Finite Group Databasebeta

← #11887057

Subgroups — #11887057

Order 1152.

1058 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5551C211yesmaximal, characteristic, complemented
2D122C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591515C212yesmaximal, complemented
6#10591449C212yesmaximal, complemented
7D3×#809C212yesmaximal, complemented
8#10590422C212yesmaximal, complemented
9C3⋊C8×D12C211yesmaximal, characteristic, complemented
10#10590281C211yesmaximal, characteristic, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#83525—31nomaximal
13#79608—31nomaximal
14C2×C3×#235—21no—
15C2×D3×D12—21no—
16C2×D3×D12C2212yes—
17C32×C4×D4C2211yescharacteristic, complemented
18C2×#3753C2212yescomplemented
19#64083C2211yescharacteristic
20C3×#938C2212yescomplemented
21C2×C3×#213C2211yescharacteristic
22C3×#924—21no—
23C3×D3×C4⋊C4C2212yescomplemented
24C3×#883—22no—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#869C2211yescharacteristic, complemented
28#63923—22no—
29#63909—21no—
30#63909C2212yes—
31C2×D3×C3⋊C8C2212yescomplemented
32#63636C2212yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
34C3×#832C2211yescharacteristic, complemented
35C3×#809C2211yescharacteristic
36C3×#807C2211yescharacteristic, complemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63576C2212yescomplemented
39#63564C2212yescomplemented
40#63564C2212yescomplemented
41#63562C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×#547—31no—
44#5551D311yescharacteristic, complemented
45D4×D12—31no—
46D4×D12—31no—
47C3×C4×D8—31no—
48#5156—32no—
49#5088—31no—
50#5087—31no—
51#5038—32no—
52#5036—32no—
53#5015—31no—
54#5015—31no—
55#5015—61no—
56C4×#213D311yescharacteristic, complemented
57D4×C3⋊C8—31no—
58#5007—31no—
59#4967—32no—
60C2×#809—32no—
61#4882—32no—
62#4775—32no—
63D3×#102—32no—
64#4694—31no—
65C8×D12—31no—
66C22×D32—22no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C3×#67—22no—
73C3×#235—44no—
74C2×C3×D12D411yescharacteristic
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3C2312yes—
79C2×C3×Dic6—21no—
80C2×#626—22no—
81C2×#626—22no—
82D3×D12—24no—
83D3×D12—42no—
84D3×D12—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3753—42no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—22no—
91C3×#213—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4D412yes—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101#3722—22no—
102D3×C3⋊C8—42no—
103#3294—91noSylow
104C2×C3×#41—61no—
105C2×D3×D4—32no—
106C2×D3×D4—61no—
107C2×#235—21no—
108C22×D12—32no—
109C22×D12—61no—
110C2×C3×D8—31no—
111C3×C4⋊Q8—31no—
112C3×#123—62no—
113C3×C22⋊Q8—61no—
114C3×#121—32no—
115C3×C4×D4—21no—
116C3×C4×D4—31no—
117C3×C4×D4—31no—
118C3×C4×D4C2×D311yescharacteristic, complemented
119C3×C4×D4C2×D311yescharacteristic, complemented
120C2×C3×C4⋊C4—32no—
121#938C2×D312yescomplemented
122C2×#213—32no—
123C2×#213—32no—
124C2×#213—62no—
125C2×#213C2×D311yescharacteristic
126#930—32no—
127#930—61no—
128#924—21no—
129C22×C3⋊C8—32no—
130C2×D3×C8—32no—
131#895—32no—
132#895—61no—
133D3×C4⋊C4C2×D312yescomplemented
134#883—22no—
135#882—62no—
136#882—62no—
137#874—31no—
138#874—31no—
139#874—61no—
140C4×D12C2×D311yescharacteristic
141C4×D12C2×D311yescharacteristic
142#869C2×D311yescharacteristic, complemented
