Finite Group Databasebeta

← #11868028

Subgroups — #11868028

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5773C211yesmaximal, characteristic, complemented
2#10595470C211yesmaximal, characteristic, complemented
3D3×#948C211yesmaximal, characteristic, complemented
4C2×#63935C211yesmaximal, characteristic, complemented
5#10592898C211yesmaximal, characteristic, complemented
6C3×#5200C211yesmaximal, characteristic, complemented
7#10591683C211yesmaximal, characteristic, complemented
8#10591680C211yesmaximal, characteristic, complemented
9#10591508C211yesmaximal, characteristic, complemented
10#10591506C211yesmaximal, characteristic, complemented
11#10591501C211yesmaximal, characteristic, complemented
12#10591007C211yesmaximal, characteristic, complemented
13#10590985C211yesmaximal, characteristic, complemented
14#10590981C211yesmaximal, characteristic, complemented
15D3×#822C211yesmaximal, characteristic, complemented
16#84001—31nomaximal
17#80929—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C32×AGL(1,ℤ/8)C2211yescharacteristic
22#64158C2211yescharacteristic
23#64157C2211yescharacteristic
24C2×#3753C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic
26C3×#951C2211yescharacteristic
27C3×#948C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic, complemented
29C3×#932C2211yescharacteristic
30C3×#916—21no—
31C3×#915—21no—
32C3×#912—21no—
33C3×#911—21no—
34C3×#909C2211yescharacteristic
35C3×D3×M16C2211yescharacteristic
36#63949—21no—
37#63948—21no—
38#63935—21no—
39#63935—21no—
40#63935—21no—
41#63935—21no—
42#63935—21no—
43#63934—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46#63827C2211yescharacteristic
47#63825C2211yescharacteristic
48#63815—21no—
49#63815C2211yescharacteristic
50#63814—21no—
51#63814C2211yescharacteristic
52D3×#208—21no—
53D3×#208C2211yescharacteristic
54D3×#208C2211yescharacteristic
55C2×D3×C3⋊C8—21no—
56C2×D3×C3⋊C8C2211yescharacteristic
57#63660C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#824C2211yescharacteristic, complemented
62C3×#822C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63560C2211yescharacteristic, complemented
68#63559C2211yescharacteristic, complemented
69C3×#575—31no—
70#5822—31no—
71C2×#950—31no—
72C2×#948—31no—
73#5777—31no—
74#5773D311yescharacteristic, complemented
75C2×#916—31no—
76D3×#131—31no—
77C3×#471—31no—
78#5237—31no—
79#5204—31no—
80#5204—31no—
81#5204—31no—
82#5203—31no—
83#5203—31no—
84#5200—31no—
85#5200D311yescharacteristic, complemented
86#5199—31no—
87#5199—31no—
88#5199—31no—
89#5199—61no—
90#5177—31no—
91#5141—31no—
92#5132—31no—
93C2×#822—31no—
94#4898—31no—
95D3×#108—31no—
96#4755—31no—
97#4751—31no—
98#4749—31no—
99#4745—31no—
100C32×#41C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×#239D411yescharacteristic
106C3×D3×Q8D411yescharacteristic
107C3×#237—21no—
108C3×#237—21no—
109C3×#237—21no—
110C3×#237—21no—
111C3×#237—21no—
112C3×#237D411yescharacteristic
113C3×D3×D4—21no—
114C3×D3×D4D411yescharacteristic
115C3×#235—21no—
116C3×#235C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#626—21no—
122C2×#624—21no—
123#3799—21no—
124#3799—21no—
125#3799—21no—
