Finite Group Databasebeta

← C3×#10595462 #13175059

Subgroups — C3×#10595462 #13175059

Order 1728.

1348 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64367C211yesmaximal, characteristic, complemented
2C3×#64307C211yesmaximal, characteristic, complemented
3C32×#950C211yesmaximal, characteristic, complemented
4C32×#949C211yesmaximal, characteristic, complemented
5C3×#63951C212yesmaximal, complemented
6C3×#63940C212yesmaximal, complemented
7C3×#63936C212yesmaximal, complemented
8C3×#63927C212yesmaximal, complemented
9C3×#63831C211yesmaximal, characteristic, complemented
10C2×C3×#3716C211yesmaximal, characteristic, complemented
11C3×#63817C211yesmaximal, characteristic, complemented
12C3×#5775—31nomaximal
13C3×#5770—31nomaximal
14#10595462C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic, complemented
16C3×Q8×C3⋊D3C2212yescomplemented
17C3×#3830—22no—
18C3×#3830C2212yescomplemented
19C3×#3828—21no—
20C3×#3828C2211yescharacteristic
21C2×C3×#634—21no—
22C2×C3×#634C2211yescharacteristic, complemented
23C32×#235C2211yescharacteristic
24C2×C32×D12C2211yescharacteristic
25C3×D3×#67—22no—
26C3×#3802C2212yes—
27C3×D3×D12—21no—
28C3×#3796C2212yes—
29C3×#3795—21no—
30C32×#216C2211yescharacteristic, complemented
31C32×#215C2211yescharacteristic, complemented
32C32×#215C2212yescomplemented
33C32×#214C2211yescharacteristic, complemented
34C32×#213C2212yescomplemented
35C32×#213C2211yescharacteristic, complemented
36C32×#208C2211yescharacteristic, complemented
37C2×C32×C3⋊C8C2211yescharacteristic, complemented
38C3×#3719C2212yescomplemented
39C3×#3716C2212yescomplemented
40C3×#3716C2212yescomplemented
41C3×#3716C2212yescomplemented
42C3×#3712C2212yescomplemented
43C3×#3710C2212yescomplemented
44#64367C2×C311yescharacteristic, complemented
45C3×#1010—31no—
46C3×#1010—31no—
47C3×#1010—61no—
48C3×#1009—31no—
49C3×#1004—31no—
50#64307C2×C311yescharacteristic, complemented
51C32×AGL(1,ℤ/8)—31no—
52C32×#135—31no—
53C3×#951—31no—
54C3×#950—21no—
55C3×#950D311yescharacteristic, complemented
56C3×#950C2×C311yescharacteristic, complemented
57C3×#949—21no—
58C3×#949D311yescharacteristic, complemented
59C3×#949C2×C311yescharacteristic, complemented
60C2×C3×#214—31no—
61C3×#918—32no—
62C3×#916—32no—
63C3×#915—32no—
64C3×D3×SD16—32no—
65C3×D3×SD16—32no—
66C3×#912—32no—
67C3×#911—32no—
68C3×#911—32no—
69C3×#909—31no—
70C3×#907—31no—
71C2×C3×#204—31no—
72C3×#901—31no—
73#63951C2×C312yescomplemented
74#63940C2×C312yescomplemented
75#63936C2×C312yescomplemented
76#63927C2×C312yescomplemented
77#63831C2×C311yescharacteristic, complemented
78C2×#3716C2×C311yescharacteristic, complemented
79#63817C2×C311yescharacteristic, complemented
80C22×C32×D3—21no—
81C2×C3×D32—22no—
82C33×Q8C2311yescharacteristic
83C33×D4—21no—
