Finite Group Databasebeta

← #11864526

Subgroups — #11864526

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×#64298C211yesmaximal, characteristic
2C3×#5526C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592703C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7#10591070C211yesmaximal, characteristic, complemented
8#10590614C214yesmaximal, complemented
9#10590604C214yesmaximal, complemented
10#83411—31nomaximal
11#78837—31nomaximal
12C22×#634C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×#3805—22no—
17#64298—24no—
18#64298—24no—
19C2×#3795—21no—
20C2×#3795C2212yes—
21C2×D3×Dic6—21no—
22C2×D3×Dic6C2212yes—
23C32×#117C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#897C2214yes—
27C3×#886—22no—
28C3×#875—21no—
29C3×#869—21no—
30C2×#3719—24no—
31C2×#3719C2214yes—
32C2×#3718C2212yes—
33#63827—24no—
34C2×#3715C2212yes—
35#63637C2214yes—
36C3×#810C2212yes—
37C3×#809C2212yes—
38(C2×D3)⋊(C3⋊C8)C2214yes—
39C2×#1010—31no—
40C2×#1010—31no—
41C3×#536—31no—
42C2×#951—31no—
43C22×#216—31no—
44C2×#942—31no—
45C22×Dic12—31no—
46#5526D311yescharacteristic, complemented
47C3×#416—31no—
48#5234—31no—
49#5110—31no—
50#5050—34no—
51#5047—34no—
52#5004—31no—
53#5004—31no—
54#5004—61no—
55#5002D311yescharacteristic, complemented
56#4809—34no—
57#4783—34no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C2×#634—21no—
61C2×#634—22no—
62C2×#634D414yes—
63C2×#634C2312yes—
64C2×C3×#67—21no—
65C2×C3×#67D412yes—
66C22×C3×Dic3—21no—
67C3×#235—22no—
68C3×#235—22no—
69C3×#235—22no—
70C3×#235D414yes—
71C2×C3×D12D411yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6D411yescharacteristic
79C2×C3×Dic6C2312yes—
80C2×C3×Dic6C2311yescharacteristic
81C2×#627—22no—
82C2×#625—22no—
83#3805—216no—
84C2×D3×Dic3—22no—
85C2×D3×Dic3—22no—
86#3795—28no—
87#3795—24no—
88#3795—24no—
89D3×Dic6—28no—
90D3×Dic6—24no—
91D3×Dic6—24no—
92C32×C4⋊C4C2312yes—
93C32×C22⋊C4—21no—
94C32×C42—21no—
95#3748—22no—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×(C2×D3)⋊C4—24no—
98C3×C4⋊Dic3—24no—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2312yes—
101#3719—28no—
102#3718—24no—
103#3715—24no—
104#3011—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108#1010—64no—
109#1010—64no—
110#1010—64no—
111#1010—64no—
112C2×D3×Q8—32no—
113C2×D3×Q8—61no—
114C2×#237—32no—
115C2×#237—61no—
116C2×#237—62no—
117C2×#237—62no—
118C2×#235—32no—
119C2×#235—61no—
120C2×#235C2×D311yescharacteristic
121C2×#235C2×D311yescharacteristic
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—32no—
125C22×Dic6—61no—
126C22×Dic6—61no—
127C22×Dic6C2×D311yescharacteristic
128C22×C3×C8—31no—
129C3×C4⋊Q8—61no—
130C3×#124—61no—
131C3×#123—62no—
132C3×C22⋊Q8—34no—
133C3×#117—21no—
134C3×#117C2×D311yescharacteristic
135C3×#117C2×D311yescharacteristic
136#951—64no—
137C2×#216—32no—
138C2×#216—32no—
139C2×#216—34no—
140C2×#216—64no—
141#942—64no—
142C2×#215—32no—
143C2×#214—32no—
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C22×C3⋊C8C2×D311yescharacteristic
148C2×Dic12—34no—
149C2×Dic12—64no—
150#897C2×D314yes—
151#886—22no—
152#875—21no—
153#869—21no—
154C3×#103—32no—
155C3×#102—32no—
156#830—34no—
157(C2×D3)⋊C8—34no—
158#810—34no—
159#810—34no—
160#810—64no—
161#810C2×D312yes—
162#809C2×D312yes—
163C23×C32C2×D411yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3C2×D412yes—
166C2×C32×C4—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—24no—
172C2×C3⋊Dic3—22no—
173#634—24no—
174#634—22no—
175#634C2×D414yes—
176C3×#67—24no—
177C3×#67—24no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3C2×D412yes—
182C3×D12—22no—
183C3×D12—21no—
184C3×D12C2×D412yes—
185C3×C4×D3—24no—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×Dic6—22no—
