Finite Group Databasebeta

← #11904912

Subgroups — #11904912

Order 1152.

2993 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×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5493C211yesmaximal, characteristic, complemented
3C3×#5483C211yesmaximal, characteristic, complemented
4C2×#63981C212yesmaximal, complemented
5#10595506C212yesmaximal, complemented
6#10594979C214yesmaximal, complemented
7#10594922C214yesmaximal, complemented
8#10594164C218yesmaximal, complemented
9#10594063C218yesmaximal, complemented
10#86579—31nomaximal
11#86309—31nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2212yescomplemented
14C22×C3×#67C2212yes—
15C22×#626C2214yescomplemented
16C2×#3796C2214yescomplemented
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×#3752C2212yescomplemented
20C22⋊C4×C3⋊D3C2218yescomplemented
21C2×C3×#217C2212yes—
22C3×#930C2214yescomplemented
23C3×#924C2214yescomplemented
24C3×#886C2214yescomplemented
25C3×#882C2214yescomplemented
26C3×#878C2218yescomplemented
27#63981C2218yes—
28#63981C2214yescomplemented
29#63981C2214yescomplemented
30#67⋊Dic3C2218yescomplemented
31Dic3×#67C2218yescomplemented
32D3×#217C2214yescomplemented
33C2×#3722C2214yescomplemented
34#63955C2214yescomplemented
35#63916C2214yescomplemented
36#63907C2218yescomplemented
37#63890C2218yescomplemented
38#63886C2218yescomplemented
39#63881C2218yescomplemented
40#63871C2214yescomplemented
41#63853C2218yescomplemented
42#63849C2214yescomplemented
43#63848C2218yescomplemented
44C3×#543—31no—
45C3×#534—31no—
46C2×#937—32no—
47#5798—32no—
48#5658—38no—
49#5644—34no—
50#5637—38no—
51#5630—38no—
52#5627—34no—
53#5617—34no—
54#5606—34no—
55#5591—38no—
56#5493D311yescharacteristic, complemented
57C2×#882—32no—
58#5486—32no—
59C2×D3×C22⋊C4—31no—
60C2×D3×C22⋊C4—31no—
61C2×D3×C22⋊C4—61no—
62#5483D311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C23×C3⋊D3—24no—
65C23×C3⋊D3—44no—
66C23×C3⋊D3C2311yescharacteristic
67C23×C3⋊D3C2314yes—
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3C2312yes—
70C22×C32×C4C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×C4×C3⋊D3—44no—
73C2×C4×C3⋊D3C2314yes—
74C2×C4×C3⋊D3C2314yes—
75C2×C3×#67—28no—
76C2×C3×#67C2314yes—
77C2×C3×#67C2314yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2314yes—
80C2×C3×D12C2314yescomplemented
81C2×C3×Dic6C2314yescomplemented
82C2×#626—48no—
83C2×#626C2318yes—
84C2×#626C2318yes—
85C2×D3×Dic3C2318yescomplemented
86#3796—48no—
87C32×C22⋊C4C2314yes—
88#3757C2314yes—
89#3752C2318yes—
90C3×#217C2314yes—
91C3×#217C2314yes—
92C3×(C2×D3)⋊C4C2318yescomplemented
93C3×C4⋊Dic3C2314yescomplemented
94C3×C4⋊Dic3C2314yescomplemented
95C3×Dic3⋊C4C2318yescomplemented
96Dic3⋊Dic3C2318yescomplemented
97#3722C2318yes—
98#3722C2318yes—
99(C2×D3)⋊Dic3C2318yescomplemented
100Dic32C2318yescomplemented
101#3490—91noSylow
102C24×D3—31no—
103C24×D3—31no—
