Finite Group Databasebeta

← #11887062

Subgroups — #11887062

Order 1152.

1202 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596188C211yesmaximal, characteristic, complemented
2#10593869C211yesmaximal, characteristic, complemented
3C3×#5072C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591456C212yesmaximal, complemented
6#10591455C212yesmaximal, complemented
7#10591417C212yesmaximal, complemented
8#10591416C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic, complemented
10#10590327C211yesmaximal, characteristic, complemented
11#10590313C211yesmaximal, characteristic, complemented
12#81576—31nomaximal
13#80352—31nomaximal
14C2×D4×C3⋊D3—21no—
15C2×D4×C3⋊D3C2212yes—
16C2×#3799—21no—
17C32×#127C2211yescharacteristic
18#64147—21no—
19#64147C2212yes—
20#64146—22no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×#213C2212yescomplemented
24C3×C4×D12C2211yescharacteristic, complemented
25C3×#869C2211yescharacteristic, complemented
26#63916C2212yescomplemented
27#63900C2212yescomplemented
28#63856—21no—
29#63854—22no—
30C2×#3714C2211yescharacteristic
31C2×#3710C2212yescomplemented
32C3×#832C2212yescomplemented
33C3×#832C2212yescomplemented
34C3×#832C2212yescomplemented
35C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37#63575C2212yescomplemented
38#63575C2211yescharacteristic, complemented
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic, complemented
42#63557C2212yescomplemented
43#5726—31no—
44#5717—31no—
45#5717—31no—
46#5717—61no—
47#5551—31no—
48C3×#486—31no—
49C3×#459—31no—
50#5157—32no—
51#5156—32no—
52#5087—31no—
53#5072D311yescharacteristic, complemented
54#5070D311yescharacteristic, complemented
55C4×#213—31no—
56#4846—31no—
57#4834—31no—
58#4775—32no—
59#4774—32no—
60#4774—32no—
61#4773—32no—
62D3×#102—32no—
63D3×#102—32no—
64C4×D24—31no—
65C8×D12—31no—
66C23×C3⋊D3—22no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C2×#638—22no—
71C2×#638—22no—
72D4×C3⋊D3—24no—
73D4×C3⋊D3—42no—
74D4×C3⋊D3—44no—
75C2×C4⋊(C3⋊D3)D411yescharacteristic
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3C2312yes—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6—21no—
82C2×#626—22no—
83C2×#624—22no—
84#3799—44no—
85C32×C42C2311yescharacteristic
86#3757—22no—
87#3752—21no—
88#3752D412yes—
89C4⋊(C3⋊Dic3)D411yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C3×#213—42no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2312yes—
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99#3724—22no—
100(C2×D3)⋊Dic3—22no—
101#3714—22no—
102#3710—42no—
103#3294—91noSylow
104C2×#239—61no—
105C2×D3×D4—32no—
106C2×D3×D4—32no—
107C2×D3×D4—62no—
108C2×D3×D4—61no—
109C2×D3×D4—61no—
110C2×D3×D4—62no—
111C2×#235—61no—
112C2×C3×D8—32no—
113C3×C4⋊Q8—31no—
114C3×#127—21no—
115C3×#127C2×D311yescharacteristic
116C3×#127C2×D311yescharacteristic
117C3×C4×D4—31no—
118#946—61no—
119#938—32no—
120#938—32no—
121#938—32no—
122#938—62no—
123#938—61no—
124#938—61no—
125#938—62no—
126#937—62no—
127#937—62no—
128#937—64no—
129C2×#213—31no—
130C2×#213C2×D312yescomplemented
131#924—61no—
132C2×D24—31no—
133C2×D3×C8—32no—
134C2×D3×C8—32no—
135#895—32no—
136#894—62no—
137D3×C4⋊C4—32no—
138D3×C4⋊C4—32no—
139#883—62no—
140C4×D12—31no—
