Finite Group Databasebeta

← C2×#10589609 #11902495

Subgroups — C2×#10589609 #11902495

Order 1152.

2448 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3697C212yesmaximal, complemented
2C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#63492C211yesmaximal, characteristic, complemented
4C2×#63491C212yesmaximal, complemented
5C2×C4×#611C211yesmaximal, characteristic, complemented
6C2×#63458C212yesmaximal, complemented
7#10589609C2116yesmaximal, direct product factor
8C2×#63457C211yesmaximal, characteristic, complemented
9C2×#63456C212yesmaximal, complemented
10C2×#63455C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
12C2×#63450C211yesmaximal, characteristic, complemented
13C2×#5507—31nomaximal
14C23×C4×C9C2212yes—
15C23×C4×C9C2211yescharacteristic
16C22×#611C2212yes—
17C22×#611C2211yescharacteristic
18C2×#3697—216no—
19C2×#3697C22116yescomplemented
20C22×D36C2212yes—
21C22×D36C2211yescharacteristic
22C22×C4×D9C2212yes—
23C22×C4×D9C2212yes—
24C22×C4×D9C2211yescharacteristic
25C22×Dic18C2212yes—
26C2×C9×C4⋊C4C2211yescharacteristic
27C2×C9×C4⋊C4C2211yescharacteristic
28C2×C9×C4⋊C4C2212yes—
29C2×C9×C4⋊C4C2218yescomplemented
30C2×#3676C2211yescharacteristic
31#63492C2218yescomplemented
32#63491C22116yescomplemented
33C4×#611C2218yescomplemented
34C2×(C2×D9)⋊C4C2212yes—
35C2×(C2×D9)⋊C4C2211yescharacteristic
36C2×(C2×D9)⋊C4C2212yes—
37C2×(C2×D9)⋊C4C2212yes—
38C2×C4⋊Dic9C2211yescharacteristic
39C2×Dic9⋊C4C2212yes—
40C2×Dic9⋊C4C2212yes—
41C2×Dic9⋊C4C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43#63458C22116yescomplemented
44#63457C2218yescomplemented
45#63456C22116yescomplemented
46#63455C2218yescomplemented
47C4⋊C4×D9C2218yescomplemented
48#63450C2218yescomplemented
49C22×#235—32no—
50C22×C3×C4⋊C4D311yescharacteristic
51C2×#930—31no—
52C2×#929—32no—
53C2×C4×#67—31no—
54C2×#896—32no—
55#5507—316no—
56C2×#895—31no—
57C2×#894—32no—
58C2×#893—31no—
59C2×D3×C4⋊C4—31no—
60C2×#888—31no—
61C24×C9C2311yescharacteristic
62C23×D9C2312yes—
63C23×D9C2311yescharacteristic
64C22×C4×C9—28no—
65C22×C4×C9—24no—
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2312yes—
68C22×C4×C9C2312yes—
69C22×C4×C9C2314yes—
70C22×C4×C9C2318yes—
71C22×C4×C9C2311yescharacteristic
72C2×#611—28no—
73C2×#611D418yescomplemented
74C2×#611C2318yes—
75C2×#611C2314yes—
76C22×Dic9C2311yescharacteristic
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2312yes—
79C22×Dic9C2311yescharacteristic
80#3697—264no—
81C2×D36—28no—
82C2×D36—24no—
83C2×D36C2314yes—
84C2×D36C2318yes—
85C2×C4×D9—28no—
86C2×C4×D9—24no—
87C2×C4×D9—28no—
88C2×C4×D9C2314yes—
89C2×C4×D9C2318yes—
90C2×C4×D9C2318yes—
91C2×Dic18—28no—
92C2×Dic18C2318yes—
93C9×C4⋊C4C2314yes—
94C9×C4⋊C4C2314yes—
95C9×C4⋊C4C2318yes—
96#3676C2314yes—
97(C2×D9)⋊C4C2314yes—
98(C2×D9)⋊C4C2318yes—
99(C2×D9)⋊C4C2318yes—
100(C2×D9)⋊C4C2318yes—
101C4⋊Dic9C2314yes—
