Finite Group Databasebeta

← #11900874

Subgroups — #11900874

Order 1152.

3636 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic, complemented
2#10596299C212yesmaximal, complemented
3#41×C3⋊Dic3C212yesmaximal, complemented
4#10596199C212yesmaximal, complemented
5#10596187C212yesmaximal, complemented
6#10596151C214yesmaximal, complemented
7#10596077C214yesmaximal, complemented
8#10596071C214yesmaximal, complemented
9#10596028C214yesmaximal, complemented
10C4×#3830C214yesmaximal, complemented
11C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
12#10595941C211yesmaximal, characteristic, complemented
13#86219—34nomaximal
14C2×C32×#41C2212yes—
15C2×#3830C2214yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C4×C3⋊D3C2212yes—
18C32×C4⋊Q8C2211yescharacteristic, complemented
19C32×#127C2211yescharacteristic, complemented
20C32×#124C2212yescomplemented
21C32×#121C2214yes—
22C32×C4×D4C2214yescomplemented
23C2×C32×C42C2211yescharacteristic
24#64155C2214yes—
25Q8×C3⋊Dic3C2214yescomplemented
26#64147C2214yes—
27#64147C2214yes—
28#64146C2214yes—
29#64145C2214yescomplemented
30#64144C2214yes—
31D4×C3⋊Dic3C2218yes—
32D4×C3⋊Dic3C2214yescomplemented
33D4×C3⋊Dic3C2214yescomplemented
34C4×#638C2218yes—
35#64135C2212yes—
36#64135C2214yescomplemented
37#64133C2214yes—
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2212yes—
40C2×C4×C3⋊Dic3C2214yescomplemented
41#64106C2214yes—
42#64101C2214yes—
43#64099C2214yescomplemented
44#64096C2214yescomplemented
45#64092C2218yes—
46#64090C2218yes—
47#64088C2218yescomplemented
48#64086C2218yescomplemented
49C42×C3⋊D3C2212yes—
50C42×C3⋊D3C2212yes—
51C42×C3⋊D3C2212yes—
52C42×C3⋊D3C2212yes—
53#64079C2212yescomplemented
54#64078C2212yescomplemented
55C4×#634C2214yescomplemented
56C3×#532D314yescomplemented
57#5828—38no—
58Dic3×#41—38no—
59#5728—38no—
60#5716—38no—
61#5680—316no—
62#5606—316no—
63#5600—316no—
64#5557—316no—
65C4×#237—316no—
66C2×C42×D3—34no—
67#5470—34no—
68C23×C3⋊D3C2311yescharacteristic
69C32×#41—28no—
70C2×C32×Q8C2312yes—
71C2×C32×D4C2314yes—
72C2×C32×D4C2314yes—
73C2×C32×D4C2312yes—
74C22×C32×C4C2312yes—
75C22×C32×C4C2314yes—
76C22×C32×C4C2311yescharacteristic
77C2×#638C2318yes—
78C22×C3⋊Dic3C2318yes—
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2311yescharacteristic
81#3830—216no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—28no—
84C2×C4×C3⋊D3C2312yes—
85C2×C4×C3⋊D3C2312yes—
86C2×C4×C3⋊D3C2312yes—
87C2×C4×C3⋊D3C2312yes—
88C2×C4×C3⋊D3C2312yes—
89C2×C4×C3⋊D3C2312yes—
90C2×#634C2314yes—
91C32×C4⋊C4C2314yes—
92C32×C22⋊C4C2318yes—
93C32×C42C2312yes—
94C32×C42C2311yescharacteristic
95C32×C42C2311yescharacteristic
96#3757C2318yes—
97#3757C2318yes—
98#3757C2314yes—
99#3752C2318yes—
100C4⋊(C3⋊Dic3)C2314yes—
101C4⋊(C3⋊Dic3)C2314yes—
102C4⋊(C3⋊Dic3)C2318yes—
103#3750C2318yes—
104#3750C2318yes—
