Finite Group Databasebeta

← #11886551

Subgroups — #11886551

Order 1152.

1072 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63806C212yesmaximal, complemented
2#10593906C211yesmaximal, characteristic, complemented
3#10593902C211yesmaximal, characteristic, complemented
4#10592547C211yesmaximal, characteristic, complemented
5C3×#4848C211yesmaximal, characteristic, complemented
6C3×#4834C211yesmaximal, characteristic, complemented
7#10590968C212yesmaximal, complemented
8#10590826C212yesmaximal, complemented
9#10590823C212yesmaximal, complemented
10C4×#3719C211yesmaximal, characteristic, complemented
11#10590350C211yesmaximal, characteristic, complemented
12#80394—31nomaximal
13#79446—31nomaximal
14C2×#3799C2212yes—
15C2×#3795C2212yes—
16C2×#3744C2212yes—
17#64083C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C2×C3×#204C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×#874C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63914—21no—
25#63911—21no—
26#63910—22no—
27#63909C2212yes—
28#63908C2212yes—
29#63898—21no—
30#63894—21no—
31#63885—22no—
32C2×#3719C2211yescharacteristic
33C2×#3714C2212yes—
34C2×#3714C2212yes—
35#63806—28no—
36C32×C4⋊C8C2211yescharacteristic
37#63648C2212yes—
38C3×#821C2212yes—
39C3×(C2×D3)⋊C8C2212yes—
40C3×C4×C3⋊C8C2211yescharacteristic
41#63575C2211yescharacteristic
42#63567C2211yescharacteristic
43#63566C2211yescharacteristic
44C2×#916—32no—
45C2×#904—32no—
46#5718—31no—
47#5577—31no—
48#5553—31no—
49#5553—31no—
50C3×#460—31no—
51C3×C8×D4—31no—
52#5172—32no—
53#5115—32no—
54#5073—31no—
55C4×#216—31no—
56#4848—31no—
57#4848—31no—
58#4848—61no—
59#4848D311yescharacteristic, complemented
60#4834D311yescharacteristic, complemented
61#4781—32no—
62#4775—32no—
63#4734—32no—
64#4734—32no—
65C4×Dic12—31no—
66#4695—31no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×#634C2311yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12D411yescharacteristic
74C2×C3×D12C2312yes—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6C2311yescharacteristic
77C2×#626—22no—
78C2×#626—22no—
79C2×#625—22no—
80C2×#625—22no—
81C2×#624—22no—
82C2×D3×Dic3—22no—
83#3799—24no—
84#3799—42no—
85#3795—24no—
86#3795—42no—
87C2×C32×C8C2312yes—
88C32×C42C2311yescharacteristic
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91C4×C3⋊Dic3—21no—
92#3744—24no—
93C3×(C2×D3)⋊C4D412yes—
94C3×C4⋊Dic3D411yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3—21no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C3×#204—24no—
101C3×D3×C8—24no—
102#3722—22no—
103(C2×D3)⋊Dic3—22no—
104#3719D414yescomplemented
105#3714—24no—
106#3714—42no—
107#3287—91noSylow
108C2×#239—32no—
109C2×#237—32no—
110C2×#235—32no—
111C2×#235—32no—
112C2×C3×SD16—32no—
113C22×C3×C8—32no—
114C3×#127—31no—
115C3×C4×Q8—31no—
116C3×C4×D4—31no—
117C2×#216—31no—
118#940—61no—
119#940—61no—
120#940—61no—
121#939—62no—
122#938—32no—
123D4×Dic3—61no—
124C2×#213—32no—
125C2×#213—32no—
126#930—32no—
127#930—32no—
128#916—68no—
129C2×Dic12—31no—
130#904—68no—
