Finite Group Databasebeta

← #13177989

Subgroups — #13177989

Order 1728.

1820 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D3×#41C211yesmaximal, characteristic, complemented
2D3×#3828C211yesmaximal, characteristic, complemented
3#11723991C211yesmaximal, characteristic, complemented
4C3×#64159C211yesmaximal, characteristic, complemented
5#11723581C211yesmaximal, characteristic, complemented
6#11723579C211yesmaximal, characteristic, complemented
7#11723574C211yesmaximal, characteristic, complemented
8#11723568C211yesmaximal, characteristic, complemented
9#11723557C211yesmaximal, characteristic, complemented
10#11723555C211yesmaximal, characteristic, complemented
11#11723550C211yesmaximal, characteristic, complemented
12#11723544C211yesmaximal, characteristic, complemented
13#11723377C211yesmaximal, characteristic, complemented
14#11723363C211yesmaximal, characteristic, complemented
15C2×#88786C211yesmaximal, characteristic, complemented
16#10596293—31nomaximal
17#10595453—34nomaximal
18C33×#41C2211yescharacteristic, complemented
19#89076C2211yescharacteristic, complemented
20C3×#3828C2211yescharacteristic, complemented
21C32×#239C2211yescharacteristic
22C32×D3×Q8C2211yescharacteristic, complemented
23C32×#237—21no—
24C32×#237C2211yescharacteristic
25C32×D3×D4—21no—
26C32×D3×D4C2211yescharacteristic, complemented
27C32×#235—21no—
28C32×#235C2211yescharacteristic, complemented
29C2×C32×C4×D3—21no—
30C2×C32×C4×D3C2211yescharacteristic
31D3×#638—21no—
32#89031—21no—
33D3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
34C4×D3×C3⋊D3—21no—
35#89022C2211yescharacteristic
36#89021C2211yescharacteristic
37#89020—21no—
38D3×#634C2211yescharacteristic, complemented
39#88863C2211yescharacteristic, complemented
40#88862C2211yescharacteristic, complemented
41#88861C2211yescharacteristic, complemented
42#88860C2211yescharacteristic, complemented
43C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
44C3×#3756C2211yescharacteristic, complemented
45C3×#3755C2211yescharacteristic, complemented
46C3×#3754C2211yescharacteristic, complemented
47C3×#3753C2211yescharacteristic, complemented
48C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
49#88799C2211yescharacteristic, complemented
50#88798C2211yescharacteristic, complemented
51#88795C2211yescharacteristic, complemented
52#88794C2211yescharacteristic, complemented
53#88793C2211yescharacteristic, complemented
54#88792C2211yescharacteristic, complemented
55#88790C2211yescharacteristic, complemented
56#88789C2211yescharacteristic, complemented
57#88786C2211yescharacteristic, complemented
58#88786C2211yescharacteristic, complemented
59#88786C2211yescharacteristic, complemented
60#88786C2211yescharacteristic, complemented
61C2×C32×#41—31no—
62C2×#3828—31no—
63C3×D3×#41D314yescomplemented
