Finite Group Databasebeta

← #11919052

Subgroups — #11919052

Order 1152.

3062 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#10596697C211yesmaximal, characteristic, complemented
3#10596306C211yesmaximal, characteristic, complemented
4C3×#5836C211yesmaximal, characteristic, complemented
5#10595470C213yesmaximal, complemented
6#10595464C213yesmaximal, complemented
7#10595456C213yesmaximal, complemented
8#10595453C213yesmaximal, complemented
9#10595449C211yesmaximal, characteristic, complemented
10#10595446C211yesmaximal, characteristic, complemented
11#10595441C211yesmaximal, characteristic, complemented
12C2×#63934C213yesmaximal, complemented
13#10595105C213yesmaximal, complemented
14#10595097C213yesmaximal, complemented
15D3×#932C213yesmaximal, complemented
16#87277—31nomaximal
17#87207—31nomaximal
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19#64366C2211yescharacteristic, complemented
20C3×#1010C2211yescharacteristic, complemented
21C3×#1009—21no—
22C3×#1009C2213yescomplemented
23C3×#1009C2211yescharacteristic, complemented
24C3×D3×#41—21no—
25C3×D3×#41C2211yescharacteristic
26C3×D3×#41C2213yescomplemented
27C3×#1004—23no—
28C3×#1004C2213yescomplemented
29C2×C3×D3×D4—23no—
30C2×C3×D3×D4C2213yescomplemented
31D3×#239—21no—
32#64316—21no—
33#64314—23no—
34#64312—23no—
35#64308C2213yescomplemented
36D3×#235C2213yescomplemented
37C2×#3799C2213yescomplemented
38#64297C2213yescomplemented
39#64159C2213yescomplemented
40#64158C2213yescomplemented
41#64157C2211yescharacteristic, complemented
42#64141C2213yescomplemented
43C2×#3753C2213yescomplemented
44C3×#951C2213yescomplemented
45C3×#950C2213yescomplemented
46C3×#948C2211yescharacteristic, complemented
47C2×C3×#214C2213yescomplemented
48C3×#932C2213yescomplemented
49#63949C2216yescomplemented
50#63948C2213yescomplemented
51#63946C2211yescharacteristic, complemented
52#63943C2213yescomplemented
53#63939C2213yescomplemented
54#63935C2216yescomplemented
55#63934C2216yescomplemented
56#63934C2213yescomplemented
57#63934C2216yescomplemented
58#63934C2216yescomplemented
59#63932C2213yescomplemented
60#63929C2213yescomplemented
61D3×#214C2216yescomplemented
62#63925C2213yescomplemented
63D3×#213C2216yescomplemented
64#63830C2213yescomplemented
65#63829C2213yescomplemented
66#63827C2213yescomplemented
67C2×#3715C2213yescomplemented
68#63825C2213yescomplemented
69C2×#3714C2213yescomplemented
70#63823C2213yescomplemented
71#63822C2213yescomplemented
72C2×#3711C2213yescomplemented
73#63815C2213yescomplemented
74#63814C2213yescomplemented
75D3×#208C2213yescomplemented
76C2×C3×H(5,𝔽2)—31no—
77#5968—31no—
78D3×H(5,𝔽2)D311yescharacteristic, complemented
79#5964—31no—
