Finite Group Databasebeta

← #11824455

Subgroups — #11824455

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×#64083C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic, complemented
3C2×#63911C211yesmaximal, characteristic, complemented
4C2×#63910C214yesmaximal, complemented
5C2×#63894C211yesmaximal, characteristic, complemented
6C3×#4939C211yesmaximal, characteristic, complemented
7C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8#10591395C214yesmaximal, complemented
9#10591320C211yesmaximal, characteristic, complemented
10#76348—31nomaximal
11#73799—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2214yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626C2212yes—
17C22×#626C2214yes—
18C22×#626C2212yes—
19C22×#624C2212yes—
20C2×C32×C42C2211yescharacteristic
21#64083—24no—
22C2×C3×(C2×D3)⋊C4C2214yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×#3722C2214yes—
28C2×#3722C2212yes—
29#63911—24no—
30#63911—24no—
31#63910—216no—
32#63894—24no—
33C3×C3⋊#95C2212yes—
34C2×#940—31no—
35C2×#940—31no—
36C2×#895—34no—
37C2×#893—31no—
38C2×#884—34no—
39C2×#874—31no—
40C2×#874—31no—
41C2×#874—31no—
42C2×#874—31no—
43C2×#874—61no—
44C2×C4×D12—31no—
45C3×#390—31no—
46C3×C4×C4⋊C4—31no—
47#4988—31no—
48#4960—34no—
49#4939—31no—
50#4939D311yescharacteristic, complemented
51C4×Dic3⋊C4D311yescharacteristic, complemented
52#4671—34no—
53C23×C3⋊D3C2312yes—
54C23×C3⋊D3C2312yes—
55C23×C3×D3C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—28no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—28no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—44no—
66C2×C4⋊(C3⋊D3)D414yescomplemented
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C2×C3×D12—22no—
72C2×C3×D12—22no—
73C2×C3×D12—22no—
74C2×#626—28no—
75C2×#626—28no—
76C2×#626—28no—
77C2×#626—24no—
78C2×#626—24no—
79C2×#626—44no—
80C2×#626—44no—
81C2×#624—24no—
82C2×#624—28no—
83C32×C42—22no—
84C3×(C2×D3)⋊C4—28no—
85C3×C4⋊Dic3—22no—
86C3×Dic3⋊C4D418yescomplemented
87C3×C4×Dic3—22no—
88C3×C4×Dic3D414yescomplemented
89#3722—24no—
90#3722—28no—
91#2541—91noSylow
92C22×C3×D4—31no—
93C22×#67—32no—
94C22×#67—34no—
95C22×#67—32no—
96C22×D12—31no—
97C22×D12—31no—
98C22×D12—32no—
99C22×D12—31no—
100C22×D12—31no—
101C22×D12—34no—
102C22×D12—34no—
103C22×D12—34no—
104C22×D12—32no—
105C22×D12—61no—
106C22×D12—61no—
107C22×D12—64no—
108C22×D12C2×D311yescharacteristic
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—34no—
114C2×C3×C42—21no—
115C2×C3×C42—31no—
116C2×C3×C42—31no—
117C2×C3×C42C2×D311yescharacteristic
118C2×C3×C42C2×D311yescharacteristic
119#940—64no—
120#940—64no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—34no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4C2×D314yes—
126C2×C4⋊Dic3C2×D311yescharacteristic
127C2×Dic3⋊C4C2×D312yes—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×C4×Dic3C2×D311yescharacteristic
130#895—616no—
131#893—64no—
132#884—616no—
133#874—64no—
134#874—64no—
135#874—68no—
136#874—64no—
137#874—64no—
138C4×D12—64no—
139C3×#95—32no—
140C3⋊#95C2×D312yes—
