Finite Group Databasebeta

← #11868114

Subgroups — #11868114

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3#10594795C211yesmaximal, characteristic, complemented
4#10594776C211yesmaximal, characteristic, complemented
5C2×C3×#833C211yesmaximal, characteristic, complemented
6#10591508C214yesmaximal, complemented
7#10591507C214yesmaximal, complemented
8#10591143C211yesmaximal, characteristic, complemented
9#10591078C211yesmaximal, characteristic, complemented
10#83943—31nomaximal
11#78703—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×#3754C2212yescomplemented
16#64141—22no—
17#64141—22no—
18C2×#3753C2212yescomplemented
19C2×#3748C2211yescharacteristic
20C2×C3×#214—21no—
21C3×#932—22no—
22C3×#932C2214yes—
23C2×C3×#213—21no—
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63833—21no—
28#63831C2212yescomplemented
29#63830—21no—
30#63829—22no—
31#63825C2212yescomplemented
32#63815C2214yescomplemented
33#63814—22no—
34D3×#208—22no—
35C3×#833C2214yescomplemented
36#63578C2214yescomplemented
37#63561C2212yescomplemented
38#63559C2212yescomplemented
39C2×C3×AGL(1,ℤ/8)—31no—
40#5822—31no—
41#5819—31no—
42C2×#932—31no—
43C2×#932—31no—
44C2×#932—61no—
45C2×#932D311yescharacteristic, complemented
46#5748—31no—
47#5745—31no—
48C2×C3×#100—31no—
49C2×#833D311yescharacteristic, complemented
50#5200—34no—
51#5199—34no—
52#5132—31no—
53#5132—31no—
54#5124—31no—
55#5124—31no—
56#4749—34no—
57#4748—34no—
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×#638—21no—
67#3828—21no—
68#3828—21no—
69#3828—21no—
70#3828—21no—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634C2311yescharacteristic
74C2×C3×#67—21no—
75C3×#235—21no—
76C3×#235—21no—
77C3×#235D412yes—
78C3×#235C2312yes—
79C2×C3×D12D411yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6D411yescharacteristic
82#3754—24no—
83#3753—24no—
84#3748D412yes—
85#3748D412yes—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#214—24no—
88C3×#213—24no—
89C3×#208—21no—
90C3×#208—21no—
91C3×#208—21no—
92C3×#208C2312yes—
93C3×#208C2312yes—
94C3×#208C2312yes—
95C2×C3×C3⋊C8—21no—
96C2×C3×C3⋊C8—21no—
97C2×C3×C3⋊C8—21no—
98#3719—22no—
99#3717—22no—
100#3716—22no—
101#3714—22no—
102#3711—24no—
103D3×C3⋊C8—24no—
104#3068—91noSylow
105C2×C3×#41—31no—
106C22×C3×D4—21no—
107C22×C3×D4C2×D311yescharacteristic
108C22×C3×D4C2×D311yescharacteristic
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C3×AGL(1,ℤ/8)—34no—
114C3×AGL(1,ℤ/8)—62no—
115C2×C3×SD16—61no—
116C2×C3×D8—61no—
117C2×C3×M16—31no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120#951—32no—
121#950—62no—
122#949—32no—
123#948—34no—
124#948—62no—
125#942—61no—
126C2×#214—21no—
127C2×#214—32no—
128C2×#214—32no—
129C2×#214—62no—
130#932—22no—
131#932—61no—
132#932—62no—
133#932—62no—
134#932—62no—
135#932—62no—
136#932—64no—
137#932—64no—
138#932C2×D314yes—
139C2×#213—21no—
140C2×#213—32no—
141C2×#213—32no—
142C2×#213—62no—
143C2×#208—31no—
144C2×#208—31no—
145C2×#208—61no—
146C2×#208—62no—
147C2×#208C2×D311yescharacteristic
148C2×#208C2×D311yescharacteristic
149C2×#208C2×D311yescharacteristic
150#909—32no—
151#909—61no—
152#908—32no—
153#908—61no—
154#907—34no—
