Finite Group Databasebeta

← #11860909

Subgroups — #11860909

Order 1152.

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

normal subgroups only

This group has 778 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
1C2×#64223C211yesmaximal, characteristic
2#10594509C212yesmaximal, complemented
3#10593748C211yesmaximal, characteristic, complemented
4#10593445C212yesmaximal, complemented
5#10593431C214yesmaximal, complemented
6C4×#3774C212yesmaximal, complemented
7#10593396C211yesmaximal, characteristic, complemented
8#10593360C212yesmaximal, complemented
9C2×#3798C2212yes—
10C2×#3788C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×#3776C2211yescharacteristic
13C2×#3775C2212yes—
14C2×#3774C2211yescharacteristic
15#64223C418yescomplemented
16#64101C2211yescharacteristic
17C3×D3×C4⋊C4—22no—
18#63904—24no—
19C4×#625C2214yes—
20#63900C2212yes—
21#63841—22no—
22#63838C2214yes—
23#63777C2212yes—
24C4×#622C2212yes—
25#63743C2212yes—
26#63743C2212yes—
27#63740C2214yes—
28#63739C2214yes—
29#5504—62no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C3×C4×D3—22no—
32C2×C3×C4×D3—24no—
33C2×#627C2312yes—
34C2×#626—22no—
35C2×#625C2312yes—
36C2×#624—22no—
37#3798—24no—
38#3798C2×C418yescomplemented
39C2×#622C2312yes—
40C2×#622C2311yescharacteristic
41C2×#622C2311yescharacteristic
42#3788—22no—
43#3787C2×C414yescomplemented
44#3776C2×C414yescomplemented
45#3775C2×C418yescomplemented
46#3774C2×C414yescomplemented
47C32×C4⋊C4D411yescharacteristic
48#3752D412yes—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C4×C3⋊Dic3C2312yes—
51C3×C4⋊Dic3—22no—
52C3×Dic3⋊C4—24no—
53#3724C2314yes—
54(C2×D3)⋊Dic3—24no—
55Dic32—24no—
56#2951—91nomaximal, Sylow
57C2×#235—62no—
58C2×C3×C4⋊C4—62no—
59C4×#67—64no—
60C4×#67—64no—
61#926—62no—
62#893—64no—
63#892—62no—
64#892—62no—
65D3×C4⋊C4—22no—
66D3×C4⋊C4—62no—
67#887—64no—
68C22×C3⋊D3C2×D411yescharacteristic
69C22×C3×D3—22no—
70C2×C32×C4C2×D412yes—
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3C2×D412yes—
73C2×C3⋊Dic3C2411yescharacteristic
74C4×C3⋊D3C22×C412yes—
75C4×C3⋊D3#4112yes—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—24no—
78C3×C4×D3—28no—
79C3×C4×D3—84no—
80#627—22no—
81#627C22×C414yes—
82#626—28no—
83#625—22no—
84#625C22×C414yes—
85#624—82no—
86#622—22no—
87#622C22×C412yes—
88#622C22×C412yes—
89C2×#135—91no—
90#520—92no—
91#440—94no—
92C4×Q16—92no—
93C4×D8—92no—
94C2×#107—91no—
95#417—92no—
96#405—91no—
97C22×C3×C4—62no—
98C22×C3×C4—64no—
99C2×#67—62no—
100C2×#67—62no—
101#235—68no—
102#235—68no—
103C2×D12—62no—
104C2×C4×D3—22no—
105C2×C4×D3—24no—
106C2×C4×D3—62no—
107C2×C4×D3—64no—
108C2×Dic6—62no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—64no—
111C3×C4⋊C4—62no—
112#217—64no—
113(C2×D3)⋊C4—64no—
114(C2×D3)⋊C4—64no—
115C4⋊Dic3—22no—
116C4⋊Dic3—62no—
117Dic3⋊C4—24no—
118Dic3⋊C4—64no—
119C4×Dic3—64no—
120C4×Dic3—64no—
121C4×Dic3—64no—
122C22×C32C22×D411yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3C4×D412yes—
126C2×C3×D3—24no—
127C2×C3×D3—42no—
128C2×C3×D3—42no—
129C32×C4—22no—
130C32×C4C4×D412yes—
131C3⋊Dic3—22no—
132C3⋊Dic3C23×C411yescharacteristic