141C23×C32C2411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—24no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—24no—
147C22×C3⋊D3—24no—
148C22×C3⋊D3—22no—
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—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D414yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4#4112yes—
163C4⋊(C3⋊D3)—28no—
164C4⋊(C3⋊D3)—416no—
165C4⋊(C3⋊D3)—44no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—24no—
171C2×C3×Dic3C2×D412yes—
172C2×C3×Dic3C2×D414yes—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D414yes—
175C3×D12—44no—
176#626—416no—
177#626—48no—
178#626—48no—
179#624—48no—
180C2×#127—91no—
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—31no—
189C24×C3—32no—
190C23×D3—32no—
191C23×D3—32no—
192C23×D3—32no—
193C23×D3—32no—
194C23×D3—62no—
195C23×D3—62no—
196C23×D3C22×D312yes—
197C2×C3×D4—62no—
198C2×C3×D4—62no—
199C2×C3×D4—62no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—68no—
211C2×#67—68no—
212C2×#67—68no—
213C2×#67—64no—
214C2×#67—64no—
215C2×#67—124no—
216C2×#67—124no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D311yescharacteristic
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D311yescharacteristic
221C2×D12—22no—
222C2×D12—22no—
223C2×D12—22no—
224C2×D12—34no—
225C2×D12—34no—
226C2×D12—64no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—62no—
230C2×D12—62no—
231C2×D12—68no—
232C2×D12—68no—
233C2×D12—616no—
234C2×D12—64no—
235C2×D12—64no—
236C2×D12—64no—
237C2×D12—68no—
238C2×D12—68no—
239C2×D12—68no—
240C2×D12—68no—
241C2×D12—62no—
242C2×D12—62no—
243C2×D12—62no—
244C2×D12—62no—
245C2×D12—62no—
246C2×D12—68no—
247C2×D12—62no—
248C2×D12—122no—
249C2×D12—122no—
250C2×D12—122no—
251C2×D12—128no—
252C2×D12—122no—
253C2×D12—124no—
254C2×D12—124no—
255C2×D12—128no—
256C2×D12—124no—
257C2×D12—124no—
258C2×C4×D3—64no—
259C2×C4×D3—68no—
260C2×C4×D3—68no—
261C2×C4×D3—64no—
262C3×C4⋊C4—38no—
263C3×C4⋊C4—62no—
264C3×C22⋊C4—68no—
265C3×C42—24no—
266C3×C42—22no—
267C3×C42—22no—
268C3×C42—34no—
269C3×C42—62no—
270(C2×D3)⋊C4—28no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—68no—
273(C2×D3)⋊C4—68no—
274(C2×D3)⋊C4—64no—
275C4⋊Dic3—22no—
276Dic3⋊C4D1218yescomplemented
277C4×Dic3—22no—
278C4×Dic3D1214yescomplemented
279C22×C32C22×D411yescharacteristic
280C22×C32C22×D412yes—
281C22×C32C22×D411yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32H(5,𝔽2)12yes—
284C2×C3⋊D3—24no—
285C2×C3⋊D3—28no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—44no—
288C2×C3⋊D3—42no—
289C2×C3⋊D3—42no—
290C2×C3⋊D3—44no—
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—24no—
300C32×C4#12114yescomplemented
301C3×Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C3×Dic3#12714yescomplemented
305C22×D4—31no—
306C22×D4—92no—
307C22×D4—94no—
308C22×D4—92no—
309C22×D4—91no—
310C22×D4—91no—
311C22×D4—94no—
312C23×C4—92no—
313#127—184no—
314#127—184no—
315#127—184no—
316#121—1816no—
317C4×D4—184no—
318C2×C4⋊C4—32no—
319C2×C4⋊C4—31no—
320C2×C22⋊C4—34no—
321C2×C22⋊C4—92no—
322C2×C22⋊C4—94no—
323C2×C42—31no—
324C2×C42—31no—
325C2×C42D3211yescharacteristic
326#95—32no—
327C23×C3—21no—
