Finite Group Databasebeta

← D3×#63827 #13170547

Subgroups — D3×#63827 #13170547

Order 1728.

1240 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3#11723663C211yesmaximal, characteristic, complemented
4#11723375C211yesmaximal, characteristic, complemented
5#11723373C211yesmaximal, characteristic, complemented
6D3×#3748C211yesmaximal, characteristic, complemented
7C3×#63827C211yesmaximal, characteristic, complemented
8#11722883C212yesmaximal, complemented
9#11722882C212yesmaximal, complemented
10D3×#3718C212yesmaximal, complemented
11D3×#3715C212yesmaximal, complemented
12D3×#951—31nomaximal
13D3×#942—31nomaximal
14C2×#63827—31nomaximal
15C3×#3828C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic, complemented
17C32×#235C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic, complemented
20C3×D3×#67—21no—
21C2×C3×#627—21no—
22C3×#3804—21no—
23C2×C3×D3×Dic3—21no—
24C3×D3×D12C2211yescharacteristic
25C3×C4×D32—21no—
26C3×#3799C2211yescharacteristic
27C3×#3798—21no—
28C3×#3795C2211yescharacteristic
29C3×D3×Dic6—21no—
30C3×D3×Dic6—21no—
31C3×D3×Dic6C2212yes—
32C3×D3×Dic6C2211yescharacteristic
33C3×D3×Dic6C2212yescomplemented
34#88855C2211yescharacteristic, complemented
35C3×#3748C2211yescharacteristic, complemented
36#88812C2212yescomplemented
37#88811C2212yescomplemented
38#88798C2212yescomplemented
39#88798C2212yescomplemented
40#88793C2212yescomplemented
41#88792C2212yescomplemented
42#88786C2212yescomplemented
43D3×C3⋊(C3⋊C8)C2212yes—
44C3×#3718C2212yescomplemented
45C3×#3715C2212yescomplemented
46C3×D3×#41—31no—
47C2×C3×D3×Q8—31no—
48C2×C3×#235—31no—
49C22×C3×Dic6—31no—
50D3×#235D311yescharacteristic
51C2×D3×Dic6D311yescharacteristic, complemented
52#64160—31no—
53#64151—31no—
54C2×#3748—31no—
55C3×#951—31no—
56C3×#942—31no—
57#63948—32no—
58#63946—32no—
59#63943—32no—
60D3×#216—32no—
61D3×#216—32no—
62D3×#215—32no—
63#63929—32no—
64D3×#214—32no—
65C2×#3718—32no—
66#63833—31no—
67#63831—31no—
68#63827—31no—
69#63827—31no—
70#63827—31no—
71#63827—31no—
72#63827—31no—
73#63827—32no—
74#63827—32no—
75#63827—61no—
76#63827—61no—
77#63827D311yescharacteristic, direct product factor
78C2×#3715—32no—
79D3×#208—31no—
80D3×#208—31no—
81D3×#208—61no—
82C22×C32×D3D411yescharacteristic
83C2×C3×D32—21no—
84C2×C33×C4C2311yescharacteristic
85C3×#638—21no—
86C2×C3×C3⋊Dic3—21no—
87C3×C4⋊(C3⋊D3)C2311yescharacteristic
88C3×C4×C3⋊D3—21no—
89C3×#634—21no—
90C3×#634C2312yes—
91C3×#634C2311yescharacteristic
92C32×#67—21no—
93C2×C32×Dic3—21no—
94C2×C32×Dic3D411yescharacteristic
95C32×D12C2311yescharacteristic
96C32×C4×D3—21no—
97C32×C4×D3D411yescharacteristic
98C32×C4×D3D411yescharacteristic
99C32×C4×D3C2311yescharacteristic
100C32×C4×D3C2311yescharacteristic
101C32×Dic6—21no—
102C32×Dic6C2312yes—
103C32×Dic6C2311yescharacteristic
104C3×#627—22no—
105C3×#627—22no—
106C3×#627—21no—
107C3×#626—21no—
108C3×#626—21no—
