Finite Group Databasebeta

← #11792556

Subgroups — #11792556

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71768—31nomaximal
9#70210—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×#67—22no—
13C22×C3×D12C2211yescharacteristic
14C2×#3754—22no—
15C2×#3754—22no—
16C2×#3754—22no—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#940—22no—
19C3×#940—22no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3716—22no—
24C2×#3716—22no—
25C2×#3716—22no—
26C3×#832—22no—
27#63579—22no—
28#63562—22no—
29C2×C3×#127—31no—
30C2×#940D311yescharacteristic
31C22×#214—31no—
32C22×#214—31no—
33C22×#214—31no—
34C22×#214—61no—
35C22×#204—31no—
36C2×C3×#102—31no—
37C2×#832—31no—
38C2×#832D311yescharacteristic, complemented
39#4973—31no—
40C2×#809—31no—
41#4929—31no—
42#4550—31no—
43#4524—31no—
44C24×C32—21no—
45C23×C3×D3—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4D412yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634D412yescomplemented
60C2×C3×#67—28no—
61C2×C3×#67—44no—
62C2×C3×#67—44no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3D412yes—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12D412yes—
71#3754—28no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)D412yescomplemented
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#3716—28no—
83#2014—91noSylow
84C22×C3×D4—21no—
85C22×C3×D4—31no—
86C22×C3×D4—62no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×#67—22no—
90C22×D12C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×C3×C8—31no—
95C3×#127—62no—
96C3×#127—62no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C42—31no—
99#940—22no—
100#940—22no—
101C2×#214—62no—
102C2×#214—62no—
103C2×#214—62no—
104C2×#214—62no—
105C2×#214—62no—
106C2×#214—62no—
107C2×#214—64no—
108C2×#214—64no—
109C2×#214—64no—
110C2×#214—62no—
111C2×#214—62no—
112C2×#214—62no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×C4×Dic3C2×D311yescharacteristic
115C22×C3⋊C8—31no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—61no—
118C22×C3⋊C8C2×D311yescharacteristic
119C2×#204—62no—
120C2×#204—62no—
121C2×#204—62no—
122C3×#102—62no—
123#832—22no—
124#832—62no—
125C3⋊#95—62no—
126C3⋊#95—62no—
127#809—62no—
128C23×C32—22no—
129C23×C32—41no—
130C23×C32—41no—
131C23×C32—42no—
132C23×C32—42no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C32×D4—22no—
140C32×D4—22no—
141C32×D4—41no—
142C32×D4—41no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3—41no—
152#634—22no—
153#634—22no—
154#634—41no—
155#634—41no—
156C3×#67—416no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3SD1614yescomplemented
162C3×D12—22no—
163C3×D12—22no—
164C3×D12—41no—
165C3×D12—41no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C22×SD16—91no—
169C22×SD16—91no—
170C2×#127—31no—
171C2×#102—31no—
172C2×#102—91no—
173#391—91no—
174#336—91no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—41no—
178C24×C3—61no—
179C23×D3—21no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—32no—
194C2×C3×D4—41no—
195C2×C3×D4—41no—
196C2×C3×D4—41no—
197C2×C3×D4—68no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4—61no—
202C2×C3×D4—61no—
203C2×C3×D4—124no—
204C2×C3×D4—124no—
205C2×C3×D4D1212yes—
206C2×C3×D4#6712yes—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4—61no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—28no—
213C2×#67—44no—
214C2×#67—44no—
215C22×Dic3—21no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—121no—
219C22×Dic3#6712yes—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12#6712yes—
226C2×Dic6—32no—
227C2×Dic6—32no—
228C2×Dic6—62no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6—61no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—121no—
