Finite Group Databasebeta

← #11867811

Subgroups — #11867811

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3#10594855C211yesmaximal, characteristic, complemented
4C2×#63815C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591638C212yesmaximal, complemented
7#10591635C212yesmaximal, complemented
8#10591502C212yesmaximal, complemented
9#10591499C212yesmaximal, complemented
10#10591130C211yesmaximal, characteristic, complemented
11C2×#63565C211yesmaximal, characteristic, complemented
12#83986—31nomaximal
13#83423—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17#64135C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#951—24no—
20C3×#946C2212yes—
21C2×C3×#216C2212yes—
22C3×#939—22no—
23C3×#938C2212yes—
24C2×C3×#214C2212yes—
25C3×#930—21no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#924—21no—
28C2×C3×#208C2211yescharacteristic
29#63961—22no—
30#63873—21no—
31#63863—21no—
32#63856C2212yes—
33#63856C2212yes—
34C2×#3711C2212yes—
35#63815—24no—
36C2×D3×C3⋊C8C2212yes—
37#63662C2211yescharacteristic
38#63662C2211yescharacteristic
39#63659C2211yescharacteristic
40#63659C2211yescharacteristic
41#63575C2212yes—
42#63573C2212yes—
43#63565C2212yes—
44#63565C2212yes—
45C2×C3×#137—31no—
46C3×#537—31no—
47#5833D311yescharacteristic
48#5825—31no—
49C2×#951D311yescharacteristic, complemented
50C2×#948—31no—
51#5816—31no—
52C2×#907—31no—
53#5233—31no—
54#5233—31no—
55#5233—61no—
56C2×#835—31no—
57#5189—32no—
58#5188—32no—
59#5174—32no—
60#5171—32no—
61#5121—31no—
62#5052—32no—
63#5051—32no—
64#5042—32no—
65#5041—32no—
66C2×#810—31no—
67#4964—31no—
68C32×#41—22no—
69C32×#41—22no—
70C2×C32×Q8C2311yescharacteristic
71C2×C32×D4—21no—
72C2×C32×D4C2311yescharacteristic
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—22no—
76C2×C3×#67D412yes—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C3×#235—22no—
80C3×#235—22no—
81C2×C3×D12D411yescharacteristic
82C2×C3×C4×D3C2312yes—
83C2×C3×Dic6—22no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6D411yescharacteristic
87C2×C3×Dic6C2312yes—
88#3757—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4×C3⋊Dic3—21no—
92C2×C3⋊(C3⋊C8)—22no—
93C2×C3⋊(C3⋊C8)C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2311yescharacteristic
95C3×#217—22no—
96C3×#216—24no—
97C3×#214—24no—
98C3×(C2×D3)⋊C4—22no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3C2312yes—
101C3×Dic3⋊C4—22no—
102C3×#208D414yescomplemented
103C2×C3×C3⋊C8C2312yes—
104#3724—22no—
105#3724—22no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3711—24no—
109D3×C3⋊C8—24no—
110#3063—91noSylow
111C2×C3×#41—21no—
112C2×C3×#41—31no—
113C2×C3×#41C2×D311yescharacteristic
114C2×C3×#41C2×D311yescharacteristic
115C22×C3×Q8—31no—
116C2×#235C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C3×#137—64no—
119C2×C3×Q16—32no—
120C2×C3×SD16—32no—
121C2×C3×M16—31no—
122C3×C22⋊Q8—32no—
123C3×C22⋊Q8—61no—
124C3×#121—32no—
125C3×#121—61no—
126C3×#121—62no—
127C2×C3×C4⋊C4—31no—
128#951—24no—
129#948—64no—
130#947—61no—
131#946—32no—
132#946—32no—
133#946C2×D312yes—
134#944—61no—
135#944—61no—
136C2×#216C2×D312yes—
137#939—22no—
