Finite Group Databasebeta

← #11779060

Subgroups — #11779060

Order 1152.

527 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 527 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic62C211yesmaximal, characteristic, complemented
2#10592392C211yesmaximal, characteristic
3#10590367C212yesmaximal
4C3×#4456C212yesmaximal, complemented
5#10589096C211yesmaximal, characteristic, complemented
6#68264—32nomaximal
7C2×#3744—22no—
8#64083C2211yescharacteristic
9#64078C2211yescharacteristic
10C3×C4×Dic6C2212yes—
11#63918—22no—
12Dic3×Dic6—22no—
13#63840—22no—
14C2×#3717—22no—
15C32×C4×C8C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2212yes—
17#63564—22no—
18Q8×Dic6—32no—
19#5027—32no—
20#4848—32no—
21#4693—32no—
22#4693—61no—
23C3×Q8⋊C8—32no—
24#4481—32no—
25#4456D312yescomplemented
26C2×C4⋊(C3⋊D3)—21no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×#634D412yes—
29C2×C3×Dic6D412yes—
30C2×#627—22no—
31C2×C32×C8—21no—
32C32×C42C2311yescharacteristic
33C4⋊(C3⋊Dic3)—22no—
34#3744—44no—
35C3×C4⋊Dic3D412yes—
36C3×Dic3⋊C4—22no—
37C3×C4×Dic3—22no—
38C2×C3×C3⋊C8—22no—
39Dic3⋊Dic3—24no—
40Dic32—22no—
41#3717—44no—
42#1623—91noSylow
43C3×C4×Q8—32no—
44Q8×Dic3—62no—
45C2×#215—62no—
46C2×#204—64no—
47C2×#204—64no—
48C2×#204—62no—
49#888—62no—
50#888—64no—
51#874—32no—
52#874—61no—
53#869—32no—
54#869—61no—
55#869—62no—
56C4×Dic6—62no—
57C4×Dic6C2×D312yes—
58C3×C4⋊C8—32no—
59C3×C4×C8—21no—
60C3×C4×C8C2×D312yes—
61#821—62no—
62#809—62no—
63C4⋊(C3⋊C8)C2×D312yes—
64C22×C3⋊D3—41no—
65C2×C32×C4C2×D412yes—
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—22no—
68C4⋊(C3⋊D3)—42no—
69C4⋊(C3⋊D3)—42no—
70C4⋊(C3⋊D3)—42no—
71#634—42no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C3×Dic6—22no—
75C3×Dic6SD1614yescomplemented
76#627—82no—
77C32×C8—22no—
78C3×C3⋊C8—42no—
79Q82—91no—
80#492—91no—
81#460—92no—
82#333—91no—
83Q8⋊C8—32no—
84C2×C3×Q8—32no—
85C2×D12—62no—
86C2×D12—62no—
87C2×D12—62no—
88C2×D12—62no—
89C2×D12—122no—
90C2×Dic6—34no—
91C2×Dic6—62no—
92C2×Dic6—64no—
93C2×Dic6D1212yes—
94C2×C3×C8—22no—
95C2×C3×C8—22no—
96C2×C3×C8—62no—
97C3×C4⋊C4—32no—
98C3×C4⋊C4—62no—
99C3×C42—21no—
100C3×C42—62no—
101C3×C42C22×D312yes—
102#215—124no—
103C4⋊Dic3—64no—
104C4⋊Dic3—62no—
105C4⋊Dic3—62no—
106C4⋊Dic3—122no—
107C4⋊Dic3D1212yes—
108Dic3⋊C4—22no—
109Dic3⋊C4—64no—
110C4×Dic3—22no—
111C4×Dic3—64no—
112C2×C3⋊C8—22no—
113#204—128no—
114#204—128no—
115#204—124no—
116C22×C32#12011yescharacteristic
117C2×C3⋊D3—82no—
118C2×C3⋊D3—81no—
119C32×C4—21no—
120C32×C4C2×SD1612yes—
121C32×C4#13712yes—
122C3⋊Dic3—42no—
