Finite Group Databasebeta

← #13170527

Subgroups — #13170527

Order 1728.

1294 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64308C211yesmaximal, characteristic, complemented
2C3×#64307C211yesmaximal, characteristic, complemented
3#11723661C211yesmaximal, characteristic, complemented
4#11723363C211yesmaximal, characteristic, complemented
5C2×#88789C211yesmaximal, characteristic, complemented
6#11723350C211yesmaximal, characteristic, complemented
7C3×#63823C211yesmaximal, characteristic, complemented
8#11722867C212yesmaximal, complemented
9#11722866C212yesmaximal, complemented
10#11722851C212yesmaximal, complemented
11D3×#3713C212yesmaximal, complemented
12#10595454—31nomaximal
13#10595444—31nomaximal
14#10595097—31nomaximal
15C3×#3828C2211yescharacteristic, complemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C32×#235C2211yescharacteristic
18C32×#235C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic, complemented
20C3×#3811—22no—
21C3×D3×#67—22no—
22C3×#3802—21no—
23C3×D3×D12—21no—
24C3×D3×D12C2212yescomplemented
25C3×D3×D12C2212yescomplemented
26C3×#3799—21no—
27C3×#3799C2212yescomplemented
28C3×#3796—21no—
29C3×#3795C2212yescomplemented
30C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
31C3×#3748C2211yescharacteristic, complemented
32#88811C2212yescomplemented
33#88810C2212yescomplemented
34#88798C2211yescharacteristic, complemented
35#88793C2211yescharacteristic, complemented
36#88792C2211yescharacteristic, complemented
37#88789C2211yescharacteristic, complemented
38#88789C2212yescomplemented
39#88789C2212yescomplemented
40#88786C2212yescomplemented
41D3×C3⋊(C3⋊C8)C2212yescomplemented
42C3×#3715C2212yescomplemented
43C3×#3713C2212yescomplemented
44C3×#1009—31no—
45C3×#1009—31no—
46C3×#1009—31no—
47C3×#1004—31no—
48#64308D311yescharacteristic, complemented
49#64307D311yescharacteristic, complemented
50#64159—31no—
51#64157—31no—
52C2×#3753—31no—
53C3×#949—31no—
54C3×#932—31no—
55#63947—32no—
56#63939—32no—
57#63935—32no—
58#63934—32no—
59#63932—32no—
60#63925—32no—
61D3×#213—32no—
62D3×#213—32no—
63#63830—31no—
64#63825—31no—
65#63823—31no—
66#63823—32no—
67#63823—32no—
68#63823D311yescharacteristic, complemented
69#63822—31no—
70#63822—31no—
71#63822—32no—
72#63822—61no—
73C2×#3713—31no—
74C2×#3713—31no—
75C2×#3713—32no—
76C2×#3713—61no—
77#63815—31no—
78#63815—31no—
79#63815—61no—
80C22×C3×C3⋊D3—21no—
81C22×C32×D3—21no—
82C2×C3×D32—22no—
83C2×C3×D32—22no—
84C2×C33×C4C2311yescharacteristic
85C3×#638—21no—
86C3×C4⋊(C3⋊D3)—21no—
87C3×C4⋊(C3⋊D3)C2312yes—
88C3×C4⋊(C3⋊D3)C2311yescharacteristic
89C3×C4×C3⋊D3—21no—
90C3×#634C2311yescharacteristic
91C32×#67—21no—
92C32×#67D412yes—
93C32×D12—21no—
94C32×D12D411yescharacteristic
95C32×D12C2312yes—
96C32×D12C2311yescharacteristic
97C32×C4×D3—21no—
98C32×C4×D3C2312yes—
99C32×Dic6D411yescharacteristic
