Finite Group Databasebeta

← C3×#10595464 #13175061

Subgroups — C3×#10595464 #13175061

Order 1728.

1360 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#1009C211yesmaximal, characteristic, complemented
2C3×#64297C211yesmaximal, characteristic, complemented
3C3×#64159C211yesmaximal, characteristic, complemented
4C32×#951C211yesmaximal, characteristic, complemented
5C3×#63949C212yesmaximal, complemented
6C3×#63943C212yesmaximal, complemented
7C3×#63934C212yesmaximal, complemented
8C3×D3×#214C212yesmaximal, complemented
9C3×#63830C211yesmaximal, characteristic, complemented
10C2×C3×#3715C211yesmaximal, characteristic, complemented
11C3×#63815C211yesmaximal, characteristic, complemented
12C3×#5836—31nomaximal
13C3×#5778—31nomaximal
14#10595464C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C3×#3828C2211yescharacteristic, complemented
17C32×#239C2212yes—
18C32×D3×D4—22no—
19C32×D3×D4C2212yes—
20C32×#235—21no—
21C32×#235C2211yescharacteristic
22C2×C32×D12—21no—
23C2×C32×D12C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic, complemented
25C3×#3804—22no—
26C3×#3799C2212yescomplemented
27C3×#3797—21no—
28C3×#3796—21no—
29C3×D3×Dic6C2212yescomplemented
30C3×#3756C2211yescharacteristic, complemented
31C3×#3755C2211yescharacteristic, complemented
32C3×#3754C2211yescharacteristic, complemented
33C3×#3753C2211yescharacteristic, complemented
34C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
35C32×#216C2212yescomplemented
36C32×#214C2212yescomplemented
37C32×#208C2211yescharacteristic, complemented
38C3×#3716C2212yescomplemented
39C3×#3715C2212yescomplemented
40C3×#3715C2212yescomplemented
41C3×#3714C2212yescomplemented
42C3×#3711C2212yescomplemented
43C3×D3×C3⋊C8C2212yescomplemented
44C32×H(5,𝔽2)—31no—
45C3×#1010—31no—
46C3×#1009—21no—
47C3×#1009D311yescharacteristic, complemented
48C3×#1009C2×C311yescharacteristic, complemented
49C3×#1007—31no—
50#64297C2×C311yescharacteristic, complemented
51C32×#137—31no—
52#64159C2×C311yescharacteristic, complemented
53C3×#951—21no—
54C3×#951—32no—
55C3×#951D311yescharacteristic, complemented
56C3×#951C2×C311yescharacteristic, complemented
57C3×#950—31no—
58C3×#950—31no—
59C3×#950—32no—
60C3×#950—61no—
61C3×#948—31no—
62C2×C3×#215—31no—
63C2×C3×#214—31no—
64C2×C3×#214—32no—
65C3×#932—32no—
66C3×#932—31no—
67C3×#919—32no—
68C3×#918—32no—
69C3×#914—32no—
70C3×D3×SD16—32no—
71C3×#908—31no—
72C3×#907—31no—
73#63949C2×C312yescomplemented
74#63943C2×C312yescomplemented
75#63934C2×C312yescomplemented
76D3×#214C2×C312yescomplemented
77#63830C2×C311yescharacteristic, complemented
78C2×#3715C2×C311yescharacteristic, complemented
79#63815C2×C311yescharacteristic, complemented
80C22×C32×D3—21no—
