Finite Group Databasebeta

← #11878669

Subgroups — #11878669

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C2×C3×#874C211yesmaximal, characteristic, complemented
3C3×#4925C211yesmaximal, characteristic, complemented
4#10591162C214yesmaximal, complemented
5#10590355C214yesmaximal, complemented
6#10590350C212yesmaximal, complemented
7#10590273C212yesmaximal, complemented
8#83166—31nomaximal
9#79303—31nomaximal
10C2×#3828—21no—
11C22×C3×D12—21no—
12C22×C3×D12—21no—
13C22×C3×D12C2212yes—
14C2×C32×C42C2211yescharacteristic
15#64139—21no—
16#64139C2212yes—
17#64084—21no—
18#64083C2211yescharacteristic, complemented
19C4×C4⋊(C3⋊D3)—21no—
20C4×C4⋊(C3⋊D3)C2212yescomplemented
21#64078C2211yescharacteristic, complemented
22C3×#874—21no—
23C3×#874—21no—
24C3×#874C2212yes—
25C3×#874C2212yes—
26C2×#3714C2218yescomplemented
27C3×#830C2212yes—
28C3×C4⋊(C3⋊C8)C2212yescomplemented
29C3×C4×C3⋊C8C2212yescomplemented
30#63563C2218yescomplemented
31C2×C3×#127—31no—
32#5477—31no—
33#5477—31no—
34#5477—61no—
35C2×#874D311yescharacteristic, complemented
36C3×#431—31no—
37#5217—34no—
38#5073—32no—
39#5072—34no—
40#5070—32no—
41#4925D311yescharacteristic, complemented
42#4843—34no—
43#4732—34no—
44#4695—32no—
45#4694—32no—
46C23×C3×D3—22no—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C2×#638—22no—
51#3828—44no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C4×C3⋊D3—22no—
56C2×#634—21no—
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—22no—
62C2×C3×D12—44no—
63C2×C3×D12—44no—
64C2×C3×D12—44no—
65C2×C3×D12C2314yes—
66C32×C42D411yescharacteristic
67C32×C42D411yescharacteristic
68C32×C42C2311yescharacteristic
69C32×C42C2311yescharacteristic
70#3752—22no—
71#3752—22no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C2×C3×C3⋊C8C2314yes—
75#3714—48no—
76#3205—91noSylow
77C22×C3×D4—32no—
78C22×C3×D4—61no—
79C22×C3×D4—61no—
80C2×#235—62no—
81C2×#235—61no—
82C2×#235—61no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12C2×D312yes—
86C3×#127—32no—
87C3×#127—32no—
88C3×#127—61no—
89C3×#127—61no—
90C2×C3×C42—21no—
91C2×C3×C42C2×D311yescharacteristic
92C2×C3×C42C2×D311yescharacteristic
93C2×#213—38no—
94#930—32no—
95#930—32no—
96#930—62no—
97#930—62no—
98#930—61no—
99#930—61no—
100C2×D24—38no—
101#875—62no—
102#875—61no—
103#875—61no—
104#874—21no—
105#874—21no—
106#874—31no—
107#874—31no—
108#874—61no—
109#874C2×D312yes—
110#874C2×D312yes—
111C4×D12—32no—
112C4×D12—32no—
113C4×D12—62no—
114C4×D12—62no—
115C4×D12—61no—
116C4×D12—61no—
117#869—31no—
118#869—31no—
119#869—61no—
120C3×C4⋊C8—32no—
121C3×C22⋊C8—32no—
122C3×C4×C8—32no—
123#832—38no—
124#830C2×D312yes—
125#821—38no—
126C4⋊(C3⋊C8)C2×D312yescomplemented
127C4×C3⋊C8C2×D312yescomplemented
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3×D3—24no—
131C22×C3×D3—44no—
132C22×C3×D3—44no—
133C22×C3×D3—44no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4D814yescomplemented
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2411yescharacteristic
143#638—44no—
144C2×C3⋊Dic3—22no—
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—42no—
147C4⋊(C3⋊D3)—42no—
148C4×C3⋊D3—44no—
149#634—42no—
150C3×D12—28no—
151C3×D12—44no—
152C3×D12—44no—
153C3×D12—44no—
154C3×D12—44no—
155C3×D12—44no—
156C3×C3⋊C8—24no—
157#532—91no—
158C2×#127—31no—
159#493—92no—
160#486—92no—
161#459—94no—
162#447—94no—
163#431—31no—
164C24×C3—62no—
165C23×D3—22no—
166C2×C3×D4—34no—
167C2×C3×D4—62no—
