Finite Group Databasebeta

← #13170646

Subgroups — #13170646

Order 1728.

1264 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3#11723661C211yesmaximal, characteristic, complemented
4#11723375C211yesmaximal, characteristic, complemented
5#11723365C211yesmaximal, characteristic, complemented
6D3×#3748C211yesmaximal, characteristic, complemented
7C3×#63827C211yesmaximal, characteristic, complemented
8#11722883C212yesmaximal, complemented
9#11722867C212yesmaximal, complemented
10#11722852C212yesmaximal, complemented
11#11722851C212yesmaximal, complemented
12#10595470—31nomaximal
13#10595317—31nomaximal
14#10594786—31nomaximal
15C3×#3828C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C32×#235C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic, complemented
20C3×D3×#67—21no—
21C2×C3×#626—21no—
22C2×C3×#624—21no—
23C3×#3804—21no—
24C3×D3×D12C2211yescharacteristic, complemented
25C3×C4×D32—21no—
26C3×#3799—21no—
27C3×#3799—21no—
28C3×#3799C2212yes—
29C3×#3799C2212yescomplemented
30C3×#3799C2211yescharacteristic, complemented
31C3×#3798—21no—
32C3×#3795C2211yescharacteristic, complemented
33C3×D3×Dic6C2211yescharacteristic, complemented
34#88855C2211yescharacteristic, complemented
35C3×#3748C2211yescharacteristic, complemented
36#88811C2212yescomplemented
37#88810C2212yescomplemented
38#88798C2212yescomplemented
39#88793C2212yescomplemented
40#88793C2212yescomplemented
41#88789C2212yescomplemented
42#88786C2212yescomplemented
43D3×C3⋊(C3⋊C8)C2212yescomplemented
44C3×#3718C2212yescomplemented
45C3×#3715C2212yescomplemented
46C3×D3×#41—31no—
47C2×C3×#239—31no—
48C2×C3×#235—31no—
49C2×C3×#235—31no—
50D3×#235D311yescharacteristic, complemented
51C2×#3799D311yescharacteristic, complemented
52#64158—31no—
53#64151—31no—
54C2×#3748—31no—
55C3×#951—31no—
56C3×#942—31no—
57#63949—32no—
58#63949—32no—
59#63948—32no—
60#63947—32no—
61#63943—32no—
62#63939—32no—
63#63935—32no—
64#63934—32no—
65#63830—31no—
66#63827—31no—
67#63827—31no—
68#63827—32no—
69#63827—61no—
70#63827D311yescharacteristic, complemented
71#63825—31no—
72#63823—31no—
73#63823—31no—
74#63823—31no—
75#63823—32no—
76#63823—61no—
77#63822—32no—
78#63822—32no—
79D3×#208—31no—
80D3×#208—31no—
81D3×#208—61no—
82C22×C3×C3⋊D3—21no—
83C22×C32×D3D411yescharacteristic
84C2×C3×D32—21no—
85C2×C33×C4C2311yescharacteristic
86C3×#638—21no—
87C3×C4⋊(C3⋊D3)—21no—
88C3×C4⋊(C3⋊D3)C2312yes—
89C3×C4⋊(C3⋊D3)C2311yescharacteristic
90C3×C4×C3⋊D3—21no—
91C3×#634C2311yescharacteristic
92C32×#67—21no—
93C2×C32×Dic3—21no—
94C2×C32×Dic3D411yescharacteristic
95C32×D12C2311yescharacteristic
96C32×C4×D3—21no—
97C32×C4×D3D411yescharacteristic
98C32×C4×D3D411yescharacteristic
99C32×C4×D3C2311yescharacteristic
100C32×C4×D3C2311yescharacteristic
101C32×Dic6—21no—
102C32×Dic6C2311yescharacteristic
103C32×Dic6C2312yes—
104C3×#627—21no—
105C3×#626—21no—
106C3×#626—22no—
107C3×#626—22no—
108C3×#626—21no—
109C3×#625—21no—
110C3×#624—22no—
