Finite Group Databasebeta

← #13170549

Subgroups — #13170549

Order 1728.

1242 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64308C211yesmaximal, characteristic, complemented
2C3×#64298C211yesmaximal, characteristic, complemented
3C2×#88811C211yesmaximal, characteristic, complemented
4#11723373C211yesmaximal, characteristic, complemented
5#11723365C211yesmaximal, characteristic, complemented
6#11723349C211yesmaximal, characteristic, complemented
7C3×#63822C211yesmaximal, characteristic, complemented
8#11722883C212yesmaximal, complemented
9#11722866C212yesmaximal, complemented
10#11722851C212yesmaximal, complemented
11D3×#3715C212yesmaximal, complemented
12#10595466—31nomaximal
13#10595457—31nomaximal
14#10595446—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic, complemented
17C32×#235C2211yescharacteristic
18C32×#235C2211yescharacteristic
19C32×#235C2211yescharacteristic, complemented
20C3×#3811—22no—
21C3×#3805—22no—
22C3×D3×D12—21no—
23C3×D3×D12C2212yes—
24C3×#3799—21no—
25C3×#3799C2212yes—
26C3×#3795—21no—
27C3×#3795C2212yescomplemented
28C3×D3×Dic6—21no—
29C3×D3×Dic6C2212yescomplemented
30#88855C2211yescharacteristic, complemented
31C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
32#88811C2212yescomplemented
33#88811C2212yescomplemented
34#88798C2212yescomplemented
35#88793C2212yescomplemented
36#88792C2212yescomplemented
37#88789C2212yescomplemented
38#88786C2212yescomplemented
39D3×C3⋊(C3⋊C8)C2212yescomplemented
40C3×#3718C2211yescharacteristic, complemented
41C3×#3715C2211yescharacteristic, complemented
42C3×#3715C2211yescharacteristic, complemented
43C3×#3713C2211yescharacteristic, complemented
44C3×#1010—31no—
45C3×#1010—31no—
46C3×#1009—31no—
47C3×#1009—31no—
48#64308D311yescharacteristic, complemented
49#64298D311yescharacteristic, complemented
50#64160—31no—
51#64158—31no—
52#64157—31no—
53C3×#950—31no—
54C3×#950—31no—
55#63948—32no—
56#63947—32no—
57#63943—32no—
58D3×#215—32no—
59#63935—32no—
60#63932—32no—
61D3×#214—32no—
62#63925—32no—
63C2×#3717—31no—
64C2×#3716—31no—
65#63827—31no—
66#63827—31no—
67#63827—32no—
68#63827—61no—
69C2×#3715—31no—
70C2×#3715—32no—
71#63823—31no—
72#63823—31no—
73#63823—32no—
74#63823—61no—
75#63822—32no—
76#63822D311yescharacteristic, complemented
77#63814—31no—
78#63814—31no—
79#63814—61no—
80C22×C3×C3⋊D3—21no—
81C2×C3×D32—22no—
82C2×C33×C4C2311yescharacteristic
83C2×C3×C3⋊Dic3—21no—
84C3×C4⋊(C3⋊D3)—21no—
85C3×C4⋊(C3⋊D3)C2312yes—
86C3×#634—21no—
87C3×#634C2312yes—
88C32×#67—21no—
89C32×#67—21no—
90C32×#67D412yes—
91C32×D12D411yescharacteristic
92C32×D12C2311yescharacteristic
93C32×D12C2311yescharacteristic
94C32×C4×D3—21no—
95C32×C4×D3—21no—
96C32×C4×D3C2312yes—
97C32×Dic6D411yescharacteristic
98C32×Dic6C2311yescharacteristic
99C32×Dic6C2311yescharacteristic
100C3×#627—22no—
101C3×#626—22no—
102C3×#626—22no—
103C3×#625—22no—
104C3×#624—22no—
105C3×D3×Dic3—22no—
106C3×D3×Dic3—22no—
107C3⋊(C3⋊(C3⋊C8))C2312yes—
108C3×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×C3⋊(C3⋊C8)C2311yescharacteristic
110#5837—91no—
111#5836—91no—
112#5770—91no—
113C32×#41—31no—
