Finite Group Databasebeta

← #13170651

Subgroups — #13170651

Order 1728.

1370 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89021C211yesmaximal, characteristic, complemented
2C3×D3×#235C211yesmaximal, characteristic, complemented
3#11723661C211yesmaximal, characteristic, complemented
4#11723388C211yesmaximal, characteristic, complemented
5#11723379C211yesmaximal, characteristic, complemented
6C3×#63825C211yesmaximal, characteristic, complemented
7C3×D3×#208C211yesmaximal, characteristic, complemented
8#11722884C212yesmaximal, complemented
9#11722869C212yesmaximal, complemented
10#11722855C212yesmaximal, complemented
11#11722854C212yesmaximal, complemented
12#10595469—31nomaximal
13#10594795—31nomaximal
14#10594712—31nomaximal
15C2×#6308C2211yescharacteristic, complemented
16C3×#3828C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C32×#235C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6290—21no—
21C2×Dic3×C3⋊D3—21no—
22#89021—21no—
23#89021—21no—
24#89021C2212yes—
25#89021C2212yescomplemented
26C3×D3×#67—21no—
27C3×#3804—21no—
28C3×D3×D12C2211yescharacteristic, complemented
29C3×C4×D32—21no—
30C3×#3799C2211yescharacteristic, complemented
31C3×#3798—21no—
32C3×#3795C2211yescharacteristic, complemented
33C3×D3×Dic6C2211yescharacteristic, complemented
34C3×#3748C2211yescharacteristic, complemented
35C32×#208C2211yescharacteristic, complemented
36#88811C2212yescomplemented
37#88810C2212yescomplemented
38#88800C2212yescomplemented
39#88799C2212yescomplemented
40#88796C2212yescomplemented
41#88794C2212yescomplemented
42C3×#3717C2212yescomplemented
43C3×#3714C2212yescomplemented
44C3×#3711C2212yescomplemented
45C3×D3×C3⋊C8C2212yescomplemented
46C2×#3828—31no—
47C3×D3×#41—31no—
48C2×C3×#235—31no—
49D3×#235D311yescharacteristic, complemented
50C2×#3795—31no—
51C2×#3795—31no—
52C2×#3795—61no—
53#64160—31no—
54#64118—31no—
55C3×#949—31no—
56C2×C3×#208—31no—
57C3×#908—31no—
58C3×D3×M16—31no—
59#63947—32no—
60#63946—32no—
61#63933—32no—
62#63932—32no—
63#63833—32no—
64#63831—31no—
65#63831—31no—
66#63831—31no—
67#63831—31no—
68#63831—61no—
69#63831—61no—
70#63830—31no—
71#63830—32no—
72#63829—32no—
73#63829—32no—
74#63825—31no—
75#63825D311yescharacteristic, complemented
76#63823—31no—
77D3×#208D311yescharacteristic, complemented
78#63807—32no—
79#63806—32no—
80#63800—32no—
81#63795—32no—
82C22×C3×C3⋊D3—21no—
83C22×C32×D3D411yescharacteristic
84C2×C3×D32—21no—
85C2×C33×C4C2311yescharacteristic
86C2×C3⋊(C3⋊Dic3)—21no—
87#6308—21no—
88#6308C2312yes—
89C3×#638—21no—
90C3×C4⋊(C3⋊D3)—21no—
91C3×C4⋊(C3⋊D3)C2311yescharacteristic
92C3×C4⋊(C3⋊D3)C2312yes—
93C3×C4×C3⋊D3—21no—
94C3×#634C2311yescharacteristic
