Finite Group Databasebeta

← #11860059

Subgroups — #11860059

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63940C211yesmaximal, characteristic
3C4×#3802C211yesmaximal, characteristic
4C3×#5026C212yesmaximal, complemented
5#10591572C212yesmaximal, complemented
6#10591552C211yesmaximal, characteristic, complemented
7#10590593C211yesmaximal, characteristic
8#10590573C211yesmaximal, characteristic, complemented
9#10590461C212yesmaximal, complemented
10#10590360C212yesmaximal, complemented
11#10590322C211yesmaximal, characteristic, complemented
12D3×#440—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3802C2211yescharacteristic
15C2×C4×D32—21no—
16C32×C4×Q8C2211yescharacteristic, complemented
17Q8×C3⋊Dic3C2211yescharacteristic, complemented
18C4⋊C4×C3⋊D3—21no—
19C4⋊C4×C3⋊D3C2211yescharacteristic
20#64096—21no—
21#64096C2211yescharacteristic, complemented
22C42×C3⋊D3—21no—
23C42×C3⋊D3C2211yescharacteristic
24C4×#634—21no—
25C4×#634C2211yescharacteristic, complemented
26C2×C3×#215C2212yes—
27C3×C4×D12C2212yes—
28#63940C418yescomplemented
29#63921—21no—
30#63902—21no—
31C4×#625—21no—
32#63900C2211yescharacteristic
33#63898C2212yes—
34C2×#3716C2212yes—
35C2×#3710C2211yescharacteristic
36C2×#3710C2211yescharacteristic
37C3×#835C2212yescomplemented
38C3×#809C2212yes—
39C3×#807C2212yescomplemented
40C3×#803C2212yescomplemented
41#63575C2212yescomplemented
42#63567C2212yescomplemented
43#63563C2212yes—
44#63555C2212yescomplemented
45C2×D3×SD16—32no—
46C4×D3×Q8—32no—
47C4×D3×Q8—61no—
48C4×D3×D4—32no—
49C3×#440—32no—
50#5164—32no—
51#5026D312yescomplemented
52#5018—32no—
53#4889—32no—
54D3×#107—32no—
55#4817—32no—
56D3×#103—32no—
57D3×#102—32no—
58#4757—32no—
59#4710—32no—
60D3×#97—32no—
61C22×D32—21no—
62C2×C32×Q8C2311yescharacteristic
63Q8×C3⋊D3—22no—
64Q8×C3⋊D3C2×C414yescomplemented
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3D411yescharacteristic
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×#634—21no—
71C2×#634C2311yescharacteristic
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×#625—21no—
75C2×#624—21no—
76C2×D3×Dic3—22no—
77#3802—22no—
78#3802C2×C414yes—
79C4×D32—44no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3750—21no—
88#3750—21no—
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C3×#215C2×C418yescomplemented
96C3×(C2×D3)⋊C4—22no—
97C3×C4⋊Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101(C2×D3)⋊Dic3—22no—
102#3716C2×C418yescomplemented
103#3710—22no—
104#3710C2×C414yescomplemented
105C2×#440—91noSylow
106C2×D3×Q8—32no—
107C2×D3×Q8—61no—
108C2×D3×D4—32no—
109C22×C4×D3—62no—
110C2×C3×SD16—32no—
111C3×C4×Q8—21no—
112C3×C4×Q8C2×D312yescomplemented
113C3×C4×D4—32no—
114Q8×Dic3—32no—
115Q8×Dic3—61no—
116C2×#215C2×D312yes—
117D4×Dic3—32no—
118C2×#214—32no—
119C4×#67—62no—
120D3×SD16—316no—
121C2×#204—32no—
122C2×D3×C8—32no—
123C2×D3×C8—32no—
124#893—32no—
125D3×C4⋊C4—32no—
126D3×C4⋊C4—32no—
127D3×C4⋊C4—61no—
128D3×C4⋊C4—62no—
129D3×C4⋊C4—62no—
130#887—32no—
131#887—61no—
132#887—62no—
133#887—62no—
134#67⋊C4—62no—
135D3×C22⋊C4—62no—
136C4×D12C2×D312yes—
137C42×D3—32no—
138C42×D3—61no—
139C42×D3—62no—
140C42×D3—62no—
141C4×Dic6—32no—
142C4×Dic6—61no—
143C4×Dic6—62no—
144C4×Dic6—62no—
145C3×#107—32no—
146C3×#103—32no—
147C3×#102—32no—
148C3×#97—32no—
149#835C2×D312yescomplemented
150#832—32no—
151#821—32no—
152#818—32no—
153#816—32no—
154#815—32no—
155#815—32no—
156#810—32no—
157#809C2×D312yes—
158#807—32no—
159#807C2×D312yescomplemented
160#803C2×D312yescomplemented
161C22×C3⋊D3C2×D411yescharacteristic
162C22×C3×D3—22no—
163C2×D32—24no—
164C2×D32—42no—
165C2×D32—42no—
166C32×Q8—21no—
167C32×Q8C22×C412yescomplemented
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D411yescharacteristic