126#3799—21no—
127C32×SD16—21no—
128C32×D8—21no—
129C32×M16C2311yescharacteristic
130#3755—21no—
131#3753—21no—
132#3753—21no—
133#3753—21no—
134#3748—21no—
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137C2×C3⋊(C3⋊C8)—21no—
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139C3×#216—21no—
140C3×#216—21no—
141C3×#214—21no—
142C3×#214—21no—
143C3×#214—21no—
144C3×#214—21no—
145C3×#214—21no—
146C3×#213—21no—
147C3×#208—21no—
148C3×#208C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C2×C3×C3⋊C8—21no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×D3×C8—21no—
157#3718—21no—
158#3718—21no—
159#3718—21no—
160#3717—21no—
161#3717—21no—
162#3717—21no—
163#3715—21no—
164#3714—21no—
165#3711—21no—
166#3711—21no—
167#3711—21no—
168#3711—21no—
169D3×C3⋊C8—21no—
170D3×C3⋊C8—21no—
171D3×C3⋊C8—21no—
172D3×C3⋊C8—21no—
173D3×C3⋊C8D411yescharacteristic
174D3×C3⋊C8D411yescharacteristic
175D3×C3⋊C8D411yescharacteristic
176D3×C3⋊C8D411yescharacteristic
177#3067—91noSylow
178C2×C3×#41—31no—
179C2×C3×#41—31no—
180D3×#41C2×D311yescharacteristic
181C2×#239—31no—
182C2×#237C2×D311yescharacteristic
183C2×#235—31no—
184C3×#137—31no—
185C3×#137—31no—
186C3×#137—31no—
187C3×#137—61no—
188C3×AGL(1,ℤ/8)—21no—
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—61no—
191C3×AGL(1,ℤ/8)C2×D311yescharacteristic
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic
193C3×#135—61no—
194C3×#135—61no—
195C2×C3×SD16—31no—
196C3×#131—31no—
197C2×C3×M16—31no—
198#951—31no—
199#951C2×D311yescharacteristic
200#951C2×D311yescharacteristic
201#950—61no—
202#950—61no—
203#950—61no—
204#950—61no—
205#950—61no—
206#950—61no—
207#949—31no—
208#949—31no—
209#949—31no—
210#949—61no—
211#948—31no—
212#948—31no—
213#948—31no—
214#948—31no—
215#948—61no—
216#948—61no—
217#948—61no—
218#948C2×D311yescharacteristic
219C2×#216—31no—
220C2×#216—31no—
221#942—31no—
222#942—61no—
223C2×#215—31no—
224C2×#214C2×D311yescharacteristic, complemented
225#932—61no—
226#932C2×D311yescharacteristic
227C2×#213—31no—
228C2×#213—31no—
229C2×#213—61no—
230C2×#208—31no—
231C2×#208—31no—
232C2×#208—61no—
233C22×C3⋊C8—31no—
234C22×C3⋊C8—61no—
235#919—61no—
236#918—61no—
237#916—21no—
238#916—61no—
239#916—61no—
240#916—61no—
241#916—61no—
242#916—61no—
243#915—21no—
244#914—61no—
245#912—21no—
246#911—21no—
247#909C2×D311yescharacteristic
248#908—31no—
249#907—31no—
250#907—61no—
251D3×M16—31no—
252D3×M16—31no—
253D3×M16—61no—
254D3×M16C2×D311yescharacteristic
255C2×#204—31no—
256#901—31no—
257#901—61no—
258C2×D3×C8—31no—
259C2×D3×C8—61no—
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#836—31no—
265#836—31no—
266#833—31no—
267#833—31no—
268#833—61no—
269#833C2×D311yescharacteristic, complemented
270#824—31no—
271#824—31no—
272#824—31no—
273#824C2×D311yescharacteristic, complemented
274#823—31no—
275#823—31no—
276#823—31no—
277#823—31no—
278#823—61no—
279#822—31no—
280#822—31no—
281#822—31no—
282#822—31no—
283#822—31no—
284#822—61no—
285#822C2×D311yescharacteristic, complemented
286#819—31no—
287C23×C32—21no—
288C22×C3⋊D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3#4111yescharacteristic
