Finite Group Databasebeta

← #11887056

Subgroups — #11887056

Order 1152.

1134 conjugacy classes of subgroups.

The subgroup lattice has 635 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596022C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic, complemented
3C3×#5015C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591516C212yesmaximal, complemented
6#10591455C212yesmaximal, complemented
7#10590593C212yesmaximal, complemented
8#10590510C212yesmaximal, complemented
9#10590327C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#80352—31nomaximal
13#79608—31nomaximal
14C2×#3828—21no—
15C2×#3802C2212yes—
16C2×D3×D12—21no—
17C32×C4×D4C2211yescharacteristic, complemented
18#64147C2212yescomplemented
19#64133—21no—
20C4⋊C4×C3⋊D3C2212yescomplemented
21#64092—22no—
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23#64078C2211yescharacteristic, complemented
24C2×C3×#213C2211yescharacteristic
25C2×C3×#213C2212yescomplemented
26C3×#874C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28#63922—22no—
29#63916C2212yes—
30#63908—21no—
31C2×#3710C2212yescomplemented
32C3×#832C2211yescharacteristic, complemented
33C3×#809C2211yescharacteristic
34C3×#809C2212yescomplemented
35C3×#807C2211yescharacteristic, complemented
36C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63575C2212yescomplemented
39#63563C2212yes—
40#63563C2212yescomplemented
41#63563C2212yescomplemented
42#63557C2212yescomplemented
43#5717—31no—
44#5551—31no—
45#5551—31no—
46#5551—61no—
47D4×D12—31no—
48C3×#459—31no—
49C3×C4×D8—31no—
50#5157—32no—
51#5156—32no—
52#5156—32no—
53#5070—31no—
54#5015D311yescharacteristic, complemented
55C4×#213D311yescharacteristic, complemented
56#5007—31no—
57#4882—32no—
58#4846—31no—
59#4834—31no—
60#4775—32no—
61#4774—32no—
62D3×#102—32no—
63D3×#102—32no—
64#4694—31no—
65C8×D12—31no—
66C22×D32—22no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×#638—22no—
70#3828—44no—
71C2×C4⋊(C3⋊D3)D411yescharacteristic
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3C2312yes—
74C2×#634—21no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12C2312yes—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×#626—22no—
81C2×#625—22no—
82#3802—24no—
83#3802—42no—
84D3×D12—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3757—22no—
89#3752D412yes—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)D411yescharacteristic
92C4⋊(C3⋊Dic3)C2312yes—
93#3750—22no—
94C3×#213—22no—
95C3×#213—42no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2311yescharacteristic
101(C2×D3)⋊Dic3—22no—
102#3710—42no—
103#3294—91noSylow
104C2×D3×D4—32no—
105C2×D3×D4—32no—
106C2×D3×D4—61no—
107C2×#235—61no—
108C2×#235—61no—
109C2×#235—62no—
110C22×D12—61no—
111C2×C3×D8—31no—
112C2×C3×D8—32no—
113C3×#127—31no—
114C3×C4×D4—21no—
115C3×C4×D4—31no—
116C3×C4×D4C2×D311yescharacteristic, complemented
117C3×C4×D4C2×D311yescharacteristic, complemented
118#938—32no—
119#938—32no—
120#938—32no—
121#938—62no—
122#938—61no—
123#937—62no—
124C2×#213C2×D311yescharacteristic
125C2×#213C2×D312yescomplemented
126#930—61no—
127#924—61no—
128#924—61no—
129#924—62no—
130C2×D3×C8—32no—
131C2×D3×C8—32no—
132#895—32no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—32no—
135D3×C4⋊C4—62no—
136#883—62no—
137#883—62no—
138#883—64no—
139#882—62no—
