Finite Group Databasebeta

← #11860841

Subgroups — #11860841

Order 1152.

722 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 151 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×#3776C211yesmaximal, characteristic
2#10594245C212yesmaximal
3#10593738C211yesmaximal, characteristic
4#10593511C211yesmaximal, characteristic
5#10593503C212yesmaximal
6#10593445C212yesmaximal, complemented
7C4×#3776C212yesmaximal, complemented
8#10593369C214yesmaximal, complemented
9C22×#627C2212yes—
10C2×#3792C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×#3776C418yescomplemented
13C2×#3776C2212yes—
14C2×#3776C2211yescharacteristic
15C2×#3776C2211yescharacteristic
16#64086C2211yescharacteristic
17C3×#877—22no—
18#63957C2212yes—
19#63955—22no—
20C4×#627C2214yes—
21#63838C2214yes—
22#63837—24no—
23#63777C2212yes—
24C4×#622C2212yes—
25#63743C2212yes—
26#63742C2212yes—
27#63740C2214yes—
28#63740C2214yes—
29#5516—62no—
30C22×C3⋊Dic3C2311yescharacteristic
31C22×C3×Dic3—22no—
32C2×#627—22no—
33C2×#627—24no—
34C2×#627C2×C418yes—
35C2×#627C2312yes—
36C2×#627C2312yes—
37#3792—22no—
38C2×#622C2×C414yes—
39C2×#622C2312yes—
40C2×#622C2311yescharacteristic
41C2×#622C2311yescharacteristic
42#3776C2×C418yes—
43#3776C2×C414yes—
44#3776C2×C414yes—
45C32×C22⋊C4D411yescharacteristic
46#3757D411yescharacteristic
47#3750D412yes—
48C4×C3⋊Dic3C2312yes—
49C3×#217—22no—
50C3×Dic3⋊C4—24no—
51C3×C4×Dic3—24no—
52#3724C2314yes—
53Dic3⋊Dic3—24no—
54Dic32—22no—
55Dic32—24no—
56#2950—91nomaximal, Sylow
57C22×Dic6—62no—
58C3×#117—62no—
59#926—62no—
60#887—64no—
61#887—64no—
62#877—22no—
63#877—62no—
64#877—62no—
65#877—62no—
66C4×Dic6—64no—
67C4×Dic6—64no—
68C23×C32C2×D411yescharacteristic
69C2×C32×C4C2×D412yes—
70C2×C3⋊Dic3C22×C412yes—
71C2×C3⋊Dic3C2×D412yes—
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3#4112yes—
74C2×C3⋊Dic3C2411yescharacteristic
75C2×C3×Dic3—28no—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—24no—
79#627—28no—
80#627—22no—
81#627—22no—
82#627C22×C414yes—
83#627C22×C414yes—
84#622—22no—
85#622C22×C412yes—
86#622C22×C412yes—
87C22×Q16—91no—
88#519—92no—
89#441—94no—
90C4×Q16—92no—
91C4×Q16—92no—
92#427—91no—
93#419—92no—
94#405—91no—
95C22×C3×C4—62no—
96C22×Dic3—22no—
97C22×Dic3—62no—
98C2×Dic6—62no—
99C2×Dic6—62no—
100C2×Dic6—68no—
101C2×Dic6—62no—
102C2×Dic6—62no—
103C2×Dic6—68no—
104C3×C4⋊C4—64no—
105C3×C22⋊C4—22no—
106C3×C22⋊C4—62no—
107C3×C42—64no—
108#217—22no—
109#217—62no—
110C4⋊Dic3—64no—
111Dic3⋊C4—24no—
112Dic3⋊C4—64no—
113Dic3⋊C4—64no—
114Dic3⋊C4—64no—
115C4×Dic3—24no—
116C4×Dic3—64no—
117C4×Dic3—64no—
118C4×Dic3—64no—
119C4×Dic3—64no—
120C22×C32—22no—
121C22×C32C4×D412yes—
122C22×C32C22×D411yescharacteristic
