Finite Group Databasebeta

← C2×#10589650 #11900744

Subgroups — C2×#10589650 #11900744

Order 1152.

2592 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×#3697C212yesmaximal, complemented
2C2×C4×D4×C9C211yesmaximal, characteristic, complemented
3C2×#63502C211yesmaximal, characteristic, complemented
4C2×#63500C211yesmaximal, characteristic, complemented
5C2×C4×#611C212yesmaximal, complemented
6#10589650C2116yesmaximal, direct product factor
7C2×#63457C211yesmaximal, characteristic, complemented
8C2×#63450C211yesmaximal, characteristic, complemented
9C2×#63447C212yesmaximal, complemented
10C2×#63446C212yesmaximal, complemented
11C2×C4×D36C211yesmaximal, characteristic, complemented
12C2×C42×D9C211yesmaximal, characteristic, complemented
13C2×#5548—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2212yes—
17C22×#611C2212yes—
18C22×#611C2212yes—
19C2×#3697—216no—
20C2×#3697C22116yescomplemented
21C22×D36C2212yes—
22C22×D36C2211yescharacteristic
23C22×C4×D9C2212yes—
24C22×C4×D9C2211yescharacteristic
25C22×C4×D9C2211yescharacteristic
26C22×C4×D9C2211yescharacteristic
27C22×Dic18C2212yes—
28C4×D4×C9C2218yescomplemented
29C2×C9×C4⋊C4C2211yescharacteristic
30C2×C9×C22⋊C4C2212yes—
31C2×C42×C9C2211yescharacteristic
32C2×#3676C2212yes—
33#63502C2218yescomplemented
34#63500C2218yescomplemented
35C4×#611C22116yescomplemented
36C2×(C2×D9)⋊C4C2212yes—
37C2×(C2×D9)⋊C4C2212yes—
38C2×C4⋊Dic9C2211yescharacteristic
39C2×Dic9⋊C4C2212yes—
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43#63457C2218yescomplemented
44#63450C2218yescomplemented
45#63447C22116yescomplemented
46#63446C22116yescomplemented
47C4×D36C2218yescomplemented
48C42×D9C2218yescomplemented
49C22×#235—32no—
50C2×C3×C4×D4D311yescharacteristic
51C2×#940—31no—
52C2×#938—31no—
53C2×C4×#67—32no—
54#5548—316no—
55C2×#895—31no—
56C2×#888—31no—
57C2×#885—32no—
58C2×#884—32no—
59C2×C4×D12—31no—
60C2×C42×D3—31no—
61C24×C9C2312yes—
62C23×D9C2312yes—
63C23×D9C2311yescharacteristic
64C2×D4×C9—24no—
65C2×D4×C9C2314yes—
66C22×C4×C9—28no—
67C22×C4×C9C2311yescharacteristic
68C22×C4×C9C2312yes—
69C22×C4×C9C2318yes—
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C2×#611—28no—
73C2×#611—28no—
74C2×#611—28no—
75C2×#611C2318yes—
76C2×#611C2318yes—
77C2×#611C2318yes—
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2312yes—
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82#3697—264no—
83C2×D36—28no—
84C2×D36—24no—
85C2×D36C2314yes—
86C2×D36C2318yes—
87C2×C4×D9—28no—
88C2×C4×D9—24no—
89C2×C4×D9—24no—
90C2×C4×D9D418yescomplemented
91C2×C4×D9C2318yes—
92C2×C4×D9C2314yes—
93C2×C4×D9C2314yes—
94C2×C4×D9C2314yes—
95C2×Dic18—28no—
96C2×Dic18C2318yes—
97C9×C4⋊C4C2314yes—
98C9×C22⋊C4C2318yes—
99C42×C9C2314yes—
100#3676C2318yes—
101(C2×D9)⋊C4C2318yes—
102(C2×D9)⋊C4C2318yes—
103C4⋊Dic9C2314yes—
104Dic9⋊C4C2318yes—
105C4×Dic9C2314yes—
106C4×Dic9C2314yes—
107C4×Dic9C2314yes—
