Finite Group Databasebeta

← D3×#5836 #11918864

Subgroups — D3×#5836 #11918864

Order 1152.

3049 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2D3×#1010C211yesmaximal, characteristic, complemented
3#10596307C211yesmaximal, characteristic, complemented
4C3×#5836C211yesmaximal, characteristic, complemented
5#10595466C213yesmaximal, complemented
6#10595464C213yesmaximal, complemented
7D3×#951C213yesmaximal, complemented
8D3×#950C213yesmaximal, complemented
9#10595447C211yesmaximal, characteristic, complemented
10#10595446C211yesmaximal, characteristic, complemented
11D3×#948C211yesmaximal, characteristic, complemented
12#10595106C213yesmaximal, complemented
13#10595105C213yesmaximal, complemented
14C2×D3×#214C213yesmaximal, complemented
15D3×#932C213yesmaximal, complemented
16C2×#5836—31nomaximal
17D3×#577—31nomaximal
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19#64367C2211yescharacteristic, complemented
20C3×#1010C2211yescharacteristic, complemented
21C3×#1009—21no—
22C3×#1009C2213yescomplemented
23C3×#1009C2211yescharacteristic, complemented
24C3×D3×#41—21no—
25C3×D3×#41C2213yes—
26C3×D3×#41C2211yescharacteristic
27C3×#1004—23no—
28C3×#1004C2213yescomplemented
29C2×C3×D3×D4—23no—
30C2×C3×D3×D4C2213yes—
31D32×Q8—21no—
32#64315—21no—
33D3×#237—23no—
34#64309—23no—
35D3×#235C2213yescomplemented
36#64298C2213yescomplemented
37#64297C2213yescomplemented
38C2×D3×Dic6C2213yescomplemented
39#64160C2213yescomplemented
40#64159C2213yescomplemented
41#64157C2211yescharacteristic, complemented
42C2×#3754C2213yescomplemented
43#64141C2213yescomplemented
44C3×#951C2213yescomplemented
45C3×#950C2213yescomplemented
46C3×#948C2211yescharacteristic, complemented
47C2×C3×#214C2213yescomplemented
48C3×#932C2213yescomplemented
49#63949C2213yescomplemented
50#63947C2213yescomplemented
51#63943C2216yescomplemented
52D3×#216C2213yescomplemented
53D3×#215C2211yescharacteristic, complemented
54#63935C2213yescomplemented
55#63934C2216yescomplemented
56#63933C2213yescomplemented
57#63932C2216yescomplemented
58#63929C2216yescomplemented
59D3×#214C2216yescomplemented
60D3×#214C2213yescomplemented
61D3×#214C2216yescomplemented
62D3×#214C2216yescomplemented
63D3×#213C2213yescomplemented
64#63831C2213yescomplemented
65#63830C2213yescomplemented
66#63829C2213yescomplemented
67C2×#3716C2213yescomplemented
68#63827C2213yescomplemented
69C2×#3715C2213yescomplemented
70#63823C2213yescomplemented
71#63822C2213yescomplemented
72#63815C2213yescomplemented
73#63814C2213yescomplemented
74D3×#208C2213yescomplemented
75C2×D3×C3⋊C8C2213yescomplemented
76C2×C3×H(5,𝔽2)—31no—
77D3×2−1+4—31no—
78D3×H(5,𝔽2)D311yescharacteristic, complemented
79C2×#1010—31no—
80C3×#577—31no—
81#5837—31no—
82#5836—31no—
83#5836—31no—
84#5836—31no—
85#5836—33no—
86#5836—33no—
87#5836—31no—
88#5836—33no—
89#5836—33no—
90#5836—61no—
91#5836D311yescharacteristic, direct product factor
92C2×#951—33no—
93C2×#950—33no—
94C2×#948—31no—
95C22×#214—33no—
96C2×#932—33no—
97#5778—33no—
98D3×#137—33no—
99#5775—33no—