111C3×#624—22no—
112C3×#624—21no—
113C3×D3×Dic3—21no—
114C3×D3×Dic3—21no—
115C3⋊(C3⋊(C3⋊C8))C2312yes—
116C3×C3⋊(C3⋊C8)C2312yes—
117#5822—91no—
118#5822—91no—
119#5777—91no—
120C32×#41—31no—
121C2×C32×Q8—31no—
122C22×C32×C4—31no—
123#3828C2×D311yescharacteristic
124C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
125C2×C3×#67—61no—
126C2×C3×#67—61no—
127C3×#239—32no—
128C3×#239—32no—
129C3×#239—31no—
130C3×#239—61no—
131C3×#239—61no—
132C3×D3×Q8—31no—
133C3×#237—31no—
134C3×#237—61no—
135C3×D3×D4—31no—
136C3×D3×D4—61no—
137C3×#235—21no—
138C3×#235—31no—
139C3×#235—31no—
140C3×#235—31no—
141C3×#235—31no—
142C3×#235—32no—
143C3×#235—32no—
144C3×#235—61no—
145C3×#235—61no—
146C3×#235—61no—
147C3×#235—61no—
148C3×#235—61no—
149C3×#235—61no—
150C3×#235C2×D311yescharacteristic
151C3×#235C2×D311yescharacteristic
152C2×C3×D12—31no—
153C2×C3×D12—31no—
154C2×C3×D12—31no—
155C2×C3×D12—61no—
156C2×C3×D12—61no—
157C2×C3×C4×D3—21no—
158C2×C3×C4×D3—61no—
159C2×C3×C4×D3—61no—
160C2×C3×C4×D3—61no—
161C2×C3×C4×D3—61no—
162C2×C3×C4×D3C2×D311yescharacteristic
163C2×C3×C4×D3C2×D311yescharacteristic
164C2×C3×Dic6—21no—
165C2×C3×Dic6—31no—
166C2×C3×Dic6C2×D311yescharacteristic, complemented
167C2×C3×Dic6C2×D311yescharacteristic, complemented
168D3×#67—21no—
169C2×#626—21no—
170C2×#624—21no—
171#3804—21no—
172D3×D12C2×D311yescharacteristic, complemented
173C4×D32—21no—
174#3799—21no—
175#3799—21no—
176#3799C2×D312yes—
177#3799C2×D312yescomplemented
178#3799C2×D311yescharacteristic, complemented
179#3798—21no—
180#3795C2×D311yescharacteristic, complemented
181D3×Dic6C2×D311yescharacteristic, complemented
182#3756—32no—
183#3755—32no—
184#3755—32no—
185#3753—32no—
186#3748—31no—
187#3748—31no—
188#3748—31no—
189#3748—32no—
190#3748—61no—
191#3748—61no—
192#3748—61no—
193#3748—121no—
194#3748C2×D311yescharacteristic, complemented
195C2×C3⋊(C3⋊C8)—32no—
196C3×#216—32no—
197C3×#216—32no—
198C3×#215—32no—
199C3×#214—32no—
200C3×#208—31no—
201C3×#208—31no—
202C3×#208—61no—
203#3718—32no—
204#3718—32no—
205#3718—62no—
206#3718C2×D312yescomplemented
207#3717—32no—
208#3716—32no—
209#3715—32no—
210#3715—32no—
211#3715—32no—
212#3715—32no—
213#3715—32no—
214#3715—62no—
215#3715—62no—
216#3715C2×D312yescomplemented
217#3714—32no—
218#3714—32no—
219#3713—32no—
220#3713—32no—
221#3713—32no—
222#3713—62no—
223#3711—32no—
224#3711—32no—
225#3711—62no—
226D3×C3⋊C8—32no—
227D3×C3⋊C8—32no—
228D3×C3⋊C8—62no—
229C22×C33C2×D411yescharacteristic
230C2×C3×C3⋊D3—22no—
231C2×C3×C3⋊D3—21no—
232C2×C3×C3⋊D3—42no—
233C2×C32×D3—21no—
234C2×C32×D3—41no—
235C2×C32×D3C2×D411yescharacteristic
236C2×C32×D3C2×D411yescharacteristic
237C3×D32—42no—
238C33×C4C2×D411yescharacteristic
239C33×C4C2411yescharacteristic
240C3×C3⋊Dic3—21no—
241C32×Dic3—21no—
242C32×Dic3—22no—
243C32×Dic3C2×D411yescharacteristic
244C32×Dic3C2×D411yescharacteristic
245C2×C3×#41—91no—
246C2×C3×#41—91no—
247D3×#41—31no—
248C2×#239—31no—
249C2×#235—31no—
