Finite Group Databasebeta

← D3×#5835 #11918803

Subgroups — D3×#5835 #11918803

Order 1152.

3158 conjugacy classes of subgroups.

The subgroup lattice has 1091 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×#1009C211yesmaximal, characteristic, complemented
3#10596306C211yesmaximal, characteristic, complemented
4C3×#5835C211yesmaximal, characteristic, complemented
5#10595456C213yesmaximal, complemented
6#10595454C213yesmaximal, complemented
7D3×#950C213yesmaximal, complemented
8D3×#949C213yesmaximal, complemented
9#10595449C211yesmaximal, characteristic, complemented
10#10595444C211yesmaximal, characteristic, complemented
11D3×#948C211yesmaximal, characteristic, complemented
12#10595097C213yesmaximal, complemented
13#10595096C213yesmaximal, complemented
14D3×#932C213yesmaximal, complemented
15C2×D3×#213C213yesmaximal, complemented
16C2×#5835—31nomaximal
17D3×#576—31nomaximal
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19#64366C2211yescharacteristic, complemented
20C3×#1009—21no—
21C3×#1009C2213yescomplemented
22C3×#1009C2211yescharacteristic, complemented
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
31#64320—21no—
32D3×#239—21no—
33#64314—23no—
34D32×D4—23no—
35#64308C2213yescomplemented
36#64307C2213yescomplemented
37D3×#235C2213yescomplemented
38C2×D3×D12C2213yescomplemented
39#64159C2213yescomplemented
40#64158C2213yescomplemented
41#64157C2211yescharacteristic, complemented
42#64141C2213yescomplemented
43C2×#3753C2213yescomplemented
44C3×#950C2213yescomplemented
45C3×#949C2213yescomplemented
46C3×#948C2211yescharacteristic, complemented
47C3×#932C2213yescomplemented
48C2×C3×#213C2213yescomplemented
49#63949C2213yescomplemented
50#63947C2213yescomplemented
51D3×#216C2211yescharacteristic, complemented
52#63939C2216yescomplemented
53D3×#215C2213yescomplemented
54#63935C2213yescomplemented
55#63934C2216yescomplemented
56#63933C2213yescomplemented
57#63932C2216yescomplemented
58D3×#214C2213yescomplemented
59#63925C2216yescomplemented
60D3×#213C2213yescomplemented
61D3×#213C2216yescomplemented
62D3×#213C2216yescomplemented
63D3×#213C2216yescomplemented
64#63830C2213yescomplemented
65#63829C2213yescomplemented
66#63825C2213yescomplemented
67C2×#3714C2213yescomplemented
68#63823C2213yescomplemented
69#63823C2213yescomplemented
70#63822C2213yescomplemented
71C2×#3713C2213yescomplemented
72#63815C2213yescomplemented
73#63814C2213yescomplemented
74D3×#208C2213yescomplemented
75C2×D3×C3⋊C8C2213yescomplemented
76C2×C3×H(5,𝔽2)—31no—
77D3×H(5,𝔽2)—31no—
78D3×H(5,𝔽2)D311yescharacteristic, complemented
79C2×#1009—31no—
80C3×#576—31no—
81#5835—31no—
82#5835—31no—
83#5835—31no—
84#5835—31no—
85#5835—33no—
86#5835—33no—
87#5835—31no—
88#5835—33no—
89#5835—33no—
90#5835—61no—
91#5835D311yescharacteristic, direct product factor
92C2×#950—33no—
93C2×#949—33no—
94C2×#948—31no—
95C2×#932—33no—
96C22×#213—33no—
97#5774—33no—
98#5774—33no—
99D3×AGL(1,ℤ/8)—33no—
100D3×AGL(1,ℤ/8)—33no—
101#5769—33no—
102D3×#135—33no—
103#5757—33no—
104C2×D3×D8—33no—
105#5752—31no—
