Finite Group Databasebeta

← #16846748

Subgroups — #16846748

Order 3968.

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

normal subgroups only

This group has 362 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×#11758519C211yesmaximal, characteristic
2#14521625C211yesmaximal, characteristic
3C2×#11758521C211yesmaximal, characteristic, complemented
4C2×#11758413C211yesmaximal, characteristic
5C2×#11758412C211yesmaximal, characteristic, complemented
6#14520808C211yesmaximal, characteristic, complemented
7C31×#419C211yesmaximal, characteristic, complemented
8C22×Q8×C31C2211yescharacteristic
9C2×#92495C2211yescharacteristic
10C22×Dic62C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C31×#117C2211yescharacteristic
13#11758521—22no—
14#11758521—22no—
15C2×#92482—21no—
16#11758519—22no—
17#11758519—22no—
18C2×#92481—21no—
19C2×Dic31⋊C4—22no—
20C2×C4×Dic31C2211yescharacteristic
21C2×#92474C2211yescharacteristic
22#11758474—22no—
23#11758463—22no—
24#11758452—21no—
25#11758446—21no—
26C31×#103—22no—
27#11758413—22no—
28#11758412—22no—
29C2×Q8×C31—21no—
30C2×Q8×C31—21no—
31C2×Q8×C31—21no—
32C2×Q8×C31—21no—
33C2×Q8×C31—21no—
34C2×Q8×C31D412yes—
35C22×C4×C31—21no—
36C22×C4×C31C2311yescharacteristic
37C2×C22⋊D31—21no—
38C22×Dic31—21no—
39C22×Dic31D412yes—
40#92495—21no—
41#92495—21no—
42#92495—21no—
43#92495—21no—
44C2×D124D411yescharacteristic
45C2×C4×D31—21no—
46C2×Dic62—21no—
47C2×Dic62—21no—
48C2×Dic62—21no—
49C2×Dic62—21no—
50C2×Dic62—21no—
51C2×Dic62—21no—
52C2×Dic62D411yescharacteristic
53M16×C31—21no—
54M16×C31—21no—
55C2×C8×C31—21no—
56C4⋊C4×C31D412yes—
57C22⋊C4×C31—21no—
58C42×C31—21no—
59#92482—24no—
60#92481—24no—
61(C2×D31)⋊C4—24no—
62C4⋊Dic31—24no—
63Dic31⋊C4—28no—
64C4×Dic31—21no—
65C4×Dic31D412yes—
66#92474—21no—
67#92474D412yes—
68C2×C31⋊C8—21no—
69C23×C31C2×D411yescharacteristic
70C22×D31—21no—
71Q8×C31—22no—
72Q8×C31—22no—
73Q8×C31—41no—
74Q8×C31—41no—
75C2×C4×C31—22no—
76C2×C4×C31—22no—
77C2×C4×C31—41no—
78C2×C4×C31—41no—
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31#4111yescharacteristic
85C22⋊D31—41no—
86C22⋊D31—41no—
87C2×Dic31—24no—
88C2×Dic31—22no—
89C2×Dic31—22no—
90C2×Dic31—21no—
91C2×Dic31—22no—
92C2×Dic31—22no—
93D124—21no—
94D124—21no—
95C4×D31—41no—
96C4×D31—41no—
97Dic62—21no—
98Dic62—21no—
99Dic62—41no—
100Dic62—41no—
101Dic62—41no—
102Dic62—41no—
103C8×C31—41no—
104C31⋊C8—22no—
105#2005—311nomaximal, Sylow
106C22×C31—22no—
107C22×C31#12011yescharacteristic
108C22×C31#12011yescharacteristic
109C22×C31#12111yescharacteristic
110C2×D31—41no—
111C2×D31—42no—
112C4×C31—42no—
113C4×C31—42no—
114C4×C31#12011yescharacteristic
115C4×C31#12111yescharacteristic
116C4×C31#12111yescharacteristic
117C4×C31#12711yescharacteristic
118Dic31—24no—
119Dic31—41no—
120Dic31—42no—
121C2×#137—311no—
122#536—311no—
123C2×C4⋊Q8—311no—
124C2×#104—311no—