291C32×Q8C2×D411yescharacteristic
292C32×D4—21no—
293C32×D4—21no—
294C32×D4—21no—
295C32×D4C2×D411yescharacteristic
296C2×C32×C4—21no—
297C2×C32×C4C2411yescharacteristic
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)—21no—
300C3×#67—21no—
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—41no—
304C3×#67—41no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3#4111yescharacteristic
311C3×D12—21no—
312C3×D12C2×D411yescharacteristic
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3C2×D411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×C4×D3C2×D411yescharacteristic
319C3×C4×D3C2×D411yescharacteristic
320C3×Dic6—21no—
321C3×Dic6—21no—
322C3×Dic6—21no—
323C3×Dic6—21no—
324C3×Dic6—21no—
325C3×Dic6C2×D411yescharacteristic
326#626—41no—
327#626—41no—
328#624—41no—
329#624—41no—
330C32×C8—21no—
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)—21no—
333C3⋊(C3⋊C8)C2×D411yescharacteristic
334C3⋊(C3⋊C8)C2×D411yescharacteristic
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340#575—31no—
341#575—91no—
342C2×#135—91no—
343C2×#131—91no—
344#473—91no—
345#473—91no—
346#472—91no—
347#472—91no—
348#471—31no—
349#471—91no—
350#471—91no—
351#471—91no—
352C2×#108—91no—
353#413—91no—
354#413—91no—
355C3×#41—21no—
356C3×#41—31no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—61no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41C22×D311yescharacteristic
366C3×#41C22×D311yescharacteristic
367C2×C3×Q8—31no—
368C2×C3×Q8—31no—
369C2×C3×Q8—31no—
370C2×C3×D4—21no—
371C2×C3×D4—31no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4C22×D311yescharacteristic
375C2×C3×D4C22×D311yescharacteristic
376C22×C3×C4—31no—
377C22×C3×C4—61no—
378C22×C3×C4—61no—
379C2×#67—21no—
380C2×#67—61no—
381C22×Dic3—21no—
382#239—61no—
383#239—61no—
384#239—61no—
385#239—61no—
386#239#6711yescharacteristic
387D3×Q8#6711yescharacteristic
388#237—21no—
389#237—21no—
390#237—21no—
391#237—21no—
392#237—21no—
393#237#6711yescharacteristic
394D3×D4—21no—
395D3×D4#6711yescharacteristic
396#235—21no—
397#235—61no—
398#235—61no—
399#235—61no—
400#235—61no—
401#235C22×D311yescharacteristic
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—61no—
405C2×D12—61no—
406C2×C4×D3—21no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3C22×D311yescharacteristic
410C2×Dic6C22×D311yescharacteristic
411C2×Dic6C22×D311yescharacteristic
412C3×Q16—61no—
413C3×Q16—61no—
414C3×Q16—61no—
415C3×SD16—21no—
416C3×SD16—21no—
417C3×SD16—41no—
418C3×SD16—61no—
419C3×SD16—61no—
420C3×SD16—61no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×D8—21no—
425C3×D8—21no—
426C3×D8—41no—
427C3×D8—61no—
428C3×M16—21no—
429C3×M16—31no—
430C3×M16—31no—
431C3×M16—31no—
432C3×M16—61no—
433C3×M16—61no—
434C3×M16C22×D311yescharacteristic
435C3×M16C22×D311yescharacteristic
436C2×C3×C8—31no—
437C2×C3×C8—61no—
438C2×C3×C8—61no—
439#216—21no—
440#216—21no—
441#216—61no—
442#216—61no—
443#216—61no—
444#216—61no—
445#216—61no—
446#216—61no—
447#215—61no—
448#215—61no—
449#215—61no—
450#215—61no—
451#215—61no—
452#215—61no—
453#215—121no—
454#214—21no—
455#214—21no—
456#214—21no—
457#214—21no—
458#214—21no—
459#214—61no—
