Finite Group Databasebeta

← #11920003

Subgroups — #11920003

Order 1152.

310 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 24 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×C42⋊C9C211yesmaximal, characteristic, complemented
2C2×#63419C211yesmaximal, characteristic, complemented
3#10588303C211yesmaximal, characteristic, complemented
4#71532—31nomaximal
5#63694—41nomaximal
6C2×C42⋊C9—21no—
7C2×C42⋊C9C2211yescharacteristic
8#63419—21no—
9C22×C3×C42D311yescharacteristic
10#5791—31no—
11#5207—31no—
12C2×#805—31no—
13C2×#805—31no—
14#4523—31no—
15#4523—31no—
16C22×C22⋊C9—41no—
17C2×(C22⋊C9)⋊C2—41no—
18(C22⋊C9)⋊C4—41no—
19C42⋊C9D411yescharacteristic, complemented
20#1896—91noSylow
21C23×C3×C4—31no—
22C2×#235—31no—
23C2×C3×C42—21no—
24C2×C3×C42—31no—
25C2×C3×C42—61no—
26C2×C3×C42C2×D311yescharacteristic
27#953—61no—
28#930—31no—
29#930—31no—
30#929—61no—
31C4×#67—61no—
32C4×#67—61no—
33#926—31no—
34#924—31no—
35#924—31no—
36C2×#208—31no—
37C2×#208—31no—
38#830—61no—
39#830—61no—
40#805—61no—
41#805—62no—
42#805—61no—
43C2×C22⋊C9—41no—
44C2×C22⋊C9—81no—
45(C22⋊C9)⋊C2—81no—
46#611—161no—
47#525—91no—
48C22×C42D911yescharacteristic, complemented
49C2×#104—91no—
50C2×#104—91no—
51#407—91no—
52#339—91no—
53#339—91no—
54C24×C3S411yescharacteristic
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4—61no—
62C22×C3×C4—61no—
63C22×C3×C4—61no—
64C22×C3×C4—61no—
65C2×#67—61no—
66C2×#67—61no—
67C2×#67—61no—
68#235—61no—
69#235—61no—
70#235—61no—
71#235—61no—
72C2×D12—31no—
73C2×C4×D3—61no—
74C2×Dic6—31no—
75C3×C42—31no—
76C3×C42—32no—
77C3×C42—61no—
78C3×C42#6711yescharacteristic
79#217—61no—
80#217—61no—
81#217—61no—
82(C2×D3)⋊C4—61no—
83(C2×D3)⋊C4—61no—
84C4⋊Dic3—31no—
85C4⋊Dic3—31no—
86Dic3⋊C4—61no—
87Dic3⋊C4—61no—
88C4×Dic3—61no—
89#208—61no—
90#208—61no—
91#208—61no—
92#208—61no—
93C2×C3⋊C8—61no—
94C2×C3⋊C8—61no—
95C22×C9—161no—
96C2×D9—161no—
97C22⋊C9—41no—
98Dic9—161no—
99C2×#41—91no—
100C23×C4—31no—
101C2×M16—91no—
102C2×M16—91no—
103#123—181no—
104C22⋊Q8—91no—
105C22⋊Q8—91no—
106#121—91no—
107#121—91no—
108#120—181no—
109C4×D4—181no—
110C4×D4—181no—
111#117—91no—
112C2×C42—21no—
113C2×C42—31no—
114C2×C42—61no—
115C2×C42C2×D911yescharacteristic
116#104—181no—
117#104—182no—
118#104—181no—
119C22⋊C8—181no—
120C22⋊C8—181no—
121C23×C3—21no—
122C23×C3—31no—
123C23×C3—31no—
124C23×C3—61no—
125C23×C3C2×S411yescharacteristic
126C22×D3—61no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—31no—
131C2×C3×C4—31no—
132C2×C3×C4—31no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—61no—
136C2×C3×C4—61no—
137C2×C3×C4—61no—
138C2×C3×C4—61no—
139C2×C3×C4—61no—
140C2×C3×C4—61no—
141C2×C3×C4—61no—
142C2×C3×C4—61no—
143C2×C3×C4—61no—
144C2×C3×C4—61no—
145#67—121no—
146#67—122no—
147#67—121no—
148#67—121no—
149#67—121no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153D12—61no—
154D12—61no—
155C4×D3—121no—