84C33×D4C2311yescharacteristic
85C2×C33×C4—21no—
86C2×C33×C4C2311yescharacteristic
87C3×#638—22no—
88C3×#638D412yes—
89C2×C3×C3⋊Dic3—21no—
90C2×C3×C3⋊Dic3—22no—
91C3×C4⋊(C3⋊D3)D411yescharacteristic
92C3×C4×C3⋊D3—22no—
93C3×C4×C3⋊D3C2312yes—
94C3×#634—21no—
95C3×#634—22no—
96C3×#634D411yescharacteristic
97C3×#634C2312yes—
98C32×#67—21no—
99C32×D12—21no—
100C32×D12C2312yes—
101C32×D12C2311yescharacteristic
102C32×C4×D3—21no—
103C32×Dic6C2311yescharacteristic
104C3×#626—22no—
105C3×#625—22no—
106C3×D3×Dic3—22no—
107C32×C3⋊C8C2311yescharacteristic
108C32×C3⋊C8C2312yes—
109C32×C3⋊C8C2311yescharacteristic
110C3×#577—91no—
111#5775—31no—
112#5770—31no—
113C32×#41—21no—
114C32×#41—21no—
115C32×#41—21no—
116C32×#41—31no—
117C32×#41—41no—
118C32×#41C2×D311yescharacteristic, complemented
119C32×#41C2×D311yescharacteristic, complemented
120C32×#41C22×C311yescharacteristic, complemented
121C2×C32×D4—31no—
122Q8×C3⋊D3C22×C312yescomplemented
123#3830—22no—
124#3830C22×C312yescomplemented
125#3828—21no—
126#3828C22×C311yescharacteristic
127C2×#634—21no—
128C2×#634C22×C311yescharacteristic, complemented
129C2×C3×#67—62no—
130C3×#239—32no—
131C3×D3×Q8—32no—
132C3×D3×Q8—32no—
133C3×D3×Q8—62no—
134C3×#237—32no—
135C3×#237—32no—
136C3×#237—32no—
137C3×#237—61no—
138C3×#237—62no—
139C3×#237—62no—
140C3×#237—62no—
141C3×#237—64no—
142C3×D3×D4—32no—
143C3×D3×D4—32no—
144C3×D3×D4—61no—
145C3×D3×D4—62no—
146C3×#235—21no—
147C3×#235—31no—
148C3×#235—31no—
149C3×#235—61no—
150C3×#235—61no—
151C3×#235—61no—
152C3×#235—61no—
153C3×#235—62no—
154C3×#235C2×D311yescharacteristic
155C3×#235C22×C311yescharacteristic
156C2×C3×D12—21no—
157C2×C3×D12—61no—
158C2×C3×D12C2×D311yescharacteristic
159C2×C3×D12C22×C311yescharacteristic
160C2×C3×Dic6—31no—
161C2×C3×Dic6—31no—
162C2×C3×Dic6—61no—
163C2×C3×Dic6—61no—
164C2×C3×Dic6—61no—
165C2×C3×Dic6—62no—
166D3×#67—22no—
167#3802C22×C312yes—
168D3×D12—21no—
169#3796C22×C312yes—
170#3795—21no—
171C32×Q16—31no—
172C32×SD16—31no—
173C32×SD16—32no—
174C32×SD16—31no—
175C32×D8—31no—
176C32×D8—32no—
177C32×M16—31no—
178C2×C32×C8—31no—
179C3×#216—21no—
180C3×#216—32no—
181C3×#216C2×D311yescharacteristic, complemented
182C3×#216C22×C311yescharacteristic, complemented
183C3×#215—22no—
184C3×#215—21no—
185C3×#215C2×D311yescharacteristic, complemented
186C3×#215C2×D312yescomplemented
187C3×#215C22×C312yescomplemented
188C3×#215C22×C311yescharacteristic, complemented
189C3×#214—21no—
190C3×#214—32no—
191C3×#214—32no—
192C3×#214—32no—
193C3×#214C2×D311yescharacteristic, complemented
194C3×#214C22×C311yescharacteristic, complemented
195C3×#213—22no—
196C3×#213—21no—
197C3×#213C2×D311yescharacteristic, complemented
198C3×#213C2×D312yescomplemented
199C3×#213C22×C312yescomplemented
