Finite Group Databasebeta

← D3×#5838 #11918926

Subgroups — D3×#5838 #11918926

Order 1152.

2940 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×2−1+4C211yesmaximal, characteristic, complemented
2D3×#1010C211yesmaximal, characteristic, complemented
3#10596309C211yesmaximal, characteristic, complemented
4C3×#5838C211yesmaximal, characteristic, complemented
5#10595467C213yesmaximal, complemented
6#10595465C213yesmaximal, complemented
7D3×#951C213yesmaximal, complemented
8D3×#950C213yesmaximal, complemented
9#10595450C211yesmaximal, characteristic, complemented
10#10595445C211yesmaximal, characteristic, complemented
11D3×#948C211yesmaximal, characteristic, complemented
12#10595328C213yesmaximal, complemented
13#10595327C213yesmaximal, complemented
14C2×D3×#216C213yesmaximal, complemented
15D3×#942C213yesmaximal, complemented
16C2×#5838—31nomaximal
17D3×#578—31nomaximal
18C32×2−1+4C2211yescharacteristic, complemented
19#64367C2211yescharacteristic, complemented
20C3×#1010—23no—
21C3×#1010C2213yescomplemented
22C3×#1010C2211yescharacteristic, complemented
23C3×#1010C2211yescharacteristic, complemented
24C3×D3×#41—23no—
25C3×D3×#41C2213yes—
26C3×D3×#41C2211yescharacteristic
27C3×#1007—21no—
28C3×#1007C2213yescomplemented
29C2×C3×D3×Q8—21no—
30C2×C3×D3×Q8C2213yes—
31D32×Q8—21no—
32#64315—21no—
33D3×#237—23no—
34#64309—23no—
35D3×#235C2213yes—
36#64298C2213yescomplemented
37#64297C2213yescomplemented
38C2×D3×Dic6C2213yes—
39#64160C2213yescomplemented
40#64159C2213yescomplemented
41#64157C2211yescharacteristic, complemented
42C2×#3756C2213yescomplemented
43#64151C2213yescomplemented
44C3×#951C2213yescomplemented
45C3×#950C2213yescomplemented
46C3×#948C2211yescharacteristic, complemented
47C2×C3×#216C2213yescomplemented
48C3×#942C2213yescomplemented
49#63949C2213yescomplemented
50#63948C2216yescomplemented
51#63947C2213yescomplemented
52#63946C2216yescomplemented
53#63943C2216yescomplemented
54D3×#216C2213yes—
55D3×#216C2216yes—
56D3×#216C2216yescomplemented
57D3×#216C2216yescomplemented
58D3×#215C2213yes—
59#63935C2213yescomplemented
60#63933C2213yescomplemented
61#63929C2216yescomplemented
62D3×#214C2213yes—
63D3×#213C2211yescharacteristic
64C2×#3719C2213yescomplemented
65C2×#3718C2213yescomplemented
66#63833C2213yescomplemented
67#63831C2213yescomplemented
68#63829C2213yescomplemented
69#63827C2213yescomplemented
70#63827C2213yescomplemented
71#63822C2213yescomplemented
72#63815C2213yescomplemented
73#63814C2213yescomplemented
74D3×#208C2213yes—
75C2×D3×C3⋊C8C2213yes—
76C2×C3×2−1+4—31no—
77D3×2−1+4—31no—
78D3×2−1+4D311yescharacteristic, complemented
79C2×#1010—31no—
80C3×#578—31no—
81#5838—31no—
82#5838—31no—
83#5838—31no—
84#5838—31no—
