Finite Group Databasebeta

← #11868104

Subgroups — #11868104

Order 1152.

984 conjugacy classes of subgroups.

The subgroup lattice has 972 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
2#10595469C211yesmaximal, characteristic, complemented
3#10595441C211yesmaximal, characteristic, complemented
4C2×#63932C211yesmaximal, characteristic, complemented
5#10592899C211yesmaximal, characteristic, complemented
6C3×#5199C211yesmaximal, characteristic, complemented
7#10591679C211yesmaximal, characteristic, complemented
8#10591678C211yesmaximal, characteristic, complemented
9#10591507C211yesmaximal, characteristic, complemented
10#10591505C211yesmaximal, characteristic, complemented
11D3×#833C211yesmaximal, characteristic, complemented
12#10591006C211yesmaximal, characteristic, complemented
13#10590986C211yesmaximal, characteristic, complemented
14#10590982C211yesmaximal, characteristic, complemented
15#10590973C211yesmaximal, characteristic, complemented
16#83943—31nomaximal
17#80938—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×AGL(1,ℤ/8)C2211yescharacteristic
22#64160C2211yescharacteristic, complemented
23#64157C2211yescharacteristic, complemented
24C2×#3754C2211yescharacteristic, complemented
25C3×#949C2211yescharacteristic
26C3×#949C2211yescharacteristic, complemented
27C3×#948C2211yescharacteristic, complemented
28C3×#932C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#914—21no—
31C3×D3×SD16—21no—
32C3×#911—21no—
33C3×D3×D8—21no—
34C3×#908C2211yescharacteristic
35C3×D3×M16C2211yescharacteristic
36#63947—21no—
37#63946—21no—
38#63933—21no—
39#63932—21no—
40#63932—21no—
41#63932—21no—
42#63932—21no—
43#63932—21no—
44#63831C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46#63823C2211yescharacteristic, complemented
47C2×#3713C2211yescharacteristic, complemented
48C2×#3711—21no—
49C2×#3711C2211yescharacteristic
50#63815—21no—
51#63815C2211yescharacteristic, complemented
52#63814—21no—
53#63814C2211yescharacteristic, complemented
54D3×#208—21no—
55D3×#208C2211yescharacteristic
56D3×#208C2211yescharacteristic
57#63660C2211yescharacteristic, complemented
58#63651C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#822C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×C3×AGL(1,ℤ/8)—31no—
70#5822—31no—
71#5819—31no—
72C2×#932—31no—
73#5773—31no—
74D3×AGL(1,ℤ/8)D311yescharacteristic, complemented
75C2×#911—31no—
76#5750—31no—
77C3×#472—31no—
78C2×#833—31no—
79#5200—31no—
80#5200—31no—
81#5200—31no—
82#5200—31no—
83#5200—31no—
84#5200—61no—
85#5199—31no—
86#5199—31no—
87#5199—31no—
88#5199—31no—
89#5199D311yescharacteristic, complemented
90#5160—31no—
91#5141—31no—
92#5132—31no—
93#5124—31no—
94#4898—31no—
95#4893—31no—
96#4749—31no—
97#4748—31no—
98#4745—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×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×#625—21no—
122C2×D3×Dic3—21no—
123#3795—21no—
124#3795—21no—
125#3795—21no—
126#3795—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×#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#3719—21no—
158#3716—21no—
159#3716—21no—
160#3716—21no—
161#3715—21no—
162#3713—21no—
163#3713—21no—
164#3713—21no—
165#3711—21no—
166#3711—21no—
167#3711—21no—
168#3711—21no—
169#3711D411yescharacteristic
170#3711D411yescharacteristic
171#3711D411yescharacteristic
172#3711D411yescharacteristic
173D3×C3⋊C8—21no—
174D3×C3⋊C8—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3068—91noSylow
178C2×C3×#41—31no—
179C22×C3×D4—31no—
180D3×#41C2×D311yescharacteristic
181C2×#237—31no—
182C2×D3×D4C2×D311yescharacteristic
183C2×#235—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
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic
193C2×C3×SD16—61no—
194C2×C3×D8—31no—
195C2×C3×D8—61no—
196C3×#131—31no—
197C2×C3×M16—31no—
198#951—31no—
199#951—31no—
200#951—31no—
201#951—61no—
202#950—61no—
203#950—61no—
204#949—31no—
205#949C2×D311yescharacteristic
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
215#942—61no—
216C2×#214—31no—
217C2×#214—31no—
218C2×#214—31no—