460#213—21no—
461#213—61no—
462#213—61no—
463#213—61no—
464#213—61no—
465#213—61no—
466#213—61no—
467#213—61no—
468#213—121no—
469#213—121no—
470#213—121no—
471#208—21no—
472#208—31no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—61no—
477#208—61no—
478#208—61no—
479#208—61no—
480#208—61no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—121no—
485#208C22×D311yescharacteristic
486#208C22×D311yescharacteristic
487#208C22×D311yescharacteristic
488C2×C3⋊C8—21no—
489C2×C3⋊C8—31no—
490C2×C3⋊C8—31no—
491C2×C3⋊C8—31no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—61no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8—61no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8—121no—
503C2×C3⋊C8C22×D311yescharacteristic
504Dic12—21no—
505D24—61no—
506#204—21no—
507#204—61no—
508#204—61no—
509#204—61no—
510ΓL(1,𝔽25)—21no—
511ΓL(1,𝔽25)—61no—
512ΓL(1,𝔽25)—61no—
513ΓL(1,𝔽25)—61no—
514ΓL(1,𝔽25)—61no—
515D3×C8—21no—
516D3×C8—31no—
517D3×C8—31no—
518D3×C8—31no—
519D3×C8—31no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524C22×C32—21no—
525C22×C32—41no—
526C22×C32—81no—
527C22×C32C2×#4111yescharacteristic
528C2×C3⋊D3—41no—
529C2×C3⋊D3—81no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—42no—
533C2×C3×D3#12111yescharacteristic
534C2×C3×D3#12111yescharacteristic
535C32×C4—21no—
536C32×C4C22×D411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3×Dic3—21no—
539C3×Dic3—41no—
540C3×Dic3—41no—
541C3×Dic3#12111yescharacteristic
542C3×Dic3#12111yescharacteristic
543C2×#41—31no—
544C2×#41—31no—
545C2×#41—91no—
546#137—31no—
547#137—31no—
548#137—31no—
549#137—61no—
550#137—91no—
551#137—181no—
552AGL(1,ℤ/8)—31no—
553AGL(1,ℤ/8)—61no—
554AGL(1,ℤ/8)—91no—
555AGL(1,ℤ/8)—91no—
556AGL(1,ℤ/8)—181no—
557AGL(1,ℤ/8)D3211yescharacteristic
558#135—61no—
559#135—61no—
560#135—181no—
561#135—181no—
562#135—181no—
563#135—181no—
564#135—181no—
565#135—181no—
566C2×Q16—91no—
567C2×SD16—31no—
568C2×SD16—91no—
569C2×D8—91no—
570#131—31no—
571#131—91no—
572#131—91no—
573#131—91no—
574#131—181no—
575#131—181no—
576C2×M16—31no—
577C2×M16—91no—
578C2×M16—91no—
579C2×M16—181no—
580C22×C8—91no—
581C22×C8—181no—
582#108—31no—
583#108—91no—
584#108—91no—
585#108—91no—
586#101—31no—
587#101—91no—
588#101—91no—
589#101—91no—
590#100—31no—
591#100—91no—
592#100—91no—
593#100—91no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—31no—
597C23×C3—41no—
598C23×C3—61no—
599C22×D3—21no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—121no—
603C22×D3#23711yescharacteristic
604C3×Q8—21no—
605C3×Q8—31no—
606C3×Q8—61no—
607C3×Q8—61no—
608C3×Q8—61no—
609C3×Q8—61no—
610C3×Q8—61no—
611C3×Q8D3×D411yescharacteristic
612C3×Q8C2×#6711yescharacteristic
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—31no—
621C3×D4—41no—
622C3×D4—41no—
623C3×D4—41no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—121no—
629C3×D4—121no—
630C3×D4D3×D411yescharacteristic
631C3×D4C2×#6711yescharacteristic
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—41no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—121no—
648C2×C3×C4—121no—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651#67—21no—
