Finite Group Databasebeta

← #13170550

Subgroups — #13170550

Order 1728.

1246 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64307C211yesmaximal, characteristic, complemented
2C3×#64298C211yesmaximal, characteristic, complemented
3#11723663C211yesmaximal, characteristic, complemented
4C2×#88792C211yesmaximal, characteristic, complemented
5#11723363C211yesmaximal, characteristic, complemented
6#11723350C211yesmaximal, characteristic, complemented
7C3×#63823C211yesmaximal, characteristic, complemented
8#11722882C212yesmaximal, complemented
9#11722866C212yesmaximal, complemented
10#11722850C212yesmaximal, complemented
11D3×#3715C212yesmaximal, complemented
12#10595455—31nomaximal
13#10595446—31nomaximal
14#10595106—31nomaximal
15C3×#3828C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic, complemented
17C32×#235C2211yescharacteristic
18C32×#235C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic
20C3×D3×#67—22no—
21C3×#3805—22no—
22C3×#3802—21no—
23C3×D3×D12C2212yes—
24C3×#3796—21no—
25C3×#3795—21no—
26C3×#3795C2212yes—
27C3×#3795C2212yescomplemented
28C3×D3×Dic6—21no—
29C3×D3×Dic6C2212yescomplemented
30C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
31C3×#3748C2211yescharacteristic, complemented
32#88812C2212yescomplemented
33#88811C2212yescomplemented
34#88798C2211yescharacteristic, complemented
35#88793C2211yescharacteristic, complemented
36#88792C2212yescomplemented
37#88792C2211yescharacteristic, complemented
38#88792C2212yescomplemented
39#88789C2211yescharacteristic, complemented
40#88786C2212yescomplemented
41D3×C3⋊(C3⋊C8)C2212yescomplemented
42C3×#3715C2212yescomplemented
43C3×#3713C2212yescomplemented
44C3×#1010—31no—
45C3×#1010—31no—
46C3×#1009—31no—
47C3×#1004—31no—
48#64307D311yescharacteristic, complemented
49#64298D311yescharacteristic, complemented
50#64159—31no—
51#64157—31no—
52C2×#3754—31no—
53C3×#949—31no—
54C3×#932—31no—
55#63946—32no—
56D3×#215—32no—
57#63933—32no—
58#63933—32no—
59#63932—32no—
60#63929—32no—
61D3×#214—32no—
62#63925—32no—
63#63833—31no—
64#63831—31no—
65#63827—31no—
66#63827—32no—
67C2×#3715—31no—
68C2×#3715—31no—
69C2×#3715—32no—
70C2×#3715—61no—
71#63823—32no—
72#63823D311yescharacteristic, complemented
73#63822—31no—
74#63822—31no—
75#63822—32no—
76#63822—61no—
77#63815—31no—
78#63815—31no—
79#63815—61no—
80C22×C32×D3—21no—
81C2×C3×D32—22no—
82C2×C33×C4C2311yescharacteristic
83C3×#638—21no—
84C2×C3×C3⋊Dic3—21no—
85C3×C4⋊(C3⋊D3)C2311yescharacteristic
86C3×C4×C3⋊D3—21no—
87C3×#634—21no—
88C3×#634C2312yes—
89C3×#634C2311yescharacteristic
90C32×#67—21no—
91C32×#67D412yes—
92C32×D12—21no—
93C32×D12D411yescharacteristic
94C32×D12C2312yes—
95C32×D12C2311yescharacteristic
96C32×C4×D3—21no—
97C32×C4×D3C2312yes—
98C32×Dic6D411yescharacteristic
99C32×Dic6C2311yescharacteristic
100C3×#627—22no—
101C3×#626—22no—
102C3×#625—22no—
103C3×#625—22no—
104C3×D3×Dic3—22no—
105C3×D3×Dic3—22no—
106C3×D3×Dic3—22no—
107C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
108C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
