Finite Group Databasebeta

← D3×#5199 #11867926

Subgroups — D3×#5199 #11867926

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2D3×#949C211yesmaximal, characteristic, complemented
3D3×#948C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592898C211yesmaximal, characteristic, complemented
6C3×#5199C211yesmaximal, characteristic, complemented
7#10591678C211yesmaximal, characteristic, complemented
8#10591677C211yesmaximal, characteristic, complemented
9#10591508C211yesmaximal, characteristic, complemented
10#10591505C211yesmaximal, characteristic, complemented
11D3×#833C211yesmaximal, characteristic, complemented
12D3×#823C211yesmaximal, characteristic, complemented
13#10590984C211yesmaximal, characteristic, complemented
14#10590982C211yesmaximal, characteristic, complemented
15D3×#822C211yesmaximal, characteristic, complemented
16C2×#5199—31nomaximal
17D3×#472—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
22#64158C2211yescharacteristic, complemented
23#64157C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25C3×#949C2211yescharacteristic, complemented
26C3×#949C2211yescharacteristic, complemented
27C3×#948C2211yescharacteristic, complemented
28C3×#932C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#914—21no—
31C3×D3×SD16—21no—
32C3×#911—21no—
33C3×D3×D8—21no—
34C3×#908C2211yescharacteristic, complemented
35C3×D3×M16C2211yescharacteristic
36#63939—21no—
37D3×#215—21no—
38#63925—21no—
39D3×#213—21no—
40D3×#213—21no—
41D3×#213—21no—
42D3×#213—21no—
43D3×#213—21no—
44#63825C2211yescharacteristic, complemented
45C2×#3714C2211yescharacteristic, complemented
46#63823C2211yescharacteristic, complemented
47C2×#3713C2211yescharacteristic, 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#63650C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#822C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63559C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×C3×AGL(1,ℤ/8)—31no—
70C2×#949—31no—
71C2×#948—31no—
72C22×#213—31no—
73D3×AGL(1,ℤ/8)—31no—
74D3×AGL(1,ℤ/8)D311yescharacteristic, complemented
75C2×D3×D8—31no—
76D3×#131—31no—
77C3×#472—31no—
78C2×#833—31no—
79#5199—31no—
80#5199—31no—
81#5199—31no—
82#5199—31no—
83#5199—31no—
84#5199—31no—
85#5199—31no—
86#5199—31no—
87#5199—31no—
88#5199—61no—
89#5199D311yescharacteristic, direct product factor
90#5160—31no—
91#5142—31no—
92C2×#823—31no—
93C2×#822—31no—
94#4897—31no—
95D3×#108—31no—
96#4749—31no—
97#4749—31no—
98D3×#100—31no—
99D3×#100—31no—
100C23×C3×D3—21no—
101C22×D32—21no—
102C32×#41C2311yescharacteristic
103C2×C32×D4C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C3×#67—21no—
106C3×#239D411yescharacteristic
107C3×D3×Q8D411yescharacteristic
108C3×#237—21no—
109C3×#237D411yescharacteristic
110C3×D3×D4—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×D3×D4—21no—
114C3×D3×D4—21no—
115C3×D3×D4D411yescharacteristic
116C3×#235—21no—
117C3×#235C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×#626—21no—
123D3×D12—21no—
124D3×D12—21no—
125D3×D12—21no—
126D3×D12—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×#215—21no—
140C3×#215—21no—
141C3×#214—21no—
142C3×#213—21no—
143C3×#213—21no—