80C3×#577—31no—
81#5837—31no—
82#5836—31no—
83#5836—33no—
84#5836—33no—
85#5836D311yescharacteristic, complemented
86#5835—31no—
87#5835—31no—
88#5835—33no—
89#5835—31no—
90#5835—33no—
91#5835—61no—
92#5822—33no—
93#5822—33no—
94#5819—31no—
95C2×#932—33no—
96C2×#932—33no—
97#5778—33no—
98#5777—33no—
99#5774—33no—
100D3×AGL(1,ℤ/8)—33no—
101#5769—33no—
102#5768—33no—
103#5762—33no—
104C2×#914—33no—
105#5752—31no—
106#5750—31no—
107C23×C3×D3—23no—
108C32×#41—21no—
109C32×#41C2313yes—
110C32×#41C2311yescharacteristic
111C2×C32×D4—23no—
112C2×C32×D4C2313yes—
113#3832—21no—
114D4×C3⋊D3—23no—
115#3828C2313yescomplemented
116C2×C4⋊(C3⋊D3)C2313yescomplemented
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
149#3811—26no—
150D3×#67—23no—
151C2×#626—23no—
152C2×#624—23no—
153#3804—26no—
154#3804—23no—
155D3×D12—23no—
156D3×D12C2313yescomplemented
157C4×D32—23no—
158#3799—23no—
159#3799—23no—
160#3799—23no—
161#3799C2313yes—
162#3799C2316yescomplemented
163#3798—23no—
164#3797—23no—
165#3796—23no—
166#3795C2311yescharacteristic
167D3×Dic6C2313yescomplemented
168#3756C2311yescharacteristic, complemented
169#3755C2313yescomplemented
170#3754C2313yescomplemented
171#3753C2313yescomplemented
172#3753C2316yescomplemented
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#3719C2311yescharacteristic, complemented
183#3718C2313yescomplemented
184#3717C2313yescomplemented
185#3716C2313yescomplemented
186#3715C2311yescharacteristic, complemented
187#3715C2313yescomplemented
188#3715C2316yescomplemented
189#3714C2313yescomplemented
190#3714C2316yescomplemented
191#3713C2313yescomplemented
192#3711C2313yes—
193#3711C2311yescharacteristic
194#3711C2313yescomplemented
195#3711C2313yescomplemented
196D3×C3⋊C8C2316yescomplemented
197#3585—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—33no—
213#1010C2×D311yescharacteristic, complemented
214#1009—21no—
215#1009—31no—
216#1009—31no—
217#1009—33no—
218#1009—33no—
219#1009—61no—
220#1009—63no—
221#1009C2×D313yescomplemented
222#1009C2×D311yescharacteristic, complemented
223D3×#41—21no—
224D3×#41—33no—
225D3×#41—63no—
226D3×#41—61no—
227D3×#41—63no—
228D3×#41C2×D311yescharacteristic
229D3×#41C2×D313yescomplemented
230#1007—33no—
231#1007—61no—
232#1007—61no—
233C2×#239—33no—
234C2×#239—61no—
235#1004—23no—
236#1004—63no—
237#1004C2×D313yescomplemented
238C2×D3×D4—23no—
239C2×D3×D4C2×D313yescomplemented
240C2×#235—33no—
241C2×#235—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#951C2×D313yescomplemented
251#950—33no—
252#950—33no—
253#950—33no—
254#950—33no—
255#950—36no—
256#950—36no—
257#950—33no—
258#950—63no—
259#950C2×D313yescomplemented
260#949—33no—
261#949—33no—
262#949—33no—