328C23×C3—64no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—64no—
333C23×C3C23×D311yescharacteristic
334C23×C3C23×D311yescharacteristic
335C22×D3—22no—
336C22×D3—24no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—24no—
340C22×D3—34no—
341C22×D3—34no—
342C22×D3—64no—
343C22×D3—62no—
344C22×D3—64no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—64no—
348C22×D3—62no—
349C22×D3—64no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—64no—
356C22×D3—62no—
357C22×D3—62no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—64no—
361C22×D3—64no—
362C22×D3—122no—
363C22×D3—122no—
364C22×D3—124no—
365C22×D3—124no—
366C22×D3—122no—
367C22×D3—124no—
368C22×D3—122no—
369C22×D3—124no—
370C3×D4—124no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—32no—
382C2×C3×C4—34no—
383C2×C3×C4—32no—
384C2×C3×C4—34no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—64no—
389C2×C3×C4—62no—
390C2×C3×C4C2×D1214yes—
391C2×C3×C4C2×D1212yes—
392C2×C3×C4#23512yes—
393C2×C3×C4D3×D414yes—
394C2×C3×C4D3×D412yes—
395C2×C3×C4D3×D412yes—
396C2×C3×C4D3×D412yes—
397C2×C3×C4#23912yes—
398#67—1216no—
399#67—128no—
400#67—128no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—24no—
406C2×Dic3C2×D1212yes—
407C2×Dic3C2×D1214yes—
408C2×Dic3C2×D1212yes—
409C2×Dic3C2×D1214yes—
410D12—44no—
411D12—68no—
412D12—68no—
413D12—128no—
414D12—1216no—
415D12—1216no—
416D12—1232no—
417D12—128no—
418D12—128no—
419D12—1216no—
420D12—128no—
421D12—124no—
422D12—124no—
423C4×D3—128no—
424C4×D3—128no—
425C2×C32C2×#12111yescharacteristic
426C2×C32C2×#12711yescharacteristic
427C2×C32#53511yescharacteristic
428C2×C32D4212yes—
429C2×C32#55012yes—
430C3⋊D3—44no—
431C3⋊D3—82no—
432C3×D3—82no—
433C24—32no—
434C24—92no—
435C24—92no—
436C2×D4—62no—
437C2×D4—62no—
438C2×D4—62no—
439C2×D4—94no—
440C2×D4—188no—
441C2×D4—188no—
442C2×D4—188no—
443C2×D4—184no—
444C2×D4—184no—
445C2×D4—188no—
446C2×D4—182no—
447C2×D4—182no—
448C2×D4—182no—
449C2×D4—188no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4—364no—
453C2×D4—364no—
454C2×D4—364no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—184no—
460C22×C4—188no—
461C22×C4C2×D3212yes—
462C22×C4C2×D3211yescharacteristic
463C4⋊C4—38no—
464C4⋊C4—62no—
465C22⋊C4—68no—
466C22⋊C4—184no—
467C22⋊C4—188no—
468C42—22no—
469C42—34no—
470C42—62no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—22no—
475C22×C3—21no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—124no—
480C22×C3—124no—
481C22×C3C22×D1211yescharacteristic
482C22×C3C22×D1212yes—
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C2×D3×D412yes—
486C22×C3C2×D3×D411yescharacteristic
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C2×#23911yescharacteristic
489C22×C3#100912yes—
490C22×C3#100912yes—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—44no—
495C2×D3—44no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—68no—
499C2×D3—68no—
500C2×D3—128no—
501C2×D3—124no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—124no—
507C2×D3—124no—
508C2×D3—128no—
509C2×D3—124no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—124no—
517C2×D3—124no—
