Finite Group Databasebeta

← #11867820

Subgroups — #11867820

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5510C211yesmaximal, characteristic
2#10594856C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×#63815C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6C3×#4964C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590588C212yesmaximal, complemented
9#10590587C212yesmaximal, complemented
10#10590579C212yesmaximal, complemented
11#10590578C212yesmaximal, complemented
12#83423—31nomaximal
13#79214—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#930—22no—
20C3×#926C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#897—21no—
23C3×#897C2212yes—
24C3×#895—21no—
25C3×#895C2212yes—
26#63962—22no—
27#63866—21no—
28#63860—21no—
29#63857C2212yes—
30#63857C2212yes—
31C2×#3719C2212yes—
32#63831—24no—
33C2×#3716C2212yes—
34C2×#3711C2212yes—
35#63815—24no—
36C2×D3×C3⋊C8C2212yes—
37#63637C2212yes—
38#63637C2212yes—
39C3×#808C2212yes—
40C3×#807C2212yes—
41#63565C2211yescharacteristic
42#63565C2211yescharacteristic
43#63562C2211yescharacteristic
44#63562C2211yescharacteristic
45C3×#537—31no—
46#5825—31no—
47C2×#951—31no—
48C2×#948—31no—
49C2×#909—31no—
50C2×#907—31no—
51#5526—31no—
52#5510D311yescharacteristic
53C3×#428—31no—
54#5233—31no—
55#5052—32no—
56#5051—32no—
57#5042—32no—
58#5041—32no—
59#5002—31no—
60C2×#810—31no—
61C2×#810—31no—
62C2×#810—61no—
63#4964D311yescharacteristic, complemented
64#4887—32no—
65#4886—32no—
66#4867—32no—
67#4864—32no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×#634—22no—
72C2×#634—22no—
73C2×#634—21no—
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C2×C3×#67D412yes—
77C3×#235—22no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C2×C3×D12—22no—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6D411yescharacteristic
87C2×C3×Dic6C2311yescharacteristic
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2312yes—
90C2×C3⋊(C3⋊C8)—22no—
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C3×#217—21no—
94C3×(C2×D3)⋊C4—22no—
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4×Dic3—21no—
100C3×#208D414yescomplemented
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106#3719—24no—
107#3716—24no—
108#3711—24no—
109D3×C3⋊C8—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C2×C3×#41—31no—
113C2×#235C2×D311yescharacteristic
114C2×#235C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C2×C3×M16—31no—
119C3×C22⋊Q8—32no—
120C3×C22⋊Q8—61no—
121C3×#121—32no—
122C3×#121—61no—
123C3×#121—62no—
124C3×#117—31no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C2×D311yescharacteristic
128#951—64no—
129#948—64no—
130#944—61no—
131C2×#216—32no—
132#936—61no—
133#935—62no—
134C2×#214—32no—
135#930—22no—
136#926C2×D311yescharacteristic
137#924—32no—
138#924—32no—
139C2×#208—32no—
140C2×#208C2×D311yescharacteristic
141C22×C3⋊C8—31no—
142C22×C3⋊C8—31no—
143C22×C3⋊C8—32no—
144C22×C3⋊C8—61no—
145#909—64no—
146#907—64no—
147C2×Dic12—32no—
148C2×#204—32no—
149C2×ΓL(1,𝔽25)—32no—
150C2×D3×C8—32no—
151#897—21no—
152#897—32no—
153#897—32no—
154#897C2×D312yes—
155#895—21no—
156#895C2×D312yes—
157#886—62no—
158#875—61no—
159#869—61no—
160C3×#107—32no—
161C3×#106—32no—
162#835—31no—
163#835—31no—
164#832—31no—
165#832—31no—
166#810—31no—
167#810—31no—
168#810—32no—
169#810—32no—
170#810—32no—
171#810—32no—
172#810—62no—
173#810—62no—
174#809—31no—
175#809—31no—
176#808C2×D312yes—
177#807C2×D312yes—
178C23×C32C2×D411yescharacteristic
179C22×C3×D3—21no—
180C22×C3×D3C2×D412yes—
181C2×C32×C4—22no—
182C2×C32×C4—81no—
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—42no—
189#634—22no—
190#634—22no—
191#634—42no—
192C3×#67—24no—
193C3×#67—42no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3C2×D412yes—
198C3×D12—22no—
199C3×D12—21no—
200C3×D12—21no—
201C3×D12—82no—
202C3×C4×D3—22no—
203C3×C4×D3—22no—
204C3×C4×D3—42no—
205C3×Dic6—22no—
