Finite Group Databasebeta

← #11868117

Subgroups — #11868117

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×#64117C211yesmaximal, characteristic, complemented
2C3×#5745C211yesmaximal, characteristic, complemented
3#10594795C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5125C211yesmaximal, characteristic, complemented
6#10591078C211yesmaximal, characteristic, complemented
7C2×#63559C211yesmaximal, characteristic, complemented
8#10590931C214yesmaximal, complemented
9#10590927C214yesmaximal, complemented
10#83814—31nomaximal
11#79261—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64117—22no—
17#64117—22no—
18C2×#3745C2212yescomplemented
19C2×#3744C2212yescomplemented
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C3×#907—22no—
24C3×D3×M16—22no—
25C3×#901C2214yescomplemented
26#63833—21no—
27C2×#3717—21no—
28#63831C2212yescomplemented
29#63830—21no—
30#63829—22no—
31#63825—22no—
32#63825C2214yes—
33#63825C2212yescomplemented
34C2×#3714—21no—
35C3×#819C2214yescomplemented
36#63561C2212yescomplemented
37#63559C2214yescomplemented
38#63559C2212yescomplemented
39C3×#568—31no—
40#5822—31no—
41C2×#949—31no—
42#5748—31no—
43C2×#908—31no—
44C2×#908—31no—
45C2×#908—31no—
46C2×#908—61no—
47#5745D311yescharacteristic, complemented
48C3×#430—31no—
49#5142—34no—
50#5141—34no—
51#5132—31no—
52#5132—31no—
53C2×#823—31no—
54C2×#823—31no—
55#5125D311yescharacteristic, complemented
56#4898—34no—
57#4897—34no—
58C23×C3⋊D3—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61#3828—21no—
62#3828—21no—
63#3828—21no—
64#3828—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
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
82C32×M16D412yes—
83C32×M16D412yes—
84C2×C32×C8C2312yes—
85#3745—24no—
86#3744—24no—
87C3×#208—21no—
88C3×#208—21no—
89C3×#208—21no—
90C3×#208C2312yes—
91C3×#208C2312yes—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C2×C3×C3⋊C8—21no—
95C2×C3×C3⋊C8—21no—
96C3×ΓL(1,𝔽25)—24no—
97C3×D3×C8—24no—
98#3719—22no—
99#3717—24no—
100#3717—22no—
101#3716—22no—
102#3714—24no—
103#3714—22no—
104#3068—91noSylow
105C2×C3×#41—31no—
106C2×#235—31no—
107C2×#235—31no—
108C2×#235—61no—
109C2×#235C2×D311yescharacteristic
110C22×D12—31no—
111C22×D12—31no—
112C22×D12—61no—
113C3×#131—34no—
114C3×#131—62no—
115C2×C3×M16—21no—
116C2×C3×M16—31no—
117C2×C3×M16—31no—
118C2×C3×M16—31no—
119C2×C3×M16—62no—
120C2×C3×M16C2×D311yescharacteristic
121C2×C3×M16C2×D311yescharacteristic
122#951—32no—
123#950—62no—
124#949—34no—
125#949—32no—
126#949—62no—
127#942—61no—
128C2×#215—61no—
129#932—61no—
130C2×#213—61no—
131C2×#208C2×D311yescharacteristic
132C2×#208C2×D311yescharacteristic
133C2×#208C2×D311yescharacteristic
134#909—32no—
135#909—61no—
136#908—32no—
137#908—34no—
138#908—64no—
139#908—64no—
140#908—62no—
141#908—61no—
142#908—62no—
143#908—62no—
144#908—62no—
145#908—62no—
146#907—22no—
147D3×M16—22no—
148#904—62no—
149C2×D24—32no—
150C2×D24—32no—
151C2×D24—62no—
152C2×D24—61no—
153C2×#204—32no—
154C2×#204—32no—
