Finite Group Databasebeta

← #11886906

Subgroups — #11886906

Order 1152.

1036 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5774C211yesmaximal, characteristic, complemented
2#10595461C211yesmaximal, characteristic, complemented
3#10595449C211yesmaximal, characteristic, complemented
4#10595096C211yesmaximal, characteristic, complemented
5#10592897C211yesmaximal, characteristic, complemented
6C3×#5199C211yesmaximal, characteristic, complemented
7#10591673C211yesmaximal, characteristic, complemented
8#10591665C211yesmaximal, characteristic, complemented
9#10591510C211yesmaximal, characteristic, complemented
10#10591484C211yesmaximal, characteristic, complemented
11#10591406C211yesmaximal, characteristic, complemented
12#10591014C211yesmaximal, characteristic, complemented
13#10590997C211yesmaximal, characteristic, complemented
14#10590995C211yesmaximal, characteristic, complemented
15#10590984C211yesmaximal, characteristic, complemented
16#84010—31nomaximal
17#80941—31nomaximal
18#64366C2211yescharacteristic, complemented
19C3×#1009C2211yescharacteristic, complemented
20C3×#1004C2211yescharacteristic, complemented
21#64307C2211yescharacteristic, complemented
22C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23#64149C2211yescharacteristic, complemented
24#64141C2211yescharacteristic, complemented
25C3×#950C2211yescharacteristic
26C3×#949C2211yescharacteristic, complemented
27C3×#948C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#916—21no—
31C3×#914—21no—
32C3×#911—21no—
33C3×D3×D8—21no—
34C3×#908C2211yescharacteristic, complemented
35C3×#907C2211yescharacteristic, complemented
36#63950—21no—
37#63941—21no—
38#63937—21no—
39#63933—21no—
40#63932—21no—
41#63926—21no—
42#63925—21no—
43D3×#213—21no—
44#63914C2211yescharacteristic, complemented
45#63830—21no—
46#63830C2211yescharacteristic, complemented
47#63829—21no—
48#63829C2211yescharacteristic
49#63825—21no—
50#63825C2211yescharacteristic, complemented
51#63825C2211yescharacteristic, complemented
52C2×#3714—21no—
53C2×#3714C2211yescharacteristic, complemented
54C2×#3714C2211yescharacteristic, complemented
55#63823C2211yescharacteristic, complemented
56#63817C2211yescharacteristic, complemented
57#63814C2211yescharacteristic, complemented
58#63664C2211yescharacteristic, complemented
59#63652C2211yescharacteristic, complemented
60#63650C2211yescharacteristic, complemented
61C3×#833C2211yescharacteristic, complemented
62C3×#823C2211yescharacteristic, complemented
63C3×#822C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63568C2211yescharacteristic, complemented
66#63568C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63553C2211yescharacteristic, complemented
69C3×#576—31no—
70#5835—31no—
71#5835—31no—
72#5774—31no—
73#5774D311yescharacteristic, complemented
74#5769—31no—
75#5757—31no—
76#5752—31no—
77C3×#472—31no—
78#5241—31no—
79#5241—31no—
80#5199—31no—
81#5199D311yescharacteristic, complemented
82#5198—31no—
83#5198—31no—
84#5198—31no—
85#5198—31no—
86#5198—61no—
87#5196—31no—
88#5160—31no—
89#5151—31no—