85#5838—33no—
86#5838—33no—
87#5838—31no—
88#5838—33no—
89#5838—33no—
90#5838—61no—
91#5838D311yescharacteristic, direct product factor
92C2×#951—33no—
93C2×#950—33no—
94C2×#948—31no—
95C22×#216—33no—
96C2×#942—33no—
97#5779—33no—
98#5779—33no—
99D3×#137—33no—
100D3×#137—33no—
101#5771—33no—
102D3×#135—33no—
103#5766—33no—
104C2×D3×Q16—33no—
105#5753—31no—
106D3×#131—31no—
107C32×#41—23no—
108C32×#41C2313yes—
109C32×#41C2311yescharacteristic
110C2×C32×Q8—21no—
111C2×C32×Q8C2313yes—
112Q8×C3⋊D3—21no—
113#3830—23no—
114#3828C2313yes—
115C2×#634C2313yes—
116C3×#239—23no—
117C3×#239D411yescharacteristic
118C3×#239C2313yes—
119C3×D3×Q8—21no—
120C3×D3×Q8—21no—
121C3×D3×Q8—23no—
122C3×D3×Q8—23no—
123C3×D3×Q8—23no—
124C3×D3×Q8D411yescharacteristic
125C3×D3×Q8C2313yes—
126C3×D3×Q8C2316yes—
127C3×#237—23no—
128C3×#237—23no—
129C3×#237—26no—
130C3×#237—23no—
131C3×#237D413yes—
132C3×#237C2313yes—
133C3×D3×D4—23no—
134C3×D3×D4D413yes—
135C3×D3×D4C2311yescharacteristic
136C3×#235—26no—
137C3×#235—23no—
138C3×#235—23no—
139C3×#235C2313yes—
140C3×#235C2313yes—
141C3×#235C2313yes—
142C2×C3×C4×D3—23no—
143C2×C3×C4×D3—23no—
144C2×C3×C4×D3C2313yes—
145C2×C3×Dic6—23no—
146C2×C3×Dic6—23no—
147C2×C3×Dic6C2313yes—
148C2×C3×Dic6C2313yes—
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#3799C2313yes—
158#3798—23no—
159#3797—23no—
160#3796—23no—
161#3795—23no—
162#3795C2313yes—
163D3×Dic6—23no—
164D3×Dic6—23no—
165D3×Dic6—23no—
166D3×Dic6C2313yes—
167D3×Dic6C2316yes—
168#3756C2316yes—
169#3756C2313yes—
170#3755C2313yes—
171#3754C2313yes—
172#3753C2311yescharacteristic
173#3748C2313yes—
174C2×C3⋊(C3⋊C8)C2313yes—
175C3×#216C2316yes—
176C3×#216C2313yes—
177C3×#215C2313yes—
178C3×#214C2313yes—
179C3×#213C2311yescharacteristic
180C3×#208C2313yes—
181C2×C3×C3⋊C8C2313yes—
182#3719C2313yes—
183#3719C2316yes—
184#3718C2313yes—
185#3718C2316yes—
186#3717C2313yes—
187#3716C2313yes—
188#3715C2313yes—
189#3715C2313yes—
190#3714C2311yescharacteristic
191#3713C2311yescharacteristic
192#3711C2316yes—
193D3×C3⋊C8C2311yescharacteristic
194D3×C3⋊C8C2313yes—
195D3×C3⋊C8C2313yes—
196D3×C3⋊C8C2313yes—
197C2×#578—91noSylow
198C3×2−1+4—21no—
199C3×2−1+4—31no—
200C3×2−1+4—33no—
201C3×2−1+4—31no—
202C3×2−1+4—33no—
203C3×2−1+4—61no—
204C3×2−1+4—63no—
205C3×2−1+4C2×D311yescharacteristic, complemented
206C3×2−1+4C2×D311yescharacteristic, complemented
207C2×C3×#41—31no—
208C2×C3×#41—33no—
209C2×C3×#41—63no—
210C22×C3×Q8—33no—
211C22×C3×Q8—61no—
212#1010—23no—
213#1010—31no—
214#1010—31no—
215#1010—33no—
216#1010—33no—
217#1010—33no—
218#1010—61no—
219#1010—63no—
220#1010—61no—
221#1010—63no—
222#1010C2×D313yescomplemented
223#1010C2×D311yescharacteristic, complemented
224#1010C2×D311yescharacteristic, complemented