155C2×#204—62no—
156C2×#204—61no—
157#901C2×D314yescomplemented
158C3×#108—34no—
159#824—32no—
160#824—32no—
161#823—34no—
162#823—34no—
163#823—32no—
164#823—32no—
165#819C2×D314yescomplemented
166C23×C32#4111yescharacteristic
167C22×C3⋊D3—22no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—41no—
170C22×C3⋊D3—41no—
171C22×C3⋊D3—82no—
172C22×C3×D3—21no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4111yescharacteristic
178C2×C32×C4C2411yescharacteristic
179#638—41no—
180#638—41no—
181C2×C3⋊Dic3—21no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—21no—
186C4⋊(C3⋊D3)—41no—
187C4⋊(C3⋊D3)—41no—
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—
201C32×C8C2×D414yes—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205#575—91no—
206C2×AGL(1,ℤ/8)—91no—
207C2×AGL(1,ℤ/8)—91no—
208#568—31no—
209#472—94no—
210#471—94no—
211#430—31no—
212#413—91no—
213C2×#100—91no—
214C23×D3—61no—
215C23×D3—61no—
216C23×D3—121no—
217C3×#41—32no—
218C3×#41—32no—
219C3×#41—61no—
220C3×#41—61no—
221C2×C3×Q8—31no—
222C2×C3×D4—31no—
223C2×C3×D4—61no—
224C22×C3×C4—21no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C2×#67—61no—
230C2×#67—61no—
231C2×#67—121no—
232#235—21no—
233#235—21no—
234#235—62no—
235#235—62no—
236#235—61no—
237#235—61no—
238#235—61no—
239#235—61no—
240#235—61no—
241#235—61no—
242#235—61no—
243#235—61no—
244#235—121no—
245#235—121no—
246#235D1212yes—
247#235C22×D312yes—
248C2×D12—32no—
249C2×D12—32no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—62no—
253C2×D12—61no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—61no—
260C2×D12—61no—
261C2×D12—61no—
262C2×D12—61no—
263C2×D12—61no—
264C2×D12—61no—
265C2×D12—61no—
266C2×D12—121no—
267C2×D12—121no—
268C2×D12—121no—
269C2×D12D1211yescharacteristic
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×Dic6D1211yescharacteristic
278C3×M16—22no—
279C3×M16—22no—
280C3×M16—32no—
281C3×M16—32no—
282C3×M16—32no—
283C3×M16—61no—
284C3×M16—61no—
285C3×M16—61no—
286C3×M16—64no—
287C3×M16D1212yes—
288C3×M16D1212yes—
289C3×M16#6712yes—
290C3×M16#6712yes—
291C2×C3×C8—22no—
292C2×C3×C8—61no—
293C2×C3×C8—61no—
294C2×C3×C8—61no—
295C2×C3×C8—64no—
296C2×C3×C8C22×D312yes—
297C2×C3×C8C22×D312yes—
298#216—62no—
299#215—64no—
300#215—62no—
301#214—62no—
302#213—64no—
303#213—62no—
304#208—21no—
305#208—21no—
306#208—21no—
307#208C22×D312yes—
308#208C22×D312yes—
309#208C22×D312yes—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313Dic12—62no—
314D24—68no—
315D24—64no—
316D24—62no—
317D24—64no—
318D24—64no—
319#204—68no—
320#204—62no—
321#204—64no—
322#204—62no—
323#204—64no—
324#204—64no—
325ΓL(1,𝔽25)—24no—
326D3×C8—24no—
327C22×C32—41no—
328C22×C32#12111yescharacteristic
329C22×C32#12111yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C2×C3⋊D3—41no—
332C2×C3⋊D3—42no—
333C2×C3⋊D3—82no—
334C2×C3⋊D3—82no—
335C2×C3⋊D3—81no—
336C2×C3⋊D3—82no—
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×D4—91no—
348#137—92no—
349#137—181no—
350AGL(1,ℤ/8)—94no—
351AGL(1,ℤ/8)—92no—