109C3×#625—21no—
110C3×#624—21no—
111C3×D3×Dic3—22no—
112C3×D3×Dic3—22no—
113C3×D3×Dic3—21no—
114C3×D3×Dic3—21no—
115C3⋊(C3⋊(C3⋊C8))C2312yes—
116C3×C3⋊(C3⋊C8)C2312yes—
117C2×#951—91no—
118C2×#942—91no—
119D3×#137—91no—
120C32×#41—31no—
121C2×C32×Q8—31no—
122C22×C32×C4—31no—
123#3828C2×D311yescharacteristic
124C2×#634C2×D311yescharacteristic, complemented
125C2×C3×#67—61no—
126C22×C3×Dic3—61no—
127C3×#239—31no—
128C3×D3×Q8—32no—
129C3×D3×Q8—32no—
130C3×D3×Q8—31no—
131C3×D3×Q8—61no—
132C3×D3×Q8—61no—
133C3×#237—31no—
134C3×#237—61no—
135C3×D3×D4—31no—
136C3×D3×D4—61no—
137C3×#235—21no—
138C3×#235—31no—
139C3×#235—31no—
140C3×#235—31no—
141C3×#235—31no—
142C3×#235—61no—
143C3×#235—61no—
144C3×#235—61no—
145C3×#235—61no—
146C3×#235C2×D311yescharacteristic
147C3×#235C2×D311yescharacteristic
148C2×C3×D12—31no—
149C2×C3×C4×D3—21no—
150C2×C3×C4×D3—61no—
151C2×C3×C4×D3—61no—
152C2×C3×C4×D3—61no—
153C2×C3×C4×D3C2×D311yescharacteristic
154C2×C3×C4×D3C2×D311yescharacteristic
155C2×C3×Dic6—21no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6—31no—
158C2×C3×Dic6—32no—
159C2×C3×Dic6—32no—
160C2×C3×Dic6—31no—
161C2×C3×Dic6—61no—
162C2×C3×Dic6—61no—
163C2×C3×Dic6—61no—
164C2×C3×Dic6—61no—
165C2×C3×Dic6—61no—
166C2×C3×Dic6C2×D311yescharacteristic, complemented
167C2×C3×Dic6C2×D311yescharacteristic, complemented
168D3×#67—21no—
169C2×#627—21no—
170#3804—21no—
171C2×D3×Dic3—21no—
172D3×D12C2×D311yescharacteristic
173C4×D32—21no—
174#3799C2×D311yescharacteristic
175#3798—21no—
176#3795C2×D311yescharacteristic
177D3×Dic6—21no—
178D3×Dic6—21no—
179D3×Dic6C2×D312yes—
180D3×Dic6C2×D311yescharacteristic
181D3×Dic6C2×D312yescomplemented
182#3756—32no—
183#3756—32no—
184#3755—32no—
185#3754—32no—
186#3748—31no—
187#3748—31no—
188#3748—31no—
189#3748—32no—
190#3748—61no—
191#3748—61no—
192#3748—61no—
193#3748—121no—
194#3748C2×D311yescharacteristic, complemented
195C2×C3⋊(C3⋊C8)—32no—
196C3×#216—32no—
197C3×#216—32no—
198C3×#215—32no—
199C3×#214—32no—
200C3×#208—31no—
201C3×#208—31no—
202C3×#208—61no—
203#3719—32no—
204#3719—32no—
205#3718—32no—
206#3718—32no—
207#3718—32no—
208#3718—32no—
209#3718—32no—
210#3718—62no—
211#3718—62no—
212#3718C2×D312yescomplemented
213#3717—32no—
214#3716—32no—
215#3715—32no—
216#3715—32no—
217#3715—32no—
218#3715—32no—
219#3715—32no—
220#3715—62no—
221#3715—62no—
222#3715C2×D312yescomplemented
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—21no—
231C2×C32×D3—22no—
232C2×C32×D3—21no—
233C2×C32×D3C2×D411yescharacteristic
234C2×C32×D3C2×D411yescharacteristic
235C3×D32—42no—
236C33×C4C2×D411yescharacteristic
237C33×C4C2411yescharacteristic
238C3×C3⋊Dic3—21no—
239C3×C3⋊Dic3—22no—
240C32×Dic3—22no—
241C32×Dic3—21no—
242C32×Dic3C2×D411yescharacteristic
243C32×Dic3C2×D411yescharacteristic
244C2×C3×#41—91no—
245C22×C3×Q8—91no—
246D3×#41—31no—
247C2×D3×Q8—31no—
248C2×#235—31no—
249C22×Dic6—31no—
