Finite Group Databasebeta

← #11792446

Subgroups — #11792446

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3745C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#70209—31nomaximal
9#68674—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—22no—
14C22×C32×C8C2211yescharacteristic
15C2×#3745—22no—
16C2×#3745—22no—
17C2×#3745—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—22no—
22#63911—22no—
23#63911—22no—
24C2×#3714—22no—
25C2×#3714—22no—
26C2×#3714—22no—
27C3×#821—22no—
28#63564—22no—
29C2×#940—31no—
30C22×#213—31no—
31C22×D24—31no—
32C22×D24—31no—
33C22×D24—31no—
34C22×D24—61no—
35C2×#874—31no—
36C2×C3×#102—31no—
37C2×#821—31no—
38C2×#821D311yescharacteristic, complemented
39#4988—31no—
40C2×#809—31no—
41#4939—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C23×C3⋊D3—21no—
46C23×C3×D3—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)D412yes—
59C2×C4⋊(C3⋊D3)D412yescomplemented
60C22×C3×Dic3—21no—
61C22×C3×Dic3D412yes—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12D412yes—
68C2×#626—28no—
69C2×#626—44no—
70C2×#626—44no—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8D412yescomplemented
74#3745—28no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8D412yescomplemented
82#3722—44no—
83#3714—28no—
84#2011—91noSylow
85C22×C3×D4—31no—
86C22×#67—62no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—31no—
91C22×D12—61no—
92C22×D12—61no—
93C22×D12—62no—
94C22×D12C2×D311yescharacteristic
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C2×D311yescharacteristic
99C2×C3×C4⋊C4—31no—
100C2×C3×C42—31no—
101#940—62no—
102#940—62no—
103C2×#213—62no—
104C2×#213—62no—
105C2×#213—62no—
106C2×(C2×D3)⋊C4—62no—
107C2×(C2×D3)⋊C4—62no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×C4×Dic3C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111C2×D24—62no—
112C2×D24—62no—
113C2×D24—62no—
114C2×D24—62no—
115C2×D24—64no—
116C2×D24—64no—
117C2×D24—64no—
118C2×D24—62no—
119C2×D24—62no—
120C2×D24—62no—
121C2×D24—62no—
122C2×D24—62no—
123#874—62no—
124#874—62no—
125C3×#102—62no—
126#821—22no—
127#821—62no—
128#809—62no—
129C23×C32C2×D411yescharacteristic
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—41no—
135C22×C3⋊D3—41no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
140C22×C3×D3—22no—
141C22×C3×D3—41no—
142C22×C3×D3—41no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—41no—
156C4⋊(C3⋊D3)—41no—
157C4⋊(C3⋊D3)—41no—
158C4⋊(C3⋊D3)—41no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3D814yescomplemented
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—41no—
167C3×D12—41no—
168#626—416no—
169C32×C8—22no—
170C3×C3⋊C8—22no—
171C22×D8—91no—
172C22×D8—91no—
173C2×#127—91no—
174C2×#102—31no—
175C2×#102—91no—
176#390—91no—
177#336—31no—
178C24×C3—61no—
179C23×D3—21no—
180C23×D3—61no—
181C23×D3—61no—
182C23×D3—61no—
183C23×D3—61no—
184C23×D3—121no—
185C23×D3—121no—
186C2×C3×D4—32no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C22×C3×C4—21no—
193C22×C3×C4—32no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—68no—
198C2×#67—124no—
199C2×#67—124no—
200C22×Dic3—21no—
201C22×Dic3D1212yes—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—32no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—61no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—61no—
233C2×D12—68no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12—121no—
239C2×D12—121no—
240C2×D12—121no—
241C2×D12—121no—
242C2×D12—121no—
243C2×D12—121no—
244C2×D12—124no—
245C2×D12—124no—
246C2×D12D1212yes—
247C2×C3×C8—22no—
248C2×C3×C8—22no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—22no—
254C2×C3×C8—32no—
255C2×C3×C8—61no—
256C2×C3×C8—61no—
257C2×C3×C8D1212yescomplemented
258C2×C3×C8#6712yescomplemented
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C42—61no—
262C3×C42—61no—
263#213—68no—
264(C2×D3)⋊C4—124no—