106D3×#131—31no—
107C23×C3×D3—23no—
108C22×D32—23no—
109C32×#41—21no—
110C32×#41C2311yescharacteristic
111C32×#41C2313yescomplemented
112C2×C32×D4—23no—
113C2×C32×D4C2313yescomplemented
114#3832—21no—
115D4×C3⋊D3—23no—
116#3828C2313yescomplemented
117C2×C4⋊(C3⋊D3)C2313yescomplemented
118C2×C3×#67—26no—
119C2×C3×#67—23no—
120C3×#239—21no—
121C3×#239—21no—
122C3×#239D411yescharacteristic
123C3×#239C2313yescomplemented
124C3×D3×Q8D411yescharacteristic
125C3×D3×Q8C2311yescharacteristic
126C3×#237—23no—
127C3×#237—23no—
128C3×#237D413yes—
129C3×#237C2313yescomplemented
130C3×D3×D4—23no—
131C3×D3×D4—23no—
132C3×D3×D4—23no—
133C3×D3×D4—26no—
134C3×D3×D4—23no—
135C3×D3×D4—23no—
136C3×D3×D4—23no—
137C3×D3×D4D413yes—
138C3×D3×D4C2313yes—
139C3×D3×D4C2316yescomplemented
140C3×#235—23no—
141C3×#235—23no—
142C3×#235C2313yes—
143C3×#235C2313yescomplemented
144C3×#235C2313yescomplemented
145C2×C3×D12—23no—
146C2×C3×D12C2313yescomplemented
147C2×C3×D12C2313yescomplemented
148C2×C3×C4×D3—23no—
149C2×C3×C4×D3C2313yes—
150#3811—26no—
151D3×#67—23no—
152D3×#67—26no—
153C2×#626—23no—
154#3804—23no—
155#3802—23no—
156D3×D12—23no—
157D3×D12—23no—
158D3×D12—23no—
159D3×D12C2313yes—
160D3×D12C2316yescomplemented
161C4×D32—23no—
162#3799—23no—
163#3799C2313yescomplemented
164#3798—23no—
165#3796—23no—
166#3795C2313yescomplemented
167D3×Dic6C2311yescharacteristic
168#3756C2311yescharacteristic, complemented
169#3755C2313yescomplemented
170#3754C2313yescomplemented
171#3753C2313yescomplemented
172#3753C2316yescomplemented
173#3748C2313yescomplemented
174C2×C3⋊(C3⋊C8)C2313yescomplemented
175C3×#216C2311yescharacteristic, complemented
176C3×#215C2313yescomplemented
177C3×#214C2313yescomplemented
178C3×#213C2313yescomplemented
179C3×#213C2316yescomplemented
180C3×#208C2313yescomplemented
181C2×C3×C3⋊C8C2313yescomplemented
182#3719C2311yescharacteristic, complemented
183#3718C2311yescharacteristic, complemented
184#3717C2313yescomplemented
185#3716C2313yescomplemented
186#3715C2313yescomplemented
187#3715C2313yescomplemented
188#3714C2313yescomplemented
189#3714C2316yescomplemented
190#3713C2313yescomplemented
191#3713C2316yescomplemented
192#3711C2316yescomplemented
193D3×C3⋊C8C2311yescharacteristic
194D3×C3⋊C8C2313yes—
195D3×C3⋊C8C2313yescomplemented
196D3×C3⋊C8C2313yescomplemented
197C2×#576—91noSylow
198C3×H(5,𝔽2)—21no—
199C3×H(5,𝔽2)—31no—
200C3×H(5,𝔽2)—31no—
201C3×H(5,𝔽2)—33no—
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#1009—21no—
213#1009—31no—
214#1009—31no—
215#1009—33no—
216#1009—33no—
217#1009—33no—
218#1009—61no—
219#1009—63no—
220#1009—61no—
221#1009—61no—
222#1009C2×D313yescomplemented
223#1009C2×D311yescharacteristic, complemented
224#1009C2×D311yescharacteristic, complemented
225D3×#41—21no—
226D3×#41—33no—
227D3×#41—61no—
228D3×#41C2×D311yescharacteristic
229D3×#41C2×D313yescomplemented
230C2×#239—61no—
231#1004—23no—
232#1004—33no—
233#1004—63no—
234#1004C2×D313yescomplemented
235C2×D3×D4—23no—
236C2×D3×D4—33no—
237C2×D3×D4—63no—
238C2×D3×D4—63no—