100C32×Dic6C2311yescharacteristic
101C3×#626—22no—
102C3×#626—22no—
103C3×#626—22no—
104C3×#625—22no—
105C3×#624—22no—
106C3×D3×Dic3—22no—
107C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
108C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
109C3×C3⋊(C3⋊C8)C2312yes—
110#5835—91no—
111#5835—91no—
112#5774—91no—
113C32×#41—31no—
114C32×#41—31no—
115C2×C32×D4—31no—
116#3828C2×D311yescharacteristic, complemented
117C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
118C2×C3×#67—62no—
119C3×#239—32no—
120C3×#239—61no—
121C3×#239—61no—
122C3×#237—32no—
123C3×#237—61no—
124C3×D3×D4—32no—
125C3×D3×D4—32no—
126C3×D3×D4—61no—
127C3×D3×D4—61no—
128C3×D3×D4—62no—
129C3×D3×D4—62no—
130C3×D3×D4—62no—
131C3×D3×D4—61no—
132C3×#235—21no—
133C3×#235—21no—
134C3×#235—31no—
135C3×#235—31no—
136C3×#235—32no—
137C3×#235—32no—
138C3×#235—61no—
139C3×#235—61no—
140C3×#235C2×D311yescharacteristic
141C3×#235C2×D311yescharacteristic
142C3×#235C2×D311yescharacteristic, complemented
143C3×#235C2×D311yescharacteristic, complemented
144C2×C3×D12—21no—
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×D12—32no—
148C2×C3×D12—32no—
149C2×C3×D12—61no—
150C2×C3×D12—61no—
151C2×C3×D12C2×D311yescharacteristic, complemented
152C2×C3×D12C2×D311yescharacteristic, complemented
153#3811—22no—
154D3×#67—22no—
155#3802—21no—
156D3×D12—21no—
157D3×D12C2×D312yescomplemented
158D3×D12C2×D312yescomplemented
159#3799—21no—
160#3799C2×D312yescomplemented
161#3796—21no—
162#3795C2×D312yescomplemented
163#3756—31no—
164#3755—31no—
165#3754—31no—
166#3753—32no—
167#3753—32no—
168#3753—31no—
169#3748—32no—
170#3748C2×D311yescharacteristic, complemented
171C2×C3⋊(C3⋊C8)—31no—
172C2×C3⋊(C3⋊C8)—31no—
173C2×C3⋊(C3⋊C8)—31no—
174C2×C3⋊(C3⋊C8)—32no—
175C2×C3⋊(C3⋊C8)—61no—
176C2×C3⋊(C3⋊C8)—61no—
177C2×C3⋊(C3⋊C8)—61no—
178C2×C3⋊(C3⋊C8)—121no—
179C3×#215—32no—
180C3×#214—32no—
181C3×#213—32no—
182C3×#213—32no—
183C3×#208—31no—
184C3×#208—31no—
185C3×#208—61no—
186#3718—31no—
187#3718—31no—
188#3718—61no—
189#3717—32no—
190#3716—32no—
191#3715—31no—
192#3715—31no—
193#3715—31no—
194#3715—31no—
195#3715—32no—
196#3715—61no—
197#3715—61no—
198#3715C2×D312yescomplemented
199#3714—32no—
200#3714—32no—
201#3713—32no—
202#3713—31no—
203#3713—32no—
204#3713—32no—
205#3713—32no—
206#3713—31no—
207#3713—32no—
208#3713—62no—
209#3713—62no—
210#3713—61no—
211#3713C2×D312yescomplemented
212#3711—32no—
213#3711—32no—
214#3711—62no—
215D3×C3⋊C8—32no—
216D3×C3⋊C8—32no—
217D3×C3⋊C8—62no—
218C22×C33C2×D411yescharacteristic
219C2×C3×C3⋊D3—22no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—81no—
222C2×C32×D3—22no—
223C2×C32×D3—21no—
224C2×C32×D3—81no—
225C2×C32×D3C2×D412yes—
226C3×D32—82no—
227C3×D32—82no—
228C33×C4C2×D411yescharacteristic
229C33×C4C2411yescharacteristic
230C3×C3⋊Dic3—21no—
231C32×Dic3—21no—
232C32×Dic3C2×D412yes—