81C22×C32×D3—22no—
82C33×Q8C2311yescharacteristic
83C33×D4—21no—
84C33×D4C2311yescharacteristic
85C2×C33×C4—21no—
86C2×C33×C4C2311yescharacteristic
87C3×#638—21no—
88C3×C4⋊(C3⋊D3)C2311yescharacteristic
89C3×C4×C3⋊D3—21no—
90C3×#634C2311yescharacteristic
91C32×#67—22no—
92C32×#67D412yes—
93C2×C32×Dic3—21no—
94C32×D12—22no—
95C32×D12—21no—
96C32×D12D411yescharacteristic
97C32×D12C2312yes—
98C32×C4×D3—22no—
99C32×C4×D3C2312yes—
100C32×Dic6—21no—
101C32×Dic6D411yescharacteristic
102C32×Dic6C2312yes—
103C3×#627—22no—
104C3×#626—22no—
105C3×#624—22no—
106C3×D3×Dic3—22no—
107C3×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×C3⋊(C3⋊C8)C2311yescharacteristic
109C32×C3⋊C8C2312yes—
110C3×#577—91no—
111#5836—31no—
112#5778—31no—
113C32×#41—21no—
114C32×#41—21no—
115C32×#41—21no—
116C32×#41—31no—
117C32×#41—32no—
118C32×#41—41no—
119C32×#41—61no—
120C32×#41C2×D311yescharacteristic
121C32×#41C2×D311yescharacteristic
122C32×#41C22×C311yescharacteristic
123C2×C32×Q8—31no—
124C2×C32×D4—32no—
125C2×C32×D4—31no—
126C2×C32×D4—61no—
127C2×C32×D4—62no—
128#3828C22×C311yescharacteristic, complemented
129C3×#239—22no—
130C3×#239—32no—
131C3×#239—61no—
132C3×#239C2×D312yes—
133C3×#239C22×C312yes—
134C3×D3×Q8—32no—
135C3×D3×Q8—61no—
136C3×D3×Q8—61no—
137C3×#237—61no—
138C3×#237—62no—
139C3×D3×D4—24no—
140C3×D3×D4—22no—
141C3×D3×D4—22no—
142C3×D3×D4—22no—
143C3×D3×D4C2×D312yes—
144C3×D3×D4C22×C312yes—
145C3×#235—22no—
146C3×#235—21no—
147C3×#235—21no—
148C3×#235—21no—
149C3×#235—31no—
150C3×#235—31no—
151C3×#235—32no—
152C3×#235—62no—
153C3×#235—61no—
154C3×#235C2×D311yescharacteristic
155C3×#235C22×C311yescharacteristic
156C2×C3×D12—22no—
157C2×C3×D12—21no—
158C2×C3×D12—21no—
159C2×C3×D12—21no—
160C2×C3×D12C2×D311yescharacteristic
161C2×C3×D12C22×C311yescharacteristic
162C2×C3×Dic6—21no—
163C2×C3×Dic6—32no—
164C2×C3×Dic6C2×D311yescharacteristic, complemented
165C2×C3×Dic6C22×C311yescharacteristic, complemented
166#3804—22no—
167#3799C22×C312yescomplemented
168#3797—21no—
169#3796—21no—
170D3×Dic6C22×C312yescomplemented
171C32×Q16—32no—
172C32×SD16—32no—
173C32×M16—31no—
174#3756C22×C311yescharacteristic, complemented
175#3755C22×C311yescharacteristic, complemented
176#3754C22×C311yescharacteristic, complemented
177#3753C22×C311yescharacteristic, complemented
178C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
179C3×#216—22no—
180C3×#216—31no—
181C3×#216—31no—
182C3×#216—61no—
183C3×#216C2×D312yescomplemented
184C3×#216C22×C312yescomplemented
185C3×#215—31no—
186C3×#215—31no—
187C3×#215—32no—
188C3×#215—32no—
189C3×#215—61no—
190C3×#214—22no—
191C3×#214—31no—
192C3×#214—31no—
193C3×#214—32no—
194C3×#214—32no—
195C3×#214—32no—
196C3×#214—61no—
