Finite Group Databasebeta

← C3×#10595472 #13175069

Subgroups — C3×#10595472 #13175069

Order 1728.

1300 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64367C211yesmaximal, characteristic, complemented
2C3×#64297C211yesmaximal, characteristic, complemented
3C32×#951C211yesmaximal, characteristic, complemented
4C32×#950C211yesmaximal, characteristic, complemented
5C3×#63951C212yesmaximal, complemented
6C3×#63944C212yesmaximal, complemented
7C3×#63936C212yesmaximal, complemented
8C3×#63931C212yesmaximal, complemented
9C2×C3×#3719C211yesmaximal, characteristic, complemented
10C3×#63831C211yesmaximal, characteristic, complemented
11C3×#63817C211yesmaximal, characteristic, complemented
12C3×#5779—31nomaximal
13C3×#5771—31nomaximal
14#10595472C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C3×Q8×C3⋊D3C2212yes—
17C3×#3830—22no—
18C3×#3830C2212yes—
19C3×#3828—21no—
20C3×#3828C2211yescharacteristic
21C2×C3×#634—21no—
22C2×C3×#634C2211yescharacteristic
23C32×#235C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C3×#3804—22no—
26C3×#3799—21no—
27C3×#3797C2212yes—
28C3×#3796C2212yes—
29C3×D3×Dic6—21no—
30C32×#216C2211yescharacteristic
31C32×#216C2212yes—
32C32×#215C2211yescharacteristic
33C32×#214C2211yescharacteristic
34C32×#214C2212yes—
35C32×#213C2211yescharacteristic
36C32×#208C2211yescharacteristic
37C2×C32×C3⋊C8C2211yescharacteristic
38C3×#3719C2212yes—
39C3×#3719C2212yes—
40C3×#3719C2212yes—
41C3×#3716C2212yes—
42C3×#3712C2212yes—
43C3×#3710C2212yes—
44#64367C2×C311yescharacteristic, complemented
45C3×#1010—31no—
46C3×#1010—31no—
47C3×#1010—31no—
48C3×#1010—61no—
49C3×#1007—31no—
50#64297C2×C311yescharacteristic, complemented
51C32×#137—31no—
52C32×#135—31no—
53C3×#951—21no—
54C3×#951—31no—
55C3×#951D311yescharacteristic, complemented
56C3×#951C2×C311yescharacteristic, complemented
57C3×#950—21no—
58C3×#950D311yescharacteristic, complemented
59C3×#950C2×C311yescharacteristic, complemented
60C2×C3×#216—31no—
61C3×#918—32no—
62C3×D3×Q16—32no—
63C3×D3×Q16—32no—
64C3×#916—32no—
65C3×#915—32no—
66C3×#915—32no—
67C3×#915—32no—
68C3×#912—32no—
69C3×#909—31no—
70C3×#907—31no—
71C2×C3×Dic12—31no—
72C3×#901—31no—
73#63951C2×C312yescomplemented
74#63944C2×C312yescomplemented
75#63936C2×C312yescomplemented
76#63931C2×C312yescomplemented
77C2×#3719C2×C311yescharacteristic, complemented
78#63831C2×C311yescharacteristic, complemented
79#63817C2×C311yescharacteristic, complemented
80C33×Q8C2311yescharacteristic
81C33×D4—21no—
82C33×D4C2311yescharacteristic
83C2×C33×C4—21no—
84C2×C33×C4C2311yescharacteristic
85C3×#638—22no—
86C3×#638D412yes—
87C2×C3×C3⋊Dic3—21no—
88C2×C3×C3⋊Dic3—22no—
89C3×C4⋊(C3⋊D3)D411yescharacteristic
90C3×C4×C3⋊D3—22no—
91C3×C4×C3⋊D3C2312yes—
92C3×#634—21no—
93C3×#634—22no—
94C3×#634D411yescharacteristic
