Finite Group Databasebeta

← #11868116

Subgroups — #11868116

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#932C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3#10594786C211yesmaximal, characteristic, complemented
4#10594776C211yesmaximal, characteristic, complemented
5C2×#63660C211yesmaximal, characteristic, complemented
6#10591506C214yesmaximal, complemented
7#10591505C214yesmaximal, complemented
8#10591141C211yesmaximal, characteristic, complemented
9#10591076C211yesmaximal, characteristic, complemented
10#83963—31nomaximal
11#83943—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×#214—21no—
18C2×C3×#214C2212yescomplemented
19C3×#932—22no—
20C3×#932—22no—
21C3×#932—22no—
22C3×#932C2214yes—
23C2×C3×#213—21no—
24C2×C3×#213C2212yescomplemented
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63827—21no—
28#63827C2212yescomplemented
29#63823—21no—
30#63823C2212yescomplemented
31#63822—22no—
32#63815—22no—
33#63814C2214yescomplemented
34D3×#208—22no—
35#63660C2214yescomplemented
36#63577C2214yescomplemented
37#63560C2212yescomplemented
38#63558C2212yescomplemented
39C2×C3×AGL(1,ℤ/8)—31no—
40C2×C3×AGL(1,ℤ/8)—31no—
41#5822—31no—
42#5822—31no—
43#5819—31no—
44C2×#932D311yescharacteristic, complemented
45C2×#932D311yescharacteristic, complemented
46#5745—31no—
47#5237—31no—
48C2×#833—31no—
49C2×#833—31no—
50C2×#833—61no—
51#5200—34no—
52#5199—34no—
53#5177—34no—
54#5160—34no—
55#5132—31no—
56#5125—31no—
57#5124—31no—
58C24×C32—21no—
59C2×C32×D4—21no—
60C2×C32×D4—21no—
61C2×C32×D4—21no—
62C2×C32×D4—21no—
63C2×C32×D4—21no—
64C2×C32×D4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C2×C3×#67—21no—
67C2×C3×#67—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C3×#235—21no—
74C3×#235D412yes—
75C3×#235C2312yes—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82#3748—21no—
83#3748—21no—
84#3748C2312yes—
85#3748C2312yes—
86C2×C3⋊(C3⋊C8)—21no—
87C2×C3⋊(C3⋊C8)—21no—
88C3×#214—24no—
89C3×#214—24no—
90C3×#213—24no—
91C3×#213—24no—
92C3×#208—21no—
93C3×#208D412yes—
94C3×#208D412yes—
95C3×#208C2312yes—
96C2×C3×C3⋊C8—21no—
97C2×C3×C3⋊C8C2312yes—
98#3718—22no—
99#3715—22no—
100#3715—22no—
101#3713—22no—
102#3711—24no—
103D3×C3⋊C8—24no—
104#3068—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×D4—21no—
108C22×C3×D4C2×D311yescharacteristic
109C22×C3×D4C2×D311yescharacteristic
110C2×#235C2×D311yescharacteristic
111C2×#235C2×D311yescharacteristic
112C3×AGL(1,ℤ/8)—34no—
113C3×AGL(1,ℤ/8)—62no—
114C3×AGL(1,ℤ/8)—62no—
115C3×AGL(1,ℤ/8)—62no—
116C2×C3×SD16—32no—
117C2×C3×SD16—61no—
118C2×C3×D8—32no—
119C2×C3×D8—61no—
120C2×C3×M16—31no—
121C2×C3×M16—31no—
122#951—32no—
123#951—61no—
124#950—62no—
125#950—62no—
126#949—32no—
127#949—61no—
128#948—34no—
129#948—62no—
130#942—32no—
131#942—61no—
132C2×#214—21no—
133C2×#214C2×D312yescomplemented
134#932—22no—
135#932—22no—
136#932—22no—
137#932—32no—
138#932—61no—
139#932C2×D314yes—
140C2×#213—21no—
141C2×#213C2×D312yescomplemented
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C2×#208—61no—
148C2×#208—62no—
149C2×#208C2×D311yescharacteristic
