Finite Group Databasebeta

← #11887061

Subgroups — #11887061

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5717C211yesmaximal, characteristic, complemented
2#10593895C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591498C212yesmaximal, complemented
6#10591447C212yesmaximal, complemented
7#10591413C212yesmaximal, complemented
8D3×#832C212yesmaximal, complemented
9C4×#3713C211yesmaximal, characteristic, complemented
10#10590329C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#83482—31nomaximal
13#80352—31nomaximal
14C2×C3×D3×D4—21no—
15C2×C3×D3×D4C2212yes—
16C2×#3795—21no—
17C32×#127C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C3×#938—21no—
20C3×#938C2212yes—
21C3×#937—22no—
22C2×C3×#213C2212yescomplemented
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic, complemented
26#63908C2212yescomplemented
27#63891—22no—
28D3×C4⋊Dic3C2212yescomplemented
29#63857—21no—
30C2×#3713C2211yescharacteristic
31C2×D3×C3⋊C8C2212yescomplemented
32#63659C2212yescomplemented
33#63659C2212yescomplemented
34C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
35C3×#832C2212yescomplemented
36C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
37#63576C2211yescharacteristic, complemented
38#63575C2212yescomplemented
39#63563C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×D42—31no—
44#5717D311yescharacteristic, complemented
45#5555—31no—
46#5551—31no—
47C3×#459—31no—
48#5217—32no—
49C2×#832—32no—
50#5157—32no—
51#5156—32no—
52#5072D311yescharacteristic, complemented
53#5070—31no—
54#5070—31no—
55#5070—61no—
56#5038—32no—
57#5033—32no—
58C4×#213—31no—
59C4×#213—31no—
60D4×C3⋊C8—31no—
61#5007—31no—
62#4846—31no—
63#4834—31no—
64#4774—32no—
65D3×#102—32no—
66C23×C3×D3—22no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C2×#634—21no—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C3×D3×D4—24no—
74C3×D3×D4—42no—
75C3×D3×D4—44no—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3C2312yes—
82C2×#625—22no—
83C2×D3×Dic3—22no—
84#3795—44no—
85C32×C42C2311yescharacteristic
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C3×#217—22no—
91C3×#213—42no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4D412yes—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99Dic3⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101#3713—22no—
102D3×C3⋊C8—42no—
103#3294—91noSylow
104C22×C3×D4—32no—
105C22×C3×D4—61no—
106C2×#237—61no—
107C2×D3×D4—21no—
108C2×D3×D4C2×D312yes—
109C2×#235—61no—
110C2×C3×D8—32no—
111C3×#127—21no—
112C3×#127C2×D311yescharacteristic
113C3×#127C2×D311yescharacteristic
114C3×#121—32no—
115C3×#121—61no—
116C3×#120—62no—
117C3×C4×D4—31no—
118C3×C4×D4—31no—
119C3×C4×D4—31no—
120#938—21no—
121#938—32no—
122#938C2×D312yes—
123#937—22no—
124C2×#213—31no—
125C2×#213—31no—
126C2×#213C2×D312yescomplemented
127#930—32no—
128C2×C4⋊Dic3—32no—
129#924—61no—
130C22×C3⋊C8—32no—
131C2×D3×C8—32no—
132#897—61no—
133D3×C4⋊C4—32no—
134#886—62no—
135#883—62no—
136C4×D12C2×D311yescharacteristic
137C4×D12C2×D311yescharacteristic
138C4×D12C2×D311yescharacteristic, complemented
139#869—31no—
140#869—31no—
141#869—61no—
142C3×C4⋊C8—31no—
143C3×#102—32no—
144#832—32no—
145#832—32no—
146#832—32no—
147#832—32no—
148#832—31no—
149#832—31no—
150#832—32no—
151#832—62no—
152#832—62no—
153#832C2×D312yescomplemented
154#830—32no—
155#821—32no—
156(C2×D3)⋊C8—32no—
157#818—32no—
158#809—31no—
159#809—31no—
160#807—31no—
161#807—31no—
162#807—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
164C4×C3⋊C8—31no—
165C4×C3⋊C8—31no—
166C4×C3⋊C8—61no—
167C23×C32—22no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—44no—
171C22×C3×D3—44no—
172C22×C3×D3—82no—
173C22×C3×D3C2×D412yes—
174C32×D4—22no—
175C32×D4—22no—
176C32×D4—42no—
177C32×D4—81no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—22no—
182#634—42no—
183C3×#67—44no—
184C3×#67—44no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—21no—
189C3×D12—21no—
190C3×D12—21no—
191C3×D12D814yescomplemented
192C3×D12#4112yescomplemented
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×C4×D3—42no—
196C3×C4×D3—42no—