168C2×C3×D4—62no—
169C2×C3×D4—62no—
170C2×C3×D4—62no—
171C2×C3×D4—62no—
172C2×C3×D4—124no—
173C2×C3×D4—124no—
174C2×C3×D4—124no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4D1211yescharacteristic
179C22×C3×C4D1211yescharacteristic
180C22×C3×C4#6711yescharacteristic
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—64no—
185C2×#67—62no—
186C2×#67—62no—
187#235—128no—
188#235—124no—
189#235—124no—
190C2×D12—22no—
191C2×D12—22no—
192C2×D12—22no—
193C2×D12—22no—
194C2×D12—22no—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—44no—
198C2×D12—44no—
199C2×D12—44no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12C22×D314yes—
208C2×C4×D3—64no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×Dic6—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×C3×C8—34no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—21no—
219C3×C42D1211yescharacteristic
220C3×C42D1211yescharacteristic
221C3×C42#6711yescharacteristic
222C3×C42#6711yescharacteristic
223C3×C42C22×D311yescharacteristic
224C3×C42C22×D311yescharacteristic
225C3×C42C22×D311yescharacteristic
226C3×C42C22×D311yescharacteristic
227#213—128no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—62no—
237C4⋊Dic3—62no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C2×C3⋊C8C22×D314yes—
241D24—128no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32C2×D812yes—
245C22×C32C22×D411yescharacteristic
246C2×C3⋊D3—42no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3×D3—44no—
250C2×C3×D3—44no—
251C2×C3×D3—44no—
252C2×C3×D3—88no—
253C32×C4—21no—
254C32×C4—21no—
255C32×C4C2×D812yes—
256C32×C4C2×D812yes—
257C32×C4AGL(1,ℤ/8)12yes—
258C32×C4H(5,𝔽2)12yes—
259C3⋊Dic3—42no—
260C2×#41—181no—
261C22×D4—32no—
262C22×D4—61no—
263C22×D4—61no—
264C2×D8—98no—
265C4⋊Q8—91no—
266#127—32no—
267#127—32no—
268#127—61no—
269#127—61no—
270#127—91no—
271#124—181no—
272#121—92no—
273#121—181no—
274C4×D4—92no—
275C4×D4—181no—
276C2×C42D3211yescharacteristic
277C4⋊C8—32no—
278#102—98no—
279C22⋊C8—32no—
280C4×C8—32no—
281C23×C3—21no—
282C23×C3—64no—
283C23×C3—124no—
284C23×C3—124no—
285C23×C3—124no—
286C23×C3C2×D1211yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C22×D3—24no—
289C22×D3—44no—
290C22×D3—44no—
291C22×D3—44no—
292C22×D3—64no—
293C22×D3—62no—
294C22×D3—62no—
295C3×D4—68no—
296C3×D4—124no—
297C3×D4—124no—
298C3×D4—124no—
299C3×D4—124no—
300C3×D4—124no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—24no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4D2414yescomplemented
315C2×C3×C4#21314yescomplemented
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4C2×D1211yescharacteristic
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—128no—
329#67—124no—
330#67—124no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334D12—28no—
335D12—44no—
336D12—44no—
337D12—44no—
338D12—44no—
339D12—44no—
340D12—64no—
341D12—64no—
342D12—124no—
343D12—124no—
344D12—124no—
345D12—122no—
346D12—122no—
347D12—122no—
348D12—122no—
349C4×D3—128no—
350C4×D3—124no—
351C4×D3—124no—
352Dic6—124no—
353Dic6—122no—
354Dic6—122no—
355C3×C8—64no—
356C3⋊C8—24no—
357C2×C32—22no—
358C2×C32#53511yescharacteristic
359C2×C32C22×D811yescharacteristic
360C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
361C3⋊D3—82no—
362C3×D3—84no—
363C24—62no—
364#41—364no—
365C2×Q8—181no—
366C2×D4—34no—
367C2×D4—62no—
368C2×D4—62no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4—62no—