95C3×#634C2312yes—
96C32×#67—21no—
97C2×C32×Dic3—21no—
98C32×D12C2311yescharacteristic
99C32×C4×D3—21no—
100C32×Dic6—21no—
101C32×Dic6C2312yes—
102C32×Dic6C2311yescharacteristic
103C3×#627—22no—
104C3×#626—22no—
105C3×#624—22no—
106C3×D3×Dic3—22no—
107C32×C3⋊C8C2311yescharacteristic
108C32×C3⋊C8C2312yes—
109C32×C3⋊C8C2311yescharacteristic
110C3×#578—91no—
111#5779—31no—
112#5771—31no—
113C32×#41—21no—
114C32×#41—21no—
115C32×#41—21no—
116C32×#41—31no—
117C32×#41—41no—
118C32×#41C2×D311yescharacteristic
119C32×#41C2×D311yescharacteristic
120C32×#41C22×C311yescharacteristic
121C2×C32×Q8—31no—
122Q8×C3⋊D3C22×C312yes—
123#3830—22no—
124#3830C22×C312yes—
125#3828—21no—
126#3828C22×C311yescharacteristic
127C2×#634—21no—
128C2×#634C22×C311yescharacteristic
129C3×#239—32no—
130C3×#239—61no—
131C3×D3×Q8—32no—
132C3×D3×Q8—32no—
133C3×D3×Q8—32no—
134C3×D3×Q8—32no—
135C3×D3×Q8—61no—
136C3×D3×Q8—62no—
137C3×#237—32no—
138C3×#237—32no—
139C3×#237—32no—
140C3×#237—62no—
141C3×#237—62no—
142C3×#237—62no—
143C3×#237—62no—
144C3×#237—64no—
145C3×#235—21no—
146C3×#235—31no—
147C3×#235—31no—
148C3×#235—61no—
149C3×#235—61no—
150C3×#235—61no—
151C3×#235—62no—
152C3×#235—61no—
153C3×#235—62no—
154C3×#235C2×D311yescharacteristic
155C3×#235C22×C311yescharacteristic
156C2×C3×Dic6—21no—
157C2×C3×Dic6—31no—
158C2×C3×Dic6—31no—
159C2×C3×Dic6—61no—
160C2×C3×Dic6—61no—
161C2×C3×Dic6—61no—
162C2×C3×Dic6—61no—
163C2×C3×Dic6—62no—
164C2×C3×Dic6C2×D311yescharacteristic
165C2×C3×Dic6C22×C311yescharacteristic
166#3804—22no—
167#3799—21no—
168#3797C22×C312yes—
169#3796C22×C312yes—
170D3×Dic6—21no—
171C32×Q16—31no—
172C32×Q16—32no—
173C32×SD16—31no—
174C32×SD16—31no—
175C32×SD16—32no—
176C32×D8—31no—
177C32×M16—31no—
178C2×C32×C8—31no—
179C3×#216—21no—
180C3×#216—22no—
181C3×#216—32no—
182C3×#216—32no—
183C3×#216—32no—
184C3×#216C2×D312yes—
185C3×#216C2×D311yescharacteristic
186C3×#216C22×C311yescharacteristic
187C3×#216C22×C312yes—
188C3×#215—21no—
189C3×#215C2×D311yescharacteristic
190C3×#215C22×C311yescharacteristic
191C3×#214—21no—
192C3×#214—22no—
193C3×#214—32no—
194C3×#214C2×D312yes—
195C3×#214C2×D311yescharacteristic
196C3×#214C22×C311yescharacteristic
197C3×#214C22×C312yes—
198C3×#213—21no—
199C3×#213C2×D311yescharacteristic
200C3×#213C22×C311yescharacteristic
201C3×#208—21no—
202C3×#208C2×D311yescharacteristic
203C3×#208C22×C311yescharacteristic
204C2×C3×C3⋊C8—21no—
205C2×C3×C3⋊C8C2×D311yescharacteristic
206C2×C3×C3⋊C8C22×C311yescharacteristic
207C3×Dic12—32no—
208C3×Dic12—32no—
209C3×Dic12—32no—
210C3×#204—32no—
211C3×ΓL(1,𝔽25)—32no—
212C3×ΓL(1,𝔽25)—32no—
213C3×D3×C8—32no—
214C3×D3×C8—32no—
215#3719C22×C312yes—
216#3719C22×C312yes—
217#3719C22×C312yes—
218#3716C22×C312yes—
219#3712C22×C312yes—
220#3710C22×C312yes—
