Finite Group Databasebeta

← #11807606

Subgroups — #11807606

Order 1152.

1707 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic
2C3×#4951C212yesmaximal, complemented
3#10591722C211yesmaximal, characteristic, complemented
4#10591714C212yesmaximal, complemented
5#10591704C211yesmaximal, characteristic, complemented
6#10591380C212yesmaximal, complemented
7#10591320C212yesmaximal, complemented
8#10591266C212yesmaximal, complemented
9#10591202C212yesmaximal, complemented
10#75840—32nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C22×#638C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2212yes—
14C22×#624C2211yescharacteristic, complemented
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×#3752C2212yes—
17#64091C418yescomplemented
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×C4⋊Dic3C2212yescomplemented
21C2×C3×C4×Dic3C2212yescomplemented
22C2×#3724C2211yescharacteristic, complemented
23C2×#3722C2212yes—
24C2×#3722C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2211yescharacteristic, complemented
28C2×#3722C2212yescomplemented
29C2×Dic32C2211yescharacteristic, complemented
30C3×C3⋊#95C2212yescomplemented
31C3×C3⋊#95C2212yescomplemented
32#63579C2212yescomplemented
33C2×#882—32no—
34C2×#882—61no—
35C3×#388—32no—
36#4990—32no—
37#4988—32no—
38#4957—32no—
39#4956—32no—
40#4955—32no—
41#4955—32no—
42#4951D312yescomplemented
43#4940—32no—
44#4939—32no—
45#4670—32no—
46#4669—32no—
47#4665—32no—
48#4665—32no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3—42no—
51C23×C3⋊D3—42no—
52C23×C3⋊D3—41no—
53C23×C3⋊D3—41no—
54C23×C3⋊D3C2×C414yescomplemented
55C23×C3⋊D3C2311yescharacteristic
56C23×C3⋊D3C2312yes—
57C22×C32×C4C2312yes—
58C2×#638—41no—
59C2×#638—41no—
60C2×#638C2×C414yes—
61C22×C3⋊Dic3C2311yescharacteristic
62C2×C4⋊(C3⋊D3)—42no—
63C2×C4⋊(C3⋊D3)—42no—
64C2×C4⋊(C3⋊D3)C2×C418yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×#624—41no—
70C2×#624—42no—
71C32×C22⋊C4C2×C414yescomplemented
72#3752C2×C418yescomplemented
73C3×#217—42no—
74C3×#217—42no—
75C3×C4⋊Dic3—42no—
76C3×C4×Dic3—42no—
77#3724—41no—
78#3722—42no—
79#3722—42no—
80#3722—42no—
81#3722—42no—
82#3722—41no—
83#3722—42no—
84Dic32—41no—
85#2375—91noSylow
86C24×D3—32no—
87C24×D3—61no—
88C22×#67—32no—
89C22×#67—61no—
90C22×D12—32no—
91C22×D12—32no—
92C22×D12—62no—
93C22×C4×D3—32no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—32no—
97C2×C3×C22⋊C4—32no—
98C2×C3×C22⋊C4C2×D312yes—
99C2×C3×C42—32no—
100C2×#217C2×D312yes—
101C2×#217C2×D312yes—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—62no—
116C2×C4⋊Dic3C2×D312yescomplemented
117C2×Dic3⋊C4—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3C2×D312yescomplemented
120#882—316no—
121#882—68no—
122C3×#95—32no—
123C3×#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95C2×D312yescomplemented
127C3⋊#95C2×D312yescomplemented
128C23×C32—21no—
129C23×C32—21no—
130C23×C32—22no—
131C23×C32—22no—
132C23×C32C22×C412yes—
133C23×C32C2411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—21no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—48no—
145C22×C3⋊D3—44no—
146C22×C3⋊D3—44no—
147C22×C3⋊D3—48no—
148C22×C3⋊D3—44no—
149C22×C3⋊D3C22×C414yes—
150C22×C3⋊D3C22×C412yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C414yes—
154#638—44no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C22×C412yes—
158C4⋊(C3⋊D3)—48no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171#624—44no—
172C2×#120—91no—
173#390—92no—
174#390—91no—
175#388—32no—
176#388—92no—
177#388—92no—
178#386—92no—
179#386—91no—
180#379—92no—
181C24×C3—21no—
182C24×C3C22×D312yes—
183C23×D3—32no—
184C23×D3—32no—
185C23×D3—32no—
186C23×D3—38no—