239C2×D3×D4C2×D313yescomplemented
240C2×#235—33no—
241C22×D12—33no—
242C3×AGL(1,ℤ/8)—33no—
243C3×AGL(1,ℤ/8)—33no—
244C3×#135—33no—
245C2×C3×D8—33no—
246C3×#131—31no—
247#950—33no—
248#950—33no—
249#950—33no—
250#950—33no—
251#950—33no—
252#950—33no—
253#950—33no—
254#950—33no—
255#950—33no—
256#950—63no—
257#950C2×D313yescomplemented
258#949—33no—
259#949—33no—
260#949—33no—
261#949—33no—
262#949—36no—
263#949—36no—
264#949—33no—
265#949—63no—
266#949C2×D313yescomplemented
267#948—31no—
268#948—31no—
269#948—33no—
270#948—33no—
271#948—61no—
272#948C2×D311yescharacteristic, complemented
273C2×#216—31no—
274C2×#215—33no—
275C2×#214—33no—
276#932—33no—
277#932—33no—
278#932—33no—
279#932—33no—
280#932—36no—
281#932—36no—
282#932—33no—
283#932—63no—
284#932C2×D313yescomplemented
285C2×#213—33no—
286C2×#213—33no—
287C2×#213—33no—
288C2×#213—33no—
289C2×#213—33no—
290C2×#213—36no—
291C2×#213—36no—
292C2×#213—36no—
293C2×#213—33no—
294C2×#213—63no—
295C2×#213C2×D313yescomplemented
296C2×#208—33no—
297C22×C3⋊C8—33no—
298#919—33no—
299D3×Q16—31no—
300#916—33no—
301#916—33no—
302#914—36no—
303#914—36no—
304D3×SD16—33no—
305D3×SD16—33no—
306#912—33no—
307#911—36no—
308#911—36no—
309D3×D8—33no—
310D3×D8—36no—
311D3×D8—36no—
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×D3×C8—33no—
321C23×C32—23no—
322C22×C3⋊D3—23no—
323C22×C3×D3—23no—
324C22×C3×D3—23no—
325C22×C3×D3—23no—
326C22×C3×D3—26no—
327C22×C3×D3—86no—
328C22×C3×D3C2×D413yes—
329C2×D32—23no—
330C2×D32—26no—
331C2×D32—86no—
332C32×Q8C2×D411yescharacteristic
333C32×Q8C2411yescharacteristic
334C32×D4—23no—
335C32×D4—23no—
336C32×D4C2×D413yes—
337C32×D4C2413yes—
338C2×C32×C4—23no—
339C2×C32×C4C2413yes—
340#638—23no—
341C4⋊(C3⋊D3)—23no—
342C4⋊(C3⋊D3)C2413yes—
343C4×C3⋊D3—23no—
344#634C2411yescharacteristic
345C3×#67—23no—
346C3×#67—23no—
347C3×#67—23no—
348C3×#67—23no—
349C3×#67—26no—
350C3×#67C2×D416yes—
351C2×C3×Dic3—23no—
352C2×C3×Dic3C2×D413yes—
353C3×D12—23no—
354C3×D12—23no—
355C3×D12—23no—
356C3×D12C2×D413yes—
357C3×D12C2413yes—
358C3×D12C2413yes—
359C3×C4×D3—21no—
360C3×C4×D3—23no—
361C3×C4×D3—23no—
362C3×C4×D3—23no—
363C3×C4×D3C2×D413yes—
364C3×C4×D3C2×D413yes—
365C3×C4×D3C2411yescharacteristic
366C3×C4×D3C2413yes—
367C3×Dic6—21no—
368C3×Dic6C2×D413yes—
369C3×Dic6C2411yescharacteristic
370C3×Dic6C2411yescharacteristic
371#627—21no—
372#626—23no—
373#626—26no—
374#626—23no—
375#625—23no—
376#624—23no—
377D3×Dic3—21no—
378D3×Dic3—23no—
379C3⋊(C3⋊C8)C2411yescharacteristic
380C3⋊(C3⋊C8)C2413yes—
381C3×C3⋊C8C2411yescharacteristic
382C3×C3⋊C8C2413yes—
383C2×H(5,𝔽2)—31no—
384C2×H(5,𝔽2)—91no—
385#576—31no—
386#576—91no—
387#576—93no—
388#576—93no—
389#576—93no—
390#576—93no—
391#576—91no—
392#576—91no—
393C2×AGL(1,ℤ/8)—93no—
394C2×AGL(1,ℤ/8)—93no—
395C2×#135—93no—
396C22×D8—93no—
397C2×#131—91no—
398C24×C3—63no—
399C23×D3—23no—
400C23×D3—63no—
401C23×D3—63no—
402C3×#41—21no—
403C3×#41—21no—
404C3×#41—21no—
405C3×#41—23no—
406C3×#41—31no—
407C3×#41—33no—
408C3×#41—33no—
409C3×#41—33no—
410C3×#41—33no—
411C3×#41—33no—
412C3×#41—33no—