242C2×Dic6—121no—
243C2×Dic6—121no—
244C2×C3×C8—32no—
245C2×C3×C8—61no—
246C2×C3×C8—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C42—61no—
250C3×C42—61no—
251#214—68no—
252#214—616no—
253#214—68no—
254#214—68no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4×Dic3—21no—
258C4×Dic3—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8#6712yescomplemented
271#204—68no—
272C22×C32—42no—
273C22×C32—44no—
274C22×C32—82no—
275C22×C32—81no—
276C22×C32—81no—
277C22×C32#12011yescharacteristic
278C22×C32#12111yescharacteristic
279C22×C32#12711yescharacteristic
280C22×C32C2×SD1612yes—
281C22×C32AGL(1,ℤ/8)12yes—
282C2×C3×D3—42no—
283C2×C3×D3—44no—
284C2×C3×D3—82no—
285C2×C3×D3—81no—
286C2×C3×D3—81no—
287C32×C4#12011yescharacteristic
288C32×C4#12011yescharacteristic
289C32×C4#12111yescharacteristic
290C32×C4#12111yescharacteristic
291C3⋊Dic3—42no—
292C3×Dic3—24no—
293C3×Dic3—81no—
294C22×Q8—91no—
295C22×D4—31no—
296C22×D4—62no—
297C22×D4D3211yescharacteristic
298C2×SD16—182no—
299C2×SD16—182no—
300C2×SD16—182no—
301C2×SD16—182no—
302C2×SD16—182no—
303C2×SD16—182no—
304C22×C8—31no—
305C22×C8—91no—
306#127—62no—
307#127—62no—
308C2×C4⋊C4—31no—
309C2×C42—31no—
310#102—62no—
311#102—182no—
312#95—182no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—21no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—41no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—62no—
328C23×C3—82no—
329C23×C3—82no—
330C23×C3—121no—
331C23×C3—122no—
332C23×C3—122no—
333C23×C3—121no—
334C23×C3D3×D411yescharacteristic
335C23×C3C2×#6711yescharacteristic
336C22×D3—22no—
337C22×D3—42no—
338C22×D3—42no—
339C22×D3—41no—
340C22×D3—41no—
341C3×D4—24no—
342C3×D4—22no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—22no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—41no—
350C3×D4—41no—
351C3×D4—41no—
352C3×D4—41no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—1216no—
356C3×D4—121no—
357C3×D4—121no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—34no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—122no—
368C2×C3×C4—121no—
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4#23511yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4#23711yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381#67—416no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—42no—
385C2×Dic3—41no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390C2×Dic3—122no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3#21414yescomplemented
396D12—22no—
397D12—22no—
398D12—41no—
399D12—41no—
400Dic6—64no—
401Dic6—62no—
402Dic6—62no—
403Dic6—62no—
404Dic6—62no—
405Dic6—122no—
406Dic6—122no—
407Dic6—122no—
408Dic6—121no—
409Dic6—121no—
410Dic6—121no—
411Dic6—121no—
412C3×C8—62no—
413C3⋊C8—22no—
414C3⋊C8—64no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C2×C32—82no—
418C2×C32#39211yescharacteristic
419C2×C32#45012yes—
420C2×C32#46012yes—
421C2×C32#49211yescharacteristic
422C2×C32#49611yescharacteristic
423C3×D3—82no—
424C24—21no—
425C24—61no—
426C2×Q8—92no—
427C2×Q8—181no—
428C2×Q8—181no—
429C2×Q8—181no—
430C2×Q8—181no—
431C2×Q8—181no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—32no—
438C2×D4—68no—
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—124no—
445C2×D4—124no—
446C2×D4#62612yes—
447C22×C4—32no—
448C22×C4—61no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451SD16—188no—
452SD16—188no—
453C2×C8—32no—
454C2×C8—61no—
455C2×C8—61no—
456C2×C8—92no—
457C2×C8—181no—
458C2×C8—181no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C42—61no—
