Finite Group Databasebeta

← C2×#10589654 #11902580

Subgroups — C2×#10589654 #11902580

Order 1152.

2430 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3697C211yesmaximal, characteristic, complemented
2C23×Dic18C211yesmaximal, characteristic, complemented
3C2×C4×D4×C9C211yesmaximal, characteristic, complemented
4C2×#63501C212yesmaximal, complemented
5C2×#63492C211yesmaximal, characteristic, complemented
6C2×#63486C211yesmaximal, characteristic, complemented
7#10589654C2116yesmaximal, direct product factor
8C2×#63458C212yesmaximal, complemented
9C2×#63447C212yesmaximal, complemented
10C2×#611⋊C4C212yesmaximal, complemented
11C2×#63437C211yesmaximal, characteristic, complemented
12C2×C4×Dic18C211yesmaximal, characteristic, complemented
13C2×#5552—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2211yescharacteristic
16C23×C4×C9C2211yescharacteristic
17C22×#611C2212yes—
18C22×#611C2212yes—
19C23×Dic9C2212yes—
20C2×#3697—28no—
21C2×#3697C2218yescomplemented
22C22×D36C2211yescharacteristic
23C22×C4×D9C2212yes—
24C22×Dic18—28no—
25C22×Dic18C2211yescharacteristic
26C22×Dic18C2212yes—
27C22×Dic18C2211yescharacteristic
28C22×Dic18C2218yescomplemented
29C4×D4×C9C2218yescomplemented
30C2×C9×C4⋊C4C2211yescharacteristic
31C2×C9×C22⋊C4C2211yescharacteristic
32C2×C9×C22⋊C4C2211yescharacteristic
33C2×C42×C9C2211yescharacteristic
34C2×#3676C2212yes—
35#63501C22116yescomplemented
36#63492C2218yescomplemented
37C2×(C2×D9)⋊C4C2212yes—
38C2×(C2×D9)⋊C4C2212yes—
39C2×(C2×D9)⋊C4C2212yes—
40C2×C4⋊Dic9C2211yescharacteristic
41#63486C2218yescomplemented
42C2×Dic9⋊C4C2212yes—
43C2×Dic9⋊C4C2212yes—
44C2×C4×Dic9C2212yes—
45#63458C22116yescomplemented
46#63447C22116yescomplemented
47#611⋊C4C22116yescomplemented
48#63437C2218yescomplemented
49C4×Dic18C2218yescomplemented
50C22×#235—31no—
51C23×Dic6—31no—
52C2×C3×C4×D4D311yescharacteristic
53C2×#939—32no—
54C2×#930—31no—
55C2×#924—31no—
56#5552—316no—
57C2×#896—32no—
58C2×#885—32no—
59C2×#67⋊C4—32no—
60C2×#875—31no—
61C2×C4×Dic6—31no—
62C24×C9C2311yescharacteristic
63C24×C9C2311yescharacteristic
64C23×D9C2312yes—
65C2×D4×C9—24no—
66C2×D4×C9C2314yes—
67C22×C4×C9—24no—
68C22×C4×C9—24no—
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2314yes—
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2314yes—
75C22×C4×C9C2311yescharacteristic
76C2×#611—28no—
77C2×#611—28no—
78C2×#611C2318yes—
79C2×#611C2318yes—
80C22×Dic9—28no—
81C22×Dic9C2312yes—
82C22×Dic9C2312yes—
83C22×Dic9C2318yes—
84C22×Dic9C2312yes—
85#3697—232no—
86C2×D36—24no—
87C2×D36C2314yes—
88C2×C4×D9—28no—
89C2×C4×D9C2318yes—
90C2×Dic18—24no—
91C2×Dic18—28no—
92C2×Dic18—232no—
93C2×Dic18D418yescomplemented
94C2×Dic18C2314yes—
95C2×Dic18C2318yes—
96C2×Dic18C2314yes—
97C9×C4⋊C4C2314yes—
98C9×C22⋊C4C2314yes—
99C9×C22⋊C4C2314yes—
100C42×C9C2314yes—
101#3676C2318yes—
102(C2×D9)⋊C4C2318yes—
103(C2×D9)⋊C4C2318yes—
104(C2×D9)⋊C4C2318yes—
105C4⋊Dic9C2314yes—
106Dic9⋊C4C2318yes—
