Finite Group Databasebeta

← C2×#548⋊C9 #11919715

Subgroups — C2×#548⋊C9 #11919715

Order 1152.

757 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 757 conjugacy classes of subgroups — too many to draw. Only its 133 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, complemented
2C23×Q8⋊C9C211yesmaximal, characteristic, complemented
3#548⋊C9C214yesmaximal, direct product factor
4C2×C4×Q8⋊C9C211yesmaximal, characteristic, complemented
5C2×C3×#548C311yesmaximal, characteristic
6C2×#41⋊C9—22no—
7C2×#41⋊C9C2212yescomplemented
8C22×Q8⋊C9—22no—
9C22×Q8⋊C9C2211yescharacteristic
10C22×Q8⋊C9C2212yescomplemented
11C2×C9×C22⋊C4—41nomaximal
12C4×Q8⋊C9C2212yescomplemented
13C22×C3×#41C2×C311yescharacteristic
14C23×C3×Q8C2×C311yescharacteristic
15C3×#548—34no—
16C3×#548C2×C314yes—
17C2×C3×#124—31no—
18C2×C3×C22⋊Q8—31no—
19C2×C3×#121—31no—
20C2×C3×C4×Q8C2×C311yescharacteristic
21C2×C3×C4×D4—31no—
22C24×C9—41no—
23C22×C4×C9—41no—
24C22×C4×C9—41no—
25#41⋊C9—22no—
26C2×Q8⋊C9—22no—
27C2×Q8⋊C9D412yescomplemented
28C2×Q8⋊C9C2311yescharacteristic
29C9×C22⋊C4—44no—
30C2×#548C911yescharacteristic, complemented, Sylow
31C2×C3×#41—22no—
32C2×C3×#41—32no—
33C2×C3×#41—62no—
34C2×C3×#41C22×C312yes—
35C22×C3×Q8—22no—
36C22×C3×Q8—31no—
37C22×C3×Q8—32no—
38C22×C3×Q8—62no—
39C22×C3×Q8C22×C312yes—
40C22×C3×Q8C22×C311yescharacteristic
41C22×C3×D4—31no—
42C22×C3×D4—31no—
43C23×C3×C4—31no—
44C23×C3×C4—31no—
45C3×#124—34no—
46C3×#124—34no—
47C3×C22⋊Q8—34no—
48C3×C22⋊Q8—34no—
49C3×#121—34no—
50C3×#121—34no—
51C3×C4×Q8—32no—
52C3×C4×Q8C22×C312yes—
53C3×C4×D4—34no—
54C3×C4×D4—34no—
55C2×C3×C4⋊C4—31no—
56C2×C3×C4⋊C4—31no—
57C2×C3×C22⋊C4—32no—
58C2×C3×C22⋊C4—31no—
59C2×C3×C22⋊C4A411yescharacteristic
60C2×C3×C42—31no—
61C23×C9—44no—
62C23×C9—42no—
63C23×C9—41no—
64C23×C9—82no—
65C23×C9—82no—
66C2×C4×C9—42no—
67C2×C4×C9—42no—
68C2×C4×C9—82no—
69C2×C4×C9—82no—
70Q8⋊C9C2×D411yescharacteristic, complemented
71C22×#41C2×C911yescharacteristic, complemented
72C23×Q8C2×C911yescharacteristic
73#548—34no—
74#548C2×C914yescomplemented
75C2×#124—31no—
76C2×C22⋊Q8—31no—
77C2×#121—31no—
78C2×C4×Q8C2×C911yescharacteristic, complemented
79C2×C4×D4—31no—
80C24×C3—31no—
81C24×C3C2×A411yescharacteristic
82C3×#41—22no—
83C3×#41—64no—
84C3×#41—64no—
85C3×#41—62no—
86C2×C3×Q8—22no—
87C2×C3×Q8—32no—
88C2×C3×Q8—31no—
89C2×C3×Q8—32no—
90C2×C3×Q8—32no—
91C2×C3×Q8—62no—
92C2×C3×Q8—62no—
93C2×C3×Q8—64no—
94C2×C3×Q8—62no—
95C2×C3×Q8—64no—
96C2×C3×Q8C3×D412yes—
97C2×C3×Q8C23×C311yescharacteristic
98C2×C3×D4—32no—
99C2×C3×D4—32no—
100C2×C3×D4—34no—
101C2×C3×D4—62no—
102C2×C3×D4—62no—
103C2×C3×D4—64no—