138#938C2×D312yes—
139#936—61no—
140#935—62no—
141C2×#214C2×D312yes—
142#930—21no—
143#929—62no—
144#926—31no—
145#926—31no—
146#926—61no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148#924—21no—
149#924—32no—
150#924—32no—
151C2×#208—32no—
152C2×#208C2×D311yescharacteristic
153C22×C3⋊C8—31no—
154C22×C3⋊C8—31no—
155C22×C3⋊C8—32no—
156C22×C3⋊C8—61no—
157#907—64no—
158C2×ΓL(1,𝔽25)—32no—
159C2×D3×C8—32no—
160#835—31no—
161#835—31no—
162#835—31no—
163#835—31no—
164#835—32no—
165#835—32no—
166#835—61no—
167#835—61no—
168#832—31no—
169#832—31no—
170#832—31no—
171#832—31no—
172#832—61no—
173#832—61no—
174#818—32no—
175#817—32no—
176#810—32no—
177#810—32no—
178#808—32no—
179#807—32no—
180C23×C32—21no—
181C23×C32C2×D411yescharacteristic
182C22×C3×D3C2×D412yes—
183C32×Q8—21no—
184C32×Q8—21no—
185C32×D4—21no—
186C32×D4—21no—
187C32×D4—42no—
188C2×C32×C4—21no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D412yes—
192C2×C32×C4#4112yes—
193C2×C32×C4C2411yescharacteristic
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C3×#67—24no—
197C3×#67—82no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—42no—
201C2×C3×Dic3—81no—
202C2×C3×Dic3C2×D412yes—
203C3×D12—22no—
204C3×C4×D3—22no—
205C3×C4×D3—22no—
206C3×Dic6—22no—
207C3×Dic6—22no—
208C3×Dic6—22no—
209C3×Dic6—42no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212C3×C3⋊C8C2×D414yes—
213C2×#137—31no—
214C2×#131—91no—
215#537—31no—
216#536—91no—
217#470—92no—
218#468—92no—
219#467—92no—
220#465—92no—
221#428—91no—
222#416—91no—
223C2×#103—91no—
224C3×#41—24no—
225C3×#41—22no—
226C3×#41—22no—
227C3×#41—22no—
228C3×#41—22no—
229C3×#41—42no—
230C3×#41—62no—
231C3×#41—62no—
232C2×C3×Q8—21no—
233C2×C3×Q8—31no—
234C2×C3×Q8—32no—
235C2×C3×Q8—61no—
236C2×C3×Q8—62no—
237C2×C3×Q8—62no—
238C2×C3×Q8C22×D311yescharacteristic
239C2×C3×Q8C22×D311yescharacteristic
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—32no—
244C2×C3×D4—31no—
245C2×C3×D4—41no—
246C2×C3×D4—62no—
247C2×C3×D4C22×D311yescharacteristic
248C2×C3×D4C22×D311yescharacteristic
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—32no—
253C22×C3×C4—41no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—22no—
259C2×#67#6712yes—
260C22×Dic3—21no—
261C22×Dic3—21no—
262#235—22no—
263#235—22no—
264C2×D12#6711yescharacteristic
265C2×C4×D3C22×D312yes—
266C2×Dic6—22no—
267C2×Dic6—22no—
268C2×Dic6—21no—
269C2×Dic6#6711yescharacteristic
270C2×Dic6C22×D312yes—
271C3×Q16—64no—
272C3×SD16—64no—
273C3×M16—34no—
274C2×C3×C8—32no—
275C3×C4⋊C4—32no—
276C3×C4⋊C4—62no—
277C3×C4⋊C4—61no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—62no—
280#217—22no—
281#217—62no—
282#217—62no—
283#217—61no—
284#217—61no—
285#217—121no—
286#216—24no—
287#214—24no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—62no—
291C4⋊Dic3—21no—
292C4⋊Dic3—31no—
293C4⋊Dic3—31no—
294C4⋊Dic3—31no—
295C4⋊Dic3—31no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3C22×D312yes—
299Dic3⋊C4—22no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303Dic3⋊C4—62no—
304C4×Dic3—61no—
305C4×Dic3—61no—
306C4×Dic3—121no—
307#208—64no—
308#208#6714yescomplemented