250C2×#235—31no—
251C3×#137—91no—
252#951—31no—
253#951—92no—
254#951—91no—
255#950—92no—
256#950—92no—
257#950—92no—
258#950—92no—
259#949—91no—
260#949—92no—
261#949—91no—
262#949—91no—
263#949—181no—
264#942—31no—
265#942—92no—
266#942—91no—
267#942—91no—
268#942—181no—
269#932—91no—
270#932—92no—
271#932—91no—
272C2×#208—91no—
273C2×#208—91no—
274C2×#208—181no—
275#919—92no—
276#918—92no—
277#916—92no—
278#914—92no—
279#908—91no—
280D3×M16—91no—
281C23×C32—31no—
282C22×C3⋊D3—21no—
283C22×C3×D3—21no—
284C22×C3×D3—61no—
285C22×C3×D3—61no—
286C22×C3×D3—61no—
287C22×C3×D3—61no—
288C22×C3×D3—121no—
289C22×C3×D3#6711yescharacteristic
290C22×C3×D3#6711yescharacteristic
291C2×D32—21no—
292C32×Q8—32no—
293C32×Q8—31no—
294C32×Q8—61no—
295C32×D4—31no—
296C32×D4—61no—
297C2×C32×C4—21no—
298C2×C32×C4—21no—
299C2×C32×C4—21no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—31no—
305C2×C32×C4—41no—
306C2×C32×C4—61no—
307C2×C32×C4—61no—
308C2×C32×C4C22×D311yescharacteristic
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311#638—21no—
312C4⋊(C3⋊D3)—21no—
313C4⋊(C3⋊D3)C22×D311yescharacteristic
314C4⋊(C3⋊D3)C22×D312yes—
315C4×C3⋊D3—21no—
316#634C22×D311yescharacteristic
317C3×#67—21no—
318C3×#67—21no—
319C3×#67—41no—
320C3×#67—62no—
321C3×#67—62no—
322C3×#67—61no—
323C3×#67—61no—
324C3×#67—61no—
325C3×#67—61no—
326C3×#67—61no—
327C3×#67—61no—
328C3×#67—121no—
329C2×C3×Dic3—21no—
330C2×C3×Dic3—21no—
331C2×C3×Dic3—21no—
332C2×C3×Dic3—41no—
333C2×C3×Dic3—61no—
334C2×C3×Dic3—61no—
335C2×C3×Dic3#6711yescharacteristic
336C2×C3×Dic3#6711yescharacteristic
337C3×D12—21no—
338C3×D12—32no—
339C3×D12—31no—
340C3×D12—32no—
341C3×D12—31no—
342C3×D12—62no—
343C3×D12—61no—
344C3×D12—61no—
345C3×D12—62no—
346C3×D12—62no—
347C3×D12—61no—
348C3×D12—61no—
349C3×D12—61no—
350C3×D12—121no—
351C3×D12C22×D311yescharacteristic
352C3×D12C22×D311yescharacteristic
353C3×C4×D3—21no—
354C3×C4×D3—21no—
355C3×C4×D3—21no—
356C3×C4×D3—21no—
357C3×C4×D3—21no—
358C3×C4×D3—21no—
359C3×C4×D3—41no—
360C3×C4×D3—62no—
361C3×C4×D3—62no—
362C3×C4×D3—61no—
363C3×C4×D3—61no—
364C3×C4×D3—61no—
365C3×C4×D3—61no—
366C3×C4×D3—61no—
367C3×C4×D3—61no—
368C3×C4×D3—62no—
369C3×C4×D3—62no—
370C3×C4×D3—121no—
371C3×C4×D3#6711yescharacteristic
372C3×C4×D3#6711yescharacteristic
373C3×C4×D3#6711yescharacteristic
374C3×C4×D3#6711yescharacteristic
375C3×C4×D3C22×D311yescharacteristic
376C3×C4×D3C22×D311yescharacteristic
377C3×C4×D3C22×D311yescharacteristic
378C3×C4×D3C22×D311yescharacteristic
379C3×Dic6—21no—
380C3×Dic6—21no—
381C3×Dic6—21no—
382C3×Dic6—22no—
383C3×Dic6—31no—
384C3×Dic6—31no—
385C3×Dic6—41no—
386C3×Dic6—61no—
387C3×Dic6—61no—
388C3×Dic6—61no—
389C3×Dic6C22×D311yescharacteristic
390C3×Dic6C22×D311yescharacteristic
391C3×Dic6C22×D312yes—
392C3×Dic6C22×D312yes—
393#627—21no—
394#626—21no—
395#626—22no—
396#626—22no—
397#626—21no—
398#625—21no—
399#624—22no—
400#624—22no—
401#624—21no—
402D3×Dic3—21no—
403D3×Dic3—21no—
