Finite Group Databasebeta

← #11824458

Subgroups — #11824458

Order 1152.

2145 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×#63958C214yesmaximal, complemented
4C2×#63911C211yesmaximal, characteristic, complemented
5C2×#63894C211yesmaximal, characteristic, complemented
6C3×#5221C211yesmaximal, characteristic, complemented
7#10591724C214yesmaximal, complemented
8C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
9#10591323C211yesmaximal, characteristic, complemented
10#83188—31nomaximal
11#76348—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#638C2214yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×D12C2211yescharacteristic
18C22×#626C2214yes—
19C22×#624C2212yes—
20#64149—24no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2214yes—
23C3×#940—24no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2212yes—
29C2×(C2×D3)⋊Dic3C2214yes—
30#63958—216no—
31#63911—24no—
32#63894—24no—
33#63579C2212yes—
34C2×C3×#127—31no—
35C2×#940—31no—
36C2×#940—31no—
37C2×#940—31no—
38C2×#940—61no—
39C2×#940D311yescharacteristic, complemented
40C2×#938—34no—
41C2×#893—31no—
42C2×#884—34no—
43C2×#874—31no—
44C2×C4×D12—31no—
45C3×#390—31no—
46#5223—34no—
47#5221—31no—
48#5221D311yescharacteristic, complemented
49#4988—31no—
50#4960—34no—
51C4×C4⋊Dic3—31no—
52C4×Dic3⋊C4—31no—
53C24×C32C2312yes—
54C23×C3⋊D3C2312yes—
55C23×C3×D3C2312yes—
56C2×C32×D4—22no—
57C2×C32×D4—22no—
58C2×C32×D4—22no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—28no—
61C2×#638—28no—
62C2×#638—44no—
63C22×C3⋊Dic3C2312yes—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)D414yescomplemented
67C2×C3×#67—24no—
68C2×C3×#67—24no—
69C2×C3×#67—28no—
70C2×C3×#67—44no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×D12—22no—
76C2×C3×D12—22no—
77C2×C3×D12—22no—
78C2×#626—28no—
79C2×#626—28no—
80C2×#626—44no—
81C2×#624—24no—
82C2×#624—28no—
83C4×C3⋊Dic3—22no—
84C3×#217—28no—
85C3×C4⋊Dic3—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3D414yescomplemented
88Dic3⋊Dic3D418yescomplemented
89#3722—24no—
90(C2×D3)⋊Dic3—28no—
91#2541—91noSylow
92C22×C3×D4—21no—
93C22×C3×D4—32no—
94C22×C3×D4—32no—
95C22×C3×D4—31no—
96C22×C3×D4C2×D311yescharacteristic
97C22×C3×D4C2×D311yescharacteristic
98C22×#67—34no—
99C22×#67—34no—
100C22×#67—34no—
101C22×#67—64no—
102C22×#67C2×D312yes—
103C22×#67C2×D312yes—
104C22×D12—31no—
105C22×D12—31no—
106C22×D12—34no—
107C22×D12—61no—
108C22×D12C2×D311yescharacteristic
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C3×#127—64no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—34no—
114C2×C3×C42—31no—
115C2×C3×C42—31no—
116C2×#217—34no—
117C2×#217C2×D314yes—
118#940—24no—
119#940—64no—
120#940—64no—
121#940—64no—
122#940—68no—
123#938—616no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×Dic3⋊C4—32no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3C2×D311yescharacteristic
134C2×C4×Dic3C2×D311yescharacteristic
135#893—64no—
136#884—616no—
137#874—64no—
138C4×D12—64no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C23×C32—22no—
142C23×C32—24no—
143C23×C32—22no—
144C23×C32—22no—
145C23×C32—24no—
146C23×C32C2411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—24no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—24no—
151C22×C3⋊D3C2×D414yes—
152C22×C3×D3—24no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—24no—
157C32×D4—44no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4#4112yes—
161#638—416no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C2×D414yes—
165C4⋊(C3⋊D3)—28no—
166C3×#67—48no—
167C3×#67—48no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—24no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C2×D414yes—
174C2×C3×Dic3C2×D414yes—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—44no—
178#626—416no—
179#624—48no—
180C2×#127—31no—
181C2×#127—91no—
182C2×#127—91no—
183C2×#121—94no—
184C2×C4×D4—91no—
185#392—94no—
186#390—31no—
187#390—91no—
188C4×C4⋊C4—91no—
189C24×C3—22no—
190C24×C3—32no—
191C24×C3C22×D312yes—
192C24×C3C22×D312yes—
193C23×D3—32no—
194C23×D3—32no—
195C23×D3—62no—
196C23×D3C22×D312yes—
197C2×C3×D4—24no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—42no—