263#949—33no—
264#949—33no—
265#949—33no—
266#949—63no—
267#948—31no—
268#948—31no—
269#948—33no—
270#948—33no—
271#948—61no—
272#948C2×D311yescharacteristic, complemented
273#942—33no—
274#942—33no—
275#942—31no—
276C2×#215—33no—
277C2×#214—33no—
278C2×#214—36no—
279C2×#214C2×D313yescomplemented
280#932—33no—
281#932—33no—
282#932—33no—
283#932—33no—
284#932—36no—
285#932—36no—
286#932—36no—
287#932—33no—
288#932—33no—
289#932—63no—
290#932C2×D313yescomplemented
291C2×#213—33no—
292C2×#213—33no—
293C2×#213—36no—
294C2×#213—33no—
295C2×#213—63no—
296C2×#208—33no—
297C2×#208—33no—
298#919—36no—
299#918—33no—
300#918—33no—
301#916—36no—
302#915—31no—
303#915—33no—
304#914—33no—
305#914—33no—
306#914—36no—
307#914—36no—
308#914—36no—
309D3×SD16—36no—
310#911—33no—
311#911—33no—
312D3×D8—36no—
313#908—33no—
314#908—33no—
315#907—33no—
316D3×M16—33no—
317#904—33no—
318C2×D24—33no—
319#901—33no—
320C2×ΓL(1,𝔽25)—33no—
321C23×C32—23no—
322C22×C3⋊D3—23no—
323C22×C3×D3—23no—
324C22×C3×D3—23no—
325C22×C3×D3—26no—
326C22×C3×D3—86no—
327C22×C3×D3C2×D413yes—
328C2×D32—23no—
329C32×Q8C2×D411yescharacteristic
330C32×Q8C2411yescharacteristic
331C32×D4—23no—
332C32×D4—23no—
333C32×D4C2×D413yes—
334C32×D4C2413yes—
335C2×C32×C4—23no—
336C2×C32×C4C2413yes—
337#638—23no—
338C4⋊(C3⋊D3)—23no—
339C4⋊(C3⋊D3)C2413yes—
340C4×C3⋊D3—23no—
341#634C2411yescharacteristic
342C3×#67—23no—
343C3×#67—23no—
344C3×#67—23no—
345C3×#67—23no—
346C3×#67—26no—
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×D3C2413yes—
363C3×C4×D3C2411yescharacteristic
364C3×Dic6—23no—
365C3×Dic6—21no—
366C3×Dic6C2×D413yes—
367C3×Dic6C2413yes—
368C3×Dic6C2411yescharacteristic
369#627—23no—
370#626—26no—
371#626—23no—
372#626—23no—
373#625—21no—
374#624—26no—
375#624—23no—
376D3×Dic3—23no—
377D3×Dic3—21no—
378C3⋊(C3⋊C8)C2413yes—
379C3⋊(C3⋊C8)C2411yescharacteristic
380C3×C3⋊C8C2413yes—
381C3×C3⋊C8C2411yescharacteristic
382#585—91no—
383C2×H(5,𝔽2)—31no—
384#577—31no—
385#577—93no—
386#577—93no—
387#577—91no—
388#576—91no—
389#576—93no—
390#576—93no—
391#576—91no—
392#575—93no—
393#575—93no—
394C2×AGL(1,ℤ/8)—93no—
395C2×AGL(1,ℤ/8)—93no—
396#568—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—36no—
430C2×C3×D4—33no—
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—
449C2×#67—63no—
450#239—21no—
451#239—33no—
452#239—36no—
453#239—63no—
454#239—61no—
455#239—61no—
456#239—63no—
457#239—63no—
458#239—63no—
459#239—121no—
460#239#6711yescharacteristic
461#239C22×D313yes—
462D3×Q8—21no—
463D3×Q8—33no—
464D3×Q8—63no—
465D3×Q8—63no—
466D3×Q8#6711yescharacteristic
467D3×Q8C22×D311yescharacteristic
468#237—23no—
469#237—23no—
470#237—23no—
471#237—31no—
472#237—63no—
473#237—66no—