143C3×#107—31no—
144C3×#102—31no—
145C3×#102—31no—
146C3×C4×C8—31no—
147#832—32no—
148#832C2×D311yescharacteristic, complemented
149#830—32no—
150#821—32no—
151#821—32no—
152(C2×D3)⋊C8—32no—
153#809—32no—
154#809—32no—
155#809—32no—
156#809—32no—
157#809—32no—
158#809—62no—
159#809C2×D311yescharacteristic
160#807—32no—
161#807—32no—
162#807C2×D311yescharacteristic, complemented
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—61no—
166C4×C3⋊C8C2×D311yescharacteristic, complemented
167C23×C32—21no—
168C22×C3⋊D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3C2×D412yes—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—82no—
174C32×D4—21no—
175C32×D4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C4⋊(C3⋊D3)—22no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—42no—
184C4⋊(C3⋊D3)—81no—
185C3×#67—44no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D412yes—
189C3×D12—21no—
190C3×D12D814yescomplemented
191C3×D12#4112yescomplemented
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×C4×D3—44no—
195C3×C4×D3—42no—
196C3×Dic6—42no—
197#626—44no—
198#626—44no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—21no—
202#547—31no—
203D42—91no—
204#486—91no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—91no—
209#447—92no—
210C4×D8—31no—
211C8×D4—91no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C3×#41—124no—
216C2×C3×Q8—61no—
217C2×C3×D4—21no—
218C2×C3×D4—31no—
219C2×C3×D4—31no—
220C2×C3×D4—62no—
221C2×C3×D4C22×D311yescharacteristic
222C2×C3×D4C22×D311yescharacteristic
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—32no—
226C22×C3×C4—41no—
227C22×C3×C4—62no—
228C22×C3×C4—61no—
229C2×#67—22no—
230C2×#67—62no—
231C2×#67—62no—
232D3×D4—64no—
233D3×D4—122no—
234D3×D4—124no—
235#235—44no—
236C2×D12—32no—
237C2×D12—32no—
238C2×D12—62no—
239C2×D12—64no—
240C2×D12—62no—
241C2×D12—62no—
242C2×D12—61no—
243C2×D12—61no—
244C2×D12—61no—
245C2×D12—61no—
246C2×D12—121no—
247C2×D12—121no—
248C2×D12—122no—
249C2×D12—124no—
250C2×D12#6711yescharacteristic
251C2×D12C22×D311yescharacteristic
252C2×C4×D3—22no—
253C2×C4×D3—21no—
254C2×C4×D3C22×D312yes—
255C2×Dic6—21no—
256C3×D8—62no—
257C2×C3×C8—31no—
258C2×C3×C8—31no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—62no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4C22×D311yescharacteristic
266C3×C4⋊C4C22×D311yescharacteristic
267C3×C22⋊C4—21no—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—32no—
270C3×C22⋊C4—41no—
271C3×C22⋊C4—62no—
272C3×C22⋊C4—61no—
273C3×C42—21no—
274C3×C42C22×D311yescharacteristic
275C3×C42C22×D311yescharacteristic
276#217—22no—
277#213—22no—
278#213—122no—
279#213—122no—
280#213—124no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4#6712yes—
285C4⋊Dic3—21no—
286C4⋊Dic3#6711yescharacteristic
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289Dic3⋊C4—22no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—122no—
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D311yescharacteristic
296D3×C8—122no—
297C22×C32—41no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32C22×D411yescharacteristic
301C2×C3⋊D3—42no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—41no—
308C2×C3×D3—41no—
309C2×C3×D3C2×D814yes—
310D32—88no—
311C32×C4—21no—
312C32×C4—41no—