200C3×#213C22×C311yescharacteristic, complemented
201C3×#208—21no—
202C3×#208C2×D311yescharacteristic, complemented
203C3×#208C22×C311yescharacteristic, complemented
204C2×C3×C3⋊C8—21no—
205C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
206C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
207C3×Dic12—32no—
208C3×#204—32no—
209C3×#204—32no—
210C3×#204—32no—
211C3×ΓL(1,𝔽25)—32no—
212C3×ΓL(1,𝔽25)—32no—
213C3×D3×C8—32no—
214C3×D3×C8—32no—
215#3719C22×C312yescomplemented
216#3716C22×C312yescomplemented
217#3716C22×C312yescomplemented
218#3716C22×C312yescomplemented
219#3712C22×C312yescomplemented
220#3710C22×C312yescomplemented
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3C2×D412yes—
224C2×C32×D3—22no—
225C2×C32×D3—21no—
226C2×C32×D3—81no—
227C3×D32—82no—
228C33×C4—21no—
229C33×C4C2×D411yescharacteristic
230C33×C4C2411yescharacteristic
231C3×C3⋊Dic3—22no—
232C3×C3⋊Dic3C2×D412yes—
233C32×Dic3—21no—
234C3×2−1+4—91no—
235C3×H(5,𝔽2)—91no—
236#1010—31no—
237#1010—31no—
238#1010—61no—
239#1009—31no—
240#1004—31no—
241C3×#137—91no—
242C3×#137—92no—
243C3×AGL(1,ℤ/8)—31no—
244C3×AGL(1,ℤ/8)—31no—
245C3×AGL(1,ℤ/8)—61no—
246C3×AGL(1,ℤ/8)—92no—
247C3×#135—31no—
248C3×#135—31no—
249C3×#135—61no—
250C3×#135—92no—
251C2×C3×SD16—91no—
252C2×C3×SD16—92no—
253C3×#131—91no—
254#951—31no—
255#950C3×D311yescharacteristic, complemented
256#949C3×D311yescharacteristic, complemented
257C2×#214—31no—
258#918—32no—
259#916—32no—
260#915—32no—
261D3×SD16—32no—
262D3×SD16—32no—
263#912—32no—
264#911—32no—
265#911—32no—
266#909—31no—
267#907—31no—
268C2×#204—31no—
269#901—31no—
270C23×C32—61no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—41no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C2×D32—22no—
277C32×Q8—21no—
278C32×Q8—21no—
279C32×Q8—21no—
280C32×Q8—31no—
281C32×Q8—41no—
282C32×Q8C22×D311yescharacteristic
283C32×Q8C22×D311yescharacteristic
284C32×Q8C23×C311yescharacteristic
285C32×D4—21no—
286C32×D4—22no—
287C32×D4—21no—
288C32×D4—21no—
289C32×D4—21no—
290C32×D4—21no—
291C32×D4—21no—
292C32×D4—31no—
293C32×D4—32no—
294C32×D4—41no—
295C32×D4—41no—
296C32×D4—41no—
297C32×D4—42no—
298C32×D4—61no—
299C32×D4—61no—
300C32×D4C22×D311yescharacteristic
301C32×D4C22×D311yescharacteristic
302C32×D4C23×C311yescharacteristic
303C2×C32×C4—21no—
304C2×C32×C4—22no—
305C2×C32×C4—21no—
306C2×C32×C4—21no—
307C2×C32×C4—21no—
308C2×C32×C4—21no—
309C2×C32×C4—21no—
310C2×C32×C4—41no—
311C2×C32×C4—41no—
312C2×C32×C4—41no—
313C2×C32×C4—42no—
314C2×C32×C4—61no—
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C23×C311yescharacteristic
318#638—22no—
319#638C3×D412yes—
320C2×C3⋊Dic3—21no—
321C2×C3⋊Dic3—22no—
322C4⋊(C3⋊D3)C3×D411yescharacteristic
323C4×C3⋊D3—22no—
324C4×C3⋊D3C23×C312yes—
325#634—21no—
326#634—22no—
327#634C3×D411yescharacteristic