95C32×#67—21no—
96C2×C32×Dic3D411yescharacteristic
97C32×D12C2311yescharacteristic
98C32×C4×D3—21no—
99C32×C4×D3D411yescharacteristic
100C32×C4×D3D411yescharacteristic
101C32×C4×D3C2311yescharacteristic
102C32×C4×D3C2311yescharacteristic
103C32×Dic6C2311yescharacteristic
104#6290—22no—
105#6290—22no—
106Dic3×C3⋊D3—22no—
107Dic3×C3⋊D3—22no—
108C3×#627—21no—
109C3×#626—21no—
110C3×#626—21no—
111C3×#625—21no—
112C3×#624—21no—
113C3×D3×Dic3—21no—
114C3×D3×Dic3—21no—
115C3×C3⋊(C3⋊C8)C2312yes—
116C32×C3⋊C8C2312yes—
117#5822—91no—
118#5773—91no—
119#5748—91no—
120C32×#41—31no—
121C22×C32×C4—31no—
122C2×#638—61no—
123#3828—32no—
124#3828—32no—
125#3828—61no—
126#3828—61no—
127#3828C2×D311yescharacteristic
128C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
129C2×C4×C3⋊D3—61no—
130C2×#634—31no—
131C2×#634—31no—
132C2×#634—31no—
133C2×#634—61no—
134C2×#634—61no—
135C2×#634—61no—
136C2×#634—121no—
137C2×C3×#67—61no—
138C3×#239—31no—
139C3×D3×Q8—31no—
140C3×#237—31no—
141C3×#237—61no—
142C3×D3×D4—31no—
143C3×D3×D4—61no—
144C3×#235—21no—
145C3×#235—31no—
146C3×#235—31no—
147C3×#235—31no—
148C3×#235—31no—
149C3×#235—61no—
150C3×#235—61no—
151C3×#235—61no—
152C3×#235—61no—
153C3×#235C2×D311yescharacteristic
154C3×#235C2×D311yescharacteristic
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—61no—
159C2×C3×C4×D3—21no—
160C2×C3×C4×D3—61no—
161C2×C3×C4×D3—61no—
162C2×C3×C4×D3C2×D311yescharacteristic
163C2×C3×C4×D3C2×D311yescharacteristic
164C2×C3×Dic6—31no—
165D3×#67—21no—
166C2×#625—62no—
167C2×#625—61no—
168C2×#625—61no—
169#3804—21no—
170C2×D3×Dic3—62no—
171C2×D3×Dic3—61no—
172C2×D3×Dic3—61no—
173D3×D12C2×D311yescharacteristic, complemented
174C4×D32—21no—
175#3799C2×D311yescharacteristic, complemented
176#3798—21no—
177#3795—32no—
178#3795—32no—
179#3795—32no—
180#3795—32no—
181#3795—62no—
182#3795—62no—
183#3795—62no—
184#3795—62no—
185#3795—61no—
186#3795—61no—
187#3795—61no—
188#3795—61no—
189#3795C2×D311yescharacteristic, complemented
190D3×Dic6C2×D311yescharacteristic, complemented
191C32×M16—31no—
192#3756—32no—
193#3754—32no—
194#3748C2×D311yescharacteristic, complemented
195#3746—32no—
196#3744—32no—
197C3×#215—32no—
198C3×#213—32no—
199C3×#208—21no—
200C3×#208—31no—
201C3×#208—31no—
202C3×#208—32no—
203C3×#208—61no—
204C3×#208C2×D311yescharacteristic, complemented
205C3×#208C2×D311yescharacteristic, complemented
206C2×C3×C3⋊C8—32no—
207C3×D24—32no—
208C3×#204—32no—
209C3×ΓL(1,𝔽25)—32no—
210C3×D3×C8—32no—
211#3719—32no—
212#3719—32no—
213#3719—32no—
214#3719—32no—
215#3719—62no—
216#3719—62no—
217#3717—32no—
218#3717C2×D312yescomplemented
219#3716—32no—
220#3716—32no—
221#3716—32no—
222#3716—32no—
