Finite Group Databasebeta

← #11781505

Subgroups — #11781505

Order 1152.

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

normal subgroups only

This group has 276 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#10593447C211yesmaximal, characteristic, complemented
2#10593439C211yesmaximal, characteristic
3#10590885C211yesmaximal, characteristic
4#10590645C211yesmaximal, characteristic, complemented
5#10590171C211yesmaximal, characteristic, complemented
6#10590039C211yesmaximal, characteristic, complemented
7#10590037C211yesmaximal, characteristic
8C2×#3776—21no—
9C2×#3775—21no—
10#63919C2211yescharacteristic
11C4×#627C2211yescharacteristic
12#63914C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14C4⋊#622C2211yescharacteristic
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#3776—42no—
33#3775—42no—
34C2×C32×C8D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C3×C4⋊Dic3—21no—
38C3×C4×Dic3—21no—
39C2×C3×C3⋊C8—21no—
40#3724—21no—
41#3724D411yescharacteristic
42Dic3⋊Dic3—21no—
43#1682—91nomaximal, Sylow
44#940—61no—
45#888—61no—
46C4×Dic6—61no—
47C3×C4⋊C8—61no—
48C3×#102—61no—
49#832—61no—
50#821—21no—
51Dic3⋊C8—21no—
52Dic3⋊C8—61no—
53C8×Dic3—61no—
54C8×Dic3—61no—
55C8×Dic3—61no—
56#809—61no—
57C4×C3⋊C8—61no—
58C22×C3×D3—41no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4111yescharacteristic
62C2×C3×Dic3—21no—
63C2×C3×Dic3—21no—
64C2×C3×Dic3—41no—
65C3×D12—41no—
66C3×D12—41no—
67#627—21no—
68#627—41no—
69#627—41no—
70#627D812yes—
71#625—41no—
72#625—41no—
73#625—81no—
74#622—41no—
75#622—41no—
76C32×C8—21no—
77C3⋊(C3⋊C8)—21no—
78C3×C3⋊C8—41no—
79#486—91no—
80#462—91no—
81#460—91no—
82C8×Q8—91no—
83#335—91no—
84#332—91no—
85#331—91no—
86C2×C3×D4—61no—
87C2×#67—121no—
88C2×#67—121no—
89C2×D12—21no—
90C2×Dic6—61no—
91C2×Dic6—121no—
92C2×C3×C8—21no—
93C2×C3×C8—21no—
94C2×C3×C8—61no—
95C3×C4⋊C4—61no—
96C3×C42—61no—
97C4⋊Dic3—21no—
98C4⋊Dic3—61no—
99Dic3⋊C4—61no—
100Dic3⋊C4—61no—
101Dic3⋊C4—121no—
102C4×Dic3—21no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C2×C3⋊C8—21no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—61no—
108C22×C32#12111yescharacteristic
109C2×C3×D3—81no—
110C2×C3×D3—81no—
111C2×C3×D3—81no—
112C32×C4#13511yescharacteristic
113C32×C4#13711yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3C2×D811yescharacteristic
116C3⋊Dic3#13511yescharacteristic
117C3×Dic3—22no—
118C3×Dic3—41no—
119C3×Dic3—81no—
120C2×Q16—181no—
121C2×SD16—181no—
122C4⋊Q8—91no—
123#127—91no—
124C4×Q8—91no—
125C4⋊C8—61no—
126C4⋊C8—91no—
127C4⋊C8—91no—
128C4⋊C8—91no—
129#103—181no—
130#102—61no—
131#102—181no—
132#102—181no—
133C4×C8—91no—
134C4×C8—181no—
135C23×C3—121no—
136C22×D3—41no—
137C3×D4—121no—
138C3×D4—121no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—61no—
142C2×C3×C4—61no—
143C2×C3×C4—121no—
144#67—241no—
145#67—241no—
146#67—242no—
147C2×Dic3—21no—
148C2×Dic3—21no—
149C2×Dic3—41no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154D12—41no—
155D12—41no—
156Dic6—62no—
157Dic6—62no—
158Dic6—241no—
159Dic6—241no—
160C3×C8—41no—
161C3×C8—41no—
162C3×C8—121no—
163C3⋊C8—41no—
164C3⋊C8—62no—
165C3⋊C8—121no—
166C2×C32#46411yescharacteristic
167C2×C32#46611yescharacteristic
168C2×C32#47111yescharacteristic
169C3×D3—161no—
170C2×Q8—91no—
171C2×Q8—181no—
172C2×D4—61no—
173C2×D4—181no—
174C2×D4—181no—
175Q16—362no—
176SD16—362no—
177C2×C8—61no—
178C2×C8—91no—
179C2×C8—181no—
180C2×C8—181no—
181C2×C8GO+(4,𝔽2)11yescharacteristic
182C4⋊C4—61no—
183C4⋊C4—91no—
184C4⋊C4—181no—
185C4⋊C4—181no—
186C42—61no—
187C42—91no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—241no—
191C22×C3—241no—
192C22×C3—241no—
193C2×D3—81no—
194C2×D3—81no—
195C2×D3—81no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—62no—
201C3×C4—121no—
202C3×C4—241no—
203Dic3—22no—
204Dic3—41no—
205Dic3—61no—
206Dic3—61no—
207Dic3—61no—
208Dic3—61no—
209Dic3—62no—
210Dic3—81no—
211Dic3—121no—
212C32#168211yescharacteristic, complemented, Sylow
213C23—121no—
214Q8—92no—
215Q8—181no—
216Q8—361no—
217Q8—361no—
218D4—121no—
219D4—121no—
220D4—361no—
221D4—361no—
222D4—721no—
223C2×C4—61no—
224C2×C4—61no—
225C2×C4—91no—
226C2×C4—91no—
227C2×C4—121no—
228C2×C4C2×GO+(4,𝔽2)11yescharacteristic
229C8—21no—
230C8—121no—
231C8—181no—
232C8—361no—
233C8—361no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—481no—
241D3—161no—
242C22—241no—
243C22—241no—
244C22—241no—
245C22#6423011yescharacteristic
246C4—62no—
247C4—91no—
248C4—91no—
249C4—121no—
250C4—181no—
251C4—241no—
252C4#6422611yescharacteristic
253C4#6423711yescharacteristic
254C3—21no—
255C3—21no—
256C2—481no—
257C2#1059328511yescharacteristic
258C2#1059330211yescharacteristic
259C2#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#1682
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. #10593447C2semidirect
4. #10590645C2semidirect
5. #10590171C2semidirect
6. #10590039C2semidirect
212. C32#1682semidirect

Maximal subgroups

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

subgroupindex
#105934472
#105934392
#105908852
#105906452
#105901712
#105900392
#105900372
#16829