197C3×#214C2×D312yescomplemented
198C3×#214C22×C312yescomplemented
199C3×#213—31no—
200C3×#213—31no—
201C3×#213—32no—
202C3×#213—61no—
203C3×#208—21no—
204C3×#208—32no—
205C3×#208C2×D311yescharacteristic, complemented
206C3×#208C22×C311yescharacteristic, complemented
207C2×C3×C3⋊C8—31no—
208C2×C3×C3⋊C8—31no—
209C2×C3×C3⋊C8—32no—
210C2×C3×C3⋊C8—61no—
211C3×D24—32no—
212C3×#204—32no—
213C3×ΓL(1,𝔽25)—32no—
214C3×D3×C8—32no—
215#3716C22×C312yescomplemented
216#3715C22×C312yescomplemented
217#3715C22×C312yescomplemented
218#3714C22×C312yescomplemented
219#3711C22×C312yescomplemented
220D3×C3⋊C8C22×C312yescomplemented
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3—21no—
224C2×C32×D3—22no—
225C2×C32×D3—82no—
226C2×C32×D3—81no—
227C2×C32×D3C2×D412yes—
228C33×C4—21no—
229C33×C4C2×D411yescharacteristic
230C33×C4C2411yescharacteristic
231C3×C3⋊Dic3—21no—
232C32×Dic3—22no—
233C32×Dic3C2×D412yes—
234C3×2−1+4—91no—
235C3×H(5,𝔽2)—31no—
236C3×H(5,𝔽2)—31no—
237C3×H(5,𝔽2)—61no—
238#1010—31no—
239#1009C3×D311yescharacteristic, complemented
240#1007—31no—
241C3×#137—31no—
242C3×#137—31no—
243C3×#137—61no—
244C3×#137—92no—
245C3×AGL(1,ℤ/8)—91no—
246C3×AGL(1,ℤ/8)—92no—
247C3×#135—92no—
248C3×#135—91no—
249C2×C3×SD16—92no—
250C2×C3×SD16—91no—
251C3×#131—91no—
252#951—32no—
253#951C3×D311yescharacteristic, complemented
254#950—31no—
255#950—31no—
256#950—32no—
257#950—61no—
258#948—31no—
259C2×#215—31no—
260C2×#214—31no—
261C2×#214—32no—
262#932—32no—
263#932—31no—
264#919—32no—
265#918—32no—
266#914—32no—
267D3×SD16—32no—
268#908—31no—
269#907—31no—
270C23×C32—62no—
271C23×C32—61no—
272C22×C3×D3—22no—
273C22×C3×D3—24no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C32×Q8—21no—
279C32×Q8—21no—
280C32×Q8—21no—
281C32×Q8—31no—
282C32×Q8—32no—
283C32×Q8—41no—
284C32×Q8—61no—
285C32×Q8C22×D311yescharacteristic
286C32×Q8C22×D311yescharacteristic
287C32×Q8C23×C311yescharacteristic
288C32×D4—21no—
289C32×D4—22no—
290C32×D4—21no—
291C32×D4—21no—
292C32×D4—21no—
293C32×D4—21no—
294C32×D4—21no—
295C32×D4—32no—
296C32×D4—31no—
297C32×D4—32no—
298C32×D4—41no—
299C32×D4—41no—
300C32×D4—41no—
301C32×D4—42no—
302C32×D4—62no—
303C32×D4—62no—
304C32×D4—61no—
305C32×D4C22×D311yescharacteristic
306C32×D4C22×D311yescharacteristic
307C32×D4C23×C311yescharacteristic
308C2×C32×C4—21no—
309C2×C32×C4—22no—
310C2×C32×C4—21no—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—32no—
316C2×C32×C4—41no—
317C2×C32×C4—41no—
318C2×C32×C4—41no—
319C2×C32×C4—42no—
320C2×C32×C4—62no—
321C2×C32×C4—61no—
322C2×C32×C4C22×D311yescharacteristic
323C2×C32×C4C22×D311yescharacteristic
324C2×C32×C4C23×C311yescharacteristic
325#638—21no—
326C4⋊(C3⋊D3)C23×C311yescharacteristic