150C2×#208C2×D311yescharacteristic
151#907—62no—
152D3×M16—62no—
153#901—34no—
154#836—32no—
155#833—34no—
156#833—34no—
157#833—32no—
158#833—64no—
159#824—32no—
160#823—32no—
161#822—34no—
162#819—34no—
163C23×C32—22no—
164C23×C32—41no—
165C23×C32—41no—
166C23×C32—82no—
167C23×C32#4111yescharacteristic
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C32×D4—22no—
171C32×D4—22no—
172C32×D4—41no—
173C32×D4—41no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4#4111yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C3×#67—22no—
181C3×#67—22no—
182C3×#67—41no—
183C3×#67—41no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12—21no—
189C3×D12C2×D412yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×C4×D3—41no—
193C3×C4×D3—41no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196C3×Dic6—21no—
197C3×Dic6C2×D412yes—
198C3⋊(C3⋊C8)—22no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—22no—
201C3×C3⋊C8C2×D414yes—
202#575—91no—
203C2×AGL(1,ℤ/8)—31no—
204C2×AGL(1,ℤ/8)—31no—
205#568—91no—
206#472—94no—
207#471—94no—
208#430—91no—
209#413—91no—
210C2×#100—91no—
211C24×C3—22no—
212C24×C3—21no—
213C24×C3—21no—
214C3×#41—32no—
215C3×#41—32no—
216C3×#41—61no—
217C3×#41—61no—
218C3×#41—61no—
219C3×#41—61no—
220C3×#41—61no—
221C3×#41—61no—
222C2×C3×Q8—31no—
223C2×C3×Q8—31no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—22no—
236C2×C3×D4—31no—
237C2×C3×D4—31no—
238C2×C3×D4—41no—
239C2×C3×D4—41no—
240C2×C3×D4—41no—
241C2×C3×D4—41no—
242C2×C3×D4—61no—
243C2×C3×D4—61no—
244C2×C3×D4C22×D312yes—
245C2×C3×D4C22×D312yes—
246C22×C3×C4—21no—
247C22×C3×C4—61no—
248C22×C3×C4—61no—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C2×#67—21no—
252C2×#67—21no—
253#235—21no—
254#235—21no—
255#235—21no—
256#235—21no—
257#235—21no—
258#235—21no—
259#235#6712yes—
260#235C22×D312yes—
261C2×D12#6711yescharacteristic
262C2×D12C22×D311yescharacteristic
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×Dic6#6711yescharacteristic
266C2×Dic6C22×D311yescharacteristic
267C3×SD16—64no—
268C3×SD16—64no—
269C3×D8—64no—
270C3×D8—64no—
271C3×M16—32no—
272C3×M16—32no—
273C3×M16—32no—
274C3×M16—61no—
275C2×C3×C8—32no—
276C2×C3×C8—61no—
277#216—62no—
278#216—62no—
279#215—62no—
280#215—62no—
281#214—24no—
282#214—24no—
283#214—62no—
284#214—62no—
285#213—24no—
286#213—24no—
287#213—62no—
288#213—62no—
289#208—21no—
290#208—32no—
291#208—32no—
292#208—32no—
293#208—32no—
294#208—62no—
295#208—62no—
296#208—61no—
297#208—61no—
298#208—61no—
299#208—61no—
300#208—64no—
301#208—121no—
302#208—121no—
303#208#6712yes—
304#208#6712yes—
305#208C22×D312yes—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C2×C3⋊C8—61no—
310C2×C3⋊C8—61no—
311C2×C3⋊C8—64no—
312C2×C3⋊C8—121no—
313C2×C3⋊C8—121no—
314C2×C3⋊C8C22×D312yes—
315ΓL(1,𝔽25)—64no—
316D3×C8—64no—
317C22×C32—41no—
318C22×C32—42no—
319C22×C32—82no—
320C22×C32—82no—
321C22×C32—82no—
322C22×C32#12111yescharacteristic
323C22×C32#12111yescharacteristic
324C22×C32C2×#4111yescharacteristic
325C2×C3×D3—22no—
326C2×C3×D3—41no—
327C2×C3×D3—81no—
328C2×C3×D3—81no—
329C32×C4#12111yescharacteristic