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3C2×D412yes—
224C2×C32×D3—21no—
225C33×C4—21no—
226C33×C4C2×D411yescharacteristic
227C33×C4C2411yescharacteristic
228C3×C3⋊Dic3—22no—
229C3×C3⋊Dic3C2×D412yes—
230C32×Dic3—22no—
231C32×Dic3—21no—
232C3×2−1+4—91no—
233C3×2−1+4—91no—
234#1010—31no—
235#1010—31no—
236#1010—31no—
237#1010—61no—
238#1007—31no—
239C3×#137—31no—
240C3×#137—31no—
241C3×#137—61no—
242C3×#137—91no—
243C3×#137—92no—
244C3×#137—92no—
245C3×#135—31no—
246C3×#135—31no—
247C3×#135—61no—
248C3×#135—92no—
249C2×C3×Q16—91no—
250C2×C3×Q16—92no—
251C3×#131—91no—
252#951—31no—
253#951C3×D311yescharacteristic, complemented
254#950C3×D311yescharacteristic, complemented
255C2×#216—31no—
256#918—32no—
257D3×Q16—32no—
258D3×Q16—32no—
259#916—32no—
260#915—32no—
261#915—32no—
262#915—32no—
263#912—32no—
264#909—31no—
265#907—31no—
266C2×Dic12—31no—
267#901—31no—
268C32×Q8—21no—
269C32×Q8—21no—
270C32×Q8—21no—
271C32×Q8—31no—
272C32×Q8—32no—
273C32×Q8—41no—
274C32×Q8—61no—
275C32×Q8C22×D311yescharacteristic
276C32×Q8C22×D311yescharacteristic
277C32×Q8C23×C311yescharacteristic
278C32×D4—21no—
279C32×D4—22no—
280C32×D4—21no—
281C32×D4—21no—
282C32×D4—21no—
283C32×D4—21no—
284C32×D4—21no—
285C32×D4—31no—
286C32×D4—41no—
287C32×D4—41no—
288C32×D4—41no—
289C32×D4—42no—
290C32×D4—61no—
291C32×D4C22×D311yescharacteristic
292C32×D4C22×D311yescharacteristic
293C32×D4C23×C311yescharacteristic
294C2×C32×C4—21no—
295C2×C32×C4—22no—
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4—21no—
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4—41no—
302C2×C32×C4—41no—
303C2×C32×C4—41no—
304C2×C32×C4—42no—
305C2×C32×C4—61no—
306C2×C32×C4—61no—
307C2×C32×C4C22×D311yescharacteristic
308C2×C32×C4C22×D311yescharacteristic
309C2×C32×C4C23×C311yescharacteristic
310#638—22no—
311#638C3×D412yes—
312C2×C3⋊Dic3—21no—
313C2×C3⋊Dic3—22no—
314C4⋊(C3⋊D3)C3×D411yescharacteristic
315C4×C3⋊D3—22no—
316C4×C3⋊D3C23×C312yes—
317#634—21no—
318#634—22no—
319#634C3×D411yescharacteristic
320#634C23×C312yes—
321C3×#67—21no—
322C3×#67—21no—
323C3×#67—32no—
324C3×#67—32no—
325C3×#67—41no—
326C3×#67—62no—
327C3×#67—62no—
328C3×#67—62no—
329C3×#67—62no—
330C3×#67—64no—
331C2×C3×Dic3—21no—
332C2×C3×Dic3—21no—
333C2×C3×Dic3—41no—
334C2×C3×Dic3—62no—
335C2×C3×Dic3—62no—
336C2×C3×Dic3—62no—
337C2×C3×Dic3—64no—
338C2×C3×Dic3—62no—
339C2×C3×Dic3—61no—
340C2×C3×Dic3—61no—
341C3×D12—21no—
342C3×D12—31no—
343C3×D12—31no—
344C3×D12—61no—
345C3×D12—62no—
346C3×D12C22×D311yescharacteristic
347C3×D12C23×C311yescharacteristic
348C3×C4×D3—21no—
349C3×C4×D3—21no—
350C3×C4×D3—32no—
351C3×C4×D3—32no—
352C3×C4×D3—41no—
353C3×C4×D3—62no—
354C3×C4×D3—62no—
355C3×C4×D3—62no—
356C3×C4×D3—62no—
357C3×C4×D3—62no—
358C3×C4×D3—62no—
359C3×C4×D3—64no—
360C3×Dic6—21no—
