Finite Group Databasebeta

← #11887050

Subgroups — #11887050

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#10596197C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590598C212yesmaximal, complemented
6#10590593C212yesmaximal, complemented
7#10590510C212yesmaximal, complemented
8#10590509C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11#10590327C211yesmaximal, characteristic, complemented
12#81576—31nomaximal
13#80980—31nomaximal
14C2×#3832—21no—
15C2×#3802C2212yes—
16C2×D3×D12—21no—
17C32×C4⋊Q8C2211yescharacteristic, complemented
18#64155—21no—
19#64104C2212yescomplemented
20#64103—22no—
21C4⋊C4×C3⋊D3C2212yescomplemented
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C3×#874C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26#63922—22no—
27#63916C2212yes—
28#63908—21no—
29C2×#3714C2211yescharacteristic
30C2×#3714C2212yescomplemented
31C2×#3710C2212yescomplemented
32C3×#809C2212yes—
33C3×#809C2212yescomplemented
34C3×#809C2212yescomplemented
35C3×#807C2212yescomplemented
36C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63575C2211yescharacteristic, complemented
39#63564C2211yescharacteristic, complemented
40#63563C2211yescharacteristic
41#63563C2212yescomplemented
42#63557C2212yescomplemented
43#5726—31no—
44#5726—31no—
45#5726—61no—
46#5717—31no—
47D4×D12—31no—
48C3×#486—31no—
49C3×#474—31no—
50#5088D311yescharacteristic, complemented
51#5087D311yescharacteristic, complemented
52#5072—31no—
53C4×#213—31no—
54#4883—32no—
55#4882—32no—
56#4843—31no—
57#4834—31no—
58#4775—32no—
59#4774—32no—
60#4773—32no—
61#4773—32no—
62D3×#102—32no—
63D3×#102—32no—
64C4×D24—31no—
65C8×D12—31no—
66C22×D32—22no—
67C2×C32×Q8—21no—
68#3832—44no—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)D411yescharacteristic
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3C2312yes—
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⋊C4—21no—
86C32×C4⋊C4C2312yes—
87C32×C42C2311yescharacteristic
88#3752—21no—
89#3752—22no—
90#3752D412yes—
91C4⋊(C3⋊Dic3)D411yescharacteristic
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—22no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99(C2×D3)⋊Dic3—22no—
100#3714—22no—
101#3714—42no—
102#3710—42no—
103#3294—91noSylow
104C2×#239—61no—
105C2×#239—61no—
106C2×#239—62no—
107C2×D3×D4—32no—
108C2×D3×D4—32no—
109C2×D3×D4—61no—
110C22×D12—61no—
111C3×C4⋊Q8—21no—
112C3×C4⋊Q8C2×D311yescharacteristic, complemented
113C3×C4⋊Q8C2×D311yescharacteristic, complemented
114C3×#127—31no—
115C3×C4×D4—31no—
116#946—61no—
117#946—61no—
118#946—62no—
119#938—32no—
120#938—61no—
121#937—62no—
122C2×#213—31no—
123C2×#213—32no—
124#930—61no—
125C2×D24—31no—
126C2×D24—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129#895—32no—
130#895—32no—
131#895—32no—
132#895—62no—
133#894—62no—
134#894—62no—
135#894—64no—
136D3×C4⋊C4—32no—
137D3×C4⋊C4—32no—
138D3×C4⋊C4—62no—
139#882—62no—
140#874C2×D311yescharacteristic
141C4×D12—31no—
142C4×D12—31no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—61no—
146C4×D12—61no—
147C4×D12C2×D311yescharacteristic
148C3×#107—32no—
149C3×C4⋊C8—31no—
150C3×#102—32no—
151C3×#102—32no—
152C3×#102—32no—
153C3×C4×C8—31no—
154#832—31no—
155#832—32no—
156#821—32no—
157#821—31no—
158#821—31no—
159(C2×D3)⋊C8—32no—
160(C2×D3)⋊C8—32no—
161#818—31no—
162#809—31no—
163#809C2×D312yes—
164#809C2×D312yescomplemented
165#809C2×D312yescomplemented
166#807—31no—
167#807C2×D312yescomplemented
168C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
169C4×C3⋊C8C2×D311yescharacteristic, complemented
170C22×C3⋊D3—21no—
171C22×C3⋊D3C2×D412yes—
172C22×C3×D3—21no—
173C22×C3×D3—22no—
174C2×D32—44no—
175C2×D32—44no—
176C2×D32—82no—
177C32×Q8—42no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3C2×D412yes—
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)—21no—
186C4⋊(C3⋊D3)—44no—
187C4⋊(C3⋊D3)D814yescomplemented
188C4×C3⋊D3—22no—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—44no—
