Finite Group Databasebeta

← C2×#10595306 #11900463

Subgroups — C2×#10595306 #11900463

Order 1152.

4205 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×C4×D32C211yesmaximal, characteristic, complemented
3C2×C3×#938C212yesmaximal, complemented
4C2×#63983C212yesmaximal, complemented
5C2×#63975C212yesmaximal, complemented
6C2×#67⋊Dic3C214yesmaximal, complemented
7#10595306C2116yesmaximal, direct product factor
8C2×#63857C212yesmaximal, complemented
9C2×#63849C211yesmaximal, characteristic, complemented
10C2×#5606—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C32×D4C2211yescharacteristic, complemented
13C22×#638C2212yes—
14C23×C3⋊Dic3C2212yescomplemented
15C2×#3830—28no—
16C2×#3830C2218yescomplemented
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634C2211yescharacteristic, complemented
19C22×C3×#67C2214yes—
20C22×C3×C4×D3C2212yes—
21C22×#624C2211yescharacteristic
22C22×D3×Dic3C2212yes—
23C2×C4×D32—28no—
24C2×C4×D32C2218yescomplemented
25C2×C3×#217C2214yescomplemented
26C3×#938C22116yescomplemented
27C2×C3×C4⋊Dic3C2212yescomplemented
28#63983C22116yescomplemented
29#63975C22116yescomplemented
30#67⋊Dic3C22132yescomplemented
31C2×Dic3⋊Dic3C2214yescomplemented
32C2×#3722C2212yes—
33C2×(C2×D3)⋊Dic3C2214yes—
34C2×Dic32C2212yescomplemented
35#63857C22116yescomplemented
36#63849C2218yescomplemented
37C22×#237—32no—
38C22×#237—61no—
39C23×C4×D3—32no—
40C2×C3×#121—32no—
41C2×#938D312yescomplemented
42C2×#937—34no—
43C2×D4×Dic3—34no—
44C2×#924—32no—
45#5606—332no—
46C2×#897—32no—
47C2×#892—32no—
48C2×#883—34no—
49C2×#67⋊C4—34no—
50C24×C32C2312yes—
51C23×C3⋊D3C2311yescharacteristic
52C23×C3×D3C2312yes—
53C22×D32—24no—
54C22×D32—28no—
55C22×D32C2314yes—
56C2×C32×D4—24no—
57C2×C32×D4C2314yescomplemented
58C22×C32×C4C2311yescharacteristic
59C2×#638—28no—
60C2×#638C2318yes—
61C22×C3⋊Dic3—28no—
62C22×C3⋊Dic3C2312yes—
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2318yescomplemented
65#3830—232no—
66C2×C4×C3⋊D3D418yescomplemented
67C2×C4×C3⋊D3C2314yes—
68C2×#634—24no—
69C2×#634C2314yescomplemented
70C2×C3×#67—216no—
71C2×C3×#67C23116yes—
72C22×C3×Dic3C2314yes—
73C22×C3×Dic3C2312yes—
74C2×C3×C4×D3—28no—
75C2×C3×C4×D3C2318yes—
76C2×#624—24no—
77C2×#624C2314yes—
78C2×D3×Dic3—28no—
79C2×D3×Dic3C2318yes—
80C4×D32—232no—
81C3×#217C23116yescomplemented
82C3×C4⋊Dic3C2318yescomplemented
83Dic3⋊Dic3C23116yescomplemented
84#3722C2318yes—
85(C2×D3)⋊Dic3C23116yes—
86Dic32C2318yescomplemented
87C2×#525—91noSylow
88C24×D3—32no—
89C22×C3×D4—21no—
90C22×C3×D4—34no—
91C22×C3×D4C2×D312yescomplemented
92C23×C3×C4—32no—
93C22×#67—34no—
94C22×#67—62no—
95C22×#67C2×D314yes—
96C23×Dic3—34no—
97C23×Dic3—32no—
98C23×Dic3—62no—
99C2×#237—316no—
100C2×#237—68no—
101C2×#237—616no—
102C2×#237—616no—
103C22×C4×D3—32no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—316no—
107C22×C4×D3—61no—
108C22×C4×D3—616no—
109C22×C4×D3C2×D312yes—
110C22×Dic6—32no—
111C22×Dic6—61no—