104C24×D3—61no—
105C22×C3×D4—32no—
106C22×#67—34no—
107C22×#67C2×D312yes—
108C2×#239—34no—
109C2×#237—34no—
110C22×D12—34no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3—62no—
114C3×#123—34no—
115C3×C22⋊Q8—34no—
116C3×C22⋊Q8—38no—
117C3×#121—34no—
118C3×#120—34no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C22⋊C4C2×D311yescharacteristic
122C2×C3×C22⋊C4C2×D311yescharacteristic
123C2×#217—31no—
124C2×#217—31no—
125C2×#217—34no—
126C2×#217—61no—
127C2×#217C2×D312yes—
128#947—38no—
129#946—34no—
130#939—38no—
131#938—34no—
132#937—38no—
133#937—34no—
134#937—34no—
135D4×Dic3—38no—
136D4×Dic3—38no—
137#930C2×D314yescomplemented
138C4×#67—38no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—34no—
142C2×(C2×D3)⋊C4—34no—
143C2×(C2×D3)⋊C4—62no—
144#926—34no—
145#924C2×D314yescomplemented
146#898—38no—
147#898—38no—
148#897—34no—
149#895—38no—
150#895—34no—
151#894—38no—
152#894—38no—
153#893—38no—
154#892—34no—
155#892—34no—
156#886—38no—
157#886C2×D314yescomplemented
158#885—38no—
159#883—38no—
160#882—38no—
161#882—34no—
162#882—34no—
163#882C2×D314yescomplemented
164#67⋊C4—38no—
165#67⋊C4—38no—
166D3×C22⋊C4—34no—
167D3×C22⋊C4—38no—
168D3×C22⋊C4—38no—
169D3×C22⋊C4—68no—
170#878C2×D318yescomplemented
171#877—34no—
172C23×C32—42no—
173C23×C32#4114yescomplemented
174C23×C32C2412yes—
175C23×C32C2411yescharacteristic
176C22×C3⋊D3—22no—
177C22×C3⋊D3—24no—
178C22×C3⋊D3—28no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—28no—
181C22×C3⋊D3—44no—
182C22×C3⋊D3—42no—
183C22×C3⋊D3—416no—
184C22×C3⋊D3C2412yes—
185C22×C3⋊D3C2412yes—
186C22×C3×D3—24no—
187C22×C3×D3—44no—
188C22×C3×D3C2414yes—
189C2×C32×C4—42no—
190C2×C32×C4C2414yes—
191C2×C3⋊Dic3—42no—
192C2×C3⋊Dic3C2414yes—
193C4×C3⋊D3—28no—
194C4×C3⋊D3—44no—
195C3×#67—28no—
196C3×#67—28no—
197C2×C3×Dic3—24no—
198C2×C3×Dic3—44no—
199C2×C3×Dic3C2414yes—
200C2×C3×Dic3C2418yes—
201C3×D12—44no—
202C3×Dic6—44no—
203#626—216no—
204#626—48no—
205D3×Dic3—48no—
206#551—98no—
207#546—98no—
208#543—31no—
209#538—94no—
210#534—31no—
211#525—94no—
212C2×#120—92no—
213#518—92no—
214C22×C22⋊C4—91no—
215C24×C3—21no—
216C24×C3—32no—
217C24×C3C22×D311yescharacteristic
218C24×C3C22×D311yescharacteristic
219C23×D3—31no—
220C23×D3—31no—
221C23×D3—34no—
222C23×D3—34no—
223C23×D3—31no—
224C23×D3—31no—
225C23×D3—61no—
226C23×D3—64no—
227C23×D3—61no—
228C23×D3—68no—
229C23×D3—64no—
230C23×D3—64no—
231C23×D3—124no—
232C23×D3—124no—
233C23×D3—128no—
234C23×D3C22×D312yes—
235C2×C3×Q8—34no—
236C2×C3×D4—34no—
237C2×C3×D4—34no—
238C2×C3×D4—34no—
239C2×C3×D4—68no—
240C22×C3×C4—22no—
241C22×C3×C4—32no—
242C22×C3×C4—34no—
243C22×C3×C4C22×D312yes—
244C22×C3×C4C22×D312yes—
245C2×#67—28no—
246C2×#67—38no—
247C2×#67—38no—
248C2×#67—128no—
249C2×#67C22×D314yes—
250C2×#67C22×D314yes—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—38no—
254C22×Dic3—62no—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D314yes—