250C3×#137—91no—
251#951—31no—
252#951—91no—
253#951—92no—
254#951—92no—
255#951—91no—
256#951—91no—
257#951—91no—
258#951—181no—
259C2×#216—92no—
260C2×#216—92no—
261#942—31no—
262#942—91no—
263#942—92no—
264#942—92no—
265#942—91no—
266#942—91no—
267#942—91no—
268#942—181no—
269C2×#215—92no—
270C2×#214—92no—
271C2×#208—91no—
272C2×#208—91no—
273C2×#208—181no—
274#918—92no—
275D3×Q16—92no—
276#915—92no—
277D3×SD16—92no—
278#909—91no—
279D3×M16—91no—
280C23×C32—31no—
281C22×C3×D3—21no—
282C22×C3×D3—61no—
283C22×C3×D3—61no—
284C22×C3×D3#6711yescharacteristic
285C22×C3×D3#6711yescharacteristic
286C2×D32—21no—
287C32×Q8—32no—
288C32×Q8—31no—
289C32×Q8—61no—
290C32×D4—31no—
291C32×D4—61no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—31no—
296C2×C32×C4—31no—
297C2×C32×C4—31no—
298C2×C32×C4—31no—
299C2×C32×C4—31no—
300C2×C32×C4—41no—
301C2×C32×C4—61no—
302C2×C32×C4—61no—
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C22×D311yescharacteristic
306#638—21no—
307C2×C3⋊Dic3—21no—
308C4⋊(C3⋊D3)C22×D311yescharacteristic
309C4×C3⋊D3—21no—
310#634—21no—
311#634C22×D312yes—
312#634C22×D311yescharacteristic
313C3×#67—21no—
314C3×#67—21no—
315C3×#67—41no—
316C3×#67—61no—
317C3×#67—61no—
318C3×#67—61no—
319C3×#67—61no—
320C3×#67—61no—
321C3×#67—61no—
322C3×#67—121no—
323C2×C3×Dic3—21no—
324C2×C3×Dic3—21no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—41no—
327C2×C3×Dic3—62no—
328C2×C3×Dic3—62no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3—61no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—61no—
333C2×C3×Dic3—121no—
334C2×C3×Dic3#6711yescharacteristic
335C2×C3×Dic3#6711yescharacteristic
336C3×D12—21no—
337C3×D12—31no—
338C3×D12—31no—
339C3×D12—61no—
340C3×D12—61no—
341C3×D12—61no—
342C3×D12C22×D311yescharacteristic
343C3×D12C22×D311yescharacteristic
344C3×C4×D3—21no—
345C3×C4×D3—21no—
346C3×C4×D3—21no—
347C3×C4×D3—21no—
348C3×C4×D3—21no—
349C3×C4×D3—21no—
350C3×C4×D3—41no—
351C3×C4×D3—61no—
352C3×C4×D3—61no—
353C3×C4×D3—61no—
354C3×C4×D3—62no—
355C3×C4×D3—62no—
356C3×C4×D3—61no—
357C3×C4×D3—61no—
358C3×C4×D3—61no—
359C3×C4×D3—121no—
360C3×C4×D3#6711yescharacteristic
361C3×C4×D3#6711yescharacteristic
362C3×C4×D3#6711yescharacteristic
363C3×C4×D3#6711yescharacteristic
364C3×C4×D3C22×D311yescharacteristic
365C3×C4×D3C22×D311yescharacteristic
366C3×C4×D3C22×D311yescharacteristic
367C3×C4×D3C22×D311yescharacteristic
368C3×Dic6—21no—
369C3×Dic6—21no—
370C3×Dic6—22no—
371C3×Dic6—21no—
372C3×Dic6—32no—
373C3×Dic6—32no—
374C3×Dic6—31no—
375C3×Dic6—31no—
376C3×Dic6—41no—
377C3×Dic6—62no—
378C3×Dic6—61no—
379C3×Dic6—62no—
380C3×Dic6—62no—
381C3×Dic6—61no—
382C3×Dic6—61no—
383C3×Dic6—61no—
384C3×Dic6—62no—
385C3×Dic6—62no—
386C3×Dic6—61no—
387C3×Dic6—121no—
388C3×Dic6C22×D312yes—
389C3×Dic6C22×D312yes—
390C3×Dic6C22×D311yescharacteristic
391C3×Dic6C22×D311yescharacteristic
392#627—22no—
