Finite Group Databasebeta

← D3×#5200 #11867867

Subgroups — D3×#5200 #11867867

Order 1152.

988 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×AGL(1,ℤ/8)C211yesmaximal, characteristic
2D3×#951C211yesmaximal, characteristic, complemented
3D3×#948C211yesmaximal, characteristic, complemented
4C2×D3×#214C211yesmaximal, characteristic, complemented
5#10592899C211yesmaximal, characteristic, complemented
6C3×#5200C211yesmaximal, characteristic, complemented
7#10591681C211yesmaximal, characteristic, complemented
8#10591679C211yesmaximal, characteristic, complemented
9#10591507C211yesmaximal, characteristic, complemented
10#10591506C211yesmaximal, characteristic, complemented
11D3×#833C211yesmaximal, characteristic, complemented
12D3×#824C211yesmaximal, characteristic, complemented
13#10590986C211yesmaximal, characteristic, complemented
14#10590980C211yesmaximal, characteristic, complemented
15D3×#822C211yesmaximal, characteristic, complemented
16C2×#5200—31nomaximal
17D3×#471—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×AGL(1,ℤ/8)C2211yescharacteristic
22#64160C2211yescharacteristic, complemented
23#64157C2211yescharacteristic, complemented
24C2×#3754C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic, complemented
26C3×#949C2211yescharacteristic
27C3×#948C2211yescharacteristic, complemented
28C2×C3×#214C2211yescharacteristic, complemented
29C3×#932C2211yescharacteristic
30C3×#914—21no—
31C3×D3×SD16—21no—
32C3×#911—21no—
33C3×D3×D8—21no—
34C3×#908C2211yescharacteristic
35C3×D3×M16C2211yescharacteristic
36#63943—21no—
37D3×#216—21no—
38#63929—21no—
39D3×#214—21no—
40D3×#214—21no—
41D3×#214—21no—
42D3×#214—21no—
43D3×#214—21no—
44#63831C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46#63827C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48#63815—21no—
49#63815C2211yescharacteristic, complemented
50#63814—21no—
51#63814C2211yescharacteristic, complemented
52D3×#208—21no—
53D3×#208C2211yescharacteristic
54D3×#208C2211yescharacteristic
55C2×D3×C3⋊C8—21no—
56C2×D3×C3⋊C8C2211yescharacteristic
57#63660C2211yescharacteristic, complemented
58#63651C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#824C2211yescharacteristic, complemented
62C3×#822C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×C3×AGL(1,ℤ/8)—31no—
70C2×#951—31no—
71C2×#948—31no—
72C22×#214—31no—
73D3×#137—31no—
74D3×AGL(1,ℤ/8)D311yescharacteristic
75C2×D3×SD16—31no—
76D3×#131—31no—
77C3×#471—31no—
78C2×#833—31no—
79#5203—31no—
80#5200—31no—
81#5200—31no—
82#5200—31no—
83#5200—31no—
84#5200—31no—
85#5200—31no—
86#5200—31no—
87#5200—31no—
88#5200—61no—
89#5200D311yescharacteristic, direct product factor
90#5177—31no—
91#5141—31no—
92C2×#824—31no—
93C2×#822—31no—
94#4898—31no—
95D3×#108—31no—
96#4754—31no—
97D3×#101—31no—
98#4748—31no—
99D3×#100—31no—
100C23×C3×D3—21no—
101C32×#41C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C3×#239D411yescharacteristic
106C3×D3×Q8D411yescharacteristic
107C3×#237—21no—
108C3×#237D411yescharacteristic
109C3×D3×D4—21no—
110C3×D3×D4—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×D3×D4—21no—
114C3×D3×D4D411yescharacteristic
115C3×#235—21no—