189C3×Dic6—21no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192C3×Dic6—42no—
193C3×Dic6C2×D412yes—
194#627—28no—
195#625—28no—
196D3×Dic3—28no—
197D3×Dic3—28no—
198C3⋊(C3⋊C8)—22no—
199C3×C3⋊C8—22no—
200C2×2−1+4—91no—
201C2×#137—91no—
202C22×Q16—91no—
203#536—31no—
204#452—94no—
205#451—94no—
206#419—91no—
207#416—31no—
208#408—91no—
209C3×#41—34no—
210C3×#41—62no—
211C3×#41—62no—
212C3×#41—62no—
213C2×C3×Q8—31no—
214C2×C3×Q8—31no—
215C2×C3×Q8—32no—
216C2×C3×Q8—61no—
217C2×C3×Q8—62no—
218C2×C3×Q8—62no—
219C2×C3×D4—32no—
220C2×C3×D4—31no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—21no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67#6712yes—
233C22×Dic3—21no—
234C22×Dic3—62no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—62no—
238C22×Dic3—121no—
239D3×Q8—64no—
240D3×Q8—64no—
241D3×Q8—68no—
242#237—64no—
243#237—64no—
244#237—68no—
245#237—616no—
246#237—616no—
247#235—22no—
248#235—22no—
249#235—22no—
250#235—64no—
251#235—68no—
252#235—64no—
253#235D1214yes—
254C2×D12#6711yescharacteristic
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3C22×D312yes—
260C2×Dic6—22no—
261C2×Dic6—22no—
262C2×Dic6—21no—
263C2×Dic6—34no—
264C2×Dic6—34no—
265C2×Dic6—32no—
266C2×Dic6—32no—
267C2×Dic6—62no—
268C2×Dic6—64no—
269C2×Dic6—64no—
270C2×Dic6—68no—
271C2×Dic6—62no—
272C2×Dic6—62no—
273C2×Dic6—61no—
274C2×Dic6—62no—
275C2×Dic6—61no—
276C2×Dic6—62no—
277C2×Dic6—64no—
278C2×Dic6—122no—
279C2×Dic6—121no—
280C2×Dic6#6711yescharacteristic
281C2×Dic6C22×D312yes—
282C2×Dic6C22×D311yescharacteristic
283C2×C3×C8—32no—
284C2×C3×C8—62no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—64no—
287C3×C4⋊C4C22×D312yes—
288C3×C4⋊C4C22×D312yes—
289C3×C22⋊C4—21no—
290C3×C22⋊C4—21no—
291C3×C22⋊C4—41no—
292C3×C22⋊C4—64no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42—41no—
296#216—68no—
297#216—64no—
298#216—64no—
299#215—64no—
300#214—64no—
301(C2×D3)⋊C4—24no—
302C4⋊Dic3—24no—
303#208—62no—
304#208—62no—
305#208—122no—
306C2×C3⋊C8—22no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8C22×D312yes—
311Dic12—68no—
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—42no—
320C32×C4#12012yes—
321C32×C4C22×D411yescharacteristic
322C32×C4C22×D411yescharacteristic
323C3⋊Dic3—24no—
324C3×Dic3—22no—
325C3×Dic3—22no—
326C3×Dic3—42no—
3272−1+4—184no—
3282−1+4—184no—
329C2×#41—31no—
330C2×#41—31no—
331C2×#41—92no—
332C2×#41—181no—
333C2×#41—182no—
334C22×Q8—31no—
335C22×Q8—92no—
336C22×Q8—91no—
337C22×Q8—181no—
338#137—184no—
339C2×Q16—94no—
340C2×Q16—92no—
341C2×Q16—184no—
342C2×SD16—92no—
343C2×M16—91no—
344C22×C8—31no—
345C4⋊Q8—61no—
346#124—61no—
347#123—62no—
348C22⋊Q8—34no—
349#117D3211yescharacteristic
350#103—32no—
351#103—94no—
352#102—32no—
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—32no—
362C3×Q8—62no—
363C3×Q8—61no—
364C3×Q8—62no—
365C3×Q8—62no—
366C3×Q8—122no—
367C3×D4—32no—
368C3×D4—64no—
369C3×D4—64no—
370C3×D4—62no—
371C3×D4—61no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—32no—
379C2×C3×C4—42no—
380C2×C3×C4—61no—
381C2×C3×C4—64no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—122no—
386C2×C3×C4C2×D1212yes—
387C2×C3×C4D3×D412yes—
388C2×C3×C4D3×D412yes—
389C2×C3×C4D3×D412yes—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394#67—24no—
395#67—24no—
396#67—68no—
397#67—68no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—42no—
401C2×Dic3—68no—
402C2×Dic3—68no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—122no—
408C2×Dic3—124no—
409C2×Dic3C2×#6712yes—
410D12—22no—
411D12—21no—
412D12C2×D1212yes—
413C4×D3—24no—
414C4×D3—22no—
415C4×D3—22no—
416C4×D3—68no—
417C4×D3—68no—
418Dic6—22no—