225D3×#41—23no—
226D3×#41—33no—
227D3×#41—63no—
228D3×#41C2×D313yes—
229D3×#41C2×D311yescharacteristic
230#1007—21no—
231#1007—33no—
232#1007—61no—
233#1007C2×D313yescomplemented
234C2×D3×Q8—21no—
235C2×D3×Q8—33no—
236C2×D3×Q8—61no—
237C2×D3×Q8—61no—
238C2×D3×Q8C2×D313yes—
239C2×#237—63no—
240C2×#235—33no—
241C22×Dic6—33no—
242C3×#137—33no—
243C3×#137—33no—
244C3×#135—33no—
245C2×C3×Q16—33no—
246C3×#131—31no—
247#951—33no—
248#951—33no—
249#951—33no—
250#951—33no—
251#951—36no—
252#951—36no—
253#951—33no—
254#951—63no—
255#951C2×D313yescomplemented
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—33no—
265#950—63no—
266#950C2×D313yescomplemented
267#948—31no—
268#948—31no—
269#948—33no—
270#948—33no—
271#948—61no—
272#948C2×D311yescharacteristic, complemented
273C2×#216—33no—
274C2×#216—33no—
275C2×#216—33no—
276C2×#216—33no—
277C2×#216—36no—
278C2×#216—33no—
279C2×#216—36no—
280C2×#216—36no—
281C2×#216—33no—
282C2×#216—63no—
283C2×#216C2×D313yescomplemented
284#942—33no—
285#942—33no—
286#942—33no—
287#942—33no—
288#942—36no—
289#942—36no—
290#942—33no—
291#942—63no—
292#942C2×D313yescomplemented
293C2×#215—33no—
294C2×#214—33no—
295C2×#213—31no—
296C2×#208—33no—
297C22×C3⋊C8—33no—
298#919—33no—
299#918—36no—
300#918—36no—
301D3×Q16—33no—
302D3×Q16—36no—
303D3×Q16—36no—
304D3×Q16—36no—
305#916—33no—
306#916—33no—
307#915—36no—
308#915—36no—
309D3×SD16—33no—
310D3×SD16—33no—
311#912—33no—
312D3×D8—31no—
313#909—33no—
314#909—33no—
315#907—33no—
316D3×M16—33no—
317C2×Dic12—33no—
318#904—33no—
319#901—33no—
320C2×D3×C8—33no—
321C22×C3×D3—21no—
322C22×C3×D3C2×D413yes—
323C2×D32—21no—
324C32×Q8—23no—
325C32×Q8C2×D411yescharacteristic
326C32×Q8C2413yes—
327C32×D4—23no—
328C32×D4C2×D413yes—
329C32×D4C2411yescharacteristic
330C2×C32×C4—23no—
331C2×C32×C4—23no—
332C2×C32×C4C2413yes—
333#638—23no—
334C2×C3⋊Dic3—23no—
335C4⋊(C3⋊D3)C2411yescharacteristic
336C4×C3⋊D3—23no—
337#634—23no—
338#634C2413yes—
339C3×#67—23no—
340C3×#67—23no—
341C3×#67—23no—
342C3×#67—21no—
343C3×#67C2×D416yes—
344C2×C3×Dic3—23no—
345C2×C3×Dic3—23no—
346C2×C3×Dic3—23no—
347C2×C3×Dic3C2×D413yes—
348C3×D12—23no—
349C3×D12C2×D413yes—
350C3×D12C2411yescharacteristic
351C3×D12C2411yescharacteristic
352C3×C4×D3—23no—
353C3×C4×D3—26no—
354C3×C4×D3—23no—
355C3×C4×D3—23no—
356C3×C4×D3—23no—
357C3×C4×D3C2×D413yes—
358C3×C4×D3C2×D413yes—
359C3×C4×D3C2411yescharacteristic
360C3×C4×D3C2413yes—
361C3×Dic6—23no—
362C3×Dic6—23no—
363C3×Dic6—26no—
364C3×Dic6—23no—
365C3×Dic6C2×D413yes—
366C3×Dic6C2413yes—
367C3×Dic6C2413yes—
368#627—26no—
369#627—23no—
370#626—23no—
371#626—21no—
372#625—23no—
373#624—23no—
374D3×Dic3—23no—
375D3×Dic3—26no—
376D3×Dic3—23no—
