Finite Group Databasebeta

← C3×#10595461 #13175058

Subgroups — C3×#10595461 #13175058

Order 1728.

1408 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64366C211yesmaximal, characteristic, complemented
2C3×#64307C211yesmaximal, characteristic, complemented
3C32×#950C211yesmaximal, characteristic, complemented
4C32×#949C211yesmaximal, characteristic, complemented
5C3×#63950C212yesmaximal, complemented
6C3×#63941C212yesmaximal, complemented
7C3×#63937C212yesmaximal, complemented
8C3×#63926C212yesmaximal, complemented
9C3×#63825C211yesmaximal, characteristic, complemented
10C2×C3×#3714C211yesmaximal, characteristic, complemented
11C3×#63817C211yesmaximal, characteristic, complemented
12C3×#5774—31nomaximal
13C3×#5769—31nomaximal
14#10595461C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic, complemented
16C3×#3832C2212yescomplemented
17C3×D4×C3⋊D3—22no—
18C3×D4×C3⋊D3C2212yescomplemented
19C3×#3828—21no—
20C3×#3828C2211yescharacteristic
21C2×C3×C4⋊(C3⋊D3)—21no—
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C32×#235C2211yescharacteristic, complemented
24C2×C32×D12C2211yescharacteristic, complemented
25C3×D3×#67—22no—
26C3×#3802C2212yescomplemented
27C3×D3×D12—21no—
28C3×#3796C2212yescomplemented
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×#3717C2212yescomplemented
39C3×#3714C2212yescomplemented
40C3×#3714C2212yescomplemented
41C3×#3714C2212yescomplemented
42C3×#3712C2212yescomplemented
43C3×#3710C2212yescomplemented
44#64366C2×C311yescharacteristic, complemented
45C3×#1009—31no—
46C3×#1009—31no—
47C3×#1009—31no—
48C3×#1009—61no—
49C3×#1004—31no—
50#64307C2×C311yescharacteristic, complemented
51C32×AGL(1,ℤ/8)—31no—
52C32×#135—31no—
53C3×#950—21no—
54C3×#950D311yescharacteristic, complemented
55C3×#950C2×C311yescharacteristic, complemented
56C3×#949—21no—
57C3×#949—31no—
58C3×#949D311yescharacteristic, complemented
59C3×#949C2×C311yescharacteristic, complemented
60C2×C3×#213—31no—
61C3×#919—32no—
62C3×#916—32no—
63C3×#914—32no—
64C3×#914—32no—
65C3×#914—32no—
66C3×#911—32no—
67C3×D3×D8—32no—
68C3×D3×D8—32no—
69C3×#908—31no—
70C3×#907—31no—
71C2×C3×D24—31no—
72C3×#901—31no—
73#63950C2×C312yescomplemented
74#63941C2×C312yescomplemented
75#63937C2×C312yescomplemented
76#63926C2×C312yescomplemented
77#63825C2×C311yescharacteristic, complemented
78C2×#3714C2×C311yescharacteristic, complemented
79#63817C2×C311yescharacteristic, complemented
80C22×C3×C3⋊D3—21no—
81C22×C3×C3⋊D3—22no—
82C22×C32×D3—21no—
83C2×C3×D32—22no—
84C33×Q8C2311yescharacteristic
85C33×D4—21no—
86C33×D4C2311yescharacteristic
87C2×C33×C4—21no—
88C2×C33×C4C2311yescharacteristic
89C3×#638—22no—
90C3×#638D412yes—
91C3×C4⋊(C3⋊D3)—22no—
92C3×C4⋊(C3⋊D3)—21no—