123C3×Dic3—24no—
124C3×Dic3—42no—
125C2×SD16—182no—
126C2×SD16—182no—
127C4⋊Q8—91no—
128C4⋊Q8—182no—
129C4⋊Q8—182no—
130#127—91no—
131C4×Q8—32no—
132C4×Q8—182no—
133C4⋊C8—32no—
134#102—182no—
135C4×C8D3211yescharacteristic
136C22×D3—122no—
137C22×D3—122no—
138C3×Q8—34no—
139C3×Q8—62no—
140C2×C3×C4—22no—
141C2×C3×C4—21no—
142C2×C3×C4—62no—
143C2×C3×C4—62no—
144C2×C3×C4C2×D1212yes—
145C2×C3×C4D3×D412yes—
146C2×C3×C4D3×D412yes—
147C2×Dic3—22no—
148C2×Dic3—22no—
149C2×Dic3—64no—
150C2×Dic3—122no—
151D12—124no—
152D12—124no—
153D12—122no—
154D12—122no—
155D12—122no—
156D12—122no—
157D12—242no—
158D12—242no—
159Dic6—22no—
160Dic6—124no—
161Dic6—124no—
162Dic6—244no—
163Dic6#20414yescomplemented
164C3×C8—24no—
165C3×C8—24no—
166C3×C8—122no—
167C3⋊C8—42no—
168C2×C32#44812yes—
169C2×C32#45311yescharacteristic
170C3⋊D3—161no—
171C2×Q8—32no—
172C2×Q8—92no—
173C2×Q8—182no—
174C2×D4—182no—
175C2×D4—181no—
176SD16—364no—
177SD16—364no—
178C2×C8—21no—
179C2×C8—62no—
180C4⋊C4—32no—
181C4⋊C4—62no—
182C4⋊C4—184no—
183C4⋊C4—182no—
184C42—62no—
185C42—182no—
186C42C2×D3211yescharacteristic
187C22×C3—21no—
188C22×C3#88212yes—
189C2×D3—242no—
190C2×D3—244no—
191C2×D3—242no—
192C2×D3—242no—
193C2×D3—242no—
194C3×C4—22no—
195C3×C4—22no—
196C3×C4—22no—
197C3×C4—22no—
198C3×C4—64no—
199C3×C4—122no—
200C3×C4C2×#20412yes—
201C3×C4#90912yes—
202C3×C4D3×SD1612yes—
203C3×C4#91812yes—
204Dic3—24no—
205Dic3—42no—
206Dic3—124no—
207Dic3—242no—
208C32#162311yescharacteristic, complemented, Sylow
209C23—361no—
210Q8—34no—
211Q8—62no—
212Q8—362no—
213Q8—722no—
214D4—362no—
215D4—362no—
216D4—362no—
217C2×C4—62no—
218C2×C4—62no—
219C2×C4—182no—
220C2×C4D3×D1212yes—
221C2×C4#381111yescharacteristic
222C8—22no—
223C8—122no—
224C2×C3—21no—
225C2×C3—22no—
226C2×C3#473812yes—
227C2×C3#480612yes—
228C2×C3#482212yes—
229D3—482no—
230D3—482no—
231C22—721no—
232C22—722no—
233C22#6392311yescharacteristic
234C4—21no—
235C4—64no—
236C4—122no—
237C4—362no—
238C4D3×#20412yes—
239C4#6380112yes—
240C3—21no—
241C3#6826412yescomplemented
242C2—1441no—
243C2#1059039711yescharacteristic
244C2#1059095112yes—
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4×C8D32
hypocenterC32#1623
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. Dic62C2semidirect
4. C3×#4456C2semidirect
5. #10589096C2semidirect
25. #4456D3semidirect
75. C3×Dic6SD16semidirect
163. Dic6#204semidirect
208. C32#1623semidirect
241. C3#68264semidirect

Maximal subgroups

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

subgroupindex
Dic622
#105923922
#105903672
C3×#44562
#105890962
#682643