Finite Group Databasebeta

← C2×#10589926 #11902489

Subgroups — C2×#10589926 #11902489

Order 1152.

2448 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×C9×#41C211yesmaximal, characteristic, complemented
2C22×#3699C211yesmaximal, characteristic, complemented
3#10589926C2116yesmaximal, direct product factor
4C2×#63508C211yesmaximal, characteristic, complemented
5C2×#63506C211yesmaximal, characteristic, complemented
6C2×#63501C212yesmaximal, complemented
7C2×#63497C212yesmaximal, complemented
8C2×D4×Dic9C211yesmaximal, characteristic, complemented
9C2×#63491C212yesmaximal, complemented
10C2×C4×#611C211yesmaximal, characteristic, complemented
11C2×#63486C211yesmaximal, characteristic, complemented
12C22×Dic9⋊C4C212yesmaximal, complemented
13C2×#5824—31nomaximal
14C2×C9×#41—28no—
15C2×C9×#41C2218yescomplemented
16C22×Q8×C9C2211yescharacteristic
17C22×D4×C9C2212yes—
18C22×D4×C9C2211yescharacteristic
19C23×C4×C9C2212yes—
20C23×C4×C9C2211yescharacteristic
21C22×#611C2212yes—
22C22×#611C2211yescharacteristic
23C23×Dic9C2212yes—
24C23×Dic9C2212yes—
25C2×#3699—28no—
26C2×#3699C2218yescomplemented
27C22×C4×D9C2211yescharacteristic
28C22×Dic18C2211yescharacteristic
29C2×#3676C2212yes—
30C2×#3676C2211yescharacteristic
31C2×#3676C2212yes—
32#63508C2218yescomplemented
33#63506C2218yescomplemented
34#63501C22116yescomplemented
35#63497C22116yescomplemented
36D4×Dic9C2218yescomplemented
37#63491C22116yescomplemented
38C4×#611C2218yescomplemented
39C2×(C2×D9)⋊C4C2211yescharacteristic
40C2×(C2×D9)⋊C4C2212yes—
41C2×C4⋊Dic9C2211yescharacteristic
42#63486C2218yescomplemented
43C2×Dic9⋊C4C2211yescharacteristic
44C2×Dic9⋊C4C2212yes—
45C2×Dic9⋊C4C2212yes—
46C2×Dic9⋊C4C2212yes—
47C2×Dic9⋊C4C2212yes—
48C2×Dic9⋊C4C22116yescomplemented
49C2×C4×Dic9C2211yescharacteristic
50C22×C3×#41D311yescharacteristic
51C22×#237—31no—
52#5824—316no—
53C2×#946—31no—
54C2×#944—31no—
55C2×#939—32no—
56C2×#935—32no—
57C2×D4×Dic3—31no—
58C2×#929—32no—
59C2×C4×#67—31no—
60C2×#924—31no—
61C22×Dic3⋊C4—32no—
62C24×C9C2311yescharacteristic
63C24×C9C2312yes—
64C23×D9C2311yescharacteristic
65C9×#41—232no—
66C2×Q8×C9—24no—
67C2×Q8×C9C2314yes—
68C2×D4×C9—28no—
69C2×D4×C9D418yescomplemented
70C2×D4×C9C2318yes—
71C2×D4×C9C2314yes—
72C22×C4×C9—28no—
73C22×C4×C9—24no—
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2312yes—
76C22×C4×C9C2314yes—
77C22×C4×C9C2318yes—
78C22×C4×C9C2311yescharacteristic
79C2×#611—28no—
80C2×#611—24no—
81C2×#611C2314yes—
82C2×#611C2318yes—
83C22×Dic9—28no—
84C22×Dic9—28no—
85C22×Dic9C2311yescharacteristic
86C22×Dic9C2312yes—
87C22×Dic9C2318yes—
88C22×Dic9C2318yes—
89C22×Dic9C2312yes—
90C22×Dic9C2311yescharacteristic
91C22×Dic9C2311yescharacteristic
92#3699—232no—
93C2×C4×D9—24no—
94C2×C4×D9C2314yes—
95C2×Dic18—24no—
96C2×Dic18C2314yes—
97#3676C2314yes—
98#3676C2318yes—
99#3676C2318yes—
100(C2×D9)⋊C4C2314yes—
101(C2×D9)⋊C4C2318yes—
102C4⋊Dic9C2314yes—