377C3⋊(C3⋊C8)C2411yescharacteristic
378C3⋊(C3⋊C8)C2413yes—
379C3×C3⋊C8C2411yescharacteristic
380C3×C3⋊C8C2413yes—
381C2×2−1+4—31no—
382C2×2−1+4—91no—
383#578—31no—
384#578—91no—
385#578—93no—
386#578—93no—
387#578—93no—
388#578—93no—
389#578—91no—
390#578—91no—
391C2×#137—93no—
392C2×#137—93no—
393C2×#135—93no—
394C22×Q16—93no—
395C2×#131—91no—
396C3×#41—23no—
397C3×#41—23no—
398C3×#41—23no—
399C3×#41—21no—
400C3×#41—31no—
401C3×#41—33no—
402C3×#41—33no—
403C3×#41—33no—
404C3×#41—33no—
405C3×#41—33no—
406C3×#41—33no—
407C3×#41—43no—
408C3×#41—63no—
409C3×#41—66no—
410C3×#41—63no—
411C3×#41—63no—
412C3×#41—66no—
413C3×#41—63no—
414C3×#41—63no—
415C3×#41—63no—
416C3×#41C22×D313yes—
417C3×#41C22×D313yes—
418C3×#41C22×D311yescharacteristic
419C3×#41C22×D311yescharacteristic
420C2×C3×Q8—21no—
421C2×C3×Q8—21no—
422C2×C3×Q8—23no—
423C2×C3×Q8—31no—
424C2×C3×Q8—33no—
425C2×C3×Q8—36no—
426C2×C3×Q8—33no—
427C2×C3×Q8—33no—
428C2×C3×Q8—41no—
429C2×C3×Q8—63no—
430C2×C3×Q8—63no—
431C2×C3×Q8—63no—
432C2×C3×Q8—63no—
433C2×C3×Q8—63no—
434C2×C3×Q8—61no—
435C2×C3×Q8—61no—
436C2×C3×Q8C22×D313yes—
437C2×C3×Q8C22×D313yes—
438C2×C3×D4—33no—
439C2×C3×D4—31no—
440C2×C3×D4—63no—
441C22×C3×C4—33no—
442C22×C3×C4—63no—
443C22×C3×C4—63no—
444C2×#67—63no—
445C22×Dic3—63no—
446#239—23no—
447#239—33no—
448#239—63no—
449#239#6711yescharacteristic
450#239C22×D313yes—
451D3×Q8—21no—
452D3×Q8—21no—
453D3×Q8—23no—
454D3×Q8—23no—
455D3×Q8—23no—
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×D313yes—
468D3×Q8C22×D316yes—
469#237—23no—
470#237—23no—
471#237—26no—
472#237—23no—
473#237—33no—
474#237—63no—
475#237—63no—
476#237—66no—
477#237—66no—
478#237—63no—
479#237—63no—
480#237—66no—
481#237—63no—
482#237—123no—
483#237#6713yes—
484#237C22×D313yes—
485D3×D4—23no—
486D3×D4—31no—
487D3×D4—63no—
488D3×D4#6713yes—
489D3×D4C22×D311yescharacteristic
490#235—26no—
491#235—23no—
492#235—23no—
493#235—33no—
494#235—33no—
495#235—33no—
496#235—33no—
497#235—63no—
498#235—63no—
499#235—63no—
500#235—66no—
501#235—63no—
502#235—63no—
503#235C22×D313yes—
504#235C22×D313yes—
505#235C22×D313yes—
506C2×D12—31no—
507C2×C4×D3—23no—
508C2×C4×D3—23no—
509C2×C4×D3—63no—
510C2×C4×D3—63no—
511C2×C4×D3—63no—
512C2×C4×D3C22×D313yes—
513C2×Dic6—23no—
514C2×Dic6—23no—
515C2×Dic6—33no—
516C2×Dic6—33no—
517C2×Dic6—33no—
518C2×Dic6—36no—
519C2×Dic6—63no—
520C2×Dic6—63no—
521C2×Dic6—63no—
522C2×Dic6—63no—
523C2×Dic6—63no—
524C2×Dic6—63no—
525C2×Dic6C22×D313yes—
526C2×Dic6C22×D313yes—
527C3×Q16—33no—
528C3×Q16—36no—
529C3×SD16—33no—
530C3×SD16—33no—
531C3×D8—31no—
532C3×M16—33no—
533C2×C3×C8—33no—
534#216—36no—
535#216—33no—
536#216—36no—
537#216—33no—
538#216—36no—
539#216—33no—
540#216—36no—
541#216—33no—