90#5151—31no—
91#5144—31no—
92#5144—31no—
93#5142—31no—
94#4897—31no—
95#4895—31no—
96#4749—31no—
97#4749—31no—
98#4747—31no—
99#4747—31no—
100C32×#41C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×#638—41no—
103#3832—21no—
104D4×C3⋊D3—21no—
105D4×C3⋊D3—41no—
106#3828—21no—
107#3828C2311yescharacteristic
108C2×C4⋊(C3⋊D3)—21no—
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C3×#67—41no—
111C3×#239—21no—
112C3×#237—21no—
113C3×#237—21no—
114C3×D3×D4—21no—
115C3×D3×D4—21no—
116C3×D3×D4—21no—
117C3×D3×D4—41no—
118C3×#235—21no—
119C3×#235C2311yescharacteristic
120C3×#235C2311yescharacteristic
121C2×C3×D12—21no—
122C2×C3×D12C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124D3×#67—41no—
125C2×#625—41no—
126#3802—21no—
127D3×D12—21no—
128#3796—21no—
129#3795—21no—
130C32×SD16—21no—
131C32×D8—21no—
132C32×M16C2311yescharacteristic
133#3754—21no—
134#3753—21no—
135C4×C3⋊Dic3C2311yescharacteristic
136#3748C2311yescharacteristic
137C3×#216D411yescharacteristic, complemented
138C3×#215—21no—
139C3×#215D411yescharacteristic, complemented
140C3×#214D411yescharacteristic, complemented
141C3×#213—21no—
142C3×#213—21no—
143C3×#213—21no—
144C3×#213—21no—
145C3×#213—21no—
146C3×#213D411yescharacteristic, complemented
147C3×#208—21no—
148C3×#208C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C2×C3×C3⋊C8—21no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×D24—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×D3×C8—21no—
157#3719D411yescharacteristic, complemented
158#3717—21no—
159#3717—21no—
160#3717D411yescharacteristic, complemented
161#3716—21no—
162#3716D411yescharacteristic, complemented
163#3715—21no—
164#3714—21no—
165#3714—21no—
166#3714—21no—
167#3714—21no—
168#3714—21no—
169#3714—21no—
170#3714—21no—
171#3714D411yescharacteristic, complemented
172#3713—21no—
173#3712—21no—
174#3711—21no—
175#3710—21no—
176D3×C3⋊C8—21no—
177#3292—91noSylow
178C3×H(5,𝔽2)—31no—
179C3×H(5,𝔽2)—31no—
180#1009—31no—
181#1009—31no—
182#1009—31no—
183#1009—61no—
184#1009C2×D311yescharacteristic, complemented
185#1004—31no—
186#1004C2×D311yescharacteristic, complemented
187C3×AGL(1,ℤ/8)—21no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—61no—
191C3×AGL(1,ℤ/8)—61no—
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
193C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
194C3×#135—31no—
195C3×#135—61no—
196C2×C3×D8—31no—
197C2×C3×D8—31no—
198C2×C3×D8—61no—
199C3×#131—31no—
200C3×#131—31no—
201#950—31no—
202#950—61no—
203#950—61no—
204#950C2×D311yescharacteristic
205#949—31no—
206#949—31no—
207#949—31no—
208#949—61no—
209#949—61no—
210#949C2×D311yescharacteristic, complemented
211#948—31no—
212#948C2×D311yescharacteristic, complemented
213#940—31no—
214#940—31no—
215#940—31no—
216#940—31no—
217#940—61no—
218#932—31no—
219#932—31no—
220#932—31no—
221#932—31no—
222#932—61no—
223#932—61no—
224#932—61no—
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—61no—
228C2×#213—61no—
229C2×#213C2×D311yescharacteristic, complemented
230C2×#213C2×D311yescharacteristic, complemented