309C2×C3⋊C8—31no—
310C2×C3⋊C8—31no—
311C2×C3⋊C8—31no—
312C2×C3⋊C8—31no—
313C2×C3⋊C8—61no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8—64no—
318C2×C3⋊C8—122no—
319C2×C3⋊C8C22×D312yes—
320ΓL(1,𝔽25)—64no—
321D3×C8—64no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32#12112yes—
328C22×C32C22×D411yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C32×C4—41no—
333C32×C4#12112yes—
334C32×C4C22×D411yescharacteristic
335C32×C4C2×#4111yescharacteristic
336C3⋊Dic3—41no—
337C3⋊Dic3—41no—
338C3×Dic3—22no—
339C3×Dic3—42no—
340C3×Dic3—42no—
341C2×#41—31no—
342C2×#41D3211yescharacteristic
343C22×Q8—31no—
344#137—64no—
345C2×Q16—32no—
346C2×SD16—32no—
347#131—184no—
348C2×M16—31no—
349C2×M16—92no—
350C22×C8—92no—
351C22×C8—91no—
352C4⋊Q8—181no—
353#124—181no—
354#123—182no—
355C22⋊Q8—32no—
356C22⋊Q8—61no—
357C22⋊Q8—92no—
358C22⋊Q8—92no—
359#121—32no—
360#121—61no—
361#121—62no—
362#117—91no—
363C2×C4⋊C4—31no—
364#107—92no—
365#106—92no—
366#103—92no—
367#103—92no—
368#103—91no—
369#103—91no—
370#102—91no—
371#102—91no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—32no—
376C23×C3—41no—
377C23×C3D3×D411yescharacteristic
378C23×C3C2×#6711yescharacteristic
379C22×D3C2×#6712yes—
380C3×Q8—22no—
381C3×Q8—21no—
382C3×Q8—21no—
383C3×Q8—21no—
384C3×Q8—21no—
385C3×Q8—41no—
386C3×Q8—62no—
387C3×Q8—62no—
388C3×Q8—62no—
389C3×Q8—122no—
390C3×D4—22no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—21no—
394C3×D4—21no—
395C3×D4—41no—
396C3×D4—44no—
397C3×D4—42no—
398C3×D4—42no—
399C3×D4—64no—
400C3×D4—62no—
401C3×D4—242no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—32no—
409C2×C3×C4—41no—
410C2×C3×C4—44no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—122no—
418C2×C3×C4—241no—
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D412yes—
421C2×C3×C4#23712yes—
422C2×C3×C4#23712yes—
423C2×C3×C4C2×#6712yes—
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427#67—24no—
428#67—82no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—42no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—81no—
437C2×Dic3—121no—
438C2×Dic3—121no—
439C2×Dic3C2×#6712yes—
440D12—22no—
441C4×D3—22no—
442C4×D3—22no—
443Dic6—22no—
444Dic6—22no—
445Dic6—22no—
446Dic6—42no—
447C3×C8—34no—
448C3⋊C8—61no—
449C3⋊C8—61no—
450C3⋊C8—61no—
451C3⋊C8—61no—
452C3⋊C8—121no—
453C3⋊C8—121no—
454C3⋊C8C2×#6714yes—
455C2×C32—22no—
456C2×C32—81no—
457C2×C32C2×#12111yescharacteristic
458C2×C32#57711yescharacteristic
459C2×C32#57811yescharacteristic
460C3×D3—42no—
461#41—22no—
462#41—22no—
463#41—62no—
464#41—62no—
465C2×Q8—31no—
466C2×Q8—32no—
467C2×Q8—61no—
468C2×Q8—62no—
469C2×Q8—62no—
470C2×Q8C2×D3211yescharacteristic
471C2×D4—21no—
472C2×D4—32no—
473C2×D4—31no—
474C2×D4—62no—
475C2×D4C2×D3211yescharacteristic
476C22×C4—21no—
477C22×C4—32no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4C2×D3211yescharacteristic
481Q16—64no—
482SD16—64no—
483M16—34no—
484M16—184no—
485C2×C8—32no—
486C2×C8—91no—
487C2×C8—91no—
488C2×C8—184no—
489C2×C8—182no—
490C4⋊C4—32no—
491C4⋊C4—62no—
492C4⋊C4—61no—
493C4⋊C4—91no—
494C4⋊C4—91no—
495C4⋊C4—182no—
496C4⋊C4—182no—
497C22⋊C4—62no—