93C3×C4⋊(C3⋊D3)D411yescharacteristic
94C3×C4⋊(C3⋊D3)C2312yes—
95C3×C4×C3⋊D3—22no—
96C3×C4×C3⋊D3C2312yes—
97C3×#634D411yescharacteristic
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×#576—91no—
111#5774—31no—
112#5769—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—
122#3832C22×C312yescomplemented
123D4×C3⋊D3—22no—
124D4×C3⋊D3C22×C312yescomplemented
125#3828—21no—
126#3828C22×C311yescharacteristic
127C2×C4⋊(C3⋊D3)—21no—
128C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
129C2×C3×#67—62no—
130C3×#239—32no—
131C3×#239—32no—
132C3×#239—32no—
133C3×#239—62no—
134C3×#237—32no—
135C3×#237—61no—
136C3×D3×D4—32no—
137C3×D3×D4—32no—
138C3×D3×D4—32no—
139C3×D3×D4—32no—
140C3×D3×D4—61no—
141C3×D3×D4—62no—
142C3×D3×D4—62no—
143C3×D3×D4—62no—
144C3×D3×D4—62no—
145C3×D3×D4—64no—
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, complemented
155C3×#235C22×C311yescharacteristic, complemented
156C2×C3×D12—21no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12—61no—
160C2×C3×D12—61no—
161C2×C3×D12—61no—
162C2×C3×D12—61no—
163C2×C3×D12—62no—
164C2×C3×D12C2×D311yescharacteristic, complemented
165C2×C3×D12C22×C311yescharacteristic, complemented
166D3×#67—22no—
167#3802C22×C312yescomplemented
168D3×D12—21no—
169#3796C22×C312yescomplemented
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×#216C2×D311yescharacteristic, complemented
181C3×#216C22×C311yescharacteristic, complemented
182C3×#215—22no—
183C3×#215—21no—
184C3×#215—32no—
185C3×#215C2×D311yescharacteristic, complemented
186C3×#215C2×D312yescomplemented
187C3×#215C22×C312yescomplemented
188C3×#215C22×C311yescharacteristic, complemented
189C3×#214—21no—
190C3×#214C2×D311yescharacteristic, complemented
191C3×#214C22×C311yescharacteristic, complemented
192C3×#213—22no—
193C3×#213—21no—
194C3×#213—32no—
195C3×#213—32no—
196C3×#213—32no—
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×D24—32no—
208C3×D24—32no—
209C3×D24—32no—
210C3×#204—32no—
211C3×ΓL(1,𝔽25)—32no—
212C3×ΓL(1,𝔽25)—32no—
213C3×D3×C8—32no—
214C3×D3×C8—32no—
215#3717C22×C312yescomplemented
216#3714C22×C312yescomplemented
217#3714C22×C312yescomplemented
218#3714C22×C312yescomplemented
219#3712C22×C312yescomplemented
220#3710C22×C312yescomplemented
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3—22no—
224C2×C3×C3⋊D3—82no—
225C2×C3×C3⋊D3—81no—
226C2×C3×C3⋊D3C2×D412yes—
227C2×C32×D3—22no—
228C2×C32×D3—21no—
229C2×C32×D3—81no—
230C3×D32—82no—
231C33×C4—21no—
232C33×C4C2×D411yescharacteristic
233C33×C4C2411yescharacteristic
234C3×C3⋊Dic3C2×D412yes—
235C32×Dic3—21no—
236C3×H(5,𝔽2)—91no—
237C3×H(5,𝔽2)—91no—
238#1009—31no—
239#1009—31no—
240#1009—31no—
241#1009—61no—
242#1004—31no—