140#874C2×D311yescharacteristic
141C4×D12—31no—
142C4×D12—31no—
143C4×D12—61no—
144C4×D12C2×D311yescharacteristic
145#869—31no—
146#869—31no—
147#869—61no—
148C3×#107—31no—
149C3×C4⋊C8—31no—
150C3×#102—31no—
151C3×#102—31no—
152C3×#102—32no—
153C3×C4×C8—31no—
154#832—32no—
155#832—32no—
156#832—32no—
157#832C2×D311yescharacteristic, complemented
158#821—32no—
159#821—32no—
160#821—32no—
161(C2×D3)⋊C8—32no—
162(C2×D3)⋊C8—32no—
163#818—32no—
164#809C2×D311yescharacteristic
165#809C2×D312yescomplemented
166#807—32no—
167#807C2×D311yescharacteristic, complemented
168C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
169C4×C3⋊C8C2×D311yescharacteristic, complemented
170C23×C32—21no—
171C22×C3⋊D3C2×D412yes—
172C22×C3×D3—21no—
173C22×C3×D3—22no—
174C2×D32—44no—
175C2×D32—44no—
176C2×D32—82no—
177C32×D4—21no—
178C32×D4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—44no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C2×D412yes—
187C4⋊(C3⋊D3)D814yescomplemented
188C4×C3⋊D3—22no—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—44no—
191#634—42no—
192C2×C3×Dic3—21no—
193C3×D12—22no—
194C3×D12—21no—
195C3×D12—22no—
196C3×D12—42no—
197C3×D12—81no—
198C3×D12#4112yescomplemented
199C3×C4×D3—42no—
200#626—44no—
201#625—44no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—21no—
204C3×C3⋊C8—22no—
205#547—91no—
206D42—91no—
207#486—91no—
208#480—92no—
209#474—91no—
210#466—92no—
211#459—31no—
212#447—92no—
213C4×D8—31no—
214C8×D4—91no—
215C2×#102—92no—
216C23×D3—62no—
217C23×D3—62no—
218C2×C3×D4—21no—
219C2×C3×D4—31no—
220C2×C3×D4—32no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×C3×D4C22×D311yescharacteristic
224C2×C3×D4C22×D311yescharacteristic
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—61no—
229C2×#67—62no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—64no—
235D3×D4—64no—
236D3×D4—64no—
237D3×D4—124no—
238D3×D4—122no—
239D3×D4—122no—
240#235—124no—
241#235—124no—
242#235—128no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—31no—
246C2×D12—31no—
247C2×D12—61no—
248C2×D12—62no—
249C2×D12—124no—
250C2×D12C22×D312yes—
251C2×D12C22×D311yescharacteristic
252C2×C4×D3—21no—
253C2×C4×D3—32no—
254C2×C4×D3—32no—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×C4×D3—64no—
259C2×Dic6—62no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C3×D8—62no—
263C3×D8—122no—
264C2×C3×C8—32no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4C22×D311yescharacteristic
270C3×C4⋊C4C22×D311yescharacteristic
271C3×C22⋊C4—22no—
272C3×C22⋊C4—21no—
273C3×C22⋊C4—21no—
274C3×C22⋊C4—61no—
275C3×C42—21no—
276C3×C42C22×D311yescharacteristic
277C3×C42C22×D311yescharacteristic
278#217—62no—
279#217—62no—
280#217—62no—
281#217—64no—
282#213—22no—
283#213—42no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—32no—
286(C2×D3)⋊C4—32no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289C4⋊Dic3—31no—
290C4⋊Dic3—31no—
291C4⋊Dic3—32no—
292C4⋊Dic3—32no—
293C4⋊Dic3—62no—
294C4⋊Dic3—61no—
295C4⋊Dic3—62no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3C22×D311yescharacteristic
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—64no—
302C2×C3⋊C8C22×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D312yes—
305D3×C8—122no—
306D3×C8—122no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3C2×D814yes—