328#634C23×C312yes—
329C3×#67—21no—
330C3×#67—21no—
331C3×#67—32no—
332C3×#67—32no—
333C3×#67—41no—
334C3×#67—62no—
335C3×#67—62no—
336C3×#67—62no—
337C3×#67—62no—
338C3×#67—62no—
339C3×#67—62no—
340C3×#67—64no—
341C2×C3×Dic3—62no—
342C2×C3×Dic3—62no—
343C2×C3×Dic3—62no—
344C2×C3×Dic3—64no—
345C2×C3×Dic3—62no—
346C2×C3×Dic3—61no—
347C2×C3×Dic3—61no—
348C3×D12—21no—
349C3×D12—21no—
350C3×D12—22no—
351C3×D12—21no—
352C3×D12—31no—
353C3×D12—31no—
354C3×D12—41no—
355C3×D12—61no—
356C3×D12—62no—
357C3×D12C22×D312yes—
358C3×D12C22×D311yescharacteristic
359C3×D12C23×C312yes—
360C3×D12C23×C311yescharacteristic
361C3×C4×D3—21no—
362C3×C4×D3—21no—
363C3×C4×D3—32no—
364C3×C4×D3—32no—
365C3×C4×D3—41no—
366C3×C4×D3—62no—
367C3×C4×D3—62no—
368C3×C4×D3—62no—
369C3×C4×D3—62no—
370C3×C4×D3—64no—
371C3×Dic6—21no—
372C3×Dic6—31no—
373C3×Dic6—31no—
374C3×Dic6—32no—
375C3×Dic6—32no—
376C3×Dic6—61no—
377C3×Dic6—62no—
378C3×Dic6—62no—
379C3×Dic6—62no—
380C3×Dic6—62no—
381C3×Dic6—64no—
382C3×Dic6—61no—
383C3×Dic6—61no—
384C3×Dic6C22×D311yescharacteristic
385C3×Dic6C23×C311yescharacteristic
386#626—22no—
387#625—22no—
388D3×Dic3—22no—
389C32×C8—31no—
390C32×C8—32no—
391C32×C8—31no—
392C3×C3⋊C8—21no—
393C3×C3⋊C8—21no—
394C3×C3⋊C8—22no—
395C3×C3⋊C8C22×D311yescharacteristic
396C3×C3⋊C8C22×D312yes—
397C3×C3⋊C8C22×D311yescharacteristic
398C3×C3⋊C8C23×C311yescharacteristic
399C3×C3⋊C8C23×C312yes—
400C3×C3⋊C8C23×C311yescharacteristic
401#577—91noSylow
402C2×C33—21no—
403C2×C33—41no—
404C2×C33C22×D411yescharacteristic
405C3×C3⋊D3—22no—
406C32×D3—41no—
407C32×D3—42no—
408C3×#41—21no—
409C3×#41—21no—
410C3×#41—21no—
411C3×#41—31no—
412C3×#41—31no—
413C3×#41—41no—
414C3×#41—61no—
415C3×#41—91no—
416C3×#41—92no—
417C3×#41—92no—
418C3×#41—181no—
419C3×#41—181no—
420C3×#41—182no—
421C3×#41D3211yescharacteristic, complemented
422C3×#41C2×C3×D311yescharacteristic, complemented
423C3×#41C2×C3×D311yescharacteristic, complemented
424C2×C3×Q8—92no—
425C2×C3×Q8—91no—
426C2×C3×Q8—181no—
427C2×C3×D4—31no—
428C2×C3×D4—31no—
429C2×C3×D4—61no—
430C2×C3×D4—92no—
431C2×C3×D4—181no—
432C2×C3×D4—182no—
433C2×#67—62no—
434#239—32no—
435D3×Q8—32no—
436D3×Q8—32no—
437D3×Q8—62no—
438#237—32no—
439#237—32no—
440#237—32no—
441#237—62no—
442#237—61no—
443#237—62no—
444#237—62no—
445#237—64no—
446D3×D4—32no—
447D3×D4—32no—
448D3×D4—61no—
449D3×D4—62no—
450#235—31no—
451#235—31no—
452#235—61no—
453#235—61no—
454#235—61no—
455#235—61no—
456#235—62no—
457#235C2×C3×D311yescharacteristic
458C2×D12—61no—
459C2×D12C2×C3×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—61no—
463C2×Dic6—61no—
464C2×Dic6—61no—
465C2×Dic6—62no—
466C3×Q16—31no—
467C3×Q16—31no—
468C3×Q16—61no—
469C3×Q16—92no—
470C3×SD16—31no—
471C3×SD16—32no—
472C3×SD16—31no—