100D3×AGL(1,ℤ/8)—33no—
101#5770—33no—
102D3×#135—33no—
103#5762—33no—
104C2×D3×SD16—33no—
105#5751—31no—
106D3×#131—31no—
107C23×C3×D3—23no—
108C32×#41—21no—
109C32×#41C2313yes—
110C32×#41C2311yescharacteristic
111C2×C32×D4—23no—
112C2×C32×D4C2313yes—
113Q8×C3⋊D3—21no—
114#3830—23no—
115#3828C2313yescomplemented
116C2×#634C2313yescomplemented
117C2×C3×#67—26no—
118C2×C3×#67—23no—
119C3×#239—21no—
120C3×#239D411yescharacteristic
121C3×#239C2313yes—
122C3×D3×Q8—21no—
123C3×D3×Q8D411yescharacteristic
124C3×D3×Q8C2311yescharacteristic
125C3×#237—23no—
126C3×#237—23no—
127C3×#237—23no—
128C3×#237D413yes—
129C3×#237C2313yes—
130C3×D3×D4—23no—
131C3×D3×D4—23no—
132C3×D3×D4—26no—
133C3×D3×D4—23no—
134C3×D3×D4—23no—
135C3×D3×D4—23no—
136C3×D3×D4D413yes—
137C3×D3×D4C2313yes—
138C3×D3×D4C2316yes—
139C3×#235—23no—
140C3×#235—23no—
141C3×#235C2313yes—
142C3×#235C2313yes—
143C3×#235C2313yescomplemented
144C2×C3×D12—23no—
145C2×C3×D12C2313yes—
146C2×C3×C4×D3—23no—
147C2×C3×C4×D3C2313yes—
148C2×C3×Dic6C2313yescomplemented
149D3×#67—23no—
150C2×#627—23no—
151#3805—26no—
152#3804—26no—
153#3804—23no—
154C2×D3×Dic3—23no—
155D3×D12C2311yescharacteristic
156C4×D32—23no—
157#3799C2313yescomplemented
158#3798—23no—
159#3797—23no—
160#3796—23no—
161#3795—23no—
162#3795C2313yescomplemented
163D3×Dic6—23no—
164D3×Dic6—23no—
165D3×Dic6—23no—
166D3×Dic6C2313yes—
167D3×Dic6C2316yescomplemented
168#3756C2313yescomplemented
169#3755C2311yescharacteristic, complemented
170#3754C2316yescomplemented
171#3754C2313yescomplemented
172#3753C2313yescomplemented
173#3748C2313yescomplemented
174C2×C3⋊(C3⋊C8)C2313yescomplemented
175C3×#216C2313yescomplemented
176C3×#215C2311yescharacteristic, complemented
177C3×#214C2316yescomplemented
178C3×#214C2313yescomplemented
179C3×#213C2313yescomplemented
180C3×#208C2313yescomplemented
181C2×C3×C3⋊C8C2313yescomplemented
182#3719C2313yescomplemented
183#3718C2313yescomplemented
184#3717C2311yescharacteristic, complemented
185#3716C2313yescomplemented
186#3716C2316yescomplemented
187#3715C2311yescharacteristic, complemented
188#3715C2313yescomplemented
189#3715C2316yescomplemented
190#3714C2313yescomplemented
191#3713C2313yescomplemented
192#3711C2316yescomplemented
193D3×C3⋊C8C2311yescharacteristic
194D3×C3⋊C8C2313yes—
195D3×C3⋊C8C2313yescomplemented
196D3×C3⋊C8C2313yescomplemented
197C2×#577—91noSylow
198C3×2−1+4—31no—
199C3×H(5,𝔽2)—21no—
200C3×H(5,𝔽2)—33no—
201C3×H(5,𝔽2)—31no—
202C3×H(5,𝔽2)—33no—
203C3×H(5,𝔽2)—63no—
204C3×H(5,𝔽2)—61no—
205C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
206C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
207C2×C3×#41—31no—
208C2×C3×#41—33no—
209C2×C3×#41—61no—
210C22×C3×D4—33no—
211C22×C3×D4—63no—
212#1010—31no—
213#1010—31no—
214#1010—33no—
215#1010—33no—
216#1010—33no—
217#1010—61no—
218#1010—63no—
219#1010—61no—
220#1010—63no—
221#1010C2×D311yescharacteristic, complemented
222#1009—21no—
223#1009C2×D313yescomplemented
224#1009C2×D311yescharacteristic, complemented
225D3×#41—21no—
226D3×#41—33no—
227D3×#41—63no—