64D3×#235—34no—
65#64160—31no—
66#64160—31no—
67#64159—31no—
68#64159—31no—
69#64159—34no—
70#64159—31no—
71#64159—64no—
72#64159D311yescharacteristic, complemented
73#64158—31no—
74#64158—31no—
75#64151—31no—
76#64151—31no—
77#64141—31no—
78#64141—31no—
79C2×#3748—31no—
80C3×#950—34no—
81#63948—34no—
82#63946—34no—
83#63943—34no—
84#63939—34no—
85#63934—34no—
86#63932—34no—
87#63929—34no—
88#63925—34no—
89#63829—34no—
90#63822—34no—
91C2×#3711—34no—
92C22×C32×D3—21no—
93C22×C32×D3D411yescharacteristic
94C2×D3×C3⋊D3—21no—
95C33×Q8C2311yescharacteristic
96C33×D4—21no—
97C33×D4C2311yescharacteristic
98C2×C33×C4—21no—
99C2×C33×C4C2311yescharacteristic
100#6312—21no—
101C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic
102C4×C3⋊(C3⋊D3)—21no—
103#6308C2311yescharacteristic
104C3×#638—21no—
105C3×C4⋊(C3⋊D3)C2311yescharacteristic
106C3×C4×C3⋊D3—21no—
107C3×#634C2311yescharacteristic
108C32×#67—21no—
109C32×#67—21no—
110C32×#67—21no—
111C2×C32×Dic3—21no—
112C2×C32×Dic3D411yescharacteristic
113C32×D12—21no—
114C32×D12C2311yescharacteristic
115C32×C4×D3—21no—
116C32×C4×D3—21no—
117C32×C4×D3—21no—
118C32×C4×D3D411yescharacteristic
119C32×C4×D3D411yescharacteristic
120C32×C4×D3C2311yescharacteristic
121C32×C4×D3C2311yescharacteristic
122C32×Dic6—21no—
123C32×Dic6C2311yescharacteristic
124#6293—21no—
125#6292—21no—
126#6291—21no—
127#6290—21no—
128#6289—21no—
129Dic3×C3⋊D3—21no—
130D3×C3⋊Dic3—21no—
131C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
132C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
133C3×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×C3⋊(C3⋊C8)C2311yescharacteristic
135#5822—94no—
136#5768—91no—
137C32×#41—24no—
138C32×#41—31no—
139C32×#41—31no—
140C32×#41—31no—
141C32×#41—61no—
142C32×#41—61no—
143C32×#41C2×D314yescomplemented
144C32×#41C2×D311yescharacteristic, complemented
145C2×C32×Q8—31no—
146C2×C32×D4—31no—
147C2×C32×D4—61no—
148C22×C32×C4—31no—
149C22×C32×C4—61no—
150C2×#638—61no—
151#3828—31no—
152#3828—34no—
153#3828—31no—
154#3828—31no—
155#3828—61no—
156#3828—61no—
157#3828—64no—
158#3828C2×D311yescharacteristic, complemented
159C2×C4⋊(C3⋊D3)—31no—
160C2×C4×C3⋊D3—61no—
161C2×#634—31no—
162C3×#239C2×D314yes—
163C3×D3×Q8C2×D314yescomplemented
164C3×#237—24no—
165C3×#237C2×D314yes—
166C3×D3×D4—24no—
167C3×D3×D4C2×D314yescomplemented
168C3×#235—24no—
169C3×#235—34no—
170C3×#235C2×D314yescomplemented
171C2×C3×C4×D3—24no—
172C2×C3×C4×D3C2×D314yes—
173D3×#67—64no—
174#3804—64no—
175D3×D12—34no—
176C4×D32—64no—
177#3799—34no—
178#3798—64no—
179#3795—34no—
180D3×Dic6—34no—
181#3756—31no—
182#3756—34no—
183#3756—31no—
184#3756—31no—
185#3756—64no—
186#3756C2×D311yescharacteristic, complemented
187#3755—31no—
188#3755—34no—
189#3755—31no—
190#3755—31no—
191#3755—64no—
