Finite Group Databasebeta

← #11864183

Subgroups — #11864183

Order 1152.

2262 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic
2C2×#64127C212yesmaximal, complemented
3C3⋊D3×C22⋊Q8C211yesmaximal, characteristic, complemented
4C32×#451C211yesmaximal, characteristic, complemented
5#10592927C211yesmaximal, characteristic, complemented
6#10592886C212yesmaximal, complemented
7#10592745C211yesmaximal, characteristic, complemented
8#10592507C212yesmaximal, complemented
9#10592502C212yesmaximal, complemented
10#10592430C211yesmaximal, characteristic, complemented
11#10592425C211yesmaximal, characteristic, complemented
12#80184—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C2×#3832—28no—
15C2×#3832—21no—
16C2×#3832—21no—
17C2×#3832C2212yes—
18C2×#3832C2212yes—
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C22×C4⋊(C3⋊D3)—21no—
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3—21no—
23C22×C4×C3⋊D3C2211yescharacteristic
24C2×C32×Q16C2212yescomplemented
25C32×C22⋊Q8C2211yescharacteristic
26#64155C2211yescharacteristic, complemented
27C2×#3756C2212yescomplemented
28C2×#3755C2212yescomplemented
29#64133C2211yescharacteristic
30#64127—28no—
31C2×#3744C2212yescomplemented
32C2×#3743C2212yescomplemented
33#64106C2211yescharacteristic, complemented
34#64105—21no—
35C4⋊C4×C3⋊D3—21no—
36C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
37C22⋊C4×C3⋊D3—21no—
38#64087—21no—
39C32×#103C2212yescomplemented
40C32×C22⋊C8C2211yescharacteristic
41#63662C2212yescomplemented
42#63657C2211yescharacteristic
43#63648C2212yescomplemented
44#63647C2212yescomplemented
45#63636C2212yescomplemented
46C22×#239—34no—
47C2×#918—38no—
48D3×C22⋊Q8—34no—
49C3×#451D314yescomplemented
50#5228—34no—
51#5187—38no—
52#5046—34no—
53#4808—38no—
54#4803—38no—
55#4731—34no—
56#4726—34no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3D411yescharacteristic
59C2×C32×Q8—24no—
60C2×C32×Q8—21no—
61C2×C32×Q8C2311yescharacteristic
62C2×C32×Q8C2312yes—
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3D411yescharacteristic
66#3832—28no—
67#3832—28no—
68#3832—24no—
69#3832—24no—
70#3832—24no—
71#3832D418yes—
72Q8×C3⋊D3—24no—
73C2×C4⋊(C3⋊D3)—28no—
74C2×C4⋊(C3⋊D3)—22no—
75C2×C4⋊(C3⋊D3)—22no—
76C2×C4⋊(C3⋊D3)—21no—
77C2×C4⋊(C3⋊D3)—24no—
78C2×C4⋊(C3⋊D3)C2312yes—
79C2×C4×C3⋊D3—28no—
80C2×C4×C3⋊D3—22no—
81C2×C4×C3⋊D3—22no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3D411yescharacteristic
86C2×C4×C3⋊D3D411yescharacteristic
87C2×C4×C3⋊D3C2311yescharacteristic
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C32×Q16—24no—
92C2×C32×C8C2312yes—
93C32×C4⋊C4—21no—
94C32×C4⋊C4C2311yescharacteristic
95C32×C22⋊C4—21no—
96#3757—21no—
97#3756—24no—
98#3755—24no—
99#3752—21no—
100#3752—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103#3750—21no—
104#3750—21no—
105#3750—21no—