228D3×#41C2×D313yes—
229D3×#41C2×D311yescharacteristic
230#1007—33no—
231#1007—61no—
232C2×D3×Q8—33no—
233C2×D3×Q8—61no—
234C2×D3×Q8—61no—
235#1004—23no—
236#1004C2×D313yescomplemented
237C2×#237—63no—
238C2×D3×D4—23no—
239C2×D3×D4C2×D313yes—
240C2×#235—33no—
241C22×Dic6—33no—
242C3×#137—33no—
243C3×AGL(1,ℤ/8)—33no—
244C3×#135—33no—
245C2×C3×SD16—33no—
246C3×#131—31no—
247#951—33no—
248#951—33no—
249#951—33no—
250#951—36no—
251#951—36no—
252#951—33no—
253#951—63no—
254#951C2×D313yescomplemented
255#950—33no—
256#950—33no—
257#950—33no—
258#950—33no—
259#950—33no—
260#950—33no—
261#950—33no—
262#950—33no—
263#950—33no—
264#950—63no—
265#950C2×D313yescomplemented
266#949—33no—
267#948—31no—
268#948—31no—
269#948—33no—
270#948—33no—
271#948—61no—
272#948C2×D311yescharacteristic, complemented
273C2×#216—33no—
274#942—33no—
275C2×#215—33no—
276C2×#215—31no—
277C2×#214—33no—
278C2×#214—33no—
279C2×#214—33no—
280C2×#214—36no—
281C2×#214—33no—
282C2×#214—36no—
283C2×#214—36no—
284C2×#214—33no—
285C2×#214—63no—
286C2×#214C2×D313yescomplemented
287#932—33no—
288#932—33no—
289#932—33no—
290#932—36no—
291#932—36no—
292#932—33no—
293#932—63no—
294#932C2×D313yescomplemented
295C2×#213—33no—
296C2×#208—33no—
297C22×C3⋊C8—33no—
298#919—33no—
299#918—36no—
300D3×Q16—33no—
301#916—33no—
302#916—33no—
303#915—36no—
304#914—36no—
305D3×SD16—31no—
306D3×SD16—33no—
307D3×SD16—36no—
308D3×SD16—36no—
309D3×SD16—36no—
310#912—33no—
311#911—36no—
312D3×D8—33no—
313#909—33no—
314#908—33no—
315#907—33no—
316D3×M16—33no—
317#904—33no—
318C2×#204—33no—
319#901—33no—
320C2×D3×C8—33no—
321C23×C32—23no—
322C22×C3×D3—23no—
323C22×C3×D3—23no—
324C22×C3×D3—26no—
325C22×C3×D3—86no—
326C22×C3×D3C2×D413yes—
327C2×D32—21no—
328C32×Q8C2×D411yescharacteristic
329C32×Q8C2411yescharacteristic
330C32×D4—23no—
331C32×D4—23no—
332C32×D4C2×D413yes—
333C32×D4C2413yes—
334C2×C32×C4—23no—
335C2×C32×C4C2413yes—
336#638—23no—
337C2×C3⋊Dic3—23no—
338C4⋊(C3⋊D3)C2411yescharacteristic
339C4×C3⋊D3—23no—
340#634—23no—
341#634C2413yes—
342C3×#67—23no—
343C3×#67—23no—
344C3×#67—23no—
345C3×#67—26no—
346C3×#67—23no—
347C3×#67C2×D416yes—
348C2×C3×Dic3—23no—
349C2×C3×Dic3—23no—
350C2×C3×Dic3C2×D413yes—
351C3×D12—23no—
352C3×D12—23no—
353C3×D12C2×D413yes—
354C3×D12C2411yescharacteristic
355C3×D12C2413yes—
356C3×C4×D3—21no—
357C3×C4×D3—23no—
358C3×C4×D3—23no—
359C3×C4×D3—23no—
360C3×C4×D3C2×D413yes—
361C3×C4×D3C2×D413yes—
362C3×C4×D3C2411yescharacteristic
363C3×C4×D3C2413yes—
364C3×Dic6—23no—
365C3×Dic6—21no—
366C3×Dic6C2×D413yes—
367C3×Dic6C2413yes—
368C3×Dic6C2411yescharacteristic
369#627—23no—
370#627—26no—
371#626—23no—
372#626—21no—
373#625—23no—
374#624—23no—
375D3×Dic3—23no—
376D3×Dic3—26no—
377D3×Dic3—23no—
378C3⋊(C3⋊C8)C2411yescharacteristic
379C3⋊(C3⋊C8)C2413yes—
380C3×C3⋊C8C2411yescharacteristic
381C3×C3⋊C8C2413yes—
382C2×2−1+4—91no—
383C2×H(5,𝔽2)—31no—
384#577—31no—
385#577—91no—
386#577—93no—
387#577—93no—
388#577—93no—
389#577—93no—
390#577—91no—
391#577—91no—
392C2×#137—93no—
393C2×AGL(1,ℤ/8)—93no—