361C3×Dic6—21no—
362C3×Dic6—22no—
363C3×Dic6—21no—
364C3×Dic6—31no—
365C3×Dic6—31no—
366C3×Dic6—32no—
367C3×Dic6—32no—
368C3×Dic6—41no—
369C3×Dic6—61no—
370C3×Dic6—62no—
371C3×Dic6—62no—
372C3×Dic6—62no—
373C3×Dic6—62no—
374C3×Dic6—62no—
375C3×Dic6—62no—
376C3×Dic6—64no—
377C3×Dic6—61no—
378C3×Dic6—61no—
379C3×Dic6C22×D312yes—
380C3×Dic6C22×D311yescharacteristic
381C3×Dic6C23×C312yes—
382C3×Dic6C23×C311yescharacteristic
383#627—22no—
384#626—22no—
385#624—22no—
386D3×Dic3—22no—
387C32×C8—31no—
388C32×C8—32no—
389C32×C8—31no—
390C3×C3⋊C8—21no—
391C3×C3⋊C8—21no—
392C3×C3⋊C8—22no—
393C3×C3⋊C8C22×D311yescharacteristic
394C3×C3⋊C8C22×D312yes—
395C3×C3⋊C8C22×D311yescharacteristic
396C3×C3⋊C8C23×C311yescharacteristic
397C3×C3⋊C8C23×C312yes—
398C3×C3⋊C8C23×C311yescharacteristic
399#578—91noSylow
400C2×C33—21no—
401C2×C33—41no—
402C2×C33C22×D411yescharacteristic
403C3×C3⋊D3—22no—
404C32×D3—41no—
405C3×#41—21no—
406C3×#41—21no—
407C3×#41—21no—
408C3×#41—31no—
409C3×#41—31no—
410C3×#41—41no—
411C3×#41—61no—
412C3×#41—91no—
413C3×#41—92no—
414C3×#41—92no—
415C3×#41—181no—
416C3×#41—182no—
417C3×#41—181no—
418C3×#41—182no—
419C3×#41D3211yescharacteristic
420C3×#41C2×C3×D311yescharacteristic
421C3×#41C2×C3×D311yescharacteristic
422C2×C3×Q8—31no—
423C2×C3×Q8—31no—
424C2×C3×Q8—61no—
425C2×C3×Q8—92no—
426C2×C3×Q8—92no—
427C2×C3×Q8—91no—
428C2×C3×Q8—181no—
429C2×C3×Q8—181no—
430#239—32no—
431#239—61no—
432D3×Q8—32no—
433D3×Q8—32no—
434D3×Q8—32no—
435D3×Q8—32no—
436D3×Q8—62no—
437D3×Q8—61no—
438#237—32no—
439#237—32no—
440#237—32no—
441#237—62no—
442#237—62no—
443#237—62no—
444#237—62no—
445#237—64no—
446#235—31no—
447#235—31no—
448#235—61no—
449#235—61no—
450#235—61no—
451#235—61no—
452#235—62no—
453#235—62no—
454#235C2×C3×D311yescharacteristic
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6—61no—
458C2×Dic6—61no—
459C2×Dic6—61no—
460C2×Dic6—61no—
461C2×Dic6—62no—
462C2×Dic6C2×C3×D311yescharacteristic
463C3×Q16—31no—
464C3×Q16—32no—
465C3×Q16—31no—
466C3×Q16—32no—
467C3×Q16—61no—
468C3×Q16—62no—
469C3×Q16—92no—
470C3×Q16—92no—
471C3×Q16—92no—
472C3×SD16—31no—
473C3×SD16—31no—
474C3×SD16—31no—
475C3×SD16—32no—
476C3×SD16—31no—
477C3×SD16—32no—
478C3×SD16—61no—
479C3×SD16—62no—
480C3×SD16—61no—
481C3×SD16—92no—
482C3×D8—31no—
483C3×D8—31no—
484C3×D8—61no—
485C3×M16—31no—
486C3×M16—31no—
487C3×M16—61no—
488C3×M16—92no—
489C2×C3×C8—31no—
490C2×C3×C8—31no—
491C2×C3×C8—61no—
492C2×C3×C8—92no—
493#216—32no—
494#216—32no—
495#216—32no—
496#216C2×C3×D312yes—
497#216C2×C3×D311yescharacteristic
498#215C2×C3×D311yescharacteristic
499#214—32no—
500#214C2×C3×D312yes—
501#214C2×C3×D311yescharacteristic
502#213C2×C3×D311yescharacteristic
503#208C2×C3×D311yescharacteristic
504C2×C3⋊C8C2×C3×D311yescharacteristic
505Dic12—32no—
506Dic12—32no—