413C3×#41—41no—
414C3×#41—63no—
415C3×#41—63no—
416C3×#41—63no—
417C3×#41—63no—
418C3×#41—61no—
419C3×#41—61no—
420C3×#41C22×D311yescharacteristic
421C3×#41C22×D311yescharacteristic
422C3×#41C22×D313yescomplemented
423C3×#41C22×D313yescomplemented
424C2×C3×Q8—31no—
425C2×C3×Q8—31no—
426C2×C3×D4—23no—
427C2×C3×D4—23no—
428C2×C3×D4—23no—
429C2×C3×D4—33no—
430C2×C3×D4—33no—
431C2×C3×D4—36no—
432C2×C3×D4—33no—
433C2×C3×D4—33no—
434C2×C3×D4—43no—
435C2×C3×D4—63no—
436C2×C3×D4—63no—
437C2×C3×D4—63no—
438C2×C3×D4—63no—
439C2×C3×D4—66no—
440C2×C3×D4—63no—
441C2×C3×D4—63no—
442C2×C3×D4—66no—
443C2×C3×D4—63no—
444C2×C3×D4—63no—
445C2×C3×D4C22×D313yescomplemented
446C2×C3×D4C22×D313yescomplemented
447C22×C3×C4—33no—
448C22×C3×C4—63no—
449C2×#67—26no—
450C2×#67—23no—
451C2×#67—63no—
452C2×#67—66no—
453C2×#67—63no—
454#239—21no—
455#239—21no—
456#239—33no—
457#239—63no—
458#239—63no—
459#239—61no—
460#239—61no—
461#239—121no—
462#239#6711yescharacteristic
463#239C22×D313yescomplemented
464D3×Q8—31no—
465D3×Q8#6711yescharacteristic
466D3×Q8C22×D311yescharacteristic
467#237—23no—
468#237—23no—
469#237—33no—
470#237—63no—
471#237—63no—
472#237#6713yes—
473#237C22×D313yescomplemented
474D3×D4—23no—
475D3×D4—23no—
476D3×D4—23no—
477D3×D4—26no—
478D3×D4—23no—
479D3×D4—23no—
480D3×D4—23no—
481D3×D4—33no—
482D3×D4—36no—
483D3×D4—63no—
484D3×D4—63no—
485D3×D4—66no—
486D3×D4—66no—
487D3×D4—63no—
488D3×D4—63no—
489D3×D4—63no—
490D3×D4—66no—
491D3×D4—63no—
492D3×D4—63no—
493D3×D4—63no—
494D3×D4—123no—
495D3×D4#6713yes—
496D3×D4C22×D313yes—
497D3×D4C22×D316yescomplemented
498#235—23no—
499#235—23no—
500#235—33no—
501#235—33no—
502#235—33no—
503#235—33no—
504#235—63no—
505#235—63no—
506#235—63no—
507#235—63no—
508#235—63no—
509#235C22×D313yes—
510#235C22×D313yescomplemented
511#235C22×D313yescomplemented
512C2×D12—23no—
513C2×D12—33no—
514C2×D12—33no—
515C2×D12—33no—
516C2×D12—36no—
517C2×D12—63no—
518C2×D12—63no—
519C2×D12—63no—
520C2×D12—63no—
521C2×D12—63no—
522C2×D12C22×D313yescomplemented
523C2×D12C22×D313yescomplemented
524C2×C4×D3—23no—
525C2×C4×D3—63no—
526C2×C4×D3—63no—
527C2×C4×D3C22×D313yes—
528C2×Dic6—31no—
529C3×Q16—31no—
530C3×SD16—33no—
531C3×SD16—33no—
532C3×D8—33no—
533C3×D8—36no—
534C3×M16—33no—
535C2×C3×C8—33no—
536#216—31no—
537#216—31no—
538#216—31no—
539#216—31no—
540#216—31no—
541#216—61no—
542#216C22×D311yescharacteristic, complemented
543#215—33no—
544#215—33no—
545#215—33no—
546#215—33no—
547#215—33no—
548#215—63no—
549#215C22×D313yescomplemented
550#214—33no—
551#214—33no—
552#214—33no—
553#214—33no—
554#214—33no—
555#214—63no—
556#214C22×D313yescomplemented
557#213—33no—
558#213—36no—
559#213—33no—
560#213—36no—
561#213—33no—
562#213—36no—
563#213—33no—
564#213—36no—
565#213—33no—
566#213—36no—
567#213—63no—
568#213—66no—
569#213C22×D313yescomplemented
570#213C22×D316yescomplemented
571#208—33no—
572#208—33no—
573#208—36no—
574#208—63no—
575#208C22×D313yescomplemented
576C2×C3⋊C8—33no—
577C2×C3⋊C8—33no—
578C2×C3⋊C8—31no—
579C2×C3⋊C8—33no—
580C2×C3⋊C8—33no—