102Dic9⋊C4C2314yes—
103Dic9⋊C4C2318yes—
104Dic9⋊C4C2318yes—
105C4×Dic9C2314yes—
106C2×#547—91noSylow
107C23×C3×C4C2×D312yes—
108C23×C3×C4C2×D311yescharacteristic
109C22×#67—31no—
110C22×#67—32no—
111C2×#235—316no—
112C2×#235—616no—
113C22×D12—32no—
114C22×D12—31no—
115C22×C4×D3—32no—
116C22×C4×D3—32no—
117C22×C4×D3—31no—
118C22×Dic6—32no—
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C4⋊C4C2×D312yes—
122C2×C3×C4⋊C4C2×D318yes—
123C2×#217—31no—
124#930—38no—
125#929—316no—
126C4×#67—38no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×C4⋊Dic3—31no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—31no—
135C2×C4×Dic3—31no—
136#896—316no—
137#895—38no—
138#894—316no—
139#893—38no—
140D3×C4⋊C4—38no—
141#888—38no—
142C23×C9—22no—
143C23×C9—22no—
144C23×C9C2×D414yes—
145C23×C9C2412yes—
146C23×C9C2411yescharacteristic
147C22×D9—22no—
148C22×D9—22no—
149C22×D9—24no—
150C22×D9—24no—
151C22×D9—24no—
152C22×D9C2×D414yes—
153C22×D9C2414yes—
154C22×D9C2412yes—
155C2×C4×C9—24no—
156C2×C4×C9—24no—
157C2×C4×C9—216no—
158C2×C4×C9—22no—
159C2×C4×C9—28no—
160C2×C4×C9#4114yescomplemented
161C2×C4×C9C2412yes—
162C2×C4×C9C2414yes—
163C2×C4×C9C2414yes—
164C2×C4×C9C2412yes—
165#611—216no—
166#611C2×D4116yescomplemented
167C2×Dic9—24no—
168C2×Dic9—22no—
169C2×Dic9—22no—
170C2×Dic9C2×D414yes—
171C2×Dic9C2412yes—
172C2×Dic9C2412yes—
173C2×Dic9C2414yes—
174C2×Dic9C2412yes—
175D36—216no—
176D36—28no—
177C4×D9—216no—
178C4×D9—28no—
179C4×D9—216no—
180Dic18—216no—
181C22×#41—92no—
182#547—916no—
183C2×C4⋊Q8—91no—
184C2×#123—92no—
185C2×#123—92no—
186C2×C22⋊Q8—92no—
187C2×#121—91no—
188C2×#121—91no—
189C2×C4×D4—91no—
190C2×C4×D4—91no—
191C22×C4⋊C4—91no—
192C22×C4⋊C4D911yescharacteristic, complemented
193C24×C3C22×D311yescharacteristic
194C23×D3—31no—
195C23×D3—32no—
196C22×C3×C4—28no—
197C22×C3×C4—24no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D314yes—
202C22×C3×C4C22×D318yes—
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—38no—
205C2×#67—34no—
206C2×#67—38no—
207C2×#67—68no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—32no—
212#235—664no—
213C2×D12—34no—
214C2×D12—38no—
215C2×D12—68no—
216C2×D12—64no—
217C2×C4×D3—38no—
218C2×C4×D3—34no—
219C2×C4×D3—38no—
220C2×C4×D3—68no—
221C2×C4×D3—68no—
222C2×C4×D3—64no—
223C2×Dic6—38no—
224C2×Dic6—68no—
225C3×C4⋊C4C22×D314yes—
226C3×C4⋊C4C22×D314yes—
227C3×C4⋊C4C22×D318yes—
228#217—34no—
229(C2×D3)⋊C4—38no—
230(C2×D3)⋊C4—34no—
231(C2×D3)⋊C4—38no—
232(C2×D3)⋊C4—38no—
233C4⋊Dic3—34no—
234Dic3⋊C4—38no—
235Dic3⋊C4—38no—
236Dic3⋊C4—34no—
237C4×Dic3—34no—
238C22×C9—28no—
239C22×C9—22no—
240C22×C9—22no—
241C22×C9C22×D414yes—
242C22×C9C22×D412yes—
243C22×C9C2×#4112yes—
244C22×C92−1+412yes—
245C22×C9C2511yescharacteristic
246C2×D9—28no—
247C2×D9—22no—
248C2×D9—22no—
249C2×D9—24no—
250C2×D9—24no—
251C2×D9—24no—
252C2×D9—48no—
253C2×D9C22×D414yes—