257#239—128no—
258#237—128no—
259C2×D12—38no—
260C2×D12—38no—
261C2×D12—128no—
262C2×D12C22×D314yescomplemented
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×C4×D3—38no—
266C2×C4×D3—34no—
267C2×C4×D3—34no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×C4×D3—124no—
271C2×C4×D3—124no—
272C2×C4×D3—128no—
273C2×Dic6C22×D314yescomplemented
274C3×C4⋊C4—34no—
275C3×C4⋊C4—34no—
276C3×C4⋊C4—38no—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—34no—
279C3×C22⋊C4—34no—
280C3×C22⋊C4—38no—
281C3×C22⋊C4C22×D314yes—
282C3×C22⋊C4C22×D314yes—
283#217—34no—
284#217—34no—
285#217—38no—
286#217—64no—
287#217C22×D314yes—
288#217C22×D314yes—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—68no—
297(C2×D3)⋊C4C22×D318yescomplemented
298C4⋊Dic3—38no—
299C4⋊Dic3C22×D314yescomplemented
300C4⋊Dic3C22×D314yescomplemented
301Dic3⋊C4—38no—
302Dic3⋊C4C22×D318yescomplemented
303C4×Dic3—38no—
304C4×Dic3—38no—
305C22×C32—22no—
306C22×C32—24no—
307C22×C32—44no—
308C22×C32C2×#4114yes—
309C22×C32C2×#4112yes—
310C22×C32C2511yescharacteristic
311C2×C3⋊D3—28no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—24no—
316C2×C3⋊D3—416no—
317C2×C3⋊D3—44no—
318C2×C3⋊D3H(5,𝔽2)14yes—
319C2×C3×D3—24no—
320C2×C3×D3—28no—
321C2×C3×D3—84no—
322C32×C4—24no—
323C3⋊Dic3—24no—
324C3×Dic3—24no—
325C3×Dic3—28no—
326C25—91no—
327C2×#41—94no—
328C22×D4—32no—
329C22×D4—94no—
330C23×C4—92no—
331#126—98no—
332#124—98no—
333#123—34no—
334#123—98no—
335#123—98no—
336C22⋊Q8—34no—
337C22⋊Q8—38no—
338C22⋊Q8—94no—
339#121—34no—
340#121—94no—
341#121—98no—
342#120—34no—
343#120—94no—
344#120—94no—
345#120—98no—
346C4×D4—98no—
347C4×D4—98no—
348C4×D4—98no—
349#117—94no—
350#117—94no—
351C2×C22⋊C4—32no—
352C2×C22⋊C4—94no—
353C2×C22⋊C4—94no—
354C2×C22⋊C4—91no—
355C2×C22⋊C4—92no—
356C2×C22⋊C4—98no—
357C2×C22⋊C4D3211yescharacteristic
358C23×C3—21no—
359C23×C3—22no—
360C23×C3—24no—
361C23×C3—34no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—44no—
365C23×C3—64no—
366C23×C3—124no—
367C23×C3#23714yescomplemented
368C23×C3#23914yescomplemented
369C23×C3C23×D312yes—
370C23×C3C23×D311yescharacteristic
371C23×C3C23×D312yes—
372C23×C3C23×D311yescharacteristic
373C22×D3—24no—
374C22×D3—32no—
375C22×D3—32no—
376C22×D3—32no—
377C22×D3—32no—
378C22×D3—44no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—64no—
382C22×D3—64no—
383C22×D3—68no—
384C22×D3—68no—
385C22×D3—68no—
386C22×D3—64no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—616no—
390C22×D3—64no—
391C22×D3—68no—
392C22×D3—62no—
393C22×D3—68no—
394C22×D3—62no—
395C22×D3—128no—
396C22×D3—124no—
397C22×D3—124no—
398C22×D3—122no—
399C22×D3—122no—
400C22×D3—128no—
401C22×D3—1216no—
402C22×D3—1216no—
403C22×D3—1232no—
404C22×D3—124no—
405C22×D3C23×D314yes—
406C3×Q8—124no—
407C3×D4—68no—
408C3×D4—68no—
409C3×D4—124no—
410C2×C3×C4—24no—
411C2×C3×C4—34no—