144C3×#213—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#3717—21no—
158#3715—21no—
159#3714—21no—
160#3714—21no—
161#3714—21no—
162#3713—21no—
163#3713—21no—
164#3713—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×#472—91noSylow
178C2×C3×#41—31no—
179C22×C3×D4—31no—
180D3×#41C2×D311yescharacteristic
181C2×D3×D4—31no—
182C2×D3×D4C2×D311yescharacteristic
183C22×D12—31no—
184C3×AGL(1,ℤ/8)—21no—
185C3×AGL(1,ℤ/8)—31no—
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, complemented
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
193C2×C3×SD16—61no—
194C2×C3×D8—31no—
195C2×C3×D8—61no—
196C3×#131—31no—
197C2×C3×M16—31no—
198#949—31no—
199#949—31no—
200#949—31no—
201#949—31no—
202#949—61no—
203#949—61no—
204#949—61no—
205#949C2×D311yescharacteristic, complemented
206#949C2×D311yescharacteristic, complemented
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×#215—61no—
216#932—31no—
217#932C2×D311yescharacteristic, complemented
218C2×#213—31no—
219C2×#213—31no—
220C2×#213—31no—
221C2×#213—31no—
222C2×#213—31no—
223C2×#213—61no—
224C2×#213—61no—
225C2×#213—61no—
226C2×#213—61no—
227C2×#213—61no—
228C2×#213—61no—
229C2×#213C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C2×#208—31no—
232C2×#208—61no—
233C22×C3⋊C8—31no—
234C22×C3⋊C8—61no—
235#914—21no—
236#914—61no—
237D3×SD16—21no—
238D3×SD16—61no—
239#911—21no—
240#911—61no—
241D3×D8—21no—
242D3×D8—61no—
243D3×D8—61no—
244D3×D8—61no—
245D3×D8—61no—
246D3×D8—61no—
247#908—31no—
248#908C2×D311yescharacteristic, complemented
249#907—31no—
250#907—61no—
251D3×M16—31no—
252D3×M16—31no—
253D3×M16—61no—
254D3×M16C2×D311yescharacteristic
255C2×D24—31no—
256#901—31no—
257#901—61no—
258C2×D3×C8—31no—
259C2×D3×C8—61no—
260C3×#108—31no—
261C3×#100—31no—
262C3×#100—31no—
263#833—31no—
264#833—31no—
265#833—31no—
266#833—31no—
267#833—31no—
268#833—61no—
269#833C2×D311yescharacteristic, complemented
270#823—31no—
271#823—31no—
272#823—31no—
273#823—31no—
274#823—31no—
275#823—31no—
276#823—31no—
277#823—61no—
278#823C2×D311yescharacteristic, complemented
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—21no—
291C22×C3×D3—21no—
292C22×C3×D3—41no—
293C22×C3×D3—41no—
294C22×C3×D3—82no—
295C22×C3×D3#4111yescharacteristic
296C2×D32—41no—
297C2×D32—41no—
298C2×D32—82no—
299C32×Q8C2×D411yescharacteristic
300C32×D4—21no—
301C32×D4—21no—
302C32×D4—21no—
303C32×D4C2×D411yescharacteristic
304C2×C32×C4—21no—
305C2×C32×C4C2411yescharacteristic
306C4⋊(C3⋊D3)—21no—
307C4⋊(C3⋊D3)—21no—
308C3×#67—21no—
309C3×#67—21no—
310C3×#67—21no—
311C3×#67—41no—
312C3×#67—41no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3#4111yescharacteristic
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—21no—
318C3×D12—21no—
319C3×D12—21no—
320C3×D12C2×D411yescharacteristic
321C3×C4×D3—21no—
322C3×C4×D3—21no—
323C3×C4×D3—21no—
324C3×C4×D3C2×D411yescharacteristic
325C3×C4×D3C2×D411yescharacteristic
326C3×C4×D3C2×D411yescharacteristic
327C3×C4×D3C2×D411yescharacteristic
328C3×Dic6—21no—
329C3×Dic6C2×D411yescharacteristic
330#626—41no—
331#626—41no—
332C32×C8—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3⋊(C3⋊C8)C2×D411yescharacteristic