231#919—61no—
232#916—21no—
233#916—61no—
234#914—21no—
235#914—61no—
236#914—61no—
237#914—61no—
238#912—61no—
239#911—21no—
240#911—61no—
241#911—61no—
242#911—61no—
243D3×D8—21no—
244D3×D8—61no—
245D3×D8—61no—
246D3×D8—61no—
247#908—31no—
248#908—31no—
249#908—31no—
250#908—61no—
251#908—61no—
252#908C2×D311yescharacteristic, complemented
253#907—31no—
254#907C2×D311yescharacteristic, complemented
255#904—31no—
256#904—61no—
257C2×D24—31no—
258C2×D24—31no—
259C2×D24—61no—
260#901—31no—
261#901—31no—
262C3×#108—31no—
263C3×#100—31no—
264C3×#100—31no—
265#837—31no—
266#837—31no—
267#837—31no—
268#837—31no—
269#837—61no—
270#833—31no—
271#833C2×D311yescharacteristic, complemented
272#825—31no—
273#825—31no—
274#825—31no—
275#825—31no—
276#825—61no—
277#823—31no—
278#823—31no—
279#823—31no—
280#823—61no—
281#823C2×D311yescharacteristic, complemented
282#822—31no—
283#822C2×D311yescharacteristic, complemented
284#819—31no—
285C8×Dic3—31no—
286C8×Dic3—31no—
287C23×C32—21no—
288C22×C3⋊D3—21no—
289C22×C3⋊D3—41no—
290C22×C3×D3—21no—
291C22×C3×D3—21no—
292C22×C3×D3—41no—
293C22×C3×D3—41no—
294C2×D32—41no—
295C32×Q8C2×D411yescharacteristic
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4C2×D411yescharacteristic
300C2×C32×C4—21no—
301C2×C32×C4C2411yescharacteristic
302#638—21no—
303#638—41no—
304#638—82no—
305C2×C3⋊Dic3—21no—
306C4⋊(C3⋊D3)—21no—
307C4⋊(C3⋊D3)—21no—
308C4⋊(C3⋊D3)—41no—
309C4⋊(C3⋊D3)C2×D411yescharacteristic
310C4×C3⋊D3—21no—
311C4×C3⋊D3—41no—
312#634C2×D411yescharacteristic
313C3×#67—21no—
314C3×#67—21no—
315C3×#67—41no—
316C3×#67—41no—
317C3×#67—41no—
318C2×C3×Dic3—41no—
319C3×D12—21no—
320C3×D12—21no—
321C3×D12—21no—
322C3×D12—21no—
323C3×D12—41no—
324C3×D12C2×D411yescharacteristic
325C3×D12C2×D411yescharacteristic
326C3×C4×D3—21no—
327C3×C4×D3—21no—
328C3×C4×D3—41no—
329C3×Dic6C2×D411yescharacteristic
330C3×Dic6C2×D411yescharacteristic
331#626—41no—
332#625—41no—
333#625—82no—
334D3×Dic3—41no—
335C32×C8—21no—
336C3⋊(C3⋊C8)—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342C3×C3⋊C8C2×D411yescharacteristic
343#576—31no—
344#576—91no—
345#576—91no—
346#576—91no—
347#493—91no—
348#472—31no—
349#472—91no—
350#472—91no—
351#472—91no—
352#453—91no—
353#453—91no—
354#453—91no—
355#453—91no—
356#443—91no—
357#443—91no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41C22×D311yescharacteristic
366C3×#41C22×D311yescharacteristic
367C2×C3×D4—21no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—121no—
375C2×C3×D4—121no—
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C2×#67—41no—
379C2×#67—121no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67—121no—
383C2×#67—121no—
384C2×#67—122no—
385#239—21no—
386#239—61no—
387#239—61no—
388#239—61no—
389#239—121no—
390#237—21no—
391#237—21no—
392#237—61no—
393#237—61no—
394D3×D4—21no—
395D3×D4—21no—
396D3×D4—21no—
397D3×D4—41no—
398D3×D4—61no—
399D3×D4—61no—
400D3×D4—61no—
401D3×D4—61no—
402D3×D4—61no—
403D3×D4—121no—
404D3×D4—121no—
405D3×D4—121no—
406D3×D4—121no—
407D3×D4—122no—
408#235—21no—
409#235—31no—