197#625—44no—
198D3×Dic3—44no—
199C3⋊(C3⋊C8)—21no—
200C3⋊(C3⋊C8)—21no—
201C3×C3⋊C8—22no—
202#547—91no—
203D42—31no—
204#486—91no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—31no—
209#447—92no—
210C4×D8—91no—
211C8×D4—91no—
212C2×#102—92no—
213C24×C3—62no—
214C23×D3—22no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—22no—
220C2×C3×D4—31no—
221C2×C3×D4—31no—
222C2×C3×D4—31no—
223C2×C3×D4—41no—
224C2×C3×D4—41no—
225C2×C3×D4—62no—
226C2×C3×D4—64no—
227C2×C3×D4—62no—
228C2×C3×D4—122no—
229C2×C3×D4—124no—
230C2×C3×D4C22×D312yes—
231C2×C3×D4C22×D312yes—
232C22×C3×C4—32no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C2×#67—22no—
236C2×#67—22no—
237C2×#67—62no—
238C2×#67—62no—
239C22×Dic3—62no—
240#237—124no—
241D3×D4—24no—
242D3×D4—42no—
243D3×D4—44no—
244#235—124no—
245C2×D12#6711yescharacteristic
246C2×D12C22×D311yescharacteristic
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—62no—
251C2×C4×D3C22×D312yes—
252C2×Dic6—61no—
253C2×Dic6—61no—
254C2×Dic6—121no—
255C3×D8—122no—
256C2×C3×C8—32no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—31no—
260C3×C22⋊C4—32no—
261C3×C22⋊C4—62no—
262C3×C22⋊C4—61no—
263C3×C22⋊C4—61no—
264C3×C42—21no—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D311yescharacteristic
267#217—22no—
268#217—62no—
269#213—42no—
270#213—62no—
271#213—62no—
272(C2×D3)⋊C4—21no—
273(C2×D3)⋊C4—21no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4#6712yes—
276C4⋊Dic3—32no—
277C4⋊Dic3—32no—
278C4⋊Dic3—62no—
279C4⋊Dic3—62no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—121no—
283C4⋊Dic3#6711yescharacteristic
284C4⋊Dic3C22×D311yescharacteristic
285C4⋊Dic3C22×D311yescharacteristic
286Dic3⋊C4—62no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—122no—
294C2×C3⋊C8C22×D312yes—
295D3×C8—122no—
296C22×C32—42no—
297C22×C32—42no—
298C22×C32—42no—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—22no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C2×C3×D3—41no—
307C2×C3×D3—41no—
308C2×C3×D3—88no—
309C2×C3×D3C2×D814yes—
310C32×C4—21no—
311C32×C4C2×D812yes—
312C32×C4C2×#4111yescharacteristic
313C32×C4H(5,𝔽2)11yescharacteristic
314C3⋊Dic3—42no—
315C3×Dic3—22no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C2×#41—181no—
319C22×D4—32no—
320C22×D4—61no—
321C2×D8—32no—
322C2×D8—91no—
323C22×C8—92no—
324C4⋊Q8—91no—
325#127D3211yescharacteristic
326#123—182no—
327C22⋊Q8—181no—
328#121—32no—
329#121—61no—
330#121—92no—
331#120—62no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4—31no—
335C2×C4⋊C4—92no—
336#107—91no—
337#107—92no—
338C4⋊C8—31no—
339#102—32no—
340#102—91no—
341#102—91no—
342#102—92no—
343#102—92no—
344#102—92no—
345C22⋊C8—92no—
346C4×C8—91no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—32no—
350C23×C3—42no—
351C23×C3—61no—
352C23×C3—61no—
353C23×C3—124no—
354C23×C3—124no—
355C23×C3—242no—
356C22×D3—21no—
357C22×D3—21no—
358C22×D3—44no—
359C22×D3—44no—
360C22×D3—82no—
361C22×D3C2×#6712yes—
362C3×D4—22no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—22no—
366C3×D4—34no—
367C3×D4—32no—
368C3×D4—42no—
369C3×D4—42no—
370C3×D4—42no—
371C3×D4—42no—
372C3×D4—61no—
373C3×D4—61no—
374C3×D4—61no—
375C3×D4—82no—
376C3×D4—81no—
377C3×D4—81no—
378C3×D4—82no—
379C3×D4—124no—
380C3×D4—124no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—32no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—122no—
390C2×C3×C4—122no—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—44no—
398#67—44no—
399#67—124no—
400#67—124no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—122no—
406C2×Dic3—124no—
407C2×Dic3C2×#6712yes—
408D12—21no—
409D12—21no—
410D12—21no—
411D12#21314yescomplemented
412D12#23712yescomplemented
413C4×D3—22no—
414C4×D3—22no—
415C4×D3—42no—
416C4×D3—42no—
417C4×D3—124no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—61no—
424C3⋊C8—61no—
425C3⋊C8—61no—
426C3⋊C8—61no—
427C3⋊C8—121no—
428C3⋊C8—121no—
429C2×C32—82no—
430C2×C32#54611yescharacteristic
431C2×C32C22×D811yescharacteristic
432C2×C32#57711yescharacteristic
433C3×D3—24no—
434C3×D3—42no—
435C3×D3—81no—
436C24—62no—
437#41—364no—
