Finite Group Databasebeta

← #11860623

Subgroups — #11860623

Order 1152.

1021 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3#10594992C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5#10591576C212yesmaximal, complemented
6Dic3×#216C212yesmaximal, complemented
7#10591566C212yesmaximal, complemented
8Dic3×#215C212yesmaximal, complemented
9#10591131C211yesmaximal, characteristic, complemented
10#10591083C211yesmaximal, characteristic
11#10591057C211yesmaximal, characteristic, complemented
12#83965—31nomaximal
13#82547—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×Q8×Dic3—21no—
19C3×Q8×Dic3—21no—
20C3×Q8×Dic3C2212yes—
21C3×Q8×Dic3C2212yes—
22C2×C3×#216C2212yes—
23C3×#942C418yescomplemented
24C2×C3×#215C2212yes—
25C3×#926—22no—
26C3×#926C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29#67⋊Dic3—22no—
30Dic3×D12C2212yes—
31D3×C4⋊Dic3—21no—
32Dic3×Dic6C2212yes—
33#63841—21no—
34#63662C2212yes—
35#63662C2212yes—
36#63575C2212yes—
37#63573C2212yes—
38#63565C2211yescharacteristic
39#63565C2211yescharacteristic
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C2×C3×#137—31no—
45C3×#519—31no—
46#5827—31no—
47#5812D311yescharacteristic, complemented
48C2×#942D311yescharacteristic
49#5523—31no—
50#5233—31no—
51C2×#835—31no—
52C2×#835—31no—
53C2×#835—61no—
54#5184—32no—
55Dic3×Q16—32no—
56#5164—32no—
57Dic3×SD16—32no—
58#5122—31no—
59#5121—31no—
60#5030—32no—
61C4×#216—32no—
62#5026—32no—
63C4×#215—32no—
64#5002—31no—
65#4997—31no—
66#4995—31no—
67C2×C32×Q8—21no—
68C2×C32×Q8—22no—
69C2×C32×Q8C2×C414yescomplemented
70C2×C32×Q8C2312yes—
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3—21no—
74C2×C3×#67—21no—
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×Dic6C2311yescharacteristic
80C2×D3×Dic3—22no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C3×#217—21no—
87C3×#217D412yes—
88C3×#216C2×C418yescomplemented
89C3×#215C2×C418yescomplemented
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3D411yescharacteristic
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4×Dic3—21no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3C2312yes—
100C3×#208C2×C414yescomplemented
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104Dic32—22no—
105#2947—91noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—21no—
108C22×C3×Q8C2×D311yescharacteristic
109C22×C3×Q8C2×D311yescharacteristic
110C2×#235C2×D311yescharacteristic
111C3×#137—38no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C2×C3×M16—31no—
115C3×C4×Q8—32no—
116C3×C4×Q8—32no—
117C3×C4×Q8—61no—
118C3×C4×Q8—61no—
119C3×#117—31no—
120C3×#117—31no—
121C3×#117—62no—
122Q8×Dic3—21no—
123Q8×Dic3—21no—
124Q8×Dic3—32no—
125Q8×Dic3C2×D312yes—
126Q8×Dic3C2×D312yes—
127C2×#216C2×D312yes—
128#942Dic318yescomplemented
129C2×#215C2×D312yes—
130D4×Dic3—32no—
131D4×Dic3—62no—
132#926—22no—
133#926—61no—
134#926C2×D311yescharacteristic
135#926C2×D311yescharacteristic
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—61no—
139C2×C4⋊Dic3—61no—
140C2×#208C2×D311yescharacteristic
141C22×C3⋊C8—31no—
142C22×C3⋊C8—31no—
143C22×C3⋊C8—61no—
144#892—61no—
145D3×C4⋊C4—61no—
146#67⋊C4—62no—
147C4×D12—32no—
148C4×Dic6—32no—
149#835—32no—
150#835—32no—
151#835—32no—
152#835—32no—
153#835—31no—
154#835—31no—
155#835—62no—
156#835—62no—
157#832—31no—
158#832—31no—
159#818—32no—
160#817—32no—
161#815—32no—
162C8×Dic3—32no—
163#810—31no—
164#810—31no—
165#809—31no—
166#809—31no—
167#808—32no—
168#807—32no—
169#803—32no—
170C4×C3⋊C8—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C32×Q8—24no—
174C32×Q8—22no—
175C32×Q8C22×C414yes—
176C2×C32×C4—24no—
177C2×C32×C4—22no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—81no—
184C3×#67—24no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D412yes—
189C2×C3×Dic3C2×D412yes—
190C3×D12—21no—
