Finite Group Databasebeta

← #11864519

Subgroups — #11864519

Order 1152.

1475 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3#10594855C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592924C211yesmaximal, characteristic, complemented
6#10591597C214yesmaximal, complemented
7#10591594C214yesmaximal, complemented
8#10591084C211yesmaximal, characteristic, complemented
9#10591070C211yesmaximal, characteristic, complemented
10#84117—31nomaximal
11#83884—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C3×#1007—24no—
14C3×#1007—24no—
15C2×C3×#239—21no—
16C2×C3×#239C2212yes—
17C2×C3×D3×Q8—21no—
18C2×C3×D3×Q8C2212yes—
19C2×C3×#235—22no—
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23#64135C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C2×C3×#216—24no—
26C2×C3×#216C2214yes—
27C22×C3×C3⋊C8C2211yescharacteristic
28#63961—22no—
29#63873—21no—
30#63863—21no—
31#63856C2214yes—
32C2×#3718C2212yes—
33#63827—24no—
34C2×#3715C2212yes—
35#63662C2214yes—
36#63566C2212yes—
37#63563C2212yes—
38(C2×D3)⋊(C3⋊C8)C2214yes—
39C2×C3×2−1+4—31no—
40C2×#1007D311yescharacteristic
41C22×C3×Q16—31no—
42#5825—31no—
43C2×#951—31no—
44#5816—31no—
45C22×#216D311yescharacteristic, complemented
46C2×#942—31no—
47#5239—34no—
48#5234—31no—
49#5233—31no—
50#5228—34no—
51#5225—31no—
52#5225—31no—
53#5225—61no—
54#5187—34no—
55#5186—34no—
56#5113—31no—
57#5110—31no—
58C2×C32×Q8—21no—
59C2×C32×Q8—22no—
60C2×C32×Q8D414yes—
61C2×C32×Q8C2312yes—
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C2×C3×#67—21no—
65C2×C3×#67D412yes—
66C22×C3×Dic3—21no—
67C3×#239—28no—
68C3×#239—24no—
69C3×#239—24no—
70C3×D3×Q8—28no—
71C3×D3×Q8—24no—
72C3×D3×Q8—24no—
73C3×#235—216no—
74C3×#235—22no—
75C3×#235—22no—
76C3×#235—22no—
77C3×#235D414yes—
78C2×C3×D12—22no—
79C2×C3×D12D411yescharacteristic
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2312yes—
85C2×C3×Dic6—22no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—21no—
89C2×C3×Dic6D411yescharacteristic
90C2×C3×Dic6C2312yes—
91C2×C3×Dic6C2311yescharacteristic
92#3757—21no—
93C4⋊(C3⋊Dic3)C2312yes—
94C4×C3⋊Dic3—21no—
95#3748—22no—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#216—28no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2312yes—
100#3724—24no—
101(C2×D3)⋊Dic3—24no—
102#3718—24no—
103#3715—24no—
104#3011—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C22×C3×Q8—21no—
113C22×C3×Q8—32no—
114C22×C3×Q8—31no—
115C22×C3×Q8—61no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118#1007—24no—
119#1007—24no—
120C2×#239—21no—
121C2×#239C2×D312yes—
122C2×D3×Q8—21no—
123C2×D3×Q8C2×D312yes—
124C2×#235—22no—
125C2×#235C2×D311yescharacteristic
126C2×#235C2×D311yescharacteristic
127C22×Dic6C2×D311yescharacteristic
128C2×C3×Q16—34no—
129C2×C3×Q16—64no—
130C22×C3×C8—31no—
131#951—64no—
132#947—61no—
133#946—34no—
134#944—61no—
135#944—61no—
136C2×#216—24no—