192#3755C2×D311yescharacteristic, complemented
193#3754—31no—
194#3754—34no—
195#3754—31no—
196#3754—31no—
197#3754—64no—
198#3754C2×D311yescharacteristic, complemented
199#3753—31no—
200#3753—34no—
201#3753—31no—
202#3753—31no—
203#3753—64no—
204#3753C2×D311yescharacteristic, complemented
205#3748—31no—
206#3748—31no—
207#3748—31no—
208#3748—31no—
209C2×C3⋊(C3⋊C8)—31no—
210C2×C3⋊(C3⋊C8)—34no—
211C2×C3⋊(C3⋊C8)—64no—
212C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
213C3×#216—34no—
214C3×#215—34no—
215C3×#214—34no—
216C3×#213—34no—
217C2×C3×C3⋊C8—34no—
218#3719—34no—
219#3718—34no—
220#3717—34no—
221#3716—34no—
222#3715—34no—
223#3715—34no—
224#3714—34no—
225#3713—34no—
226#3711—34no—
227#3711—34no—
228#3711—34no—
229#3711—34no—
230C22×C33—21no—
231C22×C33C2×D411yescharacteristic
232C2×C3⋊(C3⋊D3)—21no—
233C2×C3×C3⋊D3—21no—
234C2×C32×D3—21no—
235C2×C32×D3—41no—
236C2×C32×D3—42no—
237C2×C32×D3C2×D411yescharacteristic
238C2×C32×D3C2×D411yescharacteristic
239D3×C3⋊D3—42no—
240C33×C4—21no—
241C33×C4C2×D411yescharacteristic
242C33×C4C2411yescharacteristic
243C3⋊(C3⋊Dic3)—21no—
244C3×C3⋊Dic3—21no—
245C32×Dic3—21no—
246C32×Dic3C2×D411yescharacteristic
247C32×Dic3C2×D411yescharacteristic
248C2×C3×#41—34no—
249D3×#41—91no—
250D3×#41C3⋊D311yescharacteristic, complemented
251C2×#235—94no—
252C3×#135—91no—
253#951—94no—
254#951—94no—
255#950—34no—
256#950—94no—
257#950—94no—
258#950—94no—
259#950—91no—
260#950—91no—
261#950—184no—
262#949—94no—
263#949—94no—
264#942—94no—
265#942—94no—
266#932—94no—
267#932—94no—
268C2×#208—94no—
269#918—91no—
270#918—91no—
271#915—91no—
272#915—91no—
273#914—91no—
274#914—91no—
275#911—91no—
276#911—91no—
277#904—91no—
278C2×ΓL(1,𝔽25)—91no—
279C23×C32—31no—
280C23×C32—61no—
281C22×C3⋊D3—61no—
282C22×C3×D3—24no—
283C22×C3×D3#6714yes—
284C2×D32—64no—
285C32×Q8—24no—
286C32×Q8—31no—
287C32×Q8—61no—
288C32×Q8C22×D314yes—
289C32×Q8C22×D311yescharacteristic
290C32×D4—21no—
291C32×D4—24no—
292C32×D4—24no—
293C32×D4—31no—
294C32×D4—44no—
295C32×D4—61no—
296C32×D4—61no—
297C32×D4—61no—
298C32×D4—61no—
299C32×D4C22×D314yes—
300C32×D4C22×D311yescharacteristic
301C2×C32×C4—21no—
302C2×C32×C4—24no—
303C2×C32×C4—24no—
304C2×C32×C4—31no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—31no—
308C2×C32×C4—31no—
309C2×C32×C4—44no—
310C2×C32×C4—61no—
311C2×C32×C4—61no—
312C2×C32×C4—61no—
313C2×C32×C4—61no—
314C2×C32×C4C22×D314yes—
315C2×C32×C4C22×D311yescharacteristic
316#638—21no—
317#638—61no—
318#638—61no—
319#638—61no—
320#638—64no—
321#638—124no—
322C2×C3⋊Dic3—61no—
323C4⋊(C3⋊D3)—31no—
324C4⋊(C3⋊D3)—34no—
325C4⋊(C3⋊D3)—64no—
326C4⋊(C3⋊D3)—61no—
327C4⋊(C3⋊D3)C22×D311yescharacteristic
328C4×C3⋊D3—21no—
329C4×C3⋊D3—61no—
330C4×C3⋊D3—61no—
331C4×C3⋊D3—61no—
332C4×C3⋊D3—64no—
333C4×C3⋊D3—124no—
334#634—31no—
335#634—34no—