473C3×SD16—32no—
474C3×SD16—31no—
475C3×SD16—31no—
476C3×SD16—61no—
477C3×SD16—61no—
478C3×SD16—62no—
479C3×SD16—92no—
480C3×SD16—92no—
481C3×SD16—92no—
482C3×D8—31no—
483C3×D8—32no—
484C3×D8—31no—
485C3×D8—32no—
486C3×D8—61no—
487C3×D8—62no—
488C3×M16—31no—
489C3×M16—31no—
490C3×M16—61no—
491C3×M16—92no—
492C2×C3×C8—31no—
493C2×C3×C8—31no—
494C2×C3×C8—61no—
495C2×C3×C8—92no—
496#216—32no—
497#216C2×C3×D311yescharacteristic, complemented
498#215C2×C3×D311yescharacteristic, complemented
499#215C2×C3×D312yescomplemented
500#214—32no—
501#214—32no—
502#214—32no—
503#214C2×C3×D311yescharacteristic, complemented
504#213C2×C3×D311yescharacteristic, complemented
505#213C2×C3×D312yescomplemented
506#208C2×C3×D311yescharacteristic, complemented
507C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
508Dic12—32no—
509#204—32no—
510#204—32no—
511#204—32no—
512ΓL(1,𝔽25)—32no—
513ΓL(1,𝔽25)—32no—
514D3×C8—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—41no—
524C22×C32—41no—
525C22×C32—41no—
526C22×C32—42no—
527C22×C32—62no—
528C22×C32—61no—
529C22×C32—241no—
530C22×C32D3×D411yescharacteristic
531C22×C32D3×D411yescharacteristic
532C22×C32C2×C3×D411yescharacteristic
533C2×C3⋊D3C2×C3×D412yes—
534C2×C3×D3—21no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—21no—
538C2×C3×D3—32no—
539C2×C3×D3—32no—
540C2×C3×D3—41no—
541C2×C3×D3—42no—
542C2×C3×D3—62no—
543C2×C3×D3—81no—
544C2×C3×D3—81no—
545C2×C3×D3—82no—
546C2×C3×D3—242no—
547C2×C3×D3—242no—
548D32—82no—
549C32×C4—21no—
550C32×C4—22no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—21no—
559C32×C4—41no—
560C32×C4—41no—
561C32×C4—41no—
562C32×C4—41no—
563C32×C4—42no—
564C32×C4—61no—
565C32×C4D3×D411yescharacteristic
566C32×C4D3×D411yescharacteristic
567C32×C4C2×C3×D411yescharacteristic
568C32×C4C23×D311yescharacteristic
569C32×C4C23×D311yescharacteristic
570C32×C4C24×C311yescharacteristic
571C3⋊Dic3—22no—
572C3⋊Dic3C2×C3×D412yes—
573C3×Dic3—21no—
574C3×Dic3—21no—
575C3×Dic3—32no—
576C3×Dic3—32no—
577C3×Dic3—41no—
578C3×Dic3—62no—
579C3×Dic3—64no—
580C3×Dic3—62no—
581C3×Dic3—62no—
5822−1+4—91no—
583H(5,𝔽2)—91no—
584#137—91no—
585#137—92no—
586AGL(1,ℤ/8)—31no—
587AGL(1,ℤ/8)—92no—
588#135—31no—
589#135—92no—
590C2×SD16—91no—
591C2×SD16—92no—
592#131—91no—
593C33#57711yescharacteristic, complemented, Sylow
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—121no—
597C23×C3—182no—
598C22×D3—21no—
599C22×D3—62no—
600C22×D3—62no—
601C3×Q8—21no—
602C3×Q8—21no—
603C3×Q8—21no—
604C3×Q8—31no—
605C3×Q8—31no—
606C3×Q8—41no—
607C3×Q8—61no—
608C3×Q8—91no—
609C3×Q8—92no—
610C3×Q8—182no—
611C3×Q8—181no—
612C3×Q8C2×D3211yescharacteristic
613C3×Q8C22×C3×D311yescharacteristic
614C3×Q8C22×C3×D311yescharacteristic
615C3×D4—22no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—32no—