233C3×H(5,𝔽2)—91no—
234C3×H(5,𝔽2)—91no—
235#1009—31no—
236#1009—31no—
237#1009—31no—
238#1004—31no—
239C3×AGL(1,ℤ/8)—91no—
240#950—92no—
241#950—92no—
242#950—91no—
243#950—91no—
244#950—91no—
245#950—181no—
246#949—31no—
247#949—91no—
248#949—92no—
249#949—92no—
250#948—91no—
251#948—91no—
252#948—181no—
253#932—31no—
254#932—91no—
255#932—92no—
256#932—92no—
257C2×#213—92no—
258C2×#213—92no—
259C2×#213—91no—
260C2×#213—91no—
261C2×#213—91no—
262C2×#213—181no—
263#916—92no—
264#914—92no—
265#911—92no—
266D3×D8—92no—
267#908—91no—
268#907—91no—
269C23×C32—61no—
270C22×C3⋊D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—41no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C22×C3×D3—61no—
277C22×C3×D3—61no—
278C22×C3×D3—62no—
279C22×C3×D3—62no—
280C22×C3×D3—121no—
281C2×D32—22no—
282C2×D32—22no—
283C32×Q8—31no—
284C32×Q8—31no—
285C32×D4—32no—
286C32×D4—31no—
287C32×D4—31no—
288C32×D4—32no—
289C32×D4—61no—
290C32×D4—61no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—32no—
295C2×C32×C4—41no—
296C2×C32×C4—61no—
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300#638—21no—
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)C22×D311yescharacteristic
303C4⋊(C3⋊D3)C22×D312yes—
304C4×C3⋊D3—21no—
305#634C22×D311yescharacteristic
306C3×#67—21no—
307C3×#67—21no—
308C3×#67—22no—
309C3×#67—41no—
310C3×#67—62no—
311C3×#67—62no—
312C3×#67—61no—
313C3×#67—61no—
314C3×#67—62no—
315C3×#67—62no—
316C3×#67—62no—
317C3×#67—121no—
318C3×#67#6712yes—
319C3×#67#6712yes—
320C2×C3×Dic3—62no—
321C3×D12—21no—
322C3×D12—21no—
323C3×D12—21no—
324C3×D12—22no—
325C3×D12—21no—
326C3×D12—32no—
327C3×D12—31no—
328C3×D12—32no—
329C3×D12—31no—
330C3×D12—41no—
331C3×D12—62no—
332C3×D12—61no—
333C3×D12—62no—
334C3×D12—62no—
335C3×D12—62no—
336C3×D12—61no—
337C3×D12—61no—
338C3×D12—121no—
339C3×D12#6711yescharacteristic
340C3×D12#6711yescharacteristic
341C3×D12C22×D312yes—
342C3×D12C22×D312yes—
343C3×D12C22×D311yescharacteristic
344C3×D12C22×D311yescharacteristic
345C3×C4×D3—21no—
346C3×C4×D3—21no—
347C3×C4×D3—22no—
348C3×C4×D3—41no—
349C3×C4×D3—62no—
350C3×C4×D3—62no—
351C3×C4×D3—61no—
352C3×C4×D3—61no—
353C3×C4×D3—62no—
354C3×C4×D3—121no—
355C3×C4×D3C22×D312yes—
356C3×C4×D3C22×D312yes—
357C3×Dic6—21no—
358C3×Dic6—21no—
359C3×Dic6—31no—
360C3×Dic6—31no—
361C3×Dic6—61no—
362C3×Dic6#6711yescharacteristic
363C3×Dic6#6711yescharacteristic
364C3×Dic6C22×D311yescharacteristic
365C3×Dic6C22×D311yescharacteristic
366#626—22no—
367#626—22no—
368#626—22no—
369#625—22no—
370#624—22no—
371D3×Dic3—22no—
372C3⋊(C3⋊C8)—31no—
373C3⋊(C3⋊C8)—31no—
374C3⋊(C3⋊C8)—31no—
375C3⋊(C3⋊C8)—31no—
376C3⋊(C3⋊C8)—31no—
377C3⋊(C3⋊C8)—31no—
378C3⋊(C3⋊C8)—61no—
379C3⋊(C3⋊C8)—61no—
380C3⋊(C3⋊C8)—61no—
381C3⋊(C3⋊C8)—61no—
382C3⋊(C3⋊C8)—61no—
383C3⋊(C3⋊C8)—61no—
384C3⋊(C3⋊C8)—121no—
385C3⋊(C3⋊C8)—121no—
386C3⋊(C3⋊C8)C22×D312yes—