372C2×D4—92no—
373C2×D4—124no—
374C2×D4—124no—
375C2×D4—124no—
376C2×D4—182no—
377C2×D4—181no—
378C2×D4—181no—
379C22×C4—182no—
380C22×C4#62611yescharacteristic
381C22×C4#62611yescharacteristic
382C22×C4C2×D3211yescharacteristic
383D8—368no—
384C2×C8—34no—
385C4⋊C4—92no—
386C4⋊C4—181no—
387C22⋊C4—182no—
388C22⋊C4—182no—
389C42#62611yescharacteristic
390C42#62611yescharacteristic
391C42C2×D3211yescharacteristic
392C42C2×D3211yescharacteristic
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—124no—
402C22×C3—124no—
403C22×C3—124no—
404C22×C3—248no—
405C22×C3C2×D2412yes—
406C22×C3C2×#21312yes—
407C22×C3C22×D1211yescharacteristic
408C22×C3C22×#6711yescharacteristic
409C2×D3—44no—
410C2×D3—44no—
411C2×D3—44no—
412C2×D3—88no—
413C2×D3—124no—
414C2×D3—124no—
415C2×D3—124no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—22no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4C2×D2412yes—
433C3×C4C2×D2412yes—
434C3×C4#90812yes—
435C3×C4C2×#21312yes—
436C3×C4C2×#21312yes—
437C3×C4#93212yes—
438C3×C4#100412yes—
439C3×C4#100912yes—
440Dic3—124no—
441Dic3—122no—
442Dic3—122no—
443C32#320511yescharacteristic, complemented, Sylow
444C23—64no—
445C23—124no—
446C23—124no—
447C23—124no—
448C23—182no—
449C23C2×#62611yescharacteristic
450Q8—362no—
451D4—68no—
452D4—124no—
453D4—124no—
454D4—124no—
455D4—124no—
456D4—124no—
457D4—184no—
458D4—364no—
459D4—362no—
460D4—362no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—182no—
464C2×C4—364no—
465C2×C4#371414yescomplemented
466C2×C4C2×#62611yescharacteristic
467C2×C4C2×#62611yescharacteristic
468C2×C4C2×#62611yescharacteristic
469C2×C4C2×#62611yescharacteristic
470C2×C4C2×#62611yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—64no—
473C2×C3—22no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—42no—
479C2×C3—244no—
480C2×C3#552511yescharacteristic
481C2×C3C22×D2411yescharacteristic
482C2×C3C2×#90811yescharacteristic
483C2×C3C22×#21311yescharacteristic
484C2×C3C2×#93211yescharacteristic
485C2×C3#580511yescharacteristic
486D3—84no—
487D3—244no—
488D3—242no—
489D3—242no—
490C22—21no—
491C22—21no—
492C22—124no—
493C22—124no—
494C22—124no—
495C22—248no—
496C22—362no—
497C22—362no—
498C22—362no—
499C22C2×#371412yes—
500C22C22×#62611yescharacteristic
501C4—21no—
502C4—21no—
503C4—362no—
504C4C2×#371412yes—
505C4C2×#371412yes—
506C4#6383012yes—
507C4#6430712yes—
508C3—21no—
509C3#7930311yescharacteristic, complemented
510C3#8316611yescharacteristic, complemented
511C2—22no—
512C2—244no—
513C2—722no—
514C2C22×#371411yescharacteristic
515C2C2×#6383011yescharacteristic
516C2#1059504211yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C2×C3×#874C2semidirect
3. C3×#4925C2semidirect
4. #10591162C2semidirect
5. #10590355C2semidirect
6. #10590350C2semidirect
7. #10590273C2semidirect
18. #64083C22semidirect
20. C4×C4⋊(C3⋊D3)C22semidirect
21. #64078C22semidirect
26. C2×#3714C22semidirect
28. C3×C4⋊(C3⋊C8)C22semidirect
29. C3×C4×C3⋊C8C22semidirect
30. #63563C22semidirect
35. C2×#874D3semidirect
41. #4925D3semidirect
126. C4⋊(C3⋊C8)C2×D3semidirect
127. C4×C3⋊C8C2×D3semidirect
136. C2×C32×C4D8semidirect
314. C2×C3×C4D24semidirect
315. C2×C3×C4#213semidirect
443. C32#3205semidirect
465. C2×C4#3714semidirect
509. C3#79303semidirect
510. C3#83166semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C3×#8742
C3×#49252
#105911622
#105903552
#105903502
#105902732
#831663
#793033