313C32×C4C2×D812yes—
314C32×C4C2×#4111yescharacteristic
315C32×C4H(5,𝔽2)11yescharacteristic
316C3×Dic3—22no—
317C3×Dic3—41no—
318C3×Dic3—42no—
319C2×#41—61no—
320C22×D4—92no—
321C22×D4—181no—
322C2×D8—31no—
323C2×D8—92no—
324C22×C8—92no—
325C4⋊Q8—31no—
326#127—91no—
327#123—62no—
328C22⋊Q8—61no—
329#121—32no—
330#121—92no—
331#121—181no—
332#120—182no—
333C4×D4—31no—
334C4×D4—31no—
335C4×D4D3211yescharacteristic, complemented
336C2×C4⋊C4—32no—
337#107—31no—
338#107—92no—
339C4⋊C8—91no—
340#102—31no—
341#102—31no—
342#102—92no—
343#102—92no—
344#102—92no—
345#102—92no—
346C22⋊C8—92no—
347C4×C8—31no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—32no—
351C23×C3—41no—
352C23×C3—61no—
353C22×D3—21no—
354C22×D3—62no—
355C22×D3—62no—
356C22×D3—122no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—124no—
360C22×D3—124no—
361C22×D3—242no—
362C22×D3—242no—
363C22×D3C2×#6712yes—
364C3×Q8—122no—
365C3×D4—22no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—21no—
369C3×D4—21no—
370C3×D4—34no—
371C3×D4—32no—
372C3×D4—41no—
373C3×D4—61no—
374C3×D4—124no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—32no—
381C2×C3×C4—41no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—61no—
388C2×C3×C4—82no—
389C2×C3×C4—124no—
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—124no—
399#67—124no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3C2×#6712yes—
403D12—21no—
404D12—62no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—122no—
409D12—122no—
410D12—124no—
411D12—124no—
412D12—122no—
413D12—122no—
414D12—242no—
415D12—241no—
416D12—241no—
417D12—242no—
418D12#21314yescomplemented
419D12#23512yescomplemented
420C4×D3—22no—
421C4×D3—22no—
422C4×D3—44no—
423C4×D3—42no—
424Dic6—42no—
425C3×C8—61no—
426C3×C8—61no—
427C3⋊C8—21no—
428C3⋊C8—21no—
429C3⋊C8—62no—
430C3⋊C8—62no—
431C3⋊C8—122no—
432C2×C32—81no—
433C2×C32#54611yescharacteristic
434C2×C32C22×D811yescharacteristic
435C2×C32#57711yescharacteristic
436C3⋊D3—82no—
437C3×D3—24no—
438C3×D3—42no—
439C24—182no—
440#41—124no—
441C2×Q8—61no—
442C2×D4—31no—
443C2×D4—31no—
444C2×D4—62no—
445C2×D4—92no—
446C2×D4—182no—
447C2×D4—184no—
448C2×D4—182no—
449C2×D4—181no—
450C2×D4—181no—
451C2×D4—362no—
452C2×D4—364no—
453C2×D4C2×D3211yescharacteristic
454C22×C4—21no—
455C22×C4—32no—
456C22×C4—62no—
457C22×C4—61no—
458D8—62no—
459D8—362no—
460C2×C8—31no—
461C2×C8—31no—
462C2×C8—92no—
463C2×C8—362no—
464C4⋊C4—31no—
465C4⋊C4—31no—
466C4⋊C4—32no—
467C4⋊C4—62no—
468C4⋊C4—61no—
469C4⋊C4C2×D3211yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—32no—
472C22⋊C4—62no—
473C22⋊C4—61no—
474C22⋊C4—182no—
475C42C2×D3211yescharacteristic
476C22×C3—21no—
477C22×C3—34no—
478C22×C3—42no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—62no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3C2×D3×D411yescharacteristic
493C22×C3C22×#6711yescharacteristic
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—22no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—242no—
506C2×D3—242no—
507C2×D3—242no—
508C2×D3—248no—
509C2×D3—248no—
510C2×D3C2×#21314yes—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—22no—
516C3×C4—41no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—62no—
520C3×C4—81no—
521C3×C4—122no—
522C3×C4—121no—