114C32×#41—31no—
115C32×#41—31no—
116C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
117C2×#634C2×D311yescharacteristic, complemented
118C3×#239—32no—
119C3×#239—61no—
120C3×D3×Q8—32no—
121C3×D3×Q8—61no—
122C3×#237—32no—
123C3×#237—61no—
124C3×#237—62no—
125C3×#237—62no—
126C3×D3×D4—32no—
127C3×D3×D4—61no—
128C3×D3×D4—62no—
129C3×D3×D4—62no—
130C3×#235—21no—
131C3×#235—21no—
132C3×#235—21no—
133C3×#235—32no—
134C3×#235—32no—
135C3×#235—61no—
136C3×#235—61no—
137C3×#235C2×D311yescharacteristic
138C3×#235C2×D311yescharacteristic
139C3×#235C2×D311yescharacteristic
140C3×#235C2×D311yescharacteristic
141C3×#235C2×D311yescharacteristic, complemented
142C3×#235C2×D311yescharacteristic, complemented
143C2×C3×D12—31no—
144C2×C3×D12—31no—
145C2×C3×D12—32no—
146C2×C3×D12—61no—
147C2×C3×D12—61no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6—32no—
151C2×C3×Dic6—61no—
152C2×C3×Dic6—61no—
153#3811—22no—
154#3805—22no—
155D3×D12—21no—
156D3×D12C2×D312yes—
157#3799—21no—
158#3799C2×D312yes—
159#3795—21no—
160#3795C2×D312yescomplemented
161D3×Dic6—21no—
162D3×Dic6C2×D312yescomplemented
163#3756—32no—
164#3755—32no—
165#3754—32no—
166#3753—32no—
167#3748—31no—
168#3748—31no—
169#3748—31no—
170#3748—32no—
171#3748—61no—
172#3748—61no—
173#3748—61no—
174#3748—121no—
175C2×C3⋊(C3⋊C8)—32no—
176C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
177C3×#216—31no—
178C3×#216—31no—
179C3×#215—31no—
180C3×#215—31no—
181C3×#214—31no—
182C3×#214—31no—
183C3×#213—31no—
184C3×#213—31no—
185C2×C3×C3⋊C8—31no—
186C2×C3×C3⋊C8—31no—
187C2×C3×C3⋊C8—61no—
188#3718—32no—
189#3718—32no—
190#3718—62no—
191#3718C2×D311yescharacteristic, complemented
192#3717—32no—
193#3717—32no—
194#3716—32no—
195#3716—32no—
196#3715—32no—
197#3715—32no—
198#3715—32no—
199#3715—32no—
200#3715—32no—
201#3715—32no—
202#3715—62no—
203#3715—62no—
204#3715C2×D311yescharacteristic, complemented
205#3715C2×D311yescharacteristic, complemented
206#3713—32no—
207#3713—32no—
208#3713—62no—
209#3713C2×D311yescharacteristic, complemented
210#3711—32no—
211#3711—32no—
212#3711—62no—
213D3×C3⋊C8—32no—
214D3×C3⋊C8—32no—
215D3×C3⋊C8—62no—
216C22×C33C2×D411yescharacteristic
217C2×C3×C3⋊D3—22no—
218C2×C3×C3⋊D3—81no—
219C2×C32×D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3C2×D412yes—
222C3×D32—82no—
223C33×C4C2×D411yescharacteristic
224C33×C4C2411yescharacteristic
225C3×C3⋊Dic3—22no—
226C32×Dic3—21no—
227C32×Dic3—21no—
228C32×Dic3C2×D412yes—
229C3×2−1+4—91no—
230C3×H(5,𝔽2)—91no—
231#1010—31no—
232#1010—31no—
233#1009—31no—
234#1009—31no—
235C3×#135—91no—
236#951—92no—
237#951—91no—
238#951—91no—
239#951—181no—
240#950—31no—
241#950—31no—
242#950—92no—
243#950—92no—
244#949—92no—
245#949—91no—
246#949—91no—
247#949—181no—
248#948—91no—
249#948—91no—
250#948—181no—
251#942—92no—
252#942—91no—
253C2×#215—91no—
254C2×#215—92no—
255C2×#214—91no—
256C2×#214—92no—
257#932—92no—
258#932—91no—
259#918—92no—
260#916—92no—
261D3×SD16—92no—
262#911—92no—
263C2×#204—91no—
264#901—91no—
265C22×C3⋊D3—21no—
266C22×C3×D3—62no—
267C22×C3×D3—61no—
268C22×C3×D3—61no—
269C22×C3×D3—62no—
270C22×C3×D3—121no—