108C2×#532—91noSylow
109C22×C3×D4C2×D311yescharacteristic
110C23×C3×C4C2×D312yes—
111C22×#67—32no—
112C22×#67—32no—
113C22×#67—32no—
114C2×#235—316no—
115C2×#235—616no—
116C22×D12—32no—
117C22×D12—31no—
118C22×C4×D3—31no—
119C22×C4×D3—32no—
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×Dic6—32no—
123C3×C4×D4C2×D318yes—
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C22⋊C4C2×D312yes—
126C2×C3×C42C2×D311yescharacteristic
127C2×#217—32no—
128#940—38no—
129#938—38no—
130C4×#67—316no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×C4⋊Dic3—31no—
134C2×Dic3⋊C4—32no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138#895—38no—
139#888—38no—
140#885—316no—
141#884—316no—
142C4×D12—38no—
143C42×D3—38no—
144C23×C9—24no—
145C23×C9—24no—
146C23×C9—24no—
147C23×C9C2414yes—
148C23×C9C2411yescharacteristic
149C22×D9—22no—
150C22×D9—22no—
151C22×D9—24no—
152C22×D9—24no—
153C22×D9—24no—
154C22×D9C2×D414yes—
155C22×D9C2414yes—
156C22×D9C2412yes—
157D4×C9—28no—
158C2×C4×C9—24no—
159C2×C4×C9—22no—
160C2×C4×C9—216no—
161C2×C4×C9C2×D414yes—
162C2×C4×C9#4114yescomplemented
163C2×C4×C9C2412yes—
164C2×C4×C9C2414yes—
165C2×C4×C9C2412yes—
166C2×C4×C9C2412yes—
167#611—216no—
168#611—216no—
169#611—216no—
170C2×Dic9—24no—
171C2×Dic9—22no—
172C2×Dic9C2×D414yes—
173C2×Dic9#4114yescomplemented
174C2×Dic9C2412yes—
175C2×Dic9C2414yes—
176C2×Dic9C2412yes—
177C2×Dic9C2412yes—
178D36—216no—
179D36—28no—
180C4×D9—216no—
181C4×D9—28no—
182C4×D9—28no—
183C4×D9C2×D4116yescomplemented
184Dic18—216no—
185C22×#41—92no—
186#532—916no—
187C2×C4⋊Q8—91no—
188C2×#127—91no—
189C2×#124—92no—
190C2×#121—91no—
191C2×#121—91no—
192C2×#121—92no—
193C2×C4×D4—92no—
194C2×C4×D4—91no—
195C2×C4×D4D911yescharacteristic, complemented
196C22×C42—91no—
197C24×C3C22×D312yes—
198C23×D3—31no—
199C23×D3—32no—
200C2×C3×D4—24no—
201C2×C3×D4C22×D314yes—
202C22×C3×C4—28no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D312yes—
205C22×C3×C4C22×D318yes—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—38no—
209C2×#67—38no—
210C2×#67—38no—
211C2×#67—68no—
212C2×#67—68no—
213C2×#67—68no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—32no—
218#235—664no—
219C2×D12—34no—
220C2×D12—38no—
221C2×D12—68no—
222C2×D12—64no—
223C2×C4×D3—38no—
224C2×C4×D3—34no—
225C2×C4×D3—34no—
226C2×C4×D3—34no—
227C2×C4×D3—38no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—68no—
231C2×Dic6—38no—
232C2×Dic6—68no—
233C3×C4⋊C4C22×D314yes—
234C3×C22⋊C4C22×D318yes—
235C3×C42C22×D314yes—
236#217—38no—
237(C2×D3)⋊C4—38no—
238(C2×D3)⋊C4—38no—
239C4⋊Dic3—34no—
240Dic3⋊C4—38no—
241C4×Dic3—34no—
242C4×Dic3—34no—
243C4×Dic3—34no—
244C22×C9—24no—
245C22×C9—24no—
246C22×C9—24no—
247C22×C9—48no—
248C22×C9C22×D412yes—
249C22×C9C2×#4112yes—
250C22×C9C2×#4112yes—
251C22×C9C2511yescharacteristic
252C2×D9—28no—
253C2×D9—22no—
254C2×D9—22no—
255C2×D9—24no—
256C2×D9—24no—
257C2×D9—24no—
258C2×D9—48no—