137C2×#216—32no—
138C2×#216—32no—
139C2×#216C2×D314yes—
140#942—64no—
141C2×#215—32no—
142#936—61no—
143#935—62no—
144C2×#214—32no—
145#929—62no—
146#926—31no—
147#926—31no—
148#926—61no—
149#924—34no—
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—61no—
153C22×C3⋊C8C2×D311yescharacteristic
154#835—34no—
155#835—34no—
156#835—32no—
157#835—64no—
158#832—32no—
159#830—34no—
160#821—32no—
161(C2×D3)⋊C8—34no—
162#816—32no—
163C23×C32C2×D411yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3C2×D412yes—
166C32×Q8—24no—
167C32×Q8—22no—
168C32×Q8C2×D414yes—
169C2×C32×C4—24no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176C3×#67—24no—
177C3×#67—24no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3C2×D412yes—
182C3×D12—28no—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12C2×D412yes—
186C3×C4×D3—28no—
187C3×C4×D3—28no—
188C3×C4×D3—24no—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×Dic6—28no—
192C3×Dic6—22no—
193C3×Dic6—21no—
194C3×Dic6—22no—
195C3×Dic6—22no—
196C3×Dic6—42no—
197C3×Dic6C2×D412yes—
198C3⋊(C3⋊C8)—22no—
199C3×C3⋊C8—22no—
200C2×2−1+4—31no—
201C2×#137—91no—
202C22×Q16—31no—
203#536—91no—
204#452—94no—
205#451—94no—
206#419—91no—
207#416—91no—
208#408—91no—
209C3×#41—34no—
210C3×#41—616no—
211C3×#41—64no—
212C3×#41—68no—
213C3×#41—64no—
214C3×#41—62no—
215C3×#41—62no—
216C3×#41—62no—
217C2×C3×Q8—21no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8—22no—
221C2×C3×Q8—24no—
222C2×C3×Q8—22no—
223C2×C3×Q8—31no—
224C2×C3×Q8—31no—
225C2×C3×Q8—32no—
226C2×C3×Q8—41no—
227C2×C3×Q8—42no—
228C2×C3×Q8—62no—
229C2×C3×Q8—64no—
230C2×C3×Q8—68no—
231C2×C3×Q8—64no—
232C2×C3×Q8—61no—
233C2×C3×Q8—62no—
234C2×C3×Q8—62no—
235C2×C3×Q8#6714yes—
236C2×C3×Q8#6714yes—
237C2×C3×Q8C22×D312yes—
238C2×C3×Q8C22×D312yes—
239C2×C3×D4—32no—
240C2×C3×D4—31no—
241C2×C3×D4—31no—
242C2×C3×D4—62no—
243C2×C3×D4—61no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—32no—
248C22×C3×C4—41no—
249C22×C3×C4—62no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C2×#67—21no—
256C2×#67#6712yes—
257C22×Dic3—21no—
258#239—28no—
259#239—24no—
260#239—24no—
261D3×Q8—28no—
262D3×Q8—24no—
263D3×Q8—24no—
264#235—216no—
265#235—22no—
266#235—22no—
267#235—22no—
268#235#6714yes—
269C2×D12—22no—
270C2×D12#6711yescharacteristic
271C2×D12C22×D311yescharacteristic
272C2×C4×D3—22no—
273C2×C4×D3—21no—
274C2×C4×D3—22no—
275C2×C4×D3C22×D312yes—
276C2×Dic6—22no—
277C2×Dic6—22no—
278C2×Dic6—22no—
279C2×Dic6—21no—
280C2×Dic6#6711yescharacteristic
281C2×Dic6C22×D312yes—
282C2×Dic6C22×D311yescharacteristic
283C3×Q16—68no—
284C2×C3×C8—32no—
285C2×C3×C8—62no—
286#217—64no—
287#217—61no—
288#217—61no—
289#217—121no—
290#216—28no—
291#216—64no—
292#216—64no—
293#215—64no—
294#214—64no—
295(C2×D3)⋊C4—64no—
296C4⋊Dic3—32no—
297C4⋊Dic3—32no—
298C4⋊Dic3—62no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301C4×Dic3—61no—
302C4×Dic3—61no—