327C4×C3⋊D3—21no—
328#634C23×C311yescharacteristic
329C3×#67—24no—
330C3×#67—22no—
331C3×#67—22no—
332C3×#67—22no—
333C3×#67—62no—
334C3×#67—61no—
335C3×#67—61no—
336C3×#67—121no—
337C3×#67#6712yes—
338C3×#67C3×D412yes—
339C2×C3×Dic3—21no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—41no—
342C2×C3×Dic3—62no—
343C3×D12—22no—
344C3×D12—24no—
345C3×D12—22no—
346C3×D12—22no—
347C3×D12—21no—
348C3×D12—21no—
349C3×D12—21no—
350C3×D12—22no—
351C3×D12—31no—
352C3×D12—31no—
353C3×D12—61no—
354C3×D12—62no—
355C3×D12#6711yescharacteristic
356C3×D12C3×D411yescharacteristic
357C3×D12C22×D312yes—
358C3×D12C23×C312yes—
359C3×C4×D3—24no—
360C3×C4×D3—22no—
361C3×C4×D3—22no—
362C3×C4×D3—22no—
363C3×C4×D3—62no—
364C3×C4×D3—62no—
365C3×C4×D3—61no—
366C3×C4×D3—61no—
367C3×C4×D3—62no—
368C3×C4×D3—121no—
369C3×C4×D3C22×D312yes—
370C3×C4×D3C23×C312yes—
371C3×Dic6—21no—
372C3×Dic6—21no—
373C3×Dic6—21no—
374C3×Dic6—22no—
375C3×Dic6—31no—
376C3×Dic6—31no—
377C3×Dic6—41no—
378C3×Dic6—61no—
379C3×Dic6—62no—
380C3×Dic6—62no—
381C3×Dic6#6711yescharacteristic
382C3×Dic6C3×D411yescharacteristic
383C3×Dic6C22×D312yes—
384C3×Dic6C23×C312yes—
385#627—22no—
386#626—22no—
387#624—22no—
388D3×Dic3—22no—
389C32×C8—32no—
390C3⋊(C3⋊C8)C23×C311yescharacteristic
391C3⋊(C3⋊C8)C23×C311yescharacteristic
392C3×C3⋊C8—22no—
393C3×C3⋊C8—31no—
394C3×C3⋊C8—31no—
395C3×C3⋊C8—31no—
396C3×C3⋊C8—31no—
397C3×C3⋊C8—61no—
398C3×C3⋊C8—61no—
399C3×C3⋊C8C22×D312yes—
400C3×C3⋊C8C23×C312yes—
401#577—91noSylow
402C2×C33—21no—
403C2×C33—41no—
404C2×C33C22×D411yescharacteristic
405C3×C3⋊D3—41no—
406C32×D3—22no—
407C32×D3—42no—
408C3×#41—21no—
409C3×#41—21no—
410C3×#41—21no—
411C3×#41—31no—
412C3×#41—31no—
413C3×#41—32no—
414C3×#41—32no—
415C3×#41—41no—
416C3×#41—61no—
417C3×#41—62no—
418C3×#41—61no—
419C3×#41—61no—
420C3×#41—62no—
421C3×#41—92no—
422C3×#41—91no—
423C3×#41—182no—
424C3×#41—181no—
425C3×#41D3211yescharacteristic
426C3×#41C2×C3×D311yescharacteristic
427C3×#41C2×C3×D311yescharacteristic
428C2×C3×Q8—31no—
429C2×C3×Q8—31no—
430C2×C3×Q8—61no—
431C2×C3×Q8—92no—
432C2×C3×Q8—181no—
433C2×C3×D4—32no—
434C2×C3×D4—32no—
435C2×C3×D4—31no—
436C2×C3×D4—31no—
437C2×C3×D4—61no—
438C2×C3×D4—62no—
439C2×C3×D4—61no—
440C2×C3×D4—61no—
441C2×C3×D4—62no—
442C2×C3×D4—62no—
443C2×C3×D4—62no—
444C2×C3×D4—64no—
445#239—32no—
446#239—61no—
447#239C2×C3×D312yes—
448D3×Q8—32no—
449D3×Q8—61no—
450D3×Q8—61no—
451#237—61no—
452#237—62no—
453D3×D4—22no—
454D3×D4C2×C3×D312yes—
455#235—21no—
456#235—31no—
457#235—31no—
458#235—32no—
459#235—61no—
460#235—62no—
461#235C2×C3×D311yescharacteristic
462C2×D12—21no—
463C2×D12C2×C3×D311yescharacteristic
464C2×Dic6—32no—
465C2×Dic6C2×C3×D311yescharacteristic, complemented