259C2×D9C22×D414yes—
260C4×C9—24no—
261C4×C9—22no—
262C4×C9C22×D414yes—
263C4×C9C2×#4114yescomplemented
264Dic9—24no—
265Dic9—22no—
266Dic9C22×D414yes—
267Dic9C2×#4114yescomplemented
268C2×#41—916no—
269C2×#41—1816no—
270C22×Q8—92no—
271C22×D4—92no—
272C22×D4—92no—
273C22×D4—92no—
274C22×D4—91no—
275C22×D4—92no—
276C22×D4C2×D911yescharacteristic
277C23×C4—91no—
278C23×C4—91no—
279C23×C4—91no—
280C23×C4—92no—
281C23×C4C2×D912yes—
282C4⋊Q8—98no—
283#127—98no—
284#124—916no—
285#121—98no—
286#121—98no—
287#121—916no—
288C4×D4—916no—
289C4×D4—98no—
290C4×D4C2×D918yescomplemented
291C2×C4⋊C4—92no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4C2×D911yescharacteristic
294C2×C22⋊C4—92no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4C2×D912yes—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—98no—
302C2×C42C2×D911yescharacteristic
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3C23×D314yes—
307C23×C3C23×D311yescharacteristic
308C22×D3—34no—
309C22×D3—32no—
310C22×D3—34no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—64no—
316C3×D4—28no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—216no—
320C2×C3×C4#23514yes—
321C2×C3×C4D3×D414yes—
322C2×C3×C4C23×D312yes—
323C2×C3×C4C23×D314yes—
324C2×C3×C4C23×D312yes—
325C2×C3×C4C23×D312yes—
326#67—616no—
327#67—616no—
328#67—616no—
329C2×Dic3—34no—
330C2×Dic3—34no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—34no—
335C2×Dic3—62no—
336C2×Dic3—64no—
337D12—616no—
338D12—68no—
339C4×D3—316no—
340C4×D3—68no—
341C4×D3—68no—
342C4×D3—616no—
343Dic6—616no—
344C2×C9—44no—
345C2×C9#53214yescomplemented
346C2×C9C23×D411yescharacteristic
347C2×C9C22×#4111yescharacteristic
348C2×C9C22×#4111yescharacteristic
349D9—24no—
350D9—44no—
351C24—91no—
352C24—92no—
353C24C22×D912yes—
354#41—1864no—
355C2×Q8—98no—
356C2×Q8—188no—
357C2×D4—24no—
358C2×D4—98no—
359C2×D4—98no—
360C2×D4—98no—
361C2×D4—94no—
362C2×D4—98no—
363C2×D4—188no—
364C2×D4—188no—
365C2×D4—188no—
366C2×D4—188no—
367C2×D4—184no—
368C2×D4C22×D914yes—
369C22×C4—28no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—98no—
373C22×C4—94no—
374C22×C4—91no—
375C22×C4—92no—
376C22×C4—94no—
377C22×C4—94no—
378C22×C4—98no—
379C22×C4—184no—
380C22×C4—184no—
381C22×C4—188no—
382C22×C4C22×D911yescharacteristic
383C22×C4C22×D912yes—
384C22×C4C22×D918yes—
385C22×C4C22×D911yescharacteristic
386C22×C4C22×D911yescharacteristic
387C4⋊C4—98no—
388C4⋊C4—94no—
389C4⋊C4C22×D914yes—
390C22⋊C4—98no—
391C22⋊C4—98no—
392C22⋊C4—98no—
393C22⋊C4C22×D918yes—
394C42—94no—
395C42—94no—
396C42—94no—
397C42C22×D914yes—
398C22×C3—24no—
399C22×C3—24no—
400C22×C3—24no—
401C22×C3—48no—
402C22×C3C2×#23512yes—
403C22×C3C2×D3×D412yes—
404C22×C3D3×#4112yes—
405C22×C3C24×D311yescharacteristic
406C2×D3—34no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—68no—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—64no—
413C2×D3—128no—