223#3716—32no—
224#3716—62no—
225#3716—62no—
226#3715—32no—
227#3714—32no—
228#3714—32no—
229#3714C2×D312yescomplemented
230#3713—32no—
231#3711C2×D312yescomplemented
232D3×C3⋊C8C2×D312yescomplemented
233C22×C33C2×D411yescharacteristic
234C2×C3×C3⋊D3—22no—
235C2×C3×C3⋊D3—21no—
236C2×C3×C3⋊D3—42no—
237C2×C32×D3—21no—
238C2×C32×D3—41no—
239C2×C32×D3C2×D411yescharacteristic
240C2×C32×D3C2×D411yescharacteristic
241C3×D32—42no—
242C33×C4C2×D411yescharacteristic
243C33×C4C2411yescharacteristic
244C3⋊(C3⋊Dic3)—22no—
245C3×C3⋊Dic3—21no—
246C32×Dic3—21no—
247C32×Dic3C2×D411yescharacteristic
248C32×Dic3C2×D411yescharacteristic
249C2×C3×#41—91no—
250D3×#41—31no—
251C2×#237—91no—
252C2×#235—31no—
253C2×#235—91no—
254C2×#235—91no—
255C2×#235—181no—
256C3×AGL(1,ℤ/8)—91no—
257C2×C3×M16—91no—
258#951—91no—
259#951—91no—
260#951—91no—
261#951—181no—
262#950—92no—
263#950—92no—
264#949—31no—
265#949—91no—
266#942—92no—
267#932—92no—
268#932—91no—
269C2×#208—31no—
270#916—92no—
271#915—92no—
272#912—92no—
273#911—92no—
274#909—92no—
275#909—91no—
276#909—91no—
277#909—91no—
278#909—181no—
279#908—31no—
280#908—92no—
281#908—91no—
282D3×M16—31no—
283#904—92no—
284#904—92no—
285C23×C32—31no—
286C22×C3⋊D3—21no—
287C22×C3×D3—21no—
288C22×C3×D3—61no—
289C22×C3×D3—62no—
290C22×C3×D3—61no—
291C22×C3×D3—61no—
292C22×C3×D3—61no—
293C22×C3×D3D1211yescharacteristic
294C22×C3×D3#6711yescharacteristic
295C2×D32—21no—
296C32×Q8—31no—
297C32×D4—31no—
298C32×D4—61no—
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4—21no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—31no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—41no—
308C2×C32×C4—61no—
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311C2×C32×C4C22×D311yescharacteristic
312#638—21no—
313#638—62no—
314#638—62no—
315C2×C3⋊Dic3—61no—
316C2×C3⋊Dic3—62no—
317C2×C3⋊Dic3—61no—
318C2×C3⋊Dic3—61no—
319C2×C3⋊Dic3—121no—
320C2×C3⋊Dic3—121no—
321C2×C3⋊Dic3—122no—
322C4⋊(C3⋊D3)—21no—
323C4⋊(C3⋊D3)C22×D311yescharacteristic
324C4⋊(C3⋊D3)C22×D312yes—
325C4×C3⋊D3—21no—
326C4×C3⋊D3—62no—
327C4×C3⋊D3—62no—
328#634—32no—
329#634—32no—
330#634—32no—
331#634—62no—
332#634—62no—
333#634—62no—
334#634—61no—
335#634—62no—
336#634—61no—
337#634—61no—
338#634—122no—
339#634—121no—
340#634—121no—
341#634—122no—
342#634C22×D311yescharacteristic
343C3×#67—21no—
344C3×#67—21no—
345C3×#67—41no—
346C3×#67—61no—
347C3×#67—61no—
348C3×#67—61no—
349C3×#67—61no—
350C3×#67—61no—
351C3×#67—61no—
352C3×#67—121no—
353C2×C3×Dic3—21no—
354C2×C3×Dic3—61no—
355C2×C3×Dic3—61no—
356C2×C3×Dic3D1211yescharacteristic
357C2×C3×Dic3#6711yescharacteristic
358C3×D12—21no—
359C3×D12—31no—
360C3×D12—32no—
361C3×D12—31no—