336#634—64no—
337#634—61no—
338#634C22×D311yescharacteristic
339C3×#67—24no—
340C3×#67—24no—
341C3×#67—24no—
342C3×#67—64no—
343C2×C3×Dic3—24no—
344C2×C3×Dic3#6714yes—
345C3×D12—24no—
346C3×D12—34no—
347C3×D12C22×D314yes—
348C3×C4×D3—24no—
349C3×C4×D3—24no—
350C3×C4×D3—24no—
351C3×C4×D3—64no—
352C3×C4×D3#6714yes—
353C3×C4×D3#6714yes—
354C3×C4×D3C22×D314yes—
355C3×C4×D3C22×D314yes—
356C3×Dic6—24no—
357C3×Dic6—34no—
358C3×Dic6C22×D314yes—
359#627—64no—
360#626—64no—
361#626—64no—
362#625—64no—
363#624—64no—
364D3×Dic3—64no—
365D3×Dic3—64no—
366C3⋊(C3⋊C8)—31no—
367C3⋊(C3⋊C8)—31no—
368C3⋊(C3⋊C8)—34no—
369C3⋊(C3⋊C8)—34no—
370C3⋊(C3⋊C8)—64no—
371C3⋊(C3⋊C8)—64no—
372C3⋊(C3⋊C8)C22×D311yescharacteristic
373C3⋊(C3⋊C8)C22×D311yescharacteristic
374C3×C3⋊C8—34no—
375C3×C3⋊C8—34no—
376#575—271noSylow
377C2×C33—21no—
378C2×C33—41no—
379C2×C33C22×D411yescharacteristic
380C3⋊(C3⋊D3)—41no—
381C3×C3⋊D3—41no—
382C32×D3—21no—
383C32×D3—21no—
384C32×D3—41no—
385C3×#41—24no—
386C3×#41—34no—
387C3×#41—34no—
388C3×#41—34no—
389C3×#41—64no—
390C3×#41—64no—
391C3×#41—91no—
392C3×#41D3214yescomplemented
393C3×#41C2×C3⋊D311yescharacteristic, complemented
394C2×C3×Q8—34no—
395C2×C3×D4—34no—
396C2×C3×D4—64no—
397C22×C3×C4—34no—
398C22×C3×C4—64no—
399C2×#67—184no—
400#239—91no—
401#239C2×C3⋊D311yescharacteristic
402D3×Q8—91no—
403D3×Q8C2×C3⋊D311yescharacteristic, complemented
404#237—21no—
405#237—91no—
406#237—181no—
407#237C2×C3⋊D311yescharacteristic
408D3×D4—21no—
409D3×D4—91no—
410D3×D4—181no—
411D3×D4C2×C3⋊D311yescharacteristic, complemented
412#235—21no—
413#235—34no—
414#235—94no—
415#235—94no—
416#235—94no—
417#235—91no—
418#235—184no—
419#235—184no—
420#235—184no—
421#235—181no—
422#235C2×C3⋊D311yescharacteristic, complemented
423C2×D12—94no—
424C2×C4×D3—21no—
425C2×C4×D3—184no—
426C2×C4×D3—181no—
427C2×C4×D3C2×C3⋊D311yescharacteristic
428C2×Dic6—94no—
429C3×Q16—91no—
430C3×SD16—91no—
431C3×SD16—91no—
432C3×D8—91no—
433C2×C3×C8—91no—
434#216—34no—
435#216—94no—
436#216—94no—
437#216—94no—
438#216—91no—
439#216—91no—
440#216—184no—
441#215—34no—
442#215—94no—
443#215—94no—
444#215—94no—
445#215—91no—
446#215—91no—
447#215—184no—
448#214—34no—
449#214—94no—
450#214—94no—
451#214—94no—
452#214—91no—
453#214—91no—
454#214—184no—
455#213—34no—
456#213—94no—
457#213—94no—
458#213—94no—
459#213—91no—
460#213—91no—
461#213—184no—
462#208—94no—
463#208—94no—
464#208—94no—
465#208—94no—
466C2×C3⋊C8—34no—
467C2×C3⋊C8—94no—
468C2×C3⋊C8—91no—
469C2×C3⋊C8—184no—
470Dic12—91no—
471D24—91no—
472#204—91no—
473#204—91no—
474ΓL(1,𝔽25)—91no—
475ΓL(1,𝔽25)—91no—
476ΓL(1,𝔽25)—91no—
477ΓL(1,𝔽25)—91no—
478C22×C32—21no—
479C22×C32—24no—
480C22×C32—24no—
481C22×C32—31no—
482C22×C32—31no—
483C22×C32—44no—
484C22×C32—61no—
485C22×C32—121no—
486C22×C32—122no—