303C4×Dic3—121no—
304#208—62no—
305#208—62no—
306#208—122no—
307C2×C3⋊C8—22no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8C22×D312yes—
312C22×C32—22no—
313C22×C32#12012yes—
314C22×C32C22×D411yescharacteristic
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—24no—
318C2×C3×D3—42no—
319C32×C4—24no—
320C32×C4#12012yes—
321C32×C4C22×D411yescharacteristic
322C32×C4C22×D411yescharacteristic
323C3⋊Dic3—42no—
324C3×Dic3—22no—
325C3×Dic3—22no—
326C3×Dic3—42no—
3272−1+4—64no—
3282−1+4—64no—
329C2×#41—31no—
330C2×#41—32no—
331C2×#41—31no—
332C2×#41—62no—
333C2×#41—61no—
334C22×Q8—32no—
335C22×Q8—31no—
336C22×Q8—61no—
337C22×Q8D3211yescharacteristic
338#137—184no—
339C2×Q16—34no—
340C2×Q16—64no—
341C2×Q16—92no—
342C2×SD16—92no—
343C2×M16—91no—
344C22×C8—31no—
345C4⋊Q8—181no—
346#124—181no—
347#123—182no—
348C22⋊Q8—94no—
349#117—91no—
350#103—92no—
351#103—94no—
352#102—92no—
353C22⋊C8—94no—
354C23×C3—21no—
355C23×C3—32no—
356C23×C3—61no—
357C23×C3D3×D411yescharacteristic
358C23×C3C2×#6711yescharacteristic
359C22×D3—21no—
360C22×D3C2×#6712yes—
361C3×Q8—24no—
362C3×Q8—24no—
363C3×Q8—22no—
364C3×Q8—22no—
365C3×Q8—24no—
366C3×Q8—32no—
367C3×Q8—42no—
368C3×Q8—44no—
369C3×Q8—68no—
370C3×Q8—62no—
371C3×Q8—61no—
372C3×Q8—62no—
373C3×Q8—62no—
374C3×Q8—122no—
375C3×Q8C2×#6714yes—
376C3×Q8C2×#6714yes—
377C3×D4—32no—
378C3×D4—68no—
379C3×D4—64no—
380C3×D4—64no—
381C3×D4—62no—
382C3×D4—61no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—32no—
392C2×C3×C4—42no—
393C2×C3×C4—44no—
394C2×C3×C4—68no—
395C2×C3×C4—68no—
396C2×C3×C4—61no—
397C2×C3×C4—64no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—122no—
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D412yes—
404C2×C3×C4C2×#6712yes—
405C2×C3×C4C2×#6712yes—
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C2×#6712yes—
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—24no—
411#67—24no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—42no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—122no—
418C2×Dic3C2×#6712yes—
419D12—28no—
420D12—22no—
421D12—21no—
422D12C2×#6712yes—
423C4×D3—28no—
424C4×D3—28no—
425C4×D3—24no—
426C4×D3—22no—
427C4×D3—22no—
428Dic6—28no—
429Dic6—22no—
430Dic6—21no—
431Dic6—22no—
432Dic6—22no—
433Dic6—42no—
434Dic6C2×#6712yes—
435C3×C8—62no—
436C3⋊C8—22no—
437C3⋊C8—62no—
438C3⋊C8—62no—
439C3⋊C8—122no—
440C2×C32—22no—
441C2×C32C2×#12011yescharacteristic
442C2×C32#57812yes—
443C3×D3—42no—
444C3×D3—42no—
445#41—34no—
446#41—616no—
447#41—64no—
448#41—68no—
449#41—64no—
450#41—62no—
451#41—62no—
452#41—62no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—31no—
456C2×Q8—31no—
457C2×Q8—32no—
458C2×Q8—62no—
459C2×Q8—64no—
460C2×Q8—68no—
461C2×Q8—64no—
462C2×Q8—61no—
463C2×Q8—62no—
464C2×Q8—62no—
465C2×Q8#62514yes—
466C2×Q8C2×D3212yes—
467C2×D4—32no—
468C2×D4—31no—
469C2×D4—31no—
470C2×D4—62no—
471C2×D4—61no—