219C2×#214—61no—
220#932—31no—
221#932—61no—
222#932—61no—
223#932—61no—
224#932—61no—
225#932—61no—
226#932C2×D311yescharacteristic
227C2×#213—31no—
228C2×#213—31no—
229C2×#213C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C2×#208—31no—
232C2×#208—31no—
233C2×#208—61no—
234C2×#208—61no—
235#916—61no—
236#915—61no—
237#914—21no—
238D3×SD16—21no—
239#912—61no—
240#911—21no—
241#911—61no—
242#911—61no—
243#911—61no—
244#911—61no—
245#911—61no—
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×ΓL(1,𝔽25)—31no—
259C2×ΓL(1,𝔽25)—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#824—31no—
271#824—31no—
272#824—31no—
273#824—31no—
274#824—61no—
275#823—31no—
276#823—31no—
277#823—31no—
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—41no—
292C22×C3×D3—41no—
293C22×C3×D3—82no—
294C22×C3×D3#4111yescharacteristic
295C32×Q8C2×D411yescharacteristic
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4C2×D411yescharacteristic
300C2×C32×C4—21no—
301C2×C32×C4C2411yescharacteristic
302C2×C3⋊Dic3—21no—
303#634—21no—
304#634—21no—
305C3×#67—21no—
306C3×#67—21no—
307C3×#67—21no—
308C3×#67—41no—
309C3×#67—41no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3#4111yescharacteristic
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12C2×D411yescharacteristic
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3C2×D411yescharacteristic
322C3×C4×D3C2×D411yescharacteristic
323C3×C4×D3C2×D411yescharacteristic
324C3×C4×D3C2×D411yescharacteristic
325C3×Dic6—21no—
326C3×Dic6C2×D411yescharacteristic
327#625—41no—
328#625—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
341#575—91no—
342C2×AGL(1,ℤ/8)—31no—
343C2×AGL(1,ℤ/8)—91no—
344#568—91no—
345#472—31no—
346#472—91no—
347#472—91no—
348#472—91no—
349#471—91no—
350#471—91no—
351#471—91no—
352#471—91no—
353#430—91no—
354#413—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×D4—21no—
368C2×C3×D4—31no—
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—
382C2×#67—61no—
383C2×#67—61no—
384C22×Dic3—61no—
385#239#6711yescharacteristic
386D3×Q8#6711yescharacteristic
387#237—21no—
388#237—61no—
389#237—61no—
390#237—61no—
391#237—61no—
392#237#6711yescharacteristic
393D3×D4—21no—
394D3×D4—21no—
395D3×D4—21no—
396D3×D4—21no—
397D3×D4—21no—
398D3×D4#6711yescharacteristic
399#235—21no—
400#235—61no—
401#235—61no—
402#235—61no—
403#235—61no—
404#235C22×D311yescharacteristic
405C2×D12C22×D311yescharacteristic
406C2×D12C22×D311yescharacteristic
407C2×C4×D3—21no—
408C2×C4×D3—61no—
409C2×C4×D3C22×D311yescharacteristic
410C2×Dic6—31no—
411C2×Dic6—31no—
412C2×Dic6—61no—
413C3×SD16—21no—
414C3×SD16—21no—
415C3×SD16—41no—
416C3×SD16—61no—
417C3×SD16—61no—
418C3×SD16—61no—
419C3×SD16—61no—
420C3×D8—21no—
421C3×D8—21no—
422C3×D8—41no—
423C3×D8—61no—
424C3×D8—61no—
425C3×D8—61no—
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—61no—
441#216—61no—
442#216—61no—
443#216—121no—
444#215—21no—
445#215—21no—
446#215—61no—
447#214—21no—
448#214—61no—
449#214—61no—
450#214—61no—
451#214—61no—
452#214—61no—
453#214—61no—
454#214—61no—
455#214—61no—
456#214—61no—
457#214—61no—
458#214—121no—
459#214—121no—
460#214—121no—
461#213—21no—
462#213—21no—
463#213—21no—
464#213—21no—
465#213—21no—
466#213—61no—
467#213—61no—
468#213—61no—
469#213—61no—
470#213—61no—
471#213—61no—
472#208—21no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—31no—
478#208—31no—
479#208—31no—
480#208—31no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—61no—
486#208—61no—
487#208—61no—
488#208—61no—
489#208—121no—
490#208C22×D311yescharacteristic
491#208C22×D311yescharacteristic
492#208C22×D311yescharacteristic
493C2×C3⋊C8—21no—
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)—31no—
513ΓL(1,𝔽25)—31no—
514ΓL(1,𝔽25)—31no—
515ΓL(1,𝔽25)—31no—
516ΓL(1,𝔽25)—61no—
517ΓL(1,𝔽25)—61no—
518ΓL(1,𝔽25)—61no—
519ΓL(1,𝔽25)—61no—
520D3×C8—21no—
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—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—81no—
534C2×C3×D3—82no—
535C2×C3×D3—82no—
536C2×C3×D3—81no—
537C2×C3×D3—81no—