412C2×C3×C4—38no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—44no—
416C2×C3×C4—64no—
417C2×C3×C4—124no—
418C2×C3×C4C23×D314yes—
419C2×C3×C4C23×D314yes—
420#67—28no—
421#67—28no—
422#67—616no—
423#67—128no—
424C2×Dic3—24no—
425C2×Dic3—34no—
426C2×Dic3—34no—
427C2×Dic3—44no—
428C2×Dic3—64no—
429C2×Dic3—128no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432C2×Dic3—124no—
433C2×Dic3C23×D314yes—
434C2×Dic3C23×D318yes—
435D12—44no—
436D12—616no—
437D12—128no—
438C4×D3—68no—
439C4×D3—68no—
440C4×D3—128no—
441C4×D3—124no—
442C4×D3—124no—
443C4×D3—128no—
444C4×D3—128no—
445Dic6—44no—
446C2×C32—22no—
447C2×C32—24no—
448C2×C32C22×#4111yescharacteristic
449C2×C32C2×H(5,𝔽2)12yes—
450C3⋊D3—24no—
451C3⋊D3—42no—
452C3×D3—44no—
453C24—32no—
454C24—91no—
455C24—94no—
456C24—91no—
457C24—184no—
458C24—364no—
459C24C2×D3211yescharacteristic
460#41—368no—
461C2×Q8—34no—
462C2×D4—34no—
463C2×D4—34no—
464C2×D4—34no—
465C2×D4—68no—
466C2×D4—98no—
467C2×D4—98no—
468C2×D4—368no—
469C22×C4—32no—
470C22×C4—34no—
471C22×C4—98no—
472C22×C4—92no—
473C22×C4—94no—
474C22×C4—94no—
475C22×C4—364no—
476C22×C4C2×D3212yes—
477C4⋊C4—34no—
478C4⋊C4—34no—
479C4⋊C4—38no—
480C4⋊C4—98no—
481C22⋊C4—34no—
482C22⋊C4—34no—
483C22⋊C4—38no—
484C22⋊C4—98no—
485C22⋊C4—98no—
486C22⋊C4—98no—
487C22⋊C4—94no—
488C22⋊C4—98no—
489C22⋊C4C2×D3214yes—
490C42—98no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—24no—
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—21no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—44no—
502C22×C3—48no—
503C22×C3—64no—
504C22×C3—68no—
505C22×C3—244no—
506C22×C3C2×#23714yes—
507C22×C3C2×#23712yes—
508C22×C3C2×#23914yes—
509C22×C3C2×#23912yes—
510C22×C3C24×D311yescharacteristic
511C22×C3C24×D311yescharacteristic
512C2×D3—24no—
513C2×D3—28no—
514C2×D3—34no—
515C2×D3—34no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—616no—
520C2×D3—68no—
521C2×D3—68no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—64no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3—64no—
530C2×D3—64no—
531C2×D3—84no—
532C2×D3—124no—
533C2×D3—1216no—
534C2×D3—1216no—
535C2×D3—1232no—
536C2×D3—128no—
537C2×D3—124no—
538C2×D3—124no—
539C3×C4—24no—
540C3×C4—24no—
541C3×C4—44no—
542C3×C4—64no—
543C3×C4—68no—
544Dic3—24no—
545Dic3—28no—
546Dic3—64no—
547Dic3—64no—
548Dic3—124no—
549C32#349011yescharacteristic, complemented, Sylow
550C23—34no—
551C23—42no—
552C23—64no—
553C23—92no—
554C23—92no—
555C23—124no—
556C23—184no—
557C23—188no—
558C23—182no—
559C23—188no—
560C23—182no—
561C23—362no—
562C23—364no—
563C23—3616no—
564C23#379614yescomplemented
565C23C22×D3211yescharacteristic
566C23C22×D3212yes—
567Q8—124no—
568D4—68no—
569D4—68no—
570D4—124no—
571D4—1816no—
572D4—368no—
573C2×C4—34no—
574C2×C4—38no—
575C2×C4—42no—
576C2×C4—64no—
577C2×C4—94no—
578C2×C4—124no—
579C2×C4—188no—
580C2×C4—364no—
581C2×C4—368no—