206C3×Dic6—21no—
207C3×Dic6—21no—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210C3×C3⋊C8C2×D414yes—
211C2×#137—91no—
212C2×#131—91no—
213#537—31no—
214#536—91no—
215#470—92no—
216#468—92no—
217#467—92no—
218#465—92no—
219#428—31no—
220#416—91no—
221C2×#103—91no—
222C3×#41—62no—
223C3×#41—62no—
224C3×#41—62no—
225C3×#41—62no—
226C2×C3×Q8—31no—
227C2×C3×Q8—31no—
228C2×C3×D4—32no—
229C2×C3×D4—31no—
230C2×C3×D4—31no—
231C2×C3×D4—62no—
232C2×C3×D4—61no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—32no—
237C22×C3×C4—41no—
238C22×C3×C4—61no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—21no—
242C2×#67#6712yes—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—121no—
246#235—22no—
247#235—22no—
248#235—22no—
249#235—22no—
250C2×D12—22no—
251C2×D12#6711yescharacteristic
252C2×D12C22×D311yescharacteristic
253C2×C4×D3—21no—
254C2×C4×D3C22×D312yes—
255C2×Dic6—32no—
256C2×Dic6—32no—
257C2×Dic6—62no—
258C2×Dic6—64no—
259C2×Dic6—62no—
260C2×Dic6—62no—
261C2×Dic6—62no—
262C2×Dic6—62no—
263C2×Dic6—61no—
264C2×Dic6—61no—
265C2×Dic6—121no—
266C2×Dic6—122no—
267C2×Dic6#6711yescharacteristic
268C2×Dic6C22×D311yescharacteristic
269C3×M16—34no—
270C2×C3×C8—32no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—22no—
274C3×C4⋊C4—31no—
275C3×C4⋊C4—31no—
276C3×C4⋊C4—41no—
277C3×C4⋊C4—62no—
278C3×C4⋊C4C22×D312yes—
279C3×C4⋊C4C22×D312yes—
280C3×C22⋊C4—62no—
281C3×C22⋊C4—62no—
282C3×C22⋊C4—61no—
283C3×C42—61no—
284#217—21no—
285#217—62no—
286#217—62no—
287#216—64no—
288#214—64no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293C4⋊Dic3—22no—
294C4⋊Dic3—62no—
295C4⋊Dic3—62no—
296C4⋊Dic3C22×D311yescharacteristic
297C4⋊Dic3C22×D311yescharacteristic
298Dic3⋊C4—62no—
299Dic3⋊C4—62no—
300C4×Dic3—21no—
301#208—64no—
302#208D1214yescomplemented
303C2×C3⋊C8—31no—
304C2×C3⋊C8—31no—
305C2×C3⋊C8—31no—
306C2×C3⋊C8—31no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8—64no—
312C2×C3⋊C8—122no—
313C2×C3⋊C8C22×D312yes—
314Dic12—64no—
315#204—64no—
316ΓL(1,𝔽25)—64no—
317D3×C8—64no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32#12112yes—
321C22×C32C22×D411yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—42no—
329C32×C4#12112yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C2×#4111yescharacteristic
332C3⋊Dic3—42no—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3—41no—
336C3×Dic3—41no—
337C2×#41—31no—
338C2×#41—31no—
339C22×Q8—91no—
340#137—184no—
341C2×Q16—92no—
342C2×SD16—92no—
343#131—184no—
344C2×M16—31no—
345C2×M16—92no—
346C22×C8—92no—
347C22×C8—91no—
348C4⋊Q8—181no—
349#124—181no—
350#123—182no—
351C22⋊Q8—32no—
352C22⋊Q8—61no—
353C22⋊Q8—92no—
354C22⋊Q8—92no—
355#121—32no—
356#121—61no—
357#121—62no—
358#117—31no—
359C2×C4⋊C4D3211yescharacteristic
360#107—32no—
361#106—32no—
362#103—91no—
363#103—91no—
364#103—92no—
365#103—92no—
366#102—91no—
367#102—91no—
368C23×C3—21no—
369C23×C3—32no—
370C23×C3—61no—
371C23×C3D3×D411yescharacteristic
372C23×C3C2×#6711yescharacteristic
373C22×D3—21no—
374C22×D3C2×#6712yes—
375C3×Q8—62no—
376C3×Q8—61no—
377C3×Q8—61no—
378C3×D4—64no—
379C3×D4—62no—
380C3×D4—61no—
381C3×D4—61no—
382C3×D4—122no—
383C3×D4—242no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—32no—
391C2×C3×C4—42no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—81no—
398C2×C3×C4—81no—
399C2×C3×C4—82no—
400C2×C3×C4—122no—
401C2×C3×C4C2×D1212yes—
402C2×C3×C4D3×D412yes—
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4#23712yes—
405C2×C3×C4#23912yes—
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409#67—24no—
410#67—42no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—122no—
417C2×Dic3—124no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3C2×#6712yes—
421D12—22no—
422D12—21no—
423D12—21no—
424D12—82no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—42no—
428Dic6—22no—
429Dic6—21no—
430Dic6—21no—
431Dic6—64no—
432Dic6—62no—
433Dic6—62no—
434Dic6—62no—