387C3×C3⋊C8—32no—
388C3×C3⋊C8—32no—
389C3×C3⋊C8—62no—
390#576—271noSylow
391C2×C33—21no—
392C2×C33C22×D411yescharacteristic
393C3×C3⋊D3—41no—
394C3×C3⋊D3—42no—
395C32×D3—22no—
396C32×D3—41no—
397C32×D3—42no—
398C3×#41—31no—
399C3×#41—31no—
400C3×#41—31no—
401C3×#41—31no—
402C3×#41—61no—
403C3×#41—61no—
404C3×#41—92no—
405C3×#41—92no—
406C3×#41—91no—
407C3×#41—181no—
408C3×#41—181no—
409C2×C3×D4—31no—
410C2×C3×D4—31no—
411C2×C3×D4—61no—
412C2×C3×D4—92no—
413C2×C3×D4—92no—
414C2×C3×D4—91no—
415C2×C3×D4—181no—
416C2×C3×D4—182no—
417C2×C3×D4—181no—
418C2×C3×D4—182no—
419C2×#67—62no—
420#239—32no—
421#239—61no—
422#239—61no—
423#237—32no—
424#237—61no—
425D3×D4—32no—
426D3×D4—32no—
427D3×D4—61no—
428D3×D4—61no—
429D3×D4—62no—
430D3×D4—62no—
431D3×D4—62no—
432D3×D4—61no—
433#235—31no—
434#235—31no—
435#235—32no—
436#235—32no—
437#235—61no—
438#235—61no—
439#235D3211yescharacteristic
440#235D3211yescharacteristic, complemented
441C2×D12—31no—
442C2×D12—31no—
443C2×D12—32no—
444C2×D12—32no—
445C2×D12—61no—
446C2×D12—61no—
447C2×D12D3211yescharacteristic, complemented
448C3×SD16—92no—
449C3×D8—92no—
450C3×M16—91no—
451#216—91no—
452#216—91no—
453#216—91no—
454#216—181no—
455#215—32no—
456#215—92no—
457#215—91no—
458#215—91no—
459#215—91no—
460#215—181no—
461#214—32no—
462#214—92no—
463#214—91no—
464#214—91no—
465#214—91no—
466#214—181no—
467#213—32no—
468#213—32no—
469#213—92no—
470#213—92no—
471#213—91no—
472#213—92no—
473#213—92no—
474#213—91no—
475#213—92no—
476#213—92no—
477#213—91no—
478#213—92no—
479#213—92no—
480#213—182no—
481#213—182no—
482#213—181no—
483#208—31no—
484#208—31no—
485#208—61no—
486#208—92no—
487#208—92no—
488#208—182no—
489C2×C3⋊C8—92no—
490C2×C3⋊C8—92no—
491C2×C3⋊C8—91no—
492C2×C3⋊C8—91no—
493C2×C3⋊C8—91no—
494C2×C3⋊C8—182no—
495C2×C3⋊C8—181no—
496C2×C3⋊C8—181no—
497C2×C3⋊C8—181no—
498C2×C3⋊C8—361no—
499D24—92no—
500#204—92no—
501ΓL(1,𝔽25)—92no—
502D3×C8—92no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—21no—
506C22×C32—32no—
507C22×C32—41no—
508C22×C32—62no—
509C22×C32—61no—
510C22×C32—241no—
511C22×C32D3×D411yescharacteristic
512C22×C32C2×#6711yescharacteristic
513C22×C32C2×#6711yescharacteristic
514C2×C3⋊D3—22no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—81no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—21no—
521C2×C3×D3—22no—
522C2×C3×D3—41no—
523C2×C3×D3—42no—
524C2×C3×D3—62no—
525C2×C3×D3—61no—
526C2×C3×D3—62no—
527C2×C3×D3—61no—
528C2×C3×D3—81no—
529C2×C3×D3—81no—
530C2×C3×D3—82no—
531C2×C3×D3—121no—
532C2×C3×D3—122no—
533C2×C3×D3—242no—
534C2×C3×D3—242no—
535C2×C3×D3—242no—
536C2×C3×D3—242no—
537C2×C3×D3—241no—
538C2×C3×D3—241no—
539C2×C3×D3—242no—
540C2×C3×D3C2×#6712yes—
541C2×C3×D3C2×#6712yes—
542D32—82no—
543D32—82no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—21no—
547C32×C4—21no—
548C32×C4—21no—