131C2×D24—32no—
132C2×D24—32no—
133C2×#204—32no—
134C2×#204—32no—
135C2×#204—62no—
136C2×#204C2×D312yes—
137C2×D3×C8C2×D312yes—
138#895—32no—
139#895—62no—
140#893—61no—
141#893—61no—
142#884—62no—
143#884—62no—
144#874—31no—
145#874—31no—
146#874—61no—
147#874—61no—
148#874C2×D311yescharacteristic
149C4×D12—61no—
150C4×D12C2×D311yescharacteristic
151C4×Dic6—31no—
152C4×Dic6—31no—
153C4×Dic6—61no—
154C4×Dic6C2×D311yescharacteristic
155C3×C4⋊C8—21no—
156C3×C4⋊C8C2×D311yescharacteristic
157C3×C4⋊C8C2×D311yescharacteristic
158C3×#102—32no—
159C3×C22⋊C8—32no—
160C3×C4×C8—31no—
161#835—31no—
162#821—32no—
163#821—32no—
164#821—62no—
165#821C2×D312yes—
166(C2×D3)⋊C8C2×D312yes—
167#818—31no—
168#816—31no—
169#816—31no—
170#810—31no—
171#807—31no—
172C4×C3⋊C8C2×D311yescharacteristic
173C22×C3⋊D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C4⋊(C3⋊D3)—22no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—42no—
184C4⋊(C3⋊D3)—81no—
185#634—21no—
186#634C2×D412yes—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×D412yes—
190C3×D12—22no—
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—81no—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×Dic6—21no—
198C3×Dic6C2×D412yes—
199#626—44no—
200#626—82no—
201#625—44no—
202#625—82no—
203#624—44no—
204D3×Dic3—44no—
205C32×C8—22no—
206C3×C3⋊C8—21no—
207C3×C3⋊C8C2×D412yes—
208C2×#135—92no—
209#550—91no—
210#550—91no—
211#493—91no—
212#466—92no—
213#460—31no—
214#460—91no—
215#449—92no—
216#449—92no—
217C4×Q16—91no—
218C8×D4—31no—
219C2×C3×Q8—31no—
220C2×C3×D4—31no—
221C2×C3×D4—32no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C22×C3×C4—32no—
225C2×#67—62no—
226C2×#67—62no—
227C2×#67—62no—
228C2×#67—62no—
229C2×#67—62no—
230C2×#67—62no—
231C22×Dic3—62no—
232#239—64no—
233#239—122no—
234#237—64no—
235#237—122no—
236#235—64no—
237#235—64no—
238#235—122no—
239#235—122no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—32no—
243C2×D12—32no—
244C2×D12—62no—
245C2×D12—62no—
246C2×D12—61no—
247C2×D12—61no—
248C2×D12—62no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—121no—
252C2×D12—121no—
253C2×D12D1211yescharacteristic
254C2×D12C22×D312yes—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×C4×D3C22×D312yes—
259C2×Dic6—31no—
260C2×Dic6—31no—
261C2×Dic6—61no—
262C2×Dic6C22×D311yescharacteristic
263C3×SD16—64no—
264C2×C3×C8—22no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—64no—
268C2×C3×C8C22×D312yes—
269C2×C3×C8C22×D312yes—
270C3×C4⋊C4—31no—
271C3×C4⋊C4—31no—
272C3×C4⋊C4—61no—
273C3×C22⋊C4—32no—
274C3×C42—21no—
275C3×C42—61no—
276C3×C42C22×D311yescharacteristic
277C3×C42C22×D311yescharacteristic
278#217—62no—
279#216—34no—
280#213—64no—
281#213—122no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4D1212yes—
286C4⋊Dic3—31no—
287C4⋊Dic3—31no—
288C4⋊Dic3—61no—
289C4⋊Dic3D1211yescharacteristic
290C4⋊Dic3C22×D311yescharacteristic
291Dic3⋊C4—21no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—121no—
295C4×Dic3—21no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—121no—
