Finite Group Databasebeta

← #11781318

Subgroups — #11781318

Order 1152.

270 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593439C211yesmaximal, characteristic
2#10593393C211yesmaximal, characteristic, complemented
3#10590885C211yesmaximal, characteristic
4#10590645C211yesmaximal, characteristic, complemented
5#10590170C211yesmaximal, characteristic, complemented
6#10590040C211yesmaximal, characteristic, complemented
7#10590037C211yesmaximal, characteristic
8C2×#3775—21no—
9#63919C2211yescharacteristic
10C4×#627C2211yescharacteristic
11#63914C2211yescharacteristic
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14#63743—21no—
15#63740—21no—
16#63739—21no—
17C8×C3⋊Dic3C2211yescharacteristic
18C3×#821—21no—
19C3×Dic3⋊C8—21no—
20#63572C2211yescharacteristic
21#63562—21no—
22Dic3×C3⋊C8—21no—
23#4830—61no—
24#4760—61no—
25C2×C3×D12—21no—
26C2×#627—21no—
27C2×#627D411yescharacteristic
28C2×#625—21no—
29C2×#625—21no—
30C2×#622—21no—
31C2×#622—21no—
32#3775—42no—
33C2×C32×C8D411yescharacteristic
34C4×C3⋊Dic3C2311yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C3×C4⋊Dic3—21no—
37C3×C4×Dic3—21no—
38C2×C3×C3⋊C8—21no—
39#3724—21no—
40#3724D411yescharacteristic
41Dic3⋊Dic3—21no—
42#1678—91nomaximal, Sylow
43#940—61no—
44#888—61no—
45C4×Dic6—61no—
46C3×C4⋊C8—61no—
47C3×#102—61no—
48#832—61no—
49#821—21no—
50Dic3⋊C8—21no—
51Dic3⋊C8—61no—
52C8×Dic3—61no—
53C8×Dic3—61no—
54C8×Dic3—61no—
55#809—61no—
56C4×C3⋊C8—61no—
57C22×C3×D3—41no—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3#4111yescharacteristic
61C2×C3×Dic3—21no—
62C2×C3×Dic3—21no—
63C2×C3×Dic3—41no—
64C3×D12—41no—
65C3×D12—41no—
66#627—21no—
67#627—81no—
68#627SD1612yes—
69#625—41no—
70#625—41no—
71#625—81no—
72#622—41no—
73#622—41no—
74C32×C8—21no—
75C3⋊(C3⋊C8)—21no—
76C3×C3⋊C8—41no—
77#486—91no—
78#477—91no—
79#460—91no—
80C8×Q8—91no—
81#334—91no—
82#333—91no—
83#331—91no—
84C2×C3×D4—61no—
85C2×#67—121no—
86C2×#67—121no—
87C2×D12—21no—
88C2×Dic6—61no—
89C2×Dic6—121no—
90C2×C3×C8—21no—
91C2×C3×C8—21no—
92C2×C3×C8—61no—
93C3×C4⋊C4—61no—
94C3×C42—61no—
95C4⋊Dic3—21no—
96C4⋊Dic3—61no—
97Dic3⋊C4—61no—
98Dic3⋊C4—61no—
99Dic3⋊C4—121no—
100C4×Dic3—21no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C2×C3⋊C8—21no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C22×C32#12111yescharacteristic
107C2×C3×D3—81no—
108C2×C3×D3—81no—
109C2×C3×D3—81no—
110C32×C4#13511yescharacteristic
111C32×C4#13711yescharacteristic
112C3⋊Dic3—21no—
113C3⋊Dic3C2×SD1611yescharacteristic
114C3⋊Dic3#13511yescharacteristic
115C3×Dic3—22no—
116C3×Dic3—41no—
117C3×Dic3—81no—
118C2×SD16—181no—
119C4⋊Q8—91no—
120#127—91no—
121C4×Q8—91no—
122#107—181no—
123C4⋊C8—61no—
124C4⋊C8—91no—
125C4⋊C8—91no—
126C4⋊C8—91no—
127#103—181no—
128#102—61no—
129#102—181no—
130#102—181no—
131C4×C8—91no—
132C4×C8—181no—
133C23×C3—121no—
134C22×D3—41no—
135C3×D4—121no—
136C3×D4—121no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—61no—
140C2×C3×C4—61no—
141C2×C3×C4—121no—
142#67—241no—
143#67—241no—
144#67—242no—
145C2×Dic3—21no—
146C2×Dic3—21no—
147C2×Dic3—41no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152D12—41no—
153D12—41no—
154Dic6—62no—
155Dic6—62no—
156Dic6—242no—
157C3×C8—41no—
158C3×C8—41no—
159C3×C8—121no—
160C3⋊C8—41no—
161C3⋊C8—62no—
162C3⋊C8—121no—
163C2×C32#46411yescharacteristic
164C2×C32#46511yescharacteristic
165C2×C32#47211yescharacteristic
166C3×D3—161no—
167C2×Q8—91no—
168C2×Q8—181no—
169C2×D4—61no—
170C2×D4—181no—
171C2×D4—181no—
172SD16—362no—
173C2×C8—61no—
174C2×C8—91no—
175C2×C8—181no—
176C2×C8—181no—
177C2×C8GO+(4,𝔽2)11yescharacteristic
178C4⋊C4—61no—
179C4⋊C4—91no—
180C4⋊C4—181no—
181C4⋊C4—181no—
182C42—61no—
183C42—91no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—241no—
187C22×C3—241no—
188C22×C3—241no—
189C2×D3—81no—
190C2×D3—81no—
191C2×D3—81no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—62no—
197C3×C4—121no—
198C3×C4—241no—
199Dic3—22no—
200Dic3—41no—
201Dic3—61no—
202Dic3—61no—
203Dic3—61no—
204Dic3—61no—
205Dic3—62no—
206Dic3—81no—
207Dic3—121no—
208C32#167811yescharacteristic, complemented, Sylow
209C23—121no—
210Q8—92no—
211Q8—181no—
212Q8—721no—
213D4—121no—
214D4—121no—
215D4—361no—
216D4—361no—
217D4—721no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—121no—
223C2×C4C2×GO+(4,𝔽2)11yescharacteristic
224C8—21no—
225C8—121no—
226C8—181no—
227C8—361no—
228C8—361no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—481no—
236D3—161no—
237C22—241no—
238C22—241no—
239C22—241no—
240C22#6423011yescharacteristic
241C4—62no—
242C4—91no—
243C4—91no—
244C4—121no—
245C4—181no—
246C4—241no—
247C4#6422611yescharacteristic
248C4#6423711yescharacteristic
249C3—21no—
250C3—21no—
251C2—481no—
252C2#1059328411yescharacteristic
253C2#1059330311yescharacteristic
254C2#1059344011yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radical#63914C22
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1678
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
2. #10593393C2semidirect
4. #10590645C2semidirect
5. #10590170C2semidirect
6. #10590040C2semidirect
208. C32#1678semidirect

Maximal subgroups

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

subgroupindex
#105934392
#105933932
#105908852
#105906452
#105901702
#105900402
#105900372
#16789