Finite Group Databasebeta

← #11781459

Subgroups — #11781459

Order 1152.

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

normal subgroups only

This group has 308 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#10593437C211yesmaximal, characteristic, complemented
2#10593417C211yesmaximal, characteristic
3#10590885C211yesmaximal, characteristic, complemented
4#10590718C211yesmaximal, characteristic, complemented
5#10590171C211yesmaximal, characteristic, complemented
6#10590039C211yesmaximal, characteristic, complemented
7#10590037C211yesmaximal, characteristic, complemented
8C2×#3775—21no—
9C2×#3774—21no—
10#63919C2211yescharacteristic
11#63914C2211yescharacteristic
12C4×#625C2211yescharacteristic
13C2×D3×C3⋊C8—21no—
14C4⋊#622C2211yescharacteristic
15C4⋊#622C2211yescharacteristic
16#63740—21no—
17#63739—21no—
18C8×C3⋊Dic3C2211yescharacteristic
19C3×#821—21no—
20C3×(C2×D3)⋊C8—21no—
21#63572C2211yescharacteristic
22#63562—21no—
23#4760—61no—
24#67⋊C8—61no—
25C2×C3×D12—21no—
26C2×C3×C4×D3—21no—
27C2×#627—21no—
28C2×#625—21no—
29C2×#625—21no—
30C2×#625D411yescharacteristic
31C2×#622—21no—
32C2×#622—21no—
33#3775—42no—
34#3774—42no—
35C2×C32×C8D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C3×C4⋊Dic3—21no—
39C2×C3×C3⋊C8—21no—
40#3724—21no—
41#3724D411yescharacteristic
42(C2×D3)⋊Dic3—21no—
43D3×C3⋊C8—42no—
44#1681—91nomaximal, Sylow
45#940—61no—
46C4×#67—61no—
47C22×C3⋊C8—61no—
48C2×D3×C8—61no—
49#888—61no—
50C3×#102—61no—
51C3×C22⋊C8—61no—
52#832—61no—
53#821—21no—
54(C2×D3)⋊C8—21no—
55Dic3⋊C8—61no—
56C8×Dic3—61no—
57C8×Dic3—61no—
58#809—61no—
59C22×C3×D3—21no—
60C22×C3×D3—41no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3#4111yescharacteristic
64C2×C3×Dic3—21no—
65C2×C3×Dic3—41no—
66C3×D12—41no—
67C3×D12—41no—
68C3×C4×D3—41no—
69C3×C4×D3—41no—
70#627—41no—
71#627—41no—
72#625—21no—
73#625—41no—
74#625—41no—
75#625—81no—
76#625D812yes—
77#622—41no—
78#622—41no—
79C32×C8—21no—
80C3⋊(C3⋊C8)—21no—
81C3×C3⋊C8—41no—
82#486—91no—
83#461—91no—
84#459—91no—
85C8×D4—91no—
86#335—91no—
87#332—91no—
88#331—91no—
89C2×C3×D4—61no—
90C22×C3×C4—61no—
91C2×#67—61no—
92C2×#67—121no—
93C2×#67—121no—
94C2×D12—21no—
95C2×C4×D3—21no—
96C2×Dic6—121no—
97C2×C3×C8—21no—
98C2×C3×C8—21no—
99C2×C3×C8—61no—
100C3×C4⋊C4—61no—
101#217—61no—
102(C2×D3)⋊C4—61no—
103C4⋊Dic3—21no—
104Dic3⋊C4—61no—
105Dic3⋊C4—121no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C2×C3⋊C8—21no—
109C2×C3⋊C8—61no—
110C2×C3⋊C8—61no—
111C2×C3⋊C8—122no—
112D3×C8—122no—
113C22×C32#12111yescharacteristic
114C2×C3×D3—22no—
115C2×C3×D3—41no—
116C2×C3×D3—41no—
117C2×C3×D3—81no—
118C2×C3×D3—81no—
119C2×C3×D3—81no—
120C32×C4#13511yescharacteristic
121C32×C4AGL(1,ℤ/8)11yescharacteristic
122C3⋊Dic3—21no—
123C3⋊Dic3C2×D811yescharacteristic
124C3⋊Dic3#13511yescharacteristic
125C3×Dic3—41no—
126C3×Dic3—81no—
127C2×SD16—181no—
128C2×D8—181no—
129C22×C8—181no—
130C4⋊Q8—91no—
131#127—91no—
132C4×D4—91no—
133C4⋊C8—91no—
