Finite Group Databasebeta

← #11868127

Subgroups — #11868127

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
2#10594795C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4#10594780C211yesmaximal, characteristic, complemented
5C3×#5132C211yesmaximal, characteristic, complemented
6C3×#5124C211yesmaximal, characteristic, complemented
7C2×#63559C211yesmaximal, characteristic, complemented
8#10590990C214yesmaximal, complemented
9#10590987C214yesmaximal, complemented
10#79261—31nomaximal
11#78720—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64117—22no—
17#64117C2214yes—
18C2×#3745—21no—
19C2×#3744—21no—
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23#63833C2212yescomplemented
24C2×#3717C2212yescomplemented
25#63831—21no—
26#63830C2212yescomplemented
27#63829—22no—
28#63825—21no—
29#63825—22no—
30#63825—22no—
31C2×#3714C2212yescomplemented
32#63818—22no—
33#63817—22no—
34#63817C2214yescomplemented
35C3×#824C2212yescomplemented
36C3×#823C2212yescomplemented
37C3×#822C2214yescomplemented
38#63559C2214yescomplemented
39#5822—31no—
40C2×#949—31no—
41#5748—31no—
42C2×#908—31no—
43C2×#908—31no—
44C2×#908—31no—
45C2×#908—61no—
46#5745—31no—
47#5745—31no—
48C3×#430—31no—
49C3×#413—31no—
50#5132D311yescharacteristic, complemented
51C2×#823—31no—
52C2×#823—31no—
53#5124D311yescharacteristic, complemented
54#4898—34no—
55#4897—34no—
56#4754—34no—
57#4749—34no—
58C23×C3⋊D3—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61#3828—21no—
62#3828—21no—
63#3828D412yes—
64#3828C2312yes—
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)D411yescharacteristic
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C4×C3⋊D3—21no—
73C2×#634D411yescharacteristic
74C2×C3×#67—21no—
75C3×#235—21no—
76C3×#235—21no—
77C3×#235—21no—
78C3×#235—21no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×M16—21no—
83C32×M16C2312yes—
84C2×C32×C8—21no—
85#3745—24no—
86#3744—24no—
87C3×#208—21no—
88C3×#208—21no—
89C3×#208D412yes—
90C3×#208D412yes—
91C3×#208C2312yes—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C2×C3×C3⋊C8—21no—
95C2×C3×C3⋊C8C2312yes—
96#3719—22no—
97#3717—22no—
98#3717—24no—
99#3716—22no—
100#3714—22no—
101#3714—24no—
102#3712—24no—
103#3710—24no—
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—
113C2×C3×M16—21no—
114C2×C3×M16—31no—
115C2×C3×M16—31no—
116C2×C3×M16—31no—
117C2×C3×M16C2×D311yescharacteristic
118C2×C3×M16C2×D311yescharacteristic
119#951—61no—
120#950—62no—
121#949—61no—
122#949—62no—
123#949—62no—
124#942—32no—
125C2×#215—32no—
126#932—32no—
127C2×#213—32no—
128C2×#208C2×D311yescharacteristic
129C2×#208C2×D311yescharacteristic
130C2×#208C2×D311yescharacteristic
131#909—32no—
132#909—61no—
133#908—32no—
134#908—34no—
135#908—34no—
136#908—64no—
137#908—62no—
138#908—62no—
139#908—64no—
140#908—62no—
141#908—62no—
142#908—61no—
143#907—34no—
144#907—62no—
145D3×M16—62no—
146D3×M16—62no—
147#904—62no—
148C2×D24—32no—
149C2×D24—61no—
150C2×D24—61no—