474#237—63no—
475#237#6713yes—
476#237C22×D313yes—
477D3×D4—23no—
478D3×D4—23no—
479D3×D4—26no—
480D3×D4—23no—
481D3×D4—23no—
482D3×D4—23no—
483D3×D4—33no—
484D3×D4—63no—
485D3×D4—66no—
486D3×D4—63no—
487D3×D4—63no—
488D3×D4—63no—
489D3×D4—66no—
490D3×D4—123no—
491D3×D4#6713yes—
492D3×D4C22×D316yes—
493D3×D4C22×D313yes—
494#235—23no—
495#235—23no—
496#235—33no—
497#235—33no—
498#235—31no—
499#235—33no—
500#235—36no—
501#235—63no—
502#235—63no—
503#235—63no—
504#235—63no—
505#235—63no—
506#235—66no—
507#235—63no—
508#235—63no—
509#235C22×D313yes—
510#235C22×D313yes—
511#235C22×D313yescomplemented
512C2×D12—23no—
513C2×D12—33no—
514C2×D12—33no—
515C2×D12—33no—
516C2×D12—63no—
517C2×D12—63no—
518C2×D12—63no—
519C2×D12C22×D313yes—
520C2×C4×D3—23no—
521C2×C4×D3—63no—
522C2×C4×D3—63no—
523C2×C4×D3—63no—
524C2×C4×D3—63no—
525C2×C4×D3C22×D313yes—
526C2×Dic6—33no—
527C2×Dic6C22×D313yescomplemented
528C3×Q16—33no—
529C3×SD16—31no—
530C3×SD16—36no—
531C3×SD16—33no—
532C3×D8—33no—
533C3×M16—33no—
534C2×C3×C8—33no—
535#216—31no—
536#216—31no—
537#216—33no—
538#216—33no—
539#216—31no—
540#216—61no—
541#216C22×D313yescomplemented
542#215—33no—
543#215—33no—
544#215—36no—
545#215—33no—
546#215—31no—
547#215—33no—
548#215—63no—
549#215C22×D311yescharacteristic, complemented
550#214—33no—
551#214—33no—
552#214—31no—
553#214—33no—
554#214—36no—
555#214—33no—
556#214—63no—
557#214C22×D313yescomplemented
558#214C22×D316yescomplemented
559#213—36no—
560#213—33no—
561#213—33no—
562#213—36no—
563#213—33no—
564#213—33no—
565#213—36no—
566#213—33no—
567#213—63no—
568#213—66no—
569#213C22×D313yescomplemented
570#208—33no—
571#208—33no—
572#208—33no—
573#208—31no—
574#208—33no—
575#208—33no—
576#208—63no—
577#208C22×D313yescomplemented
578C2×C3⋊C8—33no—
579C2×C3⋊C8—33no—
580C2×C3⋊C8—36no—
581C2×C3⋊C8—63no—
582C2×C3⋊C8C22×D313yescomplemented
583Dic12—31no—
584D24—33no—
585D24—36no—
586#204—33no—
587#204—33no—
588ΓL(1,𝔽25)—31no—
589ΓL(1,𝔽25)—33no—
590ΓL(1,𝔽25)—33no—
591ΓL(1,𝔽25)—33no—
592D3×C8—36no—
593C22×C32—23no—
594C22×C32—83no—
595C22×C32C22×D413yes—
596C2×C3⋊D3—23no—
597C2×C3⋊D3—83no—
598C2×C3×D3—21no—
599C2×C3×D3—23no—
600C2×C3×D3—43no—
601C2×C3×D3—46no—
602C2×C3×D3—86no—
603C2×C3×D3—83no—
604C2×C3×D3C22×D413yes—
605C2×C3×D3C22×D411yescharacteristic
606D32—83no—
607C32×C4—21no—
608C32×C4C22×D413yes—
609C32×C4C2511yescharacteristic
610C3⋊Dic3—21no—
611C3×Dic3—23no—
612C3×Dic3—21no—
613C3×Dic3C22×D411yescharacteristic
614C3×Dic3C22×D413yes—
6152−1+4—31no—
6162−1+4—93no—
6172−1+4—181no—
618H(5,𝔽2)—33no—
619H(5,𝔽2)—31no—
620H(5,𝔽2)—33no—
621H(5,𝔽2)—63no—
622H(5,𝔽2)—61no—
623H(5,𝔽2)—93no—
624H(5,𝔽2)—91no—
625H(5,𝔽2)—183no—
626H(5,𝔽2)D3211yescharacteristic, complemented