393#627—22no—
394#627—21no—
395#626—21no—
396#626—21no—
397#625—21no—
398#624—21no—
399D3×Dic3—22no—
400D3×Dic3—22no—
401D3×Dic3—21no—
402D3×Dic3—21no—
403C3⋊(C3⋊C8)—32no—
404C3⋊(C3⋊C8)—32no—
405C3⋊(C3⋊C8)—32no—
406C3⋊(C3⋊C8)—62no—
407C3⋊(C3⋊C8)—62no—
408C3⋊(C3⋊C8)—62no—
409C3⋊(C3⋊C8)—122no—
410C3⋊(C3⋊C8)C22×D312yes—
411C3×C3⋊C8—32no—
412C3×C3⋊C8—32no—
413C3×C3⋊C8—62no—
414C2×#137—271noSylow
415C2×C33—21no—
416C2×C33C22×D411yescharacteristic
417C3×C3⋊D3—41no—
418C32×D3—21no—
419C32×D3—41no—
420C32×D3#13712yescomplemented
421C3×#41—31no—
422C3×#41—31no—
423C3×#41—61no—
424C3×#41—91no—
425C3×#41—91no—
426C3×#41—91no—
427C3×#41—181no—
428C3×#41—181no—
429C2×C3×Q8—31no—
430C2×C3×Q8—31no—
431C2×C3×Q8—61no—
432C2×C3×Q8—92no—
433C2×C3×Q8—92no—
434C2×C3×Q8—91no—
435C2×C3×Q8—91no—
436C2×C3×Q8—181no—
437C2×C3×Q8—181no—
438C2×C3×Q8—181no—
439C2×C3×D4—91no—
440C2×C3×D4—181no—
441C22×C3×C4—31no—
442C22×C3×C4—31no—
443C22×C3×C4—61no—
444C22×C3×C4—181no—
445C22×C3×C4—181no—
446C2×#67—61no—
447C22×Dic3—61no—
448#239—31no—
449D3×Q8—32no—
450D3×Q8—32no—
451D3×Q8—31no—
452D3×Q8—61no—
453D3×Q8—61no—
454#237—31no—
455#237—61no—
456D3×D4—31no—
457D3×D4—61no—
458#235—31no—
459#235—31no—
460#235—31no—
461#235—31no—
462#235—61no—
463#235—61no—
464#235—61no—
465#235—61no—
466#235D3211yescharacteristic
467C2×D12—31no—
468C2×C4×D3—61no—
469C2×C4×D3—61no—
470C2×C4×D3—61no—
471C2×C4×D3D3211yescharacteristic
472C2×Dic6—31no—
473C2×Dic6—31no—
474C2×Dic6—32no—
475C2×Dic6—31no—
476C2×Dic6—32no—
477C2×Dic6—61no—
478C2×Dic6—61no—
479C2×Dic6—61no—
480C2×Dic6—61no—
481C2×Dic6—61no—
482C2×Dic6D3211yescharacteristic, complemented
483C3×Q16—92no—
484C3×SD16—92no—
485C3×M16—91no—
486#216—32no—
487#216—32no—
488#216—92no—
489#216—92no—
490#216—92no—
491#216—92no—
492#216—92no—
493#216—92no—
494#216—92no—
495#216—92no—
496#216—182no—
497#216—182no—
498#215—32no—
499#215—92no—
500#215—92no—
501#215—92no—
502#215—92no—
503#215—182no—
504#214—32no—
505#214—92no—
506#214—92no—
507#214—92no—
508#214—92no—
509#214—182no—
510#208—31no—
511#208—31no—
512#208—61no—
513#208—92no—
514#208—92no—
515#208—91no—
516#208—91no—
517#208—91no—
518#208—182no—
519#208—181no—
520#208—181no—
521#208—181no—
522#208—361no—
523C2×C3⋊C8—92no—
524C2×C3⋊C8—92no—
525C2×C3⋊C8—182no—
526Dic12—92no—
527#204—92no—
528ΓL(1,𝔽25)—92no—
529D3×C8—92no—
530C22×C32—21no—
531C22×C32—21no—
532C22×C32—21no—
533C22×C32—31no—
534C22×C32—31no—
535C22×C32—41no—
536C22×C32—62no—
537C22×C32—61no—
538C22×C32D3×D411yescharacteristic
539C22×C32C2×#6711yescharacteristic
540C22×C32C2×#6711yescharacteristic
541C2×C3⋊D3—21no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—21no—
545C2×C3×D3—21no—
546C2×C3×D3—21no—
547C2×C3×D3—21no—
548C2×C3×D3—42no—
549C2×C3×D3—41no—
550C2×C3×D3—61no—
551C2×C3×D3—61no—
552C2×C3×D3—121no—
553C2×C3×D3—122no—
554C2×C3×D3—122no—
555C2×C3×D3C2×#6711yescharacteristic