438C2×Q8—181no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—31no—
442C2×D4—31no—
443C2×D4—31no—
444C2×D4—62no—
445C2×D4—64no—
446C2×D4—62no—
447C2×D4—122no—
448C2×D4—124no—
449C2×D4—182no—
450C2×D4C2×D3212yes—
451C22×C4—32no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—182no—
455D8—122no—
456D8—182no—
457C2×C8—32no—
458C2×C8—91no—
459C2×C8—91no—
460C2×C8—362no—
461C4⋊C4—31no—
462C4⋊C4—31no—
463C4⋊C4—31no—
464C4⋊C4—92no—
465C4⋊C4—182no—
466C4⋊C4—181no—
467C22⋊C4—32no—
468C22⋊C4—62no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—182no—
472C42C2×D3211yescharacteristic
473C22×C3—21no—
474C22×C3—34no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—62no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—82no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3—248no—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—22no—
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3—88no—
504C2×D3C2×#21314yes—
505C3×C4—22no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—62no—
512C3×C4—121no—
513C3×C4—121no—
514C3×C4D3×D812yes—
515C3×C4C2×#21312yes—
516C3×C4C2×#23711yescharacteristic
517C3×C4#100411yescharacteristic
518C3×C4#100411yescharacteristic
519C3×C4D3×#4111yescharacteristic
520Dic3—22no—
521Dic3—41no—
522Dic3—41no—
523Dic3—122no—
524Dic3—122no—
525Dic3—242no—
526C32#329411yescharacteristic, complemented, Sylow
527C23—22no—
528C23—32no—
529C23—61no—
530C23—61no—
531C23—124no—
532C23—124no—
533C23—242no—
534Q8—362no—
535D4—22no—
536D4—22no—
537D4—32no—
538D4—34no—
539D4—42no—
540D4—61no—
541D4—61no—
542D4—61no—
543D4—81no—
544D4—124no—
545D4—124no—
546D4—364no—
547C2×C4—32no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—122no—
553C2×C4—122no—
554C2×C4—182no—
555C2×C4—364no—
556C2×C4D3×#6711yescharacteristic
557C2×C4D3×#6711yescharacteristic
558C2×C4C22×D3211yescharacteristic
559C8—62no—
560C8—181no—
561C8—181no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—64no—
566C2×C3—82no—
567C2×C3—82no—
568C2×C3—122no—
569C2×C3—162no—
570C2×C3—241no—
571C2×C3#561211yescharacteristic
572C2×C3C2×D3×D811yescharacteristic
573C2×C3#577511yescharacteristic
574C2×C3C22×#21311yescharacteristic
575C2×C3#580611yescharacteristic
576C2×C3#583611yescharacteristic
577D3—24no—
578D3—42no—
579D3—81no—
580C22—34no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—62no—
585C22—62no—
586C22—62no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—121no—
591C22—121no—
592C22—248no—
593C22C2×D3×#6711yescharacteristic
594C4—21no—
595C4—62no—
596C4—121no—
597C4—121no—
598C4—362no—
599C4D3×#21312yes—
600C4D3×#23711yescharacteristic
601C4#6431311yescharacteristic
602C3—21no—
603C3#8035211yescharacteristic, complemented
604C3#8348211yescharacteristic, complemented
605C2—64no—
606C2—82no—
607C2—122no—
608C2—241no—
609C2C2×D3×#21311yescharacteristic
610C2#1059510611yescharacteristic
611C2#1059522811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5717C2semidirect
2. #10593895C2semidirect
3. #10592769C2semidirect
4. C3×#5072C2semidirect
5. #10591498C2semidirect
6. #10591447C2semidirect
7. #10591413C2semidirect
8. D3×#832C2semidirect
9. C4×#3713C2semidirect
10. #10590329C2semidirect
11. #10590272C2semidirect
18. #64078C22semidirect
22. C2×C3×#213C22semidirect
25. C3×C4×D12C22semidirect
26. #63908C22semidirect
28. D3×C4⋊Dic3C22semidirect
31. C2×D3×C3⋊C8C22semidirect
32. #63659C22semidirect
33. #63659C22semidirect
34. C4×C3⋊(C3⋊C8)C22semidirect
35. C3×#832C22semidirect
36. C3×C4⋊(C3⋊C8)C22semidirect
37. #63576C22semidirect
38. #63575C22semidirect
41. #63562C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
44. #5717D3semidirect
52. #5072D3semidirect
126. C2×#213C2×D3semidirect
138. C4×D12C2×D3semidirect
153. #832C2×D3semidirect
163. C4⋊(C3⋊C8)C2×D3semidirect
191. C3×D12D8semidirect
192. C3×D12#41semidirect
411. D12#213semidirect
412. D12#237semidirect
526. C32#3294semidirect
603. C3#80352semidirect
604. C3#83482semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
#105938952
#105927692
C3×#50722
#105914982
#105914472
#105914132
D3×#8322
C4×#37132
#105903292
#105902722
#834823
#803523