Finite Group Databasebeta

← #11864529

Subgroups — #11864529

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×#64160C211yesmaximal, characteristic, complemented
3#10594856C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591595C214yesmaximal, complemented
7#10591463C214yesmaximal, complemented
8#10591099C211yesmaximal, characteristic, complemented
9#10591070C211yesmaximal, characteristic, complemented
10#84117—31nomaximal
11#78837—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C3×#1010—24no—
15C3×#1010—24no—
16C2×C3×D3×Q8C2212yes—
17C2×C3×#237—22no—
18C2×C3×#237C2212yes—
19C2×C3×#235—21no—
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6—21no—
22C22×C3×Dic6C2211yescharacteristic
23#64160—24no—
24C2×#3756C2212yes—
25C2×#3754C2212yes—
26C2×#3748C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63962—22no—
30#63866—21no—
31#63860—21no—
32#63857C2214yes—
33C2×#3719—24no—
34C2×#3719C2214yes—
35C3×#835C2212yes—
36C3×#832C2212yes—
37#63565C2214yes—
38(C2×D3)⋊(C3⋊C8)C2214yes—
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic
41#5825—31no—
42C2×#951—31no—
43C2×#951—31no—
44C2×#951—61no—
45C22×#216—31no—
46C22×Dic12—31no—
47#5526—31no—
48C3×#416—31no—
49#5239—34no—
50#5234—31no—
51#5233D311yescharacteristic, complemented
52#5228—34no—
53#5225—31no—
54#5110—31no—
55#5004—31no—
56#4809—34no—
57#4783—34no—
58C32×#41—22no—
59C32×#41D414yes—
60C2×C32×Q8C2311yescharacteristic
61C2×C32×D4—21no—
62C2×C32×D4C2311yescharacteristic
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3—21no—
66C2×#634—22no—
67C2×#634—22no—
68C2×#634—21no—
69C2×#634C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67D412yes—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—22no—
74C3×D3×Q8—24no—
75C3×D3×Q8—24no—
76C3×#237—216no—
77C3×#237—24no—
78C3×#237—24no—
79C3×#235—28no—
80C3×#235—22no—
81C3×#235—22no—
82C2×C3×D12D411yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2312yes—
85C2×C3×Dic6—28no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6D411yescharacteristic
90C2×C3×Dic6D414yes—
91C2×C3×Dic6C2312yes—
92#3756—24no—
93#3754—24no—
94#3748—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—24no—
102(C2×D3)⋊Dic3—24no—
103#3719—28no—
104#3011—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41—62no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—32no—
115C22×C3×Q8—31no—
116C22×C3×Q8—61no—
117#1010—24no—
118#1010—24no—
119C2×D3×Q8C2×D312yes—
120C2×#237—22no—
121C2×#237C2×D312yes—
122C2×#235—21no—
123C2×#235C2×D311yescharacteristic
124C22×Dic6—21no—
125C22×Dic6—31no—
126C22×Dic6—31no—
127C22×Dic6—61no—
128C22×Dic6C2×D311yescharacteristic
129C22×C3×C8—31no—
130C3×#117—31no—
131#951—68no—
132#951—64no—
133#951—64no—
134#944—61no—
135C2×#216—32no—
136C2×#216—32no—
137C2×#216—34no—
138C2×#216—62no—
139C2×#216—64no—
140#936—61no—
141#935—62no—
142C2×#214—32no—
143C2×#214—32no—
144C2×#214—62no—
145#926C2×D311yescharacteristic
146#924—34no—
147C2×#208—31no—
148C2×#208—31no—
149C2×#208—61no—
150C22×C3⋊C8C2×D311yescharacteristic
151C2×Dic12—34no—
152C2×Dic12—64no—
153#897—34no—
154#886—62no—
155#875—61no—
156#869—61no—
157C3×#103—32no—
158C3×#102—32no—
159#835—34no—
160#835C2×D312yes—
161#832C2×D312yes—
162#830—34no—
163(C2×D3)⋊C8—34no—
164#810—34no—
165C23×C32—21no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3C2×D412yes—
168C32×Q8—21no—
169C32×Q8C2×D412yes—
170C32×D4—24no—
171C32×D4—21no—
172C32×D4C2×D412yes—
173C2×C32×C4—21no—
174C2×C32×C4—24no—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—42no—
181#634—22no—
182#634—22no—
183#634—42no—
184C3×#67—28no—
185C3×#67—24no—
186C2×C3×Dic3—28no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D412yes—
191C3×D12—22no—
192C3×C4×D3—28no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—28no—
196C3×Dic6—22no—
197C3×Dic6—24no—
198C3×Dic6—22no—