103Dic9⋊C4C2314yes—
104Dic9⋊C4C2318yes—
105Dic9⋊C4C2318yes—
106Dic9⋊C4C2318yes—
107Dic9⋊C4C2318yes—
108C4×Dic9C2314yes—
109C2×#547—91noSylow
110C2×C3×#41—28no—
111C2×C3×#41C2×D318yes—
112C22×C3×Q8C2×D311yescharacteristic
113C22×C3×D4C2×D312yes—
114C22×C3×D4C2×D311yescharacteristic
115C23×C3×C4C2×D312yes—
116C23×C3×C4C2×D311yescharacteristic
117C22×#67—32no—
118C22×#67—31no—
119C23×Dic3—32no—
120C23×Dic3—32no—
121C2×#237—38no—
122C2×#237—68no—
123C22×C4×D3—31no—
124C22×Dic6—31no—
125C2×#217—32no—
126C2×#217—31no—
127C2×#217—32no—
128#946—38no—
129#944—38no—
130#939—316no—
131#935—316no—
132D4×Dic3—38no—
133#929—316no—
134C4×#67—38no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—32no—
137C2×C4⋊Dic3—31no—
138#924—38no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—316no—
144C2×Dic3⋊C4—32no—
145C2×C4×Dic3—31no—
146C23×C9—24no—
147C23×C9—24no—
148C23×C9—22no—
149C23×C9—22no—
150C23×C9—22no—
151C23×C9C2×D418yes—
152C23×C9C2412yes—
153C23×C9C2414yes—
154C23×C9C2411yescharacteristic
155C22×D9—22no—
156C22×D9—22no—
157C22×D9—22no—
158C22×D9C2412yes—
159Q8×C9—28no—
160D4×C9—216no—
161D4×C9C2×D4116yescomplemented
162C2×C4×C9—22no—
163C2×C4×C9—24no—
164C2×C4×C9—216no—
165C2×C4×C9—28no—
166C2×C4×C9C2×D414yes—
167C2×C4×C9C2412yes—
168C2×C4×C9C2414yes—
169C2×C4×C9C2412yes—
170#611—216no—
171#611—28no—
172C2×Dic9—24no—
173C2×Dic9—22no—
174C2×Dic9—216no—
175C2×Dic9—24no—
176C2×Dic9—22no—
177C2×Dic9—216no—
178C2×Dic9#4114yescomplemented
179C2×Dic9C2412yes—
180C2×Dic9C2414yes—
181C2×Dic9C2412yes—
182C2×Dic9C2414yes—
183C2×Dic9C2412yes—
184C4×D9—28no—
185Dic18—28no—
186C22×#41—91no—
187C22×#41D911yescharacteristic, complemented
188#547—916no—
189C2×C4⋊Q8—91no—
190C2×#123—92no—
191C2×#123—92no—
192C2×C22⋊Q8—91no—
193C2×C22⋊Q8—91no—
194C2×#121—92no—
195C2×C4×D4—91no—
196C2×C4×D4—91no—
197C22×C4⋊C4—92no—
198C24×C3C22×D311yescharacteristic
199C24×C3C22×D312yes—
200C23×D3—31no—
201C3×#41—232no—
202C2×C3×Q8—24no—
203C2×C3×Q8C22×D314yes—
204C2×C3×D4—28no—
205C2×C3×D4#6718yes—
206C2×C3×D4C22×D318yes—
207C2×C3×D4C22×D314yes—
208C22×C3×C4—28no—
209C22×C3×C4—24no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D318yes—
213C22×C3×C4C22×D314yes—
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—34no—
216C2×#67—38no—
217C2×#67—64no—
218C2×#67—68no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—32no—
222C22×Dic3—31no—
223C22×Dic3—32no—
224C22×Dic3—38no—
225C22×Dic3—38no—
226C22×Dic3—68no—
227C22×Dic3—68no—
228#237—632no—
229C2×C4×D3—34no—
230C2×C4×D3—64no—
231C2×Dic6—34no—
232C2×Dic6—64no—
233#217—38no—
234#217—34no—
235#217—38no—
236(C2×D3)⋊C4—34no—
237(C2×D3)⋊C4—38no—
238C4⋊Dic3—34no—
239Dic3⋊C4—34no—
240Dic3⋊C4—38no—
241Dic3⋊C4—38no—
242Dic3⋊C4—38no—
243Dic3⋊C4—38no—
244C4×Dic3—34no—
245C22×C9—216no—
246C22×C9—24no—
247C22×C9—24no—
248C22×C9—22no—
249C22×C9—22no—
250C22×C9—22no—
251C22×C9—44no—
252C22×C9C22×D418yes—
253C22×C9C22×D412yes—