205C2×C3×D4—42no—
206C2×C3×D4—68no—
207C2×C3×D4—64no—
208C2×C3×D4—64no—
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—124no—
213C22×C3×C4—21no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—28no—
221C2×#67—24no—
222C2×#67—24no—
223C2×#67—44no—
224C2×#67—68no—
225C2×#67—68no—
226C2×#67—68no—
227C2×#67—68no—
228C2×#67—68no—
229C2×#67—616no—
230C2×#67—68no—
231C2×#67—128no—
232C2×#67—124no—
233C2×#67—124no—
234C2×#67—124no—
235C2×#67—128no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—62no—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D311yescharacteristic
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—22no—
246C2×D12—34no—
247C2×D12—34no—
248C2×D12—64no—
249C2×D12—62no—
250C2×D12—62no—
251C2×D12—62no—
252C2×D12—62no—
253C2×D12—68no—
254C2×D12—68no—
255C2×D12—122no—
256C2×D12—122no—
257C2×D12—124no—
258C2×C4×D3—64no—
259C2×C4×D3—68no—
260C2×C4×D3—68no—
261C2×C4×D3—64no—
262C3×C4⋊C4—62no—
263C3×C22⋊C4—68no—
264C3×C42—34no—
265C3×C42—62no—
266#217—28no—
267#217—68no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—68no—
270(C2×D3)⋊C4—64no—
271C4⋊Dic3—22no—
272C4⋊Dic3—38no—
273Dic3⋊C4—38no—
274C4×Dic3—22no—
275C4×Dic3—64no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3#6714yescomplemented
279C22×C32—42no—
280C22×C32—44no—
281C22×C32—42no—
282C22×C32—42no—
283C22×C32—44no—
284C22×C32C22×D411yescharacteristic
285C22×C32C22×D412yes—
286C22×C32C22×D411yescharacteristic
287C22×C32C2×#4111yescharacteristic
288C22×C32H(5,𝔽2)12yes—
289C2×C3⋊D3—24no—
290C2×C3⋊D3—28no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—42no—
293C2×C3⋊D3—44no—
294C2×C3×D3—42no—
295C2×C3×D3—42no—
296C2×C3×D3—42no—
297C2×C3×D3—44no—
298C2×C3×D3—44no—
299C32×C4#12114yescomplemented
300C3⋊Dic3—24no—
301C3×Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C3×Dic3#12714yescomplemented
305C22×D4—32no—
306C22×D4—32no—
307C22×D4—31no—
308C22×D4—94no—
309C22×D4—94no—
310C22×D4—91no—
311C22×D4D3211yescharacteristic
312C23×C4—92no—
313#127—64no—
314#127—184no—
315#127—184no—
316#121—1816no—
317C4×D4—184no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—92no—
320C2×C22⋊C4—34no—
321C2×C22⋊C4—92no—
322C2×C22⋊C4—94no—
323C2×C42—31no—
324C2×C42—31no—
325C2×C42—91no—
326#95—92no—
327C23×C3—24no—
328C23×C3—22no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—44no—
340C23×C3—44no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—62no—
344C23×C3—64no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—64no—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C22×D3—24no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—24no—
354C22×D3—22no—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—64no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—64no—
361C22×D3—64no—
362C22×D3—62no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—124no—
369C22×D3—124no—
370C3×D4—48no—
371C3×D4—44no—
372C3×D4—44no—
373C3×D4—128no—
374C3×D4—128no—
375C3×D4—124no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—34no—
380C2×C3×C4—32no—
381C2×C3×C4—34no—
382C2×C3×C4—32no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—64no—
387C2×C3×C4—62no—
388C2×C3×C4#23512yes—
389C2×C3×C4D3×D412yes—
390C2×C3×C4D3×D412yes—
391C2×C3×C4D3×D412yes—
392C2×C3×C4#23712yes—
393C2×C3×C4C2×#6712yes—
394#67—48no—
395#67—48no—
396#67—1216no—
397#67—1216no—
398#67—1216no—
399#67—1232no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—24no—
405C2×Dic3—34no—
406C2×Dic3—34no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3D3×D414yes—
415C2×Dic3D3×D414yes—
416C2×Dic3C2×#6712yes—
417C2×Dic3C2×#6712yes—
418D12—44no—
419D12—68no—
420D12—68no—
421D12—128no—
422D12—1216no—
423C4×D3—128no—
424C4×D3—128no—
425C2×C32—82no—
426C2×C32C2×#12111yescharacteristic
427C2×C32C2×#12711yescharacteristic
428C2×C32#53511yescharacteristic
429C2×C32D4212yes—
430C2×C32#55012yes—
431C3⋊D3—44no—
432C3×D3—82no—
433C24—32no—
434C24—92no—
435C24C2×D3212yes—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—68no—
440C2×D4—64no—
441C2×D4—64no—
442C2×D4—62no—
443C2×D4—62no—
444C2×D4—62no—
445C2×D4—94no—
446C2×D4—124no—
447C2×D4—188no—
448C2×D4—188no—
449C2×D4—188no—
450C2×D4—188no—
451C2×D4—182no—