352AGL(1,ℤ/8)—181no—
353AGL(1,ℤ/8)—182no—
354AGL(1,ℤ/8)—182no—
355AGL(1,ℤ/8)—182no—
356#135—182no—
357C2×SD16—92no—
358C2×SD16—181no—
359C2×D8—92no—
360C2×D8—181no—
361#131—34no—
362#131—62no—
363C2×M16—31no—
364C2×M16—31no—
365C2×M16—31no—
366C2×M16—62no—
367C2×M16D3211yescharacteristic
368#108—34no—
369#101—92no—
370#100—94no—
371#100—92no—
372C23×C3—21no—
373C23×C3—61no—
374C23×C3#23511yescharacteristic
375C23×C3#23911yescharacteristic
376C22×D3—21no—
377C22×D3—61no—
378C22×D3—62no—
379C22×D3—61no—
380C22×D3—62no—
381C22×D3—121no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—121no—
386C22×D3—121no—
387C22×D3—121no—
388C22×D3—121no—
389C22×D3—244no—
390C22×D3—242no—
391C22×D3—242no—
392C3×Q8—32no—
393C3×Q8—61no—
394C3×D4—32no—
395C3×D4—62no—
396C3×D4—62no—
397C3×D4—61no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—61no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4C2×D1211yescharacteristic
408C2×C3×C4C2×D1211yescharacteristic
409C2×C3×C4C2×D1211yescharacteristic
410C2×C3×C4C2×D1211yescharacteristic
411C2×C3×C4#23511yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4#23911yescharacteristic
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—22no—
420#67—22no—
421#67—122no—
422#67—122no—
423#67—121no—
424#67—121no—
425#67—121no—
426#67—121no—
427C2×Dic3—21no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—121no—
431D12—21no—
432D12—64no—
433D12—62no—
434D12—62no—
435D12—62no—
436D12—61no—
437D12—61no—
438D12—62no—
439D12—61no—
440D12—62no—
441D12—61no—
442D12—122no—
443D12—121no—
444D12—122no—
445D12—122no—
446D12—121no—
447D12—121no—
448D12—121no—
449D12—121no—
450D12C2×D1212yes—
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×D1212yes—
467C3×C8—24no—
468C3×C8—62no—
469C3×C8—62no—
470C3×C8—62no—
471C3×C8C2×D1214yes—
472C3×C8C2×#6714yes—
473C3⋊C8—22no—
474C3⋊C8—22no—
475C3⋊C8—22no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32C2×#12111yescharacteristic
480C3⋊D3—81no—
481C3⋊D3—82no—
482C3×D3—42no—
483C24—181no—
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—31no—
495C2×D4—61no—
496C2×D4—91no—
497C2×D4—92no—
498C2×D4—181no—
499C2×D4—181no—
500C2×D4—181no—
501C2×D4—181no—
502C2×D4—181no—
503C2×D4—181no—
504C22×C4—61no—
505C22×C4—181no—
506C22×C4C2×D3211yescharacteristic
507Q16—182no—
508SD16—182no—
509SD16—184no—
510SD16—182no—
511SD16—184no—
512D8—184no—
513D8—182no—
514D8—184no—
515M16—32no—
516M16—32no—
517M16—32no—
518M16—61no—
519M16—61no—
520M16—61no—
521M16—64no—
522M16#62612yes—
523M16#62612yes—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—64no—
528C2×C8C2×D3212yes—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—42no—
535C22×C3—62no—
536C22×C3—241no—
537C22×C3#89511yescharacteristic
538C22×C3#89511yescharacteristic
539C22×C3#93011yescharacteristic
540C22×C3#93011yescharacteristic
541C22×C3C2×#23511yescharacteristic
542C22×C3C2×#23911yescharacteristic
543C2×D3—22no—
544C2×D3—81no—
545C2×D3—122no—
546C2×D3—124no—
547C2×D3—121no—
548C2×D3—122no—
549C2×D3—121no—