254C4×C9—24no—
255C4×C9—24no—
256C4×C9—22no—
257C4×C9C2×#4114yescomplemented
258Dic9—24no—
259Dic9—22no—
260Dic9—22no—
261Dic9C22×D414yes—
262C2×#41—916no—
263C2×#41—1816no—
264C22×Q8—92no—
265C22×D4—91no—
266C22×D4—92no—
267C22×D4—91no—
268C22×D4—92no—
269C23×C4—91no—
270C23×C4—92no—
271C23×C4—92no—
272C23×C4C2×D911yescharacteristic
273C23×C4C2×D912yes—
274C4⋊Q8—98no—
275#123—916no—
276#123—916no—
277C22⋊Q8—916no—
278#121—98no—
279#121—98no—
280C4×D4—98no—
281C4×D4—98no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—92no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—92no—
286C2×C4⋊C4—98no—
287C2×C4⋊C4C2×D911yescharacteristic
288C2×C4⋊C4C2×D911yescharacteristic
289C2×C4⋊C4C2×D912yes—
290C2×C4⋊C4C2×D918yescomplemented
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—92no—
294C2×C22⋊C4—92no—
295C2×C22⋊C4—92no—
296C2×C42—91no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3D3×D414yes—
300C23×C3C23×D312yes—
301C23×C3C23×D311yescharacteristic
302C22×D3—34no—
303C22×D3—32no—
304C22×D3—34no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—64no—
308C22×D3—64no—
309C22×D3—64no—
310C2×C3×C4—22no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—216no—
314C2×C3×C4—28no—
315C2×C3×C4#23514yes—
316C2×C3×C4C23×D312yes—
317C2×C3×C4C23×D314yes—
318C2×C3×C4C23×D314yes—
319C2×C3×C4C23×D312yes—
320#67—316no—
321#67—616no—
322C2×Dic3—34no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—34no—
327C2×Dic3—62no—
328C2×Dic3—64no—
329C2×Dic3—62no—
330D12—616no—
331D12—68no—
332C4×D3—616no—
333C4×D3—616no—
334C4×D3—68no—
335Dic6—616no—
336C2×C9—24no—
337C2×C9#54714yescomplemented
338C2×C9C23×D411yescharacteristic
339C2×C9C22×#4111yescharacteristic
340C2×C9C2×2−1+411yescharacteristic
341D9—24no—
342D9—44no—
343C24—91no—
344C24—92no—
345C24C22×D911yescharacteristic
346#41—1864no—
347C2×Q8—98no—
348C2×Q8—188no—
349C2×D4—98no—
350C2×D4—94no—
351C2×D4—98no—
352C2×D4—94no—
353C2×D4—98no—
354C2×D4—188no—
355C2×D4—188no—
356C2×D4—184no—
357C22×C4—28no—
358C22×C4—24no—
359C22×C4—91no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—92no—
363C22×C4—94no—
364C22×C4—98no—
365C22×C4—98no—
366C22×C4—188no—
367C22×C4—188no—
368C22×C4—184no—
369C22×C4C22×D914yes—
370C22×C4C22×D918yes—
371C22×C4C22×D911yescharacteristic
372C22×C4C22×D912yes—
373C22×C4C22×D912yes—
374C22×C4C22×D911yescharacteristic
375C4⋊C4—94no—
376C4⋊C4—98no—
377C4⋊C4—94no—
378C4⋊C4—98no—
379C4⋊C4C22×D914yes—
380C4⋊C4C22×D914yes—
381C4⋊C4C22×D918yes—
382C22⋊C4—94no—
383C22⋊C4—94no—
384C22⋊C4—98no—
385C22⋊C4—98no—
386C22⋊C4—98no—
387C42—94no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—28no—
391C22×C3C2×#23512yes—
392C22×C3C2×D3×D414yes—
393C22×C3C2×D3×D412yes—
394C22×C3#100712yes—
395C22×C3C24×D311yescharacteristic
396C2×D3—34no—
397C2×D3—62no—
398C2×D3—62no—
399C2×D3—68no—
400C2×D3—64no—
401C2×D3—64no—
