Finite Group Databasebeta

← #11860711

Subgroups — #11860711

Order 1152.

866 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 866 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C22×#3774C211yesmaximal, characteristic
2#10594181C212yesmaximal, complemented
3#10593738C211yesmaximal, characteristic, complemented
4#10593511C211yesmaximal, characteristic, complemented
5#10593493C212yesmaximal, complemented
6#10593420C212yesmaximal, complemented
7#10593419C214yesmaximal, complemented
8C4×#3774C212yesmaximal, complemented
9C22×#625C2212yes—
10C2×#3792C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×#3774C418yescomplemented
13C2×#3774C2211yescharacteristic
14C2×#3774C2212yes—
15C2×#3774C2211yescharacteristic
16#64086C2211yescharacteristic
17C3×D3×C22⋊C4—22no—
18D3×#217—22no—
19#63957C2212yes—
20#63902C2214yescomplemented
21C4×#625C2214yescomplemented
22#63879—24no—
23#63777C2212yescomplemented
24C4×#622C2212yescomplemented
25#63743C2212yescomplemented
26#63742C2212yescomplemented
27#63739C2214yescomplemented
28#63739C2214yescomplemented
29#5486—62no—
30C23×C3×D3—22no—
31C22×C3⋊Dic3C2311yescharacteristic
32C2×C3×C4×D3—24no—
33C2×#625—22no—
34C2×#625—24no—
35C2×#625C2×C418yescomplemented
36C2×#625C2312yes—
37C2×#625C2312yes—
38C2×D3×Dic3—24no—
39#3792—22no—
40C2×#622C2×C414yescomplemented
41C2×#622C2312yes—
42C2×#622C2311yescharacteristic
43C2×#622C2311yescharacteristic
44#3774C2×C414yescomplemented
45#3774C2×C418yescomplemented
46#3774C2×C414yescomplemented
47C32×C22⋊C4D411yescharacteristic
48#3757D411yescharacteristic
49#3750D412yes—
50C4×C3⋊Dic3C2312yes—
51C3×#217—22no—
52C3×(C2×D3)⋊C4—24no—
53#3724C2314yes—
54(C2×D3)⋊Dic3—24no—
55Dic32—22no—
56#2948—91nomaximal, Sylow
57C22×#67—62no—
58C2×C3×C22⋊C4—62no—
59C2×#217—62no—
60C4×#67—64no—
61C4×#67—64no—
62#67⋊C4—64no—
63#67⋊C4—64no—
64D3×C22⋊C4—22no—
65D3×C22⋊C4—62no—
66#877—62no—
67#877—62no—
68C23×C32C2×D411yescharacteristic
69C22×C3×D3—22no—
70C22×C3×D3—22no—
71C22×C3×D3—28no—
72C22×C3×D3—84no—
73C2×C32×C4C2×D412yes—
74C2×C3⋊Dic3C22×C412yes—
75C2×C3⋊Dic3C2×D412yes—
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3#4112yes—
78C2×C3⋊Dic3C2411yescharacteristic
79C2×C3×Dic3—24no—
80C3×C4×D3—84no—
81#625—28no—
82#625—22no—
83#625—22no—
84#625C22×C414yes—
85#625C22×C414yes—
86D3×Dic3—84no—
87#622—22no—
88#622C22×C412yes—
89#622C22×C412yes—
90C22×D8—91no—
91#518—92no—
92#442—94no—
93C4×D8—92no—
94C4×D8—92no—
95#427—91no—
96#418—92no—
97#405—91no—
98C24×C3—62no—
99C23×D3—22no—
100C22×C3×C4—64no—
101C2×#67—62no—
102C2×#67—62no—
103C2×#67—68no—
104C2×#67—62no—
105C2×#67—62no—
106C2×#67—68no—
107C22×Dic3—62no—
108C22×Dic3—64no—
109C2×C4×D3—24no—
110C2×C4×D3—64no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—64no—
113C3×C22⋊C4—62no—
114#217—22no—
115#217—62no—
116#217—64no—
117(C2×D3)⋊C4—24no—
118(C2×D3)⋊C4—64no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121C4×Dic3—64no—
122C4×Dic3—64no—
123C22×C32—22no—
124C22×C32C4×D412yes—
125C22×C32C22×D411yescharacteristic
126C2×C3×D3—24no—
127C2×C3×D3—24no—
128C2×C3×D3—44no—
129C2×C3×D3—44no—
130C2×C3×D3—88no—
131C32×C4—22no—
132C3⋊Dic3—22no—
133C3⋊Dic3C4×D412yes—
134C3⋊Dic3C23×C411yescharacteristic
135C3⋊Dic3C2×#4111yescharacteristic
136C3×Dic3—44no—
137C22×D4—92no—
138C2×D8—91no—
139C2×D8—91no—
140C2×D8—92no—