538C2×C3×D3#12111yescharacteristic
539C2×C3×D3#12111yescharacteristic
540C32×C4—21no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—41no—
544C3×Dic3—21no—
545C3×Dic3#12111yescharacteristic
546C3×Dic3#12111yescharacteristic
547C2×#41—31no—
548C2×#41—91no—
549C22×D4—31no—
550#137—91no—
551#137—91no—
552#137—181no—
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—31no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—61no—
558AGL(1,ℤ/8)—61no—
559AGL(1,ℤ/8)—91no—
560AGL(1,ℤ/8)—181no—
561AGL(1,ℤ/8)—181no—
562AGL(1,ℤ/8)—181no—
563AGL(1,ℤ/8)—181no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)D3211yescharacteristic
566#135—181no—
567#135—181no—
568C2×SD16—61no—
569C2×SD16—91no—
570C2×SD16—91no—
571C2×D8—31no—
572C2×D8—61no—
573C2×D8—91no—
574#131—31no—
575#131—91no—
576#131—91no—
577#131—91no—
578#131—181no—
579#131—181no—
580C2×M16—31no—
581C2×M16—91no—
582C2×M16—91no—
583C2×M16—91no—
584C2×M16—181no—
585C2×M16—181no—
586#108—31no—
587#108—91no—
588#108—91no—
589#108—91no—
590#101—91no—
591#101—91no—
592#100—31no—
593#100—31no—
594#100—91no—
595#100—91no—
596#100—91no—
597#100—91no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—121no—
606C23×C3—121no—
607C23×C3—242no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—82no—
614C22×D3#23711yescharacteristic
615C3×Q8—21no—
616C3×Q8—31no—
617C3×Q8—61no—
618C3×Q8D3×D411yescharacteristic
619C3×Q8C2×#6711yescharacteristic
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—31no—
628C3×D4—41no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—121no—
640C3×D4—121no—
641C3×D4D3×D411yescharacteristic
642C3×D4C2×#6711yescharacteristic
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—41no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658#67—21no—
659#67—21no—
660#67—21no—
661#67—41no—
662#67—41no—
663#67—121no—
664#67—121no—
665#67—121no—
666#67—121no—
667C2×Dic3—21no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3#23711yescharacteristic
674D12—21no—
675D12—21no—
676D12—21no—
677D12—21no—
678D12—21no—
679D12C2×#6711yescharacteristic
680C4×D3—21no—
681C4×D3—21no—
682C4×D3—21no—
683C4×D3—121no—
684C4×D3—121no—
685C4×D3D3×D411yescharacteristic
686C4×D3D3×D411yescharacteristic
687C4×D3C2×#6711yescharacteristic
688C4×D3C2×#6711yescharacteristic
689Dic6—21no—
690Dic6—61no—
691Dic6—61no—
692Dic6—61no—
693Dic6—61no—
694Dic6—121no—
695Dic6—121no—
696Dic6C2×#6711yescharacteristic
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—31no—
700C3×C8—31no—
701C3×C8—41no—
702C3×C8—61no—
703C3×C8—61no—
704C3×C8—61no—
705C3⋊C8—21no—
706C3⋊C8—21no—
707C3⋊C8—21no—
708C3⋊C8—31no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—31no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—121no—
719C3⋊C8—121no—
720C3⋊C8D3×D411yescharacteristic
721C3⋊C8D3×D411yescharacteristic
722C2×C32—21no—
723C2×C32—41no—
724C2×C32—81no—
725C2×C32C2×#12111yescharacteristic
726C3×D3—21no—
727C3×D3—21no—
728C3×D3—41no—
729C3×D3—81no—
730C3×D3—81no—
731C24—61no—
732#41—31no—
733#41—31no—
734#41—31no—
735#41—61no—
736#41—61no—
737#41—181no—
738#41—181no—
739#41—181no—
740#41—181no—
741#41C2×D3211yescharacteristic
742C2×Q8—31no—
743C2×Q8—91no—
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—31no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4—181no—
754C2×D4C2×D3211yescharacteristic
755C22×C4—31no—
756C22×C4—61no—
757C22×C4—181no—
758Q16—181no—
759Q16—181no—
760SD16—21no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772D8—21no—
773D8—61no—
774D8—61no—
775D8—61no—
776D8—61no—
777D8—61no—
778D8—61no—
779D8—181no—
780D8—181no—
781D8—181no—
782M16—31no—
783M16—31no—
784M16—31no—
785M16—61no—
786M16—61no—
787M16—91no—
788M16—91no—
789M16—91no—
790M16—91no—
791M16—91no—
792M16—91no—
793M16—181no—
794M16—181no—
795M16—181no—
796M16—181no—
797M16—181no—
798M16C2×D3211yescharacteristic
799C2×C8—31no—
800C2×C8—61no—
801C2×C8—61no—
802C2×C8—91no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C2×C8—181no—
807C2×C8—181no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—31no—