105C4×C3⋊Dic3C2314yes—
106C4×C3⋊Dic3C2312yes—
107C4×C3⋊Dic3C2312yes—
108C4×C3⋊Dic3C2312yes—
109C4×C3⋊Dic3C2312yes—
110C4×C3⋊Dic3C2311yescharacteristic
111C4×C3⋊Dic3C2311yescharacteristic
112C4×C3⋊Dic3C2312yes—
113C4×C3⋊Dic3C2318yes—
114#3444—91noSylow
115C2×C3×#41C2×D318yes—
116C2×#237—316no—
117C22×C4×D3—34no—
118C22×C4×D3—38no—
119C3×C4⋊Q8C2×D314yescomplemented
120C3×#127C2×D314yescomplemented
121C3×#124C2×D318yescomplemented
122C3×#121C2×D3116yes—
123C3×C4×D4C2×D3116yescomplemented
124C2×C3×C42C2×D314yes—
125#946—316no—
126Q8×Dic3—316no—
127#938—316no—
128#938—316no—
129#937—316no—
130#936—316no—
131#935—316no—
132D4×Dic3—316no—
133D4×Dic3—316no—
134D4×Dic3—332no—
135C4×#67—332no—
136#926—38no—
137#926—316no—
138#924—316no—
139C2×C4×Dic3—34no—
140C2×C4×Dic3—38no—
141C2×C4×Dic3—316no—
142#897—316no—
143#892—316no—
144#890—316no—
145#887—316no—
146#883—332no—
147#67⋊C4—332no—
148#879—332no—
149#877—332no—
150C42×D3—38no—
151C42×D3—38no—
152C42×D3—38no—
153C42×D3—38no—
154#870—38no—
155#869—38no—
156C4×Dic6—316no—
157C23×C32C2414yes—
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—22no—
160C22×C3⋊D3—24no—
161C22×C3⋊D3C2412yes—
162C32×Q8—24no—
163C32×D4—28no—
164C32×D4—28no—
165C32×D4—24no—
166C2×C32×C4—24no—
167C2×C32×C4—28no—
168C2×C32×C4#4114yescomplemented
169C2×C32×C4C2412yes—
170C2×C32×C4C2414yes—
171C2×C32×C4C2411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C32×C4C2412yes—
174#638—216no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—24no—
177C2×C3⋊Dic3—216no—
178C2×C3⋊Dic3C2412yes—
179C2×C3⋊Dic3C2412yes—
180C2×C3⋊Dic3C2418yes—
181C2×C3⋊Dic3C2412yes—
182C4×C3⋊D3—24no—
183C4×C3⋊D3—24no—
184C4×C3⋊D3—24no—
185C4×C3⋊D3—24no—
186C4×C3⋊D3—24no—
187C4×C3⋊D3#4118yescomplemented
188#634—28no—
189#533—92no—
190#533—91no—
191#532—92no—
192#532C3⋊D311yescharacteristic, complemented
193#529—94no—
194#529—94no—
195#529—94no—
196#525—92no—
197#525—94no—
198C4×#41—92no—
199C4×#41—94no—
200C22×C42—91no—
201C23×D3—34no—
202C3×#41—232no—
203C2×C3×Q8C22×D318yes—
204C2×C3×D4C22×D3116yes—
205C2×C3×D4C22×D318yes—
206C2×C3×D4C22×D3116yes—
207C22×C3×C4C22×D318yes—
208C22×C3×C4C22×D3116yes—
209C22×C3×C4C22×D314yes—
210C2×#67—332no—
211C22×Dic3—332no—
212C22×Dic3—38no—
213C22×Dic3—34no—
214#237—664no—
215C2×C4×D3—38no—
216C2×C4×D3—38no—
217C2×C4×D3—38no—
218C2×C4×D3—38no—
219C2×C4×D3—38no—
220C2×C4×D3—38no—
221C2×C4×D3—632no—
222C2×C4×D3—616no—
223C2×Dic6—316no—
224C3×C4⋊C4C22×D3116yes—
225C3×C22⋊C4C22×D3132yes—
226C3×C42C22×D318yes—
227C3×C42C22×D314yes—
228C3×C42C22×D314yes—
229#217—332no—
230#217—332no—
231#217—316no—
232(C2×D3)⋊C4—332no—
233C4⋊Dic3—316no—
234C4⋊Dic3—316no—
235C4⋊Dic3—332no—
236Dic3⋊C4—332no—
237Dic3⋊C4—332no—
238C4×Dic3—316no—
239C4×Dic3—38no—
240C4×Dic3—38no—
241C4×Dic3—38no—
242C4×Dic3—38no—
243C4×Dic3—34no—
244C4×Dic3—34no—
245C4×Dic3—38no—
