Finite Group Databasebeta

← #11792554

Subgroups — #11792554

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×#3755C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63911C211yesmaximal, characteristic
4C3×#5229C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72056—31nomaximal
9#69688—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—22no—
14C2×#3755—22no—
15C2×#3755—22no—
16C2×#3755—22no—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#215—22no—
19C2×C3×#215—22no—
20C2×C3×#215—22no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24#63911—22no—
25#63911—22no—
26C3×C3⋊#95—22no—
27#63564—22no—
28#63562—22no—
29C22×C3×SD16—31no—
30C22×#215—31no—
31C22×#215—31no—
32C22×#215—61no—
33C22×#215D311yescharacteristic, complemented
34C2×#940—31no—
35C2×#874—31no—
36C3×#391—31no—
37#5229D311yescharacteristic, complemented
38C2×#832—31no—
39C2×#821—31no—
40C2×#809—31no—
41C2×#809—31no—
42#4550—31no—
43#4524—31no—
44C23×C3⋊D3—21no—
45C23×C3×D3—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8D412yescomplemented
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)D412yes—
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—
71#3755—28no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)D412yescomplemented
75C3×#215—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yescomplemented
83#2014—91noSylow
84C22×C3×Q8—21no—
85C22×C3×Q8C2×D311yescharacteristic
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×D4—31no—
88C22×#67—62no—
89C22×D12—31no—
90C22×D12—31no—
91C22×D12—61no—
92C22×D12—62no—
93C22×D12C2×D311yescharacteristic
94C2×C3×SD16—62no—
95C2×C3×SD16—62no—
96C2×C3×SD16—62no—
97C22×C3×C8—31no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C42—31no—
100C2×#215—22no—
101C2×#215—22no—
102C2×#215—22no—
103C2×#215—62no—
104C2×#215—62no—
105C2×#215—62no—
106C2×#215—62no—
107C2×#215—64no—
108C2×#215—64no—
109C2×#215—64no—
110C2×#215—62no—
111C2×#215—62no—
112#940—62no—
113#940—62no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×C4×Dic3C2×D311yescharacteristic
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—61no—
119C22×C3⋊C8C2×D311yescharacteristic
120#874—62no—
121#874—62no—
122C3×#95—62no—
123#832—62no—
124C3⋊#95—22no—
125#821—62no—
126#809—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—
139C32×Q8—22no—
140C32×Q8—22no—
141C32×Q8—41no—
142C32×Q8—41no—
143C2×C32×C4—22no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—41no—
155C4⋊(C3⋊D3)—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—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C22×SD16—31no—
169C22×SD16—91no—
170C2×#127—91no—
171C2×#102—91no—
172C2×#102—91no—
173#391—31no—
174#336—91no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—22no—
193C2×C3×Q8—41no—
194C2×C3×Q8—41no—
195C2×C3×Q8—41no—
196C2×C3×Q8D1212yescomplemented
197C2×C3×Q8#6712yescomplemented
198C2×C3×D4—32no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4—61no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—32no—
208C22×C3×C4—41no—
209C22×C3×C4—61no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—68no—
213C2×#67—124no—
214C2×#67—124no—
215C22×Dic3—21no—
216C22×Dic3#6712yes—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—32no—
223C2×D12—32no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—62no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—61no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—61no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—68no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12—121no—
239C2×D12—121no—
240C2×D12—121no—
241C2×D12—124no—
242C2×D12—124no—
243C2×D12#6712yes—
244C3×SD16—68no—
245C2×C3×C8—32no—
246C2×C3×C8—61no—
247C2×C3×C8—61no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C42—61no—
251C3×C42—61no—
252#215—28no—
253#215—616no—
254#215—68no—
255#215—68no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8#6712yescomplemented
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—42no—
288C32×C4#12011yescharacteristic
289C32×C4#12011yescharacteristic
290C32×C4#12111yescharacteristic
291C32×C4#12111yescharacteristic
292C3×Dic3—24no—
293C3×Dic3—81no—
294C22×Q8D3211yescharacteristic
295C22×D4—31no—
296C22×D4—91no—
297C22×D4—182no—
298C2×SD16—62no—
299C2×SD16—62no—
300C2×SD16—62no—
301C2×SD16—182no—
302C2×SD16—182no—
303C2×SD16—182no—
304C22×C8—31no—
305C22×C8—91no—
306#127—182no—
307#127—182no—
308C2×C4⋊C4—31no—
309C2×C42—31no—
310#102—182no—
311#102—182no—
312#95—62no—
313C23×C3—21no—
314C23×C3—62no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—122no—
318C23×C3—122no—
319C23×C3D3×D411yescharacteristic
320C23×C3C2×#6711yescharacteristic
321C22×D3—22no—
322C22×D3—42no—
323C22×D3—42no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—122no—
331C22×D3—122no—
332C22×D3—122no—
333C22×D3—121no—
334C22×D3—121no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—122no—
338C22×D3—122no—
339C22×D3—242no—
