yescharacteristic
10C22×Dic62C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C2×C42×C31C2211yescharacteristic
13#11758528—22no—
14#11758528—22no—
15#11758523—21no—
16C2×#92482—21no—
17#11758516—22no—
18#11758515—21no—
19C2×#92480—21no—
20#11758507—21no—
21C2×C4⋊Dic31C2211yescharacteristic
22#11758501—21no—
23C2×#92474C2211yescharacteristic
24#11758486—22no—
25#11758486—22no—
26C2×Dic124—21no—
27C2×#92470—21no—
28C31×#104—22no—
29C31⋊#95—22no—
30#11758393—22no—
31#41×C31—21no—
32#41×C31—21no—
33#41×C31—21no—
34#41×C31—21no—
35C2×Q8×C31D411yescharacteristic
36C2×D4×C31—21no—
37C2×D4×C31D411yescharacteristic
38C22×C4×C31—21no—
39C22×C4×C31—21no—
40C22×C4×C31C2311yescharacteristic
41C2×C22⋊D31—21no—
42C2×C22⋊D31—22no—
43C22×Dic31—21no—
44C22×Dic31D412yes—
45#92495—21no—
46#92495—21no—
47#92495—21no—
48#92495—21no—
49C2×D124D411yescharacteristic
50C2×C4×D31—21no—
51C2×Dic62—21no—
52C2×Dic62—21no—
53C2×Dic62—21no—
54C2×Dic62—21no—
55C2×Dic62—21no—
56C2×Dic62D411yescharacteristic
57C2×Dic62D412yescomplemented
58M16×C31—21no—
59M16×C31D412yescomplemented
60C2×C8×C31—21no—
61C42×C31—21no—
62C42×C31—21no—
63C22⋊Dic31—22no—
64#92482—24no—
65#92480—24no—
66(C2×D31)⋊C4—22no—
67C4⋊Dic31—21no—
68C4⋊Dic31—21no—
69Dic31⋊C4—22no—
70#92474—21no—
71#92474D412yescomplemented
72C2×C31⋊C8—21no—
73Dic124—24no—
74#92470—24no—
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×C31C2×D411yescharacteristic
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D411yescharacteristic
93C2×C4×C31C2×D411yescharacteristic
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31#4111yescharacteristic
96C22⋊D31—41no—
97C22⋊D31—41no—
98C22⋊D31—82no—
99C2×Dic31—21no—
100C2×Dic31—22no—
101C2×Dic31—22no—
102C2×Dic31—41no—
103C2×Dic31—41no—
104C2×Dic31—42no—
105D124—21no—
106D124—21no—
107C4×D31—41no—
108C4×D31—41no—
109Dic62—22no—
110Dic62—21no—
111Dic62—22no—
112Dic62—21no—
113Dic62—41no—
114Dic62—41no—
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—42no—
130C4×C31—41no—
131C4×C31#12011yescharacteristic
132C4×C31#12011yescharacteristic
133C4×C31#12111yescharacteristic
134C4×C31#12111yescharacteristic
135Dic31—42no—
136Dic31—41no—
137Dic31—42no—
138C2×#137—311no—
139C2×#137—311no—
140#537—311no—
141C2×#104—311no—
142C2×#104D3111yescharacteristic, complemented
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×Q8—311no—
155#137—622no—
156#137—622no—
157#137—622no—
158#137—622no—
159C2×Q16—621no—
160C2×Q16—621no—
161C2×SD16—621no—
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×C42C2×D3111yescharacteristic
172#104—22no—
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—311no—
185C2×Q8—312no—
186C2×Q8—621no—
187C2×Q8—621no—
188C2×Q8—621no—
189C2×Q8—621no—
190C2×Q8—621no—
191C2×Q8D12411yescharacteristic
192C2×D4—21no—
193C2×D4—311no—
194C2×D4—621no—
195C2×D4—622no—
196C2×D4D12411yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—312no—
200C22×C4—621no—
201C22×C4—621no—
202C22×C4C22×D3111yescharacteristic
203Q16—624no—
204Q16—624no—
205SD16—624no—
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—21no—
219C42—21no—
220C23—21no—
221C23—621no—
222C23D4×D3111yescharacteristic
223Q8—21no—
224Q8—21no—
225Q8—622no—
226Q8—621no—
227Q8—622no—
228Q8—621no—
229Q8—1241no—
230Q8—1241no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—621no—
236D4—621no—
237D4—1241no—
238D4—1241no—
239D4—2482no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—622no—
247C2×C4—621no—
248C2×C4—622no—
249C2×C4—1241no—
250C2×C4—1241no—
251C2×C4—1241no—
252C2×C4—1241no—
253C2×C4—1242no—
254C2×C4C2×D12411yescharacteristic
255C2×C4#9249511yescharacteristic
256C2×C4D4×D3111yescharacteristic
257C2×C4D4×D3111yescharacteristic
258C2×C4D4×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#1175845911yescharacteristic
271C22#1175846111yescharacteristic
272C22#1175851711yescharacteristic
273C4—42no—
274C4—41no—
275C4—1241no—
276C4—1242no—
277C4—1242no—
278C4#1175845911yescharacteristic
279C4#1175846111yescharacteristic
280C4#1175850711yescharacteristic
281C4#1175851411yescharacteristic
282C2—21no—
283C2—21no—
284C2—81no—
285C2—2481no—
286C2#1452095811yescharacteristic
287C2#1452122811yescharacteristic
288C2#1452123311yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#104C2
socleC22×C31#120
prime radical#14521627C2
hypercenterC2×#104D31
hypocenterC31#2007
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#11758486C2semidirect
2. C2×#11758528C2semidirect
4. C2×#11758393C2semidirect
5. #14520955C2semidirect
6. #14520817C2semidirect
7. C2×C31×#104C2semidirect
57. C2×Dic62D4semidirect
59. M16×C31D4semidirect
71. #92474D4semidirect
142. C2×#104D31semidirect
175. C31#2007semidirect
210. M16C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584862
C2×#117585282
#145216272
C2×#117583932
#145209552
#145208172
C2×C31×#1042
#200731