550C2×D3—122no—
551C2×D3—244no—
552C2×D3—242no—
553C2×D3—242no—
554C2×D3—242no—
555C2×D3—242no—
556C2×D3—242no—
557C2×D3—244no—
558C2×D3—244no—
559C2×D3—242no—
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#89511yescharacteristic
569C3×C4#89511yescharacteristic
570C3×C4#93011yescharacteristic
571C3×C4#93011yescharacteristic
572C3×C4C22×D1211yescharacteristic
573C3×C4C22×D1211yescharacteristic
574C3×C4C2×D3×D411yescharacteristic
575C3×C4C22×#6711yescharacteristic
576Dic3—22no—
577Dic3—122no—
578Dic3—121no—
579Dic3—121no—
580C32#306811yescharacteristic, complemented, Sylow
581C23—61no—
582C23—181no—
583C23—182no—
584C23—361no—
585C23—361no—
586C23—722no—
587C23#379911yescharacteristic
588Q8—32no—
589Q8—61no—
590Q8—181no—
591Q8—181no—
592D4—32no—
593D4—62no—
594D4—62no—
595D4—61no—
596D4—182no—
597D4—181no—
598D4—181no—
599D4—182no—
600D4—361no—
601D4—361no—
602D4—361no—
603D4—361no—
604C2×C4—61no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—181no—
608C2×C4—361no—
609C2×C4—361no—
610C2×C4#379911yescharacteristic
611C2×C4D3×D1211yescharacteristic
612C2×C4D3×D1211yescharacteristic
613C2×C4C2×#62611yescharacteristic
614C2×C4C2×#62611yescharacteristic
615C2×C4C22×D3211yescharacteristic
616C8—62no—
617C8—62no—
618C8—62no—
619C8C2×#62614yes—
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—122no—
631C2×C3C2×#89511yescharacteristic
632C2×C3C2×#93011yescharacteristic
633D3—42no—
634D3—244no—
635D3—242no—
636D3—242no—
637D3—241no—
638D3—242no—
639D3—241no—
640C22—41no—
641C22—62no—
642C22—241no—
643C22—361no—
644C22—362no—
645C22—722no—
646C22—721no—
647C22—722no—
648C22—722no—
649C22#6390911yescharacteristic
650C22#6390911yescharacteristic
651C22C2×#379911yescharacteristic
652C4—62no—
653C4—361no—
654C4#6390911yescharacteristic
655C4#6390911yescharacteristic
656C4C2×D3×D1211yescharacteristic
657C4C22×#62611yescharacteristic
658C3—21no—
659C3#7926111yescharacteristic, complemented
660C3#8381411yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—21no—
664C2—122no—
665C2—722no—
666C2—721no—
667C2C2×#6390911yescharacteristic
subgroupG/H
centerC2C2×#63909
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×#121
hypercenterC2×M16D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64117C2semidirect
2. C3×#5745C2semidirect
3. #10594795C2semidirect
4. C2×#63825C2semidirect
5. C3×#5125C2semidirect
6. #10591078C2semidirect
7. C2×#63559C2semidirect
8. #10590931C2semidirect
9. #10590927C2semidirect
18. C2×#3745C22semidirect
19. C2×#3744C22semidirect
25. C3×#901C22semidirect
28. #63831C22semidirect
33. #63825C22semidirect
35. C3×#819C22semidirect
36. #63561C22semidirect
37. #63559C22semidirect
38. #63559C22semidirect
47. #5745D3semidirect
55. #5125D3semidirect
157. #901C2×D3semidirect
165. #819C2×D3semidirect
580. C32#3068semidirect
659. C3#79261semidirect
660. C3#83814semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
C3×#57452
#105947952
C2×#638252
C3×#51252
#105910782
C2×#635592
#105909312
#105909272
#838143
#792613