652#67—21no—
653#67—21no—
654#67—41no—
655#67—41no—
656#67—121no—
657#67—121no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3#23711yescharacteristic
664D12—21no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—121no—
670D12—121no—
671D12—121no—
672D12—121no—
673D12C2×#6711yescharacteristic
674C4×D3—21no—
675C4×D3—21no—
676C4×D3—21no—
677C4×D3—121no—
678C4×D3—121no—
679C4×D3—121no—
680C4×D3—121no—
681C4×D3D3×D411yescharacteristic
682C4×D3D3×D411yescharacteristic
683C4×D3C2×#6711yescharacteristic
684C4×D3C2×#6711yescharacteristic
685Dic6—21no—
686Dic6—21no—
687Dic6—21no—
688Dic6—21no—
689Dic6—21no—
690Dic6C2×#6711yescharacteristic
691C3×C8—21no—
692C3×C8—21no—
693C3×C8—31no—
694C3×C8—31no—
695C3×C8—41no—
696C3×C8—61no—
697C3×C8—61no—
698C3×C8—61no—
699C3⋊C8—21no—
700C3⋊C8—21no—
701C3⋊C8—21no—
702C3⋊C8—31no—
703C3⋊C8—31no—
704C3⋊C8—31no—
705C3⋊C8—31no—
706C3⋊C8—61no—
707C3⋊C8—61no—
708C3⋊C8—61no—
709C3⋊C8—61no—
710C3⋊C8—61no—
711C3⋊C8—61no—
712C3⋊C8—121no—
713C3⋊C8—121no—
714C3⋊C8D3×D411yescharacteristic
715C3⋊C8D3×D411yescharacteristic
716C2×C32—21no—
717C2×C32—41no—
718C2×C32—81no—
719C2×C32C2×#12111yescharacteristic
720C3⋊D3—81no—
721C3×D3—21no—
722C3×D3—21no—
723C3×D3—41no—
724#41—31no—
725#41—31no—
726#41—31no—
727#41—61no—
728#41—61no—
729#41—61no—
730#41—61no—
731#41—61no—
732#41—61no—
733#41—181no—
734#41—181no—
735#41—181no—
736#41—181no—
737#41C2×D3211yescharacteristic
738C2×Q8—31no—
739C2×Q8—31no—
740C2×Q8—31no—
741C2×D4—31no—
742C2×D4—61no—
743C2×D4—61no—
744C2×D4—91no—
745C2×D4—181no—
746C2×D4C2×D3211yescharacteristic
747C22×C4—31no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—181no—
751Q16—61no—
752Q16—61no—
753Q16—61no—
754Q16—181no—
755Q16—181no—
756Q16—181no—
757SD16—21no—
758SD16—61no—
759SD16—61no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—181no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769D8—21no—
770D8—61no—
771D8—181no—
772D8—181no—
773D8—181no—
774D8—181no—
775M16—31no—
776M16—31no—
777M16—31no—
778M16—61no—
779M16—61no—
780M16—91no—
781M16—91no—
782M16—181no—
783M16—181no—
784M16—181no—
785M16—181no—
786M16—181no—
787M16C2×D3211yescharacteristic
788C2×C8—31no—
789C2×C8—61no—
790C2×C8—61no—
791C2×C8—91no—
792C2×C8—91no—
793C2×C8—91no—
794C2×C8—91no—
795C2×C8—91no—
796C2×C8—181no—
797C2×C8—181no—
798C2×C8—181no—
799C2×C8—181no—
800C2×C8—181no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—31no—
805C22×C3—31no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—61no—
810C22×C3—81no—
811C22×C3—81no—
812C22×C3—81no—
813C22×C3—121no—
814C22×C3—122no—
815C22×C3—161no—
816C22×C3C2×#23711yescharacteristic
817C22×C3D3×#4111yescharacteristic
818C2×D3—21no—
819C2×D3—41no—
820C2×D3—42no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—241no—
824C2×D3—241no—
825C2×D3—241no—
826C2×D3—481no—
827C2×D3#93911yescharacteristic
828C2×D3#93911yescharacteristic
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—21no—
833C3×C4—31no—
834C3×C4—31no—
835C3×C4—41no—
836C3×C4—61no—
837C3×C4—121no—
838C3×C4—121no—
839C3×C4C2×D3×D411yescharacteristic
840C3×C4C2×D3×D411yescharacteristic
841C3×C4C2×D3×D411yescharacteristic