155D3×M16—62no—
156#904—62no—
157#901—62no—
158C3×#100—34no—
159#833C2×D314yescomplemented
160#824—32no—
161#824—32no—
162#823—32no—
163#823—32no—
164#822—34no—
165#822—34no—
166C23×C32—22no—
167C23×C32—41no—
168C23×C32—41no—
169C23×C32—82no—
170C23×C32#4111yescharacteristic
171C22×C3⋊D3—21no—
172C22×C3×D3—21no—
173C32×D4—22no—
174C32×D4—22no—
175C32×D4—41no—
176C32×D4—41no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4#4111yescharacteristic
182C2×C32×C4C2411yescharacteristic
183#638—41no—
184#638—41no—
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—21no—
188C4×C3⋊D3—41no—
189C4×C3⋊D3—41no—
190#634—21no—
191#634—21no—
192C3×#67—22no—
193C3×#67—22no—
194C2×C3×Dic3—21no—
195C3×D12—21no—
196C3×D12C2×D412yes—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×Dic6—21no—
200C3×Dic6C2×D412yes—
201C3⋊(C3⋊C8)C2×D414yes—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205#575—91no—
206C2×AGL(1,ℤ/8)—31no—
207C2×AGL(1,ℤ/8)—91no—
208#568—91no—
209#472—94no—
210#471—94no—
211#430—91no—
212#413—91no—
213C2×#100—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—41no—
217C3×#41—32no—
218C3×#41—32no—
219C3×#41—61no—
220C3×#41—61no—
221C2×C3×Q8—31no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—21no—
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—22no—
235C2×C3×D4—31no—
236C2×C3×D4—41no—
237C2×C3×D4—41no—
238C2×C3×D4—41no—
239C2×C3×D4—61no—
240C2×C3×D4C22×D312yes—
241C2×C3×D4C22×D312yes—
242C22×C3×C4—21no—
243C22×C3×C4—61no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—21no—
247C2×#67—61no—
248C2×#67—61no—
249C2×#67—121no—
250#235—21no—
251#235—21no—
252#235—62no—
253#235—62no—
254#235—61no—
255#235—61no—
256#235—61no—
257#235—61no—
258#235—61no—
259#235—61no—
260#235—61no—
261#235—61no—
262#235—121no—
263#235—121no—
264#235#6712yes—
265#235C22×D312yes—
266C2×D12—31no—
267C2×D12—31no—
268C2×D12—61no—
269C2×D12#6711yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×C4×D3—121no—
274C2×Dic6—31no—
275C2×Dic6—31no—
276C2×Dic6—61no—
277C2×Dic6#6711yescharacteristic
278C3×SD16—64no—
279C3×D8—64no—
280C3×M16—32no—
281C3×M16—32no—
282C3×M16—32no—
283C3×M16—61no—
284C3×M16—61no—
285C3×M16—61no—
286C2×C3×C8—61no—
287C2×C3×C8—61no—
288C2×C3×C8—61no—
289#216—62no—
290#215—62no—
291#214—24no—
292#214—62no—
293#214—64no—
294#214—64no—
295#214—68no—
296#213—24no—
297#213—62no—
298#213—64no—
299#213—64no—
300#213—68no—
301#208—21no—
302#208—21no—
303#208—21no—
304#208—32no—
305#208—32no—
306#208—32no—
307#208—32no—
308#208—62no—
309#208—62no—
310#208—64no—
311#208C22×D312yes—
312#208C22×D312yes—
313#208C22×D312yes—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—32no—
318C2×C3⋊C8—32no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8—64no—
321Dic12—62no—
322D24—62no—
323#204—62no—
324#204—62no—
325ΓL(1,𝔽25)—64no—
326D3×C8—64no—
327C22×C32—41no—
328C22×C32—42no—
329C22×C32—82no—
330C22×C32—82no—
331C22×C32—82no—
332C22×C32#12111yescharacteristic
333C22×C32#12111yescharacteristic
334C22×C32C2×#4111yescharacteristic
335C2×C3⋊D3—41no—
336C2×C3⋊D3—81no—
337C2×C3×D3—22no—
338C2×C3×D3—81no—
339C32×C4#12111yescharacteristic
340C32×C4#12111yescharacteristic
