Finite Group Databasebeta

← #11920240

Subgroups — #11920240

Order 1152.

469 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 65 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×#63691C211yesmaximal, characteristic
2C4×#41⋊C9C211yesmaximal, characteristic, complemented
3#10589526C211yesmaximal, characteristic, complemented
4#10589496C212yesmaximal, complemented
5#10589490C212yesmaximal, complemented
6#82506—31nomaximal
7C2×#41⋊C9C2211yescharacteristic
8#63691C414yescomplemented
9C2×#3689C2211yescharacteristic
10C2×#3688C2211yescharacteristic
11#63434—41nomaximal
12C4×Q8⋊C9C2212yes—
13#63421C2212yes—
14C3×C4×#41D311yescharacteristic
15C2×#950—31no—
16C4×#235—31no—
17#5233—31no—
18#5030—32no—
19#5026—32no—
20#5018—32no—
21#5014—32no—
22#5002—31no—
23#4998—31no—
24C2×#803—31no—
25C2×C4×D9—41no—
26#41⋊C9C2×C412yescomplemented
27C2×Q8⋊C9C2311yescharacteristic
28#3689C2×C412yescomplemented
29#3688C2×C412yescomplemented
30C42×C9—41no—
31(C2×D9)⋊C4—42no—
32Dic9⋊C4—42no—
33C4×Dic9—41no—
34#2943—91noSylow
35C2×C3×#41C2×D311yescharacteristic
36C2×#235—31no—
37C3×C4×Q8C2×D312yes—
38C3×C4×D4—32no—
39C3×#117—31no—
40C2×C3×C42—31no—
41#950—34no—
42#950—34no—
43C2×#216—31no—
44C2×#215—31no—
45C2×#214—31no—
46C2×#213—31no—
47C4×#67—62no—
48#926—31no—
49C22×C3⋊C8—31no—
50C22×C3⋊C8—31no—
51C4×D12—32no—
52#872—61no—
53C42×D3—61no—
54C4×Dic6—32no—
55#835—32no—
56#832—32no—
57#810—32no—
58#809—32no—
59#808—32no—
60#807—32no—
61#803—32no—
62#803—32no—
63C22×D9—41no—
64C2×C4×C9—41no—
65C2×C4×C9—42no—
66C2×Dic9—41no—
67C2×Dic9—42no—
68C4×D9—44no—
69Q8⋊C9C22×C411yescharacteristic
70C2×#135—91no—
71C4×#41—91no—
72C4×#41D911yescharacteristic, complemented
73#442—92no—
74#441—92no—
75#440—92no—
76#440—92no—
77#427—91no—
78#416—91no—
79#416—91no—
80C2×#97—91no—
81C3×#41—32no—
82C3×#41C4×D312yes—
83C2×C3×Q8C22×D311yescharacteristic
84C2×C3×D4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—32no—
87C2×#67—61no—
88#235—34no—
89#235—62no—
90C2×D12—31no—
91C2×C4×D3—61no—
92C2×C4×D3—62no—
93C2×Dic6—31no—
94C3×C4⋊C4—32no—
95C3×C22⋊C4—61no—
96C3×C42—32no—
97C3×C42—31no—
98C3×C42S411yescharacteristic
99#217—61no—
100#216—32no—
101#216—32no—
102#215—32no—
103#215—32no—
104#214—34no—
105#213—34no—
106(C2×D3)⋊C4—62no—
107C4⋊Dic3—32no—
108Dic3⋊C4—62no—
109C4×Dic3—62no—
110C4×Dic3—61no—
111C2×C3⋊C8—31no—
112C2×C3⋊C8—31no—
113C2×C3⋊C8—34no—
114C2×C3⋊C8—32no—
115C2×C3⋊C8—62no—
116C22×C9—41no—
117C2×D9—42no—
118C2×D9—82no—
119C4×C9—42no—
120C4×C9—82no—
121Dic9—42no—
122Dic9—82no—
123C2×#41—91no—
124C2×#41C2×D911yescharacteristic
125#135—94no—
126#135—94no—
127C2×Q16—91no—
128C2×SD16—91no—
129C2×SD16—91no—
130C2×D8—91no—
131C22×C8—91no—
132C22×C8—91no—
133C4×Q8—92no—
134C4×Q8C2×D912yes—
135C4×D4—32no—
136C4×D4—92no—
137C4×D4—182no—
138#117—31no—
139#117—91no—
140#117—181no—
141C2×C42—31no—
142C2×C42—181no—