623C3×D4—31no—
624C3×D4—31no—
625C3×D4—32no—
626C3×D4—41no—
627C3×D4—41no—
628C3×D4—42no—
629C3×D4—41no—
630C3×D4—62no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—92no—
637C3×D4—91no—
638C3×D4—121no—
639C3×D4—121no—
640C3×D4—182no—
641C3×D4—182no—
642C3×D4—182no—
643C3×D4C2×D3211yescharacteristic
644C3×D4C22×C3×D311yescharacteristic
645C3×D4C22×C3×D311yescharacteristic
646C2×C3×C4—22no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—42no—
656C2×C3×C4—41no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—92no—
660C2×C3×C4—121no—
661C2×C3×C4—182no—
662C2×C3×C4—182no—
663C2×C3×C4—182no—
664C2×C3×C4—181no—
665C2×C3×C4C2×D3211yescharacteristic
666C2×C3×C4C22×C3×D311yescharacteristic
667C2×C3×C4C22×C3×D311yescharacteristic
668#67—21no—
669#67—32no—
670#67—32no—
671#67—62no—
672#67—62no—
673#67—62no—
674#67—62no—
675#67—62no—
676#67—62no—
677#67—64no—
678C2×Dic3—62no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—64no—
682C2×Dic3—62no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685D12—21no—
686D12—31no—
687D12—31no—
688D12—61no—
689D12—62no—
690D12C22×C3×D312yes—
691D12C22×C3×D311yescharacteristic
692C4×D3—21no—
693C4×D3—32no—
694C4×D3—32no—
695C4×D3—62no—
696C4×D3—62no—
697C4×D3—62no—
698C4×D3—62no—
699C4×D3—64no—
700Dic6—31no—
701Dic6—31no—
702Dic6—32no—
703Dic6—32no—
704Dic6—61no—
705Dic6—62no—
706Dic6—62no—
707Dic6—62no—
708Dic6—62no—
709Dic6—64no—
710Dic6—61no—
711Dic6—61no—
712Dic6C22×C3×D311yescharacteristic
713C3×C8—31no—
714C3×C8—31no—
715C3×C8—32no—
716C3×C8—31no—
717C3×C8—32no—
718C3×C8—31no—
719C3×C8—61no—
720C3×C8—61no—
721C3×C8—62no—
722C3⋊C8C22×C3×D311yescharacteristic
723C3⋊C8C22×C3×D312yes—
724C3⋊C8C22×C3×D311yescharacteristic
725C2×C32—21no—
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—41no—
732C2×C32—41no—
733C2×C32—41no—
734C2×C32—41no—
735C2×C32—41no—
736C2×C32—42no—
737C2×C32—41no—
738C2×C32—41no—
739C2×C32—81no—
740C2×C32—81no—
741C2×C32—81no—
742C2×C32—82no—
743C2×C32—122no—
744C2×C32—121no—
745C2×C32C2×D3×D411yescharacteristic
746C2×C32C2×D3×D411yescharacteristic
747C2×C32C22×C3×D411yescharacteristic
748C3⋊D3—22no—
749C3×D3—41no—
750C3×D3—42no—
751C3×D3—41no—
752C3×D3—42no—
753C3×D3—62no—
754C3×D3—62no—
755C3×D3—81no—
756C3×D3—82no—
757C3×D3—122no—
758#41—31no—
759#41—91no—
760#41—92no—
761#41—92no—
762#41—181no—
763#41—181no—
764#41—182no—
765#41C3×D3211yescharacteristic, complemented
766C2×Q8—92no—
767C2×Q8—91no—
768C2×Q8—181no—
769C2×D4—31no—
770C2×D4—92no—
771C2×D4—181no—
772C2×D4—182no—
773Q16—31no—
774Q16—92no—
775SD16—31no—
776SD16—32no—
777SD16—31no—
778SD16—92no—
779SD16—92no—
780SD16—92no—
781D8—31no—
782D8—32no—
783M16—31no—
784M16—92no—
785C2×C8—31no—
786C2×C8—92no—
787C22×C3—22no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—42no—