243C3×AGL(1,ℤ/8)—31no—
244C3×AGL(1,ℤ/8)—31no—
245C3×AGL(1,ℤ/8)—61no—
246C3×AGL(1,ℤ/8)—91no—
247C3×AGL(1,ℤ/8)—92no—
248C3×AGL(1,ℤ/8)—92no—
249C3×#135—31no—
250C3×#135—31no—
251C3×#135—61no—
252C3×#135—92no—
253C2×C3×D8—91no—
254C2×C3×D8—92no—
255C3×#131—91no—
256#950C3×D311yescharacteristic, complemented
257#949—31no—
258#949C3×D311yescharacteristic, complemented
259C2×#213—31no—
260#919—32no—
261#916—32no—
262#914—32no—
263#914—32no—
264#914—32no—
265#911—32no—
266D3×D8—32no—
267D3×D8—32no—
268#908—31no—
269#907—31no—
270C2×D24—31no—
271#901—31no—
272C23×C32—61no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3—22no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—41no—
278C22×C3×D3—62no—
279C22×C3×D3—62no—
280C22×C3×D3—62no—
281C22×C3×D3—62no—
282C22×C3×D3—64no—
283C22×C3×D3—62no—
284C22×C3×D3—61no—
285C22×C3×D3—61no—
286C2×D32—22no—
287C32×Q8—21no—
288C32×Q8—21no—
289C32×Q8—21no—
290C32×Q8—31no—
291C32×Q8—41no—
292C32×Q8C22×D311yescharacteristic
293C32×Q8C22×D311yescharacteristic
294C32×Q8C23×C311yescharacteristic
295C32×D4—21no—
296C32×D4—22no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4—21no—
300C32×D4—21no—
301C32×D4—21no—
302C32×D4—31no—
303C32×D4—32no—
304C32×D4—41no—
305C32×D4—41no—
306C32×D4—41no—
307C32×D4—42no—
308C32×D4—61no—
309C32×D4—61no—
310C32×D4C22×D311yescharacteristic
311C32×D4C22×D311yescharacteristic
312C32×D4C23×C311yescharacteristic
313C2×C32×C4—21no—
314C2×C32×C4—22no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—21no—
318C2×C32×C4—21no—
319C2×C32×C4—21no—
320C2×C32×C4—41no—
321C2×C32×C4—41no—
322C2×C32×C4—41no—
323C2×C32×C4—42no—
324C2×C32×C4—61no—
325C2×C32×C4C22×D311yescharacteristic
326C2×C32×C4C22×D311yescharacteristic
327C2×C32×C4C23×C311yescharacteristic
328#638—22no—
329#638C3×D412yes—
330C4⋊(C3⋊D3)—22no—
331C4⋊(C3⋊D3)—21no—
332C4⋊(C3⋊D3)C3×D411yescharacteristic
333C4⋊(C3⋊D3)C23×C312yes—
334C4×C3⋊D3—22no—
335C4×C3⋊D3C23×C312yes—
336#634C3×D411yescharacteristic
337C3×#67—21no—
338C3×#67—21no—
339C3×#67—32no—
340C3×#67—32no—
341C3×#67—41no—
342C3×#67—62no—
343C3×#67—62no—
344C3×#67—62no—
345C3×#67—62no—
346C3×#67—62no—
347C3×#67—62no—
348C3×#67—64no—
349C2×C3×Dic3—62no—
350C3×D12—21no—
351C3×D12—21no—
352C3×D12—22no—
353C3×D12—21no—
354C3×D12—31no—
355C3×D12—31no—
356C3×D12—32no—
357C3×D12—32no—
358C3×D12—41no—
359C3×D12—61no—
360C3×D12—62no—
361C3×D12—62no—
362C3×D12—62no—
363C3×D12—62no—
364C3×D12—64no—
365C3×D12—62no—
366C3×D12—61no—
367C3×D12—61no—
368C3×D12C22×D312yes—
369C3×D12C22×D311yescharacteristic
370C3×D12C23×C312yes—
371C3×D12C23×C311yescharacteristic
372C3×C4×D3—21no—
373C3×C4×D3—21no—
374C3×C4×D3—32no—
375C3×C4×D3—32no—
376C3×C4×D3—41no—
377C3×C4×D3—62no—
378C3×C4×D3—62no—