187C23×D3—62no—
188C23×D3—64no—
189C23×D3—61no—
190C23×D3—122no—
191C23×D3—122no—
192C23×D3—122no—
193C23×D3—122no—
194C23×D3—122no—
195C23×D3—122no—
196C23×D3—124no—
197C23×D3—124no—
198C23×D3—122no—
199C23×D3—122no—
200C22×C3×C4—22no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4C22×D312yes—
206C22×C3×C4C22×D312yes—
207C2×#67—38no—
208C2×#67—64no—
209C2×#67—122no—
210C2×#67—122no—
211C2×#67—122no—
212C2×#67—122no—
213C22×Dic3—32no—
214C22×Dic3—61no—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C2×D12—38no—
220C2×D12—38no—
221C2×D12—68no—
222C2×D12—122no—
223C2×D12—122no—
224C2×D12—122no—
225C2×D12—122no—
226C2×D12—124no—
227C2×D12—124no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×C4×D3—122no—
231C3×C4⋊C4—122no—
232C3×C22⋊C4—24no—
233C3×C22⋊C4—122no—
234C3×C22⋊C4—122no—
235C3×C22⋊C4C4×D318yescomplemented
236C3×C42—122no—
237#217—42no—
238#217—42no—
239(C2×D3)⋊C4—38no—
240(C2×D3)⋊C4—38no—
241(C2×D3)⋊C4—68no—
242(C2×D3)⋊C4—122no—
243(C2×D3)⋊C4—122no—
244(C2×D3)⋊C4—122no—
245(C2×D3)⋊C4—122no—
246(C2×D3)⋊C4—122no—
247(C2×D3)⋊C4—122no—
248(C2×D3)⋊C4—122no—
249(C2×D3)⋊C4—122no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4—122no—
252(C2×D3)⋊C4—122no—
253C4⋊Dic3—42no—
254Dic3⋊C4—122no—
255C4×Dic3—42no—
256C4×Dic3—122no—
257C22×C32—22no—
258C22×C32—24no—
259C22×C32—41no—
260C22×C32—42no—
261C22×C32—41no—
262C22×C32C23×C411yescharacteristic
263C22×C32H(5,𝔽2)12yes—
264C22×C32H(5,𝔽2)12yes—
265C22×C32H(5,𝔽2)11yescharacteristic
266C22×C32H(5,𝔽2)11yescharacteristic
267C2×C3⋊D3—24no—
268C2×C3⋊D3—24no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—24no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3—416no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—41no—
280C32×C4—24no—
281C3⋊Dic3—22no—
282C3×Dic3—42no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C3×Dic3—42no—
286C25—91no—
287C22×D4—91no—
288C22×D4—92no—
289C23×C4—91no—
290#120—98no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—91no—
293C2×C22⋊C4—32no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C22⋊C4—92no—
301C2×C22⋊C4—91no—
302C2×C22⋊C4D3211yescharacteristic
303C2×C42—32no—
304C2×C42—91no—
305#95—32no—
306#95—32no—
307#95—92no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—22no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3C2×C4×D314yes—
321C23×C3C23×D312yes—
322C22×D3—34no—
323C22×D3—34no—
324C22×D3—34no—
325C22×D3—64no—
326C22×D3—62no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—122no—
352C22×D3—122no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—128no—
356C22×D3—128no—
357C22×D3—128no—
358C22×D3—1216no—
359C22×D3—128no—
360C22×D3—128no—
361C22×D3—1216no—
362C22×D3—128no—
363C22×D3—128no—
364C22×D3—128no—
365C22×D3—128no—
366C22×D3—128no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4C2×C4×D314yes—
387C2×C3×C4C2×C4×D314yes—
388#67—128no—
389#67—128no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—34no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408D12—128no—
409D12—128no—
410D12—1216no—
411C4×D3—128no—
412C2×C32—42no—
413C2×C32#51811yescharacteristic
414C2×C32#51812yes—
415C2×C32#56011yescharacteristic
416C2×C32#56012yes—
417C2×C32H(3,𝔽4)11yescharacteristic
418C3⋊D3—44no—
419C3⋊D3—42no—
420C24—92no—
421C24—91no—
422C24—94no—
423C24—361no—
424C24—361no—
425C24—362no—
426C24—362no—
427C24C2×D3211yescharacteristic
428C2×D4—94no—
429C2×D4—98no—
430C2×D4—362no—
431C2×D4—362no—
432C2×D4—361no—
433C2×D4—361no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—32no—
438C22×C4—91no—
439C22×C4—361no—
440C22×C4—362no—
441C22×C4C2×D3212yes—
442C4⋊C4—122no—
443C4⋊C4—361no—
444C22⋊C4—98no—
445C22⋊C4—122no—
446C22⋊C4—122no—
447C22⋊C4—362no—