472C22×C4—21no—
473C22×C4—32no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4C2×D3211yescharacteristic
479Q16—68no—
480Q16—184no—
481SD16—184no—
482M16—182no—
483C2×C8—32no—
484C2×C8—62no—
485C2×C8—92no—
486C4⋊C4—92no—
487C4⋊C4—184no—
488C22⋊C4—184no—
489C22⋊C4—181no—
490C42—181no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—22no—
495C22×C3—42no—
496C22×C3—64no—
497C22×C3—62no—
498C22×C3—62no—
499C22×C3—122no—
500C22×C3#93712yes—
501C22×C3#95312yes—
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C22×#6711yescharacteristic
504C2×D3—24no—
505C2×D3—22no—
506C2×D3—22no—
507C2×D3—42no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—44no—
514C3×C4—62no—
515C3×C4—62no—
516C3×C4—122no—
517C3×C4#93712yes—
518C3×C4#95312yes—
519C3×C4C2×D3×D411yescharacteristic
520C3×C4C22×#6711yescharacteristic
521C3×C4C22×#6711yescharacteristic
522C3×C4C22×#6711yescharacteristic
523Dic3—22no—
524Dic3—22no—
525Dic3—42no—
526Dic3—122no—
527Dic3—122no—
528Dic3—242no—
529C32#301111yescharacteristic, complemented, Sylow
530C23—32no—
531C23—61no—
532C23D3×#6711yescharacteristic
533Q8—22no—
534Q8—24no—
535Q8—32no—
536Q8—68no—
537Q8—61no—
538Q8—62no—
539Q8—62no—
540Q8—62no—
541Q8—122no—
542Q8C2×#62514yes—
543D4—32no—
544D4—68no—
545D4—64no—
546D4—64no—
547D4—61no—
548D4—62no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—32no—
552C2×C4—68no—
553C2×C4—68no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—64no—
558C2×C4—62no—
559C2×C4—122no—
560C2×C4—182no—
561C2×C4C2×#62512yes—
562C2×C4D3×#6712yes—
563C2×C4D3×#6711yescharacteristic
564C2×C4C22×D3211yescharacteristic
565C8—62no—
566C8—182no—
567C2×C3—22no—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—22no—
571C2×C3—42no—
572C2×C3—122no—
573C2×C3—122no—
574C2×C3#576612yes—
575C2×C3C2×#93711yescharacteristic
576C2×C3#583812yes—
577C2×C3C2×#95311yescharacteristic
578D3—42no—
579D3—42no—
580C22—22no—
581C22—62no—
582C22—62no—
583C22—64no—
584C22—122no—
585C22#6397612yes—
586C22C2×D3×#6711yescharacteristic
587C4—24no—
588C4—62no—
589C4—62no—
590C4—122no—
591C4—362no—
592C4#6397612yes—
593C4C22×#62511yescharacteristic
594C4C2×D3×#6711yescharacteristic
595C3—21no—
596C3#8388411yescharacteristic, complemented
597C3#8411711yescharacteristic, complemented
598C2—22no—
599C2—122no—
600C2—122no—
601C2#1059532712yes—
602C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#1007C2
hypercenterC22×Q8D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
3. #10594855C2semidirect
4. C2×#63827C2semidirect
5. #10592924C2semidirect
6. #10591597C2semidirect
7. #10591594C2semidirect
8. #10591084C2semidirect
9. #10591070C2semidirect
45. C22×#216D3semidirect
529. C32#3011semidirect
596. C3#83884semidirect
597. C3#84117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C3×#2162
#105948552
C2×#638272
#105929242
#105915972
#105915942
#105910842
#105910702
#841173
#838843