394C2×#135—93no—
395C22×SD16—93no—
396C2×#131—91no—
397C24×C3—63no—
398C23×D3—23no—
399C3×#41—21no—
400C3×#41—21no—
401C3×#41—23no—
402C3×#41—21no—
403C3×#41—31no—
404C3×#41—33no—
405C3×#41—33no—
406C3×#41—33no—
407C3×#41—33no—
408C3×#41—33no—
409C3×#41—33no—
410C3×#41—41no—
411C3×#41—63no—
412C3×#41—63no—
413C3×#41—63no—
414C3×#41—63no—
415C3×#41—61no—
416C3×#41—63no—
417C3×#41C22×D313yes—
418C3×#41C22×D313yes—
419C3×#41C22×D311yescharacteristic
420C3×#41C22×D311yescharacteristic
421C2×C3×Q8—31no—
422C2×C3×Q8—31no—
423C2×C3×Q8—33no—
424C2×C3×Q8—61no—
425C2×C3×D4—23no—
426C2×C3×D4—23no—
427C2×C3×D4—23no—
428C2×C3×D4—33no—
429C2×C3×D4—33no—
430C2×C3×D4—36no—
431C2×C3×D4—33no—
432C2×C3×D4—43no—
433C2×C3×D4—63no—
434C2×C3×D4—63no—
435C2×C3×D4—63no—
436C2×C3×D4—63no—
437C2×C3×D4—66no—
438C2×C3×D4—63no—
439C2×C3×D4—63no—
440C2×C3×D4—66no—
441C2×C3×D4—63no—
442C2×C3×D4C22×D313yes—
443C2×C3×D4C22×D313yes—
444C22×C3×C4—33no—
445C22×C3×C4—63no—
446C2×#67—26no—
447C2×#67—23no—
448C2×#67—63no—
449C22×Dic3—63no—
450#239—21no—
451#239—33no—
452#239—63no—
453#239#6711yescharacteristic
454#239C22×D313yes—
455D3×Q8—21no—
456D3×Q8—33no—
457D3×Q8—36no—
458D3×Q8—63no—
459D3×Q8—63no—
460D3×Q8—61no—
461D3×Q8—61no—
462D3×Q8—63no—
463D3×Q8—63no—
464D3×Q8—63no—
465D3×Q8—121no—
466D3×Q8#6711yescharacteristic
467D3×Q8C22×D311yescharacteristic
468#237—23no—
469#237—23no—
470#237—23no—
471#237—33no—
472#237—63no—
473#237—63no—
474#237—66no—
475#237—66no—
476#237—63no—
477#237—63no—
478#237—66no—
479#237—63no—
480#237—123no—
481#237#6713yes—
482#237C22×D313yes—
483D3×D4—23no—
484D3×D4—23no—
485D3×D4—26no—
486D3×D4—23no—
487D3×D4—23no—
488D3×D4—23no—
489D3×D4—31no—
490D3×D4—63no—
491D3×D4#6713yes—
492D3×D4C22×D313yes—
493D3×D4C22×D316yes—
494#235—23no—
495#235—23no—
496#235—33no—
497#235—33no—
498#235—33no—
499#235—33no—
500#235—63no—
501#235—63no—
502#235—63no—
503#235—66no—
504#235—63no—
505#235—63no—
506#235C22×D313yes—
507#235C22×D313yes—
508#235C22×D313yescomplemented
509C2×D12—23no—
510C2×D12—31no—
511C2×D12C22×D313yes—
512C2×C4×D3—23no—
513C2×C4×D3—63no—
514C2×C4×D3—63no—
515C2×C4×D3—63no—
516C2×C4×D3C22×D313yes—
517C2×Dic6—33no—
518C2×Dic6—33no—
519C2×Dic6—33no—
520C2×Dic6—36no—
521C2×Dic6—63no—
522C2×Dic6—63no—
523C2×Dic6—63no—
524C2×Dic6—63no—
525C2×Dic6—63no—
526C2×Dic6—63no—
527C2×Dic6C22×D313yescomplemented
528C3×Q16—33no—
529C3×SD16—31no—
530C3×SD16—33no—
531C3×SD16—36no—
532C3×D8—33no—
533C3×M16—33no—
534C2×C3×C8—33no—
535#216—33no—
536#216—33no—
537#216—33no—
538#216—33no—
539#216—33no—
540#216—63no—
541#216C22×D313yescomplemented
542#215—31no—
543#215—31no—
544#215—33no—
545#215—36no—
546#215—31no—
547#215—31no—
548#215—61no—
549#215C22×D311yescharacteristic, complemented
550#214—36no—
551#214—33no—
552#214—36no—
553#214—33no—
554#214—31no—
555#214—36no—
556#214—33no—
557#214—36no—
558#214—33no—
559#214—66no—
560#214—63no—
561#214C22×D316yescomplemented
562#214C22×D313yescomplemented
563#213—33no—
564#213—33no—
565#213—33no—
566#213—33no—
567#213—33no—
568#213—63no—