271C2×D32—22no—
272C32×Q8—31no—
273C32×Q8—31no—
274C32×Q8—31no—
275C32×D4—32no—
276C32×D4—31no—
277C32×D4—31no—
278C32×D4—31no—
279C32×D4—61no—
280C32×D4—61no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—32no—
285C2×C32×C4—41no—
286C2×C32×C4—61no—
287C2×C32×C4—61no—
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C3⋊Dic3—21no—
292C4⋊(C3⋊D3)—21no—
293C4⋊(C3⋊D3)C22×D312yes—
294#634—21no—
295#634C22×D312yes—
296C3×#67—21no—
297C3×#67—21no—
298C3×#67—21no—
299C3×#67—21no—
300C3×#67—22no—
301C3×#67—41no—
302C3×#67—41no—
303C3×#67—62no—
304C3×#67—62no—
305C3×#67—62no—
306C3×#67—62no—
307C3×#67#6712yes—
308C3×#67#6712yes—
309C2×C3×Dic3—62no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—121no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—32no—
318C3×D12—32no—
319C3×D12—62no—
320C3×D12—62no—
321C3×D12—62no—
322C3×D12—61no—
323C3×D12—61no—
324C3×D12—121no—
325C3×D12#6711yescharacteristic
326C3×D12#6711yescharacteristic
327C3×D12C22×D311yescharacteristic
328C3×D12C22×D311yescharacteristic
329C3×D12C22×D311yescharacteristic
330C3×D12C22×D311yescharacteristic
331C3×C4×D3—21no—
332C3×C4×D3—21no—
333C3×C4×D3—21no—
334C3×C4×D3—21no—
335C3×C4×D3—22no—
336C3×C4×D3—41no—
337C3×C4×D3—41no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—62no—
341C3×C4×D3—62no—
342C3×C4×D3C22×D312yes—
343C3×C4×D3C22×D312yes—
344C3×Dic6—21no—
345C3×Dic6—21no—
346C3×Dic6—21no—
347C3×Dic6—32no—
348C3×Dic6—32no—
349C3×Dic6—62no—
350C3×Dic6—62no—
351C3×Dic6—61no—
352C3×Dic6—61no—
353C3×Dic6—62no—
354C3×Dic6—121no—
355C3×Dic6#6711yescharacteristic
356C3×Dic6#6711yescharacteristic
357C3×Dic6C22×D311yescharacteristic
358C3×Dic6C22×D311yescharacteristic
359C3×Dic6C22×D311yescharacteristic
360C3×Dic6C22×D311yescharacteristic
361#627—22no—
362#626—22no—
363#626—22no—
364#625—22no—
365#624—22no—
366D3×Dic3—22no—
367D3×Dic3—22no—
368C3⋊(C3⋊C8)—32no—
369C3⋊(C3⋊C8)—32no—
370C3⋊(C3⋊C8)—32no—
371C3⋊(C3⋊C8)—62no—
372C3⋊(C3⋊C8)—62no—
373C3⋊(C3⋊C8)—62no—
374C3⋊(C3⋊C8)—122no—
375C3⋊(C3⋊C8)C22×D311yescharacteristic
376C3⋊(C3⋊C8)C22×D311yescharacteristic
377C3×C3⋊C8—31no—
378C3×C3⋊C8—31no—
379C3×C3⋊C8—31no—
380C3×C3⋊C8—31no—
381C3×C3⋊C8—61no—
382C3×C3⋊C8—61no—
383#577—271noSylow
384C2×C33—21no—
385C2×C33C22×D411yescharacteristic
386C3×C3⋊D3—42no—
387C32×D3—22no—
388C32×D3—41no—
389C32×D3—41no—
390C3×#41—31no—
391C3×#41—31no—
392C3×#41—31no—
393C3×#41—31no—
394C3×#41—31no—
395C3×#41—31no—
396C3×#41—61no—
397C3×#41—61no—
398C3×#41—61no—
399C3×#41—92no—
400C3×#41—92no—
401C3×#41—181no—
402C3×#41—181no—
403C3×#41—182no—
404C2×C3×Q8—92no—
405C2×C3×Q8—91no—
406C2×C3×Q8—181no—
407C2×C3×D4—92no—
408C2×C3×D4—91no—
409C2×C3×D4—181no—
410C2×C3×D4—182no—
411#239—32no—
412#239—61no—
413D3×Q8—32no—
414D3×Q8—61no—
415#237—32no—
416#237—61no—
417#237—62no—
418#237—62no—
419D3×D4—32no—
420D3×D4—61no—
421D3×D4—62no—
422D3×D4—62no—
423#235—32no—
424#235—32no—
425#235—61no—
426#235—61no—
427#235D3211yescharacteristic
428#235D3211yescharacteristic
429#235D3211yescharacteristic, complemented
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—32no—
433C2×D12—61no—