549C32×C4—21no—
550C32×C4—32no—
551C32×C4—41no—
552C32×C4—41no—
553C32×C4—61no—
554C32×C4D3×D411yescharacteristic
555C32×C4C2×#6711yescharacteristic
556C32×C4C2×#6711yescharacteristic
557C32×C4C23×D311yescharacteristic
558C32×C4C23×D311yescharacteristic
559C32×C4C23×D311yescharacteristic
560C3⋊Dic3—21no—
561C3×Dic3—21no—
562C3×Dic3—21no—
563C3×Dic3—22no—
564C3×Dic3—41no—
565C3×Dic3—61no—
566C3×Dic3—61no—
567C3×Dic3—121no—
568C3×Dic3C2×#6712yes—
569C3×Dic3C2×#6712yes—
570H(5,𝔽2)—91no—
571H(5,𝔽2)—91no—
572AGL(1,ℤ/8)—91no—
573AGL(1,ℤ/8)—271no—
574AGL(1,ℤ/8)—272no—
575AGL(1,ℤ/8)—272no—
576#135—272no—
577#135—271no—
578C2×D8—272no—
579C2×D8—271no—
580#131—271no—
581C33#57611yescharacteristic, complemented, Sylow
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—121no—
585C23×C3—182no—
586C23×C3—182no—
587C23×C3—181no—
588C22×D3—21no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—121no—
596C3×Q8—31no—
597C3×Q8—31no—
598C3×Q8—31no—
599C3×Q8—31no—
600C3×Q8—61no—
601C3×Q8—61no—
602C3×Q8—91no—
603C3×D4—32no—
604C3×D4—32no—
605C3×D4—31no—
606C3×D4—32no—
607C3×D4—32no—
608C3×D4—31no—
609C3×D4—31no—
610C3×D4—31no—
611C3×D4—61no—
612C3×D4—62no—
613C3×D4—61no—
614C3×D4—62no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C3×D4—92no—
620C3×D4—91no—
621C3×D4—121no—
622C3×D4—121no—
623C3×D4—182no—
624C3×D4—182no—
625C3×D4—182no—
626C3×D4—182no—
627C3×D4—181no—
628C3×D4—181no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—41no—
635C2×C3×C4—62no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—121no—
639C2×C3×C4—182no—
640C2×C3×C4—182no—
641C2×C3×C4—181no—
642C2×C3×C4C2×D3211yescharacteristic
643C2×C3×C4C2×D3211yescharacteristic
644C2×C3×C4C2×D3211yescharacteristic
645#67—21no—
646#67—62no—
647#67—62no—
648#67—61no—
649#67—61no—
650#67—62no—
651#67—62no—
652#67—62no—
653#67—121no—
654#67#62512yes—
655C2×Dic3—62no—
656D12—21no—
657D12—32no—
658D12—31no—
659D12—31no—
660D12—32no—
661D12—62no—
662D12—61no—
663D12—62no—
664D12—62no—
665D12—62no—
666D12—61no—
667D12—61no—
668D12—121no—
669D12#62511yescharacteristic
670D12C2×D3211yescharacteristic
671D12C2×D3212yes—
672C4×D3—21no—
673C4×D3—62no—
674C4×D3—62no—
675C4×D3—61no—
676C4×D3—61no—
677C4×D3—62no—
678C4×D3—121no—
679C4×D3C2×D3212yes—
680Dic6—31no—
681Dic6—31no—
682Dic6—61no—
683Dic6#62511yescharacteristic
684Dic6C2×D3211yescharacteristic
685C3×C8—92no—
686C3⋊C8—32no—
687C3⋊C8—32no—
688C3⋊C8—62no—
689C3⋊C8—91no—
690C3⋊C8—91no—
691C3⋊C8—91no—
692C3⋊C8—91no—
693C3⋊C8—91no—
694C3⋊C8—91no—
695C3⋊C8—181no—
696C3⋊C8—181no—
697C3⋊C8—181no—
698C3⋊C8—181no—
699C3⋊C8—181no—
700C3⋊C8—181no—
701C3⋊C8—361no—
702C3⋊C8—361no—
703C2×C32—21no—
704C2×C32—22no—
705C2×C32—21no—
706C2×C32—21no—
707C2×C32—21no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—41no—
711C2×C32—41no—
712C2×C32—41no—
713C2×C32—42no—
714C2×C32—62no—
715C2×C32—121no—