104C22×C3×C4—31no—
105C22×C3×C4—32no—
106C22×C3×C4—32no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—32no—
110C22×C3×C4—32no—
111C22×C3×C4—62no—
112C22×C3×C4—62no—
113C22×C3×C4—62no—
114C22×C3×C4—62no—
115C22×C3×C4C2×A411yescharacteristic
116C22×C3×C4C2×A411yescharacteristic
117C3×C4⋊C4—32no—
118C3×C4⋊C4—32no—
119C3×C4⋊C4—34no—
120C3×C22⋊C4—38no—
121C3×C22⋊C4—34no—
122C3×C22⋊C4C2×A414yes—
123C3×C42—32no—
124C3×C42—32no—
125C22×C9—42no—
126C22×C9—42no—
127C22×C9—44no—
128C22×C9—42no—
129C22×C9—41no—
130C22×C9—82no—
131C22×C9—82no—
132C22×C9—88no—
133C4×C9—82no—
134C4×C9—82no—
135C2×#41—22no—
136C2×#41—32no—
137C2×#41—62no—
138C2×#41C22×C912yescomplemented
139C22×Q8—22no—
140C22×Q8—31no—
141C22×Q8—32no—
142C22×Q8—62no—
143C22×Q8C22×C912yes—
144C22×Q8C22×C911yescharacteristic
145C22×D4—31no—
146C22×D4—31no—
147C23×C4—31no—
148C23×C4—31no—
149#124—34no—
150#124—34no—
151C22⋊Q8—34no—
152C22⋊Q8—34no—
153#121—34no—
154#121—34no—
155C4×Q8—32no—
156C4×Q8C22×C912yescomplemented
157C4×D4—34no—
158C4×D4—34no—
159C2×C4⋊C4—31no—
160C2×C4⋊C4—31no—
161C2×C22⋊C4—32no—
162C2×C22⋊C4—31no—
163C2×C22⋊C4C22⋊C911yescharacteristic
164C2×C42—31no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—32no—
168C23×C3—62no—
169C23×C3—62no—
170C23×C3—62no—
171C23×C3#41⋊C314yes—
172C23×C3C22×A412yes—
173C23×C3C22×A411yescharacteristic
174C3×Q8—32no—
175C3×Q8—31no—
176C3×Q8—32no—
177C3×Q8—62no—
178C3×Q8—62no—
179C3×Q8—64no—
180C3×Q8C2×C3×D411yescharacteristic
181C3×D4—62no—
182C3×D4—62no—
183C3×D4—64no—
184C3×D4—68no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—32no—
188C2×C3×C4—32no—
189C2×C3×C4—31no—
190C2×C3×C4—31no—
191C2×C3×C4—32no—
192C2×C3×C4—32no—
193C2×C3×C4—62no—
194C2×C3×C4—64no—
195C2×C3×C4—62no—
196C2×C3×C4—62no—
197C2×C3×C4—64no—
198C2×C3×C4—62no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4C22×A412yes—
202C2×C3×C4C22×A412yes—
203C2×C9—41no—
204C2×C9—41no—
205C2×C9—41no—
206C2×C9—44no—
207C2×C9—84no—
208C24—31no—
209C24C2×C22⋊C911yescharacteristic
210#41—22no—
211#41—64no—
212#41—64no—
213#41—62no—
214C2×Q8—22no—
215C2×Q8—32no—
216C2×Q8—31no—
217C2×Q8—32no—
218C2×Q8—32no—
219C2×Q8—62no—
220C2×Q8—62no—
221C2×Q8—64no—
222C2×Q8—62no—
223C2×Q8—64no—
224C2×Q8D4×C912yes—
225C2×Q8C23×C911yescharacteristic
226C2×D4—32no—
227C2×D4—32no—
228C2×D4—34no—
229C2×D4—62no—
230C2×D4—62no—
231C2×D4—64no—
232C22×C4—31no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—32no—
236C22×C4—32no—
237C22×C4—32no—
238C22×C4—32no—
239C22×C4—62no—
240C22×C4—62no—
241C22×C4—62no—
242C22×C4—62no—
243C22×C4C2×C22⋊C911yescharacteristic
244C22×C4C2×C22⋊C911yescharacteristic
245C4⋊C4—32no—