452C2×D4—182no—
453C2×D4—364no—
454C2×D4—364no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—92no—
460C22×C4—184no—
461C22×C4—188no—
462C22×C4C2×D3211yescharacteristic
463C4⋊C4—62no—
464C4⋊C4—98no—
465C22⋊C4—68no—
466C22⋊C4—184no—
467C22⋊C4—188no—
468C42—34no—
469C42—62no—
470C42—182no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—48no—
477C22×C3—44no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—44no—
481C22×C3—44no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—44no—
487C22×C3—44no—
488C22×C3—84no—
489C22×C3—82no—
490C22×C3—82no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3—124no—
495C22×C3—124no—
496C22×C3C2×#23511yescharacteristic
497C22×C3C2×D3×D412yes—
498C22×C3C2×D3×D412yes—
499C22×C3C2×D3×D411yescharacteristic
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C22×C3C2×#23711yescharacteristic
503C22×C3#100412yes—
504C22×C3#100912yes—
505C22×C3C22×#6711yescharacteristic
506C2×D3—44no—
507C2×D3—44no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—42no—
511C2×D3—68no—
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—68no—
515C2×D3—124no—
516C2×D3—128no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—124no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—124no—
523C2×D3—244no—
524C2×D3—242no—
525C2×D3—242no—
526C3×C4—24no—
527C3×C4—34no—
528C3×C4—62no—
529C3×C4—64no—
530C3×C4—122no—
531C3×C4#88414yescomplemented
532C3×C4#93814yescomplemented
533Dic3—22no—
534Dic3—24no—
535Dic3—42no—
536Dic3—68no—
537Dic3—64no—
538Dic3—64no—
539Dic3#94014yescomplemented
540C32#254111yescharacteristic, complemented, Sylow
541C23—24no—
542C23—24no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—64no—
547C23—64no—
548C23—62no—
549C23—62no—
550C23—62no—
551C23—94no—
552C23—184no—
553C23—184no—
554C23—182no—
555C23—182no—
556C23C22×D3211yescharacteristic
557D4—44no—
558D4—128no—
559D4—128no—
560D4—124no—
561D4—188no—
562D4—3616no—
563D4—3616no—
564C2×C4—34no—
565C2×C4—32no—
566C2×C4—34no—
567C2×C4—32no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—64no—
572C2×C4—62no—
573C2×C4—94no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—368no—
577C2×C4#380412yes—
578C2×C4D3×#6712yes—
579C2×C4#381112yes—
580C2×C3—22no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—22no—
585C2×C3—84no—
586C2×C3—82no—
587C2×C3—82no—
588C2×C3—242no—
589C2×C3C2×#88411yescharacteristic
590C2×C3#555312yes—
591C2×C3#560912yes—
592C2×C3#567411yescharacteristic
593C2×C3D3×#12711yescharacteristic
594C2×C3#571712yes—
595C2×C3#571812yes—
596C2×C3C2×#93811yescharacteristic
597C2×C3C2×#94011yescharacteristic
598C2×C3#580511yescharacteristic
599D3—82no—
600D3—124no—
601D3—124no—
602D3—244no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—44no—
608C22—124no—
609C22—122no—
610C22—122no—
611C22—122no—
612C22—124no—
613C22—184no—
614C22—188no—
615C22—364no—
616C22—362no—
617C22—362no—
618C22D32×D412yes—
619C22#6431412yes—
620C22C2×#380411yescharacteristic
621C22C2×D3×#6711yescharacteristic
622C22C2×#381111yescharacteristic
623C4—34no—
624C4—62no—
625C4—64no—
626C4—122no—
627C4—184no—
628C4#6395814yescomplemented
629C3—21no—
630C3#7634811yescharacteristic, complemented
631C3#8318811yescharacteristic, complemented
632C2—82no—
633C2—242no—
634C2—364no—
635C2#1059514312yes—
636C2#1059523511yescharacteristic
637C2D3×#94011yescharacteristic
638C2#1059529712yes—
639C2C2×#6395811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. C2×C3×#940C2semidirect
3. C2×#63958C2semidirect
4. C2×#63911C2semidirect
5. C2×#63894C2semidirect
6. C3×#5221C2semidirect
7. #10591724C2semidirect
8. C4×Dic3⋊Dic3C2semidirect
9. #10591323C2semidirect
39. C2×#940D3semidirect
48. #5221D3semidirect
66. C2×C4⋊(C3⋊D3)D4semidirect
87. C3×C4×Dic3D4semidirect
88. Dic3⋊Dic3D4semidirect
278. C4×Dic3#67semidirect
299. C32×C4#121semidirect
304. C3×Dic3#127semidirect
531. C3×C4#884semidirect
532. C3×C4#938semidirect
539. Dic3#940semidirect
540. C32#2541semidirect
628. C4#63958semidirect
630. C3#76348semidirect
631. C3#83188semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C3×#9402
C2×#639582
C2×#639112
C2×#638942
C3×#52212
#105917242
C4×Dic3⋊Dic32
#105913232
#831883
#763483