Finite Group Databasebeta

← #11782927

Subgroups — #11782927

Order 1152.

394 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#10593418C212yesmaximal, complemented
2#10593348C212yesmaximal, complemented
3#10590886C211yesmaximal, characteristic, complemented
4#10590884C211yesmaximal, characteristic, complemented
5#10590168C211yesmaximal, characteristic, complemented
6C2×#3774—24no—
7C2×C3×D24—21no—
8C2×C3×#204—21no—
9#63914C2212yes—
10#63914C2211yescharacteristic
11#63873C2211yescharacteristic
12C2×#3715—21no—
13C2×#3713—21no—
14C4×#622C2212yes—
15#63739—24no—
16C8×C3⋊Dic3C2211yescharacteristic
17#5175—61no—
18#5151—61no—
19C2×C3×D12—21no—
20C2×C3×D12—22no—
21C2×C3×Dic6—21no—
22C2×#625—22no—
23C2×#625—22no—
24C2×#625—22no—
25C2×#622D414yes—
26#3774—48no—
27C2×C32×C8D411yescharacteristic
28C4×C3⋊Dic3C2311yescharacteristic
29C2×C3⋊(C3⋊C8)D411yescharacteristic
30C3×D24—42no—
31C3×#204—42no—
32#3724—22no—
33#3715—42no—
34#3713—42no—
35#1721—91nomaximal, Sylow
36C2×C3×SD16—61no—
37C2×C3×D8—61no—
38#944—61no—
39C2×#215—61no—
40#940—62no—
41#940—61no—
42C2×#214—61no—
43C2×#213—62no—
44C2×D24—21no—
45C2×#204—21no—
46C8×Dic3—61no—
47C8×Dic3—61no—
48C22×C3×D3—41no—
49C22×C3×D3—42no—
50C2×C32×C4C2×D411yescharacteristic
51C2×C3⋊Dic3C2×D412yes—
52C2×C3×Dic3—41no—
53C3×D12—42no—
54C3×D12—41no—
55C3×D12—41no—
56C3×D12—42no—
57C3×Dic6—41no—
58C3×Dic6—41no—
59#625—44no—
60#625—44no—
61#625—44no—
62#622—24no—
63C32×C8D812yescomplemented
64C3⋊(C3⋊C8)D812yescomplemented
65#493—91no—
66#493—92no—
67#492—91no—
68#486—92no—
69#322—91no—
70C2×C3×Q8—61no—
71C2×C3×D4—62no—
72C2×C3×D4—61no—
73C2×#67—122no—
74C2×#67—122no—
75C2×#67—122no—
76C2×D12—21no—
77C2×D12—22no—
78C2×Dic6—21no—
79C3×SD16—122no—
80C3×D8—122no—
81C2×C3×C8—21no—
82C2×C3×C8—21no—
83#215—122no—
84#214—122no—
85#213—124no—
86Dic3⋊C4—122no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91D24—42no—
92#204—42no—
93C22×C32#12711yescharacteristic
94C2×C3×D3—82no—
95C2×C3×D3—81no—
96C2×C3×D3—82no—
97C2×C3×D3—82no—
98C2×C3×D3—82no—
99C32×C4C2×D811yescharacteristic
100C32×C4C2×D811yescharacteristic
101C3⋊Dic3AGL(1,ℤ/8)14yes—
102C3×Dic3—81no—
103C2×SD16—61no—
104C2×SD16—181no—
105C2×D8—61no—
106C2×D8—181no—
107C2×D8—184no—
108C4⋊Q8—91no—
109#127—92no—
110#127—91no—
111#102—184no—
112C4×C8—92no—
113C4×C8—91no—
114C23×C3—121no—
115C23×C3—122no—
116C22×D3—41no—
117C22×D3—42no—
118C3×Q8—121no—
119C3×Q8—121no—
120C3×D4—122no—
121C3×D4—121no—
122C3×D4—122no—
123C3×D4—121no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—121no—
127#67—244no—
128#67—244no—
129#67—244no—
130C2×Dic3—41no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133D12—41no—
134D12—42no—
135D12—42no—
136D12—41no—
137Dic6—41no—
138Dic6—41no—
139C3×C8—22no—
140C3×C8—22no—
141C3⋊C8—62no—
142C3⋊C8—62no—
143C2×C32#49311yescharacteristic
144C2×C32#49612yes—
145C3×D3—162no—
146C3×D3—161no—
147C2×Q8—61no—
148C2×D4—62no—
149C2×D4—61no—
150C2×D4—182no—
151C2×D4—182no—
152C2×D4—182no—
153SD16—122no—
154SD16—362no—
155D8—122no—
156D8—362no—
157D8—368no—
158C2×C8—91no—
159C2×C8—94no—
160C2×C8GO+(4,𝔽2)11yescharacteristic
161C4⋊C4—182no—
162C42—91no—
163C22×C3—21no—
164C22×C3—21no—
165C22×C3—242no—
166C22×C3—242no—
167C22×C3—242no—
168C22×C3—241no—
169C22×C3—242no—
170C2×D3—81no—
171C2×D3—82no—
172C2×D3—82no—
173C2×D3—82no—
174C2×D3—82no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—21no—
179C3×C4—241no—
180Dic3—64no—
181Dic3—64no—
182Dic3—81no—
183C32#172111yescharacteristic, complemented, Sylow
184C23—122no—
185C23—121no—
186Q8—121no—
187Q8—121no—
188D4—122no—
189D4—121no—
190D4—122no—
191D4—121no—
192D4—364no—
193D4—364no—
194D4—364no—
195C2×C4—92no—
196C2×C4—121no—
197C2×C4C2×GO+(4,𝔽2)11yescharacteristic
198C8—92no—
199C8—184no—
200C8#377412yescomplemented
201C2×C3—22no—
202C2×C3—22no—
203C2×C3—21no—
204C2×C3—21no—
205C2×C3—482no—
206C2×C3—481no—
207D3—162no—
208D3—161no—
209C22—242no—
210C22—242no—
211C22—242no—
212C22—242no—
213C22—241no—
214C22#6423111yescharacteristic
215C4—94no—
216C4—241no—
217C4#6422511yescharacteristic
218C4C2×#377411yescharacteristic
219C3—21no—
220C3—21no—
221C2—481no—
222C2—482no—
223C2#1059329412yes—
224C2#1059341811yescharacteristic
subgroupG/H
centerC22#64231
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#127
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1721
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10593418C2semidirect
2. #10593348C2semidirect
3. #10590886C2semidirect
4. #10590884C2semidirect
5. #10590168C2semidirect
63. C32×C8D8semidirect
64. C3⋊(C3⋊C8)D8semidirect
183. C32#1721semidirect
200. C8#3774semidirect

Maximal subgroups

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

subgroupindex
#105934182
#105933482
#105908862
#105908842
#105901682
#17219