191C4×C3⋊D3—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—31no—
208#480—92no—
209#474—31no—
210#466—92no—
211#459—91no—
212#447—92no—
213C4×D8—91no—
214C8×D4—91no—
215C2×#102—92no—
216C23×D3—62no—
217C23×D3—62no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×D4—31no—
222C2×C3×D4—32no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C22×C3×C4—61no—
226C2×#67—62no—
227C2×#67—62no—
228C2×#67—62no—
229#239—124no—
230#239—124no—
231#239—128no—
232D3×D4—64no—
233D3×D4—64no—
234D3×D4—124no—
235D3×D4—122no—
236D3×D4—122no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—31no—
242C2×D12—31no—
243C2×D12—61no—
244C2×D12—61no—
245C2×D12—62no—
246C2×D12—62no—
247C2×D12—64no—
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—62no—
259C2×C4×D3—64no—
260C2×C4×D3—61no—
261C2×C4×D3—61no—
262C2×C3×C8—31no—
263C2×C3×C8—32no—
264C2×C3×C8—31no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C22×D312yes—
272C3×C22⋊C4—61no—
273C3×C42—21no—
274C3×C42C22×D311yescharacteristic
275C3×C42C22×D311yescharacteristic
276#217—62no—
277#213—62no—
278#213—122no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—32no—
281(C2×D3)⋊C4—32no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—64no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290C4⋊Dic3—31no—
291C4⋊Dic3—31no—
292C4⋊Dic3—31no—
293C4⋊Dic3—31no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296C4⋊Dic3C22×D311yescharacteristic
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299Dic3⋊C4—64no—
300C2×C3⋊C8C22×D311yescharacteristic
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D312yes—
303D24—62no—
304D24—122no—
305D3×C8—122no—
306D3×C8—122no—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—22no—
309C2×C3⋊D3—22no—
310C2×C3⋊D3—41no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
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—42no—
323C32×C4C2×D812yes—
324C32×C4C2×#4111yescharacteristic
325C32×C4H(5,𝔽2)11yescharacteristic
326C3⋊Dic3—22no—
327C3⋊Dic3—41no—
328C3×Dic3—41no—
329C2×#41—181no—
330C22×D4—92no—
331C22×D4—181no—
332C2×D8—91no—
333C2×D8—92no—
334C22×C8—92no—
335C4⋊Q8D3211yescharacteristic, complemented
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×D4—91no—
346C2×C4⋊C4—92no—
347#107—32no—
348#107—91no—
349C4⋊C8—31no—
350#102—32no—
351#102—32no—
352#102—32no—
353#102—91no—
354#102—91no—
355#102—92no—
356C22⋊C8—92no—
357C4×C8—31no—
358C23×C3—61no—
359C23×C3—62no—
360C22×D3—21no—
361C22×D3—22no—
362C22×D3—32no—
363C22×D3—32no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—61no—
367C22×D3—61no—
368C22×D3—124no—
369C22×D3—124no—
370C22×D3—124no—
371C22×D3—124no—
372C22×D3—242no—
373C22×D3—242no—
374C3×Q8—44no—
375C3×Q8—42no—
376C3×Q8—42no—
377C3×D4—32no—
378C3×D4—62no—
379C3×D4—61no—
380C3×D4—62no—
381C3×D4—122no—
382C3×D4—241no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—61no—
390C2×C3×C4—122no—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—124no—
398#67—124no—
399#67—124no—
400C2×Dic3—21no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407D12—22no—
408D12—21no—
409D12—22no—
410D12—34no—
411D12—34no—
412D12—42no—
413D12—64no—
414D12—61no—
415D12—61no—
416D12—61no—
417D12—61no—
418D12—81no—
419D12—121no—
420D12—121no—
421D12—124no—
422D12—124no—
423D12—128no—
424D12—124no—
425D12#23912yescomplemented
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—124no—
436C4×D3—128no—
437C4×D3—122no—
438C4×D3—122no—
439C3×C8—61no—
440C3×C8—61no—
441C3×C8—62no—
442C3⋊C8—21no—
443C3⋊C8—21no—
444C3⋊C8—22no—
445C2×C32#54611yescharacteristic
446C2×C32C22×D811yescharacteristic
447C2×C32#57711yescharacteristic
448C3⋊D3—24no—
449C3⋊D3—81no—
450C3×D3—42no—
451C3×D3—82no—
452C24—182no—
453#41—364no—
454C2×Q8—21no—
455C2×D4—31no—
456C2×D4—32no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—91no—
460C2×D4—91no—
461C2×D4—182no—
462C2×D4—182no—
463C2×D4—182no—
464C2×D4—184no—
465C2×D4—364no—
466C2×D4—362no—
467C22×C4—61no—
468C22×C4—92no—