466C3×Q16—32no—
467C3×Q16—32no—
468C3×Q16—62no—
469C3×Q16—91no—
470C3×SD16—32no—
471C3×SD16—32no—
472C3×SD16—62no—
473C3×SD16—92no—
474C3×SD16—92no—
475C3×SD16—92no—
476C3×SD16—91no—
477C3×SD16—91no—
478C3×D8—92no—
479C3×D8—91no—
480C3×M16—31no—
481C3×M16—31no—
482C3×M16—61no—
483C3×M16—92no—
484C2×C3×C8—92no—
485C2×C3×C8—91no—
486#216—31no—
487#216—31no—
488#216—61no—
489#216C2×C3×D312yescomplemented
490#215—31no—
491#215—31no—
492#215—32no—
493#215—32no—
494#215—61no—
495#214—31no—
496#214—31no—
497#214—32no—
498#214—32no—
499#214—32no—
500#214—61no—
501#214C2×C3×D312yescomplemented
502#213—31no—
503#213—31no—
504#213—32no—
505#213—61no—
506#208—32no—
507#208C2×C3×D311yescharacteristic, complemented
508C2×C3⋊C8—31no—
509C2×C3⋊C8—31no—
510C2×C3⋊C8—32no—
511C2×C3⋊C8—61no—
512D24—32no—
513#204—32no—
514ΓL(1,𝔽25)—32no—
515D3×C8—32no—
516C22×C32—21no—
517C22×C32—22no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—21no—
521C22×C32—21no—
522C22×C32—21no—
523C22×C32—32no—
524C22×C32—41no—
525C22×C32—41no—
526C22×C32—41no—
527C22×C32—42no—
528C22×C32—62no—
529C22×C32—241no—
530C22×C32—242no—
531C22×C32D3×D411yescharacteristic
532C22×C32C2×#6711yescharacteristic
533C22×C32C2×C3×D411yescharacteristic
534C2×C3⋊D3—21no—
535C2×C3×D3—24no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—82no—
542C2×C3×D3—82no—
543C2×C3×D3—81no—
544C2×C3×D3—81no—
545C2×C3×D3—84no—
546C2×C3×D3—82no—
547C2×C3×D3—121no—
548C2×C3×D3C2×#6712yes—
549C2×C3×D3C2×C3×D412yes—
550C32×C4—21no—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—21no—
559C32×C4—21no—
560C32×C4—32no—
561C32×C4—41no—
562C32×C4—41no—
563C32×C4—41no—
564C32×C4—41no—
565C32×C4—42no—
566C32×C4—62no—
567C32×C4D3×D411yescharacteristic
568C32×C4C2×#6711yescharacteristic
569C32×C4C2×C3×D411yescharacteristic
570C32×C4C23×D311yescharacteristic
571C32×C4C23×D311yescharacteristic
572C32×C4C24×C311yescharacteristic
573C3⋊Dic3—21no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—42no—
578C3×Dic3—61no—
579C3×Dic3—61no—
580C3×Dic3—121no—
581C3×Dic3C2×#6712yes—
582C3×Dic3C2×C3×D412yes—
5832−1+4—91no—
584H(5,𝔽2)—31no—
585#137—31no—
586#137—92no—
587AGL(1,ℤ/8)—91no—
588AGL(1,ℤ/8)—92no—
589#135—92no—
590#135—91no—
591C2×SD16—92no—
592C2×SD16—91no—
593#131—91no—
594C33#57711yescharacteristic, complemented, Sylow
595C23×C3—62no—
596C23×C3—62no—
597C23×C3—64no—
598C23×C3—62no—
599C23×C3—61no—
600C23×C3—61no—
601C22×D3—21no—
602C22×D3—22no—
603C3×Q8—21no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—31no—
607C3×Q8—31no—
608C3×Q8—32no—
609C3×Q8—32no—
610C3×Q8—41no—
611C3×Q8—61no—
612C3×Q8—62no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×Q8—91no—
616C3×Q8—121no—
617C3×Q8—182no—