176C2×C3⋊Dic3C2×D411yescharacteristic
177C2×C3⋊Dic3C2×D411yescharacteristic
178C4×C3⋊D3—24no—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181C4×C3⋊D3—42no—
182C4×C3⋊D3C22×C412yes—
183C4×C3⋊D3#4112yes—
184#634—21no—
185#634—24no—
186#634C22×C412yescomplemented
187C2×C3×Dic3—22no—
188C3×D12—22no—
189C3×D12C22×C414yes—
190C3×C4×D3—44no—
191#625—24no—
192#624—42no—
193D3×Dic3—44no—
194C3×C3⋊C8—22no—
195C3×C3⋊C8C22×C414yescomplemented
196C22×SD16—91no—
197C2×C4×Q8—91no—
198C2×C4×D4—91no—
199#440—32no—
200#440—92no—
201#440—92no—
202#440—92no—
203C2×#107—91no—
204C2×#103—91no—
205C2×#102—91no—
206C2×#97—91no—
207C23×D3—62no—
208C2×C3×Q8—21no—
209C2×C3×Q8C22×D312yes—
210C2×C3×D4—32no—
211C22×C3×C4—62no—
212C2×#67—62no—
213C22×Dic3—62no—
214D3×Q8—38no—
215D3×Q8—64no—
216D3×Q8—64no—
217D3×Q8—64no—
218D3×D4—38no—
219D3×D4—64no—
220C2×D12C22×D312yes—
221C2×C4×D3—22no—
222C2×C4×D3—32no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—128no—
235C2×Dic6—32no—
236C2×Dic6—61no—
237C2×Dic6—62no—
238C2×Dic6—62no—
239C3×SD16—38no—
240C2×C3×C8—32no—
241C2×C3×C8—32no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4C22×D312yes—
247C3×C22⋊C4—62no—
248C3×C42—22no—
249C3×C42—22no—
250C3×C42—21no—
251C3×C42C22×D312yes—
252#217—62no—
253#215C4×D318yescomplemented
254#214—38no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—62no—
257C4⋊Dic3—32no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3C22×D312yes—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269C4×Dic3—32no—
270C4×Dic3—32no—
271C4×Dic3—32no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C4×Dic3—62no—
281C2×C3⋊C8C22×D312yes—
282C2×C3⋊C8C22×D312yes—
283#204—38no—
284D3×C8—38no—
285D3×C8—64no—
286C22×C32C22×D411yescharacteristic
287C2×C3⋊D3C4×D412yes—
288C2×C3⋊D3AGL(1,ℤ/8)12yes—
289C2×C3⋊D3#13712yes—
290C2×C3×D3—24no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293D32—48no—
294C32×C4—22no—
295C32×C4—21no—
296C32×C4—21no—
297C32×C4—41no—
298C32×C4C23×C411yescharacteristic
299C32×C4C2×#4111yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—21no—
302C3⋊Dic3—21no—
303C3⋊Dic3—41no—
304C3⋊Dic3C4×D412yes—
305C3×Dic3—42no—
306C22×Q8—91no—
307C22×D4—91no—
308C23×C4—181no—
309C2×SD16—32no—
310C2×SD16—92no—
311C2×SD16—98no—
312C22×C8—91no—
313C22×C8—91no—
314C4×Q8—91no—
315C4×Q8—91no—
316C4×Q8—91no—
317C4×Q8—181no—
318C4×Q8—181no—
319C4×Q8D3211yescharacteristic, complemented
320C4×D4—32no—
321C4×D4—92no—
322C4×D4—181no—
323C4×D4—181no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—181no—
327C2×C22⋊C4—181no—
328C2×C42—91no—
329C2×C42—181no—
330#107—32no—
331#107—92no—
332#103—32no—
333#103—92no—
334#102—32no—
335#102—92no—
336#97—32no—
337#97—92no—
338C23×C3—62no—
339C22×D3—22no—
340C22×D3—32no—
341C22×D3—61no—
342C22×D3—68no—
343C22×D3—124no—
344C22×D3—124no—
345C3×Q8—22no—
346C3×Q8—22no—
347C3×Q8—22no—
348C3×Q8C2×C4×D314yescomplemented
349C3×D4—34no—
350C3×D4—62no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—62no—
359C2×C3×C4—124no—
360C2×C3×C4D3×D412yes—
361C2×C3×C4D3×D412yes—
362C2×C3×C4C23×D312yes—
363#67—68no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—124no—
376D12—22no—
377D12C2×C4×D314yes—
378C4×D3—34no—
379C4×D3—34no—
380C4×D3—44no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—64no—
384C4×D3—64no—
385C4×D3—68no—
386C4×D3—64no—
387C4×D3—68no—
388C4×D3—122no—
389C4×D3—124no—
390C4×D3—124no—
391C4×D3—124no—
392C4×D3—124no—
393Dic6—34no—
394Dic6—62no—
395Dic6—68no—
396Dic6—68no—
397Dic6—62no—
398Dic6—62no—
399C3×C8—34no—
400C3×C8—62no—
401C3⋊C8—22no—
402C3⋊C8C2×C4×D314yescomplemented
403C2×C32C2×C4×D411yescharacteristic
404C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C32C2×#13711yescharacteristic
406C3⋊D3#44014yescomplemented
407C3×D3—44no—
408C24—181no—
409C2×Q8—94no—