116C3×#235C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#627—21no—
122C2×D3×Dic3—21no—
123D3×Dic6—21no—
124D3×Dic6—21no—
125D3×Dic6—21no—
126D3×Dic6—21no—
127C32×SD16—21no—
128C32×D8—21no—
129C32×M16C2311yescharacteristic
130#3756—21no—
131#3754—21no—
132#3754—21no—
133#3754—21no—
134#3748—21no—
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137C2×C3⋊(C3⋊C8)—21no—
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139C3×#216—21no—
140C3×#215—21no—
141C3×#214—21no—
142C3×#214—21no—
143C3×#214—21no—
144C3×#214—21no—
145C3×#213—21no—
146C3×#213—21no—
147C3×#208—21no—
148C3×#208C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C2×C3×C3⋊C8—21no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×D24—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×D3×C8—21no—
157#3719—21no—
158#3718—21no—
159#3716—21no—
160#3716—21no—
161#3716—21no—
162#3715—21no—
163#3715—21no—
164#3715—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
177C2×#471—91noSylow
178C2×C3×#41—31no—
179C22×C3×D4—31no—
180D3×#41C2×D311yescharacteristic
181C2×D3×Q8—31no—
182C2×D3×D4C2×D311yescharacteristic
183C22×Dic6—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—21no—
186C3×AGL(1,ℤ/8)—31no—
187C3×AGL(1,ℤ/8)—31no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—61no—
190C3×AGL(1,ℤ/8)—61no—
191C3×AGL(1,ℤ/8)C2×D311yescharacteristic
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic
193C2×C3×SD16—31no—
194C2×C3×SD16—61no—
195C2×C3×D8—61no—
196C3×#131—31no—
197C2×C3×M16—31no—
198#951—31no—
199#951—31no—
200#951—31no—
201#951—31no—
202#951—61no—
203#951—61no—
204#951—61no—
205#951C2×D311yescharacteristic, complemented
206#949C2×D311yescharacteristic
207#948—31no—
208#948—31no—
209#948—31no—
210#948—31no—
211#948—61no—
212#948—61no—
213#948—61no—
214#948C2×D311yescharacteristic, complemented
215C2×#216—61no—
216#942—31no—
217C2×#215—31no—
218C2×#214—31no—
219C2×#214—31no—
220C2×#214—31no—
221C2×#214—31no—
222C2×#214—61no—
223C2×#214—61no—
224C2×#214—61no—
225C2×#214—61no—
226C2×#214—61no—
227C2×#214—61no—
228C2×#214C2×D311yescharacteristic, complemented
229#932C2×D311yescharacteristic
230C2×#208—31no—
231C2×#208—31no—
232C2×#208—61no—
233C22×C3⋊C8—31no—
234C22×C3⋊C8—61no—
235#918—61no—
236D3×Q16—61no—
237#915—61no—
238#914—21no—
239D3×SD16—21no—
240D3×SD16—61no—
241D3×SD16—61no—
242D3×SD16—61no—
243D3×SD16—61no—
244D3×SD16—61no—
245#911—21no—
246D3×D8—21no—
247#909—31no—
248#908C2×D311yescharacteristic
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#833—31no—
265#833—31no—
266#833—31no—
267#833—31no—
268#833—61no—
269#833C2×D311yescharacteristic, complemented
270#824—31no—
271#824—31no—
272#824—31no—
273#824—31no—
274#824—31no—
275#824—61no—
276#824C2×D311yescharacteristic, complemented
277#823—31no—
278#823—31no—
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—41no—
291C22×C3×D3—41no—
292C22×C3×D3—82no—
293C22×C3×D3#4111yescharacteristic
294C32×Q8C2×D411yescharacteristic
295C32×D4—21no—
296C32×D4—21no—
297C32×D4—21no—
298C32×D4C2×D411yescharacteristic
299C2×C32×C4—21no—
300C2×C32×C4C2411yescharacteristic
301C2×C3⋊Dic3—21no—
302#634—21no—
303#634—21no—