716C2×C32—122no—
717C2×C32C2×D3×D411yescharacteristic
718C2×C32C22×#6711yescharacteristic
719C2×C32C22×#6711yescharacteristic
720C3⋊D3—41no—
721C3⋊D3—42no—
722C3×D3—22no—
723C3×D3—22no—
724C3×D3—42no—
725C3×D3—42no—
726C3×D3—41no—
727C3×D3—41no—
728C3×D3—42no—
729C3×D3—81no—
730C3×D3—82no—
731C3×D3—121no—
732C3×D3—122no—
733C3×D3—122no—
734C3×D3—121no—
735C3×D3—241no—
736C3×D3—242no—
737#41—31no—
738#41—31no—
739#41—92no—
740#41—92no—
741#41—91no—
742#41—181no—
743#41—181no—
744C2×D4—31no—
745C2×D4—92no—
746C2×D4—92no—
747C2×D4—91no—
748C2×D4—181no—
749C2×D4—182no—
750C2×D4—181no—
751C2×D4—182no—
752Q16—271no—
753SD16—92no—
754SD16—272no—
755SD16—271no—
756SD16—271no—
757D8—92no—
758D8—272no—
759D8—271no—
760D8—272no—
761D8—272no—
762M16—91no—
763M16—272no—
764C2×C8—272no—
765C2×C8—271no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—32no—
770C22×C3—32no—
771C22×C3—41no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—62no—
777C22×C3—121no—
778C22×C3—122no—
779C22×C3—182no—
780C22×C3—181no—
781C22×C3—241no—
782C22×C3—241no—
783C22×C3—242no—
784C22×C3—721no—
785C22×C3—722no—
786C22×C3—722no—
787C22×C3C2×#62511yescharacteristic
788C22×C3D3×#6711yescharacteristic
789C22×C3D3×#6711yescharacteristic
790C2×D3—21no—
791C2×D3—22no—
792C2×D3—62no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—62no—
796C2×D3—81no—
797C2×D3—121no—
798C2×D3—122no—
799C2×D3—242no—
800C2×D3—242no—
801C2×D3—242no—
802C2×D3—242no—
803C2×D3—241no—
804C2×D3—241no—
805C2×D3—242no—
806C2×D3C2×#62512yes—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—21no—
813C3×C4—32no—
814C3×C4—32no—
815C3×C4—41no—
816C3×C4—41no—
817C3×C4—62no—
818C3×C4—61no—
819C3×C4—61no—
820C3×C4—121no—
821C3×C4—181no—
822C3×C4C2×#62511yescharacteristic
823C3×C4D3×#6711yescharacteristic
824C3×C4D3×#6711yescharacteristic
825C3×C4C22×D3211yescharacteristic
826C3×C4C22×D3211yescharacteristic
827C3×C4C22×D3211yescharacteristic
828Dic3—21no—
829Dic3—61no—
830Dic3—61no—
831Dic3—121no—
832Dic3C2×#62512yes—
833C32—21no—
834C32—21no—
835C32—21no—
836C32—41no—
837C32#577411yescharacteristic, complemented
838C32#583511yescharacteristic, complemented
839C32#583511yescharacteristic, complemented
840C23—61no—
841C23—182no—
842C23—182no—
843C23—181no—
844Q8—31no—
845Q8—31no—
846Q8—91no—
847D4—32no—
848D4—31no—
849D4—32no—
850D4—31no—
851D4—61no—
852D4—61no—
853D4—91no—
854D4—92no—
855D4—182no—
856D4—182no—
857D4—182no—
858D4—182no—
859D4—181no—
860D4—181no—
861C2×C4—32no—
862C2×C4—61no—
863C2×C4—182no—
864C2×C4—182no—
865C2×C4—181no—
866C2×C4D3311yescharacteristic
867C8—92no—
868C8—271no—
869C8—271no—
870C2×C3—22no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—41no—
878C2×C3—41no—
879C2×C3—42no—
880C2×C3—41no—
881C2×C3—62no—
882C2×C3—62no—
883C2×C3—122no—
884C2×C3—121no—
885C2×C3—121no—
886C2×C3—122no—
887C2×C3—122no—