254C22×C9C2×#4112yes—
255C22×C92−1+412yes—
256C22×C9C2511yescharacteristic
257C2×D9—22no—
258C2×D9—22no—
259C2×D9—22no—
260C2×D9—44no—
261C4×C9—22no—
262C4×C9—24no—
263C4×C9C22×D414yes—
264Dic9—24no—
265Dic9—22no—
266Dic9—24no—
267Dic9—22no—
268Dic9C2×#4114yescomplemented
269C2×#41—28no—
270C2×#41—98no—
271C2×#41—188no—
272C2×#41C2×D918yescomplemented
273C22×Q8—91no—
274C22×Q8C2×D911yescharacteristic
275C22×D4—91no—
276C22×D4—92no—
277C22×D4C2×D912yes—
278C22×D4C2×D911yescharacteristic
279C23×C4—92no—
280C23×C4—92no—
281C23×C4—91no—
282C23×C4C2×D912yes—
283C23×C4C2×D911yescharacteristic
284C4⋊Q8—98no—
285#123—916no—
286#123—916no—
287C22⋊Q8—98no—
288C22⋊Q8—98no—
289#121—916no—
290C4×D4—98no—
291C4×D4—98no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—916no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C22⋊C4—91no—
301C2×C22⋊C4—92no—
302C2×C22⋊C4—91no—
303C2×C22⋊C4—92no—
304C2×C42—91no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3C2×#6718yes—
311C23×C3C23×D312yes—
312C23×C3C23×D314yes—
313C23×C3C23×D311yescharacteristic
314C22×D3—32no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—62no—
318C3×Q8—28no—
319C3×D4—216no—
320C3×D4C2×#67116yes—
321C2×C3×C4—22no—
322C2×C3×C4—24no—
323C2×C3×C4—216no—
324C2×C3×C4—28no—
325C2×C3×C4C2×#6714yes—
326C2×C3×C4C23×D312yes—
327C2×C3×C4C23×D314yes—
328C2×C3×C4C23×D312yes—
329#67—68no—
330#67—616no—
331C2×Dic3—34no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—34no—
335C2×Dic3—32no—
336C2×Dic3—34no—
337C2×Dic3—616no—
338C2×Dic3—64no—
339C2×Dic3—62no—
340C2×Dic3—64no—
341C2×Dic3—62no—
342C2×Dic3—616no—
343C4×D3—68no—
344Dic6—68no—
345C2×C9—28no—
346C2×C9—42no—
347C2×C9#54714yescomplemented
348C2×C9C23×D411yescharacteristic
349C2×C9C22×#4111yescharacteristic
350C2×C9C2×2−1+411yescharacteristic
351D9—42no—
352C24—91no—
353C24C22×D911yescharacteristic
354C24C22×D912yes—
355#41—232no—
356#41—1832no—
357C2×Q8—24no—
358C2×Q8—94no—
359C2×Q8—184no—
360C2×Q8C22×D914yes—
361C2×D4—28no—
362C2×D4—94no—
363C2×D4—98no—
364C2×D4—184no—
365C2×D4—188no—
366C2×D4#61118yescomplemented
367C2×D4C22×D918yes—
368C2×D4C22×D914yes—
369C22×C4—28no—
370C22×C4—24no—
371C22×C4—91no—
372C22×C4—98no—
373C22×C4—98no—
374C22×C4—91no—
375C22×C4—92no—
376C22×C4—91no—
377C22×C4—92no—
378C22×C4—94no—
379C22×C4—188no—
380C22×C4—188no—
381C22×C4—184no—
382C22×C4C22×D918yes—
383C22×C4C22×D914yes—
384C22×C4C22×D911yescharacteristic
385C22×C4C22×D912yes—
386C22×C4C22×D911yescharacteristic
387C4⋊C4—94no—
388C4⋊C4—98no—
389C4⋊C4—98no—
390C4⋊C4—98no—
391C4⋊C4—94no—
392C4⋊C4—98no—
393C22⋊C4—98no—
394C22⋊C4—94no—
395C22⋊C4—98no—
396C22⋊C4—94no—
397C22⋊C4—98no—
398C42—94no—
399C22×C3—24no—
400C22×C3—24no—
401C22×C3—216no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—44no—
406C22×C3D3×#4112yes—
407C22×C3#101012yes—
408C22×C3C22×#6718yes—
409C22×C3C22×#6712yes—
410C22×C3C24×D311yescharacteristic