404C3⋊(C3⋊C8)—32no—
405C3⋊(C3⋊C8)—32no—
406C3⋊(C3⋊C8)—32no—
407C3⋊(C3⋊C8)—62no—
408C3⋊(C3⋊C8)—62no—
409C3⋊(C3⋊C8)—62no—
410C3⋊(C3⋊C8)—122no—
411C3⋊(C3⋊C8)C22×D312yes—
412C3×C3⋊C8—32no—
413C3×C3⋊C8—32no—
414C3×C3⋊C8—62no—
415#575—271noSylow
416C2×C33—21no—
417C2×C33C22×D411yescharacteristic
418C3×C3⋊D3—41no—
419C3×C3⋊D3—42no—
420C32×D3—21no—
421C32×D3—21no—
422C32×D3—41no—
423C3×#41—31no—
424C3×#41—31no—
425C3×#41—61no—
426C3×#41—91no—
427C3×#41—92no—
428C3×#41—92no—
429C3×#41—91no—
430C3×#41—91no—
431C3×#41—181no—
432C3×#41—181no—
433C3×#41—181no—
434C3×#41—181no—
435C2×C3×Q8—31no—
436C2×C3×Q8—31no—
437C2×C3×Q8—61no—
438C2×C3×Q8—91no—
439C2×C3×D4—91no—
440C2×C3×D4—91no—
441C2×C3×D4—181no—
442C2×C3×D4—181no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—61no—
446C22×C3×C4—181no—
447C22×C3×C4—181no—
448C2×#67—61no—
449C2×#67—61no—
450#239—32no—
451#239—32no—
452#239—31no—
453#239—61no—
454#239—61no—
455D3×Q8—31no—
456#237—31no—
457#237—61no—
458D3×D4—31no—
459D3×D4—61no—
460#235—31no—
461#235—31no—
462#235—31no—
463#235—32no—
464#235—32no—
465#235—31no—
466#235—61no—
467#235—61no—
468#235—61no—
469#235—61no—
470#235—61no—
471#235—61no—
472#235D3211yescharacteristic
473C2×D12—31no—
474C2×D12—31no—
475C2×D12—31no—
476C2×D12—61no—
477C2×D12—61no—
478C2×C4×D3—61no—
479C2×C4×D3—61no—
480C2×C4×D3—61no—
481C2×C4×D3—61no—
482C2×C4×D3D3211yescharacteristic
483C2×Dic6—31no—
484C2×Dic6D3211yescharacteristic, complemented
485C3×Q16—92no—
486C3×SD16—92no—
487C3×M16—91no—
488#216—32no—
489#216—32no—
490#216—92no—
491#216—92no—
492#216—92no—
493#216—182no—
494#215—32no—
495#215—92no—
496#215—92no—
497#215—92no—
498#215—92no—
499#215—92no—
500#215—182no—
501#215—182no—
502#214—32no—
503#214—92no—
504#214—92no—
505#214—92no—
506#213—92no—
507#213—92no—
508#213—92no—
509#213—92no—
510#213—92no—
511#213—182no—
512#208—31no—
513#208—31no—
514#208—61no—
515#208—92no—
516#208—92no—
517#208—91no—
518#208—91no—
519#208—91no—
520#208—182no—
521#208—181no—
522#208—181no—
523#208—181no—
524#208—361no—
525C2×C3⋊C8—92no—
526C2×C3⋊C8—92no—
527C2×C3⋊C8—182no—
528D24—92no—
529#204—92no—
530ΓL(1,𝔽25)—92no—
531D3×C8—92no—
532C22×C32—21no—
533C22×C32—21no—
534C22×C32—21no—
535C22×C32—31no—
536C22×C32—31no—
537C22×C32—41no—
538C22×C32—61no—
539C22×C32—121no—
540C22×C32D3×D411yescharacteristic
541C22×C32C2×#6711yescharacteristic
542C22×C32C2×#6711yescharacteristic
543C2×C3⋊D3—22no—
544C2×C3⋊D3—21no—
545C2×C3⋊D3—42no—
546C2×C3×D3—21no—
547C2×C3×D3—21no—
548C2×C3×D3—21no—
549C2×C3×D3—21no—
550C2×C3×D3—41no—
551C2×C3×D3—41no—
552C2×C3×D3—41no—
553C2×C3×D3—42no—
554C2×C3×D3—62no—
555C2×C3×D3—61no—
556C2×C3×D3—62no—
557C2×C3×D3—61no—
558C2×C3×D3—121no—
559C2×C3×D3—122no—
560C2×C3×D3—122no—
561C2×C3×D3—122no—
562C2×C3×D3—122no—
563C2×C3×D3—122no—
564C2×C3×D3—242no—
565C2×C3×D3C2×#6711yescharacteristic
566C2×C3×D3C2×#6711yescharacteristic
567C2×C3×D3C2×#6711yescharacteristic
568C2×C3×D3C2×#6711yescharacteristic