314C2×C3×D3—22no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320D32—88no—
321C32×C4—21no—
322C32×C4—41no—
323C32×C4C2×D812yes—
324C32×C4C2×#4111yescharacteristic
325C32×C4H(5,𝔽2)11yescharacteristic
326C3⋊Dic3—22no—
327C3⋊Dic3—42no—
328C3×Dic3—41no—
329C2×#41—181no—
330C22×D4—92no—
331C22×D4—181no—
332C2×D8—31no—
333C2×D8—32no—
334C22×C8—92no—
335C4⋊Q8—91no—
336#127—31no—
337#123—182no—
338C22⋊Q8—181no—
339#121—92no—
340#121—92no—
341#121—181no—
342#120—182no—
343C4×D4—31no—
344C4×D4—91no—
345C4×D4D3211yescharacteristic, complemented
346C2×C4⋊C4—92no—
347#107—31no—
348#107—92no—
349C4⋊C8—31no—
350#102—31no—
351#102—31no—
352#102—32no—
353#102—92no—
354#102—92no—
355#102—92no—
356C22⋊C8—92no—
357C4×C8—31no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—61no—
362C23×C3—62no—
363C22×D3—21no—
364C22×D3—22no—
365C22×D3—32no—
366C22×D3—32no—
367C22×D3—62no—
368C22×D3—124no—
369C22×D3—124no—
370C22×D3—124no—
371C22×D3—124no—
372C22×D3—242no—
373C22×D3—242no—
374C3×D4—21no—
375C3×D4—21no—
376C3×D4—21no—
377C3×D4—21no—
378C3×D4—32no—
379C3×D4—41no—
380C3×D4—41no—
381C3×D4—62no—
382C3×D4—61no—
383C3×D4—62no—
384C3×D4—122no—
385C3×D4—241no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—44no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—61no—
396C2×C3×C4—122no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—124no—
404#67—124no—
405#67—124no—
406#67—124no—
407#67—124no—
408#67—128no—
409C2×Dic3—21no—
410C2×Dic3—32no—
411C2×Dic3—32no—
412C2×Dic3—62no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416D12—22no—
417D12—22no—
418D12—21no—
419D12—34no—
420D12—34no—
421D12—42no—
422D12—64no—
423D12—81no—
424D12—124no—
425D12#23512yescomplemented
426C4×D3—42no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—122no—
432C4×D3—122no—
433C4×D3—124no—
434C4×D3—124no—
435C4×D3—128no—
436Dic6—124no—
437Dic6—122no—
438Dic6—122no—
439C3×C8—61no—
440C3×C8—61no—
441C3×C8—62no—
442C3⋊C8—21no—
443C3⋊C8—22no—
444C3⋊C8—21no—
445C2×C32—81no—
446C2×C32#54611yescharacteristic
447C2×C32C22×D811yescharacteristic
448C2×C32#57711yescharacteristic
449C3⋊D3—24no—
450C3×D3—42no—
451C3×D3—82no—
452C24—182no—
453#41—364no—
454C2×Q8—181no—
455C2×D4—31no—
456C2×D4—32no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—91no—
460C2×D4—182no—
461C2×D4—182no—
462C2×D4—184no—
463C2×D4—182no—
464C2×D4—364no—
465C2×D4—362no—
466C2×D4C2×D3211yescharacteristic
467C22×C4—21no—
468C22×C4—61no—
469C22×C4—92no—
470C22×C4—182no—
471D8—62no—
472D8—122no—
473C2×C8—31no—
474C2×C8—31no—
475C2×C8—32no—
476C2×C8—362no—
477C4⋊C4—31no—
478C4⋊C4—91no—
479C4⋊C4—92no—
480C4⋊C4—182no—
481C4⋊C4—181no—
482C4⋊C4C2×D3211yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—61no—
485C22⋊C4—92no—
486C22⋊C4—182no—
487C22⋊C4—182no—
488C42C2×D3211yescharacteristic
489C22×C3—21no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—62no—
500C22×C3—121no—
501C22×C3—121no—
502C22×C3—122no—
503C22×C3—122no—
504C22×C3—122no—
505C22×C3C2×D3×D411yescharacteristic
506C22×C3C2×D3×D411yescharacteristic
507C2×D3—22no—
508C2×D3—34no—
509C2×D3—34no—
510C2×D3—41no—
511C2×D3—41no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—64no—
516C2×D3—62no—
517C2×D3—62no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—248no—
523C2×D3—248no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—22no—
529C3×C4—41no—