151C2×D24—62no—
152C2×#204—32no—
153C2×#204—61no—
154C2×#204—61no—
155C2×#204—62no—
156#901—34no—
157#901—62no—
158C3×#108—34no—
159C3×#101—32no—
160C3×#100—32no—
161#824C2×D312yescomplemented
162#823—34no—
163#823—34no—
164#823C2×D312yescomplemented
165#822C2×D314yescomplemented
166C23×C32#4111yescharacteristic
167C22×C3⋊D3—21no—
168C22×C3⋊D3—22no—
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—22no—
180#638—22no—
181C2×C3⋊Dic3—21no—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—41no—
186C4⋊(C3⋊D3)—41no—
187C4⋊(C3⋊D3)C2×D412yes—
188C4×C3⋊D3—22no—
189C4×C3⋊D3—22no—
190#634—21no—
191#634C2×D412yes—
192C3×#67—41no—
193C3×#67—41no—
194C2×C3×Dic3—21no—
195C3×D12—21no—
196C3×D12—21no—
197C3×C4×D3—41no—
198C3×C4×D3—41no—
199C3×Dic6—21no—
200C3×Dic6—21no—
201C32×C8—22no—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8C2×D414yes—
205#575—91no—
206C2×AGL(1,ℤ/8)—91no—
207C2×AGL(1,ℤ/8)—91no—
208#568—91no—
209#472—94no—
210#471—94no—
211#430—31no—
212#413—31no—
213C2×#100—91no—
214C23×D3—61no—
215C23×D3—61no—
216C23×D3—121no—
217C3×#41—61no—
218C3×#41—61no—
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—21no—
235#235—21no—
236#235—32no—
237#235—32no—
238#235—32no—
239#235—32no—
240#235—62no—
241#235—62no—
242#235—61no—
243#235—61no—
244#235—61no—
245#235—61no—
246#235—121no—
247#235—121no—
248C2×D12—31no—
249C2×D12—31no—
250C2×D12—32no—
251C2×D12—32no—
252C2×D12—61no—
253C2×D12—62no—
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×D12C22×D311yescharacteristic
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×Dic6C22×D311yescharacteristic
278C3×M16—22no—
279C3×M16—21no—
280C3×M16—21no—
281C3×M16—22no—
282C3×M16—32no—
283C3×M16—32no—
284C3×M16—32no—
285C3×M16—32no—
286C3×M16—61no—
287C3×M16—61no—
288C3×M16C22×D312yes—
289C3×M16C22×D312yes—
290C2×C3×C8—22no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—32no—
294C2×C3×C8—61no—
295C2×C3×C8—61no—
296#216—62no—
297#215—62no—
298#215—64no—
299#214—62no—
300#213—62no—
301#213—64no—
302#208—21no—
303#208—21no—
304#208D1212yes—
305#208D1212yes—
306#208C22×D312yes—
307#208C22×D312yes—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8C22×D312yes—
311Dic12—62no—
312D24—64no—
313D24—64no—
314D24—68no—
315D24—64no—
316D24—62no—
317#204—64no—
318#204—64no—
319#204—68no—
320#204—64no—
321#204—62no—
322#204—62no—
323ΓL(1,𝔽25)—64no—
324ΓL(1,𝔽25)—64no—
325D3×C8—64no—
326D3×C8—64no—
327C22×C32—41no—
328C22×C32#12111yescharacteristic
329C22×C32#12111yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C2×C3⋊D3—22no—
332C2×C3⋊D3—42no—
333C2×C3⋊D3—81no—
334C2×C3⋊D3—82no—
335C2×C3⋊D3—82no—
336C2×C3⋊D3—82no—
337C2×C3×D3—41no—
338C2×C3×D3—81no—
339C32×C4#12111yescharacteristic
340C32×C4#12111yescharacteristic
341C32×C4C22×D411yescharacteristic
342C32×C4C22×D411yescharacteristic
343C3⋊Dic3—22no—
344C3×Dic3—41no—
345C2×#41—31no—
346C2×#41—91no—
347C22×D4—91no—
348#137—92no—
349#137—181no—
350AGL(1,ℤ/8)—92no—