362C3×D12—32no—
363C3×D12—62no—
364C3×D12—61no—
365C3×D12—62no—
366C3×D12—61no—
367C3×D12—61no—
368C3×D12—61no—
369C3×D12—61no—
370C3×D12C22×D311yescharacteristic
371C3×D12C22×D311yescharacteristic
372C3×C4×D3—21no—
373C3×C4×D3—21no—
374C3×C4×D3—21no—
375C3×C4×D3—21no—
376C3×C4×D3—21no—
377C3×C4×D3—21no—
378C3×C4×D3—41no—
379C3×C4×D3—61no—
380C3×C4×D3—61no—
381C3×C4×D3—61no—
382C3×C4×D3—61no—
383C3×C4×D3—61no—
384C3×C4×D3—61no—
385C3×C4×D3—121no—
386C3×C4×D3D1211yescharacteristic
387C3×C4×D3D1211yescharacteristic
388C3×C4×D3#6711yescharacteristic
389C3×C4×D3#6711yescharacteristic
390C3×C4×D3C22×D311yescharacteristic
391C3×C4×D3C22×D311yescharacteristic
392C3×C4×D3C22×D311yescharacteristic
393C3×C4×D3C22×D311yescharacteristic
394C3×Dic6—21no—
395C3×Dic6—31no—
396C3×Dic6—31no—
397C3×Dic6—61no—
398C3×Dic6—61no—
399C3×Dic6—61no—
400C3×Dic6C22×D311yescharacteristic
401C3×Dic6C22×D311yescharacteristic
402#627—21no—
403#626—21no—
404#626—21no—
405#625—21no—
406#625—64no—
407#625—64no—
408#625—62no—
409#625—62no—
410#625—62no—
411#625—62no—
412#624—21no—
413D3×Dic3—21no—
414D3×Dic3—21no—
415D3×Dic3—64no—
416D3×Dic3—64no—
417D3×Dic3—62no—
418D3×Dic3—62no—
419D3×Dic3—62no—
420D3×Dic3—62no—
421C32×C8—32no—
422C3⋊(C3⋊C8)C22×D312yes—
423C3×C3⋊C8—22no—
424C3×C3⋊C8—32no—
425C3×C3⋊C8—32no—
426C3×C3⋊C8—62no—
427C3×C3⋊C8C22×D312yes—
428C3×C3⋊C8C22×D312yes—
429#575—271noSylow
430C2×C33—21no—
431C2×C33C22×D411yescharacteristic
432C3×C3⋊D3—42no—
433C3×C3⋊D3—41no—
434C32×D3—21no—
435C32×D3—21no—
436C32×D3—41no—
437C3×#41—31no—
438C3×#41—31no—
439C3×#41—61no—
440C3×#41—91no—
441C3×#41—91no—
442C3×#41—91no—
443C3×#41—181no—
444C3×#41—181no—
445C2×C3×Q8—91no—
446C2×C3×D4—91no—
447C2×C3×D4—91no—
448C2×C3×D4—181no—
449C22×C3×C4—31no—
450C22×C3×C4—31no—
451C22×C3×C4—61no—
452C22×C3×C4—181no—
453C2×#67—61no—
454C2×#67—181no—
455C2×#67—181no—
456C2×#67—182no—
457C2×#67—181no—
458C22×Dic3—181no—
459#239—31no—
460D3×Q8—31no—
461#237—31no—
462#237—61no—
463#237—92no—
464#237—92no—
465#237—181no—
466#237—181no—
467D3×D4—31no—
468D3×D4—61no—
469#235—31no—
470#235—31no—
471#235—31no—
472#235—31no—
473#235—61no—
474#235—61no—
475#235—61no—
476#235—61no—
477#235—92no—
478#235—92no—
479#235—92no—
480#235—92no—
481#235—182no—
482#235—182no—
483#235—181no—
484#235—181no—
485#235—181no—
486#235—181no—
487#235—182no—
488#235—182no—
489#235D3211yescharacteristic
490C2×D12—31no—
491C2×D12—31no—
492C2×D12—31no—
493C2×D12—61no—
494C2×C4×D3—61no—
495C2×C4×D3—61no—
496C2×C4×D3—181no—
497C2×C4×D3—181no—
498C2×C4×D3—182no—
499C2×C4×D3D3211yescharacteristic
500C2×Dic6—31no—
501C2×Dic6—91no—
502C2×Dic6—91no—
503C2×Dic6—91no—
504C2×Dic6—181no—
505C2×Dic6—181no—