141C4×D12—31no—
142C4×D12—31no—
143C4×D12—31no—
144C4×D12—61no—
145C4×D12—61no—
146C4×D12C2×D311yescharacteristic, complemented
147#869C2×D311yescharacteristic, complemented
148C3×C4⋊C8—31no—
149C3×#102—32no—
150C3×#102—32no—
151C3×#102—32no—
152C3×C4×C8—31no—
153#832—31no—
154#832C2×D312yescomplemented
155#832C2×D312yescomplemented
156#832C2×D312yescomplemented
157#821—31no—
158#821—32no—
159#821—31no—
160(C2×D3)⋊C8—32no—
161(C2×D3)⋊C8—32no—
162#818—32no—
163#818—31no—
164#809—31no—
165#809—32no—
166#807—31no—
167#807—32no—
168C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
169C4×C3⋊C8C2×D311yescharacteristic, complemented
170C23×C32—22no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—44no—
173C22×C3⋊D3—44no—
174C22×C3⋊D3—82no—
175C22×C3⋊D3C2×D412yes—
176C22×C3×D3—21no—
177C32×D4—22no—
178C32×D4—22no—
179C32×D4—42no—
180C32×D4—81no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—44no—
185#638—44no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3C2×D412yes—
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)D814yescomplemented
190C4⋊(C3⋊D3)#4112yescomplemented
191C4×C3⋊D3—22no—
192C4×C3⋊D3—22no—
193C4×C3⋊D3—42no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C3×D12—21no—
197C3×D12—21no—
198C3×C4×D3—42no—
199C3×Dic6—42no—
200#626—44no—
201#624—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—91no—
210#466—92no—
211#459—31no—
212#447—92no—
213C4×D8—91no—
214C8×D4—91no—
215C2×#102—92no—
216C23×D3—62no—
217C23×D3—62no—
218C23×D3—64no—
219C2×C3×Q8—61no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—31no—
228C2×C3×D4C22×D312yes—
229C2×C3×D4C22×D312yes—
230C22×C3×C4—61no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—62no—
235C2×#67—62no—
236C2×#67—64no—
237C2×#67—64no—
238#239—124no—
239D3×D4—64no—
240D3×D4—64no—
241D3×D4—124no—
242D3×D4—122no—
243D3×D4—122no—
244D3×D4—124no—
245D3×D4—124no—
246D3×D4—124no—
247D3×D4—128no—
248#235—124no—
249C2×D12—31no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—31no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—62no—
256C2×D12C22×D311yescharacteristic
257C2×C4×D3—21no—
258C2×C4×D3—32no—
259C2×C4×D3—32no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×Dic6—21no—
267C3×D8—122no—
268C2×C3×C8—31no—
269C2×C3×C8—32no—
270C2×C3×C8—31no—
271C3×C4⋊C4—31no—
272C3×C4⋊C4—32no—
273C3×C4⋊C4—61no—
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—42no—
283#213—62no—
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—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292C4⋊Dic3—21no—
293C4⋊Dic3—31no—
294C4⋊Dic3—31no—
295C4⋊Dic3—31no—
296C4⋊Dic3—31no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3C22×D312yes—
300C4⋊Dic3C22×D311yescharacteristic
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D311yescharacteristic
305C2×C3⋊C8C22×D312yes—
306D24—62no—
307D3×C8—122no—
308D3×C8—122no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—88no—
319C2×C3⋊D3C2×D814yes—
320C2×C3×D3—41no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C32×C4—21no—
324C32×C4C2×D812yes—
325C32×C4C2×#4111yescharacteristic
326C32×C4H(5,𝔽2)11yescharacteristic
327C3⋊Dic3—22no—
328C3⋊Dic3—41no—
329C3×Dic3—41no—
330C3×Dic3—42no—
331C2×#41—181no—