351AGL(1,ℤ/8)—94no—
352AGL(1,ℤ/8)—182no—
353AGL(1,ℤ/8)—182no—
354AGL(1,ℤ/8)—182no—
355AGL(1,ℤ/8)—181no—
356#135—182no—
357C2×SD16—92no—
358C2×SD16—181no—
359C2×D8—92no—
360C2×D8—181no—
361#131—94no—
362#131—182no—
363C2×M16—31no—
364C2×M16—31no—
365C2×M16—31no—
366C2×M16—182no—
367C2×M16D3211yescharacteristic
368#108—34no—
369#101—32no—
370#100—32no—
371#100—94no—
372C23×C3—21no—
373C23×C3—61no—
374C23×C3#23511yescharacteristic
375C23×C3#23911yescharacteristic
376C22×D3—21no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—62no—
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—61no—
393C3×Q8—61no—
394C3×D4—61no—
395C3×D4—61no—
396C3×D4—121no—
397C3×D4—121no—
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—121no—
406C2×C3×C4—121no—
407C2×C3×C4C2×D1211yescharacteristic
408C2×C3×C4C2×D1211yescharacteristic
409C2×C3×C4#23511yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4#23911yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—41no—
420#67—41no—
421#67—62no—
422#67—62no—
423#67—62no—
424#67—62no—
425#67—122no—
426#67—122no—
427C2×Dic3—21no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—121no—
431D12—21no—
432D12—21no—
433D12—32no—
434D12—32no—
435D12—62no—
436D12—64no—
437D12—61no—
438D12—61no—
439D12—62no—
440D12—62no—
441D12—62no—
442D12—62no—
443D12—122no—
444D12—121no—
445D12—122no—
446D12—122no—
447D12—121no—
448D12—121no—
449D12—121no—
450D12—121no—
451C4×D3—41no—
452C4×D3—41no—
453C4×D3—62no—
454C4×D3—62no—
455C4×D3—62no—
456C4×D3—62no—
457C4×D3—122no—
458C4×D3—122no—
459Dic6—21no—
460Dic6—21no—
461Dic6—32no—
462Dic6—32no—
463Dic6—62no—
464Dic6—61no—
465Dic6—61no—
466Dic6—121no—
467C3×C8—24no—
468C3×C8—22no—
469C3×C8—22no—
470C3×C8—34no—
471C3×C8—62no—
472C3×C8—62no—
473C3⋊C8—22no—
474C3⋊C8—22no—
475C3⋊C8C2×D1214yes—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32C2×#12111yescharacteristic
480C3⋊D3—42no—
481C3⋊D3—82no—
482C3×D3—81no—
483C24—181no—
484#41—61no—
485#41—61no—
486#41—61no—
487#41—61no—
488#41—92no—
489#41—92no—
490#41—181no—
491#41—181no—
492C2×Q8—31no—
493C2×Q8—91no—
494C2×D4—31no—
495C2×D4—61no—
496C2×D4—92no—
497C2×D4—91no—
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—184no—
509SD16—184no—
510SD16—182no—
511SD16—182no—
512D8—184no—
513D8—184no—
514D8—182no—
515M16—21no—
516M16—32no—
517M16—32no—
518M16—32no—
519M16—32no—
520M16—61no—
521M16—61no—
522M16—184no—
523M16C2×D3212yes—
524C2×C8—21no—
525C2×C8—32no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—184no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—42no—
535C22×C3—121no—
536C22×C3—241no—
537C22×C3#88411yescharacteristic
538C22×C3#88411yescharacteristic
539C22×C3#89511yescharacteristic
540C22×C3#89511yescharacteristic
541C22×C3C2×#23511yescharacteristic
542C22×C3C2×#23911yescharacteristic
543C2×D3—41no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—81no—
547C2×D3—122no—
548C2×D3—124no—
549C2×D3—122no—
550C2×D3—122no—
551C2×D3—241no—