569#213C22×D313yescomplemented
570#208—33no—
571#208—33no—
572#208—36no—
573#208—63no—
574#208C22×D313yescomplemented
575C2×C3⋊C8—33no—
576C2×C3⋊C8—33no—
577C2×C3⋊C8—31no—
578C2×C3⋊C8—33no—
579C2×C3⋊C8—33no—
580C2×C3⋊C8—33no—
581C2×C3⋊C8—63no—
582C2×C3⋊C8C22×D313yescomplemented
583Dic12—33no—
584D24—33no—
585#204—33no—
586#204—36no—
587#204—31no—
588ΓL(1,𝔽25)—36no—
589D3×C8—31no—
590D3×C8—33no—
591D3×C8—33no—
592D3×C8—33no—
593C22×C32—23no—
594C22×C32—83no—
595C22×C32C22×D413yes—
596C2×C3⋊D3—21no—
597C2×C3×D3—26no—
598C2×C3×D3—21no—
599C2×C3×D3—23no—
600C2×C3×D3—46no—
601C2×C3×D3—86no—
602C2×C3×D3—83no—
603C2×C3×D3C22×D413yes—
604C2×C3×D3C22×D411yescharacteristic
605D32—42no—
606C32×C4—21no—
607C32×C4C22×D413yes—
608C32×C4C2511yescharacteristic
609C3⋊Dic3—23no—
610C3×Dic3—23no—
611C3×Dic3—21no—
612C3×Dic3C22×D413yes—
613C3×Dic3C22×D411yescharacteristic
6142−1+4—31no—
6152−1+4—93no—
6162−1+4—93no—
6172−1+4—91no—
6182−1+4—181no—
6192−1+4—183no—
620H(5,𝔽2)—33no—
621H(5,𝔽2)—31no—
622H(5,𝔽2)—33no—
623H(5,𝔽2)—63no—
624H(5,𝔽2)—61no—
625H(5,𝔽2)D3211yescharacteristic, complemented
626C2×#41—31no—
627C2×#41—33no—
628C2×#41—61no—
629C2×#41—93no—
630C2×#41—183no—
631C22×Q8—93no—
632C22×Q8—181no—
633C22×D4—33no—
634C22×D4—63no—
635#137—33no—
636#137—93no—
637#137—96no—
638#137—96no—
639#137—93no—
640#137—93no—
641AGL(1,ℤ/8)—33no—
642AGL(1,ℤ/8)—93no—
643AGL(1,ℤ/8)—96no—
644AGL(1,ℤ/8)—96no—
645AGL(1,ℤ/8)—93no—
646AGL(1,ℤ/8)—93no—
647#135—33no—
648#135—93no—
649#135—93no—
650#135—93no—
651#135—93no—
652#135—93no—
653#135—93no—
654#135—93no—
655C2×Q16—93no—
656C2×SD16—33no—
657C2×SD16—93no—
658C2×SD16—93no—
659C2×SD16—96no—
660C2×SD16—96no—
661C2×SD16—96no—
662C2×SD16—91no—
663C2×SD16—93no—
664C2×SD16—93no—
665C2×D8—93no—
666#131—31no—
667#131—93no—
668#131—93no—
669#131—91no—
670C2×M16—93no—
671C22×C8—93no—
672C23×C3—23no—
673C23×C3—23no—
674C23×C3—33no—
675C23×C3—43no—
676C23×C3—63no—
677C23×C3—66no—
678C23×C3—63no—
679C23×C3—246no—
680C22×D3—23no—
681C22×D3—23no—
682C22×D3—26no—
683C22×D3—61no—
684C22×D3—61no—
685C22×D3—86no—
686C22×D3C2×#6713yes—
687C3×Q8—21no—
688C3×Q8—21no—
689C3×Q8—33no—
690C3×Q8—33no—
691C3×Q8—31no—
692C3×Q8—61no—
693C3×Q8—63no—
694C3×Q8D3×D411yescharacteristic
695C3×Q8C2×#6711yescharacteristic
696C3×Q8C23×D311yescharacteristic
697C3×Q8C23×D311yescharacteristic
698C3×D4—23no—
699C3×D4—23no—
700C3×D4—23no—
701C3×D4—23no—
702C3×D4—23no—
703C3×D4—23no—
704C3×D4—36no—
705C3×D4—33no—
706C3×D4—31no—
707C3×D4—33no—
708C3×D4—43no—
709C3×D4—43no—
710C3×D4—63no—
711C3×D4—63no—
712C3×D4—66no—
713C3×D4—63no—
714C3×D4—63no—
715C3×D4—63no—
716C3×D4—63no—
717C3×D4D3×D413yes—
718C3×D4C2×#6713yes—
719C3×D4C23×D313yes—
720C3×D4C23×D313yes—
721C2×C3×C4—23no—
722C2×C3×C4—23no—
723C2×C3×C4—23no—
724C2×C3×C4—33no—
725C2×C3×C4—33no—
726C2×C3×C4—33no—
727C2×C3×C4—31no—
728C2×C3×C4—33no—
729C2×C3×C4—43no—
730C2×C3×C4—63no—
731C2×C3×C4—61no—
732C2×C3×C4—63no—
733C2×C3×C4—63no—
734C2×C3×C4—63no—
735C2×C3×C4—63no—
736C2×C3×C4C23×D313yes—
737C2×C3×C4C23×D313yes—
738#67—23no—
