Finite Group Databasebeta

← #11870369

Subgroups — #11870369

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595044C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic, complemented
3C2×#63644C211yesmaximal, characteristic, complemented
4C3×#5113C211yesmaximal, characteristic, complemented
5C3×#5110C211yesmaximal, characteristic, complemented
6#10591131C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic, complemented
8#10590837C212yesmaximal, complemented
9#10590711C212yesmaximal, complemented
10#10590676C212yesmaximal, complemented
11#10590675C212yesmaximal, complemented
12#78844—31nomaximal
13#78654—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63980—22no—
22#67⋊Dic3—22no—
23#63908—21no—
24#63908C2212yes—
25Dic3×D12—21no—
26D3×C4⋊Dic3C2212yes—
27#63856—21no—
28#63856C2212yes—
29Dic3×Dic6—21no—
30#63841C2212yes—
31#63644C2212yes—
32#63644C2212yes—
33C3×#821C2211yescharacteristic
34C3×#821C2211yescharacteristic
35C3×(C2×D3)⋊C8C2212yes—
36C3×(C2×D3)⋊C8C2212yes—
37C3×#816C2211yescharacteristic
38C3×#816C2211yescharacteristic
39#63575C2212yes—
40#63573C2212yes—
41#63566C2212yes—
42#63563C2212yes—
43#5833—31no—
44#5833—31no—
45#5827—31no—
46#5523—31no—
47C3×#416—31no—
48C3×#408—31no—
49#5232—31no—
50#5133—31no—
51#5121—31no—
52#5113D311yescharacteristic, complemented
53#5110D311yescharacteristic, complemented
54C2×#817—31no—
55C2×#817—31no—
56C2×#817—61no—
57#4995—31no—
58#4815—32no—
59#4805—32no—
60#4779—32no—
61#4777—32no—
62#4737—32no—
63#4735—32no—
64#4723—32no—
65#4721—32no—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3—21no—
68C22×C3⋊Dic3—21no—
69C2×C3×#67—21no—
70C2×C3×#67D412yes—
71C3×#235—22no—
72C3×#235—22no—
73C3×#235—22no—
74C3×#235—22no—
75C2×C3×D12D411yescharacteristic
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3C2312yes—
79C2×C3×Dic6D411yescharacteristic
80C2×C3×Dic6C2311yescharacteristic
81C2×#625—22no—
82C2×D3×Dic3—22no—
83C2×C32×C8—22no—
84C2×C32×C8C2311yescharacteristic
85C2×C32×C8C2311yescharacteristic
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2312yes—
90C3×#217—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×#208—22no—
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—22no—
102#3099—91noSylow
103C2×C3×#41—31no—
104C2×C3×#41—31no—
105C2×#235C2×D311yescharacteristic
106C2×#235C2×D311yescharacteristic
107C2×C3×M16—31no—
108C22×C3×C8—21no—
109C22×C3×C8C2×D311yescharacteristic
110C22×C3×C8C2×D311yescharacteristic
111C3×#117—31no—
112#946—32no—
113#946—61no—
114Q8×Dic3—61no—
115#939—62no—
116#939—62no—
117#938—32no—
118#938—61no—
119D4×Dic3—61no—
120D4×Dic3—62no—
121#930—32no—
122#930—61no—
123#926—32no—
124#926C2×D311yescharacteristic
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3—61no—
131C2×C4⋊Dic3—61no—
132#924—32no—
133#924—61no—
134C2×#208C2×D311yescharacteristic
135#892—32no—
136D3×C4⋊C4—32no—
137#67⋊C4—62no—
138C4×D12—61no—
139C4×Dic6—61no—
140C3×#103—31no—
141C3×#103—31no—
142C3×#102—31no—
143C3×#102—31no—
144C3×C22⋊C8—32no—
145C3×C22⋊C8—32no—
146#835—32no—
147#832—32no—
148#821—32no—
149#821C2×D311yescharacteristic
150#821C2×D311yescharacteristic
151(C2×D3)⋊C8C2×D312yes—
152(C2×D3)⋊C8C2×D312yes—
153#818—32no—
154#817—32no—
155#817—32no—
156#817—32no—
157#817—32no—
158#817—32no—
159#817—62no—
160#817—62no—
161#816—32no—
162#816C2×D311yescharacteristic
163#816C2×D311yescharacteristic
164#808—32no—
165#807—32no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4112yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—81no—
176C2×C3⋊Dic3—81no—
177C3×#67—24no—
178C3×#67—42no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3C2×D412yes—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—21no—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×C4×D3—42no—