581C2×C3⋊C8—33no—
582C2×C3⋊C8—63no—
583C2×C3⋊C8C22×D313yescomplemented
584Dic12—31no—
585D24—33no—
586D24—36no—
587#204—33no—
588#204—33no—
589ΓL(1,𝔽25)—36no—
590D3×C8—31no—
591D3×C8—33no—
592D3×C8—33no—
593D3×C8—33no—
594C22×C32—23no—
595C22×C32—83no—
596C22×C32C22×D413yes—
597C2×C3⋊D3—23no—
598C2×C3⋊D3—83no—
599C2×C3×D3—26no—
600C2×C3×D3—23no—
601C2×C3×D3—23no—
602C2×C3×D3—46no—
603C2×C3×D3—86no—
604C2×C3×D3—83no—
605C2×C3×D3—83no—
606C2×C3×D3C22×D413yes—
607C2×C3×D3C22×D411yescharacteristic
608D32—46no—
609D32—86no—
610C32×C4—21no—
611C32×C4C22×D413yes—
612C32×C4C2511yescharacteristic
613C3⋊Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3C22×D413yes—
617C3×Dic3C22×D411yescharacteristic
618H(5,𝔽2)—31no—
619H(5,𝔽2)—31no—
620H(5,𝔽2)—33no—
621H(5,𝔽2)—33no—
622H(5,𝔽2)—63no—
623H(5,𝔽2)—61no—
624H(5,𝔽2)—93no—
625H(5,𝔽2)—93no—
626H(5,𝔽2)—91no—
627H(5,𝔽2)—183no—
628H(5,𝔽2)—181no—
629H(5,𝔽2)D3211yescharacteristic, complemented
630C2×#41—31no—
631C2×#41—33no—
632C2×#41—61no—
633C2×#41—93no—
634C2×#41—181no—
635C22×D4—33no—
636C22×D4—63no—
637C22×D4—93no—
638C22×D4—183no—
639AGL(1,ℤ/8)—33no—
640AGL(1,ℤ/8)—33no—
641AGL(1,ℤ/8)—93no—
642AGL(1,ℤ/8)—93no—
643AGL(1,ℤ/8)—96no—
644AGL(1,ℤ/8)—96no—
645AGL(1,ℤ/8)—96no—
646AGL(1,ℤ/8)—96no—
647AGL(1,ℤ/8)—93no—
648AGL(1,ℤ/8)—93no—
649AGL(1,ℤ/8)—93no—
650AGL(1,ℤ/8)—93no—
651#135—33no—
652#135—93no—
653#135—93no—
654#135—93no—
655#135—93no—
656#135—93no—
657#135—93no—
658#135—93no—
659C2×Q16—91no—
660C2×SD16—93no—
661C2×SD16—93no—
662C2×D8—33no—
663C2×D8—93no—
664C2×D8—93no—
665C2×D8—96no—
666C2×D8—96no—
667C2×D8—96no—
668C2×D8—93no—
669C2×D8—93no—
670#131—31no—
671#131—93no—
672#131—93no—
673#131—91no—
674C2×M16—93no—
675C22×C8—93no—
676C23×C3—23no—
677C23×C3—23no—
678C23×C3—33no—
679C23×C3—43no—
680C23×C3—63no—
681C23×C3—66no—
682C23×C3—63no—
683C23×C3—63no—
684C23×C3—246no—
685C22×D3—23no—
686C22×D3—23no—
687C22×D3—23no—
688C22×D3—26no—
689C22×D3—63no—
690C22×D3—66no—
691C22×D3—63no—
692C22×D3—63no—
693C22×D3—63no—
694C22×D3—66no—
695C22×D3—86no—
696C22×D3—123no—
697C22×D3—246no—
698C22×D3—246no—
699C22×D3C2×#6713yes—
700C3×Q8—21no—
701C3×Q8—21no—
702C3×Q8—33no—
703C3×Q8—31no—
704C3×Q8—31no—
705C3×Q8—61no—
706C3×Q8D3×D411yescharacteristic
707C3×Q8C2×#6711yescharacteristic
708C3×Q8C23×D311yescharacteristic
709C3×Q8C23×D311yescharacteristic
710C3×D4—23no—
711C3×D4—23no—
712C3×D4—23no—
713C3×D4—23no—
714C3×D4—23no—
715C3×D4—23no—
716C3×D4—36no—
717C3×D4—33no—
718C3×D4—33no—
719C3×D4—33no—
720C3×D4—43no—
721C3×D4—43no—
722C3×D4—63no—
723C3×D4—63no—
724C3×D4—66no—
725C3×D4—63no—
726C3×D4—63no—
727C3×D4—63no—
728C3×D4—63no—
729C3×D4—63no—
730C3×D4D3×D413yes—
731C3×D4C2×#6713yes—
732C3×D4C23×D313yes—
733C3×D4C23×D313yes—
734C2×C3×C4—23no—
735C2×C3×C4—23no—
736C2×C3×C4—23no—
737C2×C3×C4—33no—
738C2×C3×C4—33no—
739C2×C3×C4—33no—
740C2×C3×C4—31no—
741C2×C3×C4—33no—
742C2×C3×C4—43no—
743C2×C3×C4—63no—
744C2×C3×C4—61no—
745C2×C3×C4—63no—
746C2×C3×C4—63no—
747C2×C3×C4—63no—
748C2×C3×C4C23×D313yes—
749C2×C3×C4C23×D313yes—
750#67—23no—
751#67—23no—