143#107—92no—
144#106—92no—
145#103—92no—
146#103—92no—
147#102—92no—
148#102—92no—
149#97—92no—
150#97—92no—
151C23×C3—31no—
152C22×D3—61no—
153C3×Q8—31no—
154C3×Q8C2×C4×D311yescharacteristic
155C3×D4—32no—
156C3×D4—61no—
157C2×C3×C4—31no—
158C2×C3×C4—32no—
159C2×C3×C4—32no—
160C2×C3×C4—32no—
161C2×C3×C4—122no—
162C2×C3×C4C2×S412yes—
163C2×C3×C4C2×S411yescharacteristic
164#67—64no—
165C2×Dic3—61no—
166C2×Dic3—62no—
167D12—32no—
168D12—61no—
169C4×D3—64no—
170C4×D3—124no—
171Dic6—32no—
172Dic6—61no—
173C3⋊C8—32no—
174C3⋊C8—32no—
175C3⋊C8—62no—
176C2×C9—41no—
177C2×C9—42no—
178D9—82no—
179#41—32no—
180#41—94no—
181#41—182no—
182#41C4×D912yes—
183C2×Q8—91no—
184C2×Q8C22×D911yescharacteristic
185C2×D4—31no—
186C2×D4—91no—
187C2×D4—181no—
188C22×C4—31no—
189C22×C4—32no—
190C22×C4—182no—
191C22×C4—181no—
192Q16—92no—
193Q16—92no—
194SD16—94no—
195SD16—92no—
196SD16—92no—
197D8—94no—
198C2×C8—91no—
199C2×C8—91no—
200C2×C8—94no—
201C2×C8—92no—
202C2×C8—182no—
203C4⋊C4—32no—
204C4⋊C4—92no—
205C4⋊C4—182no—
206C22⋊C4—61no—
207C22⋊C4—181no—
208C22⋊C4—182no—
209C42—32no—
210C42—31no—
211C42—182no—
212C42—181no—
213C42(C22⋊C9)⋊C211yescharacteristic
214C22×C3—32no—
215C22×C3—62no—
216C22×C3C22×S411yescharacteristic
217C2×D3—62no—
218C2×D3—122no—
219C3×C4—22no—
220C3×C4—31no—
221C3×C4—31no—
222C3×C4—62no—
223C3×C4C4×S412yes—
224Dic3—62no—
225Dic3—122no—
226C9—41noSylow
227C23—31no—
228C23—181no—
229Q8—31no—
230Q8—92no—
231Q8—181no—
232Q8C2×C4×D911yescharacteristic
233D4—32no—
234D4—61no—
235D4—92no—
236D4—181no—
237D4—184no—
238C2×C4—31no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—32no—
242C2×C4—122no—
243C2×C4—181no—
244C2×C4—184no—
245C2×C4—182no—
246C2×C4—364no—
247C2×C4C2×(C22⋊C9)⋊C212yes—
248C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
249C8—92no—
250C8—92no—
251C8—182no—
252C2×C3—62no—
253C2×C3C2×C4×S411yescharacteristic
254C2×C3#592312yes—
255D3—122no—
256C22—32no—
257C22—62no—
258C22—182no—
259C22—362no—
260C22C22×(C22⋊C9)⋊C211yescharacteristic
261C4—22no—
262C4—31no—
263C4—31no—
264C4—62no—
265C4—182no—
266C4—362no—
267C4C4×(C22⋊C9)⋊C212yes—
268C3#8534111yescharacteristic
269C2—62no—
270C2—362no—
271C2C2×C4×(C22⋊C9)⋊C211yescharacteristic
272C2#1059309812yes—
subgroupG/H
centerC2×C4C2×(C22⋊C9)⋊C2
commutator, hypocenterQ8⋊C9C22×C4
Frattini, socleC22×C3C22×S4
FittingC3×C4×#41D3
prime radicalC2×#63691C2
cosocleC2×Q8⋊C9C23
hypercenterC42(C22⋊C9)⋊C2
LCSG ▷ Q8⋊C9
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#41⋊C9C2semidirect
3. #10589526C2semidirect
4. #10589496C2semidirect
5. #10589490C2semidirect
8. #63691C4semidirect
26. #41⋊C9C2×C4semidirect
28. #3689C2×C4semidirect
29. #3688C2×C4semidirect
72. C4×#41D9semidirect

Maximal subgroups

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

subgroupindex
C2×#636912
C4×#41⋊C92
#105895262
#105894962
#105894902
#825063
#634344