123C32×C4—22no—
124C3⋊Dic3—22no—
125C3⋊Dic3C4×D412yes—
126C3⋊Dic3C23×C411yescharacteristic
127C3⋊Dic3C2×#4111yescharacteristic
128C3×Dic3—24no—
129C3×Dic3—24no—
130C3×Dic3—44no—
131C22×Q8—92no—
132C2×Q16—91no—
133C2×Q16—91no—
134C2×Q16—92no—
135C2×Q16—98no—
136C2×M16—91no—
137C22×C8—91no—
138C4×Q8—94no—
139C4×Q8—94no—
140C4×Q8—184no—
141#117—62no—
142#117—91no—
143#117—92no—
144#117—182no—
145#107—92no—
146#106—92no—
147#103—94no—
148#103—94no—
149#97—92no—
150C4×C8—92no—
151C23×C3—22no—
152C2×C3×C4—24no—
153C2×C3×C4—62no—
154C2×C3×C4—62no—
155C2×C3×C4—68no—
156C2×C3×C4—64no—
157C2×Dic3—22no—
158C2×Dic3—22no—
159C2×Dic3—28no—
160C2×Dic3—24no—
161C2×Dic3—64no—
162C2×Dic3—62no—
163C2×Dic3—64no—
164C2×Dic3—62no—
165C2×Dic3—64no—
166Dic6—64no—
167Dic6—64no—
168Dic6—68no—
169Dic6—68no—
170Dic6—64no—
171Dic6—64no—
172C2×C32—22no—
173C2×C32C2×C4×D411yescharacteristic
174C2×C32#57812yes—
175C2×Q8—92no—
176C2×Q8—92no—
177C2×Q8—98no—
178C2×Q8—182no—
179C2×Q8—184no—
180C22×C4—62no—
181C22×C4—91no—
182Q16—94no—
183Q16—94no—
184Q16—98no—
185M16—182no—
186C2×C8—91no—
187C2×C8—91no—
188C2×C8—94no—
189C2×C8—92no—
190C4⋊C4—64no—
191C4⋊C4—94no—
192C4⋊C4—92no—
193C4⋊C4—184no—
194C22⋊C4—62no—
195C22⋊C4—91no—
196C22⋊C4GO+(4,𝔽2)11yescharacteristic
197C42—64no—
198C42—92no—
199C42—182no—
200C42—184no—
201C22×C3—22no—
202C22×C3—24no—
203C22×C3—44no—
204C3×C4—44no—
205C3×C4—64no—
206C3×C4—64no—
207C3×C4—124no—
208Dic3—24no—
209Dic3—24no—
210Dic3—44no—
211Dic3—64no—
212Dic3—62no—
213Dic3—62no—
214Dic3—124no—
215C32#295011yescharacteristic, complemented, Sylow
216C23C2×GO+(4,𝔽2)11yescharacteristic
217Q8—94no—
218Q8—94no—
219Q8—182no—
220Q8—182no—
221Q8—188no—
222C2×C4—62no—
223C2×C4—62no—
224C2×C4—68no—
225C2×C4—64no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—92no—
229C2×C4—92no—
230C2×C4—92no—
231C2×C4C2×GO+(4,𝔽2)12yes—
232C8—92no—
233C8—92no—
234C8—182no—
235C2×C3—22no—
236C2×C3—24no—
237C2×C3—44no—
238C22—22no—
239C22C4×GO+(4,𝔽2)12yes—
240C22C22×GO+(4,𝔽2)11yescharacteristic
241C4—22no—
242C4—64no—
243C4—64no—
244C4—91no—
245C4—91no—
246C4—92no—
247C4—124no—
248C4—182no—
249C3—22no—
250C2—22no—
251C2C2×C4×GO+(4,𝔽2)11yescharacteristic
252C2#1059651612yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
cosocleC2×C3⋊Dic3C24
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#2950
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10593445C2semidirect
7. C4×#3776C2semidirect
8. #10593369C2semidirect
12. C2×#3776C4semidirect
215. C32#2950semidirect

Maximal subgroups

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

subgroupindex
C22×#37762
#105942452
#105937382
#105935112
#105935032
#105934452
C4×#37762
#105933692
#29509