156C4×D3—121no—
157Dic6—61no—
158Dic6—61no—
159C3⋊C8—121no—
160C3⋊C8—121no—
161C2×C9—161no—
162C2×C9—321no—
163D9—321no—
164C24(C22⋊C9)⋊C211yescharacteristic
165#41—181no—
166#41—181no—
167#41—181no—
168#41—181no—
169C2×Q8—91no—
170C2×D4—91no—
171C2×D4—181no—
172C2×D4—181no—
173C2×D4—181no—
174C22×C4—31no—
175C22×C4—31no—
176C22×C4—31no—
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—31no—
180C22×C4—61no—
181C22×C4—61no—
182C22×C4—61no—
183C22×C4—61no—
184C22×C4—181no—
185M16—181no—
186M16—181no—
187M16—181no—
188M16—181no—
189C2×C8—181no—
190C2×C8—181no—
191C4⋊C4—91no—
192C4⋊C4—91no—
193C4⋊C4—181no—
194C4⋊C4—181no—
195C22⋊C4—181no—
196C22⋊C4—181no—
197C22⋊C4—181no—
198C22⋊C4—181no—
199C22⋊C4—181no—
200C42—31no—
201C42—32no—
202C42—61no—
203C42—181no—
204C42#61111yescharacteristic, complemented
205C22×C3—31no—
206C22×C3—31no—
207C22×C3—32no—
208C22×C3—31no—
209C22×C3—61no—
210C22×C3—61no—
211C22×C3—61no—
212C22×C3#85711yescharacteristic
213C22×C3GL(2,ℤ/4)11yescharacteristic
214C2×D3—121no—
215C2×D3—121no—
216C2×D3—121no—
217C3×C4—31no—
218C3×C4—31no—
219C3×C4—31no—
220C3×C4—31no—
221C3×C4—61no—
222C3×C4—61no—
223Dic3—121no—
224Dic3—121no—
225Dic3—121no—
226C9—161noSylow
227C23—21no—
228C23—31no—
229C23—31no—
230C23—61no—
231C23—181no—
232C23C2×(C22⋊C9)⋊C211yescharacteristic
233Q8—181no—
234Q8—181no—
235D4—181no—
236D4—181no—
237D4—361no—
238D4—362no—
239D4—361no—
240D4—361no—
241D4—361no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—31no—
247C2×C4—31no—
248C2×C4—31no—
249C2×C4—31no—
250C2×C4—61no—
251C2×C4—61no—
252C2×C4—61no—
253C2×C4—61no—
254C2×C4—61no—
255C2×C4—61no—
256C2×C4—61no—
257C2×C4—61no—
258C2×C4—61no—
259C2×C4—61no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—181no—
263C2×C4—361no—
264C2×C4—361no—
265C8—361no—
266C8—361no—
267C2×C3—21no—
268C2×C3—31no—
269C2×C3—31no—
270C2×C3—61no—
271C2×C3C2×#85711yescharacteristic
272D3—241no—
273C22—31no—
274C22—31no—
275C22—32no—
276C22—31no—
277C22—61no—
278C22—61no—
279C22—61no—
280C22—361no—
281C22—361no—
282C22—361no—
283C22#6341911yescharacteristic, complemented
284C22#6369411yescharacteristic
285C4—31no—
286C4—31no—
287C4—31no—
288C4—31no—
289C4—61no—
290C4—61no—
291C4—361no—
292C4—361no—
293C4—361no—
294C3#7304811yescharacteristic
295C2—21no—
296C2—31no—
297C2—31no—
298C2—61no—
299C2—721no—
300C2C2×#6341911yescharacteristic
subgroupG/H
centerC2C2×#63419
commutator, cosocleC2×C42⋊C9C22
Frattini, socleC23×C3C2×S4
FittingC22×C3×C42D3
hypercenterC22#63419
hypocenterC42⋊C9D4
LCSG ▷ C2×C42⋊C9 ▷ C42⋊C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C42⋊C9C2semidirect
2. C2×#63419C2semidirect
3. #10588303C2semidirect
19. C42⋊C9D4semidirect
48. C22×C42D9semidirect
204. C42#611semidirect
283. C22#63419semidirect

Maximal subgroups

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

subgroupindex
C22×C42⋊C92
C2×#634192
#105883032
#715323
#636944