506C2×Dic6—181no—
507C2×Dic6—361no—
508C3×SD16—92no—
509C3×D8—92no—
510C3×M16—31no—
511C3×M16—31no—
512C3×M16—61no—
513C3×M16—92no—
514C3×M16—91no—
515C2×C3×C8—92no—
516#216—92no—
517#216—92no—
518#216—92no—
519#216—182no—
520#215—32no—
521#215—92no—
522#214—92no—
523#214—92no—
524#214—92no—
525#214—92no—
526#214—182no—
527#213—32no—
528#213—92no—
529#213—92no—
530#208—31no—
531#208—31no—
532#208—32no—
533#208—61no—
534#208D3211yescharacteristic, complemented
535C2×C3⋊C8—32no—
536Dic12—92no—
537Dic12—92no—
538Dic12—92no—
539Dic12—182no—
540D24—32no—
541D24—92no—
542#204—32no—
543#204—92no—
544#204—92no—
545#204—92no—
546#204—92no—
547#204—182no—
548ΓL(1,𝔽25)—32no—
549D3×C8—32no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—31no—
554C22×C32—31no—
555C22×C32—41no—
556C22×C32—61no—
557C22×C32—121no—
558C22×C32C2×D1211yescharacteristic
559C22×C32D3×D411yescharacteristic
560C22×C32C2×#6711yescharacteristic
561C2×C3⋊D3—22no—
562C2×C3⋊D3—21no—
563C2×C3⋊D3—42no—
564C2×C3×D3—21no—
565C2×C3×D3—21no—
566C2×C3×D3—21no—
567C2×C3×D3—21no—
568C2×C3×D3—41no—
569C2×C3×D3—41no—
570C2×C3×D3—41no—
571C2×C3×D3—42no—
572C2×C3×D3—64no—
573C2×C3×D3—62no—
574C2×C3×D3—61no—
575C2×C3×D3—61no—
576C2×C3×D3—62no—
577C2×C3×D3—121no—
578C2×C3×D3—122no—
579C2×C3×D3—122no—
580C2×C3×D3—124no—
581C2×C3×D3—122no—
582C2×C3×D3—122no—
583C2×C3×D3C2×D1211yescharacteristic
584C2×C3×D3C2×D1211yescharacteristic
585C2×C3×D3C2×#6711yescharacteristic
586C2×C3×D3C2×#6711yescharacteristic
587D32—42no—
588C32×C4—21no—
589C32×C4—21no—
590C32×C4—21no—
591C32×C4—21no—
592C32×C4—21no—
593C32×C4—21no—
594C32×C4—31no—
595C32×C4—31no—
596C32×C4—41no—
597C32×C4—41no—
598C32×C4—61no—
599C32×C4C2×D1211yescharacteristic
600C32×C4D3×D411yescharacteristic
601C32×C4C2×#6711yescharacteristic
602C32×C4C23×D311yescharacteristic
603C32×C4C23×D311yescharacteristic
604C32×C4C23×D311yescharacteristic
605C3⋊Dic3—21no—
606C3⋊Dic3—62no—
607C3⋊Dic3—64no—
608C3⋊Dic3—62no—
609C3⋊Dic3—62no—
610C3⋊Dic3—122no—
611C3⋊Dic3—122no—
612C3⋊Dic3—124no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—41no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—121no—
621C3×Dic3C2×D1211yescharacteristic
622C3×Dic3C2×D1211yescharacteristic
623C3×Dic3C2×#6711yescharacteristic
624C3×Dic3C2×#6711yescharacteristic
625C2×#41—91no—
626C2×#41—271no—
627#137—271no—
628#137—272no—
629#137—271no—
630AGL(1,ℤ/8)—91no—
631AGL(1,ℤ/8)—272no—
632AGL(1,ℤ/8)—271no—
633#135—272no—
634#135—272no—
635C2×M16—91no—
636C33#57511yescharacteristic, complemented, Sylow
637C23×C3—31no—
638C23×C3—31no—
639C23×C3—61no—
640C23×C3—181no—
641C23×C3—181no—
642C22×D3—61no—
643C22×D3—62no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3#62611yescharacteristic