498C22⋊C4—62no—
499C22⋊C4—182no—
500C22⋊C4—182no—
501C22⋊C4—181no—
502C42—181no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—42no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—62no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3—81no—
522C22×C3—81no—
523C22×C3#93812yes—
524C22×C3#93912yes—
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C22×#6711yescharacteristic
527C2×D3—22no—
528C2×D3—22no—
529C2×D3—22no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—22no—
533C3×C4—42no—
534C3×C4—41no—
535C3×C4—41no—
536C3×C4—62no—
537C3×C4—122no—
538C3×C4—122no—
539C3×C4#93812yes—
540C3×C4#93912yes—
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C2×#23711yescharacteristic
543C3×C4C2×#23711yescharacteristic
544C3×C4C22×#6711yescharacteristic
545Dic3—22no—
546Dic3—42no—
547Dic3—42no—
548Dic3—121no—
549Dic3—121no—
550Dic3—121no—
551Dic3—121no—
552Dic3—241no—
553Dic3—241no—
554C32#306311yescharacteristic, complemented, Sylow
555C23—21no—
556C23—32no—
557C23D3×#6711yescharacteristic
558Q8—21no—
559Q8—21no—
560Q8—62no—
561Q8—62no—
562Q8—62no—
563Q8—122no—
564D4—21no—
565D4—21no—
566D4—42no—
567D4—64no—
568D4—62no—
569D4—242no—
570C2×C4—21no—
571C2×C4—32no—
572C2×C4—42no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—122no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—241no—
581C2×C4#380512yes—
582C2×C4D3×#6712yes—
583C2×C4D3×#6711yescharacteristic
584C2×C4C22×D3211yescharacteristic
585C8—34no—
586C8—181no—
587C8—181no—
588C2×C3—22no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—42no—
594C2×C3—82no—
595C2×C3—81no—
596C2×C3—81no—
597C2×C3—122no—
598C2×C3#577811yescharacteristic
599C2×C3#577911yescharacteristic
600C2×C3C2×#93811yescharacteristic
601C2×C3C2×#93911yescharacteristic
602C2×C3#583611yescharacteristic
603C2×C3#583811yescharacteristic
604D3—42no—
605C22—21no—
606C22—21no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—62no—
611C22—62no—
612C22—62no—
613C22#6397012yes—
614C22C2×D3×#6711yescharacteristic
615C4—41no—
616C4—62no—
617C4—122no—
618C4—122no—
619C4—361no—
620C4—361no—
621C4#6397012yes—
622C4C2×#380511yescharacteristic
623C4C2×D3×#6711yescharacteristic
624C3—21no—
625C3#8342311yescharacteristic, complemented
626C3#8398611yescharacteristic, complemented
627C2—22no—
628C2—81no—
629C2—122no—
630C2#1059546411yescharacteristic
631C2#1059546511yescharacteristic
632C2C2×#6397011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5833C2
hypercenterC2×#41D32
hypocenterC32#3063
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×C3×#951C2semidirect
3. #10594855C2semidirect
4. C2×#63815C2semidirect
5. #10592932C2semidirect
6. #10591638C2semidirect
7. #10591635C2semidirect
8. #10591502C2semidirect
9. #10591499C2semidirect
10. #10591130C2semidirect
11. C2×#63565C2semidirect
49. C2×#951D3semidirect
102. C3×#208D4semidirect
308. #208#67semidirect
554. C32#3063semidirect
625. C3#83423semidirect
626. C3#83986semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
C2×C3×#9512
#105948552
C2×#638152
#105929322
#105916382
#105916352
#105915022
#105914992
#105911302
C2×#635652
#839863
#834233