133C3⋊Dic3C2×#4111yescharacteristic
134C3×Dic3—24no—
135C3×Dic3—44no—
136C2×#41—92no—
137#135—98no—
138C2×Q16—91no—
139C2×SD16—92no—
140C2×D8—91no—
141C2×M16—91no—
142C22×C8—91no—
143C4×Q8—94no—
144C4×D4—94no—
145C4×D4—184no—
146#117—91no—
147#117—182no—
148C2×C4⋊C4—62no—
149C2×C4⋊C4—92no—
150#107—92no—
151#107—92no—
152#103—94no—
153#102—94no—
154#97—92no—
155C4×C8—92no—
156C23×C3—62no—
157C22×D3—22no—
158C22×D3—62no—
159C2×C3×C4—22no—
160C2×C3×C4—24no—
161C2×C3×C4—68no—
162C2×C3×C4—62no—
163C2×C3×C4—64no—
164C2×C3×C4—244no—
165#67—64no—
166#67—68no—
167#67—64no—
168C2×Dic3—22no—
169C2×Dic3—24no—
170C2×Dic3—62no—
171C2×Dic3—64no—
172D12—68no—
173C4×D3—28no—
174C4×D3—64no—
175C4×D3—64no—
176C4×D3—84no—
177C4×D3—244no—
178Dic6—64no—
179Dic6—64no—
180C2×C32C2×C4×D411yescharacteristic
181C2×C32#57611yescharacteristic
182C2×C32#57811yescharacteristic
183C3⋊D3—22no—
184C3×D3—44no—
185#41—98no—
186#41—184no—
187C2×Q8—92no—
188C2×D4—92no—
189C2×D4—182no—
190C22×C4—62no—
191C22×C4—64no—
192C22×C4—91no—
193C22×C4—182no—
194Q16—94no—
195SD16—98no—
196D8—94no—
197M16—182no—
198C2×C8—91no—
199C2×C8—91no—
200C2×C8—94no—
201C2×C8—92no—
202C4⋊C4—62no—
203C4⋊C4—64no—
204C4⋊C4—94no—
205C4⋊C4—91no—
206C4⋊C4GO+(4,𝔽2)11yescharacteristic
207C22⋊C4—92no—
208C22⋊C4—184no—
209C42—92no—
210C42—184no—
211C22×C3—22no—
212C22×C3—64no—
213C22×C3—122no—
214C22×C3—122no—
215C2×D3—24no—
216C2×D3—42no—
217C2×D3—42no—
218C2×D3—64no—
219C2×D3—122no—
220C2×D3—122no—
221C3×C4—24no—
222C3×C4—44no—
223C3×C4—64no—
224C3×C4—124no—
225Dic3—24no—
226Dic3—44no—
227Dic3—62no—
228Dic3—62no—
229Dic3—124no—
230C32#295111yescharacteristic, complemented, Sylow
231C23—62no—
232C23—91no—
233Q8—94no—
234Q8—182no—
235D4—94no—
236D4—188no—
237D4—182no—
238C2×C4—62no—
239C2×C4—68no—
240C2×C4—64no—
241C2×C4—91no—
242C2×C4—92no—
243C2×C4—92no—
244C2×C4—92no—
245C2×C4—244no—
246C2×C4—722no—
247C2×C4C2×GO+(4,𝔽2)12yes—
248C2×C4C2×GO+(4,𝔽2)11yescharacteristic
249C8—92no—
250C8—92no—
251C8—182no—
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—124no—
256D3—44no—
257D3—124no—
258C22—64no—
259C22—92no—
260C22—122no—
261C22—122no—
262C22—181no—
263C22—181no—
264C22C22×GO+(4,𝔽2)11yescharacteristic
265C4—22no—
266C4—64no—
267C4—91no—
268C4—91no—
269C4—124no—
270C4—182no—
271C4C4×GO+(4,𝔽2)12yes—
272C3—22no—
273C2—124no—
274C2—182no—
275C2C2×C4×GO+(4,𝔽2)11yescharacteristic
276C2#1059651411yescharacteristic
277C2#1059652011yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#64223C2
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2951
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594509C2semidirect
3. #10593748C2semidirect
4. #10593445C2semidirect
5. #10593431C2semidirect
6. C4×#3774C2semidirect
7. #10593396C2semidirect
8. #10593360C2semidirect
15. #64223C4semidirect
38. #3798C2×C4semidirect
43. #3787C2×C4semidirect
44. #3776C2×C4semidirect
45. #3775C2×C4semidirect
46. #3774C2×C4semidirect
230. C32#2951semidirect

Maximal subgroups

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

subgroupindex
C2×#642232
#105945092
#105937482
#105934452
#105934312
C4×#37742
#105933962
#105933602
#29519