Finite Group Databasebeta

← #13170662

Subgroups — #13170662

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
1C2×#89041C211yesmaximal, characteristic, complemented
2C3×#64306C211yesmaximal, characteristic, complemented
3#11723373C211yesmaximal, characteristic, complemented
4#11723365C211yesmaximal, characteristic, complemented
5C3⋊D3×#208C211yesmaximal, characteristic, complemented
6C3×#63831C211yesmaximal, characteristic, complemented
7C3×#63825C211yesmaximal, characteristic, complemented
8#11722892C212yesmaximal, complemented
9#11722875C212yesmaximal, complemented
10#11722860C212yesmaximal, complemented
11#11722859C212yesmaximal, complemented
12#10595470—31nomaximal
13#10595469—31nomaximal
14#10594718—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic, complemented
18C32×#235C2211yescharacteristic
19C32×#235C2211yescharacteristic
20C2×#6295—21no—
21C2×#6294—21no—
22#89041—21no—
23#89041—21no—
24#89041C2212yes—
25#89041C2212yescomplemented
26C3×#3811—21no—
27C3×#3805—21no—
28C3×#3802C2211yescharacteristic, complemented
29C3×C4×D32—21no—
30C3×#3798—21no—
31C3×#3797C2211yescharacteristic, complemented
32C3×#3796C2211yescharacteristic, complemented
33C3×#3796C2211yescharacteristic, complemented
34#88855C2211yescharacteristic, complemented
35C32×#208C2211yescharacteristic, complemented
36#88798C2212yescomplemented
37#88793C2212yescomplemented
38#88792C2212yescomplemented
39#88789C2212yescomplemented
40#88787C2212yescomplemented
41C3⋊D3×C3⋊C8C2212yescomplemented
42C3×#3719C2212yescomplemented
43C3×#3717C2212yescomplemented
44C3×#3716C2212yescomplemented
45C3×#3714C2212yescomplemented
46C3×D3×#41—31no—
47C3×D3×#41—31no—
48#64306D311yescharacteristic, complemented
49C2×#3799—31no—
50C2×#3796—31no—
51C2×#3795—31no—
52#64160—31no—
53#64158—31no—
54M16×C3⋊D3—31no—
55C3×#951—31no—
56C3×#949—31no—
57C3×#909—31no—
58C3×#908—31no—
59#63949—32no—
60#63948—32no—
61#63947—32no—
62#63946—32no—
63#63935—32no—
64#63934—32no—
65#63933—32no—
66#63932—32no—
67#63831D311yescharacteristic, complemented
68#63827—31no—
69#63827—31no—
70#63827—61no—
71#63825D311yescharacteristic, complemented
72#63823—31no—
73#63823—31no—
74#63823—61no—
75D3×#208—31no—
76D3×#208—31no—
77D3×#208—61no—
78#63811—32no—
79#63810—32no—
80#63809—32no—
81#63798—32no—
82C22×C3×C3⋊D3—21no—
83C22×C3×C3⋊D3D411yescharacteristic
84C2×C3×D32—21no—
85C2×C33×C4C2311yescharacteristic
86C2×C3×C3⋊Dic3—21no—
87C2×C3×C3⋊Dic3D411yescharacteristic
88C3×C4⋊(C3⋊D3)—21no—
89C3×C4⋊(C3⋊D3)C2312yes—
90C3×C4×C3⋊D3D411yescharacteristic
91C3×C4×C3⋊D3D411yescharacteristic
92C3×C4×C3⋊D3C2311yescharacteristic
93C3×C4×C3⋊D3C2311yescharacteristic
94C3×#634—21no—
95C3×#634C2312yes—
96C32×#67—21no—
97C32×#67—21no—
98C32×D12C2311yescharacteristic
99C32×D12C2311yescharacteristic
100C32×C4×D3—21no—
101C32×C4×D3—21no—