618C3×Q8C2×D3211yescharacteristic
619C3×Q8C22×C3×D311yescharacteristic
620C3×Q8C22×C3×D311yescharacteristic
621C3×D4—22no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—32no—
629C3×D4—32no—
630C3×D4—32no—
631C3×D4—32no—
632C3×D4—31no—
633C3×D4—31no—
634C3×D4—41no—
635C3×D4—41no—
636C3×D4—42no—
637C3×D4—41no—
638C3×D4—62no—
639C3×D4—61no—
640C3×D4—62no—
641C3×D4—62no—
642C3×D4—62no—
643C3×D4—64no—
644C3×D4—62no—
645C3×D4—62no—
646C3×D4—62no—
647C3×D4—64no—
648C3×D4—61no—
649C3×D4—61no—
650C3×D4—91no—
651C3×D4—182no—
652C3×D4—181no—
653C3×D4C2×D3211yescharacteristic
654C3×D4C22×C3×D311yescharacteristic
655C3×D4C22×C3×D311yescharacteristic
656C2×C3×C4—22no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—42no—
668C2×C3×C4—41no—
669C2×C3×C4—62no—
670C2×C3×C4—62no—
671C2×C3×C4—62no—
672C2×C3×C4—64no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—121no—
676C2×C3×C4—182no—
677C2×C3×C4—182no—
678C2×C3×C4—181no—
679C2×C3×C4C2×D3211yescharacteristic
680C2×C3×C4C22×C3×D311yescharacteristic
681C2×C3×C4C22×C3×D311yescharacteristic
682#67—22no—
683#67—62no—
684#67—61no—
685#67—61no—
686#67—121no—
687#67C3×#6712yes—
688C2×Dic3—21no—
689C2×Dic3—62no—
690D12—22no—
691D12—21no—
692D12—31no—
693D12—31no—
694D12—61no—
695D12—62no—
696D12C3×#6711yescharacteristic
697D12C22×C3×D312yes—
698C4×D3—22no—
699C4×D3—62no—
700C4×D3—62no—
701C4×D3—61no—
702C4×D3—61no—
703C4×D3—62no—
704C4×D3—121no—
705C4×D3C22×C3×D312yes—
706Dic6—21no—
707Dic6—31no—
708Dic6—31no—
709Dic6—61no—
710Dic6—62no—
711Dic6—62no—
712Dic6C3×#6711yescharacteristic
713Dic6C22×C3×D312yes—
714C3×C8—32no—
715C3×C8—32no—
716C3×C8—62no—
717C3×C8—91no—
718C3×C8—91no—
719C3⋊C8—31no—
720C3⋊C8—31no—
721C3⋊C8—31no—
722C3⋊C8—31no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8C22×C3×D312yes—
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—21no—
732C2×C32—41no—
733C2×C32—41no—
734C2×C32—41no—
735C2×C32—41no—
736C2×C32—41no—
737C2×C32—42no—
738C2×C32—41no—
739C2×C32—41no—
740C2×C32—62no—
741C2×C32—81no—
742C2×C32—81no—
743C2×C32—81no—
744C2×C32—82no—
745C2×C32—122no—
746C2×C32C2×D3×D411yescharacteristic
747C2×C32C22×#6711yescharacteristic
748C2×C32C22×C3×D411yescharacteristic
749C3⋊D3—41no—
750C3×D3—22no—
751C3×D3—22no—
752C3×D3—42no—
753C3×D3—44no—
754C3×D3—42no—
755C3×D3—42no—
756C3×D3—121no—
757C3×D3—121no—
758C3×D3—241no—
759#41—31no—
760#41—32no—
761#41—61no—
762#41—92no—
763#41—91no—
764#41—182no—
765#41—181no—
766#41C3×D3211yescharacteristic
767C2×Q8—31no—
768C2×Q8—92no—
769C2×Q8—181no—
770C2×D4—32no—
771C2×D4—31no—
772C2×D4—61no—
773C2×D4—62no—
774Q16—32no—
775Q16—91no—
776SD16—32no—
777SD16—92no—
778SD16—92no—
779SD16—92no—
780SD16—91no—
781SD16—91no—