752#67—23no—
753#67—23no—
754#67—26no—
755#67—63no—
756#67—63no—
757#67—63no—
758#67—63no—
759#67—63no—
760#67—63no—
761#67—66no—
762#67—123no—
763#67C2×#6716yes—
764C2×Dic3—23no—
765C2×Dic3—61no—
766C2×Dic3—63no—
767C2×Dic3C2×#6713yes—
768D12—23no—
769D12—23no—
770D12—23no—
771D12—33no—
772D12—33no—
773D12—63no—
774D12—63no—
775D12—66no—
776D12—63no—
777D12—63no—
778D12—63no—
779D12—123no—
780D12C2×#6713yes—
781D12C23×D313yes—
782D12C23×D313yes—
783C4×D3—21no—
784C4×D3—23no—
785C4×D3—23no—
786C4×D3—23no—
787C4×D3—63no—
788C4×D3—63no—
789C4×D3—61no—
790C4×D3—63no—
791C4×D3—63no—
792C4×D3—63no—
793C4×D3—123no—
794C4×D3C2×#6713yes—
795C4×D3C2×#6713yes—
796C4×D3C23×D311yescharacteristic
797C4×D3C23×D313yes—
798Dic6—21no—
799Dic6—31no—
800Dic6—31no—
801Dic6—61no—
802Dic6—61no—
803Dic6—61no—
804Dic6C2×#6713yes—
805Dic6C23×D311yescharacteristic
806Dic6C23×D311yescharacteristic
807C3×C8—31no—
808C3×C8—33no—
809C3⋊C8—31no—
810C3⋊C8—33no—
811C3⋊C8—31no—
812C3⋊C8—33no—
813C3⋊C8—61no—
814C3⋊C8—63no—
815C3⋊C8C23×D311yescharacteristic
816C3⋊C8C23×D313yes—
817C2×C32—23no—
818C2×C32—43no—
819C2×C32C23×D411yescharacteristic
820C3⋊D3—43no—
821C3×D3—23no—
822C3×D3—43no—
823C3×D3—43no—
824C3×D3#57612yescomplemented
825C24—63no—
826C24—183no—
827#41—21no—
828#41—31no—
829#41—33no—
830#41—33no—
831#41—33no—
832#41—33no—
833#41—33no—
834#41—33no—
835#41—63no—
836#41—63no—
837#41—63no—
838#41—63no—
839#41—61no—
840#41—61no—
841#41—93no—
842#41—93no—
843#41—93no—
844#41—183no—
845#41—183no—
846#41—183no—
847#41—183no—
848#41—181no—
849#41C2×D3211yescharacteristic
850#41C2×D3213yescomplemented
851C2×Q8—31no—
852C2×Q8—31no—
853C2×Q8—91no—
854C2×D4—23no—
855C2×D4—33no—
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—63no—
870C2×D4—93no—
871C2×D4—96no—
872C2×D4—93no—
873C2×D4—183no—
874C2×D4—183no—
875C2×D4—183no—
876C2×D4—183no—
877C2×D4—186no—
878C2×D4—183no—
879C2×D4—186no—
880C2×D4—183no—
881C2×D4—183no—
882C2×D4C2×D3213yescomplemented
883C22×C4—33no—
884C22×C4—63no—
885C22×C4—183no—
886Q16—31no—
887Q16—91no—
888Q16—91no—
889Q16—91no—
890SD16—33no—
891SD16—33no—
892SD16—93no—
893SD16—93no—
894SD16—93no—
895SD16—93no—
896SD16—93no—
897SD16—93no—
898D8—33no—
899D8—36no—
900D8—93no—
901D8—96no—
902D8—93no—
903D8—96no—
904D8—93no—
905D8—96no—
906M16—33no—
907M16—96no—
908M16—93no—
909C2×C8—33no—
910C2×C8—91no—
911C2×C8—93no—
912C2×C8—93no—
913C2×C8—93no—
914C2×C8—93no—
915C22×C3—23no—
916C22×C3—23no—
917C22×C3—23no—
918C22×C3—31no—
919C22×C3—33no—
920C22×C3—43no—
921C22×C3—66no—
922C22×C3—63no—
923C22×C3—63no—
924C22×C3—83no—
925C22×C3—83no—
926C22×C3—126no—
927C22×C3—163no—
928C22×C3—243no—
929C22×C3—243no—
930C22×C3—246no—
931C22×C3C2×D3×D413yes—
932C22×C3C22×#6713yes—
933C2×D3—26no—
934C2×D3—23no—
935C2×D3—23no—
936C2×D3—46no—
937C2×D3—63no—
938C2×D3—63no—
939C2×D3—86no—
940C2×D3—83no—
941C2×D3—83no—
942C2×D3—123no—
943C2×D3—126no—
944C2×D3—126no—
945C2×D3—246no—
946C2×D3—246no—
947C2×D3—243no—
948C2×D3—243no—
949C2×D3—483no—
950C2×D3C22×#6713yes—
951C2×D3C22×#6711yescharacteristic
