Finite Group Databasebeta

← D4×#41⋊C9 #11919721

Subgroups — D4×#41⋊C9 #11919721

Order 1152.

722 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 121 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⋊C9C212yesmaximal, complemented
2C4⋊(#41⋊C9)C211yesmaximal, characteristic, complemented
3D4×Q8⋊C9C211yesmaximal, characteristic, complemented
4#548⋊C9C212yesmaximal, complemented
5C4×#41⋊C9C211yesmaximal, characteristic, complemented
6C3×D4×#41C311yesmaximal, characteristic
7C2×#41⋊C9—24no—
8C2×#41⋊C9C2211yescharacteristic
9C2×#41⋊C9C2212yescomplemented
10C22×Q8⋊C9C2212yescomplemented
11C4×D4×C9—41nomaximal
12C4×Q8⋊C9C2211yescharacteristic, complemented
13C4×Q8⋊C9C2211yescharacteristic, complemented
14C22×C3×#41C2×C312yes—
15C3×#550C2×C311yescharacteristic
16C3×D4×Q8C2×C311yescharacteristic
17C3×#548C2×C312yes—
18C3×#547—31no—
19C3×#546—32no—
20C3×D42—31no—
21C3×#532—31no—
22C3×#525—32no—
23C3×C4×#41C2×C311yescharacteristic
24C2×C3×C4×D4—31no—
25C2×D4×C9—41no—
26C22×C4×C9—42no—
27#41⋊C9—22no—
28#41⋊C9D412yesdirect product factor
29C2×Q8⋊C9—22no—
30C2×Q8⋊C9C2311yescharacteristic
31C9×C4⋊C4—41no—
32C9×C22⋊C4—42no—
33C42×C9—41no—
34D4×#41C911yescharacteristic, complemented, Sylow
35C2×C3×#41—24no—
36C2×C3×#41—32no—
37C2×C3×#41—32no—
38C2×C3×#41—64no—
39C2×C3×#41C22×C312yes—
40C2×C3×#41C22×C311yescharacteristic
41C22×C3×Q8C22×C312yes—
42C22×C3×D4—32no—
43C22×C3×D4—31no—
44C23×C3×C4—32no—
45C3×C4⋊Q8—31no—
46C3×#127—31no—
47C3×#124—32no—
48C3×#123—34no—
49C3×C22⋊Q8—32no—
50C3×C22⋊Q8—32no—
51C3×#121—32no—
52C3×#121—32no—
53C3×#121—32no—
54C3×#121—32no—
55C3×#120—34no—
56C3×C4×Q8C22×C311yescharacteristic
57C3×C4×Q8C22×C311yescharacteristic
58C3×C4×D4—32no—
59C3×C4×D4—31no—
60C3×C4×D4—32no—
61C3×C4×D4—31no—
62C3×C4×D4—31no—
63C3×C4×D4—31no—
64C3×C4×D4—32no—
65C3×C4×D4—31no—
66C3×C4×D4A411yescharacteristic
67C3×#117—31no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C22⋊C4—32no—
70C2×C3×C42—31no—
71C23×C9—42no—
72D4×C9—44no—
73C2×C4×C9—41no—
74C2×C4×C9—41no—
75C2×C4×C9—42no—
76C2×C4×C9—41no—
77C2×C4×C9—84no—
78Q8⋊C9C2×D411yescharacteristic, complemented
79C22×#41C2×C912yescomplemented
80#550C2×C911yescharacteristic, complemented
81D4×Q8C2×C911yescharacteristic
82#548C2×C912yescomplemented
83#547—31no—
84#546—32no—
85D42—31no—
86#532—31no—
87#525—32no—
88C4×#41C2×C911yescharacteristic, complemented
89C2×C4×D4—31no—
90C24×C3—32no—
91C3×#41—22no—
92C3×#41—32no—
93C3×#41—64no—
94C3×#41—64no—
95C3×#41—64no—
96C3×#41—64no—
97C3×#41—62no—
98C3×#41C3×D412yes—
99C2×C3×Q8—22no—
100C2×C3×Q8—32no—
101C2×C3×Q8—62no—
102C2×C3×Q8C23×C311yescharacteristic
103C2×C3×D4—31no—
104C2×C3×D4—32no—
105C2×C3×D4—34no—
106C2×C3×D4—32no—
107C2×C3×D4—32no—
108C2×C3×D4—31no—
109C2×C3×D4—64no—
110C2×C3×D4—64no—
111C2×C3×D4—64no—
112C2×C3×D4C2×A411yescharacteristic