379C3×C4×D3—62no—
380C3×C4×D3—62no—
381C3×C4×D3—64no—
382C3×Dic6—21no—
383C3×Dic6—31no—
384C3×Dic6—31no—
385C3×Dic6—61no—
386C3×Dic6C22×D311yescharacteristic
387C3×Dic6C23×C311yescharacteristic
388#626—22no—
389#625—22no—
390D3×Dic3—22no—
391C32×C8—31no—
392C32×C8—32no—
393C32×C8—31no—
394C3×C3⋊C8—21no—
395C3×C3⋊C8—21no—
396C3×C3⋊C8—22no—
397C3×C3⋊C8C22×D311yescharacteristic
398C3×C3⋊C8C22×D312yes—
399C3×C3⋊C8C22×D311yescharacteristic
400C3×C3⋊C8C23×C311yescharacteristic
401C3×C3⋊C8C23×C312yes—
402C3×C3⋊C8C23×C311yescharacteristic
403#576—91noSylow
404C2×C33—21no—
405C2×C33—41no—
406C2×C33C22×D411yescharacteristic
407C3×C3⋊D3—22no—
408C3×C3⋊D3—42no—
409C32×D3—41no—
410C32×D3—42no—
411C3×#41—21no—
412C3×#41—21no—
413C3×#41—21no—
414C3×#41—31no—
415C3×#41—31no—
416C3×#41—41no—
417C3×#41—61no—
418C3×#41—91no—
419C3×#41—92no—
420C3×#41—92no—
421C3×#41—181no—
422C3×#41—181no—
423C3×#41D3211yescharacteristic, complemented
424C3×#41C2×C3×D311yescharacteristic, complemented
425C3×#41C2×C3×D311yescharacteristic, complemented
426C2×C3×D4—31no—
427C2×C3×D4—31no—
428C2×C3×D4—61no—
429C2×C3×D4—92no—
430C2×C3×D4—92no—
431C2×C3×D4—91no—
432C2×C3×D4—181no—
433C2×C3×D4—181no—
434C2×C3×D4—182no—
435C2×C3×D4—182no—
436C2×#67—62no—
437#239—32no—
438#239—32no—
439#239—32no—
440#239—62no—
441#237—32no—
442#237—61no—
443D3×D4—32no—
444D3×D4—32no—
445D3×D4—32no—
446D3×D4—32no—
447D3×D4—62no—
448D3×D4—61no—
449D3×D4—62no—
450D3×D4—62no—
451D3×D4—62no—
452D3×D4—64no—
453#235—31no—
454#235—31no—
455#235—61no—
456#235—61no—
457#235—61no—
458#235—61no—
459#235—62no—
460#235C2×C3×D311yescharacteristic, complemented
461C2×D12—31no—
462C2×D12—31no—
463C2×D12—61no—
464C2×D12—61no—
465C2×D12—61no—
466C2×D12—61no—
467C2×D12—62no—
468C2×D12C2×C3×D311yescharacteristic, complemented
469C3×Q16—31no—
470C3×Q16—31no—
471C3×Q16—61no—
472C3×SD16—31no—
473C3×SD16—32no—
474C3×SD16—31no—
475C3×SD16—32no—
476C3×SD16—31no—
477C3×SD16—31no—
478C3×SD16—61no—
479C3×SD16—61no—
480C3×SD16—62no—
481C3×SD16—92no—
482C3×D8—31no—
483C3×D8—32no—
484C3×D8—31no—
485C3×D8—32no—
486C3×D8—61no—
487C3×D8—62no—
488C3×D8—92no—
489C3×D8—92no—
490C3×D8—92no—
491C3×M16—31no—
492C3×M16—31no—
493C3×M16—61no—
494C3×M16—92no—
495C2×C3×C8—31no—
496C2×C3×C8—31no—
497C2×C3×C8—61no—
498C2×C3×C8—92no—
499#216C2×C3×D311yescharacteristic, complemented
500#215—32no—
501#215C2×C3×D311yescharacteristic, complemented
502#215C2×C3×D312yescomplemented
503#214C2×C3×D311yescharacteristic, complemented
504#213—32no—
505#213—32no—
506#213—32no—
507#213C2×C3×D311yescharacteristic, complemented
508#213C2×C3×D312yescomplemented
509#208C2×C3×D311yescharacteristic, complemented
510C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