952C3×C4—21no—
953C3×C4—21no—
954C3×C4—23no—
955C3×C4—21no—
956C3×C4—31no—
957C3×C4—33no—
958C3×C4—41no—
959C3×C4—61no—
960C3×C4—61no—
961C3×C4C2×D3×D413yes—
962C3×C4C22×#6713yes—
963C3×C4C24×D311yescharacteristic
964C3×C4C24×D311yescharacteristic
965Dic3—21no—
966Dic3—21no—
967Dic3—61no—
968Dic3—61no—
969Dic3—121no—
970Dic3C22×#6711yescharacteristic
971Dic3C22×#6713yes—
972C32C2×#57611yescharacteristic, complemented, Sylow
973C23—23no—
974C23—33no—
975C23—63no—
976C23—66no—
977C23—63no—
978C23—63no—
979C23—183no—
980C23—186no—
981C23—183no—
982C23—246no—
983C23—726no—
984Q8—33no—
985Q8—31no—
986Q8—31no—
987Q8—61no—
988Q8—91no—
989Q8—181no—
990Q8D3×#6711yescharacteristic
991Q8C22×D3211yescharacteristic
992D4—23no—
993D4—23no—
994D4—36no—
995D4—33no—
996D4—33no—
997D4—33no—
998D4—63no—
999D4—63no—
1000D4—66no—
1001D4—63no—
1002D4—63no—
1003D4—63no—
1004D4—63no—
1005D4—63no—
1006D4—93no—
1007D4—183no—
1008D4—186no—
1009D4—183no—
1010D4—183no—
1011D4—183no—
1012D4—183no—
1013D4D3×#6713yes—
1014D4C22×D3213yes—
1015C2×C4—23no—
1016C2×C4—33no—
1017C2×C4—33no—
1018C2×C4—33no—
1019C2×C4—31no—
1020C2×C4—33no—
1021C2×C4—63no—
1022C2×C4—61no—
1023C2×C4—63no—
1024C2×C4—63no—
1025C2×C4—63no—
1026C2×C4—183no—
1027C2×C4—183no—
1028C2×C4—181no—
1029C2×C4—183no—
1030C2×C4C22×D3213yes—
1031C8—31no—
1032C8—33no—
1033C8—91no—
1034C8—93no—
1035C2×C3—23no—
1036C2×C3—23no—
1037C2×C3—21no—
1038C2×C3—32no—
1039C2×C3—43no—
1040C2×C3—43no—
1041C2×C3—43no—
1042C2×C3—63no—
1043C2×C3—83no—
1044C2×C3—123no—
1045C2×C3—123no—
1046C2×C3C22×D3×D411yescharacteristic
1047C2×C3C23×#6711yescharacteristic
1048D3—23no—
1049D3—43no—
1050D3—43no—
1051D3—123no—
1052D3—123no—
1053D3—243no—
1054D3#583512yesdirect product factor
1055C22—23no—
1056C22—31no—
1057C22—33no—
1058C22—66no—
1059C22—63no—
1060C22—63no—
1061C22—83no—
1062C22—126no—
1063C22—183no—
1064C22—243no—
1065C22—243no—
1066C22—246no—
1067C22—366no—
1068C22—723no—
1069C22—726no—
1070C22C2×D3×#6713yes—
1071C4—21no—
1072C4—31no—
1073C4—33no—
1074C4—61no—
1075C4—61no—
1076C4—181no—
1077C4C2×D3×#6713yes—
1078C4C23×D3211yescharacteristic
1079C3—21no—
1080C3D3×#57611yescharacteristic, complemented
1081C3C2×#583511yescharacteristic, complemented
1082C2—23no—
1083C2—32no—
1084C2—43no—
1085C2—63no—
1086C2—123no—
1087C2—123no—
1088C2—363no—
1089C2C22×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×#576
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×#1009C2semidirect
3. #10596306C2semidirect
4. C3×#5835C2semidirect
5. #10595456C2semidirect
6. #10595454C2semidirect
7. D3×#950C2semidirect
8. D3×#949C2semidirect
9. #10595449C2semidirect
10. #10595444C2semidirect
11. D3×#948C2semidirect
12. #10595097C2semidirect
13. #10595096C2semidirect
14. D3×#932C2semidirect
15. C2×D3×#213C2semidirect
18. C32×H(5,𝔽2)C22semidirect
19. #64366C22semidirect
21. C3×#1009C22semidirect
22. C3×#1009C22semidirect
23. C3×#1009C22semidirect
26. C3×D3×#41C22semidirect
28. C3×#1004C22semidirect
30. C2×C3×D3×D4C22semidirect
35. #64308C22semidirect
36. #64307C22semidirect