336C3⋊(C3⋊C8)C2×D411yescharacteristic
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8—21no—
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342C2×AGL(1,ℤ/8)—31no—
343C2×AGL(1,ℤ/8)—91no—
344C22×D8—91no—
345C2×#131—91no—
346#472—31no—
347#472—91no—
348#472—91no—
349#472—91no—
350#472—91no—
351#472—91no—
352#472—91no—
353#472—91no—
354C2×#108—91no—
355C2×#100—91no—
356C2×#100—91no—
357C24×C3—61no—
358C23×D3—21no—
359C23×D3—61no—
360C23×D3—61no—
361C3×#41—21no—
362C3×#41—31no—
363C3×#41—31no—
364C3×#41—31no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41C22×D311yescharacteristic
368C3×#41C22×D311yescharacteristic
369C2×C3×Q8—31no—
370C2×C3×D4—21no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—31no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4—61no—
377C2×C3×D4—61no—
378C2×C3×D4—61no—
379C2×C3×D4—61no—
380C2×C3×D4C22×D311yescharacteristic
381C2×C3×D4C22×D311yescharacteristic
382C22×C3×C4—31no—
383C22×C3×C4—61no—
384C2×#67—21no—
385C2×#67—61no—
386#239#6711yescharacteristic
387D3×Q8#6711yescharacteristic
388#237—21no—
389#237#6711yescharacteristic
390D3×D4—21no—
391D3×D4—21no—
392D3×D4—21no—
393D3×D4—21no—
394D3×D4—21no—
395D3×D4—61no—
396D3×D4—61no—
397D3×D4—61no—
398D3×D4—61no—
399D3×D4#6711yescharacteristic
400#235—21no—
401#235C22×D311yescharacteristic
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12C22×D311yescharacteristic
411C2×D12C22×D311yescharacteristic
412C2×C4×D3—21no—
413C2×C4×D3C22×D311yescharacteristic
414C3×SD16—21no—
415C3×SD16—21no—
416C3×SD16—41no—
417C3×SD16—61no—
418C3×SD16—61no—
419C3×SD16—61no—
420C3×SD16—61no—
421C3×D8—21no—
422C3×D8—21no—
423C3×D8—41no—
424C3×D8—61no—
425C3×D8—61no—
426C3×D8—61no—
427C3×D8—61no—
428C3×D8—61no—
429C3×D8—61no—
430C3×M16—21no—
431C3×M16—31no—
432C3×M16—31no—
433C3×M16—31no—
434C3×M16—61no—
435C3×M16—61no—
436C3×M16C22×D311yescharacteristic
437C3×M16C22×D311yescharacteristic
438C2×C3×C8—31no—
439C2×C3×C8—61no—
440C2×C3×C8—61no—
441#215—21no—
442#215—21no—
443#215—61no—
444#215—61no—
445#215—61no—
446#215—61no—
447#215—121no—
448#214—21no—
449#214—61no—
450#213—21no—
451#213—21no—
452#213—21no—
453#213—21no—
454#213—21no—
455#213—61no—
456#213—61no—
457#213—61no—
458#213—61no—
459#213—61no—
460#213—61no—
461#213—61no—
462#213—61no—
463#213—61no—
464#213—61no—
465#213—61no—
466#213—61no—
467#213—61no—
468#213—61no—
469#213—61no—
470#213—121no—
471#213—121no—
472#213—121no—
473#208—21no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—31no—
478#208—61no—
479#208—61no—
480#208—61no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—61no—
486#208—121no—
487#208C22×D311yescharacteristic
488#208C22×D311yescharacteristic
489#208C22×D311yescharacteristic
490C2×C3⋊C8—21no—
491C2×C3⋊C8—31no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
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—61no—
504C2×C3⋊C8—121no—
505C2×C3⋊C8C22×D311yescharacteristic
506D24—21no—
507D24—61no—
508D24—61no—
509D24—61no—
510#204—21no—
511#204—61no—
512ΓL(1,𝔽25)—21no—
513ΓL(1,𝔽25)—61no—
514ΓL(1,𝔽25)—61no—
515ΓL(1,𝔽25)—61no—
516ΓL(1,𝔽25)—61no—
517D3×C8—21no—
518D3×C8—31no—
519D3×C8—31no—
520D3×C8—31no—