410#235—31no—
411#235—61no—
412#235—61no—
413#235—61no—
414#235—61no—
415#235—121no—
416#235C22×D311yescharacteristic
417#235C22×D311yescharacteristic
418C2×D12—21no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—121no—
426C2×D12C22×D311yescharacteristic
427C2×D12C22×D311yescharacteristic
428C3×Q16—31no—
429C3×SD16—21no—
430C3×SD16—21no—
431C3×SD16—31no—
432C3×SD16—31no—
433C3×SD16—41no—
434C3×SD16—61no—
435C3×SD16—61no—
436C3×D8—21no—
437C3×D8—21no—
438C3×D8—31no—
439C3×D8—41no—
440C3×D8—61no—
441C3×D8—61no—
442C3×D8—61no—
443C3×D8—61no—
444C3×D8—61no—
445C3×D8—61no—
446C3×M16—21no—
447C3×M16—31no—
448C3×M16—31no—
449C3×M16—61no—
450C3×M16—61no—
451C3×M16C22×D311yescharacteristic
452C3×M16C22×D311yescharacteristic
453C2×C3×C8—31no—
454C2×C3×C8—31no—
455C2×C3×C8—61no—
456C2×C3×C8—61no—
457#216—31no—
458#216#6711yescharacteristic, complemented
459#215—21no—
460#215—31no—
461#215—61no—
462#215—61no—
463#215—61no—
464#215#6711yescharacteristic, complemented
465#214—31no—
466#214—61no—
467#214—61no—
468#214—61no—
469#214—61no—
470#214—121no—
471#214#6711yescharacteristic, complemented
472#213—21no—
473#213—21no—
474#213—21no—
475#213—21no—
476#213—21no—
477#213—31no—
478#213—61no—
479#213—61no—
480#213—61no—
481#213—61no—
482#213—61no—
483#213—61no—
484#213—61no—
485#213—61no—
486#213—61no—
487#213—61no—
488#213—61no—
489#213—121no—
490#213#6711yescharacteristic, complemented
491C4×Dic3—31no—
492C4×Dic3—31no—
493C4×Dic3—61no—
494#208—21no—
495#208—31no—
496#208—31no—
497#208—61no—
498#208—61no—
499#208C22×D311yescharacteristic
500#208C22×D311yescharacteristic
501C2×C3⋊C8—21no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8C22×D311yescharacteristic
504C2×C3⋊C8C22×D311yescharacteristic
505Dic12—31no—
506D24—21no—
507D24—31no—
508D24—61no—
509D24—61no—
510D24—61no—
511D24—61no—
512D24—61no—
513D24—61no—
514D24—61no—
515#204—21no—
516#204—31no—
517#204—31no—
518#204—61no—
519#204—61no—
520#204—61no—
521ΓL(1,𝔽25)—21no—
522ΓL(1,𝔽25)—61no—
523ΓL(1,𝔽25)—61no—
524ΓL(1,𝔽25)—61no—
525D3×C8—21no—
526D3×C8—61no—
527D3×C8—61no—
528D3×C8—61no—
529C22×C32—21no—
530C22×C32—41no—
531C22×C32—81no—
532C22×C32H(5,𝔽2)11yescharacteristic
533C2×C3⋊D3—21no—
534C2×C3⋊D3—41no—
535C2×C3⋊D3—81no—
536C2×C3⋊D3—161no—
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3—41no—
540C2×C3×D3—41no—
541C2×C3×D3—81no—
542C2×C3×D3—81no—
543C2×C3×D3—161no—
544C2×C3×D3—161no—
545D32—161no—
546C32×C4—21no—
547C32×C4C22×D411yescharacteristic
548C32×C4C22×D411yescharacteristic
549C3⋊Dic3—22no—
550C3⋊Dic3—21no—
551C3×Dic3—21no—
552C3×Dic3—21no—
553H(5,𝔽2)—31no—
554H(5,𝔽2)—31no—
555H(5,𝔽2)—91no—
556H(5,𝔽2)—91no—
557AGL(1,ℤ/8)—31no—
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—61no—
560AGL(1,ℤ/8)—61no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—91no—
564AGL(1,ℤ/8)—91no—
565AGL(1,ℤ/8)—91no—
566AGL(1,ℤ/8)—181no—
567AGL(1,ℤ/8)—181no—
568AGL(1,ℤ/8)—181no—
569AGL(1,ℤ/8)—181no—
570AGL(1,ℤ/8)—181no—
571AGL(1,ℤ/8)—181no—
572AGL(1,ℤ/8)D3211yescharacteristic, complemented
573#135—31no—
574#135—61no—
575#135—91no—