523C3×C4D3×D812yes—
524C3×C4C2×#21312yes—
525C3×C4C2×#23511yescharacteristic
526C3×C4D3×#4111yescharacteristic
527C3×C4#100911yescharacteristic
528C3×C4#100911yescharacteristic
529Dic3—22no—
530Dic3—41no—
531Dic3—42no—
532C32#329411yescharacteristic, complemented, Sylow
533C23—21no—
534C23—32no—
535C23—61no—
536C23—182no—
537C23—364no—
538C23—364no—
539C23—722no—
540Q8—122no—
541D4—21no—
542D4—21no—
543D4—32no—
544D4—34no—
545D4—61no—
546D4—124no—
547D4—182no—
548D4—182no—
549D4—364no—
550D4—364no—
551D4—362no—
552D4—721no—
553C2×C4—21no—
554C2×C4—32no—
555C2×C4—42no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—124no—
561C2×C4—122no—
562C2×C4D3×#6711yescharacteristic
563C2×C4D3×#6711yescharacteristic
564C2×C4C22×D3211yescharacteristic
565C8—61no—
566C8—61no—
567C8—182no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—64no—
572C2×C3—82no—
573C2×C3—81no—
574C2×C3—81no—
575C2×C3—122no—
576C2×C3#555011yescharacteristic
577C2×C3C2×D3×D811yescharacteristic
578C2×C3#577011yescharacteristic
579C2×C3C22×#21311yescharacteristic
580C2×C3#582911yescharacteristic
581C2×C3#583711yescharacteristic
582D3—24no—
583D3—42no—
584D3—242no—
585D3—242no—
586D3—482no—
587C22—34no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—62no—
592C22—62no—
593C22—62no—
594C22—121no—
595C22—121no—
596C22—362no—
597C22—362no—
598C22—362no—
599C22—728no—
600C22C2×D3×#6711yescharacteristic
601C4—21no—
602C4—41no—
603C4—62no—
604C4—122no—
605C4—121no—
606C4D3×#21312yes—
607C4D3×#23511yescharacteristic
608C4#6430811yescharacteristic
609C3—21no—
610C3#7960811yescharacteristic, complemented
611C3#8352511yescharacteristic, complemented
612C2—64no—
613C2—81no—
614C2—122no—
615C2—722no—
616C2#1059506711yescharacteristic
617C2C2×D3×#21311yescharacteristic
618C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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. C3×#5551C2semidirect
2. D122C2semidirect
3. #10592714C2semidirect
4. C3×C4×#213C2semidirect
5. #10591515C2semidirect
6. #10591449C2semidirect
7. D3×#809C2semidirect
8. #10590422C2semidirect
9. C3⋊C8×D12C2semidirect
10. #10590281C2semidirect
11. #10590269C2semidirect
17. C32×C4×D4C22semidirect
18. C2×#3753C22semidirect
20. C3×#938C22semidirect
23. C3×D3×C4⋊C4C22semidirect
27. C3×#869C22semidirect
31. C2×D3×C3⋊C8C22semidirect
32. #63636C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. C3×#832C22semidirect
36. C3×#807C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63576C22semidirect
39. #63564C22semidirect
40. #63564C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
44. #5551D3semidirect
56. C4×#213D3semidirect
118. C3×C4×D4C2×D3semidirect
119. C3×C4×D4C2×D3semidirect
121. #938C2×D3semidirect
133. D3×C4⋊C4C2×D3semidirect
142. #869C2×D3semidirect
148. #832C2×D3semidirect
162. #807C2×D3semidirect
166. C4×C3⋊C8C2×D3semidirect
190. C3×D12D8semidirect
191. C3×D12#41semidirect
335. C4×D4D32semidirect
418. D12#213semidirect
419. D12#235semidirect
532. C32#3294semidirect
610. C3#79608semidirect
611. C3#83525semidirect

Maximal subgroups

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

subgroupindex
C3×#55512
D1222
#105927142
C3×C4×#2132
#105915152
#105914492
D3×#8092
#105904222
C3⋊C8×D122
#105902812
#105902692
#835253
#796083