109C3×C3⋊(C3⋊C8)C2312yes—
110#5837—91no—
111#5836—91no—
112#5775—91no—
113C32×#41—31no—
114C32×#41—31no—
115C2×C32×D4—31no—
116#3828C2×D311yescharacteristic
117C2×#634C2×D311yescharacteristic, complemented
118C2×C3×#67—62no—
119C3×#239—61no—
120C3×D3×Q8—32no—
121C3×D3×Q8—61no—
122C3×#237—32no—
123C3×#237—32no—
124C3×#237—61no—
125C3×#237—62no—
126C3×#237—62no—
127C3×#237—61no—
128C3×D3×D4—32no—
129C3×D3×D4—61no—
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—32no—
146C2×C3×D12C2×D311yescharacteristic
147C2×C3×D12C2×D311yescharacteristic
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6—32no—
151C2×C3×Dic6—61no—
152C2×C3×Dic6—61no—
153D3×#67—22no—
154#3805—22no—
155#3802—21no—
156D3×D12C2×D312yes—
157#3796—21no—
158#3795—21no—
159#3795C2×D312yes—
160#3795C2×D312yescomplemented
161D3×Dic6—21no—
162D3×Dic6C2×D312yescomplemented
163#3756—31no—
164#3755—31no—
165#3754—32no—
166#3754—32no—
167#3754—31no—
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#3719—32no—
187#3719—32no—
188#3718—31no—
189#3718—31no—
190#3718—32no—
191#3718—61no—
192#3717—32no—
193#3716—32no—
194#3715—31no—
195#3715—32no—
196#3715—31no—
197#3715—32no—
198#3715—32no—
199#3715—32no—
200#3715—31no—
201#3715—31no—
202#3715—32no—
203#3715—61no—
204#3715—61no—
205#3715—62no—
206#3715—62no—
207#3715C2×D312yescomplemented
208#3713—31no—
209#3713—31no—
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—21no—
220C2×C32×D3—21no—
221C2×C32×D3—22no—
222C2×C32×D3—81no—
223C2×C32×D3C2×D412yes—
224C3×D32—82no—
225C33×C4C2×D411yescharacteristic
226C33×C4C2411yescharacteristic
227C3×C3⋊Dic3—21no—
228C3×C3⋊Dic3—22no—
229C32×Dic3—21no—
230C32×Dic3C2×D412yes—
231C3×2−1+4—91no—
232C3×H(5,𝔽2)—91no—
233#1010—31no—
234#1010—31no—
235#1009—31no—
236#1004—31no—
237C3×AGL(1,ℤ/8)—91no—
238#951—91no—
239#951—92no—
240#950—92no—
241#950—92no—
242#950—91no—
243#950—91no—
244#950—91no—
245#950—181no—
246#949—31no—
247#949—92no—
248#948—91no—
249#948—91no—
250#948—181no—
251#942—91no—
252#942—92no—
253C2×#215—92no—
254C2×#215—91no—
255C2×#214—92no—
256C2×#214—91no—
257C2×#214—91no—
258C2×#214—181no—
259#932—31no—
260#932—92no—
261#915—92no—
262D3×SD16—92no—
263#912—92no—
264#911—92no—
265#909—91no—
266#907—91no—
267C23×C32—61no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—41no—
271C22×C3×D3—62no—
272C22×C3×D3—62no—
273C2×D32—22no—
274C32×Q8—31no—
275C32×Q8—31no—
276C32×D4—32no—
277C32×D4—31no—
278C32×D4—31no—
279C32×D4—32no—
280C32×D4—61no—
281C32×D4—61no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—32no—
286C2×C32×C4—41no—
287C2×C32×C4—61no—
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—21no—
292C2×C3⋊Dic3—21no—
293C4⋊(C3⋊D3)C22×D311yescharacteristic
294C4×C3⋊D3—21no—
295#634—21no—
296#634C22×D312yes—
297#634C22×D311yescharacteristic
298C3×#67—21no—
299C3×#67—21no—
300C3×#67—22no—
301C3×#67—41no—
302C3×#67—62no—
303C3×#67—62no—
304C3×#67—61no—
305C3×#67—61no—
306C3×#67—62no—
307C3×#67—62no—
308C3×#67—62no—
309C3×#67—121no—
310C3×#67#6712yes—