556C2×C3×D3C2×#6711yescharacteristic
557C2×C3×D3C2×#6711yescharacteristic
558C2×C3×D3C2×#6711yescharacteristic
559D32—42no—
560C32×C4—21no—
561C32×C4—21no—
562C32×C4—21no—
563C32×C4—21no—
564C32×C4—21no—
565C32×C4—21no—
566C32×C4—31no—
567C32×C4—31no—
568C32×C4—41no—
569C32×C4—41no—
570C32×C4—62no—
571C32×C4—61no—
572C32×C4D3×D411yescharacteristic
573C32×C4C2×#6711yescharacteristic
574C32×C4C2×#6711yescharacteristic
575C32×C4C23×D311yescharacteristic
576C32×C4C23×D311yescharacteristic
577C32×C4C23×D311yescharacteristic
578C3⋊Dic3—21no—
579C3⋊Dic3—22no—
580C3×Dic3—22no—
581C3×Dic3—21no—
582C3×Dic3—22no—
583C3×Dic3—21no—
584C3×Dic3—21no—
585C3×Dic3—21no—
586C3×Dic3—42no—
587C3×Dic3—41no—
588C3×Dic3—62no—
589C3×Dic3—61no—
590C3×Dic3—62no—
591C3×Dic3—61no—
592C3×Dic3—122no—
593C3×Dic3—121no—
594C3×Dic3C2×#6711yescharacteristic
595C3×Dic3C2×#6711yescharacteristic
596C3×Dic3C2×#6711yescharacteristic
597C3×Dic3C2×#6711yescharacteristic
598C2×#41—91no—
599C22×Q8—91no—
600#137—91no—
601#137—271no—
602#137—272no—
603#137—272no—
604#137—271no—
605#137—271no—
606C2×Q16—272no—
607C2×SD16—272no—
608C2×M16—271no—
609C33C2×#13711yescharacteristic, complemented, Sylow
610C23×C3—31no—
611C23×C3—31no—
612C23×C3—61no—
613C23×C3—181no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3#62511yescharacteristic
617C3×Q8—32no—
618C3×Q8—32no—
619C3×Q8—31no—
620C3×Q8—31no—
621C3×Q8—62no—
622C3×Q8—61no—
623C3×Q8—61no—
624C3×Q8—61no—
625C3×Q8—92no—
626C3×Q8—91no—
627C3×Q8—121no—
628C3×Q8—182no—
629C3×Q8—182no—
630C3×Q8—181no—
631C3×Q8—181no—
632C3×D4—31no—
633C3×D4—31no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—91no—
638C3×D4—121no—
639C3×D4—181no—
640C3×D4—181no—
641C3×D4—181no—
642C3×D4—181no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—31no—
652C2×C3×C4—31no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—31no—
656C2×C3×C4—41no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4—181no—
669C2×C3×C4—181no—
670C2×C3×C4—181no—
671C2×C3×C4—182no—
672C2×C3×C4—182no—
673C2×C3×C4—181no—
674C2×C3×C4—181no—
675C2×C3×C4C2×D3211yescharacteristic
676C2×C3×C4C2×D3211yescharacteristic
677C2×C3×C4C2×D3211yescharacteristic
678#67—21no—
679#67—61no—
680#67—61no—
681#67—61no—
682#67—61no—
683#67—61no—
684#67—61no—
685#67—121no—
686C2×Dic3—21no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—121no—
694C2×Dic3#62511yescharacteristic
695D12—31no—
696D12—31no—
697D12—61no—
698D12—61no—
699D12—61no—
700D12C2×D3211yescharacteristic
701C4×D3—21no—
702C4×D3—61no—
703C4×D3—61no—
704C4×D3—61no—
705C4×D3—62no—
706C4×D3—62no—
707C4×D3—61no—
708C4×D3—61no—
709C4×D3—61no—
710C4×D3—121no—
711C4×D3#62511yescharacteristic
712C4×D3#62511yescharacteristic
713C4×D3C2×D3211yescharacteristic
714C4×D3C2×D3211yescharacteristic
715Dic6—21no—
716Dic6—32no—
717Dic6—31no—
718Dic6—32no—
719Dic6—31no—
720Dic6—62no—
721Dic6—61no—
722Dic6—62no—
723Dic6—62no—