102C32×Dic6C2311yescharacteristic
103C32×Dic6C2311yescharacteristic
104#6295—22no—
105#6295—22no—
106#6294—22no—
107#6294—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#5777—91no—
119#5773—91no—
120C32×#41—31no—
121C32×#41—31no—
122C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
123C2×C4×C3⋊D3C2×D311yescharacteristic
124C2×#634C2×D311yescharacteristic, complemented
125C3×#239—31no—
126C3×#239—31no—
127C3×D3×Q8—31no—
128C3×D3×Q8—31no—
129C3×#237—31no—
130C3×#237—31no—
131C3×#237—61no—
132C3×#237—61no—
133C3×D3×D4—31no—
134C3×D3×D4—31no—
135C3×D3×D4—61no—
136C3×D3×D4—61no—
137C3×#235—21no—
138C3×#235—21no—
139C3×#235—61no—
140C3×#235—61no—
141C3×#235C2×D311yescharacteristic
142C3×#235C2×D311yescharacteristic
143C3×#235C2×D311yescharacteristic
144C3×#235C2×D311yescharacteristic
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×D12—61no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—61no—
151C2×C3×C4×D3—61no—
152C2×C3×C4×D3—61no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—61no—
156#3811—21no—
157C2×#626—61no—
158C2×#626—61no—
159C2×#625—61no—
160C2×#624—61no—
161#3805—21no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3—61no—
164#3802C2×D311yescharacteristic, complemented
165C4×D32—21no—
166#3799—32no—
167#3799—32no—
168#3799—61no—
169#3799—61no—
170#3798—21no—
171#3797C2×D311yescharacteristic, complemented
172#3796—32no—
173#3796—32no—
174#3796—61no—
175#3796—61no—
176#3796C2×D311yescharacteristic, complemented
177#3796C2×D311yescharacteristic, complemented
178#3795—32no—
179#3795—32no—
180#3795—61no—
181#3795—61no—
182C32×M16—31no—
183#3756—32no—
184#3755—32no—
185#3754—32no—
186#3753—32no—
187#3748—31no—
188#3748—31no—
189#3748—31no—
190#3748—61no—
191#3748—61no—
192#3748—61no—
193#3748—121no—
194#3743—32no—
195C8×C3⋊D3—32no—
196C3×#216—32no—
197C3×#215—32no—
198C3×#214—32no—
199C3×#213—32no—
200C3×#208—21no—
201C3×#208C2×D311yescharacteristic, complemented
202C3×#208C2×D311yescharacteristic, complemented
203C3×Dic12—32no—
204C3×D24—32no—
205C3×#204—32no—
206C3×#204—32no—
207#3719C2×D312yescomplemented
208#3718—32no—
209#3718—32no—
210#3718—62no—
211#3717C2×D312yescomplemented
212#3716C2×D312yescomplemented
213#3715—32no—
214#3715—32no—
215#3715—32no—
216#3715—32no—
217#3715—62no—
218#3715—62no—
219#3714C2×D312yescomplemented
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—41no—
232C2×C3×C3⋊D3—42no—
233C2×C3×C3⋊D3C2×D411yescharacteristic
234C2×C3×C3⋊D3C2×D411yescharacteristic
235C2×C32×D3—21no—
236C2×C32×D3—21no—
237C3×D32—42no—
238C33×C4C2×D411yescharacteristic
239C33×C4C2411yescharacteristic
240C3×C3⋊Dic3—22no—
241C3×C3⋊Dic3C2×D411yescharacteristic
242C3×C3⋊Dic3C2×D411yescharacteristic
243C32×Dic3—21no—
244C32×Dic3—21no—
245C2×C3×#41—91no—
246D3×#41—31no—
247D3×#41—31no—
248C2×#239—91no—
249C2×#237—91no—
250C2×#235—91no—
251C3×#137—91no—