311C3×#67#6712yes—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3—62no—
317C2×C3×Dic3—121no—
318C3×D12—21no—
319C3×D12—21no—
320C3×D12—21no—
321C3×D12—21no—
322C3×D12—22no—
323C3×D12—31no—
324C3×D12—31no—
325C3×D12—41no—
326C3×D12—61no—
327C3×D12—62no—
328C3×D12#6711yescharacteristic
329C3×D12#6711yescharacteristic
330C3×D12C22×D311yescharacteristic
331C3×D12C22×D311yescharacteristic
332C3×D12C22×D312yes—
333C3×D12C22×D312yes—
334C3×C4×D3—21no—
335C3×C4×D3—21no—
336C3×C4×D3—22no—
337C3×C4×D3—41no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—62no—
341C3×C4×D3—61no—
342C3×C4×D3—61no—
343C3×C4×D3—121no—
344C3×C4×D3C22×D312yes—
345C3×C4×D3C22×D312yes—
346C3×Dic6—21no—
347C3×Dic6—21no—
348C3×Dic6—32no—
349C3×Dic6—32no—
350C3×Dic6—31no—
351C3×Dic6—31no—
352C3×Dic6—62no—
353C3×Dic6—61no—
354C3×Dic6—62no—
355C3×Dic6—61no—
356C3×Dic6—61no—
357C3×Dic6—62no—
358C3×Dic6—121no—
359C3×Dic6#6711yescharacteristic
360C3×Dic6#6711yescharacteristic
361C3×Dic6C22×D311yescharacteristic
362C3×Dic6C22×D311yescharacteristic
363#627—22no—
364#626—22no—
365#625—22no—
366#625—22no—
367D3×Dic3—22no—
368D3×Dic3—22no—
369D3×Dic3—22no—
370C3⋊(C3⋊C8)—31no—
371C3⋊(C3⋊C8)—31no—
372C3⋊(C3⋊C8)—31no—
373C3⋊(C3⋊C8)—31no—
374C3⋊(C3⋊C8)—31no—
375C3⋊(C3⋊C8)—31no—
376C3⋊(C3⋊C8)—61no—
377C3⋊(C3⋊C8)—61no—
378C3⋊(C3⋊C8)—61no—
379C3⋊(C3⋊C8)—61no—
380C3⋊(C3⋊C8)—61no—
381C3⋊(C3⋊C8)—61no—
382C3⋊(C3⋊C8)—121no—
383C3⋊(C3⋊C8)—121no—
384C3⋊(C3⋊C8)C22×D312yes—
385C3×C3⋊C8—32no—
386C3×C3⋊C8—32no—
387C3×C3⋊C8—62no—
388#577—271noSylow
389C2×C33—21no—
390C2×C33C22×D411yescharacteristic
391C3×C3⋊D3—41no—
392C32×D3—22no—
393C32×D3—42no—
394C32×D3—41no—
395C3×#41—31no—
396C3×#41—31no—
397C3×#41—31no—
398C3×#41—31no—
399C3×#41—61no—
400C3×#41—61no—
401C3×#41—92no—
402C3×#41—92no—
403C3×#41—91no—
404C3×#41—181no—
405C3×#41—182no—
406C3×#41—181no—
407C2×C3×Q8—92no—
408C2×C3×Q8—91no—
409C2×C3×Q8—181no—
410C2×C3×D4—31no—
411C2×C3×D4—31no—
412C2×C3×D4—61no—
413C2×C3×D4—92no—
414C2×C3×D4—181no—
415C2×C3×D4—182no—
416C2×#67—62no—
417#239—61no—
418D3×Q8—32no—
419D3×Q8—61no—
420#237—32no—
421#237—32no—
422#237—61no—
423#237—62no—
424#237—62no—
425#237—61no—
426D3×D4—32no—
427D3×D4—61no—
428D3×D4—62no—
429D3×D4—61no—
430#235—31no—
431#235—31no—
432#235—32no—
433#235—32no—
434#235—61no—
435#235—61no—
436#235D3211yescharacteristic
437#235D3211yescharacteristic, complemented
438C2×D12—32no—
439C2×D12D3211yescharacteristic
440C2×Dic6—31no—
441C2×Dic6—31no—
442C2×Dic6—32no—
443C2×Dic6—61no—
444C2×Dic6—61no—
445C3×SD16—92no—
446C3×D8—92no—
447C3×M16—91no—
448#216—92no—
449#216—92no—
450#216—91no—
451#216—91no—
452#216—91no—
453#216—181no—
454#215—32no—
455#215—92no—
456#215—91no—
457#215—91no—
458#215—92no—
459#215—92no—
460#215—91no—
461#215—181no—
462#214—32no—
463#214—92no—
464#214—92no—
465#214—91no—
466#214—92no—
467#214—92no—
468#214—92no—
469#214—91no—
470#214—91no—
471#214—182no—
472#214—182no—
473#214—181no—
474#213—32no—
475#213—32no—
476#213—91no—
477#213—91no—
478#213—91no—
479#213—181no—
480#208—31no—
481#208—31no—
482#208—61no—