507Dic12—32no—
508#204—32no—
509ΓL(1,𝔽25)—32no—
510ΓL(1,𝔽25)—32no—
511D3×C8—32no—
512D3×C8—32no—
513C22×C32—21no—
514C22×C32—22no—
515C22×C32—21no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32—41no—
523C22×C32—42no—
524C22×C32—61no—
525C22×C32D3×D411yescharacteristic
526C22×C32D3×D411yescharacteristic
527C22×C32C2×C3×D411yescharacteristic
528C2×C3⋊D3C2×C3×D412yes—
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—32no—
532C2×C3×D3—32no—
533C2×C3×D3—41no—
534C2×C3×D3—62no—
535C32×C4—21no—
536C32×C4—22no—
537C32×C4—21no—
538C32×C4—21no—
539C32×C4—21no—
540C32×C4—21no—
541C32×C4—21no—
542C32×C4—21no—
543C32×C4—21no—
544C32×C4—21no—
545C32×C4—41no—
546C32×C4—41no—
547C32×C4—41no—
548C32×C4—41no—
549C32×C4—42no—
550C32×C4—61no—
551C32×C4—62no—
552C32×C4D3×D411yescharacteristic
553C32×C4D3×D411yescharacteristic
554C32×C4C2×C3×D411yescharacteristic
555C32×C4C23×D311yescharacteristic
556C32×C4C23×D311yescharacteristic
557C32×C4C24×C311yescharacteristic
558C3⋊Dic3—22no—
559C3⋊Dic3C2×C3×D412yes—
560C3×Dic3—22no—
561C3×Dic3—21no—
562C3×Dic3—22no—
563C3×Dic3—21no—
564C3×Dic3—32no—
565C3×Dic3—32no—
566C3×Dic3—42no—
567C3×Dic3—41no—
568C3×Dic3—62no—
569C3×Dic3—64no—
570C3×Dic3—62no—
571C3×Dic3—62no—
5722−1+4—91no—
5732−1+4—91no—
574#137—31no—
575#137—91no—
576#137—92no—
577#137—92no—
578#135—31no—
579#135—92no—
580C2×Q16—91no—
581C2×Q16—92no—
582#131—91no—
583C33#57811yescharacteristic, complemented, Sylow
584C3×Q8—21no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—32no—
588C3×Q8—31no—
589C3×Q8—31no—
590C3×Q8—32no—
591C3×Q8—41no—
592C3×Q8—62no—
593C3×Q8—61no—
594C3×Q8—61no—
595C3×Q8—61no—
596C3×Q8—91no—
597C3×Q8—92no—
598C3×Q8—121no—
599C3×Q8—182no—
600C3×Q8—182no—
601C3×Q8—181no—
602C3×Q8C2×D3211yescharacteristic
603C3×Q8C22×C3×D311yescharacteristic
604C3×Q8C22×C3×D311yescharacteristic
605C3×D4—22no—
606C3×D4—21no—
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—31no—
613C3×D4—31no—
614C3×D4—41no—
615C3×D4—41no—
616C3×D4—42no—
617C3×D4—41no—
618C3×D4—61no—
619C3×D4—61no—
620C3×D4—61no—
621C3×D4—92no—
622C3×D4—91no—
623C3×D4—121no—
624C3×D4—182no—
625C3×D4—182no—
626C3×D4C2×D3211yescharacteristic
627C3×D4C22×C3×D311yescharacteristic
628C3×D4C22×C3×D311yescharacteristic
629C2×C3×C4—22no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—42no—
639C2×C3×C4—41no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—92no—
645C2×C3×C4—121no—
646C2×C3×C4—121no—
647C2×C3×C4—182no—
648C2×C3×C4—182no—
649C2×C3×C4—182no—
650C2×C3×C4—182no—
651C2×C3×C4—181no—
652C2×C3×C4C2×D3211yescharacteristic
653C2×C3×C4C22×C3×D311yescharacteristic
654C2×C3×C4C22×C3×D311yescharacteristic
655#67—21no—
656#67—32no—
657#67—32no—
658#67—62no—
659#67—62no—
660#67—62no—
661#67—62no—
662#67—64no—