332C22×D4—92no—
333C22×D4—181no—
334C2×D8—32no—
335C2×D8—91no—
336C22×C8—92no—
337C4⋊Q8—31no—
338#127D3211yescharacteristic
339#123—182no—
340C22⋊Q8—181no—
341#121—92no—
342#121—92no—
343#121—181no—
344#120—182no—
345C4×D4—31no—
346C4×D4—91no—
347C4×D4—91no—
348C2×C4⋊C4—92no—
349#107—91no—
350#107—92no—
351C4⋊C8—31no—
352#102—32no—
353#102—32no—
354#102—32no—
355#102—91no—
356#102—92no—
357#102—91no—
358C22⋊C8—92no—
359C4×C8—31no—
360C23×C3—24no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—61no—
364C22×D3—21no—
365C22×D3—32no—
366C22×D3—32no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—61no—
370C22×D3—61no—
371C22×D3—124no—
372C22×D3—124no—
373C22×D3—124no—
374C22×D3—124no—
375C22×D3—128no—
376C22×D3—128no—
377C22×D3—242no—
378C22×D3—242no—
379C22×D3—244no—
380C3×Q8—122no—
381C3×D4—22no—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—42no—
386C3×D4—42no—
387C3×D4—44no—
388C3×D4—42no—
389C3×D4—42no—
390C3×D4—61no—
391C3×D4—61no—
392C3×D4—81no—
393C3×D4—81no—
394C3×D4—82no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—61no—
399C2×C3×C4—62no—
400C2×C3×C4—122no—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—124no—
408#67—124no—
409#67—124no—
410#67—124no—
411#67—124no—
412#67—128no—
413#67—128no—
414C2×Dic3—21no—
415C2×Dic3—22no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422D12—21no—
423D12—21no—
424D12—34no—
425D12—34no—
426D12—32no—
427D12—32no—
428D12—64no—
429D12—62no—
430D12—62no—
431D12—61no—
432D12—61no—
433D12—124no—
434C4×D3—42no—
435C4×D3—62no—
436C4×D3—62no—
437C4×D3—62no—
438C4×D3—62no—
439C4×D3—122no—
440C4×D3—122no—
441C4×D3—124no—
442C4×D3—124no—
443C4×D3—124no—
444C4×D3—122no—
445C4×D3—122no—
446Dic6—42no—
447C3×C8—61no—
448C3×C8—61no—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—21no—
452C3⋊C8—21no—
453C2×C32—82no—
454C2×C32#54611yescharacteristic
455C2×C32C22×D811yescharacteristic
456C2×C32#57711yescharacteristic
457C3⋊D3—24no—
458C3⋊D3—42no—
459C3×D3—81no—
460C24—182no—
461#41—364no—
462C2×Q8—61no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—31no—
466C2×D4—91no—
467C2×D4—91no—
468C2×D4—182no—
469C2×D4—182no—
470C2×D4—184no—
471C2×D4—182no—
472C2×D4—362no—
473C2×D4—364no—
474C2×D4C2×D3212yes—
475C22×C4—61no—
476C22×C4—92no—
477C22×C4—182no—
478C22×C4—181no—
479D8—122no—
480D8—182no—
481C2×C8—31no—
482C2×C8—31no—
483C2×C8—32no—
484C2×C8—362no—
485C4⋊C4—31no—
486C4⋊C4—32no—
487C4⋊C4—61no—
488C4⋊C4—91no—
489C4⋊C4—91no—
490C4⋊C4—182no—
491C22⋊C4—61no—
492C22⋊C4—92no—
493C22⋊C4—182no—
494C22⋊C4—182no—
495C22⋊C4—181no—
496C42C2×D3211yescharacteristic
497C22×C3—21no—
498C22×C3—44no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3C2×D3×D411yescharacteristic
511C22×C3C2×D3×D411yescharacteristic
512C2×D3—34no—
513C2×D3—34no—
514C2×D3—41no—
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—64no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—64no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—121no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—248no—
534C2×D3—248no—
535C2×D3—2416no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—41no—
542C3×C4—121no—
543C3×C4—122no—
544C3×C4D3×D812yes—
545C3×C4D3×D812yes—
546C3×C4#100411yescharacteristic