246C4⋊C4—32no—
247C4⋊C4—34no—
248C22⋊C4—38no—
249C22⋊C4—34no—
250C22⋊C4C2×C22⋊C914yes—
251C42—32no—
252C42—32no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—28no—
256C22×C3—62no—
257C22×C3—62no—
258C22×C3—62no—
259C22×C3—124no—
260C22×C3D4×A412yes—
261C22×C3C2×#41⋊C312yes—
262C22×C3C2×#41⋊C314yes—
263C22×C32−1+4⋊C312yes—
264C22×C3C23×A411yescharacteristic
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—31no—
268C3×C4—32no—
269C3×C4—31no—
270C3×C4—62no—
271C3×C4—62no—
272C9—41noSylow
273C23—22no—
274C23—22no—
275C23—32no—
276C23—62no—
277C23—62no—
278C23—62no—
279C23#41⋊C914yescomplemented
280C23C22×C22⋊C912yes—
281C23C22×C22⋊C911yescharacteristic
282Q8—32no—
283Q8—31no—
284Q8—32no—
285Q8—62no—
286Q8—62no—
287Q8—64no—
288Q8C2×D4×C911yescharacteristic
289D4—62no—
290D4—62no—
291D4—64no—
292D4—68no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—32no—
298C2×C4—32no—
299C2×C4—32no—
300C2×C4—32no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4—64no—
304C2×C4—62no—
305C2×C4—62no—
306C2×C4—64no—
307C2×C4—62no—
308C2×C4—62no—
309C2×C4C22×C22⋊C912yes—
310C2×C4C22×C22⋊C912yes—
311C2×C3—24no—
312C2×C3—122no—
313C2×C3#548⋊C314yes—
314C2×C3C2×D4×A411yescharacteristic
315C2×C3C22×#41⋊C311yescharacteristic
316C2×C3C2×2−1+4⋊C311yescharacteristic
317C22—22no—
318C22—22no—
319C22—28no—
320C22—62no—
321C22—62no—
322C22—62no—
323C22—124no—
324C22D4×C22⋊C912yes—
325C22C2×#41⋊C912yes—
326C22C2×#41⋊C914yescomplemented
327C222−1+4⋊C912yes—
328C22C23×C22⋊C911yescharacteristic
329C4—22no—
330C4—22no—
331C4—31no—
332C4—31no—
333C4—32no—
334C4—62no—
335C4—62no—
336C3C2×#548⋊C311yescharacteristic
337C2—24no—
338C2—122no—
339C2#548⋊C914yesdirect product factor
340C2C2×D4×C22⋊C911yescharacteristic
341C2C22×#41⋊C911yescharacteristic
342C2C2×2−1+4⋊C911yescharacteristic
subgroupG/H
center, socleC23×C3C22×A4
commutatorC2×Q8C23×C9
FrattiniC22×C3C23×A4
Fitting, prime radicalC2×C3×#548C3
cosocleC2×C3×Q8C23×C3
hypercenterC2×C3×C22⋊C4A4
hypocenterQ8C2×D4×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#41⋊C9C2semidirect
2. C23×Q8⋊C9C2semidirect
3. #548⋊C9C2direct (N × H)
4. C2×C4×Q8⋊C9C2semidirect
7. C2×#41⋊C9C22semidirect
10. C22×Q8⋊C9C22semidirect
12. C4×Q8⋊C9C22semidirect
27. C2×Q8⋊C9D4semidirect
30. C2×#548C9semidirect
70. Q8⋊C9C2×D4semidirect
71. C22×#41C2×C9semidirect
74. #548C2×C9semidirect
78. C2×C4×Q8C2×C9semidirect
138. C2×#41C22×C9semidirect
156. C4×Q8C22×C9semidirect
279. C23#41⋊C9semidirect
326. C22C2×#41⋊C9semidirect
339. C2#548⋊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
C23×Q8⋊C92
#548⋊C92
C2×C4×Q8⋊C92
C2×C3×#5483
C2×C9×C22⋊C44