724Dic6—61no—
725Dic6—61no—
726Dic6—61no—
727Dic6—62no—
728Dic6—62no—
729Dic6—61no—
730Dic6—121no—
731Dic6C2×D3212yes—
732Dic6C2×D3211yescharacteristic
733C3×C8—92no—
734C3⋊C8—32no—
735C3⋊C8—32no—
736C3⋊C8—62no—
737C3⋊C8—92no—
738C3⋊C8—92no—
739C3⋊C8—92no—
740C3⋊C8—182no—
741C3⋊C8—182no—
742C3⋊C8—182no—
743C3⋊C8—362no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—32no—
751C2×C32—41no—
752C2×C32—41no—
753C2×C32—41no—
754C2×C32—41no—
755C2×C32—61no—
756C2×C32—81no—
757C2×C32—121no—
758C2×C32C2×D3×D411yescharacteristic
759C2×C32C22×#6711yescharacteristic
760C2×C32C22×#6711yescharacteristic
761C3⋊D3—41no—
762C3×D3—21no—
763C3×D3—21no—
764C3×D3—22no—
765C3×D3—41no—
766C3×D3—41no—
767C3×D3—41no—
768C3×D3—81no—
769C3×D3—121no—
770C3×D3—121no—
771C3×D3—241no—
772C3×D3#94212yescomplemented
773C3×D3#95112yescomplemented
774#41—31no—
775#41—91no—
776#41—91no—
777#41—91no—
778#41—181no—
779#41—181no—
780C2×Q8—31no—
781C2×Q8—92no—
782C2×Q8—91no—
783C2×Q8—92no—
784C2×Q8—91no—
785C2×Q8—181no—
786C2×Q8—181no—
787C2×Q8—181no—
788C2×D4—91no—
789C2×D4—181no—
790C22×C4—31no—
791C22×C4—181no—
792C22×C4—181no—
793Q16—92no—
794Q16—272no—
795Q16—272no—
796Q16—272no—
797SD16—92no—
798SD16—272no—
799SD16—272no—
800SD16—272no—
801M16—91no—
802M16—272no—
803M16—271no—
804C2×C8—272no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—31no—
809C22×C3—31no—
810C22×C3—31no—
811C22×C3—31no—
812C22×C3—41no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—121no—
820C22×C3—122no—
821C22×C3—181no—
822C22×C3—362no—
823C22×C3C2×#62511yescharacteristic
824C22×C3D3×#6711yescharacteristic
825C22×C3D3×#6711yescharacteristic
826C2×D3—22no—
827C2×D3—21no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—121no—
831C2×D3—122no—
832C2×D3—122no—
833C2×D3C2×#62511yescharacteristic
834C2×D3C2×#62511yescharacteristic
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—31no—
842C3×C4—31no—
843C3×C4—31no—
844C3×C4—31no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—62no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—62no—
853C3×C4—121no—
854C3×C4—122no—
855C3×C4—181no—
856C3×C4—182no—
857C3×C4C2×#62511yescharacteristic
858C3×C4D3×#6711yescharacteristic
859C3×C4D3×#6711yescharacteristic
860C3×C4C22×D3211yescharacteristic
861C3×C4C22×D3211yescharacteristic
862C3×C4C22×D3211yescharacteristic
863Dic3—22no—
864Dic3—21no—
865Dic3—62no—
866Dic3—61no—
867Dic3—62no—
868Dic3—61no—
869Dic3—122no—
870Dic3—121no—
871Dic3C2×#62511yescharacteristic
872Dic3C2×#62511yescharacteristic
873C32—21no—
874C32—21no—
875C32—21no—
876C32—41no—
877C32D3×#13711yescharacteristic, complemented
878C32C2×#94211yescharacteristic, complemented
879C32C2×#95111yescharacteristic, complemented
880C23—31no—
881C23—181no—
882Q8—32no—
883Q8—31no—
884Q8—61no—
885Q8—92no—
886Q8—91no—
887Q8—182no—
888Q8—182no—
889Q8—181no—
890Q8—181no—
891D4—31no—
892D4—61no—
893D4—91no—