547C3×C4D3×#4111yescharacteristic
548C3×C4D3×#4111yescharacteristic
549C3×C4#100911yescharacteristic
550Dic3—42no—
551Dic3—41no—
552Dic3—62no—
553Dic3—62no—
554Dic3—122no—
555Dic3—122no—
556Dic3—121no—
557Dic3—121no—
558C32#329411yescharacteristic, complemented, Sylow
559C23—22no—
560C23—61no—
561C23—92no—
562C23—181no—
563C23—364no—
564C23—364no—
565C23—722no—
566Q8—122no—
567D4—22no—
568D4—22no—
569D4—42no—
570D4—61no—
571D4—61no—
572D4—81no—
573D4—92no—
574D4—94no—
575D4—181no—
576D4—364no—
577D4—364no—
578D4—364no—
579C2×C4—61no—
580C2×C4—62no—
581C2×C4—92no—
582C2×C4—122no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—181no—
586C2×C4—364no—
587C2×C4—362no—
588C2×C4#381111yescharacteristic
589C2×C4#381111yescharacteristic
590C2×C4C22×D3211yescharacteristic
591C8—61no—
592C8—61no—
593C8—62no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—84no—
598C2×C3—82no—
599C2×C3—82no—
600C2×C3—241no—
601C2×C3#561211yescharacteristic
602C2×C3#567611yescharacteristic
603C2×C3C2×D3×D811yescharacteristic
604C2×C3C2×D3×D811yescharacteristic
605C2×C3#576211yescharacteristic
606C2×C3#577511yescharacteristic
607D3—64no—
608D3—64no—
609D3—81no—
610D3—124no—
611D3—124no—
612D3—122no—
613D3—122no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—94no—
618C22—121no—
619C22—121no—
620C22—121no—
621C22—182no—
622C22—182no—
623C22—182no—
624C22—361no—
625C22—361no—
626C22—728no—
627C22C2×#381111yescharacteristic
628C4—21no—
629C4—121no—
630C4—122no—
631C4—182no—
632C4—361no—
633C4#6392612yes—
634C4#6431211yescharacteristic
635C4#6431411yescharacteristic
636C3—21no—
637C3#8035211yescharacteristic, complemented
638C3#8157611yescharacteristic, complemented
639C2—82no—
640C2—184no—
641C2—241no—
642C2—362no—
643C2C2×#6392611yescharacteristic
644C2#1059511511yescharacteristic
645C2#1059524311yescharacteristic
subgroupG/H
centerC22C2×#3811
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. #10596188C2semidirect
2. #10593869C2semidirect
3. C3×#5072C2semidirect
4. C3×#5070C2semidirect
5. #10591456C2semidirect
6. #10591455C2semidirect
7. #10591417C2semidirect
8. #10591416C2semidirect
9. C4×#3714C2semidirect
10. #10590327C2semidirect
11. #10590313C2semidirect
23. C2×C3×#213C22semidirect
24. C3×C4×D12C22semidirect
25. C3×#869C22semidirect
26. #63916C22semidirect
27. #63900C22semidirect
31. C2×#3710C22semidirect
32. C3×#832C22semidirect
33. C3×#832C22semidirect
34. C3×#832C22semidirect
35. C3×C4⋊(C3⋊C8)C22semidirect
36. C3×C4×C3⋊C8C22semidirect
37. #63575C22semidirect
38. #63575C22semidirect
41. #63563C22semidirect
42. #63557C22semidirect
53. #5072D3semidirect
54. #5070D3semidirect
130. C2×#213C2×D3semidirect
146. C4×D12C2×D3semidirect
147. #869C2×D3semidirect
154. #832C2×D3semidirect
155. #832C2×D3semidirect
156. #832C2×D3semidirect
168. C4⋊(C3⋊C8)C2×D3semidirect
169. C4×C3⋊C8C2×D3semidirect
189. C4⋊(C3⋊D3)D8semidirect
190. C4⋊(C3⋊D3)#41semidirect
558. C32#3294semidirect
637. C3#80352semidirect
638. C3#81576semidirect

Maximal subgroups

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

subgroupindex
#105961882
#105938692
C3×#50722
C3×#50702
#105914562
#105914552
#105914172
#105914162
C4×#37142
#105903272
#105903132
#815763
#803523