Finite Group Databasebeta

← #11904335

Subgroups — #11904335

Order 1152.

4249 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C22×C3×D3×D4C211yesmaximal, characteristic, complemented
3C3×#5798C211yesmaximal, characteristic, complemented
4#10595519C214yesmaximal, complemented
5C2×#63977C214yesmaximal, complemented
6#10595246C218yesmaximal, complemented
7D4×#626C218yesmaximal, complemented
8#10595042C212yesmaximal, complemented
9#10595023C212yesmaximal, complemented
10#87239—31nomaximal
11#85867—31nomaximal
12C24×C3×D3C2212yescomplemented
13C22×C32×D4C2211yescharacteristic
14C22×#638C2214yescomplemented
15#64361—28no—
16C2×#3830C2214yescomplemented
17C2×D4×C3⋊D3C2214yescomplemented
18C2×#3828C2212yescomplemented
19C22×C3×#67C2212yescomplemented
20C2×C3×D3×D4—28no—
21C2×C3×D3×D4C2218yescomplemented
22C22×C3×D12C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C22×#626C2218yescomplemented
25C2×C3×#217C2214yescomplemented
26C3×D4×Dic3C2218yescomplemented
27C3×#926C2212yescomplemented
28#63981C2218yescomplemented
29#63978C22116yescomplemented
30#63977C2214yescomplemented
31#63977C22116yescomplemented
32#63977C2218yescomplemented
33#63966C2214yescomplemented
34#63962C2218yescomplemented
35C2×(C2×D3)⋊Dic3C2218yescomplemented
36#63916C2218yescomplemented
37#63911C2214yescomplemented
38#63909C2214yescomplemented
39C4×#626C2218yescomplemented
40#63860C2214yescomplemented
41#63857C2214yescomplemented
42C23×C3×D4—31no—
43C2×#1004—31no—
44C2×#1004—31no—
45C2×#1004—61no—
46C22×D3×D4D311yescharacteristic, complemented
47C3×#518—31no—
48C2×#953—34no—
49#5806—38no—
50#5805—32no—
51#5804—34no—
52D4×#67—38no—
53#5798D311yescharacteristic, complemented
54#5791—32no—
55#5554—38no—
56D4×D12—38no—
57#5525—32no—
58#5524—32no—
59#5493—34no—
60C2×#882—34no—
61C24×C32C2312yes—
62C23×C3⋊D3C2314yescomplemented
63C23×C3×D3—28no—
64C23×C3×D3—48no—
65C23×C3×D3C2311yescharacteristic
66C23×C3×D3C2318yes—
67C23×C3×D3C2312yes—
68C2×C32×D4D418yescomplemented
69C2×C32×D4C2314yes—
70C22×C32×C4C2311yescharacteristic
71C2×#638—216no—
72C2×#638C2314yes—
73C2×#638C2318yescomplemented
74C22×C3⋊Dic3C2314yescomplemented
75#3830—216no—
76D4×C3⋊D3—216no—
77#3828—28no—
78C2×C4⋊(C3⋊D3)C2312yescomplemented
79C2×C4×C3⋊D3C2314yescomplemented
80C2×#634C2312yescomplemented
81C2×C3×#67—28no—
82C2×C3×#67C2318yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2318yescomplemented
85C3×D3×D4—232no—
86C2×C3×D12—24no—
87C2×C3×D12C2314yes—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3C2314yes—
90C2×#626—416no—
91C2×#626C2318yes—
92C2×#626C23116yescomplemented
93C3×#217C2314yes—
94C3×#217C2318yescomplemented
95C3×C4⋊Dic3C2314yescomplemented
96C3×C4×Dic3C2314yescomplemented
97Dic3⋊Dic3C2318yescomplemented
98#3722C2318yescomplemented
99(C2×D3)⋊Dic3C2318yes—
100(C2×D3)⋊Dic3C23116yescomplemented
101#3484—91noSylow
102C25×C3—32no—
103C24×D3C2×D312yescomplemented
104C22×C3×D4—21no—
105C22×C3×D4—32no—
106C22×C3×D4—38no—
107C22×C3×D4—31no—
108C22×C3×D4—68no—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C2×D311yescharacteristic