189C3×Dic6—22no—
190C3×Dic6—21no—
191C3×Dic6—21no—
192#625—82no—
193D3×Dic3—82no—
194C32×C8—21no—
195C32×C8—21no—
196C3×C3⋊C8—22no—
197#537—91no—
198#520—91no—
199#485—92no—
200#483—92no—
201#482—92no—
202#481—92no—
203#428—91no—
204C2×#106—91no—
205#417—91no—
206#416—31no—
207#408—31no—
208C3×#41—62no—
209C3×#41—62no—
210C3×#41—62no—
211C3×#41—62no—
212C2×C3×Q8—31no—
213C2×C3×Q8—31no—
214C2×C3×D4—32no—
215C2×C3×D4—31no—
216C2×C3×D4—31no—
217C2×C3×D4—61no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—61no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67—21no—
224C2×#67—62no—
225C2×#67—62no—
226C2×#67D1212yes—
227C22×Dic3—62no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—121no—
233C22×Dic3—121no—
234#235—22no—
235#235—22no—
236#235—22no—
237#235—22no—
238C2×D12D1211yescharacteristic
239C2×D12C22×D311yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—62no—
242C2×C4×D3C22×D312yes—
243C2×Dic6D1211yescharacteristic
244C2×Dic6C22×D311yescharacteristic
245C3×M16—62no—
246C2×C3×C8—24no—
247C2×C3×C8—22no—
248C2×C3×C8—22no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—32no—
252C2×C3×C8C22×D311yescharacteristic
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C3×C4⋊C4—31no—
257C3×C4⋊C4—31no—
258C3×C22⋊C4—61no—
259C3×C42—61no—
260#217—21no—
261#217—62no—
262#217—62no—
263#217—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267C4⋊Dic3—32no—
268C4⋊Dic3—32no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—121no—
279C4⋊Dic3—121no—
280C4⋊Dic3C22×D311yescharacteristic
281C4⋊Dic3C22×D311yescharacteristic
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285C4×Dic3—21no—
286C4×Dic3—62no—
287C4×Dic3—62no—
288#208—22no—
289C2×C3⋊C8C22×D312yes—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32#12312yes—
293C22×C32C22×D411yescharacteristic
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—41no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C32×C4#12312yes—
301C32×C4C2×#4111yescharacteristic
302C32×C4C2×#4111yescharacteristic
303C3⋊Dic3—42no—
304C3⋊Dic3—42no—
305C3×Dic3—22no—
306C3×Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—41no—
309C2×#41—31no—
310C2×#41—31no—
311C2×M16—31no—
312C22×C8D3211yescharacteristic
313C22⋊Q8—92no—
314C22⋊Q8—181no—
315#121—92no—
316#121—181no—
317#121—182no—
318C4×Q8—181no—
319C4×D4—181no—
320C4×D4—182no—
321#117—31no—
322#117—92no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326#107—92no—
327#106—92no—
328#106—92no—
329#106—92no—
330#103—31no—
331#103—31no—
332#103—92no—
333#102—31no—
334#102—31no—
335#102—92no—
336C22⋊C8—32no—
337C22⋊C8—32no—
338C23×C3—21no—
339C23×C3—32no—
340C23×C3—61no—
341C23×C3C2×D1211yescharacteristic
342C23×C3D3×D411yescharacteristic
343C22×D3—21no—
344C22×D3C2×D1212yes—
345C3×Q8—62no—
346C3×Q8—61no—
347C3×Q8—61no—
348C3×D4—64no—
349C3×D4—62no—
350C3×D4—61no—
351C3×D4—61no—
352C3×D4—122no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—32no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—122no—
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4#23512yes—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4#23712yes—
368C2×C3×C4#23712yes—
369C2×C3×C4#23712yes—
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—24no—
373#67—42no—
374#67—242no—
375#67—242no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—242no—
386C2×Dic3—241no—
387C2×Dic3—241no—
388C2×Dic3—241no—
389C2×Dic3—241no—
390C2×Dic3—242no—
391C2×Dic3—242no—
392C2×Dic3C2×D1212yes—
393D12—22no—
394D12—21no—
395D12—21no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—42no—
399C4×D3—242no—
400Dic6—22no—
401Dic6—21no—
402Dic6—21no—
403C3×C8—22no—
404C3×C8—22no—
405C3×C8—21no—