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—21no—
307C3×#67—41no—
308C3×#67—41no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3#4111yescharacteristic
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12C2×D411yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3C2×D411yescharacteristic
320C3×C4×D3C2×D411yescharacteristic
321C3×C4×D3C2×D411yescharacteristic
322C3×C4×D3C2×D411yescharacteristic
323C3×Dic6—21no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6C2×D411yescharacteristic
327#627—41no—
328#627—41no—
329D3×Dic3—41no—
330D3×Dic3—41no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)C2×D411yescharacteristic
335C3⋊(C3⋊C8)C2×D411yescharacteristic
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341C2×#137—91no—
342C2×AGL(1,ℤ/8)—31no—
343C22×SD16—91no—
344C2×#131—91no—
345#471—31no—
346#471—91no—
347#471—91no—
348#471—91no—
349#471—91no—
350#471—91no—
351#471—91no—
352#471—91no—
353C2×#108—91no—
354C2×#101—91no—
355C2×#100—91no—
356C24×C3—61no—
357C23×D3—21no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—31no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41C22×D311yescharacteristic
365C3×#41C22×D311yescharacteristic
366C2×C3×Q8—31no—
367C2×C3×Q8—31no—
368C2×C3×D4—21no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4—61no—
377C2×C3×D4C22×D311yescharacteristic
378C2×C3×D4C22×D311yescharacteristic
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C2×#67—21no—
382C22×Dic3—61no—
383#239#6711yescharacteristic
384D3×Q8—61no—
385D3×Q8—61no—
386D3×Q8—61no—
387D3×Q8—61no—
388D3×Q8#6711yescharacteristic
389#237—21no—
390#237#6711yescharacteristic
391D3×D4—21no—
392D3×D4—21no—
393D3×D4—21no—
394D3×D4—21no—
395D3×D4—21no—
396D3×D4#6711yescharacteristic
397#235—21no—
398#235C22×D311yescharacteristic
399C2×D12C22×D311yescharacteristic
400C2×C4×D3—21no—
401C2×C4×D3—61no—
402C2×C4×D3C22×D311yescharacteristic
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—61no—
406C2×Dic6—61no—
407C2×Dic6—61no—
408C2×Dic6—61no—
409C2×Dic6—61no—
410C2×Dic6—61no—
411C2×Dic6—61no—
412C2×Dic6C22×D311yescharacteristic
413C3×Q16—61no—
414C3×SD16—21no—
415C3×SD16—21no—
416C3×SD16—41no—
417C3×SD16—61no—
418C3×SD16—61no—
419C3×SD16—61no—
420C3×SD16—61no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×D8—21no—
424C3×D8—21no—
425C3×D8—41no—
426C3×D8—61no—
427C3×D8—61no—
428C3×D8—61no—
429C3×M16—21no—
430C3×M16—31no—
431C3×M16—31no—
432C3×M16—31no—
433C3×M16—61no—
434C3×M16—61no—
435C3×M16C22×D311yescharacteristic
436C3×M16C22×D311yescharacteristic
437C2×C3×C8—31no—
438C2×C3×C8—61no—
439C2×C3×C8—61no—
440#216—21no—
441#216—61no—
442#216—61no—
443#216—61no—
444#216—61no—
445#216—61no—
446#216—121no—
447#215—21no—
448#215—61no—
449#215—61no—
450#215—61no—
451#214—21no—
452#214—21no—
453#214—21no—
454#214—21no—
455#214—61no—
456#214—61no—
457#214—61no—
458#214—61no—
459#214—61no—
460#214—61no—
461#214—61no—
462#214—61no—
463#214—61no—
464#214—61no—
465#214—61no—
466#214—61no—
467#214—121no—
468#214—121no—
469#214—121no—
470#213—21no—
471#213—21no—
472#208—21no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—61no—
478#208—61no—
479#208—61no—