419Dic6—21no—
420Dic6—22no—
421Dic6—22no—
422Dic6—34no—
423Dic6—34no—
424Dic6—42no—
425Dic6—64no—
426Dic6—68no—
427Dic6—68no—
428Dic6—64no—
429Dic6—64no—
430Dic6—62no—
431Dic6—62no—
432Dic6—122no—
433Dic6—124no—
434Dic6C2×D1212yes—
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—62no—
447#41—62no—
448#41—62no—
449#41—184no—
450#41—184no—
451#41—188no—
452#41—1816no—
453C2×Q8—31no—
454C2×Q8—31no—
455C2×Q8—32no—
456C2×Q8—61no—
457C2×Q8—62no—
458C2×Q8—62no—
459C2×Q8—92no—
460C2×Q8—94no—
461C2×Q8—182no—
462C2×Q8—184no—
463C2×Q8—184no—
464C2×Q8—188no—
465C2×Q8—182no—
466C2×Q8—181no—
467C2×D4—32no—
468C2×D4—31no—
469C2×D4—31no—
470C2×D4—61no—
471C2×D4—182no—
472C22×C4—32no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—182no—
476C22×C4—182no—
477C22×C4—181no—
478C22×C4C2×D3211yescharacteristic
479Q16—188no—
480Q16—184no—
481SD16—184no—
482M16—182no—
483C2×C8—32no—
484C2×C8—62no—
485C2×C8—92no—
486C4⋊C4—64no—
487C4⋊C4C2×D3212yes—
488C22⋊C4—21no—
489C22⋊C4—64no—
490C42—21no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—22no—
495C22×C3—42no—
496C22×C3—62no—
497C22×C3—64no—
498C22×C3—62no—
499C22×C3—122no—
500C22×C3#88212yes—
501C22×C3#93712yes—
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C22×#6711yescharacteristic
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—24no—
507C2×D3—42no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—62no—
514C3×C4—62no—
515C3×C4—82no—
516C3×C4—122no—
517C3×C4#88212yes—
518C3×C4#93712yes—
519C3×C4C22×D1211yescharacteristic
520C3×C4C2×D3×D411yescharacteristic
521C3×C4C2×D3×D411yescharacteristic
522C3×C4C2×D3×D411yescharacteristic
523Dic3—22no—
524Dic3—22no—
525Dic3—42no—
526Dic3—64no—
527Dic3—64no—
528Dic3—124no—
529C32#301111yescharacteristic, complemented, Sylow
530C23—32no—
531C23—61no—
532C23D3×#6711yescharacteristic
533Q8—32no—
534Q8—61no—
535Q8—62no—
536Q8—62no—
537Q8—62no—
538Q8—94no—
539Q8—122no—
540Q8—188no—
541Q8—182no—
542Q8—184no—
543D4—32no—
544D4—64no—
545D4—64no—
546D4—61no—
547D4—62no—
548D4—188no—
549C2×C4—22no—
550C2×C4—32no—
551C2×C4—61no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—64no—
555C2×C4—62no—
556C2×C4—122no—
557C2×C4—188no—
558C2×C4—188no—
559C2×C4—182no—
560C2×C4—184no—
561C2×C4D3×D1212yes—
562C2×C4#380212yes—
563C2×C4D3×#6711yescharacteristic
564C2×C4C22×D3211yescharacteristic
565C8—62no—
566C8—182no—
567C2×C3—22no—
568C2×C3—22no—
569C2×C3—22no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—122no—
573C2×C3—122no—
574C2×C3C2×#88211yescharacteristic
575C2×C3#577112yes—
576C2×C3C2×#93711yescharacteristic
577C2×C3#583812yes—
578D3—42no—
579D3—42no—
580C22—22no—
581C22—64no—
582C22—62no—
583C22—62no—
584C22—122no—
585C22#6392212yes—
586C22C2×D3×#6711yescharacteristic
587C4—42no—
588C4—62no—
589C4—62no—
590C4—122no—
591C4—184no—
592C4#6392212yes—
593C4C2×D3×D1211yescharacteristic
594C4C2×#380211yescharacteristic
595C3—21no—
596C3#7883711yescharacteristic, complemented
597C3#8341111yescharacteristic, complemented
598C2—22no—
599C2—122no—
600C2—122no—
601C2C2×#6392211yescharacteristic
602C2#1059546712yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#64298C2
hypercenter#117D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5526C2semidirect
3. C22×#3719C2semidirect
4. C2×#63827C2semidirect
5. #10592703C2semidirect
6. C3×#5002C2semidirect
7. #10591070C2semidirect
8. #10590614C2semidirect
9. #10590604C2semidirect
46. #5526D3semidirect
55. #5002D3semidirect
529. C32#3011semidirect
596. C3#78837semidirect
597. C3#83411semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C3×#55262
C22×#37192
C2×#638272
#105927032
C3×#50022
#105910702
#105906142
#105906042
#834113
#788373