141C2×D8—98no—
142C2×M16—91no—
143C22×C8—91no—
144C4×D4—94no—
145C4×D4—94no—
146C4×D4—184no—
147#117—91no—
148#117—92no—
149C2×C22⋊C4—62no—
150C2×C22⋊C4—182no—
151#107—92no—
152#106—92no—
153#102—94no—
154#102—94no—
155#97—92no—
156C4×C8—92no—
157C23×C3—22no—
158C23×C3—62no—
159C23×C3—62no—
160C23×C3—68no—
161C23×C3—244no—
162C22×D3—22no—
163C22×D3—22no—
164C22×D3—28no—
165C22×D3—84no—
166C2×C3×C4—24no—
167C2×C3×C4—64no—
168C2×C3×C4—244no—
169#67—64no—
170#67—64no—
171#67—68no—
172#67—68no—
173#67—64no—
174#67—64no—
175C2×Dic3—24no—
176C2×Dic3—64no—
177C2×Dic3—62no—
178C2×Dic3—64no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181C2×Dic3—244no—
182C4×D3—84no—
183C4×D3—244no—
184C2×C32—22no—
185C2×C32C2×C4×D411yescharacteristic
186C2×C32#57612yes—
187C3×D3—44no—
188C3×D3—44no—
189C24—62no—
190C2×D4—92no—
191C2×D4—92no—
192C2×D4—98no—
193C2×D4—182no—
194C2×D4—184no—
195C22×C4—64no—
196C22×C4—91no—
197C22×C4—184no—
198D8—94no—
199D8—94no—
200D8—98no—
201M16—182no—
202C2×C8—91no—
203C2×C8—91no—
204C2×C8—94no—
205C2×C8—92no—
206C4⋊C4—94no—
207C4⋊C4—92no—
208C22⋊C4—62no—
209C22⋊C4—64no—
210C22⋊C4—91no—
211C22⋊C4—184no—
212C22⋊C4GO+(4,𝔽2)11yescharacteristic
213C42—92no—
214C42—182no—
215C22×C3—22no—
216C22×C3—24no—
217C22×C3—44no—
218C22×C3—64no—
219C22×C3—64no—
220C22×C3—124no—
221C22×C3—124no—
222C22×C3—248no—
223C2×D3—24no—
224C2×D3—24no—
225C2×D3—44no—
226C2×D3—44no—
227C2×D3—88no—
228C3×C4—44no—
229C3×C4—124no—
230Dic3—44no—
231Dic3—64no—
232Dic3—62no—
233Dic3—62no—
234Dic3—124no—
235C32#294811yescharacteristic, complemented, Sylow
236C23—62no—
237C23—62no—
238C23—68no—
239C23—244no—
240C23C2×GO+(4,𝔽2)11yescharacteristic
241D4—94no—
242D4—94no—
243D4—182no—
244D4—182no—
245D4—188no—
246C2×C4—64no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—92no—
250C2×C4—92no—
251C2×C4—92no—
252C2×C4—244no—
253C2×C4—724no—
254C2×C4C2×GO+(4,𝔽2)12yes—
255C8—92no—
256C8—92no—
257C8—182no—
258C2×C3—22no—
259C2×C3—24no—
260C2×C3—44no—
261C2×C3—124no—
262C2×C3—124no—
263D3—44no—
264D3—44no—
265C22—22no—
266C22—64no—
267C22—64no—
268C22—124no—
269C22—124no—
270C22—248no—
271C22C4×GO+(4,𝔽2)12yes—
272C22C22×GO+(4,𝔽2)11yescharacteristic
273C4—22no—
274C4—91no—
275C4—91no—
276C4—92no—
277C4—124no—
278C4—182no—
279C3—22no—
280C2—22no—
281C2—124no—
282C2—124no—
283C2C2×C4×GO+(4,𝔽2)11yescharacteristic
284C2#1059651412yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
prime radicalC22×#3774C2
cosocleC2×C3⋊Dic3C24
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#2948
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594181C2semidirect
3. #10593738C2semidirect
4. #10593511C2semidirect
5. #10593493C2semidirect
6. #10593420C2semidirect
7. #10593419C2semidirect
8. C4×#3774C2semidirect
12. C2×#3774C4semidirect
20. #63902C22semidirect
21. C4×#625C22semidirect
23. #63777C22semidirect
24. C4×#622C22semidirect
25. #63743C22semidirect
26. #63742C22semidirect
27. #63739C22semidirect
28. #63739C22semidirect
35. C2×#625C2×C4semidirect
40. C2×#622C2×C4semidirect
44. #3774C2×C4semidirect
45. #3774C2×C4semidirect
46. #3774C2×C4semidirect
235. C32#2948semidirect

Maximal subgroups

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

subgroupindex
C22×#37742
#105941812
#105937382
#105935112
#105934932
#105934202
#105934192
C4×#37742
#29489