191C3×D12C22×C412yes—
192C3×C4×D3—24no—
193C3×Dic6—21no—
194C3×Dic6C22×C412yes—
195D3×Dic3—82no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198C3×C3⋊C8C22×C414yes—
199C2×#137—31no—
200#520—91no—
201#519—31no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—91no—
207#416—91no—
208C2×#103—91no—
209#405—91no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—22no—
213C2×C3×Q8—21no—
214C2×C3×Q8—22no—
215C2×C3×Q8—21no—
216C2×C3×Q8—24no—
217C2×C3×Q8—22no—
218C2×C3×Q8—31no—
219C2×C3×Q8—42no—
220C2×C3×Q8—41no—
221C2×C3×Q8C4×D314yescomplemented
222C2×C3×Q8C2×Dic314yescomplemented
223C2×C3×Q8C22×D312yes—
224C2×C3×Q8C22×D312yes—
225C2×C3×D4—31no—
226C2×C3×D4—61no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—41no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—21no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—62no—
238C22×Dic3—121no—
239#235—22no—
240#235C2×Dic314yes—
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—62no—
244C2×Dic6C22×D311yescharacteristic
245C3×Q16—38no—
246C3×SD16—38no—
247C3×M16—34no—
248C2×C3×C8—32no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—62no—
255C3×C22⋊C4—32no—
256C3×C22⋊C4—61no—
257C3×C42—32no—
258C3×C42—62no—
259C3×C42—62no—
260C3×C42—61no—
261#217—21no—
262#217—62no—
263#217#6712yes—
264#216C2×Dic318yescomplemented
265#215C2×Dic318yescomplemented
266(C2×D3)⋊C4—62no—
267C4⋊Dic3—22no—
268C4⋊Dic3—22no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—62no—
275C4⋊Dic3—121no—
276C4⋊Dic3#6711yescharacteristic
277C4⋊Dic3#6711yescharacteristic
278C4⋊Dic3C22×D311yescharacteristic
279C4⋊Dic3C22×D311yescharacteristic
280Dic3⋊C4—62no—
281C4×Dic3—21no—
282C4×Dic3—22no—
283C4×Dic3—22no—
284C4×Dic3—62no—
285C4×Dic3—62no—
286C4×Dic3C22×D312yes—
287#208C2×Dic314yescomplemented
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—62no—
295C2×C3⋊C8—62no—
296C2×C3⋊C8—122no—
297C2×C3⋊C8C22×D312yes—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32C4×D412yes—
301C22×C32C22×D411yescharacteristic
302C2×C3×D3—22no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C32×C4—24no—
306C32×C4C4×D412yes—
307C32×C4C23×C411yescharacteristic
308C32×C4C2×#4111yescharacteristic
309C3⋊Dic3—42no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—41no—
314C3×Dic3—41no—
315C2×#41—31no—
316C22×Q8D3211yescharacteristic
317#137—38no—
318C2×Q16—32no—
319C2×SD16—32no—
320C2×M16—31no—
321C22×C8—91no—
322C4×Q8—32no—
323C4×Q8—32no—
324C4×Q8—61no—
325C4×Q8—61no—
326C4×Q8—92no—
327C4×D4—92no—
328C4×D4—182no—
329#117—31no—
330#117—31no—
331#117—62no—
332#117—181no—
333C2×C4⋊C4—91no—
334C2×C4⋊C4—181no—
335#107—92no—
336#106—92no—
337#103—91no—
338#103—91no—
339#103—92no—
340#103—92no—
341#102—91no—
342#102—91no—
343#97—92no—
344C4×C8—92no—
345C23×C3—21no—
346C23×C3—61no—
347C23×C3D3×D411yescharacteristic
348C23×C3C2×#6711yescharacteristic
349C22×D3—21no—
350C3×Q8—24no—
351C3×Q8—24no—
352C3×Q8—22no—
353C3×Q8—22no—
354C3×Q8—24no—
355C3×Q8—32no—
356C3×Q8—42no—
357C3×Q8—44no—
358C3×Q8—61no—
359C3×Q8C2×C4×D314yes—
360C3×Q8C22×Dic314yes—
361C3×D4—32no—
362C3×D4—64no—
363C3×D4—61no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—32no—
373C2×C3×C4—32no—
374C2×C3×C4—42no—
375C2×C3×C4—44no—
376C2×C3×C4—61no—
377C2×C3×C4—64no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4C2×C4×D312yes—
381C2×C3×C4#23512yes—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4#23712yes—
384C2×C3×C4C22×Dic312yes—
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—24no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3—242no—
396C2×Dic3—241no—
397C2×Dic3—241no—
398C2×Dic3—242no—
399C2×Dic3C2×#6712yes—
400C2×Dic3C2×#6712yes—
401D12—21no—
402D12C22×Dic312yes—
403C4×D3—24no—
404C4×D3—242no—
405Dic6—21no—
406Dic6C22×Dic312yes—
407C3×C8—34no—
408C3⋊C8—61no—
409C3⋊C8—61no—
410C3⋊C8—61no—