246C4×Dic3—332no—
247C22×C32—22no—
248C22×C32—28no—
249C22×C32—24no—
250C22×C32C2×#4112yes—
251C22×C32C2511yescharacteristic
252C2×C3⋊D3—28no—
253C2×C3⋊D3—22no—
254C2×C3⋊D3—22no—
255C2×C3⋊D3C2×#4114yes—
256C32×C4—22no—
257C32×C4—24no—
258C32×C4C2×#4112yes—
259C32×C4C2×#4112yes—
260C32×C4C2×#4114yes—
261C3⋊Dic3—28no—
262C3⋊Dic3—22no—
263C3⋊Dic3—22no—
264C3⋊Dic3C2×#4114yes—
265C2×#41—94no—
266C2×#41C2×C3⋊D312yes—
267C23×C4—92no—
268C23×C4—91no—
269C4⋊Q8—92no—
270C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
271#127C2×C3⋊D311yescharacteristic, complemented
272#126—98no—
273#125—94no—
274#125—92no—
275#124—94no—
276#124C2×C3⋊D312yescomplemented
277#123—94no—
278#123—98no—
279C22⋊Q8—94no—
280C22⋊Q8—94no—
281C22⋊Q8—94no—
282#121—94no—
283#121—94no—
284#121C2×C3⋊D314yes—
285#120—94no—
286C4×Q8—94no—
287C4×Q8—94no—
288C4×Q8—94no—
289C4×D4—98no—
290C4×D4—94no—
291C4×D4—94no—
292C4×D4—98no—
293C4×D4—98no—
294C4×D4C2×C3⋊D314yescomplemented
295#117—92no—
296#117—94no—
297#117—94no—
298#117—98no—
299C2×C42—94no—
300C2×C42—91no—
301C2×C42—92no—
302C2×C42—92no—
303C2×C42—92no—
304C2×C42—92no—
305C2×C42—92no—
306C2×C42C2×C3⋊D311yescharacteristic
307C23×C3C23×D3116yes—
308C23×C3C23×D314yes—
309C22×D3—38no—
310C22×D3—616no—
311C22×D3—68no—
312C3×Q8—216no—
313C3×D4—232no—
314C3×D4—216no—
315C3×D4—232no—
316C2×C3×C4—232no—
317C2×C3×C4—216no—
318C2×C3×C4#237116yescomplemented
319C2×C3×C4C23×D318yes—
320C2×C3×C4C23×D3116yes—
321C2×C3×C4C23×D314yes—
322C2×C3×C4C23×D318yes—
323C2×C3×C4C23×D314yes—
324#67—664no—
325C2×Dic3—38no—
326C2×Dic3—38no—
327C2×Dic3—38no—
328C2×Dic3—332no—
329C2×Dic3—616no—
330C2×Dic3—664no—
331C2×Dic3—68no—
332C4×D3—332no—
333C4×D3—616no—
334C4×D3—616no—
335C4×D3—616no—
336C4×D3—616no—
337C4×D3—616no—
338Dic6—632no—
339C2×C32—22no—
340C2×C32—44no—
341C2×C32C22×#4111yescharacteristic
342C2×C32C22×#4112yes—
343C3⋊D3—24no—
344C24—91no—
345#41—28no—
346#41—1816no—
347C2×Q8—94no—
348C2×Q8C22×C3⋊D312yes—
349C2×D4—98no—
350C2×D4C22×C3⋊D314yes—
351C2×D4C22×C3⋊D312yes—
352C2×D4C22×C3⋊D314yes—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—91no—
356C22×C4—98no—
357C22×C4—92no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4—92no—
361C22×C4—92no—
362C22×C4—188no—
363C22×C4—184no—
364C22×C4C22×C3⋊D312yes—
365C22×C4C22×C3⋊D314yes—
366C22×C4C22×C3⋊D311yescharacteristic
367C4⋊C4—94no—
368C4⋊C4—94no—
369C4⋊C4—98no—
370C4⋊C4—98no—
371C4⋊C4—98no—
372C4⋊C4C22×C3⋊D314yes—
373C22⋊C4—94no—
374C22⋊C4—98no—
375C22⋊C4—98no—
376C22⋊C4—98no—
377C22⋊C4C22×C3⋊D318yes—
378C42—92no—
379C42—92no—
380C42—92no—
381C42—92no—
382C42—92no—
383C42—98no—
384C42—91no—
385C42—91no—
386C42—94no—
387C42C22×C3⋊D311yescharacteristic
388C42C22×C3⋊D311yescharacteristic
389C42C22×C3⋊D312yes—
390C22×C3—28no—
391C22×C3—216no—
392C22×C3—232no—
393C22×C3C2×#23718yes—
394C22×C3C24×D314yes—