739#67—23no—
740#67—23no—
741#67—23no—
742#67—26no—
743#67—63no—
744#67—63no—
745#67—63no—
746#67—63no—
747#67—63no—
748#67—61no—
749#67—123no—
750#67C2×#6716yes—
751C2×Dic3—23no—
752C2×Dic3—23no—
753C2×Dic3—63no—
754C2×Dic3—66no—
755C2×Dic3—63no—
756C2×Dic3—63no—
757C2×Dic3—63no—
758C2×Dic3—123no—
759C2×Dic3C2×#6713yes—
760D12—23no—
761D12—23no—
762D12—31no—
763D12—31no—
764D12—61no—
765D12—61no—
766D12—63no—
767D12C2×#6713yes—
768D12C23×D313yes—
769D12C23×D311yescharacteristic
770C4×D3—21no—
771C4×D3—23no—
772C4×D3—23no—
773C4×D3—23no—
774C4×D3—63no—
775C4×D3—63no—
776C4×D3—63no—
777C4×D3—66no—
778C4×D3—63no—
779C4×D3—63no—
780C4×D3—63no—
781C4×D3—123no—
782C4×D3C2×#6713yes—
783C4×D3C2×#6713yes—
784C4×D3C23×D311yescharacteristic
785C4×D3C23×D313yes—
786Dic6—23no—
787Dic6—21no—
788Dic6—33no—
789Dic6—33no—
790Dic6—63no—
791Dic6—63no—
792Dic6—66no—
793Dic6—63no—
794Dic6—63no—
795Dic6—63no—
796Dic6—66no—
797Dic6—123no—
798Dic6C2×#6713yes—
799Dic6C23×D311yescharacteristic
800Dic6C23×D313yes—
801C3×C8—31no—
802C3×C8—33no—
803C3⋊C8—31no—
804C3⋊C8—33no—
805C3⋊C8—31no—
806C3⋊C8—33no—
807C3⋊C8—61no—
808C3⋊C8—63no—
809C3⋊C8C23×D311yescharacteristic
810C3⋊C8C23×D313yes—
811C2×C32—23no—
812C2×C32—43no—
813C2×C32C23×D411yescharacteristic
814C3⋊D3—41no—
815C3×D3—23no—
816C3×D3—41no—
817C3×D3—43no—
818C3×D3#57712yescomplemented
819C24—63no—
820#41—21no—
821#41—31no—
822#41—33no—
823#41—33no—
824#41—33no—
825#41—33no—
826#41—33no—
827#41—33no—
828#41—63no—
829#41—63no—
830#41—63no—
831#41—63no—
832#41—61no—
833#41—63no—
834#41—93no—
835#41—93no—
836#41—93no—
837#41—183no—
838#41—183no—
839#41—186no—
840#41—183no—
841#41—186no—
842#41—183no—
843#41—183no—
844#41C2×D3213yes—
845#41C2×D3211yescharacteristic
846C2×Q8—31no—
847C2×Q8—31no—
848C2×Q8—33no—
849C2×Q8—61no—
850C2×Q8—93no—
851C2×Q8—96no—
852C2×Q8—93no—
853C2×Q8—183no—
854C2×Q8—183no—
855C2×Q8—183no—
856C2×Q8—183no—
857C2×Q8—183no—
858C2×Q8—181no—
859C2×D4—23no—
860C2×D4—33no—
861C2×D4—33no—
862C2×D4—36no—
863C2×D4—33no—
864C2×D4—63no—
865C2×D4—63no—
866C2×D4—63no—
867C2×D4—63no—
868C2×D4—66no—
869C2×D4—63no—
870C2×D4—63no—
871C2×D4—66no—
872C2×D4—63no—
873C2×D4—91no—
874C2×D4—183no—
875C2×D4C2×D3213yes—
876C22×C4—33no—
877C22×C4—63no—
878C22×C4—183no—
879C22×C4—183no—
880Q16—33no—
881Q16—93no—
882Q16—93no—
883Q16—93no—
884SD16—31no—
885SD16—33no—
886SD16—36no—
887SD16—93no—
888SD16—96no—
889SD16—91no—
890SD16—93no—
891SD16—96no—
892SD16—91no—
893SD16—91no—
894SD16—93no—
895SD16—96no—
896D8—33no—
897D8—93no—
898D8—93no—
899D8—93no—
900M16—33no—
901M16—96no—
902M16—93no—
903C2×C8—33no—
904C2×C8—91no—
905C2×C8—93no—
906C2×C8—93no—
907C2×C8—93no—
908C2×C8—93no—
909C22×C3—23no—
910C22×C3—23no—
911C22×C3—23no—
912C22×C3—31no—
913C22×C3—33no—
914C22×C3—43no—
915C22×C3—66no—
916C22×C3—63no—
917C22×C3—61no—
918C22×C3—83no—
919C22×C3—83no—
920C22×C3—126no—
921C22×C3—163no—
922C22×C3—243no—
923C22×C3—246no—
924C22×C3C2×D3×D413yes—
925C22×C3C22×#6713yes—
926C2×D3—26no—
927C2×D3—21no—
928C2×D3—23no—
929C2×D3—46no—
930C2×D3—61no—