252C3×AGL(1,ℤ/8)—91no—
253#951—31no—
254#951—91no—
255#951—91no—
256#951—181no—
257#950—92no—
258#950—92no—
259#949—31no—
260#949—91no—
261#949—91no—
262#949—181no—
263#942—92no—
264#942—91no—
265#932—92no—
266#932—91no—
267C2×#208—91no—
268#919—92no—
269#918—92no—
270#916—92no—
271#916—92no—
272#915—92no—
273#914—92no—
274#912—92no—
275#911—92no—
276#909—31no—
277#908—31no—
278D3×M16—91no—
279D3×M16—91no—
280D3×M16—181no—
281C22×C3⋊D3—21no—
282C22×C3⋊D3#6711yescharacteristic
283C22×C3×D3—31no—
284C22×C3×D3—31no—
285C22×C3×D3—61no—
286C22×C3×D3—61no—
287C22×C3×D3—61no—
288C22×C3×D3—61no—
289C22×C3×D3—61no—
290C22×C3×D3—121no—
291C2×D32—21no—
292C32×Q8—31no—
293C32×Q8—31no—
294C32×D4—31no—
295C32×D4—31no—
296C32×D4—61no—
297C32×D4—61no—
298C2×C32×C4—21no—
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4—41no—
302C2×C32×C4—61no—
303C2×C32×C4—61no—
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C22×D311yescharacteristic
306C2×C32×C4C22×D311yescharacteristic
307C2×C3⋊Dic3—21no—
308C2×C3⋊Dic3#6711yescharacteristic
309C4⋊(C3⋊D3)—21no—
310C4⋊(C3⋊D3)C22×D312yes—
311C4×C3⋊D3#6711yescharacteristic
312C4×C3⋊D3#6711yescharacteristic
313C4×C3⋊D3C22×D311yescharacteristic
314C4×C3⋊D3C22×D311yescharacteristic
315#634—21no—
316#634C22×D312yes—
317C3×#67—21no—
318C3×#67—21no—
319C3×#67—21no—
320C3×#67—21no—
321C3×#67—41no—
322C3×#67—41no—
323C3×#67—61no—
324C3×#67—61no—
325C3×#67—61no—
326C3×#67—61no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3—61no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—61no—
333C2×C3×Dic3—61no—
334C2×C3×Dic3—121no—
335C3×D12—21no—
336C3×D12—21no—
337C3×D12—32no—
338C3×D12—32no—
339C3×D12—62no—
340C3×D12—61no—
341C3×D12—61no—
342C3×D12—61no—
343C3×D12—61no—
344C3×D12—121no—
345C3×D12C22×D311yescharacteristic
346C3×D12C22×D311yescharacteristic
347C3×D12C22×D311yescharacteristic
348C3×D12C22×D311yescharacteristic
349C3×C4×D3—21no—
350C3×C4×D3—21no—
351C3×C4×D3—21no—
352C3×C4×D3—21no—
353C3×C4×D3—31no—
354C3×C4×D3—31no—
355C3×C4×D3—31no—
356C3×C4×D3—31no—
357C3×C4×D3—31no—
358C3×C4×D3—31no—
359C3×C4×D3—31no—
360C3×C4×D3—31no—
361C3×C4×D3—41no—
362C3×C4×D3—41no—
363C3×C4×D3—61no—
364C3×C4×D3—61no—
365C3×C4×D3—61no—
366C3×C4×D3—61no—
367C3×C4×D3—61no—
368C3×C4×D3—61no—
369C3×C4×D3—61no—
370C3×C4×D3—61no—
371C3×Dic6—21no—
372C3×Dic6—21no—
373C3×Dic6—32no—
374C3×Dic6—32no—
375C3×Dic6—62no—
376C3×Dic6—61no—
377C3×Dic6—61no—
378C3×Dic6—61no—
379C3×Dic6—61no—
380C3×Dic6—121no—
381C3×Dic6C22×D311yescharacteristic
382C3×Dic6C22×D311yescharacteristic
383C3×Dic6C22×D311yescharacteristic
384C3×Dic6C22×D311yescharacteristic
385#627—21no—
386#626—21no—
387#626—21no—
388#626—62no—
389#626—62no—
390#626—62no—
391#626—62no—
392#625—21no—
393#625—62no—
394#625—62no—
395#624—21no—
396#624—62no—
397#624—62no—
398D3×Dic3—21no—
399D3×Dic3—21no—