111C23×C3×C4—31no—
112C22×#67—34no—
113C22×#67—34no—
114C22×#67—38no—
115C22×#67—64no—
116C22×#67C2×D312yescomplemented
117#1004—616no—
118#1004—68no—
119#1004—68no—
120C2×#237—34no—
121C2×#237—34no—
122C2×#237—64no—
123C2×D3×D4—28no—
124C2×D3×D4—34no—
125C2×D3×D4—34no—
126C2×D3×D4—64no—
127C2×D3×D4C2×D318yescomplemented
128C2×#235—32no—
129C2×#235—32no—
130C2×#235—62no—
131C22×D12—38no—
132C22×D12C2×D311yescharacteristic, complemented
133C22×C4×D3C2×D311yescharacteristic, complemented
134C3×C4×D4—38no—
135C3×#117—32no—
136C2×C3×C22⋊C4—34no—
137#953—34no—
138#953—38no—
139#953—316no—
140C2×#217—38no—
141C2×#217C2×D314yescomplemented
142#940—34no—
143#939—316no—
144#938—38no—
145#937—38no—
146#936—34no—
147#935—38no—
148D4×Dic3C2×D318yescomplemented
149#930—316no—
150#930—34no—
151#929—34no—
152C4×#67—38no—
153C2×(C2×D3)⋊C4—38no—
154#926C2×D312yescomplemented
155#924—34no—
156#897—34no—
157#895—38no—
158#895—34no—
159#886—38no—
160#886—34no—
161#882—34no—
162#882—38no—
163#882—316no—
164#882—38no—
165#875—34no—
166#874—34no—
167C4×D12—38no—
168C23×C32—44no—
169C23×C32C2×D418yescomplemented
170C23×C32C2411yescharacteristic
171C23×C32C2414yes—
172C22×C3⋊D3—28no—
173C22×C3⋊D3—48no—
174C22×C3⋊D3C2414yes—
175C22×C3×D3—22no—
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3—216no—
179C22×C3×D3—216no—
180C22×C3×D3—48no—
181C22×C3×D3—44no—
182C22×C3×D3—432no—
183C22×C3×D3C2414yes—
184C22×C3×D3C2412yes—
185C32×D4C2×D4116yescomplemented
186C2×C32×C4C2×D414yescomplemented
187C2×C32×C4C2412yes—
188#638—28no—
189#638—216no—
190C2×C3⋊Dic3—28no—
191C2×C3⋊Dic3C2414yes—
192C4⋊(C3⋊D3)—24no—
193C4×C3⋊D3—28no—
194#634—24no—
195C3×#67—216no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—48no—
198C2×C3×Dic3C2418yes—
199C2×C3×Dic3C2412yes—
200C3×D12—28no—
201C3×C4×D3—28no—
202#626—216no—
203#626—416no—
204C2×H(5,𝔽2)—91no—
205C23×D4—31no—
206#546—98no—
207D42—98no—
208#535—92no—
209#534—94no—
210#525—92no—
211C2×#120—94no—
212#518—31no—
213C24×C3—22no—
214C24×C3—31no—
215C24×C3—38no—
216C24×C3—32no—
217C24×C3—68no—
218C24×C3—128no—
219C24×C3C22×D312yes—
220C24×C3C22×D312yes—
221C23×D3—28no—
222C23×D3—34no—
223C23×D3—34no—
224C23×D3—48no—
225C23×D3—64no—
226C23×D3C22×D311yescharacteristic
227C23×D3C22×D318yes—
228C23×D3C22×D312yes—
229C2×C3×D4—28no—
230C2×C3×D4—24no—
231C2×C3×D4—38no—
232C2×C3×D4—34no—
233C2×C3×D4—68no—
234C2×C3×D4—632no—
235C2×C3×D4—64no—
236C2×C3×D4D1218yescomplemented
237C2×C3×D4#6718yescomplemented
238C2×C3×D4C22×D314yes—
239C2×C3×D4C22×D314yes—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—38no—
243C22×C3×C4—34no—
244C22×C3×C4—64no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—28no—
248C2×#67—34no—
249C2×#67—38no—
250C2×#67—34no—
251C2×#67—38no—
252C2×#67—38no—
253C2×#67—316no—
254C2×#67—64no—
255C2×#67—68no—
256C2×#67—632no—
257C2×#67—616no—
258C2×#67—616no—
259C2×#67—1216no—
260C2×#67C22×D318yes—
261C22×Dic3—34no—
262C22×Dic3—34no—
263C22×Dic3—64no—
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D318yescomplemented