199C3×Dic6C2×D414yes—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C2×2−1+4—31no—
203C2×#137—91no—
204C22×Q16—91no—
205#536—91no—
206#452—94no—
207#451—94no—
208#419—91no—
209#416—31no—
210#408—91no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—24no—
214C3×#41—42no—
215C3×#41—68no—
216C3×#41—64no—
217C3×#41—616no—
218C3×#41—64no—
219C3×#41—62no—
220C3×#41—62no—
221C3×#41D1214yes—
222C3×#41#6714yes—
223C2×C3×Q8—21no—
224C2×C3×Q8—31no—
225C2×C3×Q8—34no—
226C2×C3×Q8—32no—
227C2×C3×Q8—62no—
228C2×C3×Q8—68no—
229C2×C3×Q8—64no—
230C2×C3×Q8—64no—
231C2×C3×Q8—62no—
232C2×C3×Q8—61no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—32no—
239C2×C3×D4—31no—
240C2×C3×D4—41no—
241C2×C3×D4—62no—
242C2×C3×D4C22×D311yescharacteristic
243C2×C3×D4C22×D311yescharacteristic
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×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—22no—
255C2×#67#6712yes—
256C22×Dic3—21no—
257C22×Dic3—22no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—121no—
261D3×Q8—24no—
262D3×Q8—24no—
263#237—216no—
264#237—24no—
265#237—24no—
266#235—28no—
267#235—22no—
268#235—22no—
269C2×D12#6711yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3C22×D312yes—
272C2×Dic6—28no—
273C2×Dic6—21no—
274C2×Dic6—22no—
275C2×Dic6—22no—
276C2×Dic6—32no—
277C2×Dic6—32no—
278C2×Dic6—62no—
279C2×Dic6—64no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—62no—
283C2×Dic6—62no—
284C2×Dic6—61no—
285C2×Dic6—61no—
286C2×Dic6—121no—
287C2×Dic6—122no—
288C2×Dic6#6711yescharacteristic
289C2×Dic6#6714yes—
290C2×Dic6C22×D312yes—
291C2×C3×C8—32no—
292C2×C3×C8—62no—
293C3×C4⋊C4—32no—
294C3×C22⋊C4—61no—
295C3×C42—61no—
296#217—21no—
297#217—64no—
298#216—68no—
299#216—68no—
300#216—64no—
301#216—64no—
302#214—68no—
303#214—64no—
304#214—64no—
305(C2×D3)⋊C4—64no—
306C4⋊Dic3—64no—
307C4⋊Dic3C22×D312yes—
308Dic3⋊C4—64no—
309C4×Dic3—21no—
310#208—64no—
311#208—62no—
312#208—62no—
313C2×C3⋊C8—22no—
314C2×C3⋊C8—32no—
315C2×C3⋊C8—32no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8C22×D312yes—
318Dic12—68no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—42no—
322C22×C32#12012yes—
323C22×C32C22×D411yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—24no—
326C32×C4—22no—
327C32×C4#12012yes—
328C32×C4C22×D411yescharacteristic
329C32×C4C22×D411yescharacteristic
330C3⋊Dic3—42no—
331C3×Dic3—22no—
332C3×Dic3—24no—
333C3×Dic3—42no—
3342−1+4—64no—
3352−1+4—64no—
336C2×#41—31no—
337C2×#41—32no—
338C2×#41—61no—
339C2×#41—62no—
340C2×#41D3211yescharacteristic
341C22×Q8—32no—
342C22×Q8—31no—
343C22×Q8—61no—
344C22×Q8—91no—
345#137—184no—
346C2×Q16—94no—
347C2×Q16—92no—
348C2×Q16—184no—
349C2×SD16—92no—
350C2×M16—91no—
351C22×C8—31no—
352C4⋊Q8—181no—
353#124—181no—
354#123—182no—
355C22⋊Q8—94no—
356#117—31no—
357#103—32no—
358#103—94no—
359#102—32no—
360C22⋊C8—94no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—41no—
366C23×C3D3×D411yescharacteristic
367C23×C3C2×#6711yescharacteristic
368C22×D3C2×#6712yes—
369C3×Q8—21no—
370C3×Q8—21no—
371C3×Q8—22no—
372C3×Q8—34no—
373C3×Q8—41no—
374C3×Q8—68no—
375C3×Q8—62no—
376C3×Q8—64no—
377C3×Q8—62no—
378C3×Q8C2×D1212yes—
379C3×Q8C2×#6712yes—
380C3×D4—24no—
381C3×D4—24no—
382C3×D4—21no—
383C3×D4—21no—
384C3×D4—22no—
385C3×D4—41no—
386C3×D4—44no—
387C3×D4—68no—
388C3×D4—64no—
389C3×D4—62no—
390C3×D4C2×D1212yes—
391C3×D4C2×#6712yes—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—32no—
401C2×C3×C4—44no—
402C2×C3×C4—41no—
403C2×C3×C4—68no—
404C2×C3×C4—68no—
405C2×C3×C4—64no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4C2×D1212yes—
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D412yes—
413C2×C3×C4C2×#6712yes—
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—28no—
419#67—24no—
420C2×Dic3—28no—
421C2×Dic3—24no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—122no—
427C2×Dic3—124no—
428C2×Dic3—122no—