448C22⋊C4—361no—
449C22⋊C4—362no—
450C22⋊C4—362no—
451C22⋊C4—362no—
452C22⋊C4—362no—
453C22⋊C4#62414yescomplemented
454C42—122no—
455C42—361no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—44no—
466C22×C3—42no—
467C22×C3—44no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3C22×C4×D312yes—
474C22×C3#100412yes—
475C22×C3#100412yes—
476C22×C3#100912yes—
477C22×C3#100912yes—
478C22×C3#100912yes—
479C22×C3#100912yes—
480C2×D3—68no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—64no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—124no—
491C2×D3—124no—
492C2×D3—124no—
493C2×D3—122no—
494C2×D3—124no—
495C2×D3—124no—
496C2×D3—124no—
497C2×D3—124no—
498C2×D3—1232no—
499C2×D3—1232no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—241no—
513C2×D3—242no—
514C2×D3—241no—
515C3×C4—24no—
516C3×C4—24no—
517C3×C4—44no—
518C3×C4—122no—
519C3×C4—122no—
520C3×C4—122no—
521C3×C4—122no—
522Dic3—42no—
523Dic3—42no—
524Dic3—42no—
525Dic3—42no—
526Dic3—64no—
527Dic3—122no—
528C32#237511yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—22no—
532C23—22no—
533C23—94no—
534C23—92no—
535C23—181no—
536C23—182no—
537C23—182no—
538C23—181no—
539C23—182no—
540C23—182no—
541C23—182no—
542C23—182no—
543C23—182no—
544C23—182no—
545C23—368no—
546C23—364no—
547C23—364no—
548C23—368no—
549C23—364no—
550C23C2×#62412yes—
551C23C22×D3211yescharacteristic
552D4—368no—
553D4—364no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—92no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4—364no—
572C2×C4C2×#62414yes—
573C2×C3—21no—
574C2×C3—22no—
575C2×C3—21no—
576C2×C3—22no—
577C2×C3—21no—
578C2×C3—44no—
579C2×C3—44no—
580C2×C3#552112yes—
581C2×C3#554512yes—
582C2×C3#554512yes—
583C2×C3#562012yes—
584C2×C3#566612yes—
585C2×C3#568312yes—
586C2×C3#571112yes—
587D3—128no—
588D3—124no—
589D3—124no—
590D3—124no—
591D3—242no—
592C22—24no—
593C22—22no—
594C22—41no—
595C22—42no—
596C22—41no—
597C22—184no—
598C22—184no—
599C22—184no—
600C22—182no—
601C22—184no—
602C22—3616no—
603C22—361no—
604C22—362no—
605C22—362no—
606C22—362no—
607C22—362no—
608C22—362no—
609C22—361no—
610C22#6430811yescharacteristic
611C22#6430811yescharacteristic
612C22#6431412yes—
613C22#6431412yes—
614C22C22×#62411yescharacteristic
615C4—24no—
616C4—122no—
617C4—122no—
618C4—122no—
619C4—122no—
620C4—182no—
621C3—21no—
622C3#7584012yescomplemented
623C2—42no—
624C2—364no—
625C2—362no—
626C2#1059424212yes—
627C2#1059424411yescharacteristic
628C2#1059431111yescharacteristic
629C2#1059499611yescharacteristic
630C2#1059522312yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64091C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4951C2semidirect
3. #10591722C2semidirect
4. #10591714C2semidirect
5. #10591704C2semidirect
6. #10591380C2semidirect
7. #10591320C2semidirect
8. #10591266C2semidirect
9. #10591202C2semidirect
14. C22×#624C22semidirect
17. #64091C4semidirect
20. C2×C3×C4⋊Dic3C22semidirect
21. C2×C3×C4×Dic3C22semidirect
22. C2×#3724C22semidirect
27. C2×#3722C22semidirect
28. C2×#3722C22semidirect
29. C2×Dic32C22semidirect
30. C3×C3⋊#95C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
42. #4951D3semidirect
54. C23×C3⋊D3C2×C4semidirect
71. C32×C22⋊C4C2×C4semidirect
72. #3752C2×C4semidirect
116. C2×C4⋊Dic3C2×D3semidirect
119. C2×C4×Dic3C2×D3semidirect
126. C3⋊#95C2×D3semidirect
127. C3⋊#95C2×D3semidirect
235. C3×C22⋊C4C4×D3semidirect
453. C22⋊C4#624semidirect
528. C32#2375semidirect
622. C3#75840semidirect

Maximal subgroups

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

subgroupindex
C2×#640912
C3×#49512
#105917222
#105917142
#105917042
#105913802
#105913202
#105912662
#105912022
#758403