37. D3×#235C22semidirect
38. C2×D3×D12C22semidirect
39. #64159C22semidirect
40. #64158C22semidirect
41. #64157C22semidirect
42. #64141C22semidirect
43. C2×#3753C22semidirect
44. C3×#950C22semidirect
45. C3×#949C22semidirect
46. C3×#948C22semidirect
47. C3×#932C22semidirect
48. C2×C3×#213C22semidirect
49. #63949C22semidirect
50. #63947C22semidirect
51. D3×#216C22semidirect
52. #63939C22semidirect
53. D3×#215C22semidirect
54. #63935C22semidirect
55. #63934C22semidirect
56. #63933C22semidirect
57. #63932C22semidirect
58. D3×#214C22semidirect
59. #63925C22semidirect
60. D3×#213C22semidirect
61. D3×#213C22semidirect
62. D3×#213C22semidirect
63. D3×#213C22semidirect
64. #63830C22semidirect
65. #63829C22semidirect
66. #63825C22semidirect
67. C2×#3714C22semidirect
68. #63823C22semidirect
69. #63823C22semidirect
70. #63822C22semidirect
71. C2×#3713C22semidirect
72. #63815C22semidirect
73. #63814C22semidirect
74. D3×#208C22semidirect
75. C2×D3×C3⋊C8C22semidirect
78. D3×H(5,𝔽2)D3semidirect
91. #5835D3direct (N × H)
111. C32×#41C23semidirect
113. C2×C32×D4C23semidirect
116. #3828C23semidirect
117. C2×C4⋊(C3⋊D3)C23semidirect
123. C3×#239C23semidirect
129. C3×#237C23semidirect
139. C3×D3×D4C23semidirect
143. C3×#235C23semidirect
144. C3×#235C23semidirect
146. C2×C3×D12C23semidirect
147. C2×C3×D12C23semidirect
160. D3×D12C23semidirect
163. #3799C23semidirect
166. #3795C23semidirect
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×#213C23semidirect
179. C3×#213C23semidirect
180. C3×#208C23semidirect
181. C2×C3×C3⋊C8C23semidirect
182. #3719C23semidirect
183. #3718C23semidirect
184. #3717C23semidirect
185. #3716C23semidirect
186. #3715C23semidirect
187. #3715C23semidirect
188. #3714C23semidirect
189. #3714C23semidirect
190. #3713C23semidirect
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
222. #1009C2×D3semidirect
223. #1009C2×D3semidirect
224. #1009C2×D3semidirect
229. D3×#41C2×D3semidirect
234. #1004C2×D3semidirect
239. C2×D3×D4C2×D3semidirect
257. #950C2×D3semidirect
266. #949C2×D3semidirect
272. #948C2×D3semidirect
284. #932C2×D3semidirect
295. C2×#213C2×D3semidirect
422. C3×#41C22×D3semidirect
423. C3×#41C22×D3semidirect
445. C2×C3×D4C22×D3semidirect
446. C2×C3×D4C22×D3semidirect
463. #239C22×D3semidirect
473. #237C22×D3semidirect
497. D3×D4C22×D3semidirect
510. #235C22×D3semidirect
511. #235C22×D3semidirect
522. C2×D12C22×D3semidirect
523. C2×D12C22×D3semidirect
542. #216C22×D3semidirect
549. #215C22×D3semidirect
556. #214C22×D3semidirect
569. #213C22×D3semidirect
570. #213C22×D3semidirect
575. #208C22×D3semidirect
583. C2×C3⋊C8C22×D3semidirect
629. H(5,𝔽2)D32semidirect
824. C3×D3#576semidirect
850. #41C2×D32semidirect
882. C2×D4C2×D32semidirect
972. C32C2×#576semidirect
1054. D3#5835direct (N × H)
1080. C3D3×#576semidirect
1081. C3C2×#5835semidirect

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×#10092
#105963062
C3×#58352
#105954562
#105954542
D3×#9502
D3×#9492
#105954492
#105954442
D3×#9482
#105950972
#105950962
D3×#9322
C2×D3×#2132
C2×#58353
D3×#5763