888C2×C3—242no—
889C2×C3—241no—
890C2×C3—362no—
891C2×C3—361no—
892C2×C3C22×#62511yescharacteristic
893C2×C3C2×D3×#6711yescharacteristic
894C2×C3C2×D3×#6711yescharacteristic
895D3—22no—
896D3—42no—
897D3—41no—
898D3—121no—
899D3—122no—
900D3—121no—
901D3—122no—
902D3—242no—
903D3—241no—
904C22—32no—
905C22—61no—
906C22—62no—
907C22—182no—
908C22—181no—
909C22—241no—
910C22—721no—
911C22—722no—
912C22—722no—
913C22D3×#62511yescharacteristic
914C4—32no—
915C4—61no—
916C4—181no—
917C4D3×#62511yescharacteristic
918C4C2×D3311yescharacteristic
919C3—21no—
920C3—21no—
921C3—21no—
922C3—41no—
923C3#1059509711yescharacteristic, complemented
924C3#1059544411yescharacteristic, complemented
925C3#1059545411yescharacteristic, complemented
926C2—21no—
927C2—62no—
928C2—122no—
929C2—121no—
930C2—362no—
931C2—361no—
932C2C2×D3×#62511yescharacteristic
subgroupG/H
centerC2C2×D3×#625
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC2×C33C22×D4
hypercenterC2×C4D33
hypocenterC33#576
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×#64308C2semidirect
2. C3×#64307C2semidirect
3. #11723661C2semidirect
4. #11723363C2semidirect
5. C2×#88789C2semidirect
6. #11723350C2semidirect
7. C3×#63823C2semidirect
8. #11722867C2semidirect
9. #11722866C2semidirect
10. #11722851C2semidirect
11. D3×#3713C2semidirect
15. C3×#3828C22semidirect
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
18. C32×#235C22semidirect
19. C2×C32×D12C22semidirect
24. C3×D3×D12C22semidirect
25. C3×D3×D12C22semidirect
27. C3×#3799C22semidirect
29. C3×#3795C22semidirect
30. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
31. C3×#3748C22semidirect
32. #88811C22semidirect
33. #88810C22semidirect
34. #88798C22semidirect
35. #88793C22semidirect
36. #88792C22semidirect
37. #88789C22semidirect
38. #88789C22semidirect
39. #88789C22semidirect
40. #88786C22semidirect
41. D3×C3⋊(C3⋊C8)C22semidirect
42. C3×#3715C22semidirect
43. C3×#3713C22semidirect
48. #64308D3semidirect
49. #64307D3semidirect
68. #63823D3semidirect
116. #3828C2×D3semidirect
117. C2×C4⋊(C3⋊D3)C2×D3semidirect
142. C3×#235C2×D3semidirect
143. C3×#235C2×D3semidirect
151. C2×C3×D12C2×D3semidirect
152. C2×C3×D12C2×D3semidirect
157. D3×D12C2×D3semidirect
158. D3×D12C2×D3semidirect
160. #3799C2×D3semidirect
162. #3795C2×D3semidirect
170. #3748C2×D3semidirect
198. #3715C2×D3semidirect
211. #3713C2×D3semidirect
440. #235D32semidirect
447. C2×D12D32semidirect
581. C33#576semidirect
837. C32#5774semidirect
838. C32#5835semidirect
839. C32#5835semidirect
923. C3#10595097semidirect
924. C3#10595444semidirect
925. C3#10595454semidirect

Maximal subgroups

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

subgroupindex
C3×#643082
C3×#643072
#117236612
#117233632
C2×#887892
#117233502
C3×#638232
#117228672
#117228662
#117228512
D3×#37132
#105954543
#105954443
#105950973