521D3×C8—31no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525D3×C8—61no—
526C22×C32—21no—
527C22×C32—41no—
528C22×C32—81no—
529C22×C32C2×#4111yescharacteristic
530C2×C3⋊D3—41no—
531C2×C3⋊D3—81no—
532C2×C3×D3—22no—
533C2×C3×D3—21no—
534C2×C3×D3—42no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—82no—
538C2×C3×D3—82no—
539C2×C3×D3—81no—
540C2×C3×D3—81no—
541C2×C3×D3#12111yescharacteristic
542C2×C3×D3#12111yescharacteristic
543D32—82no—
544D32—82no—
545C32×C4—21no—
546C32×C4C22×D411yescharacteristic
547C32×C4C22×D411yescharacteristic
548C3×Dic3—21no—
549C3×Dic3#12111yescharacteristic
550C3×Dic3#12111yescharacteristic
551C2×#41—31no—
552C22×D4—31no—
553C22×D4—91no—
554AGL(1,ℤ/8)—31no—
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)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—181no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)D3211yescharacteristic, complemented
566C2×SD16—61no—
567C2×SD16—181no—
568C2×D8—31no—
569C2×D8—61no—
570C2×D8—91no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—181no—
574C2×D8—181no—
575C2×D8—181no—
576C2×D8—181no—
577C2×D8—181no—
578#131—31no—
579#131—91no—
580#131—91no—
581#131—91no—
582#131—181no—
583#131—181no—
584C2×M16—31no—
585C2×M16—91no—
586C2×M16—91no—
587C2×M16—181no—
588C22×C8—91no—
589C22×C8—181no—
590#108—31no—
591#108—91no—
592#108—91no—
593#108—91no—
594#100—31no—
595#100—31no—
596#100—91no—
597#100—91no—
598#100—91no—
599#100—91no—
600#100—91no—
601#100—91no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—31no—
605C23×C3—41no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—121no—
610C23×C3—121no—
611C23×C3—242no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—82no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—242no—
626C22×D3—242no—
627C22×D3#23711yescharacteristic
628C3×Q8—21no—
629C3×Q8—31no—
630C3×Q8—61no—
631C3×Q8D3×D411yescharacteristic
632C3×Q8C2×#6711yescharacteristic
633C3×D4—21no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—31no—
641C3×D4—41no—
642C3×D4—41no—
643C3×D4—41no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4—61no—
648C3×D4—61no—
649C3×D4—61no—
650C3×D4—61no—
651C3×D4—61no—
652C3×D4—121no—
653C3×D4—121no—
654C3×D4D3×D411yescharacteristic
655C3×D4C2×#6711yescharacteristic
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—41no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671#67—21no—
672#67—21no—
673#67—21no—
674#67—41no—
675#67—41no—
676#67—121no—
677#67—121no—
678C2×Dic3—21no—
679C2×Dic3#23711yescharacteristic
680D12—21no—
681D12—21no—
682D12—21no—
683D12—21no—
684D12—21no—
685D12—61no—
686D12—61no—
687D12—61no—
688D12—61no—
689D12—121no—
690D12—121no—
691D12—121no—
692D12—121no—
693D12C2×#6711yescharacteristic
694C4×D3—21no—
695C4×D3—21no—
696C4×D3—21no—
697C4×D3D3×D411yescharacteristic
698C4×D3D3×D411yescharacteristic
699C4×D3C2×#6711yescharacteristic
700C4×D3C2×#6711yescharacteristic
701Dic6—21no—
702Dic6C2×#6711yescharacteristic
703C3×C8—21no—
704C3×C8—21no—
705C3×C8—31no—
706C3×C8—31no—
707C3×C8—41no—
708C3×C8—61no—
709C3×C8—61no—
710C3×C8—61no—
711C3⋊C8—21no—
712C3⋊C8—21no—
713C3⋊C8—21no—
714C3⋊C8—31no—
715C3⋊C8—31no—
716C3⋊C8—31no—