410C2×Q8—91no—
411C2×Q8—181no—
412C2×Q8—182no—
413C2×Q8C2×D3211yescharacteristic
414C2×D4—32no—
415C2×D4—94no—
416C2×D4—182no—
417C2×D4—181no—
418C22×C4—62no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4—182no—
426C22×C4—364no—
427SD16—38no—
428SD16—98no—
429C2×C8—32no—
430C2×C8—32no—
431C2×C8—94no—
432C2×C8—182no—
433C4⋊C4—21no—
434C4⋊C4—32no—
435C4⋊C4—91no—
436C4⋊C4—181no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4C2×D3211yescharacteristic
442C22⋊C4—62no—
443C22⋊C4—182no—
444C42—21no—
445C42—91no—
446C42—91no—
447C42—91no—
448C42—181no—
449C42—181no—
450C42—181no—
451C42C2×D3211yescharacteristic
452C22×C3—21no—
453C22×C3—64no—
454C22×C3—122no—
455C22×C3—122no—
456C22×C3C2×D3×D412yes—
457C2×D3—24no—
458C2×D3—34no—
459C2×D3—34no—
460C2×D3—34no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—1216no—
467C3×C4—24no—
468C3×C4—22no—
469C3×C4—22no—
470C3×C4—22no—
471C3×C4—24no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—41no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—122no—
478C3×C4C22×C4×D312yes—
479C3×C4D3×#4112yes—
480Dic3—34no—
481Dic3—42no—
482Dic3—62no—
483Dic3—64no—
484Dic3—62no—
485Dic3—62no—
486Dic3—62no—
487Dic3—64no—
488Dic3—121no—
489Dic3—122no—
490Dic3—122no—
491C32C2×#44011yescharacteristic, complemented, Sylow
492C23—62no—
493C23—91no—
494C23—184no—
495C23—362no—
496C23—362no—
497Q8—21no—
498Q8—92no—
499Q8—184no—
500Q8—181no—
501Q8C4×D3212yescomplemented
502D4—34no—
503D4—62no—
504D4—184no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—62no—
508C2×C4—91no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—91no—
512C2×C4—91no—
513C2×C4—124no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—184no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—362no—
520C2×C4—362no—
521C2×C4—364no—
522C2×C4#381111yescharacteristic
523C2×C4#381111yescharacteristic
524C2×C4C22×D3211yescharacteristic
525C8—34no—
526C8—62no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—124no—
531C2×C3C4×D3×D412yes—
532C2×C3D3×AGL(1,ℤ/8)12yes—
533C2×C3D3×#13712yes—
534D3—38no—
535D3—44no—
536D3—64no—
537C22—64no—
538C22—92no—
539C22—92no—
540C22—92no—
541C22—122no—
542C22—122no—
543C22—368no—
544C22C2×#381111yescharacteristic
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—92no—
550C4—122no—
551C4—181no—
552C4—182no—
553C4—181no—
554C4—361no—
555C4C2×C4×D3211yescharacteristic
556C4#6430611yescharacteristic
557C3—21no—
558C3D3×#44012yescomplemented
559C2—94no—
560C2—124no—
561C2C4×#381111yescharacteristic
562C2#1059532211yescharacteristic
563C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
4. C3×#5026C2semidirect
5. #10591572C2semidirect
6. #10591552C2semidirect
8. #10590573C2semidirect
9. #10590461C2semidirect
10. #10590360C2semidirect
11. #10590322C2semidirect
16. C32×C4×Q8C22semidirect
17. Q8×C3⋊Dic3C22semidirect
21. #64096C22semidirect
25. C4×#634C22semidirect
28. #63940C4semidirect
37. C3×#835C22semidirect
39. C3×#807C22semidirect
40. C3×#803C22semidirect
41. #63575C22semidirect
42. #63567C22semidirect
44. #63555C22semidirect
51. #5026D3semidirect
64. Q8×C3⋊D3C2×C4semidirect
95. C3×#215C2×C4semidirect
102. #3716C2×C4semidirect
104. #3710C2×C4semidirect
112. C3×C4×Q8C2×D3semidirect
149. #835C2×D3semidirect
159. #807C2×D3semidirect
160. #803C2×D3semidirect
167. C32×Q8C22×C4semidirect
186. #634C22×C4semidirect
195. C3×C3⋊C8C22×C4semidirect
253. #215C4×D3semidirect
319. C4×Q8D32semidirect
348. C3×Q8C2×C4×D3semidirect
402. C3⋊C8C2×C4×D3semidirect
406. C3⋊D3#440semidirect
491. C32C2×#440semidirect
501. Q8C4×D32semidirect
558. C3D3×#440semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C2×#639402
C4×#38022
C3×#50262
#105915722
#105915522
#105905932
#105905732
#105904612
#105903602
#105903222
D3×#4403