265(C2×D3)⋊C4—124no—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C4×Dic3—21no—
269C4×Dic3—21no—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8D1212yescomplemented
273D24—616no—
274D24—68no—
275D24—68no—
276D24—68no—
277C22×C32#12011yescharacteristic
278C22×C32#12111yescharacteristic
279C22×C32#12711yescharacteristic
280C22×C32C2×D812yes—
281C22×C32AGL(1,ℤ/8)12yes—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—44no—
285C2×C3⋊D3—44no—
286C2×C3⋊D3—82no—
287C2×C3⋊D3—82no—
288C2×C3⋊D3—81no—
289C2×C3⋊D3—81no—
290C2×C3⋊D3—81no—
291C2×C3⋊D3—81no—
292C2×C3×D3—42no—
293C2×C3×D3—44no—
294C2×C3×D3—82no—
295C2×C3×D3—81no—
296C2×C3×D3—81no—
297C32×C4#12011yescharacteristic
298C32×C4#12011yescharacteristic
299C32×C4#12111yescharacteristic
300C32×C4#12111yescharacteristic
301C3×Dic3—24no—
302C3×Dic3—81no—
303C22×D4—31no—
304C22×D4—91no—
305C22×D4—91no—
306C22×D4—182no—
307C2×D8—182no—
308C2×D8—182no—
309C2×D8—182no—
310C2×D8—182no—
311C2×D8—182no—
312C2×D8—182no—
313C22×C8—31no—
314C22×C8D3211yescharacteristic
315#127—182no—
316#127—182no—
317C2×C4⋊C4—31no—
318C2×C22⋊C4—182no—
319C2×C42—31no—
320#102—62no—
321#102—182no—
322C23×C3—21no—
323C23×C3—62no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—122no—
327C23×C3—122no—
328C23×C3C2×D1211yescharacteristic
329C23×C3D3×D411yescharacteristic
330C22×D3—22no—
331C22×D3—41no—
332C22×D3—42no—
333C22×D3—42no—
334C22×D3—41no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—122no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—122no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—122no—
355C22×D3—122no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3—122no—
359C22×D3—121no—
360C22×D3—121no—
361C22×D3—242no—
362C22×D3—242no—
363C22×D3—242no—
364C22×D3—242no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—121no—
368C3×D4—121no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—34no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—121no—
379C2×C3×C4—122no—
380C2×C3×C4C2×D1211yescharacteristic
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4#23511yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4#23911yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392#67—1216no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—42no—
396C2×Dic3—41no—
397C2×Dic3D2414yescomplemented
398D12—22no—
399D12—22no—
400D12—41no—
401D12—41no—
402D12—64no—
403D12—64no—
404D12—62no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—62no—
409D12—62no—
410D12—62no—
411D12—62no—
412D12—122no—
413D12—122no—
414D12—122no—
415D12—122no—
416D12—122no—
417D12—122no—
418D12—1216no—
419D12—121no—
420D12—121no—
421D12—121no—
422D12—121no—
423D12—121no—
424D12—121no—
425D12—121no—
426D12—121no—
427C3×C8—24no—
428C3×C8—22no—
429C3×C8—22no—
430C3×C8—62no—
431C3⋊C8—22no—
432C2×C32#39211yescharacteristic
433C2×C32#44712yes—
434C2×C32#45912yes—
435C2×C32#49311yescharacteristic
436C2×C32#49611yescharacteristic
437C3⋊D3—82no—
438C3⋊D3—82no—
439C3×D3—82no—
440C24—61no—
441C24—181no—
442C24—181no—
443C2×D4—32no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—92no—
450C2×D4—92no—
451C2×D4—188no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4—181no—
455C2×D4—181no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—181no—
459C2×D4—181no—
460C2×D4—181no—
461C2×D4—181no—
462C2×D4—364no—
463C2×D4—364no—
464C22×C4—32no—
465C22×C4—61no—
466C22×C4C2×D3211yescharacteristic
467D8—188no—
468D8—188no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—32no—
472C2×C8—61no—
473C2×C8—61no—
474C2×C8#62612yescomplemented
475C4⋊C4—61no—
476C4⋊C4—61no—
477C22⋊C4—364no—
478C42—61no—
479C42—61no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—122no—
486C22×C3—124no—
487C22×C3—241no—
488C22×C3—241no—
489C22×C3—242no—
490C22×C3#87411yescharacteristic
491C22×C3#88211yescharacteristic
492C22×C3#88211yescharacteristic
493C22×C3#88411yescharacteristic