112C3×#121—316no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C22⋊C4—34no—
115C2×#217—34no—
116C2×#217C2×D314yescomplemented
117#938C2×D3116yescomplemented
118#937—332no—
119D4×Dic3—332no—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—34no—
122C2×C4⋊Dic3—34no—
123C2×C4⋊Dic3C2×D312yescomplemented
124#924—316no—
125C2×Dic3⋊C4—34no—
126C2×C4×Dic3—34no—
127#897—316no—
128#892—316no—
129#883—332no—
130#67⋊C4—332no—
131C23×C32—24no—
132C23×C32—28no—
133C23×C32C2414yes—
134C23×C32C2411yescharacteristic
135C22×C3⋊D3—24no—
136C22×C3⋊D3C2×D414yes—
137C22×C3⋊D3C2412yes—
138C22×C3×D3—24no—
139C22×C3×D3—24no—
140C22×C3×D3#4118yescomplemented
141C22×C3×D3C2414yes—
142C2×D32—232no—
143C2×D32—28no—
144C2×D32—216no—
145C32×D4—28no—
146C2×C32×C4C2×D414yes—
147C2×C32×C4C2412yes—
148#638—216no—
149C2×C3⋊Dic3—24no—
150C2×C3⋊Dic3—216no—
151C2×C3⋊Dic3C2×D414yes—
152C2×C3⋊Dic3C2414yes—
153C2×C3⋊Dic3C2412yes—
154C4×C3⋊D3C2×D4116yescomplemented
155#634—28no—
156C3×#67—232no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—28no—
159C2×C3×Dic3C2418yes—
160C2×C3×Dic3C2414yes—
161C3×C4×D3—216no—
162#624—28no—
163D3×Dic3—216no—
164C22×#41—91no—
165C24×C4—91no—
166#525—916no—
167C2×#123—92no—
168C2×C22⋊Q8—92no—
169C2×#121—32no—
170C2×#120—92no—
171C2×C4×D4—94no—
172C2×#117—91no—
173C24×C3—22no—
174C24×C3—32no—
175C24×C3C22×D314yes—
176C23×D3—32no—
177C23×D3—38no—
178C23×D3—61no—
179C23×D3—68no—
180C23×D3—68no—
181C23×D3—68no—
182C23×D3C22×D312yes—
183C2×C3×D4—28no—
184C2×C3×D4—28no—
185C2×C3×D4—24no—
186C2×C3×D4—316no—
187C2×C3×D4—616no—
188C2×C3×D4C22×D318yescomplemented
189C22×C3×C4—21no—
190C22×C3×C4—34no—
191C22×C3×C4—32no—
192C22×C3×C4—38no—
193C22×C3×C4—68no—
194C22×C3×C4C22×D312yes—
195C2×#67—216no—
196C2×#67—316no—
197C2×#67—68no—
198C2×#67—616no—
199C2×#67—616no—
200C2×#67C22×D3116yes—
201C22×Dic3—32no—
202C22×Dic3—316no—
203C22×Dic3—34no—
204C22×Dic3—38no—
205C22×Dic3—62no—
206C22×Dic3—61no—
207C22×Dic3—68no—
208C22×Dic3—68no—
209C22×Dic3—616no—
210C22×Dic3—616no—
211C22×Dic3C22×D314yes—
212C22×Dic3C22×D312yes—
213#237—664no—
214#237—664no—
215C2×C4×D3—28no—
216C2×C4×D3—316no—
217C2×C4×D3—38no—
218C2×C4×D3—38no—
219C2×C4×D3—38no—
220C2×C4×D3—68no—
221C2×C4×D3—64no—
222C2×C4×D3—664no—
223C2×C4×D3—68no—
224C2×C4×D3—68no—
225C2×C4×D3C22×D318yes—
226C2×Dic6—38no—
227C2×Dic6—64no—
228C2×Dic6—68no—
229C2×Dic6—68no—
230C3×C4⋊C4—38no—
231C3×C22⋊C4—316no—
232#217—316no—
233#217C22×D3116yescomplemented
234(C2×D3)⋊C4—316no—
235(C2×D3)⋊C4—316no—
236C4⋊Dic3—316no—
237C4⋊Dic3C22×D318yescomplemented
238Dic3⋊C4—316no—
239C4×Dic3—316no—
240C22×C32—24no—
241C22×C32—28no—
242C22×C32—48no—
243C22×C32C22×D412yes—
244C22×C32C2×#4114yes—
245C22×C32C2511yescharacteristic
246C2×C3⋊D3—28no—
247C2×C3⋊D3—24no—
248C2×C3⋊D3C22×D414yes—
249C2×C3×D3—216no—
250C2×C3×D3—24no—
251C2×C3×D3—24no—
252C2×C3×D3C2×#4118yescomplemented
253D32—232no—
254C32×C4C22×D414yes—
255C3⋊Dic3—24no—
256C3⋊Dic3C22×D414yes—
257C3×Dic3—24no—
258C3×Dic3—28no—