106C2×C3⋊(C3⋊C8)C2312yes—
107#3744—24no—
108#3743—24no—
109#3007—91noSylow
110C22×C3×Q8C2×D314yes—
111C2×#239—38no—
112C2×#239—38no—
113C2×#239—64no—
114C2×#239—64no—
115C2×#239—632no—
116C2×D3×Q8—34no—
117C22×D12—34no—
118C22×D12—64no—
119C22×C4×D3—34no—
120C22×C4×D3—64no—
121C2×C3×Q16C2×D318yescomplemented
122C3×C22⋊Q8C2×D314yes—
123#946—34no—
124C2×#216—38no—
125C2×#215—38no—
126#924—34no—
127#918—632no—
128C2×#204—38no—
129C2×ΓL(1,𝔽25)—38no—
130#897—34no—
131#896—64no—
132D3×C4⋊C4—34no—
133D3×C4⋊C4—64no—
134D3×C22⋊C4—64no—
135#878—64no—
136C3×#103C2×D318yescomplemented
137C3×C22⋊C8C2×D314yes—
138#835—38no—
139#830—34no—
140#821—38no—
141(C2×D3)⋊C8—38no—
142#809—38no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—24no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—41no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3C2×D411yescharacteristic
152C22×C3⋊D3C2×D411yescharacteristic
153C32×Q8—24no—
154C32×Q8—22no—
155C32×Q8—22no—
156C32×Q8C2×D414yes—
157C2×C32×C4—24no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3C2×D411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C4⋊(C3⋊D3)—28no—
170C4⋊(C3⋊D3)—24no—
171C4⋊(C3⋊D3)—28no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)C2×D414yes—
174C4×C3⋊D3—28no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3—28no—
178C4×C3⋊D3—22no—
179C4×C3⋊D3—42no—
180C4×C3⋊D3—42no—
181C4×C3⋊D3C2×D414yes—
182#634—22no—
183#634—42no—
184C32×C8—22no—
185C3⋊(C3⋊C8)—22no—
186C22×#41—91no—
187C2×#137—92no—
188C2×C22⋊Q8—91no—
189#452—92no—
190#452—92no—
191#451—91no—
192#451C3⋊D311yescharacteristic, complemented
193#450—91no—
194#450—91no—
195#417—92no—
196#407—91no—
197C23×D3—34no—
198C23×D3—64no—
199C2×C3×Q8—216no—
200C2×C3×Q8—24no—
201C2×C3×Q8C22×D314yes—
202C2×C3×Q8C22×D318yes—
203C22×C3×C4—24no—
204C22×C3×C4C22×D314yes—
205C22×Dic3—34no—
206#239—332no—
207#239—616no—
208#239—616no—
209#239—632no—
210#239—632no—
211#239—616no—
212D3×Q8—616no—
213C2×D12—38no—
214C2×D12—616no—
215C2×D12—68no—
216C2×D12—68no—
217C2×D12—632no—
218C2×D12—64no—
219C2×C4×D3—34no—
220C2×C4×D3—34no—
221C2×C4×D3—34no—
222C2×C4×D3—34no—
223C2×C4×D3—616no—
224C2×C4×D3—68no—
225C2×C4×D3—68no—
226C2×C4×D3—632no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×Dic6—34no—
230C2×Dic6—64no—
231C3×Q16—216no—
232C2×C3×C8C22×D318yes—
233C3×C4⋊C4—24no—
234C3×C4⋊C4C22×D314yes—
235C3×C22⋊C4—24no—
236#217—64no—
237#216—616no—
238#215—616no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—34no—
242C4⋊Dic3—64no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—64no—
246C2×C3⋊C8—38no—
247#204—616no—
248ΓL(1,𝔽25)—616no—
249C22×C32—21no—
250C22×C32—21no—
251C22×C32#13712yescomplemented
252C22×C32C22×D411yescharacteristic
253C2×C3⋊D3—21no—
254C2×C3⋊D3—21no—
255C2×C3⋊D3—21no—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—21no—