462C42—61no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—44no—
469C22×C3—42no—
470C22×C3—44no—
471C22×C3—42no—
472C22×C3—44no—
473C22×C3—84no—
474C22×C3—82no—
475C22×C3—84no—
476C22×C3—82no—
477C22×C3—81no—
478C22×C3—81no—
479C22×C3—82no—
480C22×C3—81no—
481C22×C3—82no—
482C22×C3—81no—
483C22×C3—122no—
484C22×C3—124no—
485C22×C3—241no—
486C22×C3—241no—
487C22×C3—242no—
488C22×C3#88211yescharacteristic
489C22×C3#88411yescharacteristic
490C22×C3#91112yes—
491C22×C3D3×SD1612yes—
492C22×C3#93212yes—
493C22×C3C2×#21412yes—
494C22×C3#93811yescharacteristic
495C22×C3#94011yescharacteristic
496C22×C3#94011yescharacteristic
497C22×C3#95311yescharacteristic
498C2×D3—44no—
499C2×D3—42no—
500C2×D3—81no—
501C2×D3—82no—
502C2×D3—81no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—64no—
508C3×C4—241no—
509C3×C4#88211yescharacteristic
510C3×C4#88411yescharacteristic
511C3×C4#93011yescharacteristic
512C3×C4#93711yescharacteristic
513C3×C4#93711yescharacteristic
514C3×C4#93711yescharacteristic
515C3×C4#93911yescharacteristic
516C3×C4#93911yescharacteristic
517Dic3—24no—
518Dic3—81no—
519Dic3—124no—
520Dic3—122no—
521Dic3—122no—
522C32#201411yescharacteristic, complemented, Sylow
523C23—22no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—62no—
529C23—122no—
530C23—122no—
531C23—121no—
532C23—121no—
533C23D3×#6711yescharacteristic
534Q8—182no—
535Q8—182no—
536Q8—361no—
537Q8—361no—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542D4—62no—
543D4—62no—
544D4—1216no—
545D4—121no—
546D4—121no—
547C2×C4—34no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—122no—
551C2×C4—121no—
552C2×C4—182no—
553C2×C4—361no—
554C2×C4—361no—
555C2×C4#380411yescharacteristic
556C2×C4C2×#62611yescharacteristic
557C2×C4D3×#6711yescharacteristic
558C2×C4D3×#6711yescharacteristic
559C2×C4#381111yescharacteristic
560C2×C4#381111yescharacteristic
561C8—62no—
562C8—182no—
563C2×C3—21no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—84no—
569C2×C3—82no—
570C2×C3—82no—
571C2×C3—242no—
572C2×C3#476212yes—
573C2×C3#477612yes—
574C2×C3#496011yescharacteristic
575C2×C3#507411yescharacteristic
576C2×C3#507512yes—
577C2×C3#507611yescharacteristic
578C2×C3#515411yescharacteristic
579C2×C3#517511yescharacteristic
580C2×C3#521812yes—
581C2×C3#522311yescharacteristic
582D3—82no—
583C22—44no—
584C22—42no—
585C22—81no—
586C22—82no—
587C22—81no—
588C22—124no—
589C22—122no—
590C22—241no—
591C22—242no—
592C22—241no—
593C22D3×#21412yes—
594C22#6393212yes—
595C22#6395811yescharacteristic
596C22#6397711yescharacteristic
597C22#6397911yescharacteristic
598C4—64no—
599C4—241no—
600C4—362no—
601C4#6397111yescharacteristic
602C4#6397811yescharacteristic
603C4#6398111yescharacteristic
604C4#6398311yescharacteristic
605C3—21no—
606C3#7021011yescharacteristic, complemented
607C3#7176811yescharacteristic, complemented
608C2—82no—
609C2—242no—
610C2#1059143912yes—
611C2#1059145912yes—
612C2#1059146911yescharacteristic
613C2#1059149011yescharacteristic
614C2#1059172411yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32#2014
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3754C2semidirect
3. C22×#3716C2semidirect
4. C2×C3×#832C2semidirect
5. #10591213C2semidirect
6. C2×#63562C2semidirect
7. #10589155C2semidirect
38. C2×#832D3semidirect
59. C2×#634D4semidirect
74. C2×C3⋊(C3⋊C8)D4semidirect
81. C2×C3×C3⋊C8D4semidirect
161. C2×C3×Dic3SD16semidirect
270. C2×C3⋊C8#67semidirect
395. C2×Dic3#214semidirect
522. C32#2014semidirect
606. C3#70210semidirect
607. C3#71768semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×#9402
C22×#37162
C2×C3×#8322
#105912132
C2×#635622
#105891552
#717683
#702103