483#208—92no—
484#208—92no—
485#208—182no—
486C2×C3⋊C8—92no—
487C2×C3⋊C8—92no—
488C2×C3⋊C8—91no—
489C2×C3⋊C8—91no—
490C2×C3⋊C8—91no—
491C2×C3⋊C8—182no—
492C2×C3⋊C8—181no—
493C2×C3⋊C8—181no—
494C2×C3⋊C8—181no—
495C2×C3⋊C8—361no—
496Dic12—92no—
497#204—92no—
498ΓL(1,𝔽25)—92no—
499D3×C8—92no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—32no—
504C22×C32—41no—
505C22×C32—61no—
506C22×C32—62no—
507C22×C32—241no—
508C22×C32D3×D411yescharacteristic
509C22×C32C2×#6711yescharacteristic
510C22×C32C2×#6711yescharacteristic
511C2×C3⋊D3—21no—
512C2×C3×D3—21no—
513C2×C3×D3—22no—
514C2×C3×D3—21no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—41no—
518C2×C3×D3—42no—
519C2×C3×D3—61no—
520C2×C3×D3—61no—
521C2×C3×D3—81no—
522C2×C3×D3—81no—
523C2×C3×D3—82no—
524C2×C3×D3—121no—
525C2×C3×D3—242no—
526C2×C3×D3—242no—
527C2×C3×D3C2×#6712yes—
528C2×C3×D3C2×#6712yes—
529D32—82no—
530C32×C4—21no—
531C32×C4—21no—
532C32×C4—21no—
533C32×C4—21no—
534C32×C4—21no—
535C32×C4—21no—
536C32×C4—32no—
537C32×C4—41no—
538C32×C4—41no—
539C32×C4—61no—
540C32×C4D3×D411yescharacteristic
541C32×C4C2×#6711yescharacteristic
542C32×C4C2×#6711yescharacteristic
543C32×C4C23×D311yescharacteristic
544C32×C4C23×D311yescharacteristic
545C32×C4C23×D311yescharacteristic
546C3⋊Dic3—21no—
547C3⋊Dic3—22no—
548C3×Dic3—21no—
549C3×Dic3—21no—
550C3×Dic3—22no—
551C3×Dic3—41no—
552C3×Dic3—62no—
553C3×Dic3—61no—
554C3×Dic3—62no—
555C3×Dic3—61no—
556C3×Dic3—122no—
557C3×Dic3—121no—
558C3×Dic3C2×#6712yes—
559C3×Dic3C2×#6712yes—
5602−1+4—91no—
561H(5,𝔽2)—91no—
562#137—271no—
563#137—272no—
564AGL(1,ℤ/8)—91no—
565AGL(1,ℤ/8)—272no—
566#135—272no—
567#135—271no—
568C2×SD16—272no—
569C2×SD16—271no—
570#131—271no—
571C33#57711yescharacteristic, complemented, Sylow
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—121no—
575C23×C3—182no—
576C22×D3—21no—
577C22×D3—62no—
578C22×D3—62no—
579C3×Q8—31no—
580C3×Q8—31no—
581C3×Q8—31no—
582C3×Q8—31no—
583C3×Q8—61no—
584C3×Q8—61no—
585C3×Q8—92no—
586C3×Q8—91no—
587C3×Q8—182no—
588C3×Q8—181no—
589C3×D4—32no—
590C3×D4—32no—
591C3×D4—31no—
592C3×D4—32no—
593C3×D4—31no—
594C3×D4—32no—
595C3×D4—31no—
596C3×D4—31no—
597C3×D4—61no—
598C3×D4—61no—
599C3×D4—62no—
600C3×D4—62no—
601C3×D4—61no—
602C3×D4—61no—
603C3×D4—61no—
604C3×D4—61no—
605C3×D4—91no—
606C3×D4—121no—
607C3×D4—121no—
608C3×D4—182no—
609C3×D4—182no—
610C3×D4—182no—
611C3×D4—181no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—41no—
618C2×C3×C4—62no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—121no—
622C2×C3×C4—182no—
623C2×C3×C4—182no—
624C2×C3×C4—182no—
625C2×C3×C4—181no—
626C2×C3×C4—181no—
627C2×C3×C4C2×D3211yescharacteristic
628C2×C3×C4C2×D3211yescharacteristic
629C2×C3×C4C2×D3211yescharacteristic
630#67—21no—
631#67—62no—
632#67—62no—
633#67—61no—
634#67—61no—
635#67—62no—
636#67—62no—
637#67—62no—
638#67—121no—
639#67#62512yes—
640C2×Dic3—62no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—62no—
644C2×Dic3—62no—
645C2×Dic3—121no—
646D12—21no—
647D12—31no—
648D12—31no—
649D12—61no—