113C22×C3×C4—31no—
114C22×C3×C4—32no—
115C22×C3×C4—31no—
116C22×C3×C4—32no—
117C22×C3×C4—32no—
118C22×C3×C4—32no—
119C22×C3×C4—31no—
120C22×C3×C4—64no—
121C22×C3×C4—64no—
122C22×C3×C4C2×A412yes—
123C3×C4⋊C4—31no—
124C3×C4⋊C4—31no—
125C3×C4⋊C4—32no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—32no—
128C3×C4⋊C4C2×A411yescharacteristic
129C3×C22⋊C4—32no—
130C3×C22⋊C4—34no—
131C3×C22⋊C4—32no—
132C3×C22⋊C4—32no—
133C3×C22⋊C4—32no—
134C3×C22⋊C4C2×A412yes—
135C3×C42—31no—
136C3×C42—31no—
137C3×C42—31no—
138C3×C42C2×A411yescharacteristic
139C22×C9—44no—
140C22×C9—41no—
141C22×C9—82no—
142C22×C9—82no—
143C4×C9—42no—
144C4×C9—42no—
145C4×C9—81no—
146C4×C9—82no—
147C2×#41—24no—
148C2×#41—32no—
149C2×#41—32no—
150C2×#41—64no—
151C2×#41C22×C912yes—
152C2×#41C22×C911yescharacteristic
153C22×Q8C22×C912yes—
154C22×D4—32no—
155C22×D4—31no—
156C23×C4—32no—
157C4⋊Q8—31no—
158#127—31no—
159#124—32no—
160#123—34no—
161C22⋊Q8—32no—
162C22⋊Q8—32no—
163#121—32no—
164#121—32no—
165#121—32no—
166#121—32no—
167#120—34no—
168C4×Q8C22×C911yescharacteristic
169C4×Q8C22×C911yescharacteristic
170C4×D4—32no—
171C4×D4—31no—
172C4×D4—32no—
173C4×D4—31no—
174C4×D4—31no—
175C4×D4—31no—
176C4×D4—32no—
177C4×D4—31no—
178C4×D4C22⋊C911yescharacteristic
179#117—31no—
180C2×C4⋊C4—31no—
181C2×C22⋊C4—32no—
182C2×C42—31no—
183C23×C3—31no—
184C23×C3—32no—
185C23×C3—64no—
186C23×C3—64no—
187C23×C3—122no—
188C23×C3C22×A412yes—
189C3×Q8—31no—
190C3×Q8—62no—
191C3×Q8—62no—
192C3×Q8C2×C3×D411yescharacteristic
193C3×D4—32no—
194C3×D4—32no—
195C3×D4—62no—
196C3×D4—62no—
197C3×D4—68no—
198C3×D4—64no—
199C3×D4—62no—
200C3×D4—122no—
201C3×D4#41⋊C314yes—
202C2×C3×C4—24no—
203C2×C3×C4—31no—
204C2×C3×C4—32no—
205C2×C3×C4—32no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—32no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4—64no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4—121no—
217C2×C3×C4C22×A411yescharacteristic
218C2×C3×C4C22×A412yes—
219C2×C3×C4C22×A411yescharacteristic
220C2×C3×C4C22×A411yescharacteristic
221C2×C9—41no—
222C2×C9—41no—
223C2×C9—41no—
224C2×C9—84no—
225C24—32no—
226#41—22no—
227#41—32no—
228#41—64no—
229#41—64no—
230#41—64no—
231#41—64no—
232#41—62no—
233#41D4×C912yescomplemented
234C2×Q8—22no—
235C2×Q8—32no—
236C2×Q8—62no—
237C2×Q8C23×C911yescharacteristic
238C2×D4—31no—
239C2×D4—32no—
240C2×D4—34no—
241C2×D4—32no—
242C2×D4—32no—
243C2×D4—31no—
244C2×D4—64no—
245C2×D4—64no—
246C2×D4—64no—
247C2×D4C2×C22⋊C911yescharacteristic
248C22×C4—31no—
249C22×C4—32no—
250C22×C4—31no—
251C22×C4—32no—
252C22×C4—32no—
253C22×C4—32no—
254C22×C4—31no—
255C22×C4—64no—
256C22×C4—64no—
257C22×C4C2×C22⋊C912yes—
258C4⋊C4—31no—
259C4⋊C4—31no—
260C4⋊C4—32no—
261C4⋊C4—31no—
262C4⋊C4—32no—
263C4⋊C4C2×C22⋊C911yescharacteristic
264C22⋊C4—32no—