435Dic6—62no—
436Dic6—122no—
437Dic6—124no—
438Dic6—122no—
439Dic6—122no—
440C3×C8—34no—
441C3⋊C8—61no—
442C3⋊C8—61no—
443C3⋊C8—61no—
444C3⋊C8—61no—
445C3⋊C8—121no—
446C3⋊C8—121no—
447C3⋊C8C2×D1214yes—
448C2×C32—22no—
449C2×C32C2×#12111yescharacteristic
450C2×C32#57711yescharacteristic
451C2×C32#57811yescharacteristic
452C3×D3—42no—
453C3×D3—81no—
454#41—62no—
455#41—62no—
456#41—62no—
457#41—62no—
458C2×Q8—31no—
459C2×Q8—31no—
460C2×Q8—92no—
461C2×Q8—181no—
462C2×Q8—182no—
463C2×Q8—182no—
464C2×D4—32no—
465C2×D4—31no—
466C2×D4—31no—
467C2×D4—62no—
468C2×D4—61no—
469C22×C4—21no—
470C22×C4—32no—
471C22×C4—61no—
472C22×C4—181no—
473C22×C4C2×D3211yescharacteristic
474Q16—184no—
475SD16—184no—
476M16—34no—
477M16—184no—
478C2×C8—32no—
479C2×C8—91no—
480C2×C8—91no—
481C2×C8—184no—
482C2×C8—182no—
483C4⋊C4—21no—
484C4⋊C4—31no—
485C4⋊C4—31no—
486C4⋊C4—62no—
487C4⋊C4—182no—
488C4⋊C4—182no—
489C4⋊C4C2×D3212yes—
490C22⋊C4—62no—
491C22⋊C4—62no—
492C22⋊C4—61no—
493C22⋊C4—182no—
494C22⋊C4—182no—
495C42—61no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—62no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3#89512yes—
511C22×C3#93912yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C22×#6711yescharacteristic
514C2×D3—22no—
515C2×D3—22no—
516C2×D3—22no—
517C2×D3—41no—
518C2×D3—41no—
519C2×D3—41no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—22no—
523C3×C4—42no—
524C3×C4—42no—
525C3×C4—62no—
526C3×C4—82no—
527C3×C4—121no—
528C3×C4—121no—
529C3×C4—121no—
530C3×C4#89512yes—
531C3×C4#93912yes—
532C3×C4C22×D1211yescharacteristic
533C3×C4C2×D3×D411yescharacteristic
534C3×C4C2×#23711yescharacteristic
535C3×C4C2×#23911yescharacteristic
536Dic3—22no—
537Dic3—41no—
538Dic3—41no—
539Dic3—41no—
540Dic3—124no—
541Dic3—122no—
542Dic3—122no—
543C32#306311yescharacteristic, complemented, Sylow
544C23—32no—
545C23—61no—
546C23D3×#6711yescharacteristic
547Q8—62no—
548Q8—61no—
549Q8—61no—
550Q8—182no—
551Q8—182no—
552Q8—362no—
553D4—64no—
554D4—61no—
555D4—61no—
556D4—62no—
557D4—122no—
558D4—242no—
559C2×C4—22no—
560C2×C4—32no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—81no—
567C2×C4—122no—
568C2×C4—182no—
569C2×C4—362no—
570C2×C4#379612yes—
571C2×C4D3×D1212yes—
572C2×C4D3×#6711yescharacteristic
573C2×C4C22×D3211yescharacteristic
574C8—34no—
575C8—181no—
576C8—181no—
577C2×C3—24no—
578C2×C3—22no—
579C2×C3—22no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—122no—
584C2×C3—241no—
585C2×C3C2×#89511yescharacteristic
586C2×C3#577511yescharacteristic
587C2×C3#577911yescharacteristic
588C2×C3C2×#93911yescharacteristic
589C2×C3#583611yescharacteristic
590C2×C3#583811yescharacteristic
591D3—42no—
592D3—81no—
593C22—21no—
594C22—21no—
595C22—62no—
596C22—62no—
597C22—62no—
598C22—121no—
599C22—121no—
600C22—121no—
601C22#6388612yes—
602C22C2×D3×#6711yescharacteristic
603C4—42no—
604C4—62no—
605C4—121no—
606C4—121no—
607C4—121no—
608C4—362no—
609C4#6388612yes—
610C4C2×#379611yescharacteristic
611C4C2×D3×D1211yescharacteristic
612C3—21no—
613C3#7921411yescharacteristic, complemented
614C3#8342311yescharacteristic, complemented
615C2—22no—
616C2—122no—
617C2—241no—
618C2C2×#6388611yescharacteristic
619C2#1059510611yescharacteristic
620C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC3×#5510C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594856C2semidirect
3. C2×#63831C2semidirect
4. C2×#63815C2semidirect
5. C2×#63637C2semidirect
6. C3×#4964C2semidirect
7. #10591083C2semidirect
8. #10590588C2semidirect
9. #10590587C2semidirect
10. #10590579C2semidirect
11. #10590578C2semidirect
63. #4964D3semidirect
100. C3×#208D4semidirect
302. #208D12semidirect
543. C32#3063semidirect
613. C3#79214semidirect
614. C3#83423semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
#105948562
C2×#638312
C2×#638152
C2×#636372
C3×#49642
#105910832
#105905882
#105905872
#105905792
#105905782
#834233
#792143