648C3×Q8—31no—
649C3×Q8—31no—
650C3×Q8—61no—
651C3×Q8—91no—
652C3×Q8—181no—
653C3×D4—31no—
654C3×D4—31no—
655C3×D4—61no—
656C3×D4—61no—
657C3×D4—61no—
658C3×D4—91no—
659C3×D4—92no—
660C3×D4—121no—
661C3×D4—181no—
662C3×D4—181no—
663C3×D4—181no—
664C3×D4—181no—
665C3×D4—181no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—41no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—121no—
688C2×C3×C4—181no—
689C2×C3×C4—181no—
690C2×C3×C4—181no—
691C2×C3×C4—181no—
692C2×C3×C4C2×D3211yescharacteristic
693C2×C3×C4C2×D3211yescharacteristic
694C2×C3×C4C2×D3211yescharacteristic
695#67—21no—
696#67—61no—
697#67—61no—
698#67—61no—
699#67—61no—
700#67—61no—
701#67—61no—
702#67—121no—
703#67—182no—
704#67—182no—
705#67—182no—
706#67—182no—
707#67—184no—
708#67—184no—
709#67—182no—
710#67—182no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—182no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—182no—
718C2×Dic3—182no—
719C2×Dic3—361no—
720C2×Dic3—361no—
721C2×Dic3—362no—
722C2×Dic3#62611yescharacteristic
723D12—32no—
724D12—31no—
725D12—31no—
726D12—32no—
727D12—62no—
728D12—61no—
729D12—62no—
730D12—61no—
731D12—61no—
732D12—61no—
733D12—61no—
734D12C2×D3211yescharacteristic
735C4×D3—21no—
736C4×D3—61no—
737C4×D3—61no—
738C4×D3—61no—
739C4×D3—61no—
740C4×D3—61no—
741C4×D3—61no—
742C4×D3—121no—
743C4×D3—182no—
744C4×D3—182no—
745C4×D3—182no—
746C4×D3—182no—
747C4×D3—184no—
748C4×D3—184no—
749C4×D3#62611yescharacteristic
750C4×D3#62611yescharacteristic
751C4×D3C2×D3211yescharacteristic
752C4×D3C2×D3211yescharacteristic
753Dic6—31no—
754Dic6—31no—
755Dic6—61no—
756Dic6—61no—
757Dic6—61no—
758Dic6—92no—
759Dic6—92no—
760Dic6—92no—
761Dic6—182no—
762Dic6—182no—
763Dic6—182no—
764Dic6—182no—
765Dic6—181no—
766Dic6—181no—
767Dic6—181no—
768Dic6—362no—
769Dic6—361no—
770Dic6—361no—
771Dic6—362no—
772Dic6C2×D3211yescharacteristic
773C3×C8—32no—
774C3×C8—32no—
775C3×C8—62no—
776C3×C8—92no—
777C3⋊C8—32no—
778C3⋊C8—32no—
779C3⋊C8—62no—
780C3⋊C8C2×D3212yes—
781C2×C32—21no—
782C2×C32—22no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—41no—
789C2×C32—41no—
790C2×C32—41no—
791C2×C32—42no—
792C2×C32—61no—
793C2×C32—61no—
794C2×C32—121no—
795C2×C32C22×D1211yescharacteristic
796C2×C32C2×D3×D411yescharacteristic
797C2×C32C22×#6711yescharacteristic
798C3⋊D3—42no—
799C3⋊D3—41no—
800C3×D3—21no—
801C3×D3—21no—
802C3×D3—21no—
803C3×D3—21no—
804C3×D3—41no—
805C3×D3—41no—
806C3×D3—41no—
807C3×D3—41no—
808C3×D3—81no—
809C3×D3—124no—
810C3×D3—122no—
811C3×D3—121no—
812C3×D3—121no—
813C3×D3—122no—
814C3×D3—241no—
815#41—31no—
816#41—91no—
817#41—91no—
818#41—91no—
819#41—181no—
820#41—181no—