480#208—61no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—121no—
486#208C22×D311yescharacteristic
487#208C22×D311yescharacteristic
488#208C22×D311yescharacteristic
489C2×C3⋊C8—21no—
490C2×C3⋊C8—31no—
491C2×C3⋊C8—31no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
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—61no—
503C2×C3⋊C8—121no—
504C2×C3⋊C8C22×D311yescharacteristic
505Dic12—61no—
506D24—21no—
507#204—21no—
508#204—61no—
509#204—61no—
510#204—61no—
511ΓL(1,𝔽25)—21no—
512ΓL(1,𝔽25)—61no—
513ΓL(1,𝔽25)—61no—
514ΓL(1,𝔽25)—61no—
515ΓL(1,𝔽25)—61no—
516D3×C8—21no—
517D3×C8—31no—
518D3×C8—31no—
519D3×C8—31no—
520D3×C8—31no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525C22×C32—21no—
526C22×C32—41no—
527C22×C32—81no—
528C22×C32C2×#4111yescharacteristic
529C2×C3×D3—22no—
530C2×C3×D3—21no—
531C2×C3×D3—42no—
532C2×C3×D3—41no—
533C2×C3×D3—82no—
534C2×C3×D3—82no—
535C2×C3×D3—81no—
536C2×C3×D3#12111yescharacteristic
537C2×C3×D3#12111yescharacteristic
538C32×C4—21no—
539C32×C4C22×D411yescharacteristic
540C32×C4C22×D411yescharacteristic
541C3⋊Dic3—41no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12111yescharacteristic
545C3×Dic3#12111yescharacteristic
546C2×#41—31no—
547C22×Q8—91no—
548C22×D4—31no—
549#137—31no—
550#137—91no—
551#137—91no—
552#137—91no—
553#137—181no—
554#137—181no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—31no—
558AGL(1,ℤ/8)—61no—
559AGL(1,ℤ/8)—61no—
560AGL(1,ℤ/8)D3211yescharacteristic
561C2×Q16—181no—
562C2×SD16—31no—
563C2×SD16—61no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×SD16—91no—
567C2×SD16—181no—
568C2×SD16—181no—
569C2×SD16—181no—
570C2×SD16—181no—
571C2×SD16—181no—
572C2×D8—61no—
573#131—31no—
574#131—91no—
575#131—91no—
576#131—91no—
577#131—181no—
578#131—181no—
579C2×M16—31no—
580C2×M16—91no—
581C2×M16—91no—
582C2×M16—181no—
583C22×C8—91no—
584C22×C8—181no—
585#108—31no—
586#108—91no—
587#108—91no—
588#108—91no—
589#101—31no—
590#101—91no—
591#101—91no—
592#101—91no—
593#100—31no—
594#100—91no—
595#100—91no—
596#100—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—41no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—121no—
604C23×C3—121no—
605C23×C3—242no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—82no—
611C22×D3#23711yescharacteristic
612C3×Q8—21no—
613C3×Q8—31no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×Q8D3×D411yescharacteristic
618C3×Q8C2×#6711yescharacteristic
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—31no—
627C3×D4—41no—
628C3×D4—41no—
629C3×D4—41no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—121no—
637C3×D4—121no—
638C3×D4D3×D411yescharacteristic
639C3×D4C2×#6711yescharacteristic
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—31no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—41no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656#67—21no—
657#67—21no—
658#67—21no—
659#67—41no—
660#67—41no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3#23711yescharacteristic
669D12—21no—
670D12—21no—
671D12—21no—
672D12C2×#6711yescharacteristic
673C4×D3—21no—
674C4×D3—21no—
675C4×D3—21no—
676C4×D3—121no—
677C4×D3—121no—
678C4×D3D3×D411yescharacteristic
679C4×D3D3×D411yescharacteristic
