Finite Group Databasebeta

← C2×#568⋊C9 #11919783

Subgroups — C2×#568⋊C9 #11919783

Order 1152.

629 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 629 conjugacy classes of subgroups — too many to draw. Only its 141 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×#41⋊C9C211yesmaximal, characteristic
2#568⋊C9C214yesmaximal, direct product factor
3C2×#131⋊C9C212yesmaximal, complemented
4C2×C3×#568C311yesmaximal, characteristic
5C2×#41⋊C9C411yescharacteristic
6C2×#41⋊C9C412yes—
7C2×#41⋊C9C2211yescharacteristic
8C2×#41⋊C9C2212yes—
9C22×Q8⋊C9C411yescharacteristic
10C2×C9×M16—41nomaximal
11#131⋊C9C2214yescomplemented
12C22×C3×#41C2×C311yescharacteristic
13C3×#568—34no—
14C3×#568C2×C314yes—
15C2×C3×#131—32no—
16C2×C3×#131C2×C312yes—
17C22×C3×M16—31no—
18C22×C3×M16—31no—
19C22×C4×C9—41no—
20#41⋊C9C2×C411yescharacteristic
21#41⋊C9C2×C412yes—
22#41⋊C9C2311yescharacteristic
23C2×Q8⋊C9C2×C411yescharacteristic
24C2×Q8⋊C9C2×C412yes—
25C9×M16—44no—
26C2×C8×C9—42no—
27C2×#568C911yescharacteristic, complemented, Sylow
28C2×C3×#41—31no—
29C2×C3×#41—32no—
30C2×C3×#41—31no—
31C2×C3×#41—32no—
32C2×C3×#41C3×C411yescharacteristic
33C2×C3×#41C3×C412yes—
34C2×C3×#41C22×C311yescharacteristic
35C2×C3×#41C22×C312yes—
36C22×C3×Q8C3×C411yescharacteristic
37C22×C3×D4—31no—
38C23×C3×C4—31no—
39C3×#131—38no—
40C3×#131—38no—
41C3×#131—34no—
42C3×#131C22×C314yes—
43C2×C3×M16—34no—
44C2×C3×M16—31no—
45C2×C3×M16—34no—
46C2×C3×M16—34no—
47C2×C3×M16—34no—
48C2×C3×M16—32no—
49C2×C3×M16—32no—
50C2×C3×M16A411yescharacteristic
51C22×C3×C8—32no—
52C22×C3×C8—32no—
53C23×C9—41no—
54C2×C4×C9—41no—
55C2×C4×C9—42no—
56C2×C4×C9—42no—
57C2×C4×C9—41no—
58Q8⋊C9C22×C411yescharacteristic
59C8×C9—44no—
60C22×#41C2×C911yescharacteristic
61#568—34no—
62#568C2×C914yescomplemented
63C2×#131—32no—
64C2×#131C2×C912yescomplemented
65C22×M16—31no—
66C22×M16—31no—
67C24×C3—31no—
68C3×#41—32no—
69C3×#41—32no—
70C3×#41—34no—
71C3×#41—32no—
72C3×#41—31no—
73C3×#41—32no—
74C3×#41—32no—
75C3×#41—32no—
76C3×#41—31no—
77C3×#41—32no—
78C3×#41C2×C3×C411yescharacteristic
79C3×#41C2×C3×C412yes—
80C3×#41C23×C311yescharacteristic
81C2×C3×Q8—31no—
82C2×C3×Q8—32no—
83C2×C3×Q8C2×C3×C411yescharacteristic
84C2×C3×Q8C2×C3×C412yes—
85C2×C3×D4—31no—
86C2×C3×D4—32no—
87C2×C3×D4—31no—
88C2×C3×D4—32no—
89C2×C3×D4—32no—
90C2×C3×D4—34no—
91C22×C3×C4—31no—
92C22×C3×C4—31no—
93C22×C3×C4—32no—
94C22×C3×C4—31no—
95C22×C3×C4—32no—
96C22×C3×C4—32no—
97C22×C3×C4—32no—
98C22×C3×C4—31no—
99C22×C3×C4—31no—
100C22×C3×C4C2×A411yescharacteristic
101C3×M16—34no—
102C3×M16—34no—
103C3×M16—38no—
104C3×M16—34no—
105C3×M16C2×A414yes—
106C2×C3×C8—38no—
107C2×C3×C8—32no—
108C2×C3×C8—34no—
109C2×C3×C8—34no—
110C2×C3×C8C2×A412yes—
111C22×C9—41no—
112C22×C9—42no—
113C22×C9—82no—
114C4×C9—42no—
115C4×C9—41no—
116C4×C9—41no—
117C2×#41—31no—
118C2×#41—32no—
119C2×#41—31no—
120C2×#41—32no—
121C2×#41C4×C911yescharacteristic
122C2×#41C4×C912yes—
123C2×#41C22×C911yescharacteristic
124C2×#41C22×C912yes—
125C22×Q8C4×C911yescharacteristic
126C22×D4—31no—
127C23×C4—31no—
128#131—38no—
129#131—38no—
130#131—34no—
131#131C22×C914yescomplemented
132C2×M16—34no—
133C2×M16—31no—
134C2×M16—34no—
135C2×M16—34no—
136C2×M16—34no—
137C2×M16—32no—
138C2×M16—32no—
139C2×M16C22⋊C911yescharacteristic
140C22×C8—32no—
141C22×C8—32no—
142C23×C3—31no—
143C23×C3—31no—
144C23×C3—32no—
145C23×C3—32no—
146C23×C3—122no—
147C23×C3C4×A411yescharacteristic
148C3×Q8—32no—
149C3×Q8—31no—
150C3×Q8—32no—
151C3×Q8C22×C3×C411yescharacteristic
152C3×D4—32no—