487C22×C32D3×D411yescharacteristic
488C22×C32C2×#6714yes—
489C2×C3⋊D3—21no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—124no—
493C2×C3⋊D3—122no—
494C2×C3×D3—24no—
495C2×C3×D3—44no—
496C2×C3×D3—48no—
497C2×C3×D3—64no—
498C2×C3×D3C2×#6714yes—
499C2×C3×D3C2×#6714yes—
500D32—128no—
501C32×C4—21no—
502C32×C4—24no—
503C32×C4—24no—
504C32×C4—24no—
505C32×C4—31no—
506C32×C4—31no—
507C32×C4—44no—
508C32×C4—61no—
509C32×C4D3×D411yescharacteristic
510C32×C4C2×#6714yes—
511C32×C4C23×D314yes—
512C32×C4C23×D311yescharacteristic
513C3⋊Dic3—21no—
514C3⋊Dic3—61no—
515C3⋊Dic3—64no—
516C3⋊Dic3—124no—
517C3×Dic3—24no—
518C3×Dic3—64no—
519C3×Dic3C2×#6714yes—
520C3×Dic3C2×#6714yes—
521C2×#41—31no—
522C2×#41—271no—
523#137—271no—
524#137—271no—
525#137—271no—
526#137—271no—
527AGL(1,ℤ/8)—271no—
528AGL(1,ℤ/8)—271no—
529AGL(1,ℤ/8)—271no—
530AGL(1,ℤ/8)—271no—
531#135—91no—
532#135—271no—
533#135—271no—
534#135—271no—
535C2×M16—271no—
536C33#57511yescharacteristic, complemented, Sylow
537C23×C3—34no—
538C23×C3—64no—
539C22×D3—21no—
540C22×D3—184no—
541C22×D3—181no—
542C22×D3#63811yescharacteristic
543C3×Q8—24no—
544C3×Q8—34no—
545C3×Q8—64no—
546C3×Q8—91no—
547C3×Q8C2×D3214yes—
548C3×Q8C22×C3⋊D311yescharacteristic
549C3×D4—24no—
550C3×D4—21no—
551C3×D4—24no—
552C3×D4—34no—
553C3×D4—44no—
554C3×D4—64no—
555C3×D4—64no—
556C3×D4—64no—
557C3×D4—64no—
558C3×D4—91no—
559C3×D4—181no—
560C3×D4C2×D3214yes—
561C3×D4C22×C3⋊D311yescharacteristic
562C2×C3×C4—24no—
563C2×C3×C4—21no—
564C2×C3×C4—24no—
565C2×C3×C4—34no—
566C2×C3×C4—34no—
567C2×C3×C4—34no—
568C2×C3×C4—34no—
569C2×C3×C4—34no—
570C2×C3×C4—44no—
571C2×C3×C4—64no—
572C2×C3×C4—64no—
573C2×C3×C4—64no—
574C2×C3×C4—64no—
575C2×C3×C4—181no—
576C2×C3×C4C2×D3214yes—
577C2×C3×C4C22×C3⋊D311yescharacteristic
578#67—21no—
579#67—21no—
580#67—21no—
581#67—64no—
582#67—184no—
583#67—184no—
584#67—184no—
585#67—181no—
586#67—181no—
587#67—181no—
588#67—364no—
589C2×Dic3—21no—
590C2×Dic3—184no—
591C2×Dic3—181no—
592C2×Dic3#63811yescharacteristic
593D12—21no—
594D12—34no—
595D12—94no—
596D12—91no—
597D12—184no—
598D12—184no—
599D12—181no—
600D12C22×C3⋊D311yescharacteristic
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—64no—
605C4×D3—184no—
606C4×D3—184no—
607C4×D3—181no—
608C4×D3—184no—
609C4×D3—181no—
610C4×D3—181no—
611C4×D3—364no—
612C4×D3#63811yescharacteristic
613C4×D3#63811yescharacteristic
614C4×D3C22×C3⋊D311yescharacteristic
615C4×D3C22×C3⋊D311yescharacteristic
616Dic6—21no—
617Dic6—34no—
618Dic6—94no—
619Dic6—91no—
620Dic6—184no—
621Dic6—184no—
622Dic6—181no—
623Dic6C22×C3⋊D311yescharacteristic
624C3×C8—91no—
625C3×C8—91no—
626C3⋊C8—34no—
627C3⋊C8—34no—
628C3⋊C8—94no—
629C3⋊C8—94no—
630C3⋊C8—91no—
631C3⋊C8—91no—
632C3⋊C8—184no—
633C3⋊C8—184no—
634C2×C32—21no—
635C2×C32—24no—
636C2×C32—24no—
637C2×C32—44no—