434C2×D12—61no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—32no—
438C2×Dic6—61no—
439C2×Dic6—61no—
440C3×Q16—91no—
441C3×SD16—91no—
442C3×SD16—91no—
443C3×D8—91no—
444C2×C3×C8—91no—
445#216—31no—
446#216—31no—
447#216—92no—
448#216—92no—
449#216—92no—
450#216—182no—
451#215—31no—
452#215—31no—
453#215—92no—
454#215—92no—
455#215—92no—
456#215—92no—
457#215—92no—
458#215—182no—
459#214—31no—
460#214—31no—
461#214—92no—
462#214—92no—
463#214—92no—
464#214—92no—
465#214—92no—
466#214—182no—
467#213—31no—
468#213—31no—
469#213—92no—
470#213—92no—
471#213—92no—
472#213—182no—
473#208—92no—
474#208—92no—
475#208—91no—
476#208—91no—
477#208—91no—
478#208—182no—
479#208—181no—
480#208—181no—
481#208—181no—
482#208—361no—
483C2×C3⋊C8—31no—
484C2×C3⋊C8—31no—
485C2×C3⋊C8—61no—
486C2×C3⋊C8—92no—
487C2×C3⋊C8—92no—
488C2×C3⋊C8—182no—
489#204—92no—
490#204—92no—
491ΓL(1,𝔽25)—92no—
492D3×C8—92no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—32no—
497C22×C32—41no—
498C22×C32—61no—
499C22×C32—61no—
500C22×C32D3×D411yescharacteristic
501C22×C32C2×#6711yescharacteristic
502C22×C32C2×#6711yescharacteristic
503C2×C3⋊D3—22no—
504C2×C3⋊D3—81no—
505C2×C3×D3—21no—
506C2×C3×D3—21no—
507C2×C3×D3—21no—
508C2×C3×D3—21no—
509C2×C3×D3—22no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—62no—
513C2×C3×D3—62no—
514C2×C3×D3—122no—
515C2×C3×D3—242no—
516C2×C3×D3—242no—
517C2×C3×D3—241no—
518C2×C3×D3—241no—
519C2×C3×D3—242no—
520C2×C3×D3C2×#6712yes—
521C2×C3×D3C2×#6712yes—
522D32—82no—
523C32×C4—21no—
524C32×C4—21no—
525C32×C4—21no—
526C32×C4—21no—
527C32×C4—21no—
528C32×C4—21no—
529C32×C4—32no—
530C32×C4—41no—
531C32×C4—41no—
532C32×C4—61no—
533C32×C4—61no—
534C32×C4D3×D411yescharacteristic
535C32×C4C2×#6711yescharacteristic
536C32×C4C2×#6711yescharacteristic
537C32×C4C23×D311yescharacteristic
538C32×C4C23×D311yescharacteristic
539C32×C4C23×D311yescharacteristic
540C3⋊Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—21no—
543C3×Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3—22no—
546C3×Dic3—41no—
547C3×Dic3—41no—
548C3×Dic3—62no—
549C3×Dic3—62no—
550C3×Dic3—122no—
551C3×Dic3C2×#6712yes—
552C3×Dic3C2×#6712yes—
5532−1+4—91no—
554H(5,𝔽2)—91no—
555#137—272no—
556#137—271no—
557AGL(1,ℤ/8)—272no—
558AGL(1,ℤ/8)—271no—
559#135—91no—
560#135—272no—
561C2×SD16—271no—
562C2×SD16—272no—
563#131—271no—
564C33#57711yescharacteristic, complemented, Sylow
565C23×C3—182no—
566C23×C3—181no—
567C22×D3—62no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—62no—
571C22×D3—121no—
572C3×Q8—31no—
573C3×Q8—31no—
574C3×Q8—31no—
575C3×Q8—31no—
576C3×Q8—31no—
577C3×Q8—31no—
578C3×Q8—61no—
579C3×Q8—61no—
580C3×Q8—61no—
581C3×Q8—92no—
582C3×Q8—182no—
583C3×Q8—181no—
584C3×D4—32no—
585C3×D4—32no—
586C3×D4—31no—
587C3×D4—31no—
588C3×D4—31no—
589C3×D4—31no—
590C3×D4—31no—
591C3×D4—31no—
592C3×D4—61no—
593C3×D4—61no—
594C3×D4—61no—
595C3×D4—62no—
596C3×D4—61no—
597C3×D4—61no—
598C3×D4—61no—
599C3×D4—61no—
600C3×D4—92no—
601C3×D4—121no—
602C3×D4—121no—
603C3×D4—182no—
604C3×D4—182no—
605C3×D4—182no—
606C3×D4—181no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—41no—