821#41—272no—
822#41—272no—
823#41—541no—
824#41—541no—
825C2×Q8—91no—
826C2×Q8—271no—
827C2×D4—91no—
828C2×D4—91no—
829C2×D4—181no—
830C2×D4—541no—
831C22×C4—31no—
832C22×C4—181no—
833C22×C4—541no—
834Q16—272no—
835Q16—272no—
836SD16—92no—
837SD16—272no—
838SD16—272no—
839SD16—272no—
840D8—92no—
841D8—272no—
842M16—31no—
843M16—92no—
844M16—91no—
845C2×C8—92no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—31no—
850C22×C3—31no—
851C22×C3—31no—
852C22×C3—31no—
853C22×C3—41no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—61no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—122no—
862C22×C3—181no—
863C22×C3—182no—
864C22×C3—362no—
865C22×C3—362no—
866C22×C3D3×D1211yescharacteristic
867C22×C3C2×#62611yescharacteristic
868C22×C3D3×#6711yescharacteristic
869C2×D3—21no—
870C2×D3—41no—
871C2×D3—64no—
872C2×D3—62no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—62no—
876C2×D3—121no—
877C2×D3—122no—
878C2×D3—122no—
879C2×D3—124no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3C2×#62611yescharacteristic
883C2×D3C2×#62611yescharacteristic
884C3×C4—21no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—21no—
890C3×C4—31no—
891C3×C4—31no—
892C3×C4—31no—
893C3×C4—31no—
894C3×C4—41no—
895C3×C4—41no—
896C3×C4—61no—
897C3×C4—61no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—121no—
901C3×C4—181no—
902C3×C4D3×D1211yescharacteristic
903C3×C4C2×#62611yescharacteristic
904C3×C4D3×#6711yescharacteristic
905C3×C4C22×D3211yescharacteristic
906C3×C4C22×D3211yescharacteristic
907C3×C4C22×D3211yescharacteristic
908Dic3—21no—
909Dic3—61no—
910Dic3—61no—
911Dic3—121no—
912Dic3—184no—
913Dic3—182no—
914Dic3—182no—
915Dic3—182no—
916Dic3—362no—
917Dic3—362no—
918Dic3—364no—
919Dic3C2×#62611yescharacteristic
920Dic3C2×#62611yescharacteristic
921C32—21no—
922C32—21no—
923C32—21no—
924C32—41no—
925C32#574811yescharacteristic, complemented
926C32#577311yescharacteristic, complemented
927C32#582211yescharacteristic, complemented
928C23—31no—
929C23—181no—
930C23—181no—
931Q8—31no—
932Q8—91no—
933Q8—181no—
934Q8—272no—
935Q8—541no—
936D4—31no—
937D4—61no—
938D4—92no—
939D4—91no—
940D4—181no—
941D4—181no—
942D4—181no—
943D4—181no—
944D4—181no—
945D4—542no—
946D4—542no—
947C2×C4—31no—
948C2×C4—31no—
949C2×C4—31no—
950C2×C4—31no—
951C2×C4—31no—
952C2×C4—61no—
953C2×C4—181no—
954C2×C4—181no—
955C2×C4—181no—
956C2×C4—181no—
957C2×C4—542no—
958C2×C4—542no—
959C2×C4—541no—
960C2×C4D3311yescharacteristic
961C8—32no—
962C8—92no—
963C2×C3—22no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—41no—
971C2×C3—41no—
972C2×C3—42no—
973C2×C3—41no—
974C2×C3—61no—
975C2×C3—61no—
976C2×C3—61no—
977C2×C3—61no—