627C2×#41—31no—
628C2×#41—33no—
629C2×#41—61no—
630C2×#41—93no—
631C2×#41—93no—
632C2×#41—181no—
633C2×#41—183no—
634C22×D4—33no—
635C22×D4—63no—
636#137—33no—
637#137—91no—
638#137—93no—
639#137—93no—
640#137—93no—
641#137—93no—
642AGL(1,ℤ/8)—33no—
643AGL(1,ℤ/8)—93no—
644AGL(1,ℤ/8)—93no—
645AGL(1,ℤ/8)—93no—
646AGL(1,ℤ/8)—93no—
647AGL(1,ℤ/8)—93no—
648AGL(1,ℤ/8)—96no—
649AGL(1,ℤ/8)—96no—
650AGL(1,ℤ/8)—96no—
651AGL(1,ℤ/8)—93no—
652AGL(1,ℤ/8)—93no—
653AGL(1,ℤ/8)—93no—
654AGL(1,ℤ/8)—93no—
655#135—33no—
656#135—93no—
657#135—96no—
658#135—96no—
659#135—93no—
660#135—93no—
661C2×SD16—33no—
662C2×SD16—96no—
663C2×SD16—93no—
664C2×D8—93no—
665C2×D8—96no—
666C2×D8—93no—
667#131—31no—
668#131—93no—
669#131—93no—
670#131—91no—
671C2×M16—93no—
672C2×M16—93no—
673C23×C3—23no—
674C23×C3—23no—
675C23×C3—33no—
676C23×C3—43no—
677C23×C3—63no—
678C23×C3—66no—
679C23×C3—63no—
680C23×C3—246no—
681C22×D3—23no—
682C22×D3—23no—
683C22×D3—26no—
684C22×D3—63no—
685C22×D3—63no—
686C22×D3—63no—
687C22×D3—63no—
688C22×D3—86no—
689C22×D3—123no—
690C22×D3C2×#6713yes—
691C3×Q8—21no—
692C3×Q8—21no—
693C3×Q8—33no—
694C3×Q8—31no—
695C3×Q8—33no—
696C3×Q8—61no—
697C3×Q8—63no—
698C3×Q8D3×D411yescharacteristic
699C3×Q8C2×#6711yescharacteristic
700C3×Q8C23×D311yescharacteristic
701C3×Q8C23×D311yescharacteristic
702C3×D4—23no—
703C3×D4—23no—
704C3×D4—23no—
705C3×D4—23no—
706C3×D4—23no—
707C3×D4—23no—
708C3×D4—36no—
709C3×D4—33no—
710C3×D4—33no—
711C3×D4—31no—
712C3×D4—43no—
713C3×D4—43no—
714C3×D4—63no—
715C3×D4—66no—
716C3×D4—63no—
717C3×D4—63no—
718C3×D4—63no—
719C3×D4—63no—
720C3×D4—63no—
721C3×D4D3×D413yes—
722C3×D4C2×#6713yes—
723C3×D4C23×D313yes—
724C3×D4C23×D313yes—
725C2×C3×C4—23no—
726C2×C3×C4—23no—
727C2×C3×C4—23no—
728C2×C3×C4—33no—
729C2×C3×C4—33no—
730C2×C3×C4—33no—
731C2×C3×C4—33no—
732C2×C3×C4—31no—
733C2×C3×C4—43no—
734C2×C3×C4—63no—
735C2×C3×C4—61no—
736C2×C3×C4—63no—
737C2×C3×C4—63no—
738C2×C3×C4—63no—
739C2×C3×C4—63no—
740C2×C3×C4C23×D313yes—
741C2×C3×C4C23×D313yes—
742#67—23no—
743#67—23no—
744#67—23no—
745#67—23no—
746#67—26no—
747#67—63no—
748#67—66no—
749#67—61no—
750#67—63no—
751#67—63no—
752#67—61no—
753#67—63no—
754#67—123no—
755#67C2×#6716yes—
756C2×Dic3—23no—
757C2×Dic3—23no—
758C2×Dic3—63no—
759C2×Dic3—61no—
760C2×Dic3C2×#6713yes—
761D12—23no—
762D12—23no—
763D12—33no—
764D12—33no—
765D12—63no—
766D12—63no—
767D12—63no—
768D12—66no—
769D12—63no—
770D12—63no—
771D12—123no—
772D12C2×#6713yes—
773D12C23×D313yes—
774D12C23×D311yescharacteristic
775C4×D3—21no—
776C4×D3—23no—
777C4×D3—23no—
778C4×D3—23no—
779C4×D3—63no—
780C4×D3—66no—
781C4×D3—61no—
782C4×D3—63no—
783C4×D3—63no—
784C4×D3—63no—
785C4×D3—63no—
786C4×D3—66no—