569D32—42no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—21no—
575C32×C4—21no—
576C32×C4—31no—
577C32×C4—31no—
578C32×C4—41no—
579C32×C4—41no—
580C32×C4—61no—
581C32×C4—62no—
582C32×C4D3×D411yescharacteristic
583C32×C4C2×#6711yescharacteristic
584C32×C4C2×#6711yescharacteristic
585C32×C4C23×D311yescharacteristic
586C32×C4C23×D311yescharacteristic
587C32×C4C23×D311yescharacteristic
588C3⋊Dic3—21no—
589C3×Dic3—22no—
590C3×Dic3—21no—
591C3×Dic3—21no—
592C3×Dic3—22no—
593C3×Dic3—21no—
594C3×Dic3—21no—
595C3×Dic3—42no—
596C3×Dic3—41no—
597C3×Dic3—61no—
598C3×Dic3—61no—
599C3×Dic3—121no—
600C3×Dic3C2×#6711yescharacteristic
601C3×Dic3C2×#6711yescharacteristic
602C3×Dic3C2×#6711yescharacteristic
603C3×Dic3C2×#6711yescharacteristic
604C2×#41—91no—
605C2×#41—91no—
606#137—91no—
607#137—272no—
608#137—271no—
609AGL(1,ℤ/8)—271no—
610AGL(1,ℤ/8)—272no—
611AGL(1,ℤ/8)—271no—
612#135—272no—
613#135—272no—
614C2×M16—271no—
615C33#57511yescharacteristic, complemented, Sylow
616C23×C3—31no—
617C23×C3—31no—
618C23×C3—61no—
619C23×C3—181no—
620C23×C3—181no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—121no—
626C22×D3#62511yescharacteristic
627C3×Q8—32no—
628C3×Q8—31no—
629C3×Q8—31no—
630C3×Q8—32no—
631C3×Q8—61no—
632C3×Q8—62no—
633C3×Q8—61no—
634C3×Q8—61no—
635C3×Q8—91no—
636C3×Q8—121no—
637C3×Q8—181no—
638C3×D4—31no—
639C3×D4—31no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—92no—
644C3×D4—91no—
645C3×D4—121no—
646C3×D4—181no—
647C3×D4—181no—
648C3×D4—182no—
649C3×D4—182no—
650C3×D4—181no—
651C3×D4—181no—
652C3×D4—181no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—41no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—121no—
677C2×C3×C4—121no—
678C2×C3×C4—182no—
679C2×C3×C4—181no—
680C2×C3×C4—182no—
681C2×C3×C4—181no—
682C2×C3×C4—181no—
683C2×C3×C4—181no—
684C2×C3×C4C2×D3211yescharacteristic
685C2×C3×C4C2×D3211yescharacteristic
686C2×C3×C4C2×D3211yescharacteristic
687#67—21no—
688#67—62no—
689#67—62no—
690#67—61no—
691#67—61no—
692#67—61no—
693#67—61no—
694#67—61no—
695#67—61no—
696#67—121no—
697C2×Dic3—21no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3#62511yescharacteristic
701D12—32no—
702D12—31no—
703D12—31no—
704D12—32no—
705D12—62no—
706D12—61no—
707D12—61no—
708D12—62no—
709D12—62no—
710D12—61no—
711D12—61no—
712D12—61no—
713D12—121no—
714D12C2×D3211yescharacteristic
715C4×D3—21no—
716C4×D3—62no—
717C4×D3—62no—
718C4×D3—61no—
719C4×D3—61no—
720C4×D3—61no—
721C4×D3—61no—
722C4×D3—61no—
723C4×D3—61no—
724C4×D3—62no—
725C4×D3—62no—
726C4×D3—121no—
727C4×D3#62511yescharacteristic
728C4×D3#62511yescharacteristic
729C4×D3C2×D3211yescharacteristic
730C4×D3C2×D3211yescharacteristic
731Dic6—21no—
732Dic6—31no—
733Dic6—31no—
734Dic6—61no—
735Dic6—61no—
736Dic6—61no—
737Dic6C2×D3212yes—
738Dic6C2×D3211yescharacteristic
739C3×C8—92no—
740C3⋊C8—32no—
741C3⋊C8—32no—
742C3⋊C8—62no—
743C3⋊C8—92no—
744C3⋊C8—92no—
745C3⋊C8—92no—
746C3⋊C8—182no—
747C3⋊C8—182no—