978C2×C3—121no—
979C2×C3—121no—
980C2×C3—121no—
981C2×C3—121no—
982C2×C3—241no—
983C2×C3—361no—
984C2×C3—362no—
985C2×C3C2×D3×D1211yescharacteristic
986C2×C3C22×#62611yescharacteristic
987C2×C3C2×D3×#6711yescharacteristic
988D3—21no—
989D3—21no—
990D3—41no—
991D3—124no—
992D3—122no—
993D3—121no—
994D3—122no—
995D3—121no—
996D3—241no—
997C22—31no—
998C22—31no—
999C22—61no—
1000C22—121no—
1001C22—181no—
1002C22—182no—
1003C22—362no—
1004C22—362no—
1005C22D3×#62611yescharacteristic
1006C4—31no—
1007C4—31no—
1008C4—61no—
1009C4—181no—
1010C4—542no—
1011C4D3×#62611yescharacteristic
1012C4C2×D3311yescharacteristic
1013C3—21no—
1014C3—21no—
1015C3—21no—
1016C3—41no—
1017C3#1059471211yescharacteristic, complemented
1018C3#1059479511yescharacteristic, complemented
1019C3#1059546911yescharacteristic, complemented
1020C2—21no—
1021C2—61no—
1022C2—61no—
1023C2—121no—
1024C2—362no—
1025C2—361no—
1026C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC2C2×D3×#626
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. C2×#89021C2semidirect
2. C3×D3×#235C2semidirect
3. #11723661C2semidirect
4. #11723388C2semidirect
5. #11723379C2semidirect
6. C3×#63825C2semidirect
7. C3×D3×#208C2semidirect
8. #11722884C2semidirect
9. #11722869C2semidirect
10. #11722855C2semidirect
11. #11722854C2semidirect
15. C2×#6308C22semidirect
17. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. #89021C22semidirect
28. C3×D3×D12C22semidirect
30. C3×#3799C22semidirect
32. C3×#3795C22semidirect
33. C3×D3×Dic6C22semidirect
34. C3×#3748C22semidirect
35. C32×#208C22semidirect
36. #88811C22semidirect
37. #88810C22semidirect
38. #88800C22semidirect
39. #88799C22semidirect
40. #88796C22semidirect
41. #88794C22semidirect
42. C3×#3717C22semidirect
43. C3×#3714C22semidirect
44. C3×#3711C22semidirect
45. C3×D3×C3⋊C8C22semidirect
49. D3×#235D3semidirect
75. #63825D3semidirect
77. D3×#208D3semidirect
128. C2×C4⋊(C3⋊D3)C2×D3semidirect
173. D3×D12C2×D3semidirect
175. #3799C2×D3semidirect
189. #3795C2×D3semidirect
190. D3×Dic6C2×D3semidirect
194. #3748C2×D3semidirect
204. C3×#208C2×D3semidirect
205. C3×#208C2×D3semidirect
218. #3717C2×D3semidirect
229. #3714C2×D3semidirect
231. #3711C2×D3semidirect
232. D3×C3⋊C8C2×D3semidirect
534. #208D32semidirect
636. C33#575semidirect
925. C32#5748semidirect
926. C32#5773semidirect
927. C32#5822semidirect
1017. C3#10594712semidirect
1018. C3#10594795semidirect
1019. C3#10595469semidirect

Maximal subgroups

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

subgroupindex
C2×#890212
C3×D3×#2352
#117236612
#117233882
#117233792
C3×#638252
C3×D3×#2082
#117228842
#117228692
#117228552
#117228542
#105954693
#105947953
#105947123