258C2×C3⋊D3—21no—
259C2×C3⋊D3—44no—
260C2×C3⋊D3—48no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3#12012yes—
264C32×C4—24no—
265C32×C4—21no—
266C32×C4—41no—
267C32×C4—41no—
268C32×C4C22×D412yes—
269C3⋊Dic3—21no—
270C3⋊Dic3—41no—
271C3⋊Dic3—41no—
272C3⋊Dic3#12012yes—
273C2×#41—92no—
274C2×#41—92no—
275C2×#41—181no—
276C2×#41—181no—
277C2×#41—188no—
278C22×Q8—91no—
279C22×Q8C2×C3⋊D311yescharacteristic
280C22×D4—91no—
281C22×D4—181no—
282C23×C4—91no—
283C23×C4—181no—
284#137—188no—
285C2×Q16—92no—
286C2×Q16C2×C3⋊D312yescomplemented
287C2×SD16—92no—
288C2×SD16—92no—
289C2×M16—92no—
290C22⋊Q8—91no—
291C22⋊Q8—91no—
292C22⋊Q8—91no—
293C22⋊Q8—181no—
294C22⋊Q8—181no—
295C22⋊Q8C2×C3⋊D311yescharacteristic
296C2×C4⋊C4—91no—
297C2×C4⋊C4—181no—
298C2×C22⋊C4—181no—
299#103—92no—
300#103C2×C3⋊D312yescomplemented
301#102—92no—
302#102—92no—
303C22⋊C8—91no—
304C22⋊C8—92no—
305C22⋊C8C2×C3⋊D311yescharacteristic
306C23×C3D3×D414yes—
307C22×D3—34no—
308C22×D3—34no—
309C22×D3—68no—
310C22×D3—616no—
311C22×D3—68no—
312C22×D3—68no—
313C22×D3—124no—
314C22×D3—128no—
315C22×D3—128no—
316C3×Q8—216no—
317C3×Q8—28no—
318C3×Q8—28no—
319C3×Q8D3×D4116yes—
320C2×C3×C4—216no—
321C2×C3×C4—28no—
322C2×C3×C4—28no—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4D3×D414yes—
326C2×C3×C4C23×D314yes—
327C2×Dic3—34no—
328C2×Dic3—34no—
329C2×Dic3—68no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332D12—316no—
333D12—632no—
334D12—632no—
335D12—616no—
336D12—68no—
337C4×D3—316no—
338C4×D3—68no—
339C4×D3—632no—
340C4×D3—68no—
341C4×D3—632no—
342C4×D3—68no—
343C4×D3—128no—
344C4×D3—128no—
345Dic6—68no—
346Dic6—128no—
347C3×C8—28no—
348C3⋊C8—68no—
349C2×C32—22no—
350C2×C32C2×#12011yescharacteristic
351C2×C32C2×#13711yescharacteristic
352C2×C32#57511yescharacteristic
353C3⋊D3—22no—
354C3⋊D3—41no—
355C3⋊D3—44no—
356C24—91no—
357C24—181no—
358#41—98no—
359#41—184no—
360#41—184no—
361#41—188no—
362#41—188no—
363#41—184no—
364C2×Q8—24no—
365C2×Q8—21no—
366C2×Q8—91no—
367C2×Q8—181no—
368C2×Q8—184no—
369C2×Q8C22×C3⋊D311yescharacteristic
370C2×Q8C22×C3⋊D312yes—
371C2×D4—92no—
372C2×D4—184no—
373C2×D4—182no—
374C2×D4—182no—
375C2×D4—188no—
376C2×D4—181no—
377C22×C4—21no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—184no—
384C22×C4—182no—
385C22×C4—182no—
386C22×C4—188no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4C22×C3⋊D311yescharacteristic
390Q16—24no—
391Q16—184no—
392SD16—184no—
393SD16—184no—
394M16—184no—
395C2×C8—92no—
396C2×C8C22×C3⋊D312yes—
397C4⋊C4—21no—
398C4⋊C4—91no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4C22×C3⋊D311yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3#91818yescomplemented
411C22×C3C2×D3×D414yes—
412C2×D3—38no—
413C2×D3—64no—
414C2×D3—64no—
415C2×D3—64no—
416C2×D3—64no—
417C2×D3—616no—
418C2×D3—64no—
419C2×D3—1216no—
420C2×D3—1232no—