414C3×C4—24no—
415C3×C4—22no—
416C3×C4C2×#23514yes—
417C3×C4C2×D3×D414yes—
418Dic3—34no—
419Dic3—34no—
420Dic3—62no—
421Dic3—64no—
422C9C2×#53211yescharacteristic, complemented, Sylow
423C23—24no—
424C23—24no—
425C23—24no—
426C23—92no—
427C23—94no—
428C23—94no—
429C23—182no—
430C23—182no—
431C23—184no—
432C23—184no—
433C23—184no—
434C23C23×D914yes—
435C23C23×D911yescharacteristic
436Q8—1816no—
437D4—28no—
438D4—1816no—
439D4—1816no—
440D4—1816no—
441D4—1816no—
442D4—188no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—216no—
446C2×C4—92no—
447C2×C4—92no—
448C2×C4—94no—
449C2×C4—94no—
450C2×C4—916no—
451C2×C4—92no—
452C2×C4—94no—
453C2×C4—188no—
454C2×C4—182no—
455C2×C4—184no—
456C2×C4—188no—
457C2×C4—1816no—
458C2×C4#369714yescomplemented
459C2×C4D4×D914yes—
460C2×C4C23×D912yes—
461C2×C4C23×D914yes—
462C2×C4C23×D912yes—
463C2×C4C23×D912yes—
464C2×C3—44no—
465C2×C3#554814yes—
466C2×C3C22×#23511yescharacteristic
467C2×C3C22×D3×D411yescharacteristic
468C2×C3C2×D3×#4111yescharacteristic
469D3—64no—
470D3—124no—
471C22—24no—
472C22—24no—
473C22—24no—
474C22—48no—
475C22—94no—
476C22—182no—
477C22—182no—
478C22—188no—
479C22—184no—
480C22—184no—
481C22—184no—
482C22—368no—
483C22C2×#369712yes—
484C22C2×D4×D912yes—
485C22#41×D912yes—
486C22C24×D911yescharacteristic
487C4—24no—
488C4—22no—
489C4—94no—
490C4—94no—
491C4—182no—
492C4—184no—
493C4C2×#369714yescomplemented
494C4C2×D4×D914yes—
495C3C2×#554811yescharacteristic
496C2—44no—
497C2—184no—
498C2—364no—
499C2#1058965014yesdirect product factor
500C2C22×#369711yescharacteristic
501C2C22×D4×D911yescharacteristic
502C2C2×#41×D911yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×D4×C9C2
socleC23×C3C23×D3
hypercenterC2×C4×D4D9
hypocenterC9C2×#532
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3697C2semidirect
2. C2×C4×D4×C9C2semidirect
3. C2×#63502C2semidirect
4. C2×#63500C2semidirect
5. C2×C4×#611C2semidirect
6. #10589650C2direct (N × H)
7. C2×#63457C2semidirect
8. C2×#63450C2semidirect
9. C2×#63447C2semidirect
10. C2×#63446C2semidirect
11. C2×C4×D36C2semidirect
12. C2×C42×D9C2semidirect
20. C2×#3697C22semidirect
28. C4×D4×C9C22semidirect
33. #63502C22semidirect
34. #63500C22semidirect
35. C4×#611C22semidirect
43. #63457C22semidirect
44. #63450C22semidirect
45. #63447C22semidirect
46. #63446C22semidirect
47. C4×D36C22semidirect
48. C42×D9C22semidirect
90. C2×C4×D9D4semidirect
162. C2×C4×C9#41semidirect
173. C2×Dic9#41semidirect
183. C4×D9C2×D4semidirect
195. C2×C4×D4D9semidirect
263. C4×C9C2×#41semidirect
267. Dic9C2×#41semidirect
290. C4×D4C2×D9semidirect
345. C2×C9#532semidirect
422. C9C2×#532semidirect
458. C2×C4#3697semidirect
493. C4C2×#3697semidirect
499. C2#10589650direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36972
C2×C4×D4×C92
C2×#635022
C2×#635002
C2×C4×#6112
#105896502
C2×#634572
C2×#634502
C2×#634472
C2×#634462
C2×C4×D362
C2×C42×D92
C2×#55483