748C3⋊C8—182no—
749C3⋊C8—362no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—41no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32—61no—
761C2×C32—61no—
762C2×C32—81no—
763C2×C32—121no—
764C2×C32C2×D3×D411yescharacteristic
765C2×C32C22×#6711yescharacteristic
766C2×C32C22×#6711yescharacteristic
767C3⋊D3—41no—
768C3⋊D3—42no—
769C3×D3—22no—
770C3×D3—21no—
771C3×D3—21no—
772C3×D3—21no—
773C3×D3—21no—
774C3×D3—41no—
775C3×D3—41no—
776C3×D3—41no—
777C3×D3—81no—
778C3×D3—121no—
779C3×D3—122no—
780C3×D3—122no—
781C3×D3—121no—
782C3×D3—241no—
783C3×D3—242no—
784#41—31no—
785#41—91no—
786#41—92no—
787#41—91no—
788#41—92no—
789#41—91no—
790#41—181no—
791#41—181no—
792#41—181no—
793#41—181no—
794C2×Q8—31no—
795C2×Q8—91no—
796C2×D4—91no—
797C2×D4—91no—
798C2×D4—181no—
799C2×D4—181no—
800C22×C4—31no—
801C22×C4—181no—
802C22×C4—181no—
803Q16—92no—
804Q16—272no—
805SD16—92no—
806SD16—272no—
807SD16—272no—
808SD16—272no—
809D8—272no—
810D8—272no—
811M16—91no—
812M16—272no—
813M16—271no—
814C2×C8—272no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—31no—
819C22×C3—31no—
820C22×C3—31no—
821C22×C3—31no—
822C22×C3—41no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—61no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—122no—
831C22×C3—182no—
832C22×C3—181no—
833C22×C3—362no—
834C22×C3—362no—
835C22×C3C2×#62511yescharacteristic
836C22×C3D3×#6711yescharacteristic
837C22×C3D3×#6711yescharacteristic
838C2×D3—21no—
839C2×D3—41no—
840C2×D3—62no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—62no—
844C2×D3—121no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—122no—
850C2×D3—242no—
851C2×D3C2×#62511yescharacteristic
852C2×D3C2×#62511yescharacteristic
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—31no—
860C3×C4—31no—
861C3×C4—31no—
862C3×C4—31no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—61no—
868C3×C4—62no—
869C3×C4—61no—
870C3×C4—62no—
871C3×C4—121no—
872C3×C4—122no—
873C3×C4—181no—
874C3×C4C2×#62511yescharacteristic
875C3×C4D3×#6711yescharacteristic
876C3×C4D3×#6711yescharacteristic
877C3×C4C22×D3211yescharacteristic
878C3×C4C22×D3211yescharacteristic
879C3×C4C22×D3211yescharacteristic
880Dic3—22no—
881Dic3—21no—
882Dic3—61no—
883Dic3—61no—
884Dic3—121no—
885Dic3C2×#62511yescharacteristic
886Dic3C2×#62511yescharacteristic
887C32—21no—
888C32—21no—
889C32—21no—
890C32—41no—
891C32#577711yescharacteristic, complemented
892C32#582211yescharacteristic, complemented
893C32#582211yescharacteristic, complemented
894C23—31no—
895C23—181no—
896C23—181no—
897Q8—32no—
898Q8—31no—
899Q8—61no—
900Q8—91no—
901Q8—181no—
902D4—31no—
903D4—61no—
904D4—91no—
905D4—92no—
906D4—181no—
907D4—181no—
908D4—182no—
909D4—182no—
910D4—181no—
911D4—181no—
912D4—181no—
913C2×C4—31no—
914C2×C4—31no—
915C2×C4—31no—
916C2×C4—31no—
917C2×C4—31no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—181no—
921C2×C4—182no—
922C2×C4—182no—