153C3×D4—31no—
154C3×D4—31no—
155C3×D4—32no—
156C3×D4—34no—
157C3×D4—32no—
158C3×D4—34no—
159C2×C3×C4—32no—
160C2×C3×C4—31no—
161C2×C3×C4—32no—
162C2×C3×C4—31no—
163C2×C3×C4—32no—
164C2×C3×C4—32no—
165C2×C3×C4—32no—
166C2×C3×C4—31no—
167C2×C3×C4—32no—
168C2×C3×C4—32no—
169C2×C3×C4—31no—
170C2×C3×C4—32no—
171C2×C3×C4—31no—
172C2×C3×C4—31no—
173C2×C3×C4C4×A411yescharacteristic
174C2×C3×C4C4×A412yes—
175C2×C3×C4C22×A412yes—
176C2×C3×C4C22×A411yescharacteristic
177C3×C8—34no—
178C3×C8C22×A414yes—
179C2×C9—41no—
180C2×C9—42no—
181C2×C9—82no—
182C24—31no—
183#41—32no—
184#41—32no—
185#41—34no—
186#41—32no—
187#41—31no—
188#41—32no—
189#41—32no—
190#41—32no—
191#41—31no—
192#41—32no—
193#41C2×C4×C911yescharacteristic
194#41C2×C4×C912yes—
195#41C23×C911yescharacteristic
196C2×Q8—31no—
197C2×Q8—32no—
198C2×Q8C2×C4×C911yescharacteristic
199C2×Q8C2×C4×C912yes—
200C2×D4—31no—
201C2×D4—32no—
202C2×D4—31no—
203C2×D4—32no—
204C2×D4—32no—
205C2×D4—34no—
206C22×C4—31no—
207C22×C4—31no—
208C22×C4—32no—
209C22×C4—31no—
210C22×C4—32no—
211C22×C4—31no—
212C22×C4—31no—
213C22×C4—32no—
214C22×C4—32no—
215C22×C4C2×C22⋊C911yescharacteristic
216M16—34no—
217M16—34no—
218M16—38no—
219M16—34no—
220M16C2×C22⋊C914yes—
221C2×C8—38no—
222C2×C8—32no—
223C2×C8—34no—
224C2×C8—34no—
225C2×C8C2×C22⋊C912yes—
226C22×C3—22no—
227C22×C3—31no—
228C22×C3—31no—
229C22×C3—32no—
230C22×C3—62no—
231C22×C3—62no—
232C22×C3—122no—
233C22×C3—122no—
234C22×C3C2×C4×A412yes—
235C22×C3C2×C4×A411yescharacteristic
236C3×C4—31no—
237C3×C4—32no—
238C3×C4—31no—
239C3×C4C2×C4×A412yes—
240C3×C4C2×C4×A411yescharacteristic
241C3×C4C23×A411yescharacteristic
242C9—41noSylow
243C23—31no—
244C23—31no—
245C23—32no—
246C23—32no—
247C23—122no—
248C23C4×C22⋊C911yescharacteristic
249Q8—32no—
250Q8—31no—
251Q8—32no—
252Q8C22×C4×C911yescharacteristic
253D4—32no—
254D4—31no—
255D4—31no—
256D4—32no—
257D4—34no—
258D4—32no—
259D4—34no—
260C2×C4—32no—
261C2×C4—31no—
262C2×C4—32no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—32no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—32no—
269C2×C4—32no—
270C2×C4—32no—
271C2×C4—32no—
272C2×C4—31no—
273C2×C4—32no—
274C2×C4C4×C22⋊C912yes—
275C2×C4C4×C22⋊C911yescharacteristic
276C2×C4C22×C22⋊C911yescharacteristic
277C2×C4C22×C22⋊C912yes—
278C8—34no—
279C8C22×C22⋊C914yes—
280C2×C3—22no—
281C2×C3—61no—
282C2×C3—61no—
283C2×C3—62no—
284C2×C3#568⋊C312yes—
285C2×C3C22×C4×A411yescharacteristic
286C22—22no—
287C22—31no—
288C22—32no—
289C22—31no—
290C22—62no—
291C22—62no—
292C22—122no—
293C22—122no—
294C22C2×C4×C22⋊C912yes—
295C22C2×C4×C22⋊C911yescharacteristic
296C4—31no—
297C4—32no—
298C4—31no—
299C4C2×C4×C22⋊C911yescharacteristic
300C4C2×C4×C22⋊C912yes—
301C4C23×C22⋊C911yescharacteristic
302C3C2×#568⋊C311yescharacteristic
303C2—22no—
304C2—61no—
305C2—62no—
306C2—61no—
307C2#568⋊C912yesdirect product factor
308C2C22×C4×C22⋊C911yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutator, hypocenterQ8C22×C4×C9
FrattiniC3×C4C23×A4
FittingC2×C3×#568C3
socleC22×C3C2×C4×A4
prime radicalC22×C3×#41C2×C3
cosocleC3×#41C23×C3
hypercenterC2×C3×M16A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×M16

Complements

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

NH ≅ G/Ntype
2. #568⋊C9C2direct (N × H)
3. C2×#131⋊C9C2semidirect
11. #131⋊C9C22semidirect
27. C2×#568C9semidirect
62. #568C2×C9semidirect
64. C2×#131C2×C9semidirect
131. #131C22×C9semidirect
307. C2#568⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41⋊C92
#568⋊C92
C2×#131⋊C92
C2×C3×#5683
C2×C9×M164