542#216—36no—
543#216—33no—
544#216—66no—
545#216—63no—
546#216C22×D316yes—
547#216C22×D313yes—
548#215—33no—
549#215—33no—
550#215—33no—
551#215—33no—
552#215—33no—
553#215—63no—
554#215C22×D313yes—
555#214—33no—
556#214—33no—
557#214—33no—
558#214—33no—
559#214—33no—
560#214—63no—
561#214C22×D313yes—
562#213—31no—
563#213—31no—
564#213—31no—
565#213—31no—
566#213—31no—
567#213—61no—
568#213C22×D311yescharacteristic
569#208—33no—
570#208—33no—
571#208—36no—
572#208—63no—
573#208C22×D313yes—
574C2×C3⋊C8—33no—
575C2×C3⋊C8—33no—
576C2×C3⋊C8—31no—
577C2×C3⋊C8—33no—
578C2×C3⋊C8—33no—
579C2×C3⋊C8—33no—
580C2×C3⋊C8—63no—
581C2×C3⋊C8C22×D313yes—
582Dic12—33no—
583Dic12—36no—
584D24—31no—
585#204—33no—
586#204—33no—
587ΓL(1,𝔽25)—36no—
588D3×C8—31no—
589D3×C8—33no—
590D3×C8—33no—
591D3×C8—33no—
592C22×C32—21no—
593C22×C32C22×D413yes—
594C2×C3⋊D3—21no—
595C2×C3×D3—26no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—42no—
599C2×C3×D3C22×D413yes—
600C2×C3×D3C22×D411yescharacteristic
601D32—42no—
602C32×C4—23no—
603C32×C4C22×D413yes—
604C32×C4C2511yescharacteristic
605C3⋊Dic3—23no—
606C3×Dic3—23no—
607C3×Dic3—23no—
608C3×Dic3C22×D413yes—
609C3×Dic3C22×D411yescharacteristic
6102−1+4—33no—
6112−1+4—31no—
6122−1+4—31no—
6132−1+4—33no—
6142−1+4—61no—
6152−1+4—63no—
6162−1+4—93no—
6172−1+4—93no—
6182−1+4—91no—
6192−1+4—181no—
6202−1+4—183no—
6212−1+4D3211yescharacteristic, complemented
622C2×#41—31no—
623C2×#41—33no—
624C2×#41—63no—
625C2×#41—93no—
626C2×#41—183no—
627C22×Q8—33no—
628C22×Q8—61no—
629C22×Q8—93no—
630C22×Q8—181no—
631#137—33no—
632#137—33no—
633#137—93no—
634#137—93no—
635#137—96no—
636#137—96no—
637#137—96no—
638#137—96no—
639#137—93no—
640#137—93no—
641#137—93no—
642#137—93no—
643#135—33no—
644#135—93no—
645#135—93no—
646#135—93no—
647#135—93no—
648#135—93no—
649#135—93no—
650#135—93no—
651C2×Q16—33no—
652C2×Q16—93no—
653C2×Q16—93no—
654C2×Q16—96no—
655C2×Q16—96no—
656C2×Q16—96no—
657C2×Q16—93no—
658C2×Q16—93no—
659C2×SD16—93no—
660C2×SD16—93no—
661C2×D8—91no—
662#131—31no—
663#131—93no—
664#131—93no—
665#131—91no—
666C2×M16—93no—
667C22×C8—93no—
668C23×C3—33no—
669C23×C3—61no—
670C22×D3—21no—
671C22×D3—61no—
672C22×D3—61no—
673C22×D3C2×#6713yes—
674C3×Q8—23no—
675C3×Q8—23no—
676C3×Q8—23no—
677C3×Q8—21no—
678C3×Q8—33no—
679C3×Q8—33no—
680C3×Q8—33no—
681C3×Q8—43no—
682C3×Q8—63no—
683C3×Q8—66no—
684C3×Q8—63no—
685C3×Q8—63no—
686C3×Q8D3×D411yescharacteristic
687C3×Q8C2×#6711yescharacteristic
688C3×Q8C23×D313yes—
689C3×Q8C23×D313yes—
690C3×D4—23no—
691C3×D4—23no—
692C3×D4—21no—
693C3×D4—23no—
694C3×D4—36no—
695C3×D4—33no—
696C3×D4—31no—
697C3×D4—31no—
698C3×D4—43no—
699C3×D4—63no—
700C3×D4—61no—
701C3×D4—63no—
702C3×D4—63no—
703C3×D4—63no—