299C2×C3⋊C8C22×D311yescharacteristic
300C2×C3⋊C8C22×D311yescharacteristic
301Dic12—34no—
302D24—64no—
303D24—122no—
304#204—24no—
305#204—64no—
306#204—64no—
307#204—124no—
308D3×C8—24no—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—42no—
311C2×C3⋊D3—42no—
312C2×C3⋊D3—42no—
313C2×C3×D3—22no—
314C2×C3×D3—22no—
315C2×C3×D3—22no—
316C2×C3×D3—42no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C32×C4—21no—
320C32×C4#13512yescomplemented
321C32×C4C22×D411yescharacteristic
322C32×C4H(5,𝔽2)11yescharacteristic
323C3⋊Dic3—22no—
324C3⋊Dic3—41no—
325C3×Dic3—22no—
326C3×Dic3—22no—
327C3×Dic3—41no—
328C2×#41—92no—
329C2×#41—92no—
330#135—188no—
331C2×Q16—91no—
332C2×SD16—32no—
333C2×SD16—92no—
334C2×D8—92no—
335C2×D8—92no—
336C22×C8—32no—
337#127—31no—
338#127—91no—
339#127—181no—
340#127—181no—
341#121—92no—
342#121—92no—
343#121—182no—
344#121—182no—
345C4×Q8—31no—
346C4×Q8—91no—
347C4×D4—31no—
348C4×D4—181no—
349C4×D4—181no—
350#107—91no—
351C4⋊C8D3211yescharacteristic
352#103—91no—
353#103—91no—
354#102—32no—
355#102—92no—
356C22⋊C8—32no—
357C4×C8—31no—
358C23×C3—32no—
359C23×C3—62no—
360C22×D3—22no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—122no—
364C22×D3C2×D1212yes—
365C3×Q8—32no—
366C3×Q8—61no—
367C3×D4—62no—
368C3×D4—62no—
369C3×D4—62no—
370C3×D4—122no—
371C3×D4—241no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—32no—
376C2×C3×C4—61no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4C2×D1211yescharacteristic
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386#67—124no—
387#67—124no—
388#67—124no—
389#67—242no—
390#67—242no—
391#67—242no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—124no—
401C2×Dic3C2×D1212yes—
402D12—22no—
403D12—22no—
404D12—22no—
405D12—42no—
406D12—62no—
407D12—62no—
408D12—62no—
409D12—62no—
410D12—81no—
411D12—122no—
412D12—122no—
413D12—124no—
414D12—122no—
415D12—122no—
416D12—242no—
417D12—241no—
418D12—241no—
419D12—242no—
420D12—242no—
421C4×D3—22no—
422C4×D3—22no—
423C4×D3—124no—
424C4×D3—124no—
425C4×D3—124no—
426Dic6—21no—
427Dic6—32no—
428Dic6—32no—
429Dic6—62no—
430Dic6—61no—
431Dic6—61no—
432Dic6—121no—
433Dic6D3×D412yes—
434C3×C8—22no—
435C3×C8—22no—
436C3×C8—32no—
437C3×C8—42no—
438C3×C8—61no—
439C3⋊C8—21no—
440C3⋊C8D3×D412yes—
441C2×C32D4211yescharacteristic
442C2×C32C2×#13511yescharacteristic
443C2×C32#57611yescharacteristic
444C3⋊D3—82no—
445C3×D3—42no—
446C3×D3—82no—
447#41—184no—
448#41—184no—
449#41—362no—
450#41—362no—
451C2×Q8—31no—
452C2×Q8—91no—
453C2×D4—32no—
454C2×D4—31no—
455C2×D4—61no—
456C2×D4—61no—
457C2×D4—92no—
458C2×D4—182no—
459C2×D4—182no—
460C2×D4—182no—
461C2×D4—182no—
462C2×D4—181no—
463C2×D4—181no—
464C22×C4—32no—
465C22×C4—182no—
466C22×C4—182no—
467Q16—94no—
468SD16—64no—
469SD16—184no—
470D8—184no—
471D8—362no—
472C2×C8—31no—
473C2×C8—31no—
474C2×C8—64no—
475C2×C8C2×D3212yes—
476C4⋊C4—31no—
477C4⋊C4—31no—
478C4⋊C4—61no—
479C4⋊C4—91no—
480C4⋊C4—181no—
481C22⋊C4—32no—
482C22⋊C4—182no—
483C22⋊C4—182no—
484C42—61no—
485C42—181no—