400D3×Dic3—62no—
401D3×Dic3—62no—
402D3×Dic3—62no—
403D3×Dic3—62no—
404C32×C8—32no—
405C3⋊(C3⋊C8)—32no—
406C3⋊(C3⋊C8)—32no—
407C3⋊(C3⋊C8)—32no—
408C3⋊(C3⋊C8)—62no—
409C3⋊(C3⋊C8)—62no—
410C3⋊(C3⋊C8)—62no—
411C3⋊(C3⋊C8)—122no—
412C3×C3⋊C8—22no—
413C3×C3⋊C8C22×D312yes—
414C3×C3⋊C8C22×D312yes—
415#575—271noSylow
416C2×C33—21no—
417C2×C33C22×D411yescharacteristic
418C3×C3⋊D3—21no—
419C3×C3⋊D3—21no—
420C3×C3⋊D3—42no—
421C32×D3—41no—
422C32×D3—41no—
423C3×#41—31no—
424C3×#41—31no—
425C3×#41—31no—
426C3×#41—31no—
427C3×#41—61no—
428C3×#41—61no—
429C3×#41—91no—
430C3×#41—91no—
431C3×#41—181no—
432C3×#41—181no—
433C2×C3×Q8—91no—
434C2×C3×Q8—91no—
435C2×C3×D4—91no—
436C2×C3×D4—91no—
437C2×C3×D4—181no—
438C22×C3×C4—91no—
439C22×C3×C4—181no—
440C2×#67—181no—
441C2×#67—181no—
442C22×Dic3—181no—
443#239—31no—
444#239—31no—
445#239—92no—
446#239—92no—
447#239—181no—
448#239—181no—
449D3×Q8—31no—
450D3×Q8—31no—
451#237—31no—
452#237—31no—
453#237—61no—
454#237—61no—
455#237—92no—
456#237—92no—
457#237—181no—
458#237—181no—
459D3×D4—31no—
460D3×D4—31no—
461D3×D4—61no—
462D3×D4—61no—
463#235—61no—
464#235—61no—
465#235—92no—
466#235—92no—
467#235—181no—
468#235—181no—
469#235D3211yescharacteristic
470#235D3211yescharacteristic
471C2×D12—31no—
472C2×D12—31no—
473C2×D12—61no—
474C2×D12—181no—
475C2×C4×D3—31no—
476C2×C4×D3—31no—
477C2×C4×D3—61no—
478C2×C4×D3—61no—
479C2×C4×D3—61no—
480C2×C4×D3—181no—
481C2×C4×D3—181no—
482C2×Dic6—31no—
483C2×Dic6—31no—
484C2×Dic6—61no—
485C3×Q16—92no—
486C3×SD16—92no—
487C3×SD16—92no—
488C3×D8—92no—
489C3×M16—31no—
490C3×M16—31no—
491C3×M16—61no—
492#216—32no—
493#216—92no—
494#216—92no—
495#216—92no—
496#216—182no—
497#215—32no—
498#215—92no—
499#215—92no—
500#215—92no—
501#215—182no—
502#214—32no—
503#214—92no—
504#214—92no—
505#214—92no—
506#214—182no—
507#213—32no—
508#213—92no—
509#213—92no—
510#213—92no—
511#213—182no—
512#208—91no—
513#208—91no—
514#208—91no—
515#208—92no—
516#208—181no—
517#208—181no—
518#208—181no—
519#208—361no—
520#208D3211yescharacteristic, complemented
521C2×C3⋊C8—92no—
522Dic12—32no—
523D24—32no—
524#204—32no—
525#204—32no—
526ΓL(1,𝔽25)—92no—
527ΓL(1,𝔽25)—92no—
528ΓL(1,𝔽25)—182no—
529D3×C8—92no—
530D3×C8—92no—
531D3×C8—182no—
532C22×C32—21no—
533C22×C32—21no—
534C22×C32—21no—
535C22×C32—41no—
536C22×C32—61no—
537C22×C32—61no—
538C22×C32D3×D411yescharacteristic
539C22×C32D3×D411yescharacteristic
540C22×C32C2×#6711yescharacteristic
541C2×C3⋊D3—22no—
542C2×C3⋊D3—41no—
543C2×C3⋊D3—42no—
544C2×C3⋊D3C2×#6711yescharacteristic
545C2×C3⋊D3C2×#6711yescharacteristic
546C2×C3×D3—21no—
547C2×C3×D3—21no—
548C2×C3×D3—21no—
549C2×C3×D3—21no—
550C2×C3×D3—31no—
551C2×C3×D3—31no—
552C2×C3×D3—31no—
553C2×C3×D3—31no—
554C2×C3×D3—41no—
555C2×C3×D3—41no—
556C2×C3×D3—61no—
557C2×C3×D3—61no—
558C2×C3×D3—62no—
559C2×C3×D3—62no—
560C2×C3×D3—122no—