797C22×C3—41no—
798C22×C3—61no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—61no—
802C22×C3—92no—
803C22×C3—121no—
804C22×C3—122no—
805C22×C3—241no—
806C22×C3—241no—
807C22×C3—242no—
808C22×C3—722no—
809C22×C3#381111yescharacteristic
810C22×C3C3×D3×D411yescharacteristic
811C22×C3C3×D3×D411yescharacteristic
812C2×D3—21no—
813C2×D3—22no—
814C2×D3—32no—
815C2×D3—32no—
816C2×D3—62no—
817C2×D3—81no—
818C2×D3—242no—
819C2×D3—242no—
820C3×C4—22no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—41no—
831C3×C4—41no—
832C3×C4—42no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—92no—
838C3×C4—121no—
839C3×C4—182no—
840C3×C4#381111yescharacteristic
841C3×C4C3×D3×D411yescharacteristic
842C3×C4C3×D3×D411yescharacteristic
843C3×C4C22×D3211yescharacteristic
844C3×C4C23×C3×D311yescharacteristic
845C3×C4C23×C3×D311yescharacteristic
846Dic3—21no—
847Dic3—32no—
848Dic3—32no—
849Dic3—62no—
850Dic3—64no—
851Dic3—62no—
852Dic3—62no—
853C32—21no—
854C32—21no—
855C32—21no—
856C32—41no—
857C32#577011yescharacteristic, complemented
858C32#577511yescharacteristic, complemented
859C32C3×#57711yescharacteristic, complemented
860C23—61no—
861C23—182no—
862Q8—31no—
863Q8—91no—
864Q8—92no—
865Q8—182no—
866Q8—181no—
867Q8C2×C3×D3211yescharacteristic
868D4—21no—
869D4—32no—
870D4—31no—
871D4—61no—
872D4—61no—
873D4—92no—
874D4—91no—
875D4—182no—
876D4—182no—
877D4—182no—
878D4C2×C3×D3211yescharacteristic
879C2×C4—21no—
880C2×C4—61no—
881C2×C4—92no—
882C2×C4—182no—
883C2×C4—182no—
884C2×C4—182no—
885C2×C4—181no—
886C2×C4C2×C3×D3211yescharacteristic
887C8—31no—
888C8—31no—
889C8—32no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—41no—
897C2×C3—41no—
898C2×C3—41no—
899C2×C3—42no—
900C2×C3—41no—
901C2×C3—41no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—81no—
905C2×C3—81no—
906C2×C3—81no—
907C2×C3—82no—
908C2×C3—122no—
909C2×C3—121no—
910C2×C3—122no—
911C2×C3—121no—
912C2×C3—182no—
913C2×C3—242no—
914C2×C3—241no—
915C2×C3C2×#381111yescharacteristic
916C2×C3C2×C3×D3×D411yescharacteristic
917C2×C3C2×C3×D3×D411yescharacteristic
918D3—41no—
919D3—42no—
920D3—62no—
921D3—62no—
922D3—122no—
923C22—21no—
924C22—61no—
925C22—62no—
926C22—92no—
927C22—241no—
928C22—722no—
929C22C3×#381111yescharacteristic
930C4—21no—
931C4—61no—
932C4—92no—
933C4—182no—
934C4C3×#381111yescharacteristic
935C4C22×C3×D3211yescharacteristic
936C3—21no—
937C3—21no—
938C3—21no—
939C3—41no—
940C3#1059546211yescharacteristic, direct product factor
941C3C3×#577011yescharacteristic, complemented
942C3C3×#577511yescharacteristic, complemented
943C2—21no—
944C2—41no—
945C2—122no—
946C2—121no—
947C2—182no—
948C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3C2×#3811