134C4⋊C8—91no—
135C4⋊C8—91no—
136#103—181no—
137#102—61no—
138#102—181no—
139#102—181no—
140C22⋊C8—61no—
141C4×C8—91no—
142C23×C3—61no—
143C23×C3—121no—
144C22×D3—21no—
145C22×D3—41no—
146C3×D4—121no—
147C3×D4—121no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—61no—
151C2×C3×C4—121no—
152C2×C3×C4—121no—
153C2×C3×C4—121no—
154#67—62no—
155#67—62no—
156#67—241no—
157#67—241no—
158#67—242no—
159C2×Dic3—21no—
160C2×Dic3—41no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165D12—41no—
166D12—41no—
167C4×D3—41no—
168C4×D3—41no—
169Dic6—241no—
170Dic6—241no—
171C3×C8—41no—
172C3×C8—41no—
173C3×C8—121no—
174C3⋊C8—41no—
175C3⋊C8—62no—
176C3⋊C8—121no—
177C2×C32#46311yescharacteristic
178C2×C32#46611yescharacteristic
179C2×C32#47111yescharacteristic
180C3×D3—42no—
181C3×D3—161no—
182C2×Q8—181no—
183C2×D4—61no—
184C2×D4—91no—
185C2×D4—181no—
186C2×D4—181no—
187C22×C4—61no—
188SD16—362no—
189D8—362no—
190C2×C8—61no—
191C2×C8—91no—
192C2×C8—181no—
193C2×C8—181no—
194C2×C8—362no—
195C2×C8GO+(4,𝔽2)11yescharacteristic
196C4⋊C4—61no—
197C4⋊C4—91no—
198C4⋊C4—181no—
199C22⋊C4—181no—
200C42—91no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—62no—
204C22×C3—121no—
205C22×C3—121no—
206C22×C3—241no—
207C22×C3—241no—
208C22×C3—241no—
209C2×D3—22no—
210C2×D3—41no—
211C2×D3—41no—
212C2×D3—81no—
213C2×D3—81no—
214C2×D3—81no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—121no—
220C3×C4—241no—
221Dic3—41no—
222Dic3—61no—
223Dic3—61no—
224Dic3—61no—
225Dic3—61no—
226Dic3—62no—
227Dic3—81no—
228Dic3—121no—
229C32#168111yescharacteristic, complemented, Sylow
230C23—61no—
231C23—121no—
232Q8—361no—
233Q8—361no—
234D4—92no—
235D4—121no—
236D4—121no—
237D4—181no—
238D4—361no—
239D4—361no—
240D4—721no—
241C2×C4—61no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—121no—
245C2×C4—121no—
246C2×C4—121no—
247C2×C4C2×GO+(4,𝔽2)11yescharacteristic
248C8—21no—
249C8—121no—
250C8—181no—
251C8—361no—
252C8—361no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—122no—
260C2×C3—481no—
261D3—42no—
262D3—161no—
263C22—62no—
264C22—121no—
265C22—121no—
266C22—241no—
267C22—241no—
268C22—241no—
269C22#6423011yescharacteristic
270C4—91no—
271C4—91no—
272C4—121no—
273C4—181no—
274C4—241no—
275C4#6422411yescharacteristic
276C4#6423711yescharacteristic
277C3—21no—
278C3—21no—
279C2—122no—
280C2—481no—
281C2#1059328511yescharacteristic
282C2#1059330211yescharacteristic
283C2#1059342811yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radical#10593417C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1681
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. #10593437C2semidirect
3. #10590885C2semidirect
4. #10590718C2semidirect
5. #10590171C2semidirect
6. #10590039C2semidirect
7. #10590037C2semidirect
229. C32#1681semidirect

Maximal subgroups

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

subgroupindex
#105934372
#105934172
#105908852
#105907182
#105901712
#105900392
#105900372
#16819