561C2×C3×D3—122no—
562C2×C3×D3—122no—
563C2×C3×D3—121no—
564C2×C3×D3—121no—
565C2×C3×D3—122no—
566C2×C3×D3—122no—
567C2×C3×D3—122no—
568C2×C3×D3—242no—
569D32—42no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—21no—
575C32×C4—21no—
576C32×C4—41no—
577C32×C4—41no—
578C32×C4—61no—
579C32×C4—61no—
580C32×C4D3×D411yescharacteristic
581C32×C4D3×D411yescharacteristic
582C32×C4C2×#6711yescharacteristic
583C32×C4C23×D311yescharacteristic
584C32×C4C23×D311yescharacteristic
585C32×C4C23×D311yescharacteristic
586C3⋊Dic3—22no—
587C3⋊Dic3C2×#6711yescharacteristic
588C3⋊Dic3C2×#6711yescharacteristic
589C3×Dic3—21no—
590C3×Dic3—21no—
591C3×Dic3—21no—
592C3×Dic3—21no—
593C3×Dic3—31no—
594C3×Dic3—31no—
595C3×Dic3—31no—
596C3×Dic3—31no—
597C3×Dic3—41no—
598C3×Dic3—41no—
599C3×Dic3—61no—
600C3×Dic3—61no—
601C3×Dic3—62no—
602C3×Dic3—62no—
603C3×Dic3—122no—
604C2×#41—91no—
605C2×#41—271no—
606#137—91no—
607#137—272no—
608#137—271no—
609AGL(1,ℤ/8)—91no—
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—91no—
617C23×C3—181no—
618C23×C3—181no—
619C22×D3—31no—
620C22×D3—31no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—121no—
627C3×Q8—31no—
628C3×Q8—31no—
629C3×Q8—31no—
630C3×Q8—31no—
631C3×Q8—61no—
632C3×Q8—61no—
633C3×Q8—92no—
634C3×Q8—181no—
635C3×Q8—181no—
636C3×D4—31no—
637C3×D4—31no—
638C3×D4—31no—
639C3×D4—31no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—92no—
647C3×D4—121no—
648C3×D4—121no—
649C3×D4—181no—
650C3×D4—181no—
651C3×D4—181no—
652C3×D4—181no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—41no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—91no—
662C2×C3×C4—91no—
663C2×C3×C4—91no—
664C2×C3×C4—91no—
665C2×C3×C4—91no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4—181no—
669C2×C3×C4—181no—
670C2×C3×C4—181no—
671C2×C3×C4—181no—
672C2×C3×C4C2×D3211yescharacteristic
673C2×C3×C4C2×D3211yescharacteristic
674C2×C3×C4C2×D3211yescharacteristic
675#67—21no—
676#67—21no—
677#67—61no—
678#67—61no—
679#67—61no—
680#67—61no—
681#67—182no—
682#67—182no—
683#67—182no—
684#67—182no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—121no—
693C2×Dic3—182no—
694C2×Dic3—182no—
695D12—32no—
696D12—32no—
697D12—62no—
698D12—61no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—121no—
703D12—182no—
704D12—182no—
705D12C2×D3211yescharacteristic
706D12C2×D3211yescharacteristic
707C4×D3—21no—
708C4×D3—21no—
709C4×D3—31no—
710C4×D3—31no—
711C4×D3—31no—
712C4×D3—31no—
713C4×D3—31no—
714C4×D3—31no—
715C4×D3—31no—
716C4×D3—31no—
717C4×D3—61no—
718C4×D3—61no—
719C4×D3—61no—
720C4×D3—61no—
721C4×D3—61no—
722C4×D3—61no—
723C4×D3—61no—
724C4×D3—61no—
725C4×D3—182no—
726C4×D3—182no—
727C4×D3—182no—
728C4×D3—182no—
729Dic6—32no—
730Dic6—32no—
731Dic6—62no—
732Dic6—61no—
733Dic6—61no—
734Dic6—61no—
735Dic6—61no—
736Dic6—121no—
737Dic6C2×D3211yescharacteristic