717C3⋊C8—31no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—121no—
725C3⋊C8—121no—
726C3⋊C8D3×D411yescharacteristic
727C3⋊C8D3×D411yescharacteristic
728C2×C32—21no—
729C2×C32—41no—
730C2×C32—81no—
731C2×C32C2×#12111yescharacteristic
732C3⋊D3—81no—
733C3×D3—21no—
734C3×D3—41no—
735C3×D3—81no—
736C3×D3—81no—
737C3×D3#47212yescomplemented
738C24—61no—
739C24—181no—
740#41—31no—
741#41—31no—
742#41—31no—
743#41—61no—
744#41—61no—
745#41C2×D3211yescharacteristic
746C2×Q8—31no—
747C2×D4—31no—
748C2×D4—31no—
749C2×D4—31no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—91no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—181no—
761C2×D4—181no—
762C2×D4C2×D3211yescharacteristic
763C22×C4—31no—
764C22×C4—61no—
765SD16—21no—
766SD16—61no—
767SD16—61no—
768SD16—61no—
769SD16—61no—
770SD16—181no—
771SD16—181no—
772SD16—181no—
773D8—21no—
774D8—61no—
775D8—61no—
776D8—61no—
777D8—61no—
778D8—61no—
779D8—61no—
780D8—181no—
781D8—181no—
782D8—181no—
783D8—181no—
784D8—181no—
785D8—181no—
786D8—181no—
787D8—181no—
788D8—181no—
789M16—31no—
790M16—31no—
791M16—31no—
792M16—61no—
793M16—61no—
794M16—91no—
795M16—91no—
796M16—181no—
797M16—181no—
798M16—181no—
799M16—181no—
800M16—181no—
801M16C2×D3211yescharacteristic
802C2×C8—31no—
803C2×C8—61no—
804C2×C8—61no—
805C2×C8—91no—
806C2×C8—91no—
807C2×C8—91no—
808C2×C8—91no—
809C2×C8—91no—
810C2×C8—181no—
811C2×C8—181no—
812C2×C8—181no—
813C2×C8—181no—
814C2×C8—181no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—31no—
819C22×C3—31no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—62no—
824C22×C3—61no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—122no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—161no—
832C22×C3—241no—
833C22×C3—241no—
834C22×C3—242no—
835C22×C3—242no—
836C22×C3C2×#23711yescharacteristic
837C22×C3D3×#4111yescharacteristic
838C2×D3—22no—
839C2×D3—21no—
840C2×D3—42no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—82no—
844C2×D3—82no—
845C2×D3—81no—
846C2×D3—81no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—241no—
850C2×D3—242no—
851C2×D3—242no—
852C2×D3—242no—
853C2×D3—242no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—481no—
857C2×D3#93911yescharacteristic
858C2×D3#93911yescharacteristic
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—31no—
864C3×C4—31no—
865C3×C4—41no—
866C3×C4—61no—
867C3×C4C2×D3×D411yescharacteristic
868C3×C4C2×D3×D411yescharacteristic
869C3×C4C2×D3×D411yescharacteristic
870C3×C4C22×#6711yescharacteristic
871Dic3—21no—
872Dic3#93911yescharacteristic
873Dic3#93911yescharacteristic
874C32C2×#47211yescharacteristic, complemented, Sylow
875C23—21no—
876C23—31no—
877C23—61no—
878C23—61no—
879C23—61no—
880C23—121no—
881C23—121no—
882C23—181no—
883C23—242no—
884C23—361no—
885C23—361no—
886C23—722no—
887Q8—31no—
888Q8—61no—
889Q8D3×#6711yescharacteristic
890D4—21no—
891D4—21no—
892D4—21no—
893D4—31no—
894D4—61no—
895D4—61no—
896D4—61no—
897D4—61no—
898D4—61no—
899D4—61no—
900D4—61no—
901D4—61no—
902D4—121no—
903D4—121no—
904D4—181no—
905D4—181no—
906D4—361no—
907D4—361no—
908D4D3×#6711yescharacteristic
909C2×C4—21no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—31no—