931C2×D3—61no—
932C2×D3—86no—
933C2×D3—83no—
934C2×D3—121no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3C22×#6713yes—
938C2×D3C22×#6711yescharacteristic
939C3×C4—21no—
940C3×C4—21no—
941C3×C4—23no—
942C3×C4—21no—
943C3×C4—31no—
944C3×C4—33no—
945C3×C4—41no—
946C3×C4—61no—
947C3×C4—63no—
948C3×C4C2×D3×D413yes—
949C3×C4C22×#6713yes—
950C3×C4C24×D311yescharacteristic
951C3×C4C24×D311yescharacteristic
952Dic3—23no—
953Dic3—21no—
954Dic3—63no—
955Dic3—63no—
956Dic3—123no—
957Dic3C22×#6711yescharacteristic
958Dic3C22×#6713yes—
959C32C2×#57711yescharacteristic, complemented, Sylow
960C23—23no—
961C23—33no—
962C23—63no—
963C23—66no—
964C23—63no—
965C23—181no—
966C23—246no—
967Q8—33no—
968Q8—33no—
969Q8—31no—
970Q8—61no—
971Q8—63no—
972Q8—93no—
973Q8—183no—
974Q8—186no—
975Q8—183no—
976Q8D3×#6711yescharacteristic
977Q8C22×D3211yescharacteristic
978D4—23no—
979D4—23no—
980D4—36no—
981D4—33no—
982D4—31no—
983D4—33no—
984D4—63no—
985D4—63no—
986D4—66no—
987D4—63no—
988D4—63no—
989D4—63no—
990D4—63no—
991D4—91no—
992D4—181no—
993D4—183no—
994D4—183no—
995D4—183no—
996D4D3×#6713yes—
997D4C22×D3213yes—
998C2×C4—23no—
999C2×C4—33no—
1000C2×C4—33no—
1001C2×C4—33no—
1002C2×C4—31no—
1003C2×C4—33no—
1004C2×C4—63no—
1005C2×C4—61no—
1006C2×C4—63no—
1007C2×C4—63no—
1008C2×C4—63no—
1009C2×C4—63no—
1010C2×C4—183no—
1011C2×C4—183no—
1012C2×C4—183no—
1013C2×C4—186no—
1014C2×C4—183no—
1015C2×C4—183no—
1016C2×C4C22×D3213yes—
1017C8—31no—
1018C8—33no—
1019C8—91no—
1020C8—93no—
1021C2×C3—23no—
1022C2×C3—23no—
1023C2×C3—21no—
1024C2×C3—32no—
1025C2×C3—43no—
1026C2×C3—43no—
1027C2×C3—43no—
1028C2×C3—63no—
1029C2×C3—83no—
1030C2×C3—123no—
1031C2×C3—121no—
1032C2×C3C22×D3×D411yescharacteristic
1033C2×C3C23×#6711yescharacteristic
1034D3—23no—
1035D3—41no—
1036D3—43no—
1037D3—121no—
1038D3—121no—
1039D3—241no—
1040D3#583612yesdirect product factor
1041C22—23no—
1042C22—31no—
1043C22—33no—
1044C22—66no—
1045C22—61no—
1046C22—63no—
1047C22—83no—
1048C22—126no—
1049C22—181no—
1050C22—243no—
1051C22—246no—
1052C22—362no—
1053C22C2×D3×#6713yes—
1054C4—21no—
1055C4—31no—
1056C4—33no—
1057C4—61no—
1058C4—63no—
1059C4—183no—
1060C4C2×D3×#6713yes—
1061C4C23×D3211yescharacteristic
1062C3—21no—
1063C3D3×#57711yescharacteristic, complemented
1064C3C2×#583611yescharacteristic, complemented
1065C2—23no—
1066C2—32no—
1067C2—43no—
1068C2—63no—
1069C2—123no—
1070C2—121no—
1071C2—361no—
1072C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC2C22×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC32×H(5,𝔽2)C22
socleC2×C32C23×D4
hypercenterH(5,𝔽2)D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C3×D3×H(5,𝔽2)C2semidirect
2. D3×#1010C2semidirect
3. #10596307C2semidirect
4. C3×#5836C2semidirect
5. #10595466C2semidirect
6. #10595464C2semidirect
7. D3×#951C2semidirect
8. D3×#950C2semidirect
9. #10595447C2semidirect
10. #10595446C2semidirect
11. D3×#948C2semidirect
12. #10595106C2semidirect
13. #10595105C2semidirect
14. C2×D3×#214C2semidirect
15. D3×#932C2semidirect
18. C32×H(5,𝔽2)C22semidirect