650D12—62no—
651D12#62511yescharacteristic
652D12C2×D3211yescharacteristic
653D12C2×D3212yes—
654C4×D3—21no—
655C4×D3—62no—
656C4×D3—62no—
657C4×D3—62no—
658C4×D3—61no—
659C4×D3—61no—
660C4×D3—121no—
661C4×D3C2×D3212yes—
662Dic6—32no—
663Dic6—31no—
664Dic6—32no—
665Dic6—31no—
666Dic6—62no—
667Dic6—61no—
668Dic6—62no—
669Dic6—61no—
670Dic6—61no—
671Dic6—62no—
672Dic6—121no—
673Dic6#62511yescharacteristic
674Dic6C2×D3211yescharacteristic
675C3×C8—92no—
676C3⋊C8—32no—
677C3⋊C8—32no—
678C3⋊C8—62no—
679C3⋊C8—91no—
680C3⋊C8—91no—
681C3⋊C8—91no—
682C3⋊C8—91no—
683C3⋊C8—91no—
684C3⋊C8—91no—
685C3⋊C8—181no—
686C3⋊C8—181no—
687C3⋊C8—181no—
688C3⋊C8—181no—
689C3⋊C8—181no—
690C3⋊C8—181no—
691C3⋊C8—361no—
692C3⋊C8—361no—
693C2×C32—21no—
694C2×C32—22no—
695C2×C32—21no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32—41no—
701C2×C32—41no—
702C2×C32—41no—
703C2×C32—42no—
704C2×C32—62no—
705C2×C32—121no—
706C2×C32—122no—
707C2×C32C2×D3×D411yescharacteristic
708C2×C32C22×#6711yescharacteristic
709C2×C32C22×#6711yescharacteristic
710C3⋊D3—41no—
711C3×D3—22no—
712C3×D3—22no—
713C3×D3—42no—
714C3×D3—41no—
715C3×D3—42no—
716C3×D3—42no—
717C3×D3—41no—
718C3×D3—81no—
719C3×D3—82no—
720C3×D3—121no—
721C3×D3—121no—
722C3×D3—241no—
723#41—31no—
724#41—31no—
725#41—92no—
726#41—92no—
727#41—91no—
728#41—181no—
729#41—182no—
730#41—181no—
731C2×Q8—92no—
732C2×Q8—91no—
733C2×Q8—181no—
734C2×D4—31no—
735C2×D4—92no—
736C2×D4—181no—
737C2×D4—182no—
738Q16—272no—
739Q16—271no—
740SD16—92no—
741SD16—272no—
742SD16—272no—
743SD16—272no—
744SD16—271no—
745SD16—271no—
746D8—92no—
747D8—271no—
748M16—91no—
749M16—272no—
750C2×C8—272no—
751C2×C8—271no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—32no—
756C22×C3—32no—
757C22×C3—41no—
758C22×C3—62no—
759C22×C3—61no—
760C22×C3—62no—
761C22×C3—61no—
762C22×C3—62no—
763C22×C3—121no—
764C22×C3—122no—
765C22×C3—181no—
766C22×C3—241no—
767C22×C3—241no—
768C22×C3—242no—
769C22×C3—722no—
770C22×C3C2×#62511yescharacteristic
771C22×C3D3×#6711yescharacteristic
772C22×C3D3×#6711yescharacteristic
773C2×D3—21no—
774C2×D3—22no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—81no—
778C2×D3—121no—
779C2×D3—242no—
780C2×D3—242no—
781C2×D3C2×#62512yes—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—32no—
789C3×C4—32no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—62no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—121no—
796C3×C4—181no—
797C3×C4—182no—
798C3×C4C2×#62511yescharacteristic
799C3×C4D3×#6711yescharacteristic
800C3×C4D3×#6711yescharacteristic
801C3×C4C22×D3211yescharacteristic
802C3×C4C22×D3211yescharacteristic
803C3×C4C22×D3211yescharacteristic
804Dic3—21no—
805Dic3—62no—
806Dic3—61no—
807Dic3—62no—
808Dic3—61no—
809Dic3—122no—
810Dic3—121no—
811Dic3C2×#62512yes—
812C32—21no—
813C32—21no—
814C32—21no—
815C32—41no—
816C32#577511yescharacteristic, complemented
817C32#583611yescharacteristic, complemented
818C32#583711yescharacteristic, complemented
819C23—61no—
820C23—182no—
821Q8—31no—
822Q8—31no—
823Q8—92no—
824Q8—91no—
