Finite Group Databasebeta

← C2×#10589746 #11901276

Subgroups — C2×#10589746 #11901276

Order 1152.

2004 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#63509C212yesmaximal, complemented
3C2×#63492C211yesmaximal, characteristic, complemented
4C22×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
5#10589746C2116yesmaximal, direct product factor
6C2×#63460C212yesmaximal, complemented
7C2×#63457C212yesmaximal, complemented
8C2×#63456C212yesmaximal, complemented
9C2×#63444C212yesmaximal, complemented
10C2×#611⋊C4C212yesmaximal, complemented
11C2×#5644—31nomaximal
12C24×D9C2211yescharacteristic
13C22×Q8×C9C2211yescharacteristic, complemented
14C23×C4×C9C2211yescharacteristic
15C22×#611C2212yes—
16C23×Dic9C2211yescharacteristic
17C22×D36C2212yes—
18C22×D36C2212yes—
19C22×D36C2211yescharacteristic, complemented
20C22×C4×D9C2212yescomplemented
21C9×C22⋊Q8C2218yescomplemented
22C2×C9×C4⋊C4C2211yescharacteristic, complemented
23C2×C9×C4⋊C4C2212yescomplemented
24C2×C9×C22⋊C4C2212yes—
25#63509C22116yescomplemented
26#63492C2218yescomplemented
27C2×(C2×D9)⋊C4C2212yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×(C2×D9)⋊C4C2212yes—
30C2×(C2×D9)⋊C4C2212yes—
31C2×(C2×D9)⋊C4C2218yescomplemented
32C2×(C2×D9)⋊C4C2212yescomplemented
33C2×(C2×D9)⋊C4C2212yescomplemented
34C2×C4⋊Dic9C2211yescharacteristic, complemented
35C2×Dic9⋊C4C2212yescomplemented
36C2×C4×Dic9C2212yescomplemented
37#63460C22116yescomplemented
38#63457C22116yescomplemented
39#63456C22116yescomplemented
40#63444C22116yescomplemented
41#611⋊C4C22116yescomplemented
42C2×C3×C22⋊Q8D311yescharacteristic
43C2×#947—32no—
44C2×#930—31no—
45C22×(C2×D3)⋊C4—31no—
46#5644—316no—
47C2×#898—32no—
48C2×#895—32no—
49C2×#894—32no—
50C2×#882—32no—
51C2×#67⋊C4—32no—
52C24×C9C2311yescharacteristic
53C23×D9—24no—
54C23×D9—42no—
55C23×D9—42no—
56C23×D9C2312yes—
57C23×D9C2312yes—
58C23×D9C2314yes—
59C2×Q8×C9—42no—
60C2×Q8×C9C2314yescomplemented
61C22×C4×C9—42no—
62C22×C4×C9C2311yescharacteristic
63C22×C4×C9C2311yescharacteristic
64C22×C4×C9C2312yes—
65C22×C4×C9C2312yes—
66C22×C4×C9C2314yes—
67C2×#611—28no—
68C2×#611C2318yes—
69C22×Dic9—42no—
70C22×Dic9C2312yes—
71C22×Dic9C2312yes—
72C22×Dic9C2314yes—
73C2×D36—44no—
74C2×D36—44no—
75C2×D36—42no—
76C2×D36C2318yes—
77C2×D36C2318yes—
78C2×D36C2314yescomplemented
79C2×C4×D9—44no—
80C2×C4×D9C2318yescomplemented
81C9×C4⋊C4C2314yescomplemented
82C9×C4⋊C4C2318yescomplemented
83C9×C22⋊C4C2318yes—
84(C2×D9)⋊C4C2318yes—
85(C2×D9)⋊C4C2318yes—
86(C2×D9)⋊C4C2318yes—
87(C2×D9)⋊C4C2318yes—
88(C2×D9)⋊C4C2318yescomplemented
89(C2×D9)⋊C4C2318yescomplemented
90C4⋊Dic9C2314yescomplemented
91Dic9⋊C4C2318yescomplemented
92C4×Dic9C2318yescomplemented
93C2×#538—91noSylow
94C24×D3—31no—
95C22×C3×Q8C2×D311yescharacteristic