638C2×C32—41no—
639C2×C32—44no—
640C2×C32—61no—
641C2×C32—61no—
642C2×C32—84no—
643C2×C32—121no—
644C2×C32C2×D3×D411yescharacteristic
645C2×C32C22×#6714yes—
646C3⋊D3—41no—
647C3⋊D3—121no—
648C3⋊D3—124no—
649C3⋊D3—244no—
650C3×D3—24no—
651C3×D3—24no—
652C3×D3—44no—
653C3×D3—124no—
654#41—31no—
655#41—31no—
656#41—31no—
657#41—61no—
658#41—61no—
659#41—91no—
660#41—271no—
661#41—271no—
662#41—271no—
663#41—541no—
664#41—541no—
665#41D3×C3⋊D311yescharacteristic, complemented
666C2×Q8—31no—
667C2×Q8—271no—
668C2×D4—31no—
669C2×D4—61no—
670C2×D4—271no—
671C2×D4—541no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—541no—
675Q16—91no—
676Q16—271no—
677Q16—271no—
678Q16—271no—
679SD16—91no—
680SD16—91no—
681SD16—271no—
682SD16—271no—
683SD16—271no—
684SD16—271no—
685SD16—271no—
686SD16—271no—
687D8—91no—
688D8—271no—
689D8—271no—
690D8—271no—
691M16—271no—
692M16—271no—
693M16—271no—
694M16—271no—
695C2×C8—91no—
696C2×C8—271no—
697C22×C3—24no—
698C22×C3—21no—
699C22×C3—24no—
700C22×C3—34no—
701C22×C3—34no—
702C22×C3—44no—
703C22×C3—64no—
704C22×C3—124no—
705C22×C3—128no—
706C22×C3—181no—
707C22×C3D3×#6714yes—
708C22×C3C2×#63811yescharacteristic
709C2×D3—21no—
710C2×D3—41no—
711C2×D3—42no—
712C2×D3—64no—
713C2×D3—184no—
714C2×D3—181no—
715C2×D3—364no—
716C2×D3—362no—
717C2×D3—368no—
718C2×D3C2×#63811yescharacteristic
719C2×D3C2×#63811yescharacteristic
720C3×C4—24no—
721C3×C4—21no—
722C3×C4—24no—
723C3×C4—24no—
724C3×C4—34no—
725C3×C4—34no—
726C3×C4—44no—
727C3×C4—64no—
728C3×C4—181no—
729C3×C4D3×#6714yes—
730C3×C4C2×#63811yescharacteristic
731C3×C4C22×D3214yes—
732C3×C4C23×C3⋊D311yescharacteristic
733Dic3—21no—
734Dic3—64no—
735Dic3—184no—
736Dic3—181no—
737Dic3—364no—
738Dic3C2×#63811yescharacteristic
739Dic3C2×#63811yescharacteristic
740C32—24no—
741C32#576811yescharacteristic, complemented
742C32#582214yescomplemented
743C23—31no—
744C23—61no—
745C23—541no—
746Q8—31no—
747Q8—61no—
748Q8—91no—
749Q8—271no—
750Q8—541no—
751Q8C2×D3×C3⋊D311yescharacteristic
752D4—21no—
753D4—31no—
754D4—61no—
755D4—61no—
756D4—61no—
757D4—61no—
758D4—91no—
759D4—181no—
760D4—271no—
761D4—541no—
762D4—541no—
763D4—541no—
764D4—541no—
765D4C2×D3×C3⋊D311yescharacteristic
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—181no—
777C2×C4—541no—
778C2×C4—541no—
779C2×C4—541no—
780C2×C4—541no—
781C2×C4C2×D3×C3⋊D311yescharacteristic
782C8—91no—
783C8—91no—
784C8—271no—
785C8—271no—
786C2×C3—24no—
787C2×C3—21no—
788C2×C3—24no—
789C2×C3—44no—
790C2×C3—44no—
791C2×C3—41no—
792C2×C3—64no—
793C2×C3—64no—
794C2×C3—84no—
795C2×C3—124no—
796C2×C3—361no—
797C2×C3C2×D3×#6714yes—
798C2×C3C22×#63811yescharacteristic
799D3—21no—
800D3—21no—
801D3—41no—
802D3—124no—
803D3—364no—
804D3—361no—
805D3—724no—
806C22—21no—
807C22—31no—
808C22—31no—
809C22—61no—
810C22—121no—