842C3×C4C22×#6711yescharacteristic
843Dic3—21no—
844Dic3—41no—
845Dic3—41no—
846Dic3#93911yescharacteristic
847Dic3#93911yescharacteristic
848C32#306711yescharacteristic, complemented, Sylow
849C23—21no—
850C23—31no—
851C23—61no—
852C23—181no—
853Q8—31no—
854Q8—61no—
855Q8—61no—
856Q8—61no—
857Q8—61no—
858Q8—61no—
859Q8D3×#6711yescharacteristic
860D4—21no—
861D4—21no—
862D4—21no—
863D4—31no—
864D4—61no—
865D4—61no—
866D4—61no—
867D4—61no—
868D4—121no—
869D4—121no—
870D4—181no—
871D4—181no—
872D4—361no—
873D4—361no—
874D4D3×#6711yescharacteristic
875C2×C4—21no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—361no—
890C2×C4—361no—
891C2×C4C22×D3211yescharacteristic
892C8—21no—
893C8—31no—
894C8—31no—
895C8—61no—
896C8—61no—
897C8—61no—
898C8—91no—
899C8—91no—
900C8—181no—
901C8—181no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—41no—
906C2×C3—41no—
907C2×C3—41no—
908C2×C3—61no—
909C2×C3—61no—
910C2×C3—81no—
911C2×C3—81no—
912C2×C3—81no—
913C2×C3—121no—
914C2×C3—161no—
915C2×C3D3×#12111yescharacteristic
916C2×C3C2×#93911yescharacteristic
917D3—21no—
918D3—21no—
919D3—41no—
920D3—241no—
921D3—241no—
922D3—481no—
923C22—21no—
924C22—31no—
925C22—31no—
926C22—41no—
927C22—61no—
928C22—81no—
929C22—121no—
930C22—122no—
931C22—361no—
932C22—721no—
933C22D3×#23711yescharacteristic
934C4—21no—
935C4—31no—
936C4—31no—
937C4—61no—
938C4—121no—
939C4—121no—
940C4D32×D411yescharacteristic
941C4C2×D3×#6711yescharacteristic
942C3—21no—
943C3#8092911yescharacteristic, complemented
944C3#8400111yescharacteristic, complemented
945C2—21no—
946C2—41no—
947C2—61no—
948C2—61no—
949C2—81no—
950C2—121no—
951C2—721no—
952C2D3×#93911yescharacteristic
subgroupG/H
centerC2D3×#939
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×AGL(1,ℤ/8)C22
socleC2×C32C2×#121
hypercenterAGL(1,ℤ/8)D32
hypocenterC32#3067
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×#5773C2semidirect
2. #10595470C2semidirect
3. D3×#948C2semidirect
4. C2×#63935C2semidirect
5. #10592898C2semidirect
6. C3×#5200C2semidirect
7. #10591683C2semidirect
8. #10591680C2semidirect
9. #10591508C2semidirect
10. #10591506C2semidirect
11. #10591501C2semidirect
12. #10591007C2semidirect
13. #10590985C2semidirect
14. #10590981C2semidirect
15. D3×#822C2semidirect
24. C2×#3753C22semidirect
28. C2×C3×#214C22semidirect
44. C2×#3718C22semidirect
45. C2×#3717C22semidirect
57. #63660C22semidirect
58. #63650C22semidirect
59. #63649C22semidirect
60. C3×#833C22semidirect
61. C3×#824C22semidirect
62. C3×#822C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63560C22semidirect
66. #63560C22semidirect
67. #63560C22semidirect
68. #63559C22semidirect
74. #5773D3semidirect
85. #5200D3semidirect
224. C2×#214C2×D3semidirect
269. #833C2×D3semidirect
273. #824C2×D3semidirect
285. #822C2×D3semidirect
848. C32#3067semidirect
943. C3#80929semidirect
944. C3#84001semidirect

Maximal subgroups

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

subgroupindex
C3×#57732
#105954702
D3×#9482
C2×#639352
#105928982
C3×#52002
#105916832
#105916802
#105915082
#105915062
#105915012
#105910072
#105909852
#105909812
D3×#8222
#840013
#809293