96C23×C3×C4C2×D311yescharacteristic
97C22×#67—32no—
98C23×Dic3—31no—
99C22×D12—32no—
100C22×D12—32no—
101C22×D12—31no—
102C22×C4×D3—32no—
103C3×C22⋊Q8C2×D318yes—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C2×D312yes—
106C2×C3×C22⋊C4C2×D312yes—
107#947—316no—
108#930—38no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—38no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×C4⋊Dic3—31no—
117C2×Dic3⋊C4—32no—
118C2×C4×Dic3—32no—
119#898—316no—
120#895—316no—
121#894—316no—
122#882—316no—
123#67⋊C4—316no—
124C23×C9—22no—
125C23×C9—22no—
126C23×C9#4114yes—
127C23×C9C2412yes—
128C23×C9C2411yescharacteristic
129C22×D9—24no—
130C22×D9—28no—
131C22×D9—24no—
132C22×D9—24no—
133C22×D9—24no—
134C22×D9—24no—
135C22×D9—24no—
136C22×D9—44no—
137C22×D9—44no—
138C22×D9—416no—
139C22×D9C2414yes—
140C22×D9C2414yes—
141Q8×C9—44no—
142C2×C4×C9—24no—
143C2×C4×C9—22no—
144C2×C4×C9—24no—
145C2×C4×C9—22no—
146C2×C4×C9—44no—
147C2×C4×C9C2414yes—
148C2×C4×C9C2414yes—
149C2×C4×C9C2412yes—
150C2×C4×C9C2412yes—
151#611—216no—
152C2×Dic9—24no—
153C2×Dic9—24no—
154C2×Dic9—44no—
155C2×Dic9C2414yes—
156C2×Dic9C2414yes—
157D36—48no—
158D36—48no—
159D36—44no—
160C4×D9—48no—
161#538—916no—
162C2×#126—92no—
163C2×#124—92no—
164C2×#123—92no—
165C2×C22⋊Q8D911yescharacteristic, complemented
166C2×#121—91no—
167C2×#121—92no—
168C2×#120—92no—
169C2×C4×D4—92no—
170C22×C22⋊C4—91no—
171C24×C3C22×D311yescharacteristic
172C23×D3—32no—
173C23×D3—32no—
174C23×D3—34no—
175C23×D3—64no—
176C23×D3—122no—
177C23×D3—122no—
178C2×C3×Q8—42no—
179C2×C3×Q8C22×D314yes—
180C22×C3×C4—42no—
181C22×C3×C4C22×D312yes—
182C22×C3×C4C22×D312yes—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D314yes—
186C2×#67—38no—
187C2×#67—68no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—34no—
191C22×Dic3—122no—
192C2×D12—38no—
193C2×D12—38no—
194C2×D12—34no—
195C2×D12—122no—
196C2×D12—124no—
197C2×D12—124no—
198C2×C4×D3—38no—
199C2×C4×D3—124no—
200C3×C4⋊C4C22×D314yes—
201C3×C4⋊C4C22×D318yes—
202C3×C22⋊C4C22×D318yes—
203(C2×D3)⋊C4—38no—
204(C2×D3)⋊C4—38no—
205(C2×D3)⋊C4—38no—
206(C2×D3)⋊C4—38no—
207(C2×D3)⋊C4—38no—
208(C2×D3)⋊C4—38no—
209C4⋊Dic3—34no—
210Dic3⋊C4—38no—
211C4×Dic3—38no—
212C22×C9—28no—
213C22×C9—22no—
214C22×C9—22no—
215C22×C9C2×#4114yes—
216C22×C9C2×#4112yes—
217C22×C9H(5,𝔽2)12yes—
218C22×C9H(5,𝔽2)12yes—
219C22×C9C2511yescharacteristic
220C2×D9—24no—
221C2×D9—24no—
222C2×D9—24no—
223C2×D9—24no—
224C2×D9—24no—
225C2×D9—24no—
226C2×D9—416no—
227C2×D9—48no—
228C2×D9—48no—
229C4×C9—24no—
230C4×C9—22no—
231C4×C9—24no—
232C4×C9—22no—
233Dic9—24no—
234Dic9—24no—
235C25—91no—
236C22×Q8C2×D911yescharacteristic, complemented
237C22×D4—92no—
238C22×D4—92no—
239C22×D4—92no—
240C22×D4—91no—
241C23×C4—91no—
242C23×C4—92no—
243C23×C4C2×D911yescharacteristic