266#237—632no—
267#237—616no—
268#237—616no—
269D3×D4—232no—
270D3×D4—632no—
271D3×D4—616no—
272D3×D4—616no—
273#235—616no—
274#235—68no—
275#235—68no—
276C2×D12—24no—
277C2×D12—38no—
278C2×D12—32no—
279C2×D12—32no—
280C2×D12—316no—
281C2×D12—62no—
282C2×D12—1216no—
283C2×D12C22×D314yes—
284C2×C4×D3—24no—
285C2×C4×D3—34no—
286C2×C4×D3—34no—
287C2×C4×D3—64no—
288C2×C4×D3C22×D314yes—
289C2×Dic6—32no—
290C2×Dic6—32no—
291C2×Dic6—62no—
292C3×C4⋊C4—34no—
293C3×C22⋊C4—34no—
294C3×C22⋊C4—38no—
295C3×C42—34no—
296#217—38no—
297#217—316no—
298#217C22×D314yes—
299#217C22×D318yescomplemented
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—316no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304C4⋊Dic3—38no—
305C4⋊Dic3C22×D314yescomplemented
306Dic3⋊C4—38no—
307C4×Dic3C22×D314yescomplemented
308C22×C32—28no—
309C22×C32—22no—
310C22×C32—48no—
311C22×C32C22×D412yes—
312C22×C32C22×D418yes—
313C22×C32C2511yescharacteristic
314C2×C3⋊D3—24no—
315C2×C3⋊D3—28no—
316C2×C3⋊D3—88no—
317C2×C3×D3—28no—
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3—24no—
321C2×C3×D3—28no—
322C2×C3×D3—432no—
323C2×C3×D3—48no—
324C2×C3×D3H(5,𝔽2)14yescomplemented
325C32×C4C22×D414yes—
326C3⋊Dic3—24no—
327C3×Dic3—22no—
328C3×Dic3—28no—
329C25—32no—
330H(5,𝔽2)—188no—
331C2×#41—94no—
332C2×#41—92no—
333C22×D4—32no—
334C22×D4—38no—
335C22×D4—31no—
336C22×D4—68no—
337C22×D4—98no—
338C22×D4—94no—
339C22×D4—94no—
340C22×D4D3211yescharacteristic
341C23×C4—31no—
342#127—94no—
343#124—94no—
344#123—94no—
345#123—98no—
346C22⋊Q8—94no—
347#121—94no—
348#121—98no—
349#121—916no—
350#120—98no—
351#120—94no—
352#120—98no—
353#120—916no—
354C4×D4—38no—
355C4×D4—98no—
356#117—32no—
357C2×C22⋊C4—34no—
358C2×C22⋊C4—98no—
359C23×C3—24no—
360C23×C3—21no—
361C23×C3—28no—
362C23×C3—32no—
363C23×C3—34no—
364C23×C3—44no—
365C23×C3—44no—
366C23×C3—64no—
367C23×C3—616no—
368C23×C3—62no—
369C23×C3—616no—
370C23×C3—64no—
371C23×C3—84no—
372C23×C3—128no—
373C23×C3—124no—
374C23×C3—1232no—
375C23×C3C2×D1218yescomplemented
376C23×C3C2×#6718yescomplemented
377C23×C3C23×D311yescharacteristic
378C23×C3C23×D314yes—
379C23×C3C23×D311yescharacteristic
380C23×C3C23×D314yes—
381C22×D3—22no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—216no—
385C22×D3—216no—
386C22×D3—34no—
387C22×D3—34no—
388C22×D3—48no—
389C22×D3—44no—
390C22×D3—432no—
391C22×D3—64no—
392C22×D3—616no—
393C22×D3—68no—
394C22×D3—68no—
395C22×D3—128no—
396C22×D3—128no—
397C22×D3—248no—
398C22×D3C23×D314yes—
399C22×D3C23×D312yes—
400C3×D4—216no—
401C3×D4—616no—
402C3×D4—68no—
403C3×D4C2×D12116yescomplemented
404C3×D4C2×#67116yescomplemented
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—32no—
408C2×C3×C4—38no—
409C2×C3×C4—62no—
410C2×C3×C4—68no—
411C2×C3×C4—128no—
412C2×C3×C4C2×D1214yescomplemented
413C2×C3×C4C2×#6714yescomplemented
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D312yes—
416#67—216no—
417#67—616no—
418#67—616no—
419#67—632no—
420#67—68no—
421#67—616no—
422#67—68no—
423#67—616no—
424#67—1216no—
425C2×Dic3—22no—
426C2×Dic3—34no—
427C2×Dic3—34no—