411C3⋊C8—61no—
412C3⋊C8—121no—
413C3⋊C8—121no—
414C3⋊C8C22×Dic314yes—
415C2×C32—22no—
416C2×C32C2×C4×D411yescharacteristic
417C2×C32#57711yescharacteristic
418C2×C32#57811yescharacteristic
419C3×D3—42no—
420#41—34no—
421#41—62no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8—31no—
425C2×Q8D3×Dic314yescomplemented
426C2×Q8C2×D3212yes—
427C2×D4—31no—
428C2×D4—61no—
429C22×C4—21no—
430C22×C4—61no—
431C22×C4—182no—
432C22×C4—181no—
433C22×C4C2×D3211yescharacteristic
434Q16—38no—
435SD16—38no—
436M16—34no—
437C2×C8—32no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8—182no—
441C4⋊C4—31no—
442C4⋊C4—31no—
443C4⋊C4—31no—
444C4⋊C4—31no—
445C4⋊C4—62no—
446C4⋊C4—62no—
447C4⋊C4—92no—
448C4⋊C4—182no—
449C4⋊C4—181no—
450C22⋊C4—32no—
451C22⋊C4—61no—
452C22⋊C4—182no—
453C42—32no—
454C42—62no—
455C42—62no—
456C42—61no—
457C42—182no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—62no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3C4×#6712yes—
470C22×C3D4×Dic312yes—
471C22×C3C2×D3×D411yescharacteristic
472C22×C3C22×#6711yescharacteristic
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C3×C4—24no—
477C3×C4—24no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—22no—
481C3×C4—44no—
482C3×C4—62no—
483C3×C4—62no—
484C3×C4—62no—
485C3×C4—121no—
486C3×C4—121no—
487C3×C4C4×#6712yes—
488C3×C4D4×Dic312yes—
489C3×C4C22×C4×D311yescharacteristic
490C3×C4C2×#23511yescharacteristic
491C3×C4C2×#23711yescharacteristic
492C3×C4C23×Dic311yescharacteristic
493Dic3—22no—
494Dic3—22no—
495Dic3—22no—
496Dic3—41no—
497Dic3—41no—
498Dic3—122no—
499Dic3—122no—
500Dic3—242no—
501C32#294711yescharacteristic, complemented, Sylow
502C23—61no—
503C23D3×#6711yescharacteristic
504Q8—22no—
505Q8—24no—
506Q8—32no—
507Q8—61no—
508Q8C2×D3×Dic314yes—
509D4—32no—
510D4—64no—
511D4—61no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—32no—
515C2×C4—32no—
516C2×C4—61no—
517C2×C4—64no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—182no—
521C2×C4—722no—
522C2×C4—721no—
523C2×C4C2×D3×Dic312yes—
524C2×C4#380412yes—
525C2×C4D3×#6711yescharacteristic
526C2×C4C22×D3211yescharacteristic
527C8—34no—
528C8—181no—
529C8—181no—
530C2×C3—24no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—122no—
537C2×C3#577811yescharacteristic
538C2×C3#577911yescharacteristic
539C2×C3C2×C4×#6711yescharacteristic
540C2×C3C2×D4×Dic311yescharacteristic
541C2×C3#583711yescharacteristic
542C2×C3#583811yescharacteristic
543D3—42no—
544C22—21no—
545C22—21no—
546C22—62no—
547C22—121no—
548C22—121no—
549C22Dic3×#6712yes—
550C22C2×D3×#6711yescharacteristic
551C4—24no—
552C4—62no—
553C4—62no—
554C4—62no—
555C4—121no—
556C4—121no—
557C4—362no—
558C4Dic3×#6712yes—
559C4C22×D3×Dic311yescharacteristic
560C4C2×#380411yescharacteristic
561C3—21no—
562C3#8254711yescharacteristic, complemented
563C3#8396511yescharacteristic, complemented
564C2—22no—
565C2—122no—
566C2#1059531911yescharacteristic
567C2#1059532811yescharacteristic
568C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5812C2semidirect
4. C2×#63662C2semidirect
5. #10591576C2semidirect
6. Dic3×#216C2semidirect
7. #10591566C2semidirect
8. Dic3×#215C2semidirect
9. #10591131C2semidirect
11. #10591057C2semidirect
23. C3×#942C4semidirect
47. #5812D3semidirect
69. C2×C32×Q8C2×C4semidirect
88. C3×#216C2×C4semidirect
89. C3×#215C2×C4semidirect
100. C3×#208C2×C4semidirect
128. #942Dic3semidirect
221. C2×C3×Q8C4×D3semidirect
222. C2×C3×Q8C2×Dic3semidirect
264. #216C2×Dic3semidirect
265. #215C2×Dic3semidirect
287. #208C2×Dic3semidirect
425. C2×Q8D3×Dic3semidirect
501. C32#2947semidirect
562. C3#82547semidirect
563. C3#83965semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C2×C3×#9422
#105949922
C2×#636622
#105915762
Dic3×#2162
#105915662
Dic3×#2152
#105911312
#105910832
#105910572
#839653
#825473