680C4×D3C2×#6711yescharacteristic
681C4×D3C2×#6711yescharacteristic
682Dic6—21no—
683Dic6—21no—
684Dic6—21no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6—61no—
689Dic6—121no—
690Dic6—121no—
691Dic6—121no—
692Dic6—121no—
693Dic6—121no—
694Dic6—121no—
695Dic6C2×#6711yescharacteristic
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—31no—
699C3×C8—31no—
700C3×C8—41no—
701C3×C8—61no—
702C3×C8—61no—
703C3×C8—61no—
704C3⋊C8—21no—
705C3⋊C8—21no—
706C3⋊C8—21no—
707C3⋊C8—31no—
708C3⋊C8—31no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—61no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—121no—
718C3⋊C8—121no—
719C3⋊C8D3×D411yescharacteristic
720C3⋊C8D3×D411yescharacteristic
721C2×C32—21no—
722C2×C32—41no—
723C2×C32—81no—
724C2×C32C2×#12111yescharacteristic
725C3×D3—21no—
726C3×D3—41no—
727C3×D3—81no—
728C3×D3#47112yescomplemented
729C24—61no—
730#41—31no—
731#41—31no—
732#41—31no—
733#41—61no—
734#41—61no—
735#41C2×D3211yescharacteristic
736C2×Q8—31no—
737C2×Q8—31no—
738C2×Q8—91no—
739C2×Q8—181no—
740C2×Q8—181no—
741C2×Q8—181no—
742C2×Q8—181no—
743C2×Q8—181no—
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4C2×D3211yescharacteristic
753C22×C4—31no—
754C22×C4—61no—
755C22×C4—181no—
756Q16—61no—
757Q16—181no—
758Q16—181no—
759Q16—181no—
760SD16—21no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—61no—
766SD16—61no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772SD16—181no—
773SD16—181no—
774SD16—181no—
775SD16—181no—
776D8—21no—
777D8—61no—
778D8—61no—
779D8—61no—
780M16—31no—
781M16—31no—
782M16—31no—
783M16—61no—
784M16—61no—
785M16—91no—
786M16—91no—
787M16—181no—
788M16—181no—
789M16—181no—
790M16—181no—
791M16—181no—
792M16C2×D3211yescharacteristic
793C2×C8—31no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—91no—
797C2×C8—91no—
798C2×C8—91no—
799C2×C8—91no—
800C2×C8—91no—
801C2×C8—181no—
802C2×C8—181no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—31no—
810C22×C3—31no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—62no—
815C22×C3—61no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—122no—
820C22×C3—121no—
821C22×C3—161no—
822C22×C3—241no—
823C22×C3—242no—
824C22×C3—242no—
825C22×C3C2×#23711yescharacteristic
826C22×C3D3×#4111yescharacteristic
827C2×D3—22no—
828C2×D3—21no—
829C2×D3—42no—
830C2×D3—41no—
831C2×D3—82no—
832C2×D3—82no—
833C2×D3—81no—
834C2×D3#93911yescharacteristic
835C2×D3#93911yescharacteristic
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—31no—
841C3×C4—31no—
842C3×C4—41no—
843C3×C4—61no—
844C3×C4—121no—
845C3×C4C2×D3×D411yescharacteristic
846C3×C4C2×D3×D411yescharacteristic
847C3×C4C2×D3×D411yescharacteristic
848C3×C4C22×#6711yescharacteristic
849Dic3—21no—
850Dic3—41no—
851Dic3—121no—
852Dic3—121no—
853Dic3—241no—
854Dic3#93911yescharacteristic
855Dic3#93911yescharacteristic
856C32C2×#47111yescharacteristic, complemented, Sylow
857C23—21no—
858C23—31no—
859C23—61no—
860C23—61no—
861C23—121no—
862C23—121no—
863C23—242no—
864Q8—31no—
865Q8—61no—
866Q8—61no—
867Q8—61no—
868Q8—181no—
869Q8—181no—
870Q8—361no—
871Q8—361no—
872Q8D3×#6711yescharacteristic
873D4—21no—
874D4—21no—