244#126—916no—
245#124—916no—
246#123—916no—
247C22⋊Q8C2×D918yescomplemented
248#121—98no—
249#121—916no—
250#120—916no—
251C4×D4—916no—
252C2×C4⋊C4—92no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4C2×D912yescomplemented
255C2×C4⋊C4C2×D911yescharacteristic, complemented
256C2×C22⋊C4—92no—
257C2×C22⋊C4—92no—
258C2×C22⋊C4—98no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4—92no—
262C2×C22⋊C4—92no—
263C2×C22⋊C4C2×D912yes—
264C2×C42—92no—
265C23×C3—22no—
266C23×C3—22no—
267C23×C3#23914yes—
268C23×C3C23×D312yes—
269C23×C3C23×D311yescharacteristic
270C22×D3—34no—
271C22×D3—34no—
272C22×D3—64no—
273C22×D3—64no—
274C22×D3—64no—
275C22×D3—68no—
276C22×D3—64no—
277C22×D3—64no—
278C22×D3—64no—
279C22×D3—124no—
280C22×D3—124no—
281C22×D3—1216no—
282C3×Q8—44no—
283C2×C3×C4—22no—
284C2×C3×C4—24no—
285C2×C3×C4—22no—
286C2×C3×C4—24no—
287C2×C3×C4—44no—
288C2×C3×C4C23×D314yes—
289C2×C3×C4C23×D314yes—
290C2×C3×C4C23×D312yes—
291C2×C3×C4C23×D312yes—
292#67—616no—
293C2×Dic3—34no—
294C2×Dic3—34no—
295C2×Dic3—64no—
296C2×Dic3—64no—
297C2×Dic3—124no—
298D12—124no—
299D12—128no—
300D12—128no—
301C4×D3—128no—
302C2×C9—24no—
303C2×C9#53814yescomplemented
304C2×C9C22×#4111yescharacteristic
305C2×C9C2×H(5,𝔽2)11yescharacteristic
306C2×C9C2×H(5,𝔽2)11yescharacteristic
307D9—44no—
308D9—44no—
309C24—92no—
310C24—92no—
311C24—94no—
312C24—184no—
313C24—362no—
314C24—362no—
315C24C22×D911yescharacteristic
316C2×Q8—42no—
317C2×Q8C22×D914yescomplemented
318C2×D4—98no—
319C2×D4—98no—
320C2×D4—98no—
321C2×D4—94no—
322C2×D4—188no—
323C2×D4—362no—
324C2×D4—364no—
325C2×D4—364no—
326C22×C4—42no—
327C22×C4—92no—
328C22×C4—92no—
329C22×C4—94no—
330C22×C4—98no—
331C22×C4—364no—
332C22×C4—362no—
333C22×C4C22×D912yes—
334C22×C4C22×D911yescharacteristic
335C22×C4C22×D911yescharacteristic
336C22×C4C22×D912yes—
337C22×C4C22×D914yes—
338C4⋊C4—98no—
339C4⋊C4—94no—
340C4⋊C4C22×D918yescomplemented
341C4⋊C4C22×D914yescomplemented
342C22⋊C4—98no—
343C22⋊C4—98no—
344C22⋊C4—98no—
345C22⋊C4—98no—
346C22⋊C4—98no—
347C22⋊C4—98no—
348C22⋊C4C22×D918yes—
349C42—98no—
350C22×C3—28no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3#100412yes—
354C22×C3C2×#23914yes—
355C22×C3C2×#23912yes—
356C22×C3#100912yes—
357C22×C3C24×D311yescharacteristic
358C2×D3—64no—
359C2×D3—64no—
360C2×D3—64no—
361C2×D3—64no—
362C2×D3—64no—
363C2×D3—64no—
364C2×D3—1216no—
365C2×D3—128no—
366C2×D3—128no—
367C3×C4—22no—
368C3×C4—24no—
369C3×C4—22no—
370C3×C4—24no—
371Dic3—64no—
372Dic3—64no—
373C9C2×#53811yescharacteristic, complemented, Sylow
374C23—22no—
375C23—22no—
376C23—94no—
377C23—94no—
378C23—184no—
379C23—184no—
380C23—184no—
381C23—188no—
382C23—184no—
383C23—184no—
384C23—184no—
385C23—364no—
386C23—364no—
387C23—3616no—