704C3×D4D3×D413yes—
705C3×D4C2×#6713yes—
706C3×D4C23×D311yescharacteristic
707C3×D4C23×D311yescharacteristic
708C2×C3×C4—23no—
709C2×C3×C4—23no—
710C2×C3×C4—23no—
711C2×C3×C4—23no—
712C2×C3×C4—23no—
713C2×C3×C4—33no—
714C2×C3×C4—33no—
715C2×C3×C4—33no—
716C2×C3×C4—31no—
717C2×C3×C4—33no—
718C2×C3×C4—43no—
719C2×C3×C4—43no—
720C2×C3×C4—63no—
721C2×C3×C4—63no—
722C2×C3×C4—66no—
723C2×C3×C4—63no—
724C2×C3×C4—63no—
725C2×C3×C4—63no—
726C2×C3×C4—63no—
727C2×C3×C4—63no—
728C2×C3×C4C23×D313yes—
729C2×C3×C4C23×D313yes—
730#67—23no—
731#67—23no—
732#67—23no—
733#67—21no—
734#67—63no—
735#67—63no—
736#67—63no—
737#67—63no—
738#67—63no—
739#67—61no—
740#67—123no—
741#67C2×#6716yes—
742C2×Dic3—23no—
743C2×Dic3—23no—
744C2×Dic3—23no—
745C2×Dic3—63no—
746C2×Dic3—66no—
747C2×Dic3—63no—
748C2×Dic3—63no—
749C2×Dic3—63no—
750C2×Dic3—123no—
751C2×Dic3C2×#6713yes—
752D12—23no—
753D12—31no—
754D12—31no—
755D12—61no—
756D12—61no—
757D12—63no—
758D12C2×#6713yes—
759D12C23×D311yescharacteristic
760D12C23×D311yescharacteristic
761C4×D3—23no—
762C4×D3—26no—
763C4×D3—23no—
764C4×D3—23no—
765C4×D3—23no—
766C4×D3—63no—
767C4×D3—63no—
768C4×D3—63no—
769C4×D3—66no—
770C4×D3—63no—
771C4×D3—63no—
772C4×D3—63no—
773C4×D3—123no—
774C4×D3C2×#6713yes—
775C4×D3C2×#6713yes—
776C4×D3C23×D311yescharacteristic
777C4×D3C23×D313yes—
778Dic6—23no—
779Dic6—23no—
780Dic6—23no—
781Dic6—26no—
782Dic6—33no—
783Dic6—33no—
784Dic6—63no—
785Dic6—63no—
786Dic6—66no—
787Dic6—63no—
788Dic6—63no—
789Dic6—63no—
790Dic6—66no—
791Dic6—123no—
792Dic6C2×#6713yes—
793Dic6C23×D313yes—
794Dic6C23×D313yes—
795C3×C8—31no—
796C3×C8—33no—
797C3⋊C8—31no—
798C3⋊C8—33no—
799C3⋊C8—31no—
800C3⋊C8—33no—
801C3⋊C8—61no—
802C3⋊C8—63no—
803C3⋊C8C23×D311yescharacteristic
804C3⋊C8C23×D313yes—
805C2×C32—23no—
806C2×C32—41no—
807C2×C32C23×D411yescharacteristic
808C3⋊D3—41no—
809C3×D3—23no—
810C3×D3—41no—
811C3×D3—41no—
812C3×D3#57812yescomplemented
813#41—23no—
814#41—31no—
815#41—33no—
816#41—33no—
817#41—33no—
818#41—33no—
819#41—33no—
820#41—33no—
821#41—63no—
822#41—66no—
823#41—63no—
824#41—63no—
825#41—66no—
826#41—63no—
827#41—63no—
828#41—63no—
829#41—93no—
830#41—93no—
831#41—93no—
832#41—183no—
833#41—183no—
834#41—186no—
835#41—183no—
836#41—186no—
837#41—183no—
838#41—183no—
839#41C2×D3213yes—
840#41C2×D3211yescharacteristic
841C2×Q8—21no—
842C2×Q8—31no—
843C2×Q8—33no—
844C2×Q8—36no—
845C2×Q8—33no—
846C2×Q8—33no—
847C2×Q8—63no—
848C2×Q8—63no—
849C2×Q8—63no—
850C2×Q8—63no—
851C2×Q8—63no—
852C2×Q8—61no—
853C2×Q8—61no—
854C2×Q8—93no—
855C2×Q8—96no—
856C2×Q8—93no—
857C2×Q8—183no—
858C2×Q8—183no—
859C2×Q8—183no—
860C2×Q8—183no—
861C2×Q8—183no—
862C2×Q8—181no—
863C2×Q8C2×D3213yes—
864C2×D4—33no—
865C2×D4—31no—
866C2×D4—63no—