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. C3×#64367C2semidirect
2. C3×#64307C2semidirect
3. C32×#950C2semidirect
4. C32×#949C2semidirect
5. C3×#63951C2semidirect
6. C3×#63940C2semidirect
7. C3×#63936C2semidirect
8. C3×#63927C2semidirect
9. C3×#63831C2semidirect
10. C2×C3×#3716C2semidirect
11. C3×#63817C2semidirect
14. #10595462C3direct (N × H)
15. C33×#41C22semidirect
16. C3×Q8×C3⋊D3C22semidirect
18. C3×#3830C22semidirect
22. C2×C3×#634C22semidirect
30. C32×#216C22semidirect
31. C32×#215C22semidirect
32. C32×#215C22semidirect
33. C32×#214C22semidirect
34. C32×#213C22semidirect
35. C32×#213C22semidirect
36. C32×#208C22semidirect
37. C2×C32×C3⋊C8C22semidirect
38. C3×#3719C22semidirect
39. C3×#3716C22semidirect
40. C3×#3716C22semidirect
41. C3×#3716C22semidirect
42. C3×#3712C22semidirect
43. C3×#3710C22semidirect
44. #64367C2×C3semidirect
50. #64307C2×C3semidirect
55. C3×#950D3semidirect
56. C3×#950C2×C3semidirect
58. C3×#949D3semidirect
59. C3×#949C2×C3semidirect
73. #63951C2×C3semidirect
74. #63940C2×C3semidirect
75. #63936C2×C3semidirect
76. #63927C2×C3semidirect
77. #63831C2×C3semidirect
78. C2×#3716C2×C3semidirect
79. #63817C2×C3semidirect
118. C32×#41C2×D3semidirect
119. C32×#41C2×D3semidirect
120. C32×#41C22×C3semidirect
122. Q8×C3⋊D3C22×C3semidirect
124. #3830C22×C3semidirect
128. C2×#634C22×C3semidirect
181. C3×#216C2×D3semidirect
182. C3×#216C22×C3semidirect
185. C3×#215C2×D3semidirect
186. C3×#215C2×D3semidirect
187. C3×#215C22×C3semidirect
188. C3×#215C22×C3semidirect
193. C3×#214C2×D3semidirect
194. C3×#214C22×C3semidirect
197. C3×#213C2×D3semidirect
198. C3×#213C2×D3semidirect
199. C3×#213C22×C3semidirect
200. C3×#213C22×C3semidirect
202. C3×#208C2×D3semidirect
203. C3×#208C22×C3semidirect
205. C2×C3×C3⋊C8C2×D3semidirect
206. C2×C3×C3⋊C8C22×C3semidirect
215. #3719C22×C3semidirect
216. #3716C22×C3semidirect
217. #3716C22×C3semidirect
218. #3716C22×C3semidirect
219. #3712C22×C3semidirect
220. #3710C22×C3semidirect
255. #950C3×D3semidirect
256. #949C3×D3semidirect
421. C3×#41D32semidirect
422. C3×#41C2×C3×D3semidirect
423. C3×#41C2×C3×D3semidirect
497. #216C2×C3×D3semidirect
498. #215C2×C3×D3semidirect
499. #215C2×C3×D3semidirect
503. #214C2×C3×D3semidirect
504. #213C2×C3×D3semidirect
505. #213C2×C3×D3semidirect
506. #208C2×C3×D3semidirect
507. C2×C3⋊C8C2×C3×D3semidirect
593. C33#577semidirect
765. #41C3×D32semidirect
857. C32#5770semidirect
858. C32#5775semidirect
859. C32C3×#577semidirect
940. C3#10595462direct (N × H)
941. C3C3×#5770semidirect
942. C3C3×#5775semidirect

Maximal subgroups

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

subgroupindex
C3×#643672
C3×#643072
C32×#9502
C32×#9492
C3×#639512
C3×#639402
C3×#639362
C3×#639272
C3×#638312
C2×C3×#37162
C3×#638172
C3×#57753
C3×#57703
#105954623