Finite Group Databasebeta

← #11792559

Subgroups — #11792559

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×#3744C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#70210—31nomaximal
9#68676—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—22no—
14C22×C32×C8C2211yescharacteristic
15C2×#3744—22no—
16C2×#3744—22no—
17C2×#3744—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63911—22no—
22#63911—22no—
23C2×#3716—22no—
24C2×#3716—22no—
25C2×#3716—22no—
26C3×#821—22no—
27#63579—22no—
28#63564—22no—
29C2×#940—31no—
30C22×#214—31no—
31C22×#204—31no—
32C22×#204—31no—
33C22×#204—31no—
34C22×#204—61no—
35C2×#874—31no—
36C2×C3×#102—31no—
37C2×#821—31no—
38C2×#821D311yescharacteristic, complemented
39#4973—31no—
40C2×#809—31no—
41#4929—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
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)D412yes—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634D412yescomplemented
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#3744—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#3716—28no—
83#2014—91noSylow
84C22×C3×D4—31no—
85C22×#67—62no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×D12—62no—
90C22×D12C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×C3×C8—21no—
95C22×C3×C8—31no—
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C2×D311yescharacteristic
98C2×C3×C4⋊C4—31no—
99C2×C3×C42—31no—
100#940—62no—
101#940—62no—
102C2×#214—62no—
103C2×#214—62no—
104C2×#214—62no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4×Dic3C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×#204—62no—
109C2×#204—62no—
110C2×#204—62no—
111C2×#204—62no—
112C2×#204—64no—
113C2×#204—64no—
114C2×#204—64no—
115C2×#204—62no—
116C2×#204—62no—
117C2×#204—62no—
118C2×#204—62no—
119C2×#204—62no—
120#874—62no—
121#874—62no—
122C3×#102—62no—
123C3⋊#95—62no—
124C3⋊#95—62no—
125#821—22no—
126#821—62no—
127#809—62no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—42no—
134C22×C3×D3—22no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—41no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—41no—
151C4⋊(C3⋊D3)—41no—
152#634—22no—
153#634—22no—
154#634—41no—
155#634—41no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3SD1614yescomplemented
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—41no—
164C3×D12—41no—
165#626—416no—
166C32×C8—22no—
167C3×C3⋊C8—22no—
168C22×SD16—91no—
169C22×SD16—91no—
170C2×#127—91no—
171C2×#102—31no—
172C2×#102—91no—
173#391—91no—
174#336—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C2×C3×D4—32no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—68no—
192C2×#67—124no—
193C2×#67—124no—
194C22×Dic3—21no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—121no—
198C22×Dic3D1212yes—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—68no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—121no—
221C2×D12—121no—
222C2×D12—121no—
223C2×D12—124no—
224C2×D12—124no—
225C2×D12D1212yes—
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—22no—
245C2×C3×C8—22no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—22no—
251C2×C3×C8—32no—
252C2×C3×C8—61no—
253C2×C3×C8—61no—
254C2×C3×C8D1212yescomplemented
255C2×C3×C8#6712yescomplemented
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C42—61no—
259C3×C42—61no—
260#214—68no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4×Dic3—21no—
264C4×Dic3—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8D1212yescomplemented
268#204—616no—
269#204—68no—
270#204—68no—
271#204—68no—
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32#12711yescharacteristic
275C22×C32C2×SD1612yes—
276C22×C32AGL(1,ℤ/8)12yes—
277C2×C3⋊D3—42no—
278C2×C3⋊D3—44no—
279C2×C3⋊D3—82no—
280C2×C3⋊D3—81no—
281C2×C3⋊D3—81no—
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—91no—
297C22×D4—182no—
298C2×SD16—182no—
299C2×SD16—182no—
300C2×SD16—182no—
301C2×SD16—182no—
302C2×SD16—182no—
303C2×SD16—182no—
304C22×C8—31no—
305C22×C8D3211yescharacteristic
306#127—182no—
307#127—182no—
308C2×C4⋊C4—31no—
309C2×C42—31no—
310#102—62no—
311#102—182no—
312#95—182no—
313C23×C3—21no—
314C23×C3—62no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—122no—
318C23×C3—122no—
319C23×C3C2×D1211yescharacteristic
320C23×C3D3×D411yescharacteristic
321C22×D3—22no—
322C22×D3—41no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3—41no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—121no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C22×D3—121no—
339C22×D3—242no—
340C22×D3—242no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—121no—
344C3×D4—121no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—34no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—121no—
355C2×C3×C4—122no—
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4#23511yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4#23911yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368#67—1216no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—42no—