867C2×D4—91no—
868C2×D4—183no—
869C22×C4—33no—
870C22×C4—63no—
871C22×C4—63no—
872C22×C4—183no—
873C22×C4—183no—
874Q16—33no—
875Q16—36no—
876Q16—93no—
877Q16—96no—
878Q16—93no—
879Q16—96no—
880Q16—93no—
881Q16—96no—
882SD16—33no—
883SD16—33no—
884SD16—93no—
885SD16—93no—
886SD16—93no—
887SD16—93no—
888SD16—93no—
889SD16—93no—
890D8—31no—
891D8—91no—
892D8—91no—
893D8—91no—
894M16—33no—
895M16—96no—
896M16—93no—
897C2×C8—33no—
898C2×C8—91no—
899C2×C8—93no—
900C2×C8—93no—
901C2×C8—93no—
902C2×C8—93no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—23no—
906C22×C3—31no—
907C22×C3—33no—
908C22×C3—41no—
909C22×C3—66no—
910C22×C3—61no—
911C22×C3—61no—
912C22×C3—122no—
913C22×C3C2×D3×D413yes—
914C22×C3C22×#6713yes—
915C2×D3—26no—
916C2×D3—21no—
917C2×D3—21no—
918C2×D3—42no—
919C2×D3—61no—
920C2×D3—61no—
921C2×D3—121no—
922C2×D3—122no—
923C2×D3—122no—
924C2×D3C22×#6713yes—
925C2×D3C22×#6711yescharacteristic
926C3×C4—23no—
927C3×C4—23no—
928C3×C4—23no—
929C3×C4—21no—
930C3×C4—31no—
931C3×C4—33no—
932C3×C4—43no—
933C3×C4—63no—
934C3×C4—63no—
935C3×C4C2×D3×D413yes—
936C3×C4C22×#6713yes—
937C3×C4C24×D311yescharacteristic
938C3×C4C24×D311yescharacteristic
939Dic3—23no—
940Dic3—23no—
941Dic3—63no—
942Dic3—63no—
943Dic3—123no—
944Dic3C22×#6711yescharacteristic
945Dic3C22×#6713yes—
946C32C2×#57811yescharacteristic, complemented, Sylow
947C23—33no—
948C23—61no—
949C23—181no—
950Q8—23no—
951Q8—33no—
952Q8—33no—
953Q8—33no—
954Q8—63no—
955Q8—66no—
956Q8—63no—
957Q8—63no—
958Q8—93no—
959Q8—183no—
960Q8—186no—
961Q8—183no—
962Q8D3×#6711yescharacteristic
963Q8C22×D3213yes—
964D4—23no—
965D4—36no—
966D4—33no—
967D4—31no—
968D4—31no—
969D4—63no—
970D4—61no—
971D4—63no—
972D4—63no—
973D4—63no—
974D4—91no—
975D4—181no—
976D4—183no—
977D4—183no—
978D4—183no—
979D4D3×#6713yes—
980D4C22×D3211yescharacteristic
981C2×C4—23no—
982C2×C4—23no—
983C2×C4—33no—
984C2×C4—33no—
985C2×C4—33no—
986C2×C4—31no—
987C2×C4—33no—
988C2×C4—63no—
989C2×C4—63no—
990C2×C4—66no—
991C2×C4—63no—
992C2×C4—63no—
993C2×C4—63no—
994C2×C4—63no—
995C2×C4—63no—
996C2×C4—183no—
997C2×C4—183no—
998C2×C4—183no—
999C2×C4—186no—
1000C2×C4—183no—
1001C2×C4—183no—
1002C2×C4C22×D3213yes—
1003C8—31no—
1004C8—33no—
1005C8—91no—
1006C8—93no—
1007C2×C3—23no—
1008C2×C3—23no—
1009C2×C3—21no—
1010C2×C3—32no—
1011C2×C3—43no—
1012C2×C3—41no—
1013C2×C3—41no—
1014C2×C3—63no—
1015C2×C3—81no—
1016C2×C3—121no—
1017C2×C3—121no—
1018C2×C3C22×D3×D411yescharacteristic
1019C2×C3C23×#6711yescharacteristic
1020D3—23no—
1021D3—41no—
1022D3—41no—
1023D3—121no—
1024D3—121no—
1025D3—241no—
1026D3#583812yesdirect product factor
1027C22—21no—
1028C22—31no—
1029C22—33no—
1030C22—66no—
1031C22—61no—
1032C22—61no—
1033C22—122no—
