Finite Group Databasebeta

← #11860156

Subgroups — #11860156

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#624C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic
3#10594605C211yesmaximal, characteristic, complemented
4C3⋊D3×#102C211yesmaximal, characteristic, complemented
5C3×#4785C212yesmaximal, complemented
6#10591430C212yesmaximal, complemented
7#10590940C211yesmaximal, characteristic, complemented
8#10590746C212yesmaximal, complemented
9#10590668C211yesmaximal, characteristic, complemented
10#10590589C212yesmaximal, complemented
11#10590575C211yesmaximal, characteristic, complemented
12D3×#442—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×#624—21no—
15C2×#3802C2211yescharacteristic
16C2×C4×D32—21no—
17C2×C8×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×D4×Dic3C2212yescomplemented
20C2×C3×#213C2212yes—
21C3×#893C2212yescomplemented
22#63974—21no—
23#63952—22no—
24#63926C418yescomplemented
25#63921—21no—
26#63900C2211yescharacteristic
27#63894C2212yescomplemented
28Dic3×D12C2212yescomplemented
29C4×#624C2211yescharacteristic
30#63879—22no—
31C2×#3714C2212yes—
32C2×#3710C2211yescharacteristic
33C32×#102C2211yescharacteristic, complemented
34#63659C2211yescharacteristic, complemented
35#63648C2211yescharacteristic, complemented
36#63636C2211yescharacteristic, complemented
37C3×#821C2212yescomplemented
38C3×#815C2212yescomplemented
39C3×#808C2212yescomplemented
40#63573C2212yescomplemented
41#63562C2212yescomplemented
42#63554C2212yescomplemented
43C2×D3×D8—32no—
44C4×D3×D4—32no—
45C4×D3×D4—32no—
46C3×#442—32no—
47#5152—32no—
48#5014—32no—
49#5014—32no—
50#4869—32no—
51D3×#106—32no—
52#4785—32no—
53#4785D312yescomplemented
54D3×#102—32no—
55D3×#102—32no—
56D3×#102—61no—
57#4711—32no—
58D3×#97—32no—
59C23×C3⋊D3—21no—
60C22×D32—21no—
61C2×C32×D4C2311yescharacteristic
62C2×#638—21no—
63D4×C3⋊D3—22no—
64D4×C3⋊D3C2×C414yescomplemented
65C2×C4⋊(C3⋊D3)C2311yescharacteristic
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3C2311yescharacteristic
68C22×C3×Dic3—22no—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—22no—
71C2×#625—21no—
72C2×#624—21no—
73C2×#624—22no—
74C2×#624—44no—
75C2×#624D411yescharacteristic
76C2×#624D411yescharacteristic
77C2×D3×Dic3—22no—
78#3802—22no—
79#3802C2×C414yescomplemented
80C4×D32—44no—
81C2×C32×C8C2311yescharacteristic
82C32×C4⋊C4C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C8×C3⋊D3—22no—
87C3×#217—22no—
88C3×#213C2×C418yescomplemented
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3C2312yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—21no—
94#3722—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32D412yes—
97#3714C2×C418yescomplemented
98#3710C2×C414yescomplemented
99C2×#442—91noSylow
100C2×D3×D4—32no—
101C2×D3×D4—32no—
102C2×D3×D4—61no—
103C22×C4×D3—62no—
104C22×C4×D3—62no—
105C2×C3×D8—32no—
106C3×C4×D4—32no—
107C3×C4×D4—32no—
108D4×Dic3—32no—
109D4×Dic3C2×D312yescomplemented
110C2×#213—32no—
111C2×#213C2×D312yes—
112C4×#67—62no—
113C4×#67—62no—
114D3×D8—316no—
115C2×D24—32no—
116C2×D3×C8—32no—
117C2×D3×C8—32no—
118C2×D3×C8—61no—
119#893—32no—
120#893C2×D312yescomplemented
121D3×C4⋊C4—32no—
122D3×C4⋊C4—32no—
123D3×C4⋊C4—61no—