518C2×D3—124no—
519C2×D3—124no—
520C2×D3—244no—
521C2×D3—242no—
522C2×D3—242no—
523C2×D3—244no—
524C2×D3—242no—
525C2×D3—242no—
526C3×C4—28no—
527C3×C4—24no—
528C3×C4—24no—
529C3×C4—24no—
530C3×C4—34no—
531C3×C4—62no—
532C3×C4—64no—
533C3×C4—122no—
534C3×C4#88414yescomplemented
535C3×C4#89514yescomplemented
536Dic3—22no—
537Dic3—24no—
538Dic3—42no—
539Dic3#87414yescomplemented
540C32#254111yescharacteristic, complemented, Sylow
541C23—62no—
542C23—64no—
543C23—62no—
544C23—64no—
545C23—62no—
546C23—94no—
547C23—182no—
548C23—182no—
549C23—184no—
550C23—184no—
551C23—182no—
552C23—184no—
553C23—182no—
554C23—184no—
555C23—182no—
556C23C22×D3211yescharacteristic
557D4—124no—
558D4—188no—
559D4—3616no—
560D4—368no—
561D4—3616no—
562D4—368no—
563D4—364no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—32no—
567C2×C4—34no—
568C2×C4—32no—
569C2×C4—34no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—64no—
574C2×C4—62no—
575C2×C4—368no—
576C2×C4#379912yes—
577C2×C4D3×D1214yes—
578C2×C4D3×D1212yes—
579C2×C4#381112yes—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—242no—
586C2×C3C2×#87411yescharacteristic
587C2×C3C2×#88411yescharacteristic
588C2×C3C2×#89511yescharacteristic
589C2×C3#552511yescharacteristic
590C2×C3D4×D1212yes—
591C2×C3#555312yes—
592C2×C3#557712yes—
593C2×C3#560912yes—
594C2×C3#567411yescharacteristic
595C2×C3D3×#12711yescharacteristic
596D3—82no—
597D3—124no—
598D3—124no—
599D3—244no—
600D3—244no—
601D3—242no—
602D3—242no—
603C22—124no—
604C22—124no—
605C22—122no—
606C22—122no—
607C22—122no—
608C22—188no—
609C22—184no—
610C22—364no—
611C22—362no—
612C22—362no—
613C22—364no—
614C22—364no—
615C22—362no—
616C22—362no—
617C22—362no—
618C22C2×#379911yescharacteristic
619C22C2×D3×D1212yes—
620C22C2×D3×D1211yescharacteristic
621C22#6430812yes—
622C22C2×#381111yescharacteristic
623C4—24no—
624C4—34no—
625C4—64no—
626C4—62no—
627C4—122no—
628C4#6391014yescomplemented
629C3—21no—
630C3#7379911yescharacteristic, complemented
631C3#7634811yescharacteristic, complemented
632C2—242no—
633C2—364no—
634C2—722no—
635C2#1059390212yes—
636C2D3×#87411yescharacteristic
637C2#1059400111yescharacteristic
638C2C2×#6391011yescharacteristic
639C2#1059507412yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64083C2semidirect
2. C2×#63911C2semidirect
3. C2×#63911C2semidirect
4. C2×#63910C2semidirect
5. C2×#63894C2semidirect
6. C3×#4939C2semidirect
7. C3×C4×Dic3⋊C4C2semidirect
8. #10591395C2semidirect
9. #10591320C2semidirect
50. #4939D3semidirect
51. C4×Dic3⋊C4D3semidirect
66. C2×C4⋊(C3⋊D3)D4semidirect
86. C3×Dic3⋊C4D4semidirect
88. C3×C4×Dic3D4semidirect
276. Dic3⋊C4D12semidirect
278. C4×Dic3D12semidirect
300. C32×C4#121semidirect
304. C3×Dic3#127semidirect
534. C3×C4#884semidirect
535. C3×C4#895semidirect
539. Dic3#874semidirect
540. C32#2541semidirect
628. C4#63910semidirect
630. C3#73799semidirect
631. C3#76348semidirect

Maximal subgroups

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

subgroupindex
C2×#640832
C2×#639112
C2×#639102
C2×#638942
C3×#49392
C3×C4×Dic3⋊C42
#105913952
#105913202
#763483
#737993