782D8—92no—
783D8—91no—
784M16—31no—
785M16—92no—
786C2×C8—92no—
787C2×C8—91no—
788C22×C3—22no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—32no—
796C22×C3—32no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—42no—
800C22×C3—41no—
801C22×C3—62no—
802C22×C3—64no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—181no—
806C22×C3—241no—
807C22×C3—241no—
808C22×C3—242no—
809C22×C3—242no—
810C22×C3—242no—
811C22×C3—244no—
812C22×C3D3×#6711yescharacteristic
813C22×C3C3×D3×D411yescharacteristic
814C22×C3C2×C3×#6711yescharacteristic
815C2×D3—22no—
816C2×D3—61no—
817C2×D3—61no—
818C2×D3—82no—
819C2×D3—81no—
820C2×D3—121no—
821C2×D3C2×C3×#6712yes—
822C3×C4—22no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—32no—
833C3×C4—32no—
834C3×C4—41no—
835C3×C4—41no—
836C3×C4—42no—
837C3×C4—41no—
838C3×C4—41no—
839C3×C4—62no—
840C3×C4—62no—
841C3×C4—62no—
842C3×C4—122no—
843C3×C4—181no—
844C3×C4D3×#6711yescharacteristic
845C3×C4C3×D3×D411yescharacteristic
846C3×C4C2×C3×#6711yescharacteristic
847C3×C4C22×D3211yescharacteristic
848C3×C4C23×C3×D311yescharacteristic
849C3×C4C23×C3×D311yescharacteristic
850Dic3—22no—
851Dic3—61no—
852Dic3—61no—
853Dic3—121no—
854Dic3C2×C3×#6712yes—
855C32—21no—
856C32—21no—
857C32—21no—
858C32—41no—
859C32#577811yescharacteristic, complemented
860C32#583611yescharacteristic, complemented
861C32C3×#57711yescharacteristic, complemented
862C23—62no—
863C23—61no—
864Q8—31no—
865Q8—32no—
866Q8—61no—
867Q8—91no—
868Q8—182no—
869Q8C2×C3×D3211yescharacteristic
870D4—21no—
871D4—32no—
872D4—32no—
873D4—31no—
874D4—62no—
875D4—62no—
876D4—61no—
877D4—91no—
878D4—182no—
879D4—181no—
880D4C2×C3×D3211yescharacteristic
881C2×C4—21no—
882C2×C4—32no—
883C2×C4—62no—
884C2×C4—61no—
885C2×C4—182no—
886C2×C4—182no—
887C2×C4—181no—
888C2×C4C2×C3×D3211yescharacteristic
889C8—32no—
890C8—91no—
891C8—91no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—41no—
899C2×C3—41no—
900C2×C3—41no—
901C2×C3—42no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—62no—
907C2×C3—62no—
908C2×C3—81no—
909C2×C3—81no—
910C2×C3—81no—
911C2×C3—82no—
912C2×C3—122no—
913C2×C3—124no—
914C2×C3—122no—
915C2×C3—122no—
916C2×C3—361no—
917C2×C3C2×D3×#6711yescharacteristic
918C2×C3C2×C3×D3×D411yescharacteristic
919C2×C3C22×C3×#6711yescharacteristic
920D3—22no—
921D3—42no—
922D3—121no—
923D3—121no—
924D3—241no—
925C22—21no—
926C22—32no—
927C22—62no—
928C22—181no—
929C22—241no—
930C22—242no—
931C22C3×D3×#6711yescharacteristic
932C4—21no—
933C4—32no—
934C4—62no—
935C4—181no—
936C4C3×D3×#6711yescharacteristic
937C4C22×C3×D3211yescharacteristic
938C3—21no—
939C3—21no—
940C3—21no—
941C3—41no—
942C3#1059546411yescharacteristic, direct product factor