576#135—181no—
577#135—181no—
578#135—181no—
579C2×D8—31no—
580C2×D8—31no—
581C2×D8—61no—
582C2×D8—91no—
583C2×D8—91no—
584C2×D8—181no—
585C2×D8—181no—
586C2×D8—181no—
587#131—31no—
588#131—31no—
589#131—91no—
590#131—91no—
591#127—91no—
592#127—91no—
593#108—31no—
594#108—91no—
595#104—91no—
596#104—91no—
597#104—91no—
598#104—91no—
599#100—31no—
600#100—31no—
601#100—91no—
602#100—91no—
603C4×C8—91no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—41no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—121no—
610C23×C3—121no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—62no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—122no—
623C3×Q8—21no—
624C3×Q8—31no—
625C3×Q8—31no—
626C3×Q8D3×D411yescharacteristic
627C3×Q8C2×#6711yescharacteristic
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—21no—
634C3×D4—21no—
635C3×D4—31no—
636C3×D4—31no—
637C3×D4—41no—
638C3×D4—41no—
639C3×D4—41no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—121no—
647C3×D4—121no—
648C3×D4—121no—
649C3×D4—121no—
650C3×D4D3×D411yescharacteristic
651C3×D4C2×#6711yescharacteristic
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—41no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—121no—
659C2×C3×C4—121no—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67—21no—
663#67—21no—
664#67—41no—
665#67—41no—
666#67—41no—
667#67—61no—
668#67—61no—
669#67—121no—
670#67—121no—
671#67—121no—
672#67—121no—
673#67—121no—
674#67—121no—
675#67—122no—
676#67—242no—
677#67—242no—
678#67—242no—
679#67—242no—
680#67—244no—
681C2×Dic3—41no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686D12—21no—
687D12—21no—
688D12—21no—
689D12—21no—
690D12—31no—
691D12—31no—
692D12—41no—
693D12—61no—
694D12—61no—
695D12—61no—
696D12—61no—
697D12—61no—
698D12—121no—
699D12—121no—
700D12—121no—
701D12—121no—
702D12—122no—
703D12—121no—
704D12D3×D411yescharacteristic
705D12C2×#6711yescharacteristic
706C4×D3—21no—
707C4×D3—21no—
708C4×D3—41no—
709C4×D3—61no—
710C4×D3—61no—
711C4×D3—121no—
712C4×D3—121no—
713C4×D3—121no—
714C4×D3—121no—
715C4×D3—122no—
716Dic6—31no—
717Dic6—31no—
718Dic6—61no—
719Dic6D3×D411yescharacteristic
720Dic6C2×#6711yescharacteristic
721C3×C8—21no—
722C3×C8—21no—
723C3×C8—31no—
724C3×C8—31no—
725C3×C8—31no—
726C3×C8—31no—
727C3×C8—41no—
728C3×C8—61no—
729C3×C8—61no—
730C3⋊C8—21no—
731C3⋊C8—21no—
732C3⋊C8—61no—
733C3⋊C8—61no—
734C3⋊C8—121no—
735C3⋊C8D3×D411yescharacteristic
736C3⋊C8D3×D411yescharacteristic
737C3⋊C8C2×#6711yescharacteristic
738C3⋊C8C2×#6711yescharacteristic
739C2×C32—21no—
740C2×C32—41no—
741C2×C32—81no—
742C2×C32D4211yescharacteristic
743C3⋊D3—41no—
744C3⋊D3—81no—
745C3×D3—41no—
746C3×D3—41no—
747C3×D3—81no—
748C3×D3—81no—
749#41—31no—
750#41—31no—
751#41—61no—
752#41—61no—
753#41—61no—
754#41—61no—
755#41—91no—
756#41—181no—
757#41—181no—
758#41—181no—
759#41—181no—
760#41C2×D3211yescharacteristic
761C2×D4—31no—
762C2×D4—31no—
763C2×D4—61no—
764C2×D4—61no—
765C2×D4—61no—
766C2×D4—61no—
767C2×D4—91no—
768C2×D4—121no—
769C2×D4—121no—
770C2×D4—181no—
771C2×D4—181no—