265C22⋊C4—34no—
266C22⋊C4—32no—
267C22⋊C4—32no—
268C22⋊C4—32no—
269C22⋊C4C2×C22⋊C912yes—
270C42—31no—
271C42—31no—
272C42—31no—
273C42C2×C22⋊C911yescharacteristic
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—32no—
277C22×C3—61no—
278C22×C3—61no—
279C22×C3—62no—
280C22×C3—62no—
281C22×C3—62no—
282C22×C3—128no—
283C22×C3C2×#41⋊C314yes—
284C22×C3C23×A411yescharacteristic
285C3×C4—22no—
286C3×C4—21no—
287C3×C4—31no—
288C3×C4—31no—
289C3×C4—62no—
290C3×C4—61no—
291C3×C4—61no—
292C3×C4D4×A412yes—
293C3×C4C2×#41⋊C312yes—
294C9—41noSylow
295C23—31no—
296C23—32no—
297C23—64no—
298C23—64no—
299C23—122no—
300C23C22×C22⋊C912yes—
301Q8—31no—
302Q8—62no—
303Q8—62no—
304Q8C2×D4×C911yescharacteristic
305D4—32no—
306D4—32no—
307D4—62no—
308D4—62no—
309D4—68no—
310D4—64no—
311D4—62no—
312D4—122no—
313D4#41⋊C914yesdirect product factor
314C2×C4—24no—
315C2×C4—31no—
316C2×C4—32no—
317C2×C4—32no—
318C2×C4—31no—
319C2×C4—31no—
320C2×C4—32no—
321C2×C4—62no—
322C2×C4—62no—
323C2×C4—64no—
324C2×C4—62no—
325C2×C4—62no—
326C2×C4—64no—
327C2×C4—62no—
328C2×C4—121no—
329C2×C4C22×C22⋊C911yescharacteristic
330C2×C4C22×C22⋊C912yes—
331C2×C4C22×C22⋊C911yescharacteristic
332C2×C4C22×C22⋊C911yescharacteristic
333C2×C3—24no—
334C2×C3—62no—
335C2×C3—122no—
336C2×C3C2×D4×A411yescharacteristic
337C2×C3C22×#41⋊C311yescharacteristic
338C2×C3#594511yescharacteristic
339C22—22no—
340C22—22no—
341C22—32no—
342C22—61no—
343C22—61no—
344C22—62no—
345C22—62no—
346C22—62no—
347C22—128no—
348C22C2×#41⋊C914yescomplemented
349C22C23×C22⋊C911yescharacteristic
350C4—22no—
351C4—21no—
352C4—31no—
353C4—31no—
354C4—62no—
355C4—61no—
356C4—61no—
357C4D4×C22⋊C912yes—
358C4C2×#41⋊C912yescomplemented
359C3D4×#41⋊C311yescharacteristic
360C2—24no—
361C2—62no—
362C2—122no—
363C2C2×D4×C22⋊C911yescharacteristic
364C2C22×#41⋊C911yescharacteristic
365C2#1059312011yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutatorC2×Q8C23×C9
Frattini, socleC22×C3C23×A4
Fitting, prime radicalC3×D4×#41C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×C4×D4A4
hypocenterQ8C2×D4×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#41⋊C9C2semidirect
2. C4⋊(#41⋊C9)C2semidirect
3. D4×Q8⋊C9C2semidirect
4. #548⋊C9C2semidirect
5. C4×#41⋊C9C2semidirect
9. C2×#41⋊C9C22semidirect
10. C22×Q8⋊C9C22semidirect
12. C4×Q8⋊C9C22semidirect
13. C4×Q8⋊C9C22semidirect
28. #41⋊C9D4direct (N × H)
34. D4×#41C9semidirect
78. Q8⋊C9C2×D4semidirect
79. C22×#41C2×C9semidirect
80. #550C2×C9semidirect
82. #548C2×C9semidirect
88. C4×#41C2×C9semidirect
233. #41D4×C9semidirect
313. D4#41⋊C9direct (N × H)
348. C22C2×#41⋊C9semidirect
358. C4C2×#41⋊C9semidirect

Maximal subgroups

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

subgroupindex
C22×#41⋊C92
C4⋊(#41⋊C9)2
D4×Q8⋊C92
#548⋊C92
C4×#41⋊C92
C3×D4×#413
C4×D4×C94