787C4×D3—123no—
788C4×D3C2×#6713yes—
789C4×D3C2×#6713yes—
790C4×D3C23×D313yes—
791C4×D3C23×D311yescharacteristic
792Dic6—23no—
793Dic6—21no—
794Dic6—31no—
795Dic6—31no—
796Dic6—61no—
797Dic6—63no—
798Dic6—63no—
799Dic6C2×#6713yes—
800Dic6C23×D311yescharacteristic
801Dic6C23×D313yes—
802C3×C8—33no—
803C3×C8—31no—
804C3⋊C8—33no—
805C3⋊C8—31no—
806C3⋊C8—33no—
807C3⋊C8—31no—
808C3⋊C8—61no—
809C3⋊C8—63no—
810C3⋊C8C23×D313yes—
811C3⋊C8C23×D311yescharacteristic
812C2×C32—23no—
813C2×C32—43no—
814C2×C32C23×D411yescharacteristic
815C3⋊D3—43no—
816C3×D3—23no—
817C3×D3—21no—
818C3×D3—41no—
819C3×D3—43no—
820C24—63no—
821#41—21no—
822#41—31no—
823#41—33no—
824#41—33no—
825#41—33no—
826#41—33no—
827#41—33no—
828#41—33no—
829#41—63no—
830#41—63no—
831#41—63no—
832#41—63no—
833#41—61no—
834#41—63no—
835#41—91no—
836#41—96no—
837#41—93no—
838#41—93no—
839#41—183no—
840#41—183no—
841#41—183no—
842#41—183no—
843#41—186no—
844#41—183no—
845#41—183no—
846#41—181no—
847#41C2×D3213yes—
848#41C2×D3211yescharacteristic
849C2×Q8—31no—
850C2×Q8—31no—
851C2×Q8—33no—
852C2×Q8—61no—
853C2×Q8—93no—
854C2×Q8—183no—
855C2×D4—23no—
856C2×D4—33no—
857C2×D4—36no—
858C2×D4—33no—
859C2×D4—33no—
860C2×D4—63no—
861C2×D4—63no—
862C2×D4—63no—
863C2×D4—63no—
864C2×D4—66no—
865C2×D4—63no—
866C2×D4—63no—
867C2×D4—66no—
868C2×D4—63no—
869C2×D4—93no—
870C2×D4—93no—
871C2×D4—183no—
872C2×D4—183no—
873C2×D4—186no—
874C2×D4—183no—
875C2×D4—183no—
876C2×D4C2×D3213yes—
877C22×C4—33no—
878C22×C4—63no—
879C22×C4—183no—
880C22×C4—183no—
881Q16—33no—
882Q16—91no—
883Q16—93no—
884Q16—91no—
885SD16—31no—
886SD16—33no—
887SD16—36no—
888SD16—93no—
889SD16—93no—
890SD16—96no—
891SD16—93no—
892SD16—91no—
893SD16—93no—
894SD16—93no—
895D8—33no—
896D8—93no—
897D8—96no—
898D8—93no—
899D8—96no—
900D8—93no—
901M16—33no—
902M16—91no—
903M16—93no—
904M16—93no—
905M16—93no—
906M16—93no—
907C2×C8—33no—
908C2×C8—96no—
909C2×C8—93no—
910C22×C3—23no—
911C22×C3—23no—
912C22×C3—23no—
913C22×C3—33no—
914C22×C3—31no—
915C22×C3—43no—
916C22×C3—63no—
917C22×C3—61no—
918C22×C3—83no—
919C22×C3—83no—
920C22×C3—123no—
921C22×C3—126no—
922C22×C3—163no—
923C22×C3—243no—
924C22×C3—246no—
925C22×C3C2×D3×D413yes—
926C22×C3C22×#6713yes—
927C2×D3—21no—
928C2×D3—23no—
929C2×D3—43no—
930C2×D3—46no—
931C2×D3—63no—
932C2×D3—63no—
933C2×D3—86no—
934C2×D3—83no—
935C2×D3—123no—
936C2×D3—243no—
937C2×D3—243no—
938C2×D3—243no—
939C2×D3—243no—
940C2×D3—483no—
941C2×D3C22×#6711yescharacteristic
942C2×D3C22×#6713yes—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—23no—
946C3×C4—21no—
947C3×C4—33no—
948C3×C4—31no—
949C3×C4—41no—
950C3×C4—61no—
951C3×C4—63no—
952C3×C4C2×D3×D413yes—
953C3×C4C22×#6713yes—