341C32×C4C22×D411yescharacteristic
342C32×C4C22×D411yescharacteristic
343C3⋊Dic3—41no—
344C3×Dic3—22no—
345C2×#41—31no—
346C2×#41—91no—
347C22×D4D3211yescharacteristic
348#137—92no—
349#137—181no—
350AGL(1,ℤ/8)—34no—
351AGL(1,ℤ/8)—62no—
352AGL(1,ℤ/8)—92no—
353AGL(1,ℤ/8)—181no—
354AGL(1,ℤ/8)—182no—
355AGL(1,ℤ/8)—182no—
356#135—182no—
357C2×SD16—61no—
358C2×SD16—92no—
359C2×D8—61no—
360C2×D8—92no—
361#131—94no—
362#131—182no—
363C2×M16—31no—
364C2×M16—31no—
365C2×M16—31no—
366C2×M16—91no—
367C2×M16—182no—
368#108—94no—
369#101—92no—
370#100—34no—
371#100—92no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—21no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—61no—
383C23×C3—82no—
384C23×C3—82no—
385C23×C3—84no—
386C23×C3#23511yescharacteristic
387C23×C3#23711yescharacteristic
388C22×D3—21no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—121no—
392C3×Q8—32no—
393C3×Q8—61no—
394C3×D4—24no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—22no—
399C3×D4—32no—
400C3×D4—42no—
401C3×D4—42no—
402C3×D4—42no—
403C3×D4—41no—
404C3×D4—41no—
405C3×D4—41no—
406C3×D4—41no—
407C3×D4—62no—
408C3×D4—62no—
409C3×D4—61no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—61no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4#23511yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4D3×D411yescharacteristic
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4#23711yescharacteristic
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—22no—
432#67—22no—
433#67—122no—
434#67—122no—
435#67—121no—
436#67—121no—
437#67—121no—
438#67—121no—
439C2×Dic3—21no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—121no—
443D12—21no—
444D12—62no—
445D12—61no—
446D12—61no—
447D12—61no—
448D12—61no—
449D12—121no—
450D12C2×#6712yes—
451C4×D3—22no—
452C4×D3—22no—
453C4×D3—122no—
454C4×D3—122no—
455C4×D3—121no—
456C4×D3—121no—
457C4×D3—121no—
458C4×D3—121no—
459Dic6—21no—
460Dic6—62no—
461Dic6—61no—
462Dic6—61no—
463Dic6—61no—
464Dic6—61no—
465Dic6—121no—
466Dic6C2×#6712yes—
467C3×C8—62no—
468C3×C8—62no—
469C3×C8—62no—
470C3⋊C8—22no—
471C3⋊C8—22no—
472C3⋊C8—22no—
473C3⋊C8—34no—
474C3⋊C8—34no—
475C3⋊C8—64no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—82no—
480C2×C32C2×#12111yescharacteristic
481C3⋊D3—81no—
482C3×D3—42no—
483C24—21no—
484#41—32no—
485#41—32no—
486#41—61no—
487#41—61no—
488#41—181no—
489#41—181no—
490#41—181no—
491#41—181no—
492C2×Q8—31no—
493C2×Q8—91no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—31no—
500C2×D4—61no—
501C2×D4—91no—
502C2×D4—181no—
503C2×D4C2×D3212yes—
504C22×C4—61no—
505C22×C4—181no—
506C22×C4C2×D3211yescharacteristic
507Q16—182no—
508SD16—64no—
509SD16—182no—
510SD16—182no—
511SD16—184no—
512D8—64no—
513D8—182no—
514D8—184no—
515M16—32no—
516M16—32no—
517M16—32no—
518M16—61no—
519M16—61no—
520M16—61no—
521M16—92no—
522M16—92no—
523M16—184no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—92no—
528C2×C8—184no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—42no—
535C22×C3—44no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—62no—
539C22×C3—82no—
540C22×C3—82no—
541C22×C3—84no—
542C22×C3—82no—
543C22×C3—82no—
544C22×C3—82no—
545C22×C3—82no—