943C3C3×#577811yescharacteristic, complemented
944C3C3×#583611yescharacteristic, complemented
945C2—21no—
946C2—41no—
947C2—62no—
948C2—122no—
949C2—361no—
950C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC2×C3C2×D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#577
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. C32×#1009C2semidirect
2. C3×#64297C2semidirect
3. C3×#64159C2semidirect
4. C32×#951C2semidirect
5. C3×#63949C2semidirect
6. C3×#63943C2semidirect
7. C3×#63934C2semidirect
8. C3×D3×#214C2semidirect
9. C3×#63830C2semidirect
10. C2×C3×#3715C2semidirect
11. C3×#63815C2semidirect
14. #10595464C3direct (N × H)
16. C3×#3828C22semidirect
24. C2×C32×Dic6C22semidirect
26. C3×#3799C22semidirect
29. C3×D3×Dic6C22semidirect
30. C3×#3756C22semidirect
31. C3×#3755C22semidirect
32. C3×#3754C22semidirect
33. C3×#3753C22semidirect
34. C2×C3×C3⋊(C3⋊C8)C22semidirect
35. C32×#216C22semidirect
36. C32×#214C22semidirect
37. C32×#208C22semidirect
38. C3×#3716C22semidirect
39. C3×#3715C22semidirect
40. C3×#3715C22semidirect
41. C3×#3714C22semidirect
42. C3×#3711C22semidirect
43. C3×D3×C3⋊C8C22semidirect
47. C3×#1009D3semidirect
48. C3×#1009C2×C3semidirect
50. #64297C2×C3semidirect
52. #64159C2×C3semidirect
55. C3×#951D3semidirect
56. C3×#951C2×C3semidirect
73. #63949C2×C3semidirect
74. #63943C2×C3semidirect
75. #63934C2×C3semidirect
76. D3×#214C2×C3semidirect
77. #63830C2×C3semidirect
78. C2×#3715C2×C3semidirect
79. #63815C2×C3semidirect
128. #3828C22×C3semidirect
164. C2×C3×Dic6C2×D3semidirect
165. C2×C3×Dic6C22×C3semidirect
167. #3799C22×C3semidirect
170. D3×Dic6C22×C3semidirect
174. #3756C22×C3semidirect
175. #3755C22×C3semidirect
176. #3754C22×C3semidirect
177. #3753C22×C3semidirect
178. C2×C3⋊(C3⋊C8)C22×C3semidirect
183. C3×#216C2×D3semidirect
184. C3×#216C22×C3semidirect
197. C3×#214C2×D3semidirect
198. C3×#214C22×C3semidirect
205. C3×#208C2×D3semidirect
206. C3×#208C22×C3semidirect
215. #3716C22×C3semidirect
216. #3715C22×C3semidirect
217. #3715C22×C3semidirect
218. #3714C22×C3semidirect
219. #3711C22×C3semidirect
220. D3×C3⋊C8C22×C3semidirect
239. #1009C3×D3semidirect
253. #951C3×D3semidirect
465. C2×Dic6C2×C3×D3semidirect
489. #216C2×C3×D3semidirect
501. #214C2×C3×D3semidirect
507. #208C2×C3×D3semidirect
594. C33#577semidirect
859. C32#5778semidirect
860. C32#5836semidirect
861. C32C3×#577semidirect
942. C3#10595464direct (N × H)
943. C3C3×#5778semidirect
944. C3C3×#5836semidirect

Maximal subgroups

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

subgroupindex
C32×#10092
C3×#642972
C3×#641592
C32×#9512
C3×#639492
C3×#639432
C3×#639342
C3×D3×#2142
C3×#638302
C2×C3×#37152
C3×#638152
C3×#58363
C3×#57783
#105954643