494C22×C3#89511yescharacteristic
495C22×C3C2×D2412yes—
496C22×C3#90812yes—
497C22×C3D3×D812yes—
498C22×C3#91412yes—
499C22×C3#94011yescharacteristic
500C2×D3—42no—
501C2×D3—44no—
502C2×D3—81no—
503C2×D3—81no—
504C2×D3—82no—
505C2×D3—124no—
506C2×D3—124no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—124no—
512C2×D3—124no—
513C2×D3—124no—
514C2×D3—124no—
515C2×D3—244no—
516C2×D3—244no—
517C2×D3—244no—
518C2×D3—242no—
519C2×D3—242no—
520C2×D3—242no—
521C2×D3—242no—
522C2×D3—244no—
523C2×D3—241no—
524C2×D3—241no—
525C2×D3—241no—
526C2×D3—241no—
527C2×D3—241no—
528C2×D3—241no—
529C2×D3—241no—
530C2×D3—241no—
531C2×D3—242no—
532C2×D3—242no—
533C2×D3—242no—
534C2×D3—242no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—64no—
540C3×C4—241no—
541C3×C4#88211yescharacteristic
542C3×C4#88211yescharacteristic
543C3×C4#88211yescharacteristic
544C3×C4#88411yescharacteristic
545C3×C4#89511yescharacteristic
546C3×C4#89511yescharacteristic
547C3×C4#93011yescharacteristic
548C3×C4#93711yescharacteristic
549Dic3—24no—
550Dic3—81no—
551C32#201111yescharacteristic, complemented, Sylow
552C23—62no—
553C23—122no—
554C23—122no—
555C23—121no—
556C23—121no—
557C23—182no—
558C23—182no—
559C23—362no—
560C23—362no—
561C23—362no—
562C23—362no—
563C23—361no—
564C23—361no—
565C23—361no—
566C23—361no—
567C23D3×D1211yescharacteristic
568D4—62no—
569D4—62no—
570D4—121no—
571D4—121no—
572D4—182no—
573D4—182no—
574D4—182no—
575D4—182no—
576D4—3616no—
577D4—361no—
578D4—361no—
579D4—361no—
580D4—361no—
581C2×C4—34no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—122no—
585C2×C4—121no—
586C2×C4#379911yescharacteristic
587C2×C4D3×D1211yescharacteristic
588C2×C4D3×D1211yescharacteristic
589C2×C4C2×#62611yescharacteristic
590C2×C4#381111yescharacteristic
591C2×C4#381111yescharacteristic
592C8—22no—
593C8—62no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—22no—
599C2×C3—242no—
600C2×C3#467111yescharacteristic
601C2×C3#469511yescharacteristic
602C2×C3#471211yescharacteristic
603C2×C3#473212yes—
604C2×C3#477312yes—
605C2×C3#478612yes—
606C2×C3#484312yes—
607C2×C3#496011yescharacteristic
608C2×C3#515111yescharacteristic
609C2×C3#517611yescharacteristic
610D3—82no—
611D3—244no—
612D3—244no—
613D3—242no—
614D3—242no—
615D3—242no—
616D3—242no—
617C22—122no—
618C22—124no—
619C22—242no—
620C22—241no—
621C22—241no—
622C22—364no—
623C22—362no—
624C22—362no—
625C22—364no—
626C22—722no—
627C22—721no—
628C22—721no—
629C22—721no—
630C22—721no—
631C22—722no—
632C22D3×D2412yes—
633C22#6379412yes—
634C22#6391011yescharacteristic
635C22#6391111yescharacteristic
636C22#6392311yescharacteristic
637C4—64no—
638C4—241no—
639C4#6390911yescharacteristic
640C4#6391011yescharacteristic
641C4#6392311yescharacteristic
642C4#6398111yescharacteristic
643C3—21no—
644C3#6867411yescharacteristic, complemented
645C3#7020911yescharacteristic, complemented
646C2—242no—
647C2—722no—
648C2—722no—
649C2#1059076512yes—
650C2#1059088011yescharacteristic
651C2#1059088111yescharacteristic
652C2#1059094712yes—
653C2#1059139511yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32#2011
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3745C2semidirect
2. C2×#63911C2semidirect
3. C22×#3714C2semidirect
4. C2×C3×#821C2semidirect
5. #10591320C2semidirect
6. C2×#63564C2semidirect
7. C3×#4550C2semidirect
38. C2×#821D3semidirect
43. #4550D3semidirect
59. C2×C4⋊(C3⋊D3)D4semidirect
73. C2×C32×C8D4semidirect
81. C2×C3×C3⋊C8D4semidirect
163. C2×C3×Dic3D8semidirect
257. C2×C3×C8D12semidirect
258. C2×C3×C8#67semidirect
272. C2×C3⋊C8D12semidirect
397. C2×Dic3D24semidirect
474. C2×C8#626semidirect
551. C32#2011semidirect
644. C3#68674semidirect
645. C3#70209semidirect

Maximal subgroups

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

subgroupindex
C22×#37452
C2×#639112
C22×#37142
C2×C3×#8212
#105913202
C2×#635642
C3×#45502
#702093
#686743