107Dic9⋊C4C2318yes—
108C4×Dic9C2318yes—
109C2×#548—91noSylow
110C22×C3×D4C2×D311yescharacteristic
111C23×C3×C4C2×D311yescharacteristic
112C23×C3×C4C2×D311yescharacteristic
113C22×#67—32no—
114C22×#67—32no—
115C23×Dic3—32no—
116C2×#235—38no—
117C2×#235—68no—
118C22×D12—31no—
119C22×C4×D3—32no—
120C22×Dic6—31no—
121C22×Dic6—31no—
122C22×Dic6—32no—
123C22×Dic6—38no—
124C22×Dic6—68no—
125C3×C4×D4C2×D318yes—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C22⋊C4C2×D311yescharacteristic
128C2×C3×C22⋊C4C2×D311yescharacteristic
129C2×C3×C42C2×D311yescharacteristic
130C2×#217—32no—
131#939—316no—
132#930—38no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×C4⋊Dic3—31no—
137#924—38no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×C4×Dic3—32no—
141#896—316no—
142#885—316no—
143#67⋊C4—316no—
144#875—38no—
145C4×Dic6—38no—
146C23×C9—22no—
147C23×C9—22no—
148C23×C9—22no—
149C23×C9—22no—
150C23×C9—22no—
151C23×C9#4114yescomplemented
152C23×C9C2412yes—
153C23×C9C2412yes—
154C23×C9C2411yescharacteristic
155C22×D9—24no—
156C22×D9—24no—
157C22×D9—24no—
158C22×D9C2414yes—
159D4×C9—28no—
160C2×C4×C9—22no—
161C2×C4×C9—22no—
162C2×C4×C9—22no—
163C2×C4×C9—22no—
164C2×C4×C9—28no—
165C2×C4×C9—28no—
166C2×C4×C9C2×D414yes—
167C2×C4×C9C2412yes—
168C2×C4×C9C2412yes—
169C2×C4×C9C2412yes—
170C2×C4×C9C2412yes—
171C2×C4×C9C2412yes—
172#611—216no—
173#611—216no—
174C2×Dic9—24no—
175C2×Dic9—24no—
176C2×Dic9—216no—
177C2×Dic9C2×D418yes—
178C2×Dic9C2414yes—
179C2×Dic9C2414yes—
180C2×Dic9C2414yes—
181D36—28no—
182C4×D9—216no—
183Dic18—28no—
184Dic18—216no—
185Dic18C2×D4116yescomplemented
186C22×#41—91no—
187C23×Q8—91no—
188#548—916no—
189C2×#124—92no—
190C2×#124—91no—
191C2×C22⋊Q8—91no—
192C2×C22⋊Q8—92no—
193C2×#121—92no—
194C2×#121—91no—
195C2×C4×Q8—91no—
196C2×C4×D4—92no—
197C2×C4×D4D911yescharacteristic, complemented
198C24×C3C22×D311yescharacteristic
199C24×C3C22×D311yescharacteristic
200C23×D3—32no—
201C2×C3×D4—24no—
202C2×C3×D4C22×D314yes—
203C22×C3×C4—24no—
204C22×C3×C4—24no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D314yes—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D314yes—
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—38no—
213C2×#67—38no—
214C2×#67—68no—
215C2×#67—68no—
216C22×Dic3—32no—
217C22×Dic3—38no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—68no—
221#235—632no—
222C2×D12—34no—
223C2×D12—64no—
224C2×C4×D3—38no—
225C2×C4×D3—68no—
226C2×Dic6—38no—
227C2×Dic6—34no—
228C2×Dic6—34no—
229C2×Dic6—38no—
230C2×Dic6—632no—
231C2×Dic6—68no—
232C2×Dic6—64no—
233C3×C4⋊C4C22×D314yes—
234C3×C22⋊C4C22×D314yes—
235C3×C22⋊C4C22×D314yes—
236C3×C42C22×D314yes—
237#217—38no—
238(C2×D3)⋊C4—38no—
239(C2×D3)⋊C4—38no—
240(C2×D3)⋊C4—38no—
241C4⋊Dic3—34no—
242Dic3⋊C4—38no—
243Dic3⋊C4—38no—
244C4×Dic3—38no—
245C22×C9—28no—
246C22×C9—22no—
247C22×C9—22no—
248C22×C9—22no—
249C22×C9—22no—
250C22×C9—22no—
251C22×C9—44no—
252C22×C9C22×D412yes—