812C22×C3—31no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—61no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—161no—
824C22×C3—241no—
825C22×C3—241no—
826C22×C3—241no—
827C22×C3—242no—
828C22×C3—242no—
829C22×C3C2×#23711yescharacteristic
830C22×C3D3×#4111yescharacteristic
831C2×D3—21no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—81no—
836C2×D3—82no—
837C2×D3—82no—
838C2×D3—81no—
839C2×D3—81no—
840C2×D3#93911yescharacteristic
841C2×D3#93911yescharacteristic
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—31no—
847C3×C4—31no—
848C3×C4—41no—
849C3×C4—61no—
850C3×C4C2×D3×D411yescharacteristic
851C3×C4C2×D3×D411yescharacteristic
852C3×C4C2×D3×D411yescharacteristic
853C3×C4C22×#6711yescharacteristic
854Dic3—21no—
855Dic3—121no—
856Dic3—121no—
857Dic3—241no—
858Dic3#93911yescharacteristic
859Dic3#93911yescharacteristic
860C32#306811yescharacteristic, complemented, Sylow
861C23—21no—
862C23—31no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—121no—
867C23—121no—
868C23—242no—
869Q8—31no—
870Q8—61no—
871Q8—181no—
872Q8—181no—
873Q8D3×#6711yescharacteristic
874D4—21no—
875D4—21no—
876D4—21no—
877D4—31no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—61no—
882D4—61no—
883D4—61no—
884D4—61no—
885D4—61no—
886D4—121no—
887D4—121no—
888D4—361no—
889D4—361no—
890D4D3×#6711yescharacteristic
891C2×C4—21no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—181no—
902C2×C4—361no—
903C2×C4—361no—
904C2×C4C22×D3211yescharacteristic
905C8—21no—
906C8—31no—
907C8—31no—
908C8—61no—
909C8—61no—
910C8—61no—
911C8—91no—
912C8—91no—
913C8—181no—
914C8—181no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—41no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—61no—
922C2×C3—61no—
923C2×C3—81no—
924C2×C3—81no—
925C2×C3—81no—
926C2×C3—121no—
927C2×C3—161no—
928C2×C3—241no—
929C2×C3—241no—
930C2×C3D3×#12111yescharacteristic
931C2×C3C2×#93911yescharacteristic
932D3—21no—
933D3—21no—
934D3—41no—
935D3—81no—
936D3—81no—
937C22—21no—
938C22—31no—
939C22—31no—
940C22—41no—
941C22—61no—
942C22—81no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—241no—
947C22—241no—
948C22—241no—
949C22—242no—
950C22—242no—
951C22D3×#23711yescharacteristic
952C4—21no—
953C4—31no—
954C4—31no—
955C4—61no—
956C4—361no—
957C4D32×D411yescharacteristic
958C4C2×D3×#6711yescharacteristic
959C3—21no—
960C3#8093811yescharacteristic, complemented
961C3#8394311yescharacteristic, complemented
962C2—21no—
963C2—41no—
964C2—61no—
965C2—61no—
966C2—81no—
967C2—121no—
968C2—241no—
969C2—241no—
970C2D3×#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#3068
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. #10595469C2semidirect
3. #10595441C2semidirect
4. C2×#63932C2semidirect
5. #10592899C2semidirect
6. C3×#5199C2semidirect
7. #10591679C2semidirect
8. #10591678C2semidirect
9. #10591507C2semidirect
10. #10591505C2semidirect
11. D3×#833C2semidirect
12. #10591006C2semidirect
13. #10590986C2semidirect
14. #10590982C2semidirect
15. #10590973C2semidirect
22. #64160C22semidirect
23. #64157C22semidirect
24. C2×#3754C22semidirect
26. C3×#949C22semidirect
27. C3×#948C22semidirect
29. C2×C3×#213C22semidirect
44. #63831C22semidirect
45. C2×#3716C22semidirect
46. #63823C22semidirect
47. C2×#3713C22semidirect
51. #63815C22semidirect
53. #63814C22semidirect
57. #63660C22semidirect
58. #63651C22semidirect
59. #63649C22semidirect
60. C3×#833C22semidirect
61. C3×#823C22semidirect
62. C3×#822C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63561C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
74. D3×AGL(1,ℤ/8)D3semidirect
89. #5199D3semidirect
206. #949C2×D3semidirect
214. #948C2×D3semidirect
229. C2×#213C2×D3semidirect
269. #833C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
860. C32#3068semidirect
960. C3#80938semidirect
961. C3#83943semidirect

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
#105954692
#105954412
C2×#639322
#105928992
C3×#51992
#105916792
#105916782
#105915072
#105915052
D3×#8332
#105910062
#105909862
#105909822
#105909732
#839433
#809383