738Dic6C2×D3211yescharacteristic
739C3×C8—32no—
740C3×C8—32no—
741C3×C8—62no—
742C3⋊C8—92no—
743C3⋊C8—92no—
744C3⋊C8—92no—
745C3⋊C8—182no—
746C3⋊C8—182no—
747C3⋊C8—182no—
748C3⋊C8—362no—
749C3⋊C8C2×D3212yes—
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—81no—
761C2×C32—121no—
762C2×C32—121no—
763C2×C32C2×D3×D411yescharacteristic
764C2×C32C2×D3×D411yescharacteristic
765C2×C32C22×#6711yescharacteristic
766C3⋊D3—21no—
767C3⋊D3—21no—
768C3⋊D3—42no—
769C3×D3—41no—
770C3×D3—41no—
771C3×D3—41no—
772C3×D3—41no—
773C3×D3—62no—
774C3×D3—61no—
775C3×D3—61no—
776C3×D3—61no—
777C3×D3—61no—
778C3×D3—81no—
779C3×D3—81no—
780C3×D3—121no—
781C3×D3—122no—
782C3×D3—122no—
783C3×D3—242no—
784#41—31no—
785#41—31no—
786#41—91no—
787#41—91no—
788#41—181no—
789#41—181no—
790#41—272no—
791#41—272no—
792#41—541no—
793#41—541no—
794C2×Q8—91no—
795C2×Q8—91no—
796C2×D4—91no—
797C2×D4—91no—
798C2×D4—181no—
799C2×D4—541no—
800C22×C4—91no—
801C22×C4—181no—
802C22×C4—541no—
803Q16—92no—
804Q16—272no—
805SD16—92no—
806SD16—92no—
807SD16—272no—
808SD16—272no—
809D8—92no—
810D8—272no—
811M16—31no—
812M16—272no—
813M16—271no—
814C2×C8—272no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—41no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—91no—
824C22×C3—91no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—182no—
828C22×C3—361no—
829C22×C3—362no—
830C22×C3—362no—
831C22×C3#380211yescharacteristic
832C22×C3D3×#6711yescharacteristic
833C22×C3D3×#6711yescharacteristic
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—31no—
837C2×D3—31no—
838C2×D3—31no—
839C2×D3—31no—
840C2×D3—61no—
841C2×D3—61no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—242no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—41no—
860C3×C4—41no—
861C3×C4—61no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—91no—
866C3×C4—91no—
867C3×C4—121no—
868C3×C4—121no—
869C3×C4—182no—
870C3×C4#380211yescharacteristic
871C3×C4D3×#6711yescharacteristic
872C3×C4D3×#6711yescharacteristic
873C3×C4C22×D3211yescharacteristic
874C3×C4C22×D3211yescharacteristic
875C3×C4C22×D3211yescharacteristic
876Dic3—21no—
877Dic3—21no—
878Dic3—31no—
879Dic3—31no—
880Dic3—31no—
881Dic3—31no—
882Dic3—61no—
883Dic3—61no—
884Dic3—62no—
885Dic3—62no—
886Dic3—122no—
887C32—21no—
888C32—21no—
889C32—21no—
890C32—41no—
891C32#577311yescharacteristic, complemented
892C32#577711yescharacteristic, complemented
893C32#582211yescharacteristic, complemented
894C23—91no—
895C23—181no—
896C23—181no—
897Q8—31no—
898Q8—31no—
899Q8—92no—
900Q8—181no—
901Q8—181no—
902D4—31no—
903D4—31no—
904D4—61no—
905D4—61no—
906D4—92no—
907D4—181no—
908D4—181no—
909D4—181no—
910D4—181no—
911D4—542no—
912D4—542no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—91no—
918C2×C4—91no—
919C2×C4—91no—
920C2×C4—181no—
921C2×C4—181no—
922C2×C4—181no—