811C22—122no—
812C22—181no—
813C22—541no—
814C22—1082no—
815C22D3×#63811yescharacteristic
816C4—21no—
817C4—31no—
818C4—31no—
819C4—61no—
820C4—181no—
821C4—541no—
822C4D3×#63811yescharacteristic
823C4C22×D3×C3⋊D311yescharacteristic
824C3—24no—
825C3#1059545314yescomplemented
826C3#1059629311yescharacteristic, complemented
827C2—21no—
828C2—41no—
829C2—61no—
830C2—61no—
831C2—121no—
832C2—361no—
833C2—1081no—
834C2C2×D3×#63811yescharacteristic
subgroupG/H
centerC4D3×#638
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC33×#41C22
socleC2×C33C22×D4
hypercenter#41D3×C3⋊D3
hypocenterC33#575
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C32×D3×#41C2semidirect
2. D3×#3828C2semidirect
3. #11723991C2semidirect
4. C3×#64159C2semidirect
5. #11723581C2semidirect
6. #11723579C2semidirect
7. #11723574C2semidirect
8. #11723568C2semidirect
9. #11723557C2semidirect
10. #11723555C2semidirect
11. #11723550C2semidirect
12. #11723544C2semidirect
13. #11723377C2semidirect
14. #11723363C2semidirect
15. C2×#88786C2semidirect
18. C33×#41C22semidirect
19. #89076C22semidirect
20. C3×#3828C22semidirect
22. C32×D3×Q8C22semidirect
26. C32×D3×D4C22semidirect
28. C32×#235C22semidirect
33. D3×C4⋊(C3⋊D3)C22semidirect
38. D3×#634C22semidirect
39. #88863C22semidirect
40. #88862C22semidirect
41. #88861C22semidirect
42. #88860C22semidirect
43. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
44. C3×#3756C22semidirect
45. C3×#3755C22semidirect
46. C3×#3754C22semidirect
47. C3×#3753C22semidirect
48. C2×C3×C3⋊(C3⋊C8)C22semidirect
49. #88799C22semidirect
50. #88798C22semidirect
51. #88795C22semidirect
52. #88794C22semidirect
53. #88793C22semidirect
54. #88792C22semidirect
55. #88790C22semidirect
56. #88789C22semidirect
57. #88786C22semidirect
58. #88786C22semidirect
59. #88786C22semidirect
60. #88786C22semidirect
63. C3×D3×#41D3semidirect
72. #64159D3semidirect
143. C32×#41C2×D3semidirect
144. C32×#41C2×D3semidirect
158. #3828C2×D3semidirect
163. C3×D3×Q8C2×D3semidirect
167. C3×D3×D4C2×D3semidirect
170. C3×#235C2×D3semidirect
186. #3756C2×D3semidirect
192. #3755C2×D3semidirect
198. #3754C2×D3semidirect
204. #3753C2×D3semidirect
212. C2×C3⋊(C3⋊C8)C2×D3semidirect
250. D3×#41C3⋊D3semidirect
392. C3×#41D32semidirect
393. C3×#41C2×C3⋊D3semidirect
403. D3×Q8C2×C3⋊D3semidirect
411. D3×D4C2×C3⋊D3semidirect
422. #235C2×C3⋊D3semidirect
536. C33#575semidirect
665. #41D3×C3⋊D3semidirect
741. C32#5768semidirect
742. C32#5822semidirect
825. C3#10595453semidirect
826. C3#10596293semidirect

Maximal subgroups

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

subgroupindex
C32×D3×#412
D3×#38282
#117239912
C3×#641592
#117235812
#117235792
#117235742
#117235682
#117235572
#117235552
#117235502
#117235442
#117233772
#117233632
C2×#887862
#105962933
#105954533