825Q8—182no—
826Q8—181no—
827D4—32no—
828D4—31no—
829D4—32no—
830D4—31no—
831D4—61no—
832D4—61no—
833D4—91no—
834D4—182no—
835D4—182no—
836D4—182no—
837D4—181no—
838C2×C4—32no—
839C2×C4—61no—
840C2×C4—182no—
841C2×C4—182no—
842C2×C4—182no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4D3311yescharacteristic
846C8—92no—
847C8—271no—
848C8—271no—
849C2×C3—22no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—41no—
857C2×C3—41no—
858C2×C3—42no—
859C2×C3—41no—
860C2×C3—62no—
861C2×C3—62no—
862C2×C3—122no—
863C2×C3—121no—
864C2×C3—122no—
865C2×C3—121no—
866C2×C3—122no—
867C2×C3—242no—
868C2×C3—241no—
869C2×C3—361no—
870C2×C3C22×#62511yescharacteristic
871C2×C3C2×D3×#6711yescharacteristic
872C2×C3C2×D3×#6711yescharacteristic
873D3—22no—
874D3—42no—
875D3—41no—
876D3—121no—
877D3—121no—
878D3—241no—
879C22—32no—
880C22—61no—
881C22—62no—
882C22—181no—
883C22—241no—
884C22—722no—
885C22D3×#62511yescharacteristic
886C4—32no—
887C4—61no—
888C4—181no—
889C4—182no—
890C4D3×#62511yescharacteristic
891C4C2×D3311yescharacteristic
892C3—21no—
893C3—21no—
894C3—21no—
895C3—41no—
896C3#1059510611yescharacteristic, complemented
897C3#1059544611yescharacteristic, complemented
898C3#1059545511yescharacteristic, complemented
899C2—21no—
900C2—62no—
901C2—122no—
902C2—121no—
903C2—361no—
904C2C2×D3×#62511yescharacteristic
subgroupG/H
centerC2C2×D3×#625
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC2×C33C22×D4
hypercenterC2×C4D33
hypocenterC33#577
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×#64307C2semidirect
2. C3×#64298C2semidirect
3. #11723663C2semidirect
4. C2×#88792C2semidirect
5. #11723363C2semidirect
6. #11723350C2semidirect
7. C3×#63823C2semidirect
8. #11722882C2semidirect
9. #11722866C2semidirect
10. #11722850C2semidirect
11. D3×#3715C2semidirect
16. C2×C3×#634C22semidirect
18. C32×#235C22semidirect
27. C3×#3795C22semidirect
29. C3×D3×Dic6C22semidirect
30. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
31. C3×#3748C22semidirect
32. #88812C22semidirect
33. #88811C22semidirect
34. #88798C22semidirect
35. #88793C22semidirect
36. #88792C22semidirect
37. #88792C22semidirect
38. #88792C22semidirect
39. #88789C22semidirect
40. #88786C22semidirect
41. D3×C3⋊(C3⋊C8)C22semidirect
42. C3×#3715C22semidirect
43. C3×#3713C22semidirect
48. #64307D3semidirect
49. #64298D3semidirect
72. #63823D3semidirect
117. C2×#634C2×D3semidirect
142. C3×#235C2×D3semidirect
143. C3×#235C2×D3semidirect
160. #3795C2×D3semidirect
162. D3×Dic6C2×D3semidirect
170. #3748C2×D3semidirect
207. #3715C2×D3semidirect
211. #3713C2×D3semidirect
437. #235D32semidirect
571. C33#577semidirect
816. C32#5775semidirect
817. C32#5836semidirect
818. C32#5837semidirect
896. C3#10595106semidirect
897. C3#10595446semidirect
898. C3#10595455semidirect

Maximal subgroups

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

subgroupindex
C3×#643072
C3×#642982
#117236632
C2×#887922
#117233632
#117233502
C3×#638232
#117228822
#117228662
#117228502
D3×#37152
#105954553
#105954463
#105951063