954C3×C4C24×D311yescharacteristic
955C3×C4C24×D311yescharacteristic
956Dic3—23no—
957Dic3—21no—
958Dic3—61no—
959Dic3—61no—
960Dic3—121no—
961Dic3C22×#6711yescharacteristic
962Dic3C22×#6713yes—
963C32#358511yescharacteristic, complemented, Sylow
964C23—23no—
965C23—33no—
966C23—63no—
967C23—66no—
968C23—63no—
969C23—183no—
970C23—183no—
971C23—246no—
972Q8—33no—
973Q8—33no—
974Q8—31no—
975Q8—61no—
976Q8—63no—
977Q8—91no—
978Q8—183no—
979Q8D3×#6711yescharacteristic
980Q8C22×D3211yescharacteristic
981D4—23no—
982D4—23no—
983D4—36no—
984D4—33no—
985D4—31no—
986D4—33no—
987D4—63no—
988D4—63no—
989D4—66no—
990D4—63no—
991D4—63no—
992D4—63no—
993D4—63no—
994D4—93no—
995D4—183no—
996D4—183no—
997D4—186no—
998D4—181no—
999D4—183no—
1000D4—183no—
1001D4D3×#6713yes—
1002D4C22×D3213yes—
1003C2×C4—23no—
1004C2×C4—33no—
1005C2×C4—33no—
1006C2×C4—33no—
1007C2×C4—33no—
1008C2×C4—31no—
1009C2×C4—63no—
1010C2×C4—61no—
1011C2×C4—63no—
1012C2×C4—63no—
1013C2×C4—63no—
1014C2×C4—63no—
1015C2×C4—183no—
1016C2×C4—186no—
1017C2×C4—181no—
1018C2×C4—183no—
1019C2×C4—183no—
1020C2×C4C22×D3213yes—
1021C8—31no—
1022C8—33no—
1023C8—93no—
1024C8—91no—
1025C2×C3—23no—
1026C2×C3—23no—
1027C2×C3—21no—
1028C2×C3—43no—
1029C2×C3—43no—
1030C2×C3—43no—
1031C2×C3—63no—
1032C2×C3—61no—
1033C2×C3—83no—
1034C2×C3—123no—
1035C2×C3—121no—
1036C2×C3C22×D3×D411yescharacteristic
1037C2×C3C23×#6711yescharacteristic
1038D3—21no—
1039D3—23no—
1040D3—41no—
1041D3—43no—
1042D3—123no—
1043D3—123no—
1044D3—243no—
1045C22—23no—
1046C22—31no—
1047C22—33no—
1048C22—61no—
1049C22—63no—
1050C22—83no—
1051C22—123no—
1052C22—126no—
1053C22—183no—
1054C22—243no—
1055C22—246no—
1056C22—723no—
1057C22—723no—
1058C22C2×D3×#6713yes—
1059C4—21no—
1060C4—31no—
1061C4—33no—
1062C4—61no—
1063C4—63no—
1064C4—181no—
1065C4C2×D3×#6713yes—
1066C4C23×D3211yescharacteristic
1067C3—21no—
1068C3#8720711yescharacteristic, complemented
1069C3#8727711yescharacteristic, complemented
1070C2—23no—
1071C2—43no—
1072C2—61no—
1073C2—63no—
1074C2—123no—
1075C2—121no—
1076C2—363no—
1077C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC2C22×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC32×H(5,𝔽2)C22
socleC2×C32C23×D4
hypercenterH(5,𝔽2)D32
hypocenterC32#3585
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. #10596697C2semidirect
3. #10596306C2semidirect
4. C3×#5836C2semidirect
5. #10595470C2semidirect
6. #10595464C2semidirect
7. #10595456C2semidirect
8. #10595453C2semidirect
9. #10595449C2semidirect
10. #10595446C2semidirect
11. #10595441C2semidirect
12. C2×#63934C2semidirect
13. #10595105C2semidirect
14. #10595097C2semidirect
15. D3×#932C2semidirect
18. C32×H(5,𝔽2)C22semidirect
19. #64366C22semidirect