469C22×C4—182no—
470C22×C4—181no—
471D8—182no—
472D8—362no—
473C2×C8—31no—
474C2×C8—31no—
475C2×C8—32no—
476C2×C8—362no—
477C4⋊C4—21no—
478C4⋊C4—31no—
479C4⋊C4—91no—
480C4⋊C4—91no—
481C4⋊C4—182no—
482C4⋊C4C2×D3212yes—
483C22⋊C4—61no—
484C22⋊C4—92no—
485C22⋊C4—182no—
486C22⋊C4—182no—
487C22⋊C4—181no—
488C42C2×D3211yescharacteristic
489C22×C3—21no—
490C22×C3—62no—
491C22×C3—121no—
492C22×C3—121no—
493C22×C3—122no—
494C22×C3—122no—
495C22×C3—122no—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C2×D3—22no—
499C2×D3—34no—
500C2×D3—34no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3—42no—
504C2×D3—42no—
505C2×D3—42no—
506C2×D3—64no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—62no—
510C2×D3—62no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
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—44no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—121no—
534C3×C4D3×D812yes—
535C3×C4D3×D812yes—
536C3×C4C2×#23911yescharacteristic
537C3×C4D3×#4111yescharacteristic
538C3×C4#100911yescharacteristic
539C3×C4#100911yescharacteristic
540Dic3—41no—
541Dic3—62no—
542Dic3—62no—
543Dic3—122no—
544Dic3—122no—
545Dic3—121no—
546Dic3—121no—
547C32#329411yescharacteristic, complemented, Sylow
548C23—61no—
549C23—62no—
550C23—92no—
551C23—181no—
552C23—364no—
553C23—364no—
554C23—722no—
555Q8—42no—
556D4—32no—
557D4—62no—
558D4—61no—
559D4—62no—
560D4—94no—
561D4—122no—
562D4—181no—
563D4—181no—
564D4—241no—
565D4—364no—
566D4—364no—
567D4—364no—
568C2×C4—22no—
569C2×C4—61no—
570C2×C4—92no—
571C2×C4—122no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—181no—
575C2×C4—364no—
576C2×C4—362no—
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—122no—
587C2×C3—242no—
588C2×C3#563011yescharacteristic
589C2×C3#567611yescharacteristic
590C2×C3C2×D3×D811yescharacteristic
591C2×C3C2×D3×D811yescharacteristic
592C2×C3#576211yescharacteristic
593C2×C3#577811yescharacteristic
594D3—42no—
595D3—64no—
596D3—64no—
597D3—82no—
598D3—124no—
599D3—242no—
600D3—241no—
601D3—241no—
602C22—62no—
603C22—94no—
604C22—121no—
605C22—121no—
606C22—122no—
607C22—122no—
608C22—122no—
609C22—182no—
610C22—182no—
611C22—361no—
612C22—361no—
613C22—361no—
614C22—728no—
615C22C2×#381111yescharacteristic
616C4—21no—
617C4—42no—
618C4—121no—
619C4—182no—
620C4—361no—
621C4#6392612yes—
622C4D3×#23911yescharacteristic
623C4#6432011yescharacteristic
624C3—21no—
625C3#8098011yescharacteristic, complemented
626C3#8157611yescharacteristic, complemented
627C2—122no—
628C2—184no—
629C2—242no—
630C2—721no—
631C2C2×#6392611yescharacteristic
632C2#1059532411yescharacteristic
633C2#1059543111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3294
LCSG ▷ C2×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. #10596197C2semidirect
2. #10594004C2semidirect
3. C3×#5088C2semidirect
4. C3×#5087C2semidirect
5. #10590598C2semidirect
6. #10590593C2semidirect
7. #10590510C2semidirect
8. #10590509C2semidirect
9. #10590355C2semidirect
10. C4×#3714C2semidirect
11. #10590327C2semidirect
17. C32×C4⋊Q8C22semidirect
19. #64104C22semidirect
21. C4⋊C4×C3⋊D3C22semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
30. C2×#3714C22semidirect
31. C2×#3710C22semidirect
33. C3×#809C22semidirect
34. C3×#809C22semidirect
35. C3×#807C22semidirect
36. C3×C4⋊(C3⋊C8)C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63575C22semidirect
39. #63564C22semidirect
41. #63563C22semidirect
42. #63557C22semidirect
50. #5088D3semidirect
51. #5087D3semidirect
112. C3×C4⋊Q8C2×D3semidirect
113. C3×C4⋊Q8C2×D3semidirect
164. #809C2×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
335. C4⋊Q8D32semidirect
425. D12#239semidirect
547. C32#3294semidirect
625. C3#80980semidirect
626. C3#81576semidirect

Maximal subgroups

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

subgroupindex
#105961972
#105940042
C3×#50882
C3×#50872
#105905982
#105905932
#105905102
#105905092
#105903552
C4×#37142
#105903272
#815763
#809803