388C23#370114yes—
389C23C23×D912yes—
390C23C23×D911yescharacteristic
391Q8—44no—
392D4—1816no—
393D4—364no—
394D4—368no—
395D4—368no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—44no—
401C2×C4—94no—
402C2×C4—94no—
403C2×C4—184no—
404C2×C4—184no—
405C2×C4—368no—
406C2×C4—364no—
407C2×C4C23×D914yes—
408C2×C4C23×D912yes—
409C2×C4C23×D912yes—
410C2×C4C23×D914yes—
411C2×C3—24no—
412C2×C3#564414yes—
413C2×C3C2×#100411yescharacteristic
414C2×C3C22×#23911yescharacteristic
415C2×C3C2×#100911yescharacteristic
416D3—124no—
417D3—124no—
418C22—28no—
419C22—22no—
420C22—22no—
421C22—184no—
422C22—184no—
423C22—184no—
424C22—184no—
425C22—184no—
426C22—184no—
427C22—3616no—
428C22—368no—
429C22—368no—
430C22#6371012yes—
431C22C2×#370114yes—
432C22C2×#370112yes—
433C22#6371512yes—
434C22C24×D911yescharacteristic
435C4—22no—
436C4—22no—
437C4—24no—
438C4—24no—
439C4—184no—
440C4—184no—
441C3C2×#564411yescharacteristic
442C2—24no—
443C2—364no—
444C2—364no—
445C2#1058974614yesdirect product factor
446C2C2×#6371011yescharacteristic
447C2C22×#370111yescharacteristic
448C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×C22⋊Q8C2
socleC23×C3C23×D3
hypercenterC2×C22⋊Q8D9
hypocenterC9C2×#538
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C9×C22⋊Q8C2semidirect
2. C2×#63509C2semidirect
3. C2×#63492C2semidirect
4. C22×(C2×D9)⋊C4C2semidirect
5. #10589746C2direct (N × H)
6. C2×#63460C2semidirect
7. C2×#63457C2semidirect
8. C2×#63456C2semidirect
9. C2×#63444C2semidirect
10. C2×#611⋊C4C2semidirect
13. C22×Q8×C9C22semidirect
19. C22×D36C22semidirect
20. C22×C4×D9C22semidirect
21. C9×C22⋊Q8C22semidirect
22. C2×C9×C4⋊C4C22semidirect
23. C2×C9×C4⋊C4C22semidirect
25. #63509C22semidirect
26. #63492C22semidirect
31. C2×(C2×D9)⋊C4C22semidirect
32. C2×(C2×D9)⋊C4C22semidirect
33. C2×(C2×D9)⋊C4C22semidirect
34. C2×C4⋊Dic9C22semidirect
35. C2×Dic9⋊C4C22semidirect
36. C2×C4×Dic9C22semidirect
37. #63460C22semidirect
38. #63457C22semidirect
39. #63456C22semidirect
40. #63444C22semidirect
41. #611⋊C4C22semidirect
60. C2×Q8×C9C23semidirect
78. C2×D36C23semidirect
80. C2×C4×D9C23semidirect
81. C9×C4⋊C4C23semidirect
82. C9×C4⋊C4C23semidirect
88. (C2×D9)⋊C4C23semidirect
89. (C2×D9)⋊C4C23semidirect
90. C4⋊Dic9C23semidirect
91. Dic9⋊C4C23semidirect
92. C4×Dic9C23semidirect
165. C2×C22⋊Q8D9semidirect
236. C22×Q8C2×D9semidirect
247. C22⋊Q8C2×D9semidirect
254. C2×C4⋊C4C2×D9semidirect
255. C2×C4⋊C4C2×D9semidirect
303. C2×C9#538semidirect
317. C2×Q8C22×D9semidirect
340. C4⋊C4C22×D9semidirect
341. C4⋊C4C22×D9semidirect
373. C9C2×#538semidirect
445. C2#10589746direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×C22⋊Q82
C2×#635092
C2×#634922
C22×(C2×D9)⋊C42
#105897462
C2×#634602
C2×#634572
C2×#634562
C2×#634442
C2×#611⋊C42
C2×#56443