372C2×Dic3—41no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3#20414yescomplemented
383D12—22no—
384D12—22no—
385D12—41no—
386D12—41no—
387D12—64no—
388D12—62no—
389D12—62no—
390D12—62no—
391D12—62no—
392D12—122no—
393D12—122no—
394D12—122no—
395D12—1216no—
396D12—121no—
397D12—121no—
398D12—121no—
399D12—121no—
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—24no—
413C3×C8—22no—
414C3×C8—22no—
415C3×C8—62no—
416C3⋊C8—22no—
417C2×C32#39211yescharacteristic
418C2×C32#45012yes—
419C2×C32#46012yes—
420C2×C32#49211yescharacteristic
421C2×C32#49611yescharacteristic
422C3⋊D3—82no—
423C3×D3—82no—
424C24—61no—
425C24—181no—
426C2×Q8—92no—
427C2×Q8—181no—
428C2×Q8—181no—
429C2×Q8—181no—
430C2×Q8—181no—
431C2×Q8—181no—
432C2×D4—32no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—92no—
439C2×D4—188no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4—181no—
443C2×D4—181no—
444C2×D4—181no—
445C2×D4—364no—
446C2×D4—364no—
447C22×C4—32no—
448C22×C4—61no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451SD16—188no—
452SD16—188no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—32no—
456C2×C8—61no—
457C2×C8—61no—
458C2×C8#62612yescomplemented
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—122no—
469C22×C3—124no—
470C22×C3—241no—
471C22×C3—241no—
472C22×C3—242no—
473C22×C3#87411yescharacteristic
474C22×C3#88211yescharacteristic
475C22×C3#88211yescharacteristic
476C22×C3#88411yescharacteristic
477C22×C3#89511yescharacteristic
478C22×C3C2×#20412yes—
479C22×C3#90812yes—
480C22×C3#91112yes—
481C22×C3D3×SD1612yes—
482C22×C3#94011yescharacteristic
483C2×D3—42no—
484C2×D3—44no—
485C2×D3—81no—
486C2×D3—81no—
487C2×D3—82no—
488C2×D3—124no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—124no—
492C2×D3—124no—
493C2×D3—244no—
494C2×D3—242no—
495C2×D3—244no—
496C2×D3—242no—
497C2×D3—241no—
498C2×D3—241no—
499C2×D3—241no—
500C2×D3—241no—
501C2×D3—242no—
502C2×D3—242no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—64no—
508C3×C4—241no—
509C3×C4#88211yescharacteristic
510C3×C4#88211yescharacteristic
511C3×C4#88211yescharacteristic
512C3×C4#88411yescharacteristic
513C3×C4#89511yescharacteristic
514C3×C4#89511yescharacteristic
515C3×C4#93011yescharacteristic
516C3×C4#93711yescharacteristic
517Dic3—24no—
518Dic3—81no—
519Dic3—124no—
520Dic3—122no—
521Dic3—122no—
522C32#201411yescharacteristic, complemented, Sylow
523C23—62no—
524C23—122no—
525C23—122no—
526C23—121no—
527C23—121no—
528C23—182no—
529C23—362no—
530C23—362no—
531C23—361no—
532C23—361no—
533C23D3×D1211yescharacteristic
534Q8—182no—
535Q8—182no—
536Q8—361no—
537Q8—361no—
538D4—62no—
539D4—62no—
540D4—121no—
541D4—121no—
542D4—182no—
543D4—182no—
544D4—3616no—
545D4—361no—
546D4—361no—
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#379911yescharacteristic
556C2×C4D3×D1211yescharacteristic
557C2×C4D3×D1211yescharacteristic
558C2×C4C2×#62611yescharacteristic
559C2×C4#381111yescharacteristic
560C2×C4#381111yescharacteristic
561C8—22no—
562C8—62no—
563C2×C3—21no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—22no—
568C2×C3—242no—
569C2×C3#467111yescharacteristic
570C2×C3#469311yescharacteristic
571C2×C3#471211yescharacteristic
572C2×C3#473112yes—
573C2×C3#476212yes—
574C2×C3#477612yes—
575C2×C3#484812yes—
576C2×C3#496011yescharacteristic
577C2×C3#515411yescharacteristic
578C2×C3#517511yescharacteristic
579D3—82no—
580D3—244no—
581D3—242no—
582D3—242no—
583C22—122no—
584C22—124no—
585C22—241no—
586C22—242no—
587C22—241no—
588C22—362no—
589C22—364no—
590C22—721no—
591C22—722no—
592C22—721no—
593C22D3×#20412yes—
594C22#6379512yes—
595C22#6391011yescharacteristic
596C22#6391111yescharacteristic
597C22#6392311yescharacteristic
598C4—64no—
599C4—241no—
600C4—362no—
601C4#6390911yescharacteristic
602C4#6391011yescharacteristic
603C4#6392311yescharacteristic
604C4#6398111yescharacteristic
605C3—21no—
606C3#6867611yescharacteristic, complemented
607C3#7021011yescharacteristic, complemented
608C2—242no—
609C2—722no—
610C2#1059087711yescharacteristic
611C2#1059087912yes—
612C2#1059088311yescharacteristic
613C2#1059094612yes—
614C2#1059139511yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC22×C8D32
hypocenterC32#2014
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×#3744C2semidirect
3. C22×#3716C2semidirect
4. C2×C3×#821C2semidirect
5. #10591213C2semidirect
6. C2×#63564C2semidirect
7. C3×#4550C2semidirect
38. C2×#821D3semidirect
43. #4550D3semidirect
59. C2×#634D4semidirect
73. C2×C32×C8D4semidirect
81. C2×C3×C3⋊C8D4semidirect
160. C2×C3×Dic3SD16semidirect
254. C2×C3×C8D12semidirect
255. C2×C3×C8#67semidirect
267. C2×C3⋊C8D12semidirect
382. C2×Dic3#204semidirect
458. C2×C8#626semidirect
522. C32#2014semidirect
606. C3#68676semidirect
607. C3#70210semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#639112
C22×#37162
C2×C3×#8212
#105912132
C2×#635642
C3×#45502
#702103
#686763