613C2×C3×C4—62no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—121no—
619C2×C3×C4—121no—
620C2×C3×C4—182no—
621C2×C3×C4—182no—
622C2×C3×C4—182no—
623C2×C3×C4—181no—
624C2×C3×C4C2×D3211yescharacteristic
625C2×C3×C4C2×D3211yescharacteristic
626C2×C3×C4C2×D3211yescharacteristic
627#67—21no—
628#67—21no—
629#67—62no—
630#67—62no—
631#67—62no—
632#67—62no—
633#67#62512yes—
634C2×Dic3—62no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—62no—
638C2×Dic3—121no—
639D12—32no—
640D12—32no—
641D12—62no—
642D12—62no—
643D12—62no—
644D12—61no—
645D12—61no—
646D12—121no—
647D12#62511yescharacteristic
648D12C2×D3211yescharacteristic
649D12C2×D3211yescharacteristic
650C4×D3—21no—
651C4×D3—21no—
652C4×D3—62no—
653C4×D3—62no—
654C4×D3—62no—
655C4×D3—62no—
656C4×D3C2×D3212yes—
657Dic6—32no—
658Dic6—32no—
659Dic6—62no—
660Dic6—62no—
661Dic6—61no—
662Dic6—61no—
663Dic6—62no—
664Dic6—121no—
665Dic6#62511yescharacteristic
666Dic6C2×D3211yescharacteristic
667Dic6C2×D3211yescharacteristic
668C3×C8—91no—
669C3×C8—91no—
670C3⋊C8—31no—
671C3⋊C8—31no—
672C3⋊C8—31no—
673C3⋊C8—31no—
674C3⋊C8—61no—
675C3⋊C8—61no—
676C3⋊C8—92no—
677C3⋊C8—92no—
678C3⋊C8—92no—
679C3⋊C8—182no—
680C3⋊C8—182no—
681C3⋊C8—182no—
682C3⋊C8—362no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—41no—
690C2×C32—41no—
691C2×C32—41no—
692C2×C32—41no—
693C2×C32—62no—
694C2×C32—81no—
695C2×C32—121no—
696C2×C32—121no—
697C2×C32C2×D3×D411yescharacteristic
698C2×C32C22×#6711yescharacteristic
699C2×C32C22×#6711yescharacteristic
700C3⋊D3—42no—
701C3×D3—22no—
702C3×D3—22no—
703C3×D3—42no—
704C3×D3—41no—
705C3×D3—41no—
706C3×D3—41no—
707C3×D3—41no—
708C3×D3—81no—
709C3×D3—81no—
710C3×D3—122no—
711C3×D3—122no—
712C3×D3—242no—
713#41—31no—
714#41—31no—
715#41—31no—
716#41—92no—
717#41—92no—
718#41—181no—
719#41—181no—
720#41—182no—
721C2×Q8—92no—
722C2×Q8—91no—
723C2×Q8—181no—
724C2×D4—92no—
725C2×D4—91no—
726C2×D4—181no—
727C2×D4—182no—
728Q16—91no—
729Q16—272no—
730SD16—91no—
731SD16—91no—
732SD16—272no—
733SD16—272no—
734SD16—272no—
735SD16—272no—
736D8—91no—
737D8—272no—
738M16—272no—
739M16—271no—
740C2×C8—91no—
741C2×C8—272no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—32no—
746C22×C3—32no—
747C22×C3—41no—
748C22×C3—62no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—182no—
756C22×C3—721no—
757C22×C3—722no—
758C22×C3C2×#62511yescharacteristic
759C22×C3D3×#6711yescharacteristic
760C22×C3D3×#6711yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—122no—
766C2×D3—242no—
767C2×D3—242no—
768C2×D3—241no—
769C2×D3—241no—
770C2×D3—242no—
771C2×D3C2×#62512yes—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—32no—
779C3×C4—32no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—62no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4—182no—
790C3×C4C2×#62511yescharacteristic
791C3×C4D3×#6711yescharacteristic
792C3×C4D3×#6711yescharacteristic
793C3×C4C22×D3211yescharacteristic
794C3×C4C22×D3211yescharacteristic
795C3×C4C22×D3211yescharacteristic
796Dic3—21no—
797Dic3—21no—
798Dic3—62no—
799Dic3—62no—
800Dic3—122no—
801Dic3C2×#62512yes—
802C32—21no—
803C32—21no—
804C32—21no—
805C32—41no—