1034C22—181no—
1035C22—362no—
1036C22C2×D3×#6713yes—
1037C4—23no—
1038C4—31no—
1039C4—33no—
1040C4—63no—
1041C4—63no—
1042C4—183no—
1043C4C2×D3×#6713yes—
1044C4C23×D3211yescharacteristic
1045C3—21no—
1046C3D3×#57811yescharacteristic, complemented
1047C3C2×#583811yescharacteristic, complemented
1048C2—23no—
1049C2—32no—
1050C2—41no—
1051C2—63no—
1052C2—121no—
1053C2—121no—
1054C2—361no—
1055C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC2C22×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC32×2−1+4C22
socleC2×C32C23×D4
hypercenter2−1+4D32
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. C3×D3×2−1+4C2semidirect
2. D3×#1010C2semidirect
3. #10596309C2semidirect
4. C3×#5838C2semidirect
5. #10595467C2semidirect
6. #10595465C2semidirect
7. D3×#951C2semidirect
8. D3×#950C2semidirect
9. #10595450C2semidirect
10. #10595445C2semidirect
11. D3×#948C2semidirect
12. #10595328C2semidirect
13. #10595327C2semidirect
14. C2×D3×#216C2semidirect
15. D3×#942C2semidirect
18. C32×2−1+4C22semidirect
19. #64367C22semidirect
21. C3×#1010C22semidirect
22. C3×#1010C22semidirect
23. C3×#1010C22semidirect
28. C3×#1007C22semidirect
36. #64298C22semidirect
37. #64297C22semidirect
39. #64160C22semidirect
40. #64159C22semidirect
41. #64157C22semidirect
42. C2×#3756C22semidirect
43. #64151C22semidirect
44. C3×#951C22semidirect
45. C3×#950C22semidirect
46. C3×#948C22semidirect
47. C2×C3×#216C22semidirect
48. C3×#942C22semidirect
49. #63949C22semidirect
50. #63948C22semidirect
51. #63947C22semidirect
52. #63946C22semidirect
53. #63943C22semidirect
56. D3×#216C22semidirect
57. D3×#216C22semidirect
59. #63935C22semidirect
60. #63933C22semidirect
61. #63929C22semidirect
64. C2×#3719C22semidirect
65. C2×#3718C22semidirect
66. #63833C22semidirect
67. #63831C22semidirect
68. #63829C22semidirect
69. #63827C22semidirect
70. #63827C22semidirect
71. #63822C22semidirect
72. #63815C22semidirect
73. #63814C22semidirect
78. D3×2−1+4D3semidirect
91. #5838D3direct (N × H)
205. C3×2−1+4C2×D3semidirect
206. C3×2−1+4C2×D3semidirect
222. #1010C2×D3semidirect
223. #1010C2×D3semidirect
224. #1010C2×D3semidirect
233. #1007C2×D3semidirect
255. #951C2×D3semidirect
266. #950C2×D3semidirect
272. #948C2×D3semidirect
283. C2×#216C2×D3semidirect
292. #942C2×D3semidirect
621. 2−1+4D32semidirect
812. C3×D3#578semidirect
946. C32C2×#578semidirect
1026. D3#5838direct (N × H)
1046. C3D3×#578semidirect
1047. C3C2×#5838semidirect

Maximal subgroups

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

subgroupindex
C3×D3×2−1+42
D3×#10102
#105963092
C3×#58382
#105954672
#105954652
D3×#9512
D3×#9502
#105954502
#105954452
D3×#9482
#105953282
#105953272
C2×D3×#2162
D3×#9422
C2×#58383
D3×#5783