124#67⋊C4—62no—
125#67⋊C4—62no—
126D3×C22⋊C4—62no—
127D3×C22⋊C4—62no—
128C4×D12—32no—
129C4×D12—32no—
130C42×D3—32no—
131C3×#106—32no—
132C3×#102—21no—
133C3×#102—32no—
134C3×#102C2×D312yescomplemented
135C3×#97—32no—
136#832—32no—
137#832—32no—
138#832—61no—
139#821—32no—
140#821—61no—
141#821C2×D312yescomplemented
142#817—32no—
143#815—32no—
144#815C2×D312yescomplemented
145#809—32no—
146#809—32no—
147#809—61no—
148#808—32no—
149#808C2×D312yescomplemented
150#803—32no—
151C23×C32—21no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3—24no—
154C22×C3⋊D3—42no—
155C22×C3⋊D3—42no—
156C22×C3⋊D3C2×D411yescharacteristic
157C22×C3×D3—22no—
158C2×D32—24no—
159C2×D32—42no—
160C2×D32—42no—
161C32×D4—21no—
162C32×D4C22×C412yescomplemented
163C2×C32×C4—21no—
164C2×C32×C4C2411yescharacteristic
165#638—24no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3C2×D411yescharacteristic
168C4⋊(C3⋊D3)—21no—
169C4⋊(C3⋊D3)C22×C412yescomplemented
170C4×C3⋊D3—42no—
171C4×C3⋊D3C22×C412yes—
172C4×C3⋊D3#4112yes—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—44no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—22no—
178C3×D12C22×C414yescomplemented
179C3×C4×D3—44no—
180#625—24no—
181#624—22no—
182#624—22no—
183#624—44no—
184#624—42no—
185D3×Dic3—44no—
186C32×C8—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8C22×C414yescomplemented
189C22×D8—91no—
190C2×C4×D4—91no—
191C2×C4×D4—91no—
192#442—32no—
193#442—92no—
194#442—92no—
195#442—92no—
196C2×#106—91no—
197C2×#102—91no—
198C2×#102—91no—
199C2×#97—91no—
200C23×D3—62no—
201C23×D3—62no—
202C23×D3—121no—
203C2×C3×D4—21no—
204C2×C3×D4—32no—
205C2×C3×D4C22×D312yes—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C2×#67—62no—
209C2×#67—62no—
210C2×#67—121no—
211C22×Dic3—22no—
212C22×Dic3—62no—
213D3×D4—38no—
214D3×D4—38no—
215D3×D4—64no—
216D3×D4—64no—
217D3×D4—64no—
218D3×D4—122no—
219C2×D12—32no—
220C2×D12—61no—
221C2×D12C22×D312yes—
222C2×C4×D3—22no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—61no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—121no—
233C2×C4×D3—128no—
234C2×C4×D3—128no—
235C3×D8—38no—
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8C22×D312yes—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4C22×D312yes—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C42—32no—
245#217—22no—
246#217—62no—
247#213—38no—
248#213C4×D318yescomplemented
249(C2×D3)⋊C4—22no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253C4⋊Dic3—32no—
254C4⋊Dic3—61no—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—121no—
259C4×Dic3—32no—
260C4×Dic3—32no—
261C4×Dic3C22×D312yes—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8C22×D312yes—
265D24—38no—
266D3×C8—38no—
267D3×C8—64no—
268D3×C8—122no—
269C22×C32—22no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—48no—
277C2×C3⋊D3C4×D412yes—
278C2×C3⋊D3AGL(1,ℤ/8)12yes—
279C2×C3⋊D3AGL(1,ℤ/8)12yes—
280C2×C3×D3—24no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283D32—48no—
284C32×C4—41no—
285C32×C4C23×C411yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3⋊Dic3—41no—
288C3⋊Dic3C4×D412yes—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C22×D4—91no—
293C22×D4—91no—