772C2×D4—181no—
773C2×D4—181no—
774C2×D4—361no—
775C2×D4—361no—
776C2×D4—361no—
777C2×D4—361no—
778C2×D4C2×D3211yescharacteristic
779Q16—31no—
780Q16—91no—
781SD16—21no—
782SD16—31no—
783SD16—31no—
784SD16—61no—
785SD16—61no—
786SD16—91no—
787SD16—91no—
788SD16—181no—
789SD16—181no—
790SD16—181no—
791SD16—181no—
792SD16—181no—
793D8—21no—
794D8—31no—
795D8—61no—
796D8—61no—
797D8—61no—
798D8—61no—
799D8—61no—
800D8—61no—
801D8—91no—
802D8—181no—
803D8—181no—
804D8—181no—
805D8—181no—
806D8—181no—
807D8—181no—
808D8—181no—
809D8—181no—
810D8—181no—
811M16—31no—
812M16—31no—
813M16—61no—
814M16—61no—
815M16—91no—
816M16—181no—
817M16—181no—
818M16C2×D3211yescharacteristic
819C2×C8—31no—
820C2×C8—31no—
821C2×C8—61no—
822C2×C8—61no—
823C2×C8—181no—
824C2×C8—181no—
825C42—91no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—61no—
833C22×C3—61no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—82no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—241no—
841C22×C3—241no—
842C22×C3—481no—
843C22×C3—481no—
844C22×C3#100411yescharacteristic
845C22×C3#100911yescharacteristic
846C2×D3—21no—
847C2×D3—21no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—81no—
853C2×D3—81no—
854C2×D3—121no—
855C2×D3—122no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—161no—
859C2×D3—161no—
860C2×D3—241no—
861C2×D3—241no—
862C2×D3—242no—
863C2×D3—481no—
864C2×D3—481no—
865C2×D3—481no—
866C2×D3—481no—
867C2×D3—482no—
868C3×C4—21no—
869C3×C4—21no—
870C3×C4—21no—
871C3×C4—21no—
872C3×C4—41no—
873C3×C4—61no—
874C3×C4—61no—
875C3×C4C2×D3×D411yescharacteristic
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C22×#6711yescharacteristic
879Dic3—21no—
880Dic3—21no—
881Dic3—62no—
882Dic3—62no—
883Dic3—61no—
884Dic3—61no—
885Dic3—121no—
886Dic3—122no—
887C32#329211yescharacteristic, complemented, Sylow
888C23—21no—
889C23—61no—
890C23—61no—
891C23—121no—
892C23—121no—
893C23—181no—
894C23—361no—
895C23—361no—
896Q8—31no—
897Q8—31no—
898Q8—91no—
899Q8D3×#6711yescharacteristic
900D4—21no—
901D4—21no—
902D4—21no—
903D4—31no—
904D4—31no—
905D4—61no—
906D4—61no—
907D4—61no—
908D4—61no—
909D4—61no—
910D4—61no—
911D4—91no—
912D4—121no—
913D4—121no—
914D4—121no—
915D4—121no—
916D4—181no—
917D4—181no—
918D4—181no—
919D4—361no—
920D4—361no—
921D4—361no—
922D4—361no—
923D4—722no—
924D4—722no—
925D4D3×#6711yescharacteristic
926C2×C4—21no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—181no—
932C2×C4—181no—
933C2×C4—361no—
934C2×C4—361no—
935C2×C4C22×D3211yescharacteristic
936C8—21no—
937C8—31no—
938C8—31no—
939C8—31no—
940C8—31no—
941C8—61no—
942C8—61no—
943C8—181no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—41no—
948C2×C3—41no—
949C2×C3—41no—
950C2×C3—81no—
951C2×C3—81no—
952C2×C3—81no—
953C2×C3—121no—
954C2×C3—121no—
955C2×C3—161no—
956C2×C3—241no—
957C2×C3—241no—
958C2×C3#560911yescharacteristic
959C2×C3D4×#6711yescharacteristic
960D3—41no—
961D3—41no—
962D3—81no—
963D3—81no—
964D3—121no—
965D3—121no—
966D3—241no—
967D3—242no—
968D3—241no—
969D3—241no—
970C22—21no—
971C22—41no—
972C22—61no—