582C2×C4—362no—
583C2×C4C22×D3214yes—
584C2×C3—24no—
585C2×C3—22no—
586C2×C3—24no—
587C2×C3—22no—
588C2×C3—24no—
589C2×C3—21no—
590C2×C3—22no—
591C2×C3—44no—
592C2×C3—124no—
593C2×C3C22×#23711yescharacteristic
594C2×C3C22×#23911yescharacteristic
595C2×C3D3×H(5,𝔽2)12yes—
596C2×C3D3×H(5,𝔽2)12yes—
597D3—44no—
598D3—68no—
599D3—64no—
600D3—64no—
601D3—124no—
602D3—122no—
603D3—122no—
604C22—22no—
605C22—24no—
606C22—44no—
607C22—64no—
608C22—68no—
609C22—94no—
610C22—188no—
611C22—182no—
612C22—182no—
613C22—182no—
614C22—184no—
615C22—244no—
616C22—3616no—
617C22—364no—
618C22C2×#379614yes—
619C22C2×#379612yes—
620C22C23×D3211yescharacteristic
621C4—24no—
622C4—64no—
623C4—68no—
624C4—184no—
625C3—21no—
626C3#8630911yescharacteristic, complemented
627C3#8657911yescharacteristic, complemented
628C2—22no—
629C2—24no—
630C2—124no—
631C2—184no—
632C2—362no—
633C2C22×#379611yescharacteristic
634C2#1059667512yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3490
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊C4×C3⋊D3C2semidirect
2. C3×#5493C2semidirect
3. C3×#5483C2semidirect
4. C2×#63981C2semidirect
5. #10595506C2semidirect
6. #10594979C2semidirect
7. #10594922C2semidirect
8. #10594164C2semidirect
9. #10594063C2semidirect
13. C22×C4×C3⋊D3C22semidirect
15. C22×#626C22semidirect
16. C2×#3796C22semidirect
19. C2×#3752C22semidirect
20. C22⋊C4×C3⋊D3C22semidirect
22. C3×#930C22semidirect
23. C3×#924C22semidirect
24. C3×#886C22semidirect
25. C3×#882C22semidirect
26. C3×#878C22semidirect
28. #63981C22semidirect
29. #63981C22semidirect
30. #67⋊Dic3C22semidirect
31. Dic3×#67C22semidirect
32. D3×#217C22semidirect
33. C2×#3722C22semidirect
34. #63955C22semidirect
35. #63916C22semidirect
36. #63907C22semidirect
37. #63890C22semidirect
38. #63886C22semidirect
39. #63881C22semidirect
40. #63871C22semidirect
41. #63853C22semidirect
42. #63849C22semidirect
43. #63848C22semidirect
56. #5493D3semidirect
62. #5483D3semidirect
80. C2×C3×D12C23semidirect
81. C2×C3×Dic6C23semidirect
85. C2×D3×Dic3C23semidirect
92. C3×(C2×D3)⋊C4C23semidirect
93. C3×C4⋊Dic3C23semidirect
94. C3×C4⋊Dic3C23semidirect
95. C3×Dic3⋊C4C23semidirect
96. Dic3⋊Dic3C23semidirect
99. (C2×D3)⋊Dic3C23semidirect
100. Dic32C23semidirect
137. #930C2×D3semidirect
145. #924C2×D3semidirect
157. #886C2×D3semidirect
163. #882C2×D3semidirect
170. #878C2×D3semidirect
173. C23×C32#41semidirect
262. C2×D12C22×D3semidirect
273. C2×Dic6C22×D3semidirect
297. (C2×D3)⋊C4C22×D3semidirect
299. C4⋊Dic3C22×D3semidirect
300. C4⋊Dic3C22×D3semidirect
302. Dic3⋊C4C22×D3semidirect
367. C23×C3#237semidirect
368. C23×C3#239semidirect
549. C32#3490semidirect
564. C23#3796semidirect
626. C3#86309semidirect
627. C3#86579semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C3×#54932
C3×#54832
C2×#639812
#105955062
#105949792
#105949222
#105941642
#105940632
#865793
#863093