421C2×D3—128no—
422C2×D3—128no—
423C3×C4—216no—
424C3×C4—24no—
425C3×C4—44no—
426C3×C4—44no—
427C3×C4C2×D3×D418yes—
428Dic3—38no—
429Dic3—64no—
430Dic3—124no—
431Dic3—124no—
432C32#300711yescharacteristic, complemented, Sylow
433C23—91no—
434C23—91no—
435C23—182no—
436C23—184no—
437C23—182no—
438C23—182no—
439C23—361no—
440C23—362no—
441C23—362no—
442C23D4×C3⋊D311yescharacteristic
443Q8—24no—
444Q8—22no—
445Q8—22no—
446Q8—182no—
447Q8—362no—
448Q8D4×C3⋊D314yes—
449D4—94no—
450D4—188no—
451D4—188no—
452D4—184no—
453D4—182no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—91no—
460C2×C4—94no—
461C2×C4—91no—
462C2×C4—182no—
463C2×C4—188no—
464C2×C4—182no—
465C2×C4—188no—
466C2×C4—182no—
467C2×C4—182no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—362no—
471C2×C4—362no—
472C2×C4D4×C3⋊D311yescharacteristic
473C2×C4C23×C3⋊D311yescharacteristic
474C8—22no—
475C8—182no—
476C2×C3—28no—
477C2×C3D3×#12014yes—
478C2×C3C2×#91814yes—
479C2×C3#577714yes—
480D3—68no—
481D3—124no—
482D3—1216no—
483C22—21no—
484C22—21no—
485C22—92no—
486C22—181no—
487C22—181no—
488C22—181no—
489C22—181no—
490C22—184no—
491C22—181no—
492C22—364no—
493C22—368no—
494C22—362no—
495C22—362no—
496C22#6412712yescomplemented
497C22C2×D4×C3⋊D311yescharacteristic
498C4—24no—
499C4—21no—
500C4—41no—
501C4—41no—
502C4—92no—
503C4—181no—
504C4—361no—
505C4—361no—
506C4C2×D4×C3⋊D312yes—
507C3#8018414yescomplemented
508C2—22no—
509C2—182no—
510C2—361no—
511C2—364no—
512C2C3⋊D3×#12011yescharacteristic
513C2C2×#6412711yescharacteristic
514C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC22×#3832C2
hypercenter#451C3⋊D3
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#64127C2semidirect
3. C3⋊D3×C22⋊Q8C2semidirect
4. C32×#451C2semidirect
5. #10592927C2semidirect
6. #10592886C2semidirect
7. #10592745C2semidirect
8. #10592507C2semidirect
9. #10592502C2semidirect
10. #10592430C2semidirect
11. #10592425C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
24. C2×C32×Q16C22semidirect
26. #64155C22semidirect
27. C2×#3756C22semidirect
28. C2×#3755C22semidirect
31. C2×#3744C22semidirect
32. C2×#3743C22semidirect
33. #64106C22semidirect
36. C4⋊C4×C3⋊D3C22semidirect
39. C32×#103C22semidirect
41. #63662C22semidirect
43. #63648C22semidirect
44. #63647C22semidirect
45. #63636C22semidirect
49. C3×#451D3semidirect
121. C2×C3×Q16C2×D3semidirect
136. C3×#103C2×D3semidirect
192. #451C3⋊D3semidirect
251. C22×C32#137semidirect
286. C2×Q16C2×C3⋊D3semidirect
300. #103C2×C3⋊D3semidirect
410. C22×C3#918semidirect
432. C32#3007semidirect
496. C22#64127semidirect
507. C3#80184semidirect

Maximal subgroups

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

subgroupindex
C22×#38322
C2×#641272
C3⋊D3×C22⋊Q82
C32×#4512
#105929272
#105928862
#105927452
#105925072
#105925022
#105924302
#105924252
#801843