340C22×D3—242no—
341C3×Q8—24no—
342C3×Q8—22no—
343C3×Q8—22no—
344C3×Q8—22no—
345C3×Q8—22no—
346C3×Q8—42no—
347C3×Q8—42no—
348C3×Q8—42no—
349C3×Q8—41no—
350C3×Q8—41no—
351C3×Q8—41no—
352C3×Q8—41no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—121no—
356C3×D4—121no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—34no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—122no—
376C2×C3×C4—121no—
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4#23511yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23711yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389#67—1216no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—41no—
393C2×Dic3—42no—
394C2×Dic3#21514yescomplemented
395D12—22no—
396D12—22no—
397D12—41no—
398D12—41no—
399D12—64no—
400D12—62no—
401D12—62no—
402D12—62no—
403D12—62no—
404D12—122no—
405D12—122no—
406D12—122no—
407D12—1216no—
408D12—121no—
409D12—121no—
410D12—121no—
411D12—121no—
412C3×C8—62no—
413C3⋊C8—22no—
414C3⋊C8—64no—
415C3⋊C8—62no—
416C3⋊C8—62no—
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—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8#62612yescomplemented
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—21no—
448C22×C4—32no—
449C22×C4—61no—
450C22×C4C2×D3211yescharacteristic
451SD16—68no—
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—122no—
469C22×C3—124no—
470C22×C3—242no—
471C22×C3—241no—
472C22×C3—241no—
473C22×C3D3×SD1612yes—
474C22×C3#91412yes—
475C22×C3#93011yescharacteristic
476C22×C3#93711yescharacteristic
477C22×C3#93711yescharacteristic
478C22×C3#93911yescharacteristic
479C22×C3#94011yescharacteristic
480C22×C3#94011yescharacteristic
481C22×C3C2×#21512yes—
482C22×C3#94912yes—
483C2×D3—44no—
484C2×D3—42no—
485C2×D3—82no—
486C2×D3—81no—
487C2×D3—81no—
488C2×D3—124no—
489C2×D3—124no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—124no—
493C2×D3—244no—
494C2×D3—244no—
495C2×D3—242no—
496C2×D3—242no—
497C2×D3—242no—
498C2×D3—241no—
499C2×D3—241no—
500C2×D3—242no—
501C2×D3—241no—
502C2×D3—241no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—44no—
508C3×C4—42no—
509C3×C4—42no—
510C3×C4—64no—
511C3×C4—241no—
512C3×C4#88211yescharacteristic
513C3×C4#88211yescharacteristic
514C3×C4#88411yescharacteristic
515C3×C4#88411yescharacteristic
516C3×C4#93711yescharacteristic
517C3×C4#93811yescharacteristic
518C3×C4#93911yescharacteristic
519C3×C4#95311yescharacteristic
520Dic3—24no—
521Dic3—81no—
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×#6711yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538D4—62no—
539D4—62no—
540D4—121no—
541D4—121no—
542D4—182no—
543D4—182no—
544D4—3616no—
545D4—361no—
546D4—361no—
547C2×C4—22no—
548C2×C4—34no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—122no—
554C2×C4—121no—
555C2×C4#380411yescharacteristic
556C2×C4C2×#62611yescharacteristic
557C2×C4D3×#6711yescharacteristic
558C2×C4D3×#6711yescharacteristic
559C2×C4#381111yescharacteristic
560C2×C4#381111yescharacteristic
561C8—62no—
562C8—182no—
563C2×C3—22no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—242no—
569C2×C3#496011yescharacteristic
570C2×C3#502712yes—
571C2×C3#504612yes—
572C2×C3#505811yescharacteristic
573C2×C3#508511yescharacteristic
574C2×C3#516312yes—
575C2×C3#516912yes—
576C2×C3#517511yescharacteristic
577C2×C3#517611yescharacteristic
578C2×C3#522311yescharacteristic
579D3—82no—
580D3—244no—
581D3—242no—
582D3—242no—
583C22—124no—
584C22—122no—
585C22—242no—
586C22—241no—
587C22—241no—
588C22—364no—
589C22—362no—
590C22—722no—
591C22—721no—
592C22—721no—
593C22D3×#21512yes—
594C22#6393912yes—
595C22#6397811yescharacteristic
596C22#6397911yescharacteristic
597C22#6398311yescharacteristic
598C4—42no—
599C4—64no—
600C4—241no—
601C4#6395811yescharacteristic
602C4#6397111yescharacteristic
603C4#6397711yescharacteristic
604C4#6398111yescharacteristic
605C3—21no—
606C3#6968811yescharacteristic, complemented
607C3#7205611yescharacteristic, complemented
608C2—242no—
609C2—722no—
610C2#1059161712yes—
611C2#1059161811yescharacteristic
612C2#1059161911yescharacteristic
613C2#1059165112yes—
614C2#1059172411yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC22×Q8D32
hypocenterC32#2014
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3755C2semidirect
2. C22×C3×#215C2semidirect
4. C3×#5229C2semidirect
5. C2×#63564C2semidirect
6. C2×#63562C2semidirect
7. #10589155C2semidirect
33. C22×#215D3semidirect
37. #5229D3semidirect
51. C2×C32×Q8D4semidirect
74. C2×C3⋊(C3⋊C8)D4semidirect
82. C2×C3×C3⋊C8D4semidirect
160. C2×C3×Dic3SD16semidirect
196. C2×C3×Q8D12semidirect
197. C2×C3×Q8#67semidirect
271. C2×C3⋊C8#67semidirect
394. C2×Dic3#215semidirect
431. C2×Q8#626semidirect
522. C32#2014semidirect
606. C3#69688semidirect
607. C3#72056semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C22×C3×#2152
C2×#639112
C3×#52292
C2×#635642
C2×#635622
#105891552
#720563
#696883