663C2×Dic3—21no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—64no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671D12—31no—
672D12—31no—
673D12—61no—
674D12—62no—
675D12C22×C3×D311yescharacteristic
676C4×D3—21no—
677C4×D3—32no—
678C4×D3—32no—
679C4×D3—62no—
680C4×D3—62no—
681C4×D3—62no—
682C4×D3—62no—
683C4×D3—62no—
684C4×D3—62no—
685C4×D3—64no—
686Dic6—21no—
687Dic6—31no—
688Dic6—31no—
689Dic6—32no—
690Dic6—32no—
691Dic6—61no—
692Dic6—62no—
693Dic6—62no—
694Dic6—62no—
695Dic6—62no—
696Dic6—62no—
697Dic6—62no—
698Dic6—64no—
699Dic6—61no—
700Dic6—61no—
701Dic6C22×C3×D312yes—
702Dic6C22×C3×D311yescharacteristic
703C3×C8—31no—
704C3×C8—31no—
705C3×C8—32no—
706C3×C8—31no—
707C3×C8—32no—
708C3×C8—31no—
709C3×C8—61no—
710C3×C8—61no—
711C3×C8—62no—
712C3⋊C8C22×C3×D311yescharacteristic
713C3⋊C8C22×C3×D312yes—
714C3⋊C8C22×C3×D311yescharacteristic
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—21no—
721C2×C32—41no—
722C2×C32—41no—
723C2×C32—41no—
724C2×C32—41no—
725C2×C32—41no—
726C2×C32—42no—
727C2×C32—41no—
728C2×C32—41no—
729C2×C32—81no—
730C2×C32—81no—
731C2×C32—81no—
732C2×C32—82no—
733C2×C32—121no—
734C2×C32C2×D3×D411yescharacteristic
735C2×C32C2×D3×D411yescharacteristic
736C2×C32C22×C3×D411yescharacteristic
737C3⋊D3—22no—
738C3×D3—41no—
739C3×D3—41no—
740C3×D3—62no—
741C3×D3—62no—
742C3×D3—81no—
743C3×D3—122no—
744#41—31no—
745#41—91no—
746#41—92no—
747#41—92no—
748#41—181no—
749#41—182no—
750#41—181no—
751#41—182no—
752#41C3×D3211yescharacteristic
753C2×Q8—31no—
754C2×Q8—92no—
755C2×Q8—92no—
756C2×Q8—91no—
757C2×Q8—181no—
758C2×Q8—181no—
759Q16—31no—
760Q16—32no—
761Q16—92no—
762Q16—92no—
763Q16—92no—
764SD16—31no—
765SD16—31no—
766SD16—32no—
767SD16—92no—
768D8—31no—
769M16—31no—
770M16—92no—
771C2×C8—31no—
772C2×C8—92no—
773C22×C3—22no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—42no—
783C22×C3—41no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—92no—
787C22×C3—121no—
788C22×C3#381111yescharacteristic
789C22×C3C3×D3×D411yescharacteristic
790C22×C3C3×D3×D411yescharacteristic
791C2×D3—21no—
792C2×D3—32no—
793C2×D3—32no—
794C2×D3—62no—
795C3×C4—22no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—21no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—42no—
808C3×C4—41no—
809C3×C4—41no—
810C3×C4—61no—
811C3×C4—62no—
812C3×C4—61no—
813C3×C4—62no—
814C3×C4—92no—
815C3×C4—121no—
816C3×C4—122no—
817C3×C4—182no—
818C3×C4#381111yescharacteristic
819C3×C4C3×D3×D411yescharacteristic
820C3×C4C3×D3×D411yescharacteristic
821C3×C4C22×D3211yescharacteristic
822C3×C4C23×C3×D311yescharacteristic
823C3×C4C23×C3×D311yescharacteristic
824Dic3—22no—
825Dic3—21no—
826Dic3—32no—
827Dic3—32no—
828Dic3—62no—
829Dic3—64no—
830Dic3—62no—
831Dic3—62no—
832C32—21no—
833C32—21no—
834C32—21no—
835C32—41no—