552C2×D3—241no—
553C2×D3—244no—
554C2×D3—242no—
555C2×D3—242no—
556C2×D3—242no—
557C2×D3—242no—
558C2×D3—242no—
559C2×D3—244no—
560C2×D3—244no—
561C2×D3—242no—
562C2×D3—242no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—121no—
568C3×C4#88411yescharacteristic
569C3×C4#88411yescharacteristic
570C3×C4#89511yescharacteristic
571C3×C4#89511yescharacteristic
572C3×C4C22×D1211yescharacteristic
573C3×C4C2×D3×D411yescharacteristic
574C3×C4C2×D3×D411yescharacteristic
575C3×C4C2×D3×D411yescharacteristic
576Dic3—41no—
577Dic3—62no—
578Dic3—62no—
579Dic3—122no—
580C32#306811yescharacteristic, complemented, Sylow
581C23—61no—
582C23—181no—
583C23—182no—
584C23—361no—
585C23—361no—
586C23—722no—
587C23#379911yescharacteristic
588Q8—61no—
589Q8—61no—
590Q8—92no—
591Q8—181no—
592D4—61no—
593D4—61no—
594D4—92no—
595D4—121no—
596D4—121no—
597D4—182no—
598D4—182no—
599D4—182no—
600D4—182no—
601D4—181no—
602D4—361no—
603D4—361no—
604C2×C4—61no—
605C2×C4—121no—
606C2×C4—121no—
607C2×C4—181no—
608C2×C4—182no—
609C2×C4—182no—
610C2×C4#379911yescharacteristic
611C2×C4D3×D1211yescharacteristic
612C2×C4D3×D1211yescharacteristic
613C2×C4#381111yescharacteristic
614C2×C4#381111yescharacteristic
615C2×C4C22×D3211yescharacteristic
616C8—22no—
617C8—34no—
618C8—62no—
619C8—62no—
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—241no—
631C2×C3C2×#88411yescharacteristic
632C2×C3C2×#89511yescharacteristic
633D3—81no—
634D3—122no—
635D3—122no—
636D3—242no—
637D3—244no—
638D3—242no—
639D3—242no—
640C22—41no—
641C22—121no—
642C22—182no—
643C22—241no—
644C22—362no—
645C22—721no—
646C22—722no—
647C22—722no—
648C22—722no—
649C22#6391011yescharacteristic
650C22#6391011yescharacteristic
651C22C2×#379911yescharacteristic
652C4—121no—
653C4—182no—
654C4#6391011yescharacteristic
655C4#6391011yescharacteristic
656C4C2×D3×D1211yescharacteristic
657C4C2×#381111yescharacteristic
658C3—21no—
659C3#7872011yescharacteristic, complemented
660C3#7926111yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—21no—
664C2—241no—
665C2—362no—
666C2—722no—
667C2C2×#6391011yescharacteristic
subgroupG/H
centerC2C2×#63910
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. #10594795C2semidirect
3. C2×#63825C2semidirect
4. #10594780C2semidirect
5. C3×#5132C2semidirect
6. C3×#5124C2semidirect
7. C2×#63559C2semidirect
8. #10590990C2semidirect
9. #10590987C2semidirect
23. #63833C22semidirect
24. C2×#3717C22semidirect
26. #63830C22semidirect
31. C2×#3714C22semidirect
34. #63817C22semidirect
35. C3×#824C22semidirect
36. C3×#823C22semidirect
37. C3×#822C22semidirect
38. #63559C22semidirect
50. #5132D3semidirect
53. #5124D3semidirect
161. #824C2×D3semidirect
164. #823C2×D3semidirect
165. #822C2×D3semidirect
580. C32#3068semidirect
659. C3#78720semidirect
660. C3#79261semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105947952
C2×#638252
#105947802
C3×#51322
C3×#51242
C2×#635592
#105909902
#105909872
#792613
#787203