806C32#577011yescharacteristic, complemented
807C32#583611yescharacteristic, complemented
808C32#583711yescharacteristic, complemented
809C23—182no—
810C23—181no—
811Q8—31no—
812Q8—31no—
813Q8—31no—
814Q8—92no—
815Q8—182no—
816Q8—181no—
817D4—32no—
818D4—31no—
819D4—31no—
820D4—31no—
821D4—61no—
822D4—61no—
823D4—92no—
824D4—182no—
825D4—182no—
826D4—182no—
827D4—181no—
828C2×C4—32no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—182no—
832C2×C4—182no—
833C2×C4—182no—
834C2×C4—181no—
835C2×C4D3311yescharacteristic
836C8—91no—
837C8—91no—
838C8—272no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—41no—
846C2×C3—41no—
847C2×C3—41no—
848C2×C3—41no—
849C2×C3—62no—
850C2×C3—62no—
851C2×C3—81no—
852C2×C3—122no—
853C2×C3—121no—
854C2×C3—121no—
855C2×C3—121no—
856C2×C3—121no—
857C2×C3—241no—
858C2×C3—241no—
859C2×C3—362no—
860C2×C3C22×#62511yescharacteristic
861C2×C3C2×D3×#6711yescharacteristic
862C2×C3C2×D3×#6711yescharacteristic
863D3—22no—
864D3—41no—
865D3—41no—
866D3—122no—
867D3—122no—
868D3—242no—
869C22—32no—
870C22—61no—
871C22—61no—
872C22—182no—
873C22—721no—
874C22—722no—
875C22D3×#62511yescharacteristic
876C4—32no—
877C4—61no—
878C4—61no—
879C4—182no—
880C4D3×#62511yescharacteristic
881C4C2×D3311yescharacteristic
882C3—21no—
883C3—21no—
884C3—21no—
885C3—41no—
886C3#1059544611yescharacteristic, complemented
887C3#1059545711yescharacteristic, complemented
888C3#1059546611yescharacteristic, complemented
889C2—21no—
890C2—62no—
891C2—121no—
892C2—121no—
893C2—362no—
894C2C2×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×#64308C2semidirect
2. C3×#64298C2semidirect
3. C2×#88811C2semidirect
4. #11723373C2semidirect
5. #11723365C2semidirect
6. #11723349C2semidirect
7. C3×#63822C2semidirect
8. #11722883C2semidirect
9. #11722866C2semidirect
10. #11722851C2semidirect
11. D3×#3715C2semidirect
16. C2×C3×#634C22semidirect
19. C32×#235C22semidirect
27. C3×#3795C22semidirect
29. C3×D3×Dic6C22semidirect
30. #88855C22semidirect
31. C2×C3×C3⋊(C3⋊C8)C22semidirect
32. #88811C22semidirect
33. #88811C22semidirect
34. #88798C22semidirect
35. #88793C22semidirect
36. #88792C22semidirect
37. #88789C22semidirect
38. #88786C22semidirect
39. D3×C3⋊(C3⋊C8)C22semidirect
40. C3×#3718C22semidirect
41. C3×#3715C22semidirect
42. C3×#3715C22semidirect
43. C3×#3713C22semidirect
48. #64308D3semidirect
49. #64298D3semidirect
76. #63822D3semidirect
117. C2×#634C2×D3semidirect
141. C3×#235C2×D3semidirect
142. C3×#235C2×D3semidirect
160. #3795C2×D3semidirect
162. D3×Dic6C2×D3semidirect
176. C2×C3⋊(C3⋊C8)C2×D3semidirect
191. #3718C2×D3semidirect
204. #3715C2×D3semidirect
205. #3715C2×D3semidirect
209. #3713C2×D3semidirect
429. #235D32semidirect
564. C33#577semidirect
806. C32#5770semidirect
807. C32#5836semidirect
808. C32#5837semidirect
886. C3#10595446semidirect
887. C3#10595457semidirect
888. C3#10595466semidirect

Maximal subgroups

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

subgroupindex
C3×#643082
C3×#642982
C2×#888112
#117233732
#117233652
#117233492
C3×#638222
#117228832
#117228662
#117228512
D3×#37152
#105954663
#105954573
#105954463