429C2×Dic3—122no—
430C2×Dic3C2×#6712yes—
431D12—22no—
432C4×D3—28no—
433C4×D3—22no—
434C4×D3—22no—
435Dic6—28no—
436Dic6—22no—
437Dic6—24no—
438Dic6—22no—
439Dic6—64no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6—62no—
444Dic6—122no—
445Dic6—124no—
446Dic6—122no—
447Dic6—122no—
448Dic6C2×#6714yes—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—64no—
452C3⋊C8—62no—
453C3⋊C8—62no—
454C2×C32—22no—
455C2×C32—42no—
456C2×C32C2×#12011yescharacteristic
457C2×C32#57812yes—
458C3×D3—42no—
459#41—22no—
460#41—68no—
461#41—64no—
462#41—616no—
463#41—64no—
464#41—62no—
465#41—62no—
466#41#62614yes—
467C2×Q8—31no—
468C2×Q8—32no—
469C2×Q8—34no—
470C2×Q8—62no—
471C2×Q8—68no—
472C2×Q8—64no—
473C2×Q8—64no—
474C2×Q8—62no—
475C2×Q8—61no—
476C2×Q8—92no—
477C2×Q8—181no—
478C2×Q8—182no—
479C2×Q8—182no—
480C2×Q8C2×D3211yescharacteristic
481C2×D4—21no—
482C2×D4—32no—
483C2×D4—31no—
484C2×D4—62no—
485C2×D4C2×D3211yescharacteristic
486C22×C4—21no—
487C22×C4—32no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—61no—
491C22×C4—181no—
492C22×C4C2×D3211yescharacteristic
493Q16—188no—
494Q16—184no—
495SD16—184no—
496M16—182no—
497C2×C8—32no—
498C2×C8—62no—
499C2×C8—92no—
500C4⋊C4—32no—
501C4⋊C4—184no—
502C22⋊C4—61no—
503C22⋊C4—184no—
504C42—61no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—22no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—62no—
516C22×C3—64no—
517C22×C3—82no—
518C22×C3#88212yes—
519C22×C3#95312yes—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—24no—
523C2×D3—22no—
524C3×C4—22no—
525C3×C4—22no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—22no—
529C3×C4—42no—
530C3×C4—62no—
531C3×C4—64no—
532C3×C4—122no—
533C3×C4#88212yes—
534C3×C4#95312yes—
535C3×C4C22×D1211yescharacteristic
536C3×C4C2×D3×D411yescharacteristic
537C3×C4C22×#6711yescharacteristic
538C3×C4C22×#6711yescharacteristic
539Dic3—22no—
540Dic3—24no—
541Dic3—42no—
542Dic3—124no—
543Dic3—122no—
544Dic3—122no—
545C32#301111yescharacteristic, complemented, Sylow
546C23—21no—
547C23—32no—
548C23D3×#6711yescharacteristic
549Q8—21no—
550Q8—34no—
551Q8—68no—
552Q8—62no—
553Q8—62no—
554Q8—64no—
555Q8—182no—
556Q8—182no—
557Q8—362no—
558Q8C2×#62612yes—
559D4—24no—
560D4—21no—
561D4—68no—
562D4—64no—
563D4—62no—
564D4C2×#62612yes—
565C2×C4—21no—
566C2×C4—24no—
567C2×C4—32no—
568C2×C4—68no—
569C2×C4—68no—
570C2×C4—62no—
571C2×C4—64no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—182no—
576C2×C4—362no—
577C2×C4C2×#62612yes—
578C2×C4D3×#6712yes—
579C2×C4D3×#6711yescharacteristic
580C2×C4C22×D3211yescharacteristic
581C8—62no—
582C8—182no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—22no—
586C2×C3—21no—
587C2×C3—42no—
588C2×C3—42no—
589C2×C3—42no—
590C2×C3—82no—
591C2×C3—122no—
592C2×C3C2×#88211yescharacteristic
593C2×C3#577112yes—
594C2×C3#583812yes—
595C2×C3C2×#95311yescharacteristic
596D3—42no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—64no—
601C22—62no—
602C22#6397712yes—
603C22C2×D3×#6711yescharacteristic
604C4—22no—
605C4—62no—
606C4—64no—
607C4—122no—
608C4—362no—
609C4#6397712yes—
610C4C22×#62611yescharacteristic
611C4C2×D3×#6711yescharacteristic
612C3—21no—
613C3#7883711yescharacteristic, complemented
614C3#8411711yescharacteristic, complemented
615C2—22no—
616C2—42no—
617C2—122no—
618C2#1059546712yes—
619C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC2×#41D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64160C2semidirect
3. #10594856C2semidirect
4. C22×#3719C2semidirect
5. C3×#5233C2semidirect
6. #10591595C2semidirect
7. #10591463C2semidirect
8. #10591099C2semidirect
9. #10591070C2semidirect
51. #5233D3semidirect
545. C32#3011semidirect
613. C3#78837semidirect
614. C3#84117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#641602
#105948562
C22×#37192
C3×#52332
#105915952
#105914632
#105910992
#105910702
#841173
#788373