125#419D3111yescharacteristic, complemented
126C2×#101—311no—
127#339—311no—
128C2×C31—21no—
129C2×C31—21no—
130C2×C31#39211yescharacteristic
131C2×C31#45612yes—
132D31—81no—
133C2×#41—311no—
134C22×Q8—311no—
135C22×Q8C2×D3111yescharacteristic
136#137—622no—
137#137—622no—
138C2×Q16—621no—
139C2×SD16—621no—
140C2×M16—311no—
141C2×M16C2×D3111yescharacteristic
142C4⋊Q8—621no—
143C4⋊Q8—622no—
144C4⋊Q8—622no—
145#124—621no—
146#123—622no—
147C22⋊Q8—622no—
148#117C2×D3111yescharacteristic
149C2×C4⋊C4—622no—
150C2×C42—311no—
151#104—622no—
152#103—22no—
153#101—622no—
154C31#200511yescharacteristic, complemented, Sylow
155#41—621no—
156#41—621no—
157#41—621no—
158#41—621no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—311no—
165C2×Q8—621no—
166C2×Q8—621no—
167C2×Q8—621no—
168C2×Q8—621no—
169C2×Q8—621no—
170C2×Q8—621no—
171C2×Q8D12412yes—
172C2×D4—311no—
173C2×D4—621no—
174C22×C4—21no—
175C22×C4—312no—
176C22×C4—621no—
177C22×C4—621no—
178C22×C4C22×D3111yescharacteristic
179Q16—624no—
180SD16—624no—
181M16—21no—
182M16—21no—
183M16—312no—
184M16—621no—
185C2×C8—21no—
186C2×C8—621no—
187C4⋊C4—628no—
188C4⋊C4—624no—
189C4⋊C4C22⋊D3112yes—
190C22⋊C4—21no—
191C22⋊C4—624no—
192C42—21no—
193C42—312no—
194C42—621no—
195C23—621no—
196C23D4×D3111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—621no—
202Q8—621no—
203Q8—1241no—
204Q8—1241no—
205Q8—1241no—
206Q8—1241no—
207D4—621no—
208D4—621no—
209D4—1241no—
210D4—1241no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—624no—
216C2×C4—622no—
217C2×C4—622no—
218C2×C4—622no—
219C2×C4—622no—
220C2×C4—621no—
221C2×C4—1241no—
222C2×C4—1241no—
223C2×C4C2×D12411yescharacteristic
224C2×C4#9249511yescharacteristic
225C2×C4D4×D3111yescharacteristic
226C2×C4D4×D3111yescharacteristic
227C2×C4D4×D3111yescharacteristic
228C2×C4C2×C22⋊D3111yescharacteristic
229C8—41no—
230C8—622no—
231C22—22no—
232C22—1241no—
233C22—1242no—
234C22#1175845911yescharacteristic
235C22#1175846111yescharacteristic
236C22#1175851411yescharacteristic
237C4—42no—
238C4—42no—
239C4—624no—
240C4—1242no—
241C4—1241no—
242C4#1175845911yescharacteristic
243C4#1175846111yescharacteristic
244C4#1175850711yescharacteristic
245C4#1175851711yescharacteristic
246C2—21no—
247C2—21no—
248C2—2481no—
249C2#1452095811yescharacteristic
250C2#1452123012yes—
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#419C2
socleC22×C31#120
prime radicalC2×#92495C22
hypercenter#419D31
hypocenterC31#2005
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C2×#11758521C2semidirect
5. C2×#11758412C2semidirect
6. #14520808C2semidirect
7. C31×#419C2semidirect
125. #419D31semidirect
154. C31#2005semidirect

Maximal subgroups

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

subgroupindex
C2×#117585192
#145216252
C2×#117585212
C2×#117584132
C2×#117584122
#145208082
C31×#4192
#200531