259C25—91no—
260C2×#41—98no—
261C2×#41—188no—
262C22×Q8—91no—
263C22×D4—34no—
264C22×D4—92no—
265C22×D4D3211yescharacteristic, complemented
266C23×C4—32no—
267C23×C4—91no—
268C23×C4—98no—
269C23×C4—92no—
270C23×C4—91no—
271C23×C4—92no—
272C23×C4—188no—
273#123—916no—
274C22⋊Q8—916no—
275#121—316no—
276#120—916no—
277C4×D4—932no—
278#117—98no—
279C2×C4⋊C4—32no—
280C2×C4⋊C4—94no—
281C2×C22⋊C4—34no—
282C2×C22⋊C4—92no—
283C2×C22⋊C4—94no—
284C2×C42—92no—
285C23×C3—28no—
286C23×C3—28no—
287C23×C3—28no—
288C23×C3—28no—
289C23×C3—24no—
290C23×C3—21no—
291C23×C3—38no—
292C23×C3—34no—
293C23×C3—48no—
294C23×C3—64no—
295C23×C3—64no—
296C23×C3C23×D318yes—
297C23×C3C23×D312yes—
298C22×D3—24no—
299C22×D3—24no—
300C22×D3—38no—
301C22×D3—34no—
302C22×D3—64no—
303C22×D3—62no—
304C22×D3—616no—
305C22×D3—616no—
306C22×D3—664no—
307C22×D3—64no—
308C22×D3—64no—
309C22×D3—616no—
310C22×D3—124no—
311C22×D3#23718yescomplemented
312C22×D3C23×D314yes—
313C3×D4—216no—
314C3×D4—216no—
315C3×D4—632no—
316C2×C3×C4—22no—
317C2×C3×C4—24no—
318C2×C3×C4—38no—
319C2×C3×C4—34no—
320C2×C3×C4—64no—
321C2×C3×C4—68no—
322C2×C3×C4—616no—
323C2×C3×C4D3×D418yes—
324C2×C3×C4C23×D314yes—
325#67—232no—
326#67—632no—
327#67—632no—
328C2×Dic3—24no—
329C2×Dic3—28no—
330C2×Dic3—38no—
331C2×Dic3—34no—
332C2×Dic3—38no—
333C2×Dic3—64no—
334C2×Dic3—64no—
335C2×Dic3—62no—
336C2×Dic3—616no—
337C2×Dic3—632no—
338C2×Dic3—68no—
339C2×Dic3—632no—
340C2×Dic3—68no—
341C2×Dic3C23×D318yes—
342C2×Dic3C23×D314yes—
343C4×D3—216no—
344C4×D3—332no—
345C4×D3—616no—
346C4×D3—616no—
347C4×D3—616no—
348Dic6—616no—
349Dic6—616no—
350C2×C32—44no—
351C2×C32#52514yescomplemented
352C2×C32C23×D411yescharacteristic
353C2×C32C22×#4112yes—
354C3⋊D3—24no—
355C3×D3—28no—
356C24—32no—
357C24—94no—
358C24—91no—
359C24—188no—
360C24—184no—
361C24C2×D3212yes—
362#41—1832no—
363C2×Q8—94no—
364C2×Q8—184no—
365C2×D4—24no—
366C2×D4—316no—
367C2×D4—616no—
368C2×D4—98no—
369C2×D4—188no—
370C2×D4C2×D3214yescomplemented
371C22×C4—34no—
372C22×C4—32no—
373C22×C4—38no—
374C22×C4—68no—
375C22×C4—94no—
376C22×C4—98no—
377C22×C4—91no—
378C22×C4—94no—
379C22×C4—98no—
380C22×C4—98no—
381C22×C4—92no—
382C22×C4—1832no—
383C22×C4—184no—
384C22×C4—188no—
385C22×C4—188no—
386C22×C4C2×D3211yescharacteristic
387C4⋊C4—38no—
388C4⋊C4—916no—
389C22⋊C4—316no—
390C22⋊C4—98no—
391C22⋊C4—916no—
392C42—98no—
393C22×C3—28no—
394C22×C3—28no—
395C22×C3—28no—
396C22×C3—28no—
397C22×C3—24no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—38no—
401C22×C3—48no—
402C22×C3—416no—
403C22×C3—416no—
404C22×C3—64no—
405C22×C3—64no—
406C22×C3—616no—
407C22×C3C2×D3×D414yes—
408C22×C3C2×#23714yes—
409C22×C3D3×#4114yes—
410C22×C3C24×D312yes—
411C2×D3—24no—
412C2×D3—24no—
413C2×D3—216no—
414C2×D3—38no—
415C2×D3—64no—
416C2×D3—664no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—616no—
420C2×D3—124no—
421C2×D3—128no—
422C2×D3C2×#23718yescomplemented
423C3×C4—24no—
424C3×C4—64no—
425C3×C4—68no—