914C2×C4—31no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4C22×D3211yescharacteristic
920C8—21no—
921C8—31no—
922C8—31no—
923C8—61no—
924C8—61no—
925C8—61no—
926C8—91no—
927C8—91no—
928C8—181no—
929C8—181no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—32no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—41no—
937C2×C3—61no—
938C2×C3—81no—
939C2×C3—81no—
940C2×C3—81no—
941C2×C3—121no—
942C2×C3—161no—
943C2×C3—241no—
944C2×C3—241no—
945C2×C3D3×#12111yescharacteristic
946C2×C3C2×#93911yescharacteristic
947D3—21no—
948D3—41no—
949D3—81no—
950D3—81no—
951D3—241no—
952D3—241no—
953D3—481no—
954D3#519912yesdirect product factor
955C22—21no—
956C22—31no—
957C22—31no—
958C22—41no—
959C22—62no—
960C22—61no—
961C22—81no—
962C22—122no—
963C22—121no—
964C22—121no—
965C22—241no—
966C22—241no—
967C22—242no—
968C22—242no—
969C22—361no—
970C22—721no—
971C22—722no—
972C22—722no—
973C22D3×#23711yescharacteristic
974C4—21no—
975C4—31no—
976C4—31no—
977C4—61no—
978C4D32×D411yescharacteristic
979C4C2×D3×#6711yescharacteristic
980C3—21no—
981C3D3×#47211yescharacteristic, complemented
982C3C2×#519911yescharacteristic, complemented
983C2—21no—
984C2—32no—
985C2—41no—
986C2—61no—
987C2—81no—
988C2—121no—
989C2—241no—
990C2—241no—
991C2—721no—
992C2D3×#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
hypocenterC32C2×#472
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×D3×AGL(1,ℤ/8)C2semidirect
2. D3×#949C2semidirect
3. D3×#948C2semidirect
4. C2×D3×#213C2semidirect
5. #10592898C2semidirect
6. C3×#5199C2semidirect
7. #10591678C2semidirect
8. #10591677C2semidirect
9. #10591508C2semidirect
10. #10591505C2semidirect
11. D3×#833C2semidirect
12. D3×#823C2semidirect
13. #10590984C2semidirect
14. #10590982C2semidirect
15. D3×#822C2semidirect
21. C32×AGL(1,ℤ/8)C22semidirect
22. #64158C22semidirect
23. #64157C22semidirect
24. C2×#3753C22semidirect
25. C3×#949C22semidirect
26. C3×#949C22semidirect
27. C3×#948C22semidirect
28. C3×#932C22semidirect
29. C2×C3×#213C22semidirect
34. C3×#908C22semidirect
44. #63825C22semidirect
45. C2×#3714C22semidirect
46. #63823C22semidirect
47. C2×#3713C22semidirect
49. #63815C22semidirect
51. #63814C22semidirect
57. #63660C22semidirect
58. #63650C22semidirect
59. #63649C22semidirect
60. C3×#833C22semidirect
61. C3×#823C22semidirect
62. C3×#822C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63559C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
74. D3×AGL(1,ℤ/8)D3semidirect
89. #5199D3direct (N × H)
191. C3×AGL(1,ℤ/8)C2×D3semidirect
192. C3×AGL(1,ℤ/8)C2×D3semidirect
205. #949C2×D3semidirect
206. #949C2×D3semidirect
214. #948C2×D3semidirect
217. #932C2×D3semidirect
229. C2×#213C2×D3semidirect
248. #908C2×D3semidirect
269. #833C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
565. AGL(1,ℤ/8)D32semidirect
737. C3×D3#472semidirect
874. C32C2×#472semidirect
954. D3#5199direct (N × H)
981. C3D3×#472semidirect
982. C3C2×#5199semidirect

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×#9492
D3×#9482
C2×D3×#2132
#105928982
C3×#51992
#105916782
#105916772
#105915082
#105915052
D3×#8332
D3×#8232
#105909842
#105909822
D3×#8222
C2×#51993
D3×#4723