395C2×D3—316no—
396C2×D3—632no—
397C2×D3—68no—
398C2×D3—68no—
399C3×C4—216no—
400C3×C4—28no—
401C3×C4C2×#23718yes—
402C3×C4C2×#23718yes—
403C3×C4D3×#41116yes—
404Dic3—316no—
405Dic3—68no—
406Dic3—632no—
407Dic3—68no—
408C32#344411yescharacteristic, complemented, Sylow
409C23—92no—
410C23—184no—
411C23—182no—
412C23C23×C3⋊D314yes—
413C23C23×C3⋊D311yescharacteristic
414Q8—24no—
415Q8—188no—
416D4—28no—
417D4—24no—
418D4—28no—
419D4—1816no—
420C2×C4—28no—
421C2×C4—24no—
422C2×C4—92no—
423C2×C4—98no—
424C2×C4—92no—
425C2×C4—92no—
426C2×C4—98no—
427C2×C4—184no—
428C2×C4—184no—
429C2×C4—184no—
430C2×C4—1816no—
431C2×C4—182no—
432C2×C4—184no—
433C2×C4—184no—
434C2×C4—184no—
435C2×C4#383014yescomplemented
436C2×C4C23×C3⋊D312yes—
437C2×C4C23×C3⋊D314yes—
438C2×C4C23×C3⋊D311yescharacteristic
439C2×C4C23×C3⋊D312yes—
440C2×C4C23×C3⋊D311yescharacteristic
441C2×C3—28no—
442C2×C3—416no—
443C2×C3C22×#23714yes—
444C2×C3C2×D3×#4118yes—
445D3—616no—
446C22—22no—
447C22—24no—
448C22—28no—
449C22—94no—
450C22—188no—
451C22—182no—
452C22—182no—
453C22C2×#383012yes—
454C22C24×C3⋊D311yescharacteristic
455C4—24no—
456C4—22no—
457C4—94no—
458C4—182no—
459C4—182no—
460C4—188no—
461C4C2×#383012yes—
462C4C2×#383012yes—
463C4#41×C3⋊D314yes—
464C3#8621914yescomplemented
465C2—22no—
466C2—44no—
467C2—184no—
468C2C22×#383011yescharacteristic
469C2C2×#41×C3⋊D312yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×#532C2
hypercenter#532C3⋊D3
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. #10596299C2semidirect
3. #41×C3⋊Dic3C2semidirect
4. #10596199C2semidirect
5. #10596187C2semidirect
6. #10596151C2semidirect
7. #10596077C2semidirect
8. #10596071C2semidirect
9. #10596028C2semidirect
10. C4×#3830C2semidirect
11. C2×C42×C3⋊D3C2semidirect
12. #10595941C2semidirect
18. C32×C4⋊Q8C22semidirect
19. C32×#127C22semidirect
20. C32×#124C22semidirect
22. C32×C4×D4C22semidirect
25. Q8×C3⋊Dic3C22semidirect
29. #64145C22semidirect
32. D4×C3⋊Dic3C22semidirect
33. D4×C3⋊Dic3C22semidirect
36. #64135C22semidirect
40. C2×C4×C3⋊Dic3C22semidirect
43. #64099C22semidirect
44. #64096C22semidirect
47. #64088C22semidirect
48. #64086C22semidirect
53. #64079C22semidirect
54. #64078C22semidirect
55. C4×#634C22semidirect
56. C3×#532D3semidirect
119. C3×C4⋊Q8C2×D3semidirect
120. C3×#127C2×D3semidirect
121. C3×#124C2×D3semidirect
123. C3×C4×D4C2×D3semidirect
168. C2×C32×C4#41semidirect
187. C4×C3⋊D3#41semidirect
192. #532C3⋊D3semidirect
270. C4⋊Q8C2×C3⋊D3semidirect
271. #127C2×C3⋊D3semidirect
276. #124C2×C3⋊D3semidirect
294. C4×D4C2×C3⋊D3semidirect
318. C2×C3×C4#237semidirect
408. C32#3444semidirect
435. C2×C4#3830semidirect
464. C3#86219semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
#105962992
#41×C3⋊Dic32
#105961992
#105961872
#105961512
#105960772
#105960712
#105960282
C4×#38302
C2×C42×C3⋊D32
#105959412
#862193