294C23×C4—181no—
295C23×C4—181no—
296C2×D8—32no—
297C2×D8—92no—
298C2×D8—98no—
299C22×C8—91no—
300C22×C8—91no—
301C4×D4—32no—
302C4×D4—32no—
303C4×D4—92no—
304C4×D4—92no—
305C4×D4—182no—
306C4×D4—182no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4—91no—
309C2×C22⋊C4—181no—
310C2×C22⋊C4—181no—
311C2×C42—91no—
312#106—32no—
313#106—92no—
314#102—32no—
315#102—92no—
316#102—91no—
317#102—91no—
318#102—91no—
319#102D3211yescharacteristic, complemented
320#97—32no—
321#97—92no—
322C23×C3—22no—
323C23×C3—41no—
324C23×C3—62no—
325C22×D3—22no—
326C22×D3—32no—
327C22×D3—61no—
328C22×D3—68no—
329C22×D3—68no—
330C22×D3—62no—
331C22×D3—124no—
332C22×D3—121no—
333C22×D3—124no—
334C22×D3—124no—
335C22×D3—124no—
336C22×D3—124no—
337C22×D3—242no—
338C22×D3—242no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—34no—
342C3×D4—41no—
343C3×D4—62no—
344C3×D4C2×C4×D314yescomplemented
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—41no—
350C2×C3×C4—62no—
351C2×C3×C4—124no—
352C2×C3×C4—124no—
353C2×C3×C4C23×D312yes—
354#67—68no—
355#67—68no—
356#67—124no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—44no—
360C2×Dic3—61no—
361C2×Dic3—62no—
362C2×Dic3—121no—
363C2×Dic3—124no—
364C2×Dic3D3×D412yes—
365C2×Dic3D3×D412yes—
366D12—22no—
367D12—34no—
368D12—62no—
369D12—62no—
370D12—121no—
371D12C2×C4×D314yescomplemented
372C4×D3—34no—
373C4×D3—34no—
374C4×D3—44no—
375C4×D3—62no—
376C4×D3—62no—
377C4×D3—64no—
378C4×D3—64no—
379C4×D3—124no—
380C4×D3—124no—
381C4×D3—124no—
382C4×D3—124no—
383C4×D3—124no—
384C4×D3—242no—
385C3×C8—22no—
386C3×C8—34no—
387C3×C8—41no—
388C3⋊C8—62no—
389C3⋊C8—121no—
390C3⋊C8C2×C4×D314yescomplemented
391C2×C32—42no—
392C2×C32C2×C4×D411yescharacteristic
393C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
394C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
395C3⋊D3—42no—
396C3⋊D3#44214yescomplemented
397C3×D3—44no—
398C24—181no—
399C24—181no—
400C2×D4—32no—
401C2×D4—94no—
402C2×D4—94no—
403C2×D4—91no—
404C2×D4—182no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4C2×D3211yescharacteristic
409C22×C4—62no—
410C22×C4—62no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—181no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4—181no—
418C22×C4—364no—
419C22×C4—364no—
420D8—38no—
421D8—98no—
422C2×C8—32no—
423C2×C8—94no—
424C2×C8—91no—
425C2×C8—182no—
426C2×C8C2×D3211yescharacteristic
427C4⋊C4—32no—
428C4⋊C4—91no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4C2×D3211yescharacteristic
432C22⋊C4—62no—
433C22⋊C4—62no—
434C22⋊C4—182no—
435C22⋊C4—182no—
436C42—32no—
437C42—92no—
438C22×C3—24no—
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—64no—
444C22×C3—81no—
445C22×C3—81no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3C2×D3×D412yes—
449C2×D3—24no—
450C2×D3—34no—
451C2×D3—34no—
452C2×D3—34no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—64no—
459C2×D3—122no—
460C2×D3—1216no—
461C2×D3—1216no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—248no—
465C2×D3—241no—
466C2×D3—241no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—42no—
470C3×C4—62no—
471C3×C4—62no—
472C3×C4—81no—
473C3×C4—122no—
474C3×C4C22×C4×D312yes—
475C3×C4D3×#4112yes—
476Dic3—22no—