486C42C2×D3211yescharacteristic
487C22×C3—21no—
488C22×C3—62no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3C22×D1211yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—22no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—242no—
509C2×D3—242no—
510C2×D3—242no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—21no—
516C3×C4—41no—
517C3×C4—62no—
518C3×C4—62no—
519C3×C4—121no—
520C3×C4#90412yescomplemented
521C3×C4#91612yescomplemented
522C3×C4C2×D3×D411yescharacteristic
523C3×C4C2×D3×D411yescharacteristic
524C3×C4#100911yescharacteristic
525C3×C4#100911yescharacteristic
526Dic3—22no—
527Dic3—22no—
528Dic3—41no—
529Dic3—62no—
530Dic3—62no—
531Dic3—122no—
532Dic3—121no—
533Dic3—121no—
534Dic3—241no—
535C32#328711yescharacteristic, complemented, Sylow
536C23—32no—
537C23—62no—
538C23—182no—
539Q8—32no—
540Q8—61no—
541Q8—92no—
542Q8—181no—
543D4—62no—
544D4—62no—
545D4—62no—
546D4—122no—
547D4—182no—
548D4—182no—
549D4—241no—
550D4—364no—
551D4—364no—
552D4—362no—
553D4—721no—
554D4—722no—
555D4—722no—
556C2×C4—32no—
557C2×C4—61no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—61no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—364no—
564C2×C4—364no—
565C2×C4D3×D1211yescharacteristic
566C2×C4D3×D1211yescharacteristic
567C2×C4C22×D3211yescharacteristic
568C8—22no—
569C8—32no—
570C8—61no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—122no—
575C2×C3—242no—
576C2×C3D4×D1211yescharacteristic
577C2×C3#560911yescharacteristic
578C2×C3C2×#90411yescharacteristic
579C2×C3#575211yescharacteristic
580C2×C3C2×#91611yescharacteristic
581C2×C3#577411yescharacteristic
582D3—42no—
583D3—82no—
584D3—242no—
585D3—242no—
586D3—482no—
587C22—62no—
588C22—62no—
589C22—62no—
590C22—122no—
591C22—122no—
592C22—122no—
593C22—362no—
594C22—362no—
595C22—362no—
596C22C2×D3×D1211yescharacteristic
597C4—21no—
598C4—62no—
599C4—62no—
600C4—121no—
601C4—182no—
602C4—361no—
603C4#6380612yescomplemented
604C4D32×D411yescharacteristic
605C4#6432011yescharacteristic
606C3—21no—
607C3#7944611yescharacteristic, complemented
608C3#8039411yescharacteristic, complemented
609C2—122no—
610C2—242no—
611C2—722no—
612C2#1059462111yescharacteristic
613C2C2×#6380611yescharacteristic
614C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3287
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63806C2semidirect
2. #10593906C2semidirect
3. #10593902C2semidirect
4. #10592547C2semidirect
5. C3×#4848C2semidirect
6. C3×#4834C2semidirect
7. #10590968C2semidirect
8. #10590826C2semidirect
9. #10590823C2semidirect
10. C4×#3719C2semidirect
11. #10590350C2semidirect
59. #4848D3semidirect
60. #4834D3semidirect
104. #3719D4semidirect
320. C32×C4#135semidirect
520. C3×C4#904semidirect
521. C3×C4#916semidirect
535. C32#3287semidirect
603. C4#63806semidirect
607. C3#79446semidirect
608. C3#80394semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
#105939062
#105939022
#105925472
C3×#48482
C3×#48342
#105909682
#105908262
#105908232
C4×#37192
#105903502
#803943
#794463