875D4—21no—
876D4—31no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—61no—
882D4—61no—
883D4—121no—
884D4—121no—
885D4D3×#6711yescharacteristic
886C2×C4—21no—
887C2×C4—31no—
888C2×C4—31no—
889C2×C4—31no—
890C2×C4—31no—
891C2×C4—31no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—181no—
898C2×C4—361no—
899C2×C4—361no—
900C2×C4C22×D3211yescharacteristic
901C8—21no—
902C8—31no—
903C8—31no—
904C8—61no—
905C8—61no—
906C8—61no—
907C8—91no—
908C8—91no—
909C8—181no—
910C8—181no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—32no—
915C2×C3—41no—
916C2×C3—41no—
917C2×C3—41no—
918C2×C3—61no—
919C2×C3—81no—
920C2×C3—81no—
921C2×C3—81no—
922C2×C3—121no—
923C2×C3—161no—
924C2×C3—241no—
925C2×C3D3×#12111yescharacteristic
926C2×C3C2×#93911yescharacteristic
927D3—21no—
928D3—41no—
929D3—81no—
930D3#520012yesdirect product factor
931C22—21no—
932C22—31no—
933C22—31no—
934C22—41no—
935C22—62no—
936C22—61no—
937C22—81no—
938C22—122no—
939C22—121no—
940C22—241no—
941C22—242no—
942C22—242no—
943C22D3×#23711yescharacteristic
944C4—21no—
945C4—31no—
946C4—31no—
947C4—61no—
948C4—121no—
949C4—361no—
950C4D32×D411yescharacteristic
951C4C2×D3×#6711yescharacteristic
952C3—21no—
953C3D3×#47111yescharacteristic, complemented
954C3C2×#520011yescharacteristic, complemented
955C2—21no—
956C2—32no—
957C2—41no—
958C2—61no—
959C2—81no—
960C2—121no—
961C2—241no—
962C2D3×#93911yescharacteristic
subgroupG/H
centerC2D3×#939
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×AGL(1,ℤ/8)C22
socleC2×C32C2×#121
prime radicalC3×D3×AGL(1,ℤ/8)C2
hypercenterAGL(1,ℤ/8)D32
hypocenterC32C2×#471
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
2. D3×#951C2semidirect
3. D3×#948C2semidirect
4. C2×D3×#214C2semidirect
5. #10592899C2semidirect
6. C3×#5200C2semidirect
7. #10591681C2semidirect
8. #10591679C2semidirect
9. #10591507C2semidirect
10. #10591506C2semidirect
11. D3×#833C2semidirect
12. D3×#824C2semidirect
13. #10590986C2semidirect
14. #10590980C2semidirect
15. D3×#822C2semidirect
22. #64160C22semidirect
23. #64157C22semidirect
24. C2×#3754C22semidirect
25. C3×#951C22semidirect
27. C3×#948C22semidirect
28. C2×C3×#214C22semidirect
44. #63831C22semidirect
45. C2×#3716C22semidirect
46. #63827C22semidirect
47. C2×#3715C22semidirect
49. #63815C22semidirect
51. #63814C22semidirect
57. #63660C22semidirect
58. #63651C22semidirect
59. #63649C22semidirect
60. C3×#833C22semidirect
61. C3×#824C22semidirect
62. C3×#822C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63561C22semidirect
66. #63560C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
89. #5200D3direct (N × H)
205. #951C2×D3semidirect
214. #948C2×D3semidirect
228. C2×#214C2×D3semidirect
269. #833C2×D3semidirect
276. #824C2×D3semidirect
285. #822C2×D3semidirect
728. C3×D3#471semidirect
856. C32C2×#471semidirect
930. D3#5200direct (N × H)
953. C3D3×#471semidirect
954. C3C2×#5200semidirect

Maximal subgroups

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

subgroupindex
C3×D3×AGL(1,ℤ/8)2
D3×#9512
D3×#9482
C2×D3×#2142
#105928992
C3×#52002
#105916812
#105916792
#105915072
#105915062
D3×#8332
D3×#8242
#105909862
#105909802
D3×#8222
C2×#52003
D3×#4713