836C32#577111yescharacteristic, complemented
837C32#577911yescharacteristic, complemented
838C32C3×#57811yescharacteristic, complemented
839Q8—32no—
840Q8—31no—
841Q8—61no—
842Q8—91no—
843Q8—92no—
844Q8—182no—
845Q8—182no—
846Q8—181no—
847Q8C2×C3×D3211yescharacteristic
848D4—21no—
849D4—31no—
850D4—61no—
851D4—92no—
852D4—91no—
853D4—182no—
854D4—182no—
855D4C2×C3×D3211yescharacteristic
856C2×C4—21no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—92no—
860C2×C4—182no—
861C2×C4—182no—
862C2×C4—182no—
863C2×C4—182no—
864C2×C4—181no—
865C2×C4C2×C3×D3211yescharacteristic
866C8—31no—
867C8—31no—
868C8—32no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—41no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—42no—
879C2×C3—41no—
880C2×C3—41no—
881C2×C3—41no—
882C2×C3—41no—
883C2×C3—81no—
884C2×C3—81no—
885C2×C3—81no—
886C2×C3—82no—
887C2×C3—121no—
888C2×C3—121no—
889C2×C3—182no—
890C2×C3—241no—
891C2×C3C2×#381111yescharacteristic
892C2×C3C2×C3×D3×D411yescharacteristic
893C2×C3C2×C3×D3×D411yescharacteristic
894D3—41no—
895D3—62no—
896D3—62no—
897D3—122no—
898C22—21no—
899C22—61no—
900C22—92no—
901C22C3×#381111yescharacteristic
902C4—21no—
903C4—61no—
904C4—62no—
905C4—92no—
906C4—182no—
907C4C3×#381111yescharacteristic
908C4C22×C3×D3211yescharacteristic
909C3—21no—
910C3—21no—
911C3—21no—
912C3—41no—
913C3#1059547211yescharacteristic, direct product factor
914C3C3×#577111yescharacteristic, complemented
915C3C3×#577911yescharacteristic, complemented
916C2—21no—
917C2—41no—
918C2—121no—
919C2—182no—
920C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3C2×#3811
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
1. C3×#64367C2semidirect
2. C3×#64297C2semidirect
3. C32×#951C2semidirect
4. C32×#950C2semidirect
5. C3×#63951C2semidirect
6. C3×#63944C2semidirect
7. C3×#63936C2semidirect
8. C3×#63931C2semidirect
9. C2×C3×#3719C2semidirect
10. C3×#63831C2semidirect
11. C3×#63817C2semidirect
14. #10595472C3direct (N × H)
44. #64367C2×C3semidirect
50. #64297C2×C3semidirect
55. C3×#951D3semidirect
56. C3×#951C2×C3semidirect
58. C3×#950D3semidirect
59. C3×#950C2×C3semidirect
73. #63951C2×C3semidirect
74. #63944C2×C3semidirect
75. #63936C2×C3semidirect
76. #63931C2×C3semidirect
77. C2×#3719C2×C3semidirect
78. #63831C2×C3semidirect
79. #63817C2×C3semidirect
253. #951C3×D3semidirect
254. #950C3×D3semidirect
583. C33#578semidirect
836. C32#5771semidirect
837. C32#5779semidirect
838. C32C3×#578semidirect
913. C3#10595472direct (N × H)
914. C3C3×#5771semidirect
915. C3C3×#5779semidirect

Maximal subgroups

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

subgroupindex
C3×#643672
C3×#642972
C32×#9512
C32×#9502
C3×#639512
C3×#639442
C3×#639362
C3×#639312
C2×C3×#37192
C3×#638312
C3×#638172
C3×#57793
C3×#57713
#105954723