20. C3×#1010C22semidirect
22. C3×#1009C22semidirect
23. C3×#1009C22semidirect
26. C3×D3×#41C22semidirect
28. C3×#1004C22semidirect
30. C2×C3×D3×D4C22semidirect
35. #64308C22semidirect
36. D3×#235C22semidirect
37. C2×#3799C22semidirect
38. #64297C22semidirect
39. #64159C22semidirect
40. #64158C22semidirect
41. #64157C22semidirect
42. #64141C22semidirect
43. C2×#3753C22semidirect
44. C3×#951C22semidirect
45. C3×#950C22semidirect
46. C3×#948C22semidirect
47. C2×C3×#214C22semidirect
48. C3×#932C22semidirect
49. #63949C22semidirect
50. #63948C22semidirect
51. #63946C22semidirect
52. #63943C22semidirect
53. #63939C22semidirect
54. #63935C22semidirect
55. #63934C22semidirect
56. #63934C22semidirect
57. #63934C22semidirect
58. #63934C22semidirect
59. #63932C22semidirect
60. #63929C22semidirect
61. D3×#214C22semidirect
62. #63925C22semidirect
63. D3×#213C22semidirect
64. #63830C22semidirect
65. #63829C22semidirect
66. #63827C22semidirect
67. C2×#3715C22semidirect
68. #63825C22semidirect
69. C2×#3714C22semidirect
70. #63823C22semidirect
71. #63822C22semidirect
72. C2×#3711C22semidirect
73. #63815C22semidirect
74. #63814C22semidirect
75. D3×#208C22semidirect
78. D3×H(5,𝔽2)D3semidirect
85. #5836D3semidirect
115. #3828C23semidirect
116. C2×C4⋊(C3⋊D3)C23semidirect
143. C3×#235C23semidirect
148. C2×C3×Dic6C23semidirect
156. D3×D12C23semidirect
162. #3799C23semidirect
167. D3×Dic6C23semidirect
168. #3756C23semidirect
169. #3755C23semidirect
170. #3754C23semidirect
171. #3753C23semidirect
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. #3715C23semidirect
187. #3715C23semidirect
188. #3715C23semidirect
189. #3714C23semidirect
190. #3714C23semidirect
191. #3713C23semidirect
194. #3711C23semidirect
195. #3711C23semidirect
196. D3×C3⋊C8C23semidirect
205. C3×H(5,𝔽2)C2×D3semidirect
206. C3×H(5,𝔽2)C2×D3semidirect
213. #1010C2×D3semidirect
221. #1009C2×D3semidirect
222. #1009C2×D3semidirect
229. D3×#41C2×D3semidirect
237. #1004C2×D3semidirect
239. C2×D3×D4C2×D3semidirect
250. #951C2×D3semidirect
259. #950C2×D3semidirect
272. #948C2×D3semidirect
279. C2×#214C2×D3semidirect
290. #932C2×D3semidirect
511. #235C22×D3semidirect
527. C2×Dic6C22×D3semidirect
541. #216C22×D3semidirect
549. #215C22×D3semidirect
557. #214C22×D3semidirect
558. #214C22×D3semidirect
569. #213C22×D3semidirect
577. #208C22×D3semidirect
582. C2×C3⋊C8C22×D3semidirect
626. H(5,𝔽2)D32semidirect
963. C32#3585semidirect
1068. C3#87207semidirect
1069. C3#87277semidirect

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
#105966972
#105963062
C3×#58362
#105954702
#105954642
#105954562
#105954532
#105954492
#105954462
#105954412
C2×#639342
#105951052
#105950972
D3×#9322
#872773
#872073