253C22×C9C2×#4112yes—
254C22×C9C2×#4114yescomplemented
255C22×C92−1+412yes—
256C22×C9C2511yescharacteristic
257C2×D9—24no—
258C2×D9—24no—
259C2×D9—24no—
260C2×D9—48no—
261C4×C9—22no—
262C4×C9—22no—
263C4×C9—22no—
264C4×C9—22no—
265C4×C9C22×D414yes—
266Dic9—24no—
267Dic9—24no—
268Dic9C22×D418yes—
269C2×#41—98no—
270C2×#41—188no—
271C22×Q8—91no—
272C22×Q8—92no—
273C22×Q8—91no—
274C22×Q8—98no—
275C22×Q8—188no—
276C22×D4—92no—
277C22×D4—92no—
278C22×D4—91no—
279C22×D4C2×D911yescharacteristic
280C23×C4—92no—
281C23×C4—92no—
282C23×C4C2×D911yescharacteristic
283C23×C4C2×D911yescharacteristic
284#124—916no—
285#124—98no—
286C22⋊Q8—98no—
287C22⋊Q8—916no—
288#121—916no—
289#121—98no—
290C4×Q8—98no—
291C4×D4—916no—
292C4×D4C2×D918yescomplemented
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4C2×D911yescharacteristic
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C22⋊C4—92no—
301C2×C22⋊C4C2×D911yescharacteristic
302C2×C22⋊C4C2×D911yescharacteristic
303C2×C42—92no—
304C2×C42C2×D911yescharacteristic
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3#23514yes—
311C23×C3C23×D312yes—
312C23×C3C23×D312yes—
313C23×C3C23×D311yescharacteristic
314C22×D3—34no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—64no—
318C3×D4—28no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—28no—
324C2×C3×C4—28no—
325C2×C3×C4D3×D414yes—
326C2×C3×C4C23×D312yes—
327C2×C3×C4C23×D312yes—
328C2×C3×C4C23×D312yes—
329C2×C3×C4C23×D312yes—
330C2×C3×C4C23×D312yes—
331#67—616no—
332#67—616no—
333C2×Dic3—38no—
334C2×Dic3—34no—
335C2×Dic3—34no—
336C2×Dic3—34no—
337C2×Dic3—616no—
338C2×Dic3—64no—
339C2×Dic3—64no—
340D12—68no—
341C4×D3—616no—
342Dic6—316no—
343Dic6—616no—
344Dic6—68no—
345C2×C9—24no—
346C2×C9—42no—
347C2×C9#54814yescomplemented
348C2×C9C23×D411yescharacteristic
349C2×C9C22×#4111yescharacteristic
350C2×C9C2×2−1+411yescharacteristic
351D9—44no—
352C24—92no—
353C24C22×D911yescharacteristic
354C24C22×D911yescharacteristic
355#41—1832no—
356C2×Q8—98no—
357C2×Q8—94no—
358C2×Q8—98no—
359C2×Q8—94no—
360C2×Q8—188no—
361C2×Q8—1832no—
362C2×Q8—184no—
363C2×D4—24no—
364C2×D4—98no—
365C2×D4—98no—
366C2×D4—94no—
367C2×D4—188no—
368C2×D4—188no—
369C2×D4—184no—
370C2×D4C22×D914yes—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—92no—
374C22×C4—98no—
375C22×C4—92no—
376C22×C4—92no—
377C22×C4—98no—
378C22×C4—188no—
379C22×C4—188no—
380C22×C4C22×D914yes—
381C22×C4C22×D914yes—
382C22×C4C22×D911yescharacteristic
383C22×C4C22×D911yescharacteristic
384C22×C4C22×D911yescharacteristic
385C22×C4C22×D911yescharacteristic
386C22×C4C22×D911yescharacteristic
387C4⋊C4—98no—
388C4⋊C4—98no—
389C4⋊C4—94no—
390C4⋊C4C22×D914yes—
391C22⋊C4—98no—
392C22⋊C4—98no—
393C22⋊C4—98no—
394C22⋊C4—98no—
395C22⋊C4C22×D914yes—
396C22⋊C4C22×D914yes—
397C42—98no—
398C42C22×D914yes—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—28no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—44no—
406C22×C3C2×#23512yes—