973C22—61no—
974C22—81no—
975C22—121no—
976C22—121no—
977C22—181no—
978C22—241no—
979C22—241no—
980C22—361no—
981C22—481no—
982C22—481no—
983C22—721no—
984C22—1441no—
985C22—1441no—
986C22#6431411yescharacteristic
987C4—21no—
988C4—61no—
989C4—61no—
990C4—182no—
991C4—181no—
992C4D32×D411yescharacteristic
993C4C2×D3×#6711yescharacteristic
994C3—21no—
995C3#8094111yescharacteristic, complemented
996C3#8401011yescharacteristic, complemented
997C2—21no—
998C2—41no—
999C2—81no—
1000C2—121no—
1001C2—121no—
1002C2—241no—
1003C2—241no—
1004C2—361no—
1005C2—721no—
1006C2#1059529111yescharacteristic
subgroupG/H
centerC2#10595291
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×AGL(1,ℤ/8)C22
socleC2×C32D42
hypercenterAGL(1,ℤ/8)D32
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C3×#5774C2semidirect
2. #10595461C2semidirect
3. #10595449C2semidirect
4. #10595096C2semidirect
5. #10592897C2semidirect
6. C3×#5199C2semidirect
7. #10591673C2semidirect
8. #10591665C2semidirect
9. #10591510C2semidirect
10. #10591484C2semidirect
11. #10591406C2semidirect
12. #10591014C2semidirect
13. #10590997C2semidirect
14. #10590995C2semidirect
15. #10590984C2semidirect
18. #64366C22semidirect
19. C3×#1009C22semidirect
20. C3×#1004C22semidirect
21. #64307C22semidirect
22. C32×AGL(1,ℤ/8)C22semidirect
23. #64149C22semidirect
24. #64141C22semidirect
26. C3×#949C22semidirect
27. C3×#948C22semidirect
28. C2×C3×#213C22semidirect
29. C2×C3×#213C22semidirect
34. C3×#908C22semidirect
35. C3×#907C22semidirect
44. #63914C22semidirect
46. #63830C22semidirect
50. #63825C22semidirect
51. #63825C22semidirect
53. C2×#3714C22semidirect
54. C2×#3714C22semidirect
55. #63823C22semidirect
56. #63817C22semidirect
57. #63814C22semidirect
58. #63664C22semidirect
59. #63652C22semidirect
60. #63650C22semidirect
61. C3×#833C22semidirect
62. C3×#823C22semidirect
63. C3×#822C22semidirect
64. #63577C22semidirect
65. #63568C22semidirect
66. #63568C22semidirect
67. #63558C22semidirect
68. #63553C22semidirect
73. #5774D3semidirect
81. #5199D3semidirect
137. C3×#216D4semidirect
139. C3×#215D4semidirect
140. C3×#214D4semidirect
146. C3×#213D4semidirect
157. #3719D4semidirect
160. #3717D4semidirect
162. #3716D4semidirect
171. #3714D4semidirect
184. #1009C2×D3semidirect
186. #1004C2×D3semidirect
192. C3×AGL(1,ℤ/8)C2×D3semidirect
193. C3×AGL(1,ℤ/8)C2×D3semidirect
210. #949C2×D3semidirect
212. #948C2×D3semidirect
229. C2×#213C2×D3semidirect
230. C2×#213C2×D3semidirect
252. #908C2×D3semidirect
254. #907C2×D3semidirect
271. #833C2×D3semidirect
281. #823C2×D3semidirect
283. #822C2×D3semidirect
458. #216#67semidirect
464. #215#67semidirect
471. #214#67semidirect
490. #213#67semidirect
572. AGL(1,ℤ/8)D32semidirect
887. C32#3292semidirect
995. C3#80941semidirect
996. C3#84010semidirect

Maximal subgroups

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

subgroupindex
C3×#57742
#105954612
#105954492
#105950962
#105928972
C3×#51992
#105916732
#105916652
#105915102
#105914842
#105914062
#105910142
#105909972
#105909952
#105909842
#840103
#809413