530C3×C4—42no—
531C3×C4—41no—
532C3×C4—41no—
533C3×C4—121no—
534C3×C4D3×D812yes—
535C3×C4D3×D812yes—
536C3×C4C2×#23511yescharacteristic
537C3×C4#100411yescharacteristic
538C3×C4D3×#4111yescharacteristic
539C3×C4#100911yescharacteristic
540Dic3—41no—
541Dic3—62no—
542Dic3—62no—
543Dic3—122no—
544Dic3—124no—
545Dic3—122no—
546Dic3—122no—
547C32#329411yescharacteristic, complemented, Sylow
548C23—21no—
549C23—61no—
550C23—62no—
551C23—92no—
552C23—364no—
553C23—364no—
554C23—722no—
555Q8—362no—
556D4—21no—
557D4—21no—
558D4—32no—
559D4—62no—
560D4—61no—
561D4—62no—
562D4—94no—
563D4—122no—
564D4—241no—
565D4—364no—
566D4—364no—
567D4—364no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—61no—
571C2×C4—92no—
572C2×C4—122no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—364no—
577C2×C4#381111yescharacteristic
578C2×C4#381111yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—61no—
581C8—61no—
582C8—62no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—82no—
587C2×C3—81no—
588C2×C3—81no—
589C2×C3—122no—
590C2×C3—242no—
591C2×C3#555011yescharacteristic
592C2×C3#561211yescharacteristic
593C2×C3C2×D3×D811yescharacteristic
594C2×C3C2×D3×D811yescharacteristic
595C2×C3#577011yescharacteristic
596C2×C3#577511yescharacteristic
597D3—42no—
598D3—64no—
599D3—64no—
600D3—82no—
601D3—124no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—62no—
606C22—94no—
607C22—121no—
608C22—121no—
609C22—122no—
610C22—122no—
611C22—122no—
612C22—182no—
613C22—182no—
614C22—728no—
615C22C2×#381111yescharacteristic
616C4—21no—
617C4—41no—
618C4—121no—
619C4—182no—
620C4—362no—
621C4#6392612yes—
622C4D3×#23511yescharacteristic
623C4#6430711yescharacteristic
624C3—21no—
625C3#7960811yescharacteristic, complemented
626C3#8035211yescharacteristic, complemented
627C2—81no—
628C2—122no—
629C2—184no—
630C2—242no—
631C2#1059507811yescharacteristic
632C2C2×#6392611yescharacteristic
633C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596022C2semidirect
2. #10594004C2semidirect
3. C3×#5015C2semidirect
4. C3×C4×#213C2semidirect
5. #10591516C2semidirect
6. #10591455C2semidirect
7. #10590593C2semidirect
8. #10590510C2semidirect
9. #10590327C2semidirect
10. #10590273C2semidirect
11. #10590272C2semidirect
17. C32×C4×D4C22semidirect
18. #64147C22semidirect
20. C4⋊C4×C3⋊D3C22semidirect
23. #64078C22semidirect
25. C2×C3×#213C22semidirect
31. C2×#3710C22semidirect
32. C3×#832C22semidirect
34. C3×#809C22semidirect
35. C3×#807C22semidirect
36. C3×C4⋊(C3⋊C8)C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63575C22semidirect
40. #63563C22semidirect
41. #63563C22semidirect
42. #63557C22semidirect
54. #5015D3semidirect
55. C4×#213D3semidirect
116. C3×C4×D4C2×D3semidirect
117. C3×C4×D4C2×D3semidirect
125. C2×#213C2×D3semidirect
157. #832C2×D3semidirect
165. #809C2×D3semidirect
167. #807C2×D3semidirect
168. C4⋊(C3⋊C8)C2×D3semidirect
169. C4×C3⋊C8C2×D3semidirect
187. C4⋊(C3⋊D3)D8semidirect
198. C3×D12#41semidirect
345. C4×D4D32semidirect
425. D12#235semidirect
547. C32#3294semidirect
625. C3#79608semidirect
626. C3#80352semidirect

Maximal subgroups

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

subgroupindex
#105960222
#105940042
C3×#50152
C3×C4×#2132
#105915162
#105914552
#105905932
#105905102
#105903272
#105902732
#105902722
#803523
#796083