428C2×Dic3—48no—
429C2×Dic3—64no—
430C2×Dic3—616no—
431C2×Dic3—68no—
432C2×Dic3—68no—
433C2×Dic3C23×D318yes—
434C2×Dic3C23×D312yes—
435D12—28no—
436D12—68no—
437D12—616no—
438D12—64no—
439D12—64no—
440D12—1216no—
441C4×D3—28no—
442C4×D3—616no—
443C4×D3—68no—
444C4×D3—68no—
445Dic6—68no—
446Dic6—64no—
447Dic6—64no—
448C2×C32—22no—
449C2×C32—28no—
450C2×C32C23×D411yescharacteristic
451C2×C32C2×H(5,𝔽2)12yes—
452C3⋊D3—44no—
453C3×D3—24no—
454C3×D3—44no—
455C24—31no—
456C24—38no—
457C24—32no—
458C24—68no—
459C24—94no—
460C24—128no—
461C24C2×D3212yes—
462#41—1816no—
463#41—188no—
464C2×Q8—92no—
465C2×D4—38no—
466C2×D4—34no—
467C2×D4—68no—
468C2×D4—632no—
469C2×D4—64no—
470C2×D4—98no—
471C2×D4—916no—
472C2×D4—94no—
473C2×D4—98no—
474C2×D4—92no—
475C2×D4—1816no—
476C2×D4—1816no—
477C2×D4—3616no—
478C2×D4#62618yescomplemented
479C2×D4C2×D3214yes—
480C22×C4—31no—
481C22×C4—38no—
482C22×C4—34no—
483C22×C4—64no—
484C22×C4—94no—
485C22×C4—94no—
486C22×C4C2×D3211yescharacteristic
487C4⋊C4—34no—
488C4⋊C4—98no—
489C22⋊C4—34no—
490C22⋊C4—38no—
491C22⋊C4—98no—
492C22⋊C4—98no—
493C22⋊C4—916no—
494C42—34no—
495C22×C3—28no—
496C22×C3—22no—
497C22×C3—28no—
498C22×C3—22no—
499C22×C3—28no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—34no—
503C22×C3—48no—
504C22×C3—42no—
505C22×C3—48no—
506C22×C3—48no—
507C22×C3—68no—
508C22×C3—62no—
509C22×C3—62no—
510C22×C3—64no—
511C22×C3—68no—
512C22×C3—88no—
513C22×C3—1232no—
514C22×C3—128no—
515C22×C3C22×D1218yes—
516C22×C3C22×D1212yes—
517C22×C3C22×#6712yes—
518C22×C3C22×#6718yes—
519C22×C3C24×D311yescharacteristic
520C22×C3C24×D311yescharacteristic
521C2×D3—28no—
522C2×D3—22no—
523C2×D3—22no—
524C2×D3—28no—
525C2×D3—24no—
526C2×D3—432no—
527C2×D3—48no—
528C2×D3—68no—
529C2×D3—64no—
530C2×D3—68no—
531C2×D3—68no—
532C2×D3—64no—
533C2×D3—128no—
534C2×D3—248no—
535C2×D3—248no—
536C2×D3—2416no—
537C2×D3#100414yescomplemented
538C3×C4—24no—
539C3×C4—62no—
540C3×C4—68no—
541C3×C4C22×D1214yes—
542C3×C4C22×#6714yes—
543Dic3—28no—
544Dic3—22no—
545Dic3—68no—
546Dic3—64no—
547Dic3—64no—
548C32#348411yescharacteristic, complemented, Sylow
549C23—32no—
550C23—34no—
551C23—44no—
552C23—64no—
553C23—616no—
554C23—62no—
555C23—616no—
556C23—64no—
557C23—94no—
558C23—128no—
559C23—124no—
560C23—1232no—
561C23—188no—
562C23—368no—
563C23C2×#62618yescomplemented
564C23C22×D3211yescharacteristic
565C23C22×D3214yes—
566Q8—184no—
567D4—616no—
568D4—68no—
569D4—1816no—
570D4—188no—
571D4—1816no—
572D4—184no—
573D4—3616no—
574D4C2×#626116yescomplemented
575C2×C4—38no—
576C2×C4—32no—
577C2×C4—62no—
578C2×C4—68no—
579C2×C4—94no—
580C2×C4—128no—
581C2×C4—188no—
582C2×C4—188no—
583C2×C4C2×#62614yescomplemented
584C2×C4C22×D3212yes—
585C2×C3—28no—
586C2×C3—22no—
587C2×C3—22no—
588C2×C3—28no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—48no—
592C2×C3—42no—
593C2×C3—64no—
594C2×C3—124no—
595C2×C3C23×D1211yescharacteristic
596C2×C3C2×#100412yes—
597C2×C3D3×H(5,𝔽2)12yes—
598C2×C3C23×#6711yescharacteristic
599D3—24no—
600D3—44no—
601D3—128no—
602D3—124no—