426C3×C4C2×D3×D418yes—
427Dic3—24no—
428Dic3—28no—
429Dic3—38no—
430Dic3—64no—
431Dic3—68no—
432Dic3—68no—
433C32C2×#52511yescharacteristic, complemented, Sylow
434C23—28no—
435C23—24no—
436C23—38no—
437C23—34no—
438C23—64no—
439C23—64no—
440C23—94no—
441C23—92no—
442C23—1816no—
443C23—188no—
444C23—1832no—
445C23—184no—
446C23C22×D3214yes—
447C23C22×D3211yescharacteristic
448Q8—188no—
449D4—28no—
450D4—632no—
451D4—1816no—
452C2×C4—38no—
453C2×C4—34no—
454C2×C4—68no—
455C2×C4—64no—
456C2×C4—616no—
457C2×C4—94no—
458C2×C4—92no—
459C2×C4—916no—
460C2×C4—94no—
461C2×C4—188no—
462C2×C4—1816no—
463C2×C4—1816no—
464C2×C4—184no—
465C2×C4#381114yes—
466C2×C4C22×D3212yes—
467C2×C3—22no—
468C2×C3—21no—
469C2×C3—24no—
470C2×C3—48no—
471C2×C3—48no—
472C2×C3—68no—
473C2×C3#560618yescomplemented
474C2×C3C22×D3×D412yes—
475C2×C3C22×#23712yes—
476C2×C3C2×D3×#4112yes—
477D3—28no—
478D3—68no—
479D3—124no—
480C22—28no—
481C22—24no—
482C22—38no—
483C22—48no—
484C22—64no—
485C22—64no—
486C22—616no—
487C22—94no—
488C22—1832no—
489C22—184no—
490C22—188no—
491C22D3×#23714yes—
492C22C2×#381112yes—
493C22C23×D3211yescharacteristic
494C4—68no—
495C4—64no—
496C4—94no—
497C4—184no—
498C4C2×#381114yes—
499C3—21no—
500C3C2×#560612yescomplemented
501C2—44no—
502C2—68no—
503C2—184no—
504C2#1059530614yesdirect product factor
505C2C2×D3×#23712yes—
506C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C22×C4×D32C2semidirect
3. C2×C3×#938C2semidirect
4. C2×#63983C2semidirect
5. C2×#63975C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. #10595306C2direct (N × H)
8. C2×#63857C2semidirect
9. C2×#63849C2semidirect
12. C22×C32×D4C22semidirect
14. C23×C3⋊Dic3C22semidirect
16. C2×#3830C22semidirect
18. C22×#634C22semidirect
24. C2×C4×D32C22semidirect
25. C2×C3×#217C22semidirect
26. C3×#938C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. #63983C22semidirect
29. #63975C22semidirect
30. #67⋊Dic3C22semidirect
31. C2×Dic3⋊Dic3C22semidirect
34. C2×Dic32C22semidirect
35. #63857C22semidirect
36. #63849C22semidirect
41. C2×#938D3semidirect
57. C2×C32×D4C23semidirect
64. C22×C3⋊Dic3C23semidirect
66. C2×C4×C3⋊D3D4semidirect
69. C2×#634C23semidirect
81. C3×#217C23semidirect
82. C3×C4⋊Dic3C23semidirect
83. Dic3⋊Dic3C23semidirect
86. Dic32C23semidirect
91. C22×C3×D4C2×D3semidirect
116. C2×#217C2×D3semidirect
117. #938C2×D3semidirect
123. C2×C4⋊Dic3C2×D3semidirect
140. C22×C3×D3#41semidirect
154. C4×C3⋊D3C2×D4semidirect
188. C2×C3×D4C22×D3semidirect
233. #217C22×D3semidirect
237. C4⋊Dic3C22×D3semidirect
252. C2×C3×D3C2×#41semidirect
265. C22×D4D32semidirect
311. C22×D3#237semidirect
351. C2×C32#525semidirect
370. C2×D4C2×D32semidirect
422. C2×D3C2×#237semidirect
433. C32C2×#525semidirect
473. C2×C3#5606semidirect
500. C3C2×#5606semidirect
504. C2#10595306direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×C4×D322
C2×C3×#9382
C2×#639832
C2×#639752
C2×#67⋊Dic32
#105953062
C2×#638572
C2×#638492
C2×#56063