406C3×C8—21no—
407C3×C8—21no—
408C3×C8—21no—
409C3×C8—62no—
410C3⋊C8—22no—
411C2×C32—22no—
412C2×C32C2×#12311yescharacteristic
413C2×C32#57711yescharacteristic
414C2×C32#57711yescharacteristic
415C3×D3—42no—
416C3×D3—81no—
417#41—62no—
418#41—62no—
419#41—62no—
420#41—62no—
421C2×Q8—31no—
422C2×Q8—31no—
423C2×D4—32no—
424C2×D4—31no—
425C2×D4—31no—
426C2×D4—61no—
427C2×D4—182no—
428C22×C4—32no—
429C22×C4—61no—
430C22×C4—182no—
431C22×C4—181no—
432C22×C4—181no—
433C22×C4C2×D3211yescharacteristic
434M16—62no—
435C2×C8—22no—
436C2×C8—32no—
437C2×C8C2×D3211yescharacteristic
438C2×C8C2×D3211yescharacteristic
439C4⋊C4—31no—
440C4⋊C4—31no—
441C4⋊C4—92no—
442C4⋊C4—92no—
443C4⋊C4—182no—
444C4⋊C4—182no—
445C4⋊C4—181no—
446C4⋊C4—181no—
447C22⋊C4—61no—
448C22⋊C4—182no—
449C22⋊C4—182no—
450C22⋊C4—182no—
451C42—61no—
452C42—182no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—121no—
465C22×C3—121no—
466C22×C3—121no—
467C22×C3#88312yes—
468C22×C3#88612yes—
469C22×C3C22×D1211yescharacteristic
470C22×C3C2×D3×D411yescharacteristic
471C2×D3—22no—
472C2×D3—22no—
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—41no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—22no—
480C3×C4—62no—
481C3×C4—121no—
482C3×C4—121no—
483C3×C4—121no—
484C3×C4#88312yes—
485C3×C4#88612yes—
486C3×C4C2×#23511yescharacteristic
487C3×C4C2×#23711yescharacteristic
488C3×C4C2×#23711yescharacteristic
489C3×C4C2×#23711yescharacteristic
490Dic3—22no—
491Dic3—41no—
492Dic3—41no—
493Dic3—41no—
494Dic3—122no—
495Dic3—122no—
496Dic3—122no—
497Dic3—122no—
498Dic3—242no—
499Dic3—242no—
500C32#309911yescharacteristic, complemented, Sylow
501C23—32no—
502C23—61no—
503C23D3×D1211yescharacteristic
504Q8—62no—
505Q8—61no—
506Q8—61no—
507D4—64no—
508D4—61no—
509D4—61no—
510D4—62no—
511D4—122no—
512D4—722no—
513C2×C4—32no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—122no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—722no—
523C2×C4—721no—
524C2×C4—721no—
525C2×C4#379512yes—
526C2×C4D3×D1211yescharacteristic
527C2×C4#380512yes—
528C2×C4C22×D3211yescharacteristic
529C8—21no—
530C8—21no—
531C8—62no—
532C2×C3—24no—
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—122no—
539C2×C3—241no—
540C2×C3C2×#88311yescharacteristic
541C2×C3C2×#88611yescharacteristic
542C2×C3#575111yescharacteristic
543C2×C3#575111yescharacteristic
544C2×C3#577011yescharacteristic
545C2×C3#577011yescharacteristic
546D3—42no—
547D3—81no—
548C22—21no—
549C22—21no—
550C22—62no—
551C22—62no—
552C22—62no—
553C22—121no—
554C22—121no—
555C22—121no—
556C22#6389112yes—
557C22C2×D3×D1211yescharacteristic
558C4—62no—
559C4—121no—
560C4—121no—
561C4—121no—
562C4—362no—
563C4—362no—
564C4#6389112yes—
565C4C2×#379511yescharacteristic
566C4C2×#380511yescharacteristic
567C3—21no—
568C3#7865411yescharacteristic, complemented
569C3#7884411yescharacteristic, complemented
570C2—22no—
571C2—122no—
572C2—241no—
573C2#1059467911yescharacteristic
574C2#1059467911yescharacteristic
575C2C2×#6389111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595044C2
hypercenterC22×C8D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594992C2semidirect
3. C2×#63644C2semidirect
4. C3×#5113C2semidirect
5. C3×#5110C2semidirect
6. #10591131C2semidirect
7. #10591088C2semidirect
8. #10590837C2semidirect
9. #10590711C2semidirect
10. #10590676C2semidirect
11. #10590675C2semidirect
52. #5113D3semidirect
53. #5110D3semidirect
500. C32#3099semidirect
568. C3#78654semidirect
569. C3#78844semidirect

Maximal subgroups

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

subgroupindex
#105950442
#105949922
C2×#636442
C3×#51132
C3×#51102
#105911312
#105910882
#105908372
#105907112
#105906762
#105906752
#788443
#786543