407C22×C3C2×#23514yes—
408C22×C3C2×D3×D412yes—
409C22×C3#101012yes—
410C22×C3C24×D311yescharacteristic
411C2×D3—64no—
412C2×D3—64no—
413C2×D3—64no—
414C2×D3—128no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4C2×D3×D414yes—
420Dic3—38no—
421Dic3—64no—
422Dic3—64no—
423C9C2×#54811yescharacteristic, complemented, Sylow
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—94no—
430C23—184no—
431C23—184no—
432C23—184no—
433C23#369714yescomplemented
434C23C23×D912yes—
435C23C23×D912yes—
436C23C23×D911yescharacteristic
437Q8—916no—
438Q8—1816no—
439Q8—188no—
440D4—28no—
441D4—1816no—
442D4—1816no—
443D4—188no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—28no—
449C2×C4—28no—
450C2×C4—94no—
451C2×C4—98no—
452C2×C4—94no—
453C2×C4—94no—
454C2×C4—1816no—
455C2×C4—1816no—
456C2×C4—184no—
457C2×C4—184no—
458C2×C4D4×D914yes—
459C2×C4C23×D912yes—
460C2×C4C23×D912yes—
461C2×C4C23×D912yes—
462C2×C4C23×D912yes—
463C2×C4C23×D912yes—
464C2×C3—24no—
465C2×C3—42no—
466C2×C3#555214yes—
467C2×C3C22×#23511yescharacteristic
468C2×C3C22×D3×D411yescharacteristic
469C2×C3C2×#101011yescharacteristic
470D3—124no—
471C22—22no—
472C22—22no—
473C22—28no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—44no—
478C22—184no—
479C22—184no—
480C22—184no—
481C22—368no—
482C22C2×#369712yes—
483C22C2×#369714yescomplemented
484C22C2×D4×D912yes—
485C22#6371612yes—
486C22C24×D911yescharacteristic
487C4—22no—
488C4—22no—
489C4—22no—
490C4—22no—
491C4—98no—
492C4—184no—
493C4—184no—
494C4C2×D4×D914yes—
495C3C2×#555211yescharacteristic
496C2—24no—
497C2—42no—
498C2—364no—
499C2#1058965414yesdirect product factor
500C2C22×#369711yescharacteristic
501C2C22×D4×D911yescharacteristic
502C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×D4×C9C2
socleC23×C3C23×D3
hypercenterC2×C4×D4D9
hypocenterC9C2×#548
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3697C2semidirect
2. C23×Dic18C2semidirect
3. C2×C4×D4×C9C2semidirect
4. C2×#63501C2semidirect
5. C2×#63492C2semidirect
6. C2×#63486C2semidirect
7. #10589654C2direct (N × H)
8. C2×#63458C2semidirect
9. C2×#63447C2semidirect
10. C2×#611⋊C4C2semidirect
11. C2×#63437C2semidirect
12. C2×C4×Dic18C2semidirect
21. C2×#3697C22semidirect
28. C22×Dic18C22semidirect
29. C4×D4×C9C22semidirect
35. #63501C22semidirect
36. #63492C22semidirect
41. #63486C22semidirect
45. #63458C22semidirect
46. #63447C22semidirect
47. #611⋊C4C22semidirect
48. #63437C22semidirect
49. C4×Dic18C22semidirect
93. C2×Dic18D4semidirect
151. C23×C9#41semidirect
185. Dic18C2×D4semidirect
197. C2×C4×D4D9semidirect
254. C22×C9C2×#41semidirect
292. C4×D4C2×D9semidirect
347. C2×C9#548semidirect
423. C9C2×#548semidirect
433. C23#3697semidirect
483. C22C2×#3697semidirect
499. C2#10589654direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36972
C23×Dic182
C2×C4×D4×C92
C2×#635012
C2×#634922
C2×#634862
#105896542
C2×#634582
C2×#634472
C2×#611⋊C42
C2×#634372
C2×C4×Dic182
C2×#55523