923C2×C4—181no—
924C2×C4—542no—
925C2×C4—542no—
926C2×C4D3311yescharacteristic
927C8—32no—
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—81no—
940C2×C3—121no—
941C2×C3—121no—
942C2×C3—121no—
943C2×C3—121no—
944C2×C3—181no—
945C2×C3—181no—
946C2×C3—241no—
947C2×C3—241no—
948C2×C3—362no—
949C2×C3C2×#380211yescharacteristic
950C2×C3C2×D3×#6711yescharacteristic
951C2×C3C2×D3×#6711yescharacteristic
952D3—41no—
953D3—41no—
954D3—62no—
955D3—61no—
956D3—61no—
957D3—61no—
958D3—61no—
959D3—121no—
960D3—122no—
961D3—122no—
962D3—242no—
963C22—61no—
964C22—61no—
965C22—91no—
966C22—91no—
967C22—182no—
968C22—361no—
969C22—362no—
970C22—362no—
971C22#8895311yescharacteristic
972C4—61no—
973C4—61no—
974C4—91no—
975C4—91no—
976C4—182no—
977C4#8895311yescharacteristic
978C4C2×D3311yescharacteristic
979C3—21no—
980C3—21no—
981C3—21no—
982C3—41no—
983C3#1059471811yescharacteristic, complemented
984C3#1059546911yescharacteristic, complemented
985C3#1059547011yescharacteristic, complemented
986C2—21no—
987C2—121no—
988C2—121no—
989C2—181no—
990C2—181no—
991C2—362no—
992C2C2×#8895311yescharacteristic
subgroupG/H
centerC2C2×#88953
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×#89041C2semidirect
2. C3×#64306C2semidirect
3. #11723373C2semidirect
4. #11723365C2semidirect
5. C3⋊D3×#208C2semidirect
6. C3×#63831C2semidirect
7. C3×#63825C2semidirect
8. #11722892C2semidirect
9. #11722875C2semidirect
10. #11722860C2semidirect
11. #11722859C2semidirect
15. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C2×C3×#634C22semidirect
25. #89041C22semidirect
28. C3×#3802C22semidirect
31. C3×#3797C22semidirect
32. C3×#3796C22semidirect
33. C3×#3796C22semidirect
34. #88855C22semidirect
35. C32×#208C22semidirect
36. #88798C22semidirect
37. #88793C22semidirect
38. #88792C22semidirect
39. #88789C22semidirect
40. #88787C22semidirect
41. C3⋊D3×C3⋊C8C22semidirect
42. C3×#3719C22semidirect
43. C3×#3717C22semidirect
44. C3×#3716C22semidirect
45. C3×#3714C22semidirect
48. #64306D3semidirect
67. #63831D3semidirect
71. #63825D3semidirect
122. C2×C4⋊(C3⋊D3)C2×D3semidirect
124. C2×#634C2×D3semidirect
164. #3802C2×D3semidirect
171. #3797C2×D3semidirect
176. #3796C2×D3semidirect
177. #3796C2×D3semidirect
201. C3×#208C2×D3semidirect
202. C3×#208C2×D3semidirect
207. #3719C2×D3semidirect
211. #3717C2×D3semidirect
212. #3716C2×D3semidirect
219. #3714C2×D3semidirect
520. #208D32semidirect
615. C33#575semidirect
891. C32#5773semidirect
892. C32#5777semidirect
893. C32#5822semidirect
983. C3#10594718semidirect
984. C3#10595469semidirect
985. C3#10595470semidirect

Maximal subgroups

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

subgroupindex
C2×#890412
C3×#643062
#117233732
#117233652
C3⋊D3×#2082
C3×#638312
C3×#638252
#117228922
#117228752
#117228602
#117228592
#105954703
#105954693
#105947183