546C22×C3—84no—
547C22×C3—84no—
548C22×C3—241no—
549C22×C3#88411yescharacteristic
550C22×C3#88411yescharacteristic
551C22×C3#93911yescharacteristic
552C22×C3#93911yescharacteristic
553C22×C3C2×#23511yescharacteristic
554C22×C3C2×#23711yescharacteristic
555C2×D3—22no—
556C2×D3—81no—
557C2×D3—122no—
558C2×D3—121no—
559C2×D3—121no—
560C2×D3—242no—
561C2×D3—241no—
562C2×D3—241no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—62no—
568C3×C4#88411yescharacteristic
569C3×C4#88411yescharacteristic
570C3×C4#93911yescharacteristic
571C3×C4#93911yescharacteristic
572C3×C4C2×D3×D411yescharacteristic
573C3×C4C2×D3×D411yescharacteristic
574C3×C4C2×D3×D411yescharacteristic
575C3×C4C22×#6711yescharacteristic
576Dic3—22no—
577Dic3—122no—
578Dic3—121no—
579Dic3—121no—
580C32#306811yescharacteristic, complemented, Sylow
581C23—22no—
582C23—41no—
583C23—41no—
584C23—61no—
585C23—82no—
586C23—181no—
587C23#380411yescharacteristic
588Q8—32no—
589Q8—61no—
590Q8—181no—
591Q8—181no—
592D4—22no—
593D4—22no—
594D4—32no—
595D4—41no—
596D4—41no—
597D4—62no—
598D4—62no—
599D4—61no—
600D4—181no—
601D4—181no—
602D4—361no—
603D4—361no—
604C2×C4—61no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—181no—
608C2×C4—361no—
609C2×C4—361no—
610C2×C4#380411yescharacteristic
611C2×C4D3×#6711yescharacteristic
612C2×C4D3×#6711yescharacteristic
613C2×C4#381111yescharacteristic
614C2×C4#381111yescharacteristic
615C2×C4C22×D3211yescharacteristic
616C8—62no—
617C8—62no—
618C8—62no—
619C8—94no—
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—41no—
629C2×C3—41no—
630C2×C3—84no—
631C2×C3—82no—
632C2×C3—82no—
633C2×C3—122no—
634C2×C3C2×#88411yescharacteristic
635C2×C3C2×#93911yescharacteristic
636D3—42no—
637D3—242no—
638D3—241no—
639D3—241no—
640C22—41no—
641C22—42no—
642C22—62no—
643C22—82no—
644C22—82no—
645C22—82no—
646C22—241no—
647C22—361no—
648C22—721no—
649C22#6397111yescharacteristic
650C22#6397111yescharacteristic
651C22C2×#380411yescharacteristic
652C4—62no—
653C4—361no—
654C4#6397111yescharacteristic
655C4#6397111yescharacteristic
656C4C2×D3×#6711yescharacteristic
657C4C2×#381111yescharacteristic
658C3—21no—
659C3#7870311yescharacteristic, complemented
660C3#8394311yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—21no—
664C2—82no—
665C2—122no—
666C2—721no—
667C2C2×#6397111yescharacteristic
subgroupG/H
centerC2C2×#63971
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×#64141C2semidirect
2. C2×C3×#932C2semidirect
3. #10594795C2semidirect
4. #10594776C2semidirect
5. C2×C3×#833C2semidirect
6. #10591508C2semidirect
7. #10591507C2semidirect
8. #10591143C2semidirect
9. #10591078C2semidirect
15. C2×#3754C22semidirect
18. C2×#3753C22semidirect
28. #63831C22semidirect
31. #63825C22semidirect
32. #63815C22semidirect
35. C3×#833C22semidirect
36. #63578C22semidirect
37. #63561C22semidirect
38. #63559C22semidirect
45. C2×#932D3semidirect
49. C2×#833D3semidirect
159. #833C2×D3semidirect
580. C32#3068semidirect
659. C3#78703semidirect
660. C3#83943semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C2×C3×#9322
#105947952
#105947762
C2×C3×#8332
#105915082
#105915072
#105911432
#105910782
#839433
#787033