330C32×C4#12111yescharacteristic
331C32×C4C22×D411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3×Dic3—22no—
334C3×Dic3—41no—
335C2×#41—31no—
336C2×#41—31no—
337C22×D4D3211yescharacteristic
338#137—92no—
339#137—181no—
340AGL(1,ℤ/8)—34no—
341AGL(1,ℤ/8)—62no—
342AGL(1,ℤ/8)—62no—
343AGL(1,ℤ/8)—62no—
344AGL(1,ℤ/8)—92no—
345AGL(1,ℤ/8)—181no—
346#135—182no—
347C2×SD16—32no—
348C2×SD16—61no—
349C2×D8—32no—
350C2×D8—61no—
351#131—94no—
352#131—182no—
353C2×M16—31no—
354C2×M16—31no—
355C2×M16—91no—
356C2×M16—91no—
357C2×M16—182no—
358#108—94no—
359#101—92no—
360#100—92no—
361#100—94no—
362C23×C3—24no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—21no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—61no—
373C23×C3—61no—
374C23×C3—82no—
375C23×C3—82no—
376C23×C3—84no—
377C23×C3#23711yescharacteristic
378C23×C3#23711yescharacteristic
379C22×D3—21no—
380C22×D3—21no—
381C3×Q8—32no—
382C3×Q8—61no—
383C3×Q8—61no—
384C3×Q8—61no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—32no—
390C3×D4—42no—
391C3×D4—42no—
392C3×D4—42no—
393C3×D4—42no—
394C3×D4—41no—
395C3×D4—41no—
396C3×D4—41no—
397C3×D4—41no—
398C3×D4—62no—
399C3×D4—62no—
400C3×D4—61no—
401C3×D4—61no—
402C3×D4—61no—
403C3×D4—121no—
404C3×D4—121no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—121no—
416C2×C3×C4—121no—
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4#23711yescharacteristic
422C2×C3×C4#23711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—22no—
430#67—22no—
431#67—41no—
432#67—41no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435D12—21no—
436D12—21no—
437D12—21no—
438D12C2×#6712yes—
439C4×D3—22no—
440C4×D3—22no—
441C4×D3—41no—
442C4×D3—41no—
443Dic6—21no—
444Dic6—21no—
445Dic6—21no—
446Dic6C2×#6712yes—
447C3×C8—34no—
448C3×C8—62no—
449C3⋊C8—22no—
450C3⋊C8—62no—
451C3⋊C8—62no—
452C3⋊C8—62no—
453C3⋊C8—62no—
454C3⋊C8—122no—
455C3⋊C8—122no—
456C3⋊C8C2×#6714yes—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—82no—
461C2×C32C2×#12111yescharacteristic
462C3×D3—42no—
463C3×D3—81no—
464C24—21no—
465#41—32no—
466#41—32no—
467#41—61no—
468#41—61no—
469#41—61no—
470#41—61no—
471#41—61no—
472#41—61no—
473C2×Q8—31no—
474C2×Q8—31no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—31no—
481C2×D4—31no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4C2×D3212yes—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4C2×D3211yescharacteristic
488Q16—182no—
489SD16—64no—
490SD16—64no—
491SD16—182no—
492SD16—182no—
493D8—64no—
494D8—64no—
495D8—182no—
496M16—32no—
497M16—32no—
498M16—32no—
499M16—61no—
500M16—92no—
501M16—92no—
502M16—184no—
503M16—181no—
504M16—181no—
505C2×C8—32no—
506C2×C8—61no—
507C2×C8—184no—
508C2×C8—181no—
509C2×C8—181no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—42no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—62no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3—82no—
523C22×C3—82no—
524C22×C3—84no—
525C22×C3—82no—
526C22×C3—82no—
527C22×C3—84no—
528C22×C3—84no—
529C22×C3—121no—
530C22×C3—241no—
531C22×C3—241no—
532C22×C3#93811yescharacteristic