477Dic3—22no—
478Dic3—34no—
479Dic3—42no—
480Dic3—62no—
481Dic3—122no—
482Dic3—241no—
483C32C2×#44211yescharacteristic, complemented, Sylow
484C23—21no—
485C23—62no—
486C23—91no—
487C23—184no—
488C23—184no—
489C23—181no—
490C23—362no—
491C23—362no—
492C23—362no—
493C23—362no—
494D4—21no—
495D4—34no—
496D4—62no—
497D4—92no—
498D4—184no—
499D4—184no—
500D4—181no—
501D4C4×D3212yescomplemented
502C2×C4—21no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—62no—
506C2×C4—91no—
507C2×C4—92no—
508C2×C4—92no—
509C2×C4—124no—
510C2×C4—124no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4—181no—
514C2×C4—362no—
515C2×C4—364no—
516C2×C4—364no—
517C2×C4—362no—
518C2×C4C22×D3211yescharacteristic
519C8—21no—
520C8—34no—
521C8—181no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—44no—
526C2×C3—82no—
527C2×C3—124no—
528C2×C3C4×D3×D412yes—
529C2×C3D3×AGL(1,ℤ/8)12yes—
530C2×C3D3×AGL(1,ℤ/8)12yes—
531D3—38no—
532D3—44no—
533D3—64no—
534D3—124no—
535D3—242no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22—64no—
540C22—92no—
541C22—92no—
542C22—92no—
543C22—122no—
544C22—122no—
545C22—182no—
546C22—368no—
547C22—368no—
548C22—361no—
549C22—361no—
550C22D32×D411yescharacteristic
551C4—41no—
552C4—62no—
553C4—62no—
554C4—92no—
555C4—122no—
556C4—361no—
557C4C2×C4×D3211yescharacteristic
558C4#6431211yescharacteristic
559C3—21no—
560C3D3×#44212yescomplemented
561C2—42no—
562C2—94no—
563C2—124no—
564C2—362no—
565C2#1059425511yescharacteristic
566C2#1059472611yescharacteristic
567C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63926C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C2×#442
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#624C2semidirect
3. #10594605C2semidirect
4. C3⋊D3×#102C2semidirect
5. C3×#4785C2semidirect
6. #10591430C2semidirect
7. #10590940C2semidirect
8. #10590746C2semidirect
9. #10590668C2semidirect
10. #10590589C2semidirect
11. #10590575C2semidirect
19. C3×D4×Dic3C22semidirect
21. C3×#893C22semidirect
24. #63926C4semidirect
27. #63894C22semidirect
28. Dic3×D12C22semidirect
33. C32×#102C22semidirect
34. #63659C22semidirect
35. #63648C22semidirect
36. #63636C22semidirect
37. C3×#821C22semidirect
38. C3×#815C22semidirect
39. C3×#808C22semidirect
40. #63573C22semidirect
41. #63562C22semidirect
42. #63554C22semidirect
53. #4785D3semidirect
64. D4×C3⋊D3C2×C4semidirect
79. #3802C2×C4semidirect
88. C3×#213C2×C4semidirect
97. #3714C2×C4semidirect
98. #3710C2×C4semidirect
109. D4×Dic3C2×D3semidirect
120. #893C2×D3semidirect
134. C3×#102C2×D3semidirect
141. #821C2×D3semidirect
144. #815C2×D3semidirect
149. #808C2×D3semidirect
162. C32×D4C22×C4semidirect
169. C4⋊(C3⋊D3)C22×C4semidirect
178. C3×D12C22×C4semidirect
188. C3×C3⋊C8C22×C4semidirect
248. #213C4×D3semidirect
319. #102D32semidirect
344. C3×D4C2×C4×D3semidirect
371. D12C2×C4×D3semidirect
390. C3⋊C8C2×C4×D3semidirect
396. C3⋊D3#442semidirect
483. C32C2×#442semidirect
501. D4C4×D32semidirect
560. C3D3×#442semidirect

Maximal subgroups

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

subgroupindex
D4×#6242
C2×#639262
#105946052
C3⋊D3×#1022
C3×#47852
#105914302
#105909402
#105907462
#105906682
#105905892
#105905752
D3×#4423