894D4—181no—
895D4—181no—
896D4—181no—
897D4—181no—
898C2×C4—31no—
899C2×C4—31no—
900C2×C4—31no—
901C2×C4—31no—
902C2×C4—31no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—182no—
909C2×C4—182no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4D3311yescharacteristic
913C8—92no—
914C8—272no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—32no—
922C2×C3—32no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—62no—
928C2×C3—61no—
929C2×C3—61no—
930C2×C3—81no—
931C2×C3—121no—
932C2×C3—121no—
933C2×C3—121no—
934C2×C3—241no—
935C2×C3—361no—
936C2×C3C22×#62511yescharacteristic
937C2×C3C2×D3×#6711yescharacteristic
938C2×C3C2×D3×#6711yescharacteristic
939D3—21no—
940D3—41no—
941D3—121no—
942D3—121no—
943D3—241no—
944D3#6382712yesdirect product factor
945C22—31no—
946C22—31no—
947C22—62no—
948C22—61no—
949C22—181no—
950C22—362no—
951C22D3×#62511yescharacteristic
952C4—31no—
953C4—31no—
954C4—61no—
955C4—62no—
956C4—181no—
957C4—182no—
958C4D3×#62511yescharacteristic
959C4C2×D3311yescharacteristic
960C3—21no—
961C3—21no—
962C3—21no—
963C3—41no—
964C3C2×#6382711yescharacteristic, complemented
965C3D3×#94211yescharacteristic, complemented
966C3D3×#95111yescharacteristic, complemented
967C2—21no—
968C2—32no—
969C2—61no—
970C2—121no—
971C2—361no—
972C2C2×D3×#62511yescharacteristic
subgroupG/H
centerC2C2×D3×#625
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC2×C33C22×D4
prime radicalC3×D3×#235C2
hypercenterC2×C4D33
hypocenterC33C2×#137
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. #11723663C2semidirect
4. #11723375C2semidirect
5. #11723373C2semidirect
6. D3×#3748C2semidirect
7. C3×#63827C2semidirect
8. #11722883C2semidirect
9. #11722882C2semidirect
10. D3×#3718C2semidirect
11. D3×#3715C2semidirect
16. C2×C3×#634C22semidirect
19. C2×C32×Dic6C22semidirect
33. C3×D3×Dic6C22semidirect
34. #88855C22semidirect
35. C3×#3748C22semidirect
36. #88812C22semidirect
37. #88811C22semidirect
38. #88798C22semidirect
39. #88798C22semidirect
40. #88793C22semidirect
41. #88792C22semidirect
42. #88786C22semidirect
44. C3×#3718C22semidirect
45. C3×#3715C22semidirect
51. C2×D3×Dic6D3semidirect
77. #63827D3direct (N × H)
124. C2×#634C2×D3semidirect
166. C2×C3×Dic6C2×D3semidirect
167. C2×C3×Dic6C2×D3semidirect
181. D3×Dic6C2×D3semidirect
194. #3748C2×D3semidirect
212. #3718C2×D3semidirect
222. #3715C2×D3semidirect
420. C32×D3#137semidirect
482. C2×Dic6D32semidirect
609. C33C2×#137semidirect
772. C3×D3#942semidirect
773. C3×D3#951semidirect
877. C32D3×#137semidirect
878. C32C2×#942semidirect
879. C32C2×#951semidirect
944. D3#63827direct (N × H)
964. C3C2×#63827semidirect
965. C3D3×#942semidirect
966. C3D3×#951semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2352
C2×C3×D3×Dic62
#117236632
#117233752
#117233732
D3×#37482
C3×#638272
#117228832
#117228822
D3×#37182
D3×#37152
D3×#9513
D3×#9423
C2×#638273