402C2×D3—64no—
403C2×D3—128no—
404C3×C4—22no—
405C3×C4—24no—
406C3×C4—24no—
407C3×C4C2×#23514yes—
408Dic3—34no—
409Dic3—62no—
410Dic3—64no—
411Dic3—62no—
412C9C2×#54711yescharacteristic, complemented, Sylow
413C23—22no—
414C23—22no—
415C23—92no—
416C23—94no—
417C23—94no—
418C23—182no—
419C23—182no—
420C23—184no—
421C23—184no—
422C23—184no—
423C23D4×D914yes—
424C23C23×D912yes—
425C23C23×D911yescharacteristic
426Q8—1816no—
427D4—916no—
428D4—1816no—
429D4—1816no—
430D4—188no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—216no—
435C2×C4—28no—
436C2×C4—92no—
437C2×C4—94no—
438C2×C4—92no—
439C2×C4—92no—
440C2×C4—94no—
441C2×C4—1816no—
442C2×C4—1816no—
443C2×C4—182no—
444C2×C4—184no—
445C2×C4—182no—
446C2×C4—188no—
447C2×C4#369714yescomplemented
448C2×C4C23×D912yes—
449C2×C4C23×D914yes—
450C2×C4C23×D914yes—
451C2×C4C23×D912yes—
452C2×C3—24no—
453C2×C3#550714yes—
454C2×C3C22×#23511yescharacteristic
455C2×C3C22×D3×D411yescharacteristic
456C2×C3C2×#100711yescharacteristic
457D3—64no—
458D3—124no—
459C22—22no—
460C22—22no—
461C22—28no—
462C22—94no—
463C22—182no—
464C22—182no—
465C22—188no—
466C22—184no—
467C22—184no—
468C22—184no—
469C22—368no—
470C22C2×#369712yes—
471C22C2×D4×D914yes—
472C22C2×D4×D912yes—
473C22#6371312yes—
474C22C24×D911yescharacteristic
475C4—22no—
476C4—24no—
477C4—24no—
478C4—94no—
479C4—182no—
480C4—184no—
481C4—182no—
482C4C2×#369714yescomplemented
483C3C2×#550711yescharacteristic
484C2—24no—
485C2—184no—
486C2—364no—
487C2#1058960914yesdirect product factor
488C2C22×#369711yescharacteristic
489C2C22×D4×D911yescharacteristic
490C2C2×#6371311yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC22×C9×C4⋊C4C2
socleC23×C3C23×D3
hypercenterC22×C4⋊C4D9
hypocenterC9C2×#547
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3697C2semidirect
2. C22×C9×C4⋊C4C2semidirect
3. C2×#63492C2semidirect
4. C2×#63491C2semidirect
5. C2×C4×#611C2semidirect
6. C2×#63458C2semidirect
7. #10589609C2direct (N × H)
8. C2×#63457C2semidirect
9. C2×#63456C2semidirect
10. C2×#63455C2semidirect
11. C2×C4⋊C4×D9C2semidirect
12. C2×#63450C2semidirect
19. C2×#3697C22semidirect
29. C2×C9×C4⋊C4C22semidirect
31. #63492C22semidirect
32. #63491C22semidirect
33. C4×#611C22semidirect
43. #63458C22semidirect
44. #63457C22semidirect
45. #63456C22semidirect
46. #63455C22semidirect
47. C4⋊C4×D9C22semidirect
48. #63450C22semidirect
73. C2×#611D4semidirect
160. C2×C4×C9#41semidirect
166. #611C2×D4semidirect
192. C22×C4⋊C4D9semidirect
257. C4×C9C2×#41semidirect
290. C2×C4⋊C4C2×D9semidirect
337. C2×C9#547semidirect
412. C9C2×#547semidirect
447. C2×C4#3697semidirect
482. C4C2×#3697semidirect
487. C2#10589609direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36972
C22×C9×C4⋊C42
C2×#634922
C2×#634912
C2×C4×#6112
C2×#634582
#105896092
C2×#634572
C2×#634562
C2×#634552
C2×C4⋊C4×D92
C2×#634502
C2×#55073