533C22×C3#93811yescharacteristic
534C22×C3#93911yescharacteristic
535C22×C3#93911yescharacteristic
536C22×C3C2×#23711yescharacteristic
537C22×C3C2×#23711yescharacteristic
538C2×D3—22no—
539C2×D3—41no—
540C2×D3—81no—
541C2×D3—81no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—62no—
547C3×C4—121no—
548C3×C4#93811yescharacteristic
549C3×C4#93811yescharacteristic
550C3×C4#93911yescharacteristic
551C3×C4#93911yescharacteristic
552C3×C4C2×D3×D411yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C22×#6711yescharacteristic
555C3×C4C22×#6711yescharacteristic
556Dic3—22no—
557Dic3—41no—
558C32#306811yescharacteristic, complemented, Sylow
559C23—22no—
560C23—41no—
561C23—41no—
562C23—61no—
563C23—61no—
564C23—82no—
565C23#380511yescharacteristic
566Q8—32no—
567Q8—61no—
568Q8—61no—
569Q8—61no—
570D4—22no—
571D4—22no—
572D4—32no—
573D4—41no—
574D4—41no—
575D4—62no—
576D4—62no—
577D4—61no—
578D4—61no—
579D4—61no—
580D4—121no—
581D4—121no—
582C2×C4—61no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—61no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4#380511yescharacteristic
589C2×C4D3×#6711yescharacteristic
590C2×C4D3×#6711yescharacteristic
591C2×C4D3×#6711yescharacteristic
592C2×C4D3×#6711yescharacteristic
593C2×C4C22×D3211yescharacteristic
594C8—34no—
595C8—62no—
596C8—182no—
597C8—182no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—41no—
607C2×C3—41no—
608C2×C3—84no—
609C2×C3—82no—
610C2×C3—82no—
611C2×C3—122no—
612C2×C3—241no—
613C2×C3C2×#93811yescharacteristic
614C2×C3C2×#93911yescharacteristic
615D3—42no—
616D3—81no—
617C22—41no—
618C22—42no—
619C22—62no—
620C22—82no—
621C22—82no—
622C22—82no—
623C22—121no—
624C22—241no—
625C22—241no—
626C22#6397011yescharacteristic
627C22#6397011yescharacteristic
628C22C2×#380511yescharacteristic
629C4—62no—
630C4—121no—
631C4#6397011yescharacteristic
632C4#6397011yescharacteristic
633C4C2×D3×#6711yescharacteristic
634C4C2×D3×#6711yescharacteristic
635C3—21no—
636C3#8394311yescharacteristic, complemented
637C3#8396311yescharacteristic, complemented
638C2—21no—
639C2—21no—
640C2—21no—
641C2—82no—
642C2—122no—
643C2—241no—
644C2C2×#6397011yescharacteristic
subgroupG/H
centerC2C2×#63970
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC2×C32C2×#121
hypercenterC22×D4D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#932C2semidirect
2. C2×C3×#932C2semidirect
3. #10594786C2semidirect
4. #10594776C2semidirect
5. C2×#63660C2semidirect
6. #10591506C2semidirect
7. #10591505C2semidirect
8. #10591141C2semidirect
9. #10591076C2semidirect
18. C2×C3×#214C22semidirect
24. C2×C3×#213C22semidirect
28. #63827C22semidirect
30. #63823C22semidirect
33. #63814C22semidirect
35. #63660C22semidirect
36. #63577C22semidirect
37. #63560C22semidirect
38. #63558C22semidirect
44. C2×#932D3semidirect
45. C2×#932D3semidirect
133. C2×#214C2×D3semidirect
141. C2×#213C2×D3semidirect
558. C32#3068semidirect
636. C3#83943semidirect
637. C3#83963semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9322
#105947862
#105947762
C2×#636602
#105915062
#105915052
#105911412
#105910762
#839633
#839433