411C2×D3—62no—
412C2×D3—62no—
413C2×D3—62no—
414C2×D3—124no—
415C3×C4—22no—
416C3×C4—24no—
417C3×C4C22×#6714yes—
418Dic3—34no—
419Dic3—64no—
420Dic3—62no—
421Dic3—64no—
422Dic3—62no—
423C9C2×#54711yescharacteristic, complemented, Sylow
424C23—24no—
425C23—24no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—92no—
430C23—182no—
431C23—182no—
432C23—182no—
433C23C2×#61118yes—
434C23C23×D912yes—
435C23C23×D914yes—
436C23C23×D911yescharacteristic
437Q8—28no—
438Q8—188no—
439D4—216no—
440D4—188no—
441D4—1816no—
442D4C2×#611116yescomplemented
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—216no—
446C2×C4—28no—
447C2×C4—92no—
448C2×C4—94no—
449C2×C4—92no—
450C2×C4—94no—
451C2×C4—92no—
452C2×C4—94no—
453C2×C4—1816no—
454C2×C4—184no—
455C2×C4—182no—
456C2×C4—182no—
457C2×C4—184no—
458C2×C4—1816no—
459C2×C4—188no—
460C2×C4C2×#61114yes—
461C2×C4C23×D912yes—
462C2×C4C23×D914yes—
463C2×C4C23×D912yes—
464C2×C3—28no—
465C2×C3—42no—
466C2×C3#582414yes—
467C2×C3C2×D3×#4111yescharacteristic
468C2×C3C2×#101011yescharacteristic
469C2×C3C23×#6711yescharacteristic
470D3—122no—
471C22—24no—
472C22—24no—
473C22—216no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—44no—
478C22—182no—
479C22—182no—
480C22—182no—
481C22—364no—
482C22#41×D912yes—
483C22#6371612yes—
484C22C22×#61118yes—
485C22C22×#61112yes—
486C22C24×D911yescharacteristic
487C4—22no—
488C4—24no—
489C4—94no—
490C4—184no—
491C4—182no—
492C4—182no—
493C4—184no—
494C4C22×#61114yes—
495C3C2×#582411yescharacteristic
496C2—28no—
497C2—42no—
498C2—362no—
499C2#1058992614yesdirect product factor
500C2C2×#41×D911yescharacteristic
501C2C2×#6371611yescharacteristic
502C2C23×#61111yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC22×C9×#41C2
socleC23×C3C23×D3
hypercenterC22×#41D9
hypocenterC9C2×#547
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C9×#41C2semidirect
2. C22×#3699C2semidirect
3. #10589926C2direct (N × H)
4. C2×#63508C2semidirect
5. C2×#63506C2semidirect
6. C2×#63501C2semidirect
7. C2×#63497C2semidirect
8. C2×D4×Dic9C2semidirect
9. C2×#63491C2semidirect
10. C2×C4×#611C2semidirect
11. C2×#63486C2semidirect
12. C22×Dic9⋊C4C2semidirect
15. C2×C9×#41C22semidirect
26. C2×#3699C22semidirect
32. #63508C22semidirect
33. #63506C22semidirect
34. #63501C22semidirect
35. #63497C22semidirect
36. D4×Dic9C22semidirect
37. #63491C22semidirect
38. C4×#611C22semidirect
42. #63486C22semidirect
48. C2×Dic9⋊C4C22semidirect
69. C2×D4×C9D4semidirect
161. D4×C9C2×D4semidirect
178. C2×Dic9#41semidirect
187. C22×#41D9semidirect
268. Dic9C2×#41semidirect
272. C2×#41C2×D9semidirect
347. C2×C9#547semidirect
366. C2×D4#611semidirect
423. C9C2×#547semidirect
442. D4C2×#611semidirect
499. C2#10589926direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×#412
C22×#36992
#105899262
C2×#635082
C2×#635062
C2×#635012
C2×#634972
C2×D4×Dic92
C2×#634912
C2×C4×#6112
C2×#634862
C22×Dic9⋊C42
C2×#58243