923C2×C4—181no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4D3311yescharacteristic
927C8—92no—
928C8—272no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—41no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—41no—
939C2×C3—62no—
940C2×C3—61no—
941C2×C3—61no—
942C2×C3—61no—
943C2×C3—61no—
944C2×C3—81no—
945C2×C3—121no—
946C2×C3—121no—
947C2×C3—121no—
948C2×C3—241no—
949C2×C3—362no—
950C2×C3—361no—
951C2×C3C22×#62511yescharacteristic
952C2×C3C2×D3×#6711yescharacteristic
953C2×C3C2×D3×#6711yescharacteristic
954D3—21no—
955D3—21no—
956D3—41no—
957D3—121no—
958D3—122no—
959D3—121no—
960D3—122no—
961D3—242no—
962D3—241no—
963C22—31no—
964C22—31no—
965C22—61no—
966C22—121no—
967C22—182no—
968C22—181no—
969C22—362no—
970C22—362no—
971C22D3×#62511yescharacteristic
972C4—31no—
973C4—31no—
974C4—61no—
975C4—62no—
976C4—181no—
977C4D3×#62511yescharacteristic
978C4C2×D3311yescharacteristic
979C3—21no—
980C3—21no—
981C3—21no—
982C3—41no—
983C3#1059478611yescharacteristic, complemented
984C3#1059531711yescharacteristic, complemented
985C3#1059547011yescharacteristic, complemented
986C2—21no—
987C2—61no—
988C2—61no—
989C2—121no—
990C2—362no—
991C2—361no—
992C2C2×D3×#62511yescharacteristic
subgroupG/H
centerC2C2×D3×#625
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC2×C33C22×D4
hypercenterC2×C4D33
hypocenterC33#575
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C3×D3×#235C2semidirect
2. C2×C3×#3799C2semidirect
3. #11723661C2semidirect
4. #11723375C2semidirect
5. #11723365C2semidirect
6. D3×#3748C2semidirect
7. C3×#63827C2semidirect
8. #11722883C2semidirect
9. #11722867C2semidirect
10. #11722852C2semidirect
11. #11722851C2semidirect
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
19. C2×C32×Dic6C22semidirect
24. C3×D3×D12C22semidirect
29. C3×#3799C22semidirect
30. C3×#3799C22semidirect
32. C3×#3795C22semidirect
33. C3×D3×Dic6C22semidirect
34. #88855C22semidirect
35. C3×#3748C22semidirect
36. #88811C22semidirect
37. #88810C22semidirect
38. #88798C22semidirect
39. #88793C22semidirect
40. #88793C22semidirect
41. #88789C22semidirect
42. #88786C22semidirect
43. D3×C3⋊(C3⋊C8)C22semidirect
44. C3×#3718C22semidirect
45. C3×#3715C22semidirect
50. D3×#235D3semidirect
51. C2×#3799D3semidirect
70. #63827D3semidirect
124. C2×C4⋊(C3⋊D3)C2×D3semidirect
166. C2×C3×Dic6C2×D3semidirect
167. C2×C3×Dic6C2×D3semidirect
172. D3×D12C2×D3semidirect
177. #3799C2×D3semidirect
178. #3799C2×D3semidirect
180. #3795C2×D3semidirect
181. D3×Dic6C2×D3semidirect
194. #3748C2×D3semidirect
206. #3718C2×D3semidirect
216. #3715C2×D3semidirect
484. C2×Dic6D32semidirect
615. C33#575semidirect
891. C32#5777semidirect
892. C32#5822semidirect
893. C32#5822semidirect
983. C3#10594786semidirect
984. C3#10595317semidirect
985. C3#10595470semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2352
C2×C3×#37992
#117236612
#117233752
#117233652
D3×#37482
C3×#638272
#117228832
#117228672
#117228522
#117228512
#105954703
#105953173
#105947863