19. #64367C22semidirect
20. C3×#1010C22semidirect
22. C3×#1009C22semidirect
23. C3×#1009C22semidirect
28. C3×#1004C22semidirect
35. D3×#235C22semidirect
36. #64298C22semidirect
37. #64297C22semidirect
38. C2×D3×Dic6C22semidirect
39. #64160C22semidirect
40. #64159C22semidirect
41. #64157C22semidirect
42. C2×#3754C22semidirect
43. #64141C22semidirect
44. C3×#951C22semidirect
45. C3×#950C22semidirect
46. C3×#948C22semidirect
47. C2×C3×#214C22semidirect
48. C3×#932C22semidirect
49. #63949C22semidirect
50. #63947C22semidirect
51. #63943C22semidirect
52. D3×#216C22semidirect
53. D3×#215C22semidirect
54. #63935C22semidirect
55. #63934C22semidirect
56. #63933C22semidirect
57. #63932C22semidirect
58. #63929C22semidirect
59. D3×#214C22semidirect
60. D3×#214C22semidirect
61. D3×#214C22semidirect
62. D3×#214C22semidirect
63. D3×#213C22semidirect
64. #63831C22semidirect
65. #63830C22semidirect
66. #63829C22semidirect
67. C2×#3716C22semidirect
68. #63827C22semidirect
69. C2×#3715C22semidirect
70. #63823C22semidirect
71. #63822C22semidirect
72. #63815C22semidirect
73. #63814C22semidirect
74. D3×#208C22semidirect
75. C2×D3×C3⋊C8C22semidirect
78. D3×H(5,𝔽2)D3semidirect
91. #5836D3direct (N × H)
115. #3828C23semidirect
116. C2×#634C23semidirect
143. C3×#235C23semidirect
148. C2×C3×Dic6C23semidirect
157. #3799C23semidirect
162. #3795C23semidirect
167. D3×Dic6C23semidirect
168. #3756C23semidirect
169. #3755C23semidirect
170. #3754C23semidirect
171. #3754C23semidirect
172. #3753C23semidirect
173. #3748C23semidirect
174. C2×C3⋊(C3⋊C8)C23semidirect
175. C3×#216C23semidirect
176. C3×#215C23semidirect
177. C3×#214C23semidirect
178. C3×#214C23semidirect
179. C3×#213C23semidirect
180. C3×#208C23semidirect
181. C2×C3×C3⋊C8C23semidirect
182. #3719C23semidirect
183. #3718C23semidirect
184. #3717C23semidirect
185. #3716C23semidirect
186. #3716C23semidirect
187. #3715C23semidirect
188. #3715C23semidirect
189. #3715C23semidirect
190. #3714C23semidirect
191. #3713C23semidirect
192. #3711C23semidirect
195. D3×C3⋊C8C23semidirect
196. D3×C3⋊C8C23semidirect
205. C3×H(5,𝔽2)C2×D3semidirect
206. C3×H(5,𝔽2)C2×D3semidirect
221. #1010C2×D3semidirect
223. #1009C2×D3semidirect
224. #1009C2×D3semidirect
236. #1004C2×D3semidirect
254. #951C2×D3semidirect
265. #950C2×D3semidirect
272. #948C2×D3semidirect
286. C2×#214C2×D3semidirect
294. #932C2×D3semidirect
508. #235C22×D3semidirect
527. C2×Dic6C22×D3semidirect
541. #216C22×D3semidirect
549. #215C22×D3semidirect
561. #214C22×D3semidirect
562. #214C22×D3semidirect
569. #213C22×D3semidirect
574. #208C22×D3semidirect
582. C2×C3⋊C8C22×D3semidirect
625. H(5,𝔽2)D32semidirect
818. C3×D3#577semidirect
959. C32C2×#577semidirect
1040. D3#5836direct (N × H)
1063. C3D3×#577semidirect
1064. C3C2×#5836semidirect

Maximal subgroups

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

subgroupindex
C3×D3×H(5,𝔽2)2
D3×#10102
#105963072
C3×#58362
#105954662
#105954642
D3×#9512
D3×#9502
#105954472
#105954462
D3×#9482
#105951062
#105951052
C2×D3×#2142
D3×#9322
C2×#58363
D3×#5773