603D3—124no—
604C22—28no—
605C22—22no—
606C22—34no—
607C22—48no—
608C22—68no—
609C22—62no—
610C22—62no—
611C22—68no—
612C22—64no—
613C22—1232no—
614C22—128no—
615C22—188no—
616C22—184no—
617C22—728no—
618C22C22×#62612yes—
619C22C22×#62618yes—
620C22C23×D3211yescharacteristic
621C4—68no—
622C4—62no—
623C4—184no—
624C4C22×#62614yes—
625C3—21no—
626C3#8586711yescharacteristic, complemented
627C3#8723911yescharacteristic, complemented
628C2—22no—
629C2—28no—
630C2—64no—
631C2—124no—
632C2—364no—
633C2D3×#100412yes—
634C2C23×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3484
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C22×C3×D3×D4C2semidirect
3. C3×#5798C2semidirect
4. #10595519C2semidirect
5. C2×#63977C2semidirect
6. #10595246C2semidirect
7. D4×#626C2semidirect
8. #10595042C2semidirect
9. #10595023C2semidirect
12. C24×C3×D3C22semidirect
14. C22×#638C22semidirect
16. C2×#3830C22semidirect
17. C2×D4×C3⋊D3C22semidirect
18. C2×#3828C22semidirect
19. C22×C3×#67C22semidirect
21. C2×C3×D3×D4C22semidirect
22. C22×C3×D12C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×#626C22semidirect
25. C2×C3×#217C22semidirect
26. C3×D4×Dic3C22semidirect
27. C3×#926C22semidirect
28. #63981C22semidirect
29. #63978C22semidirect
30. #63977C22semidirect
31. #63977C22semidirect
32. #63977C22semidirect
33. #63966C22semidirect
34. #63962C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. #63916C22semidirect
37. #63911C22semidirect
38. #63909C22semidirect
39. C4×#626C22semidirect
40. #63860C22semidirect
41. #63857C22semidirect
46. C22×D3×D4D3semidirect
53. #5798D3semidirect
62. C23×C3⋊D3C23semidirect
68. C2×C32×D4D4semidirect
73. C2×#638C23semidirect
74. C22×C3⋊Dic3C23semidirect
78. C2×C4⋊(C3⋊D3)C23semidirect
79. C2×C4×C3⋊D3C23semidirect
80. C2×#634C23semidirect
84. C22×C3×Dic3C23semidirect
92. C2×#626C23semidirect
94. C3×#217C23semidirect
95. C3×C4⋊Dic3C23semidirect
96. C3×C4×Dic3C23semidirect
97. Dic3⋊Dic3C23semidirect
98. #3722C23semidirect
100. (C2×D3)⋊Dic3C23semidirect
103. C24×D3C2×D3semidirect
116. C22×#67C2×D3semidirect
127. C2×D3×D4C2×D3semidirect
132. C22×D12C2×D3semidirect
133. C22×C4×D3C2×D3semidirect
141. C2×#217C2×D3semidirect
148. D4×Dic3C2×D3semidirect
154. #926C2×D3semidirect
169. C23×C32C2×D4semidirect
185. C32×D4C2×D4semidirect
186. C2×C32×C4C2×D4semidirect
236. C2×C3×D4D12semidirect
237. C2×C3×D4#67semidirect
265. C22×Dic3C22×D3semidirect
299. #217C22×D3semidirect
305. C4⋊Dic3C22×D3semidirect
307. C4×Dic3C22×D3semidirect
324. C2×C3×D3H(5,𝔽2)semidirect
375. C23×C3C2×D12semidirect
376. C23×C3C2×#67semidirect
403. C3×D4C2×D12semidirect
404. C3×D4C2×#67semidirect
412. C2×C3×C4C2×D12semidirect
413. C2×C3×C4C2×#67semidirect
478. C2×D4#626semidirect
537. C2×D3#1004semidirect
548. C32#3484semidirect
563. C23C2×#626semidirect
574. D4C2×#626semidirect
583. C2×C4C2×#626semidirect
626. C3#85867semidirect
627. C3#87239semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C22×C3×D3×D42
C3×#57982
#105955192
C2×#639772
#105952462
D4×#6262
#105950422
#105950232
#872393
#858673