511D24—32no—
512D24—32no—
513D24—32no—
514#204—32no—
515ΓL(1,𝔽25)—32no—
516ΓL(1,𝔽25)—32no—
517D3×C8—32no—
518D3×C8—32no—
519C22×C32—21no—
520C22×C32—22no—
521C22×C32—21no—
522C22×C32—21no—
523C22×C32—21no—
524C22×C32—21no—
525C22×C32—21no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32—41no—
529C22×C32—42no—
530C22×C32—62no—
531C22×C32—61no—
532C22×C32—241no—
533C22×C32D3×D411yescharacteristic
534C22×C32D3×D411yescharacteristic
535C22×C32C2×C3×D411yescharacteristic
536C2×C3⋊D3—22no—
537C2×C3⋊D3—82no—
538C2×C3⋊D3—81no—
539C2×C3⋊D3C2×C3×D412yes—
540C2×C3×D3—21no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—21no—
544C2×C3×D3—32no—
545C2×C3×D3—32no—
546C2×C3×D3—41no—
547C2×C3×D3—42no—
548C2×C3×D3—62no—
549C2×C3×D3—64no—
550C2×C3×D3—62no—
551C2×C3×D3—62no—
552C2×C3×D3—81no—
553C2×C3×D3—81no—
554C2×C3×D3—82no—
555C2×C3×D3—242no—
556C2×C3×D3—242no—
557C2×C3×D3—242no—
558C2×C3×D3—242no—
559C2×C3×D3—241no—
560C2×C3×D3—241no—
561C2×C3×D3—242no—
562C2×C3×D3—244no—
563D32—82no—
564C32×C4—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—41no—
575C32×C4—41no—
576C32×C4—41no—
577C32×C4—41no—
578C32×C4—42no—
579C32×C4—61no—
580C32×C4D3×D411yescharacteristic
581C32×C4D3×D411yescharacteristic
582C32×C4C2×C3×D411yescharacteristic
583C32×C4C23×D311yescharacteristic
584C32×C4C23×D311yescharacteristic
585C32×C4C24×C311yescharacteristic
586C3⋊Dic3C2×C3×D412yes—
587C3×Dic3—21no—
588C3×Dic3—21no—
589C3×Dic3—32no—
590C3×Dic3—32no—
591C3×Dic3—41no—
592C3×Dic3—62no—
593H(5,𝔽2)—91no—
594H(5,𝔽2)—91no—
595AGL(1,ℤ/8)—31no—
596AGL(1,ℤ/8)—91no—
597AGL(1,ℤ/8)—92no—
598AGL(1,ℤ/8)—92no—
599#135—31no—
600#135—92no—
601C2×D8—91no—
602C2×D8—92no—
603#131—91no—
604C33#57611yescharacteristic, complemented, Sylow
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—121no—
608C23×C3—182no—
609C23×C3—182no—
610C23×C3—181no—
611C22×D3—21no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—64no—
617C22×D3—62no—
618C22×D3—61no—
619C22×D3—61no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—21no—
623C3×Q8—31no—
624C3×Q8—31no—
625C3×Q8—41no—
626C3×Q8—61no—
627C3×Q8—91no—
628C3×Q8C2×D3211yescharacteristic
629C3×Q8C22×C3×D311yescharacteristic
630C3×Q8C22×C3×D311yescharacteristic
631C3×D4—22no—
632C3×D4—21no—
633C3×D4—21no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—32no—
639C3×D4—31no—
640C3×D4—31no—
641C3×D4—32no—
642C3×D4—41no—
643C3×D4—41no—
644C3×D4—42no—
645C3×D4—41no—
646C3×D4—62no—
647C3×D4—61no—
648C3×D4—61no—
649C3×D4—61no—
650C3×D4—61no—
651C3×D4—61no—
652C3×D4—92no—
653C3×D4—92no—
654C3×D4—91no—
655C3×D4—121no—
656C3×D4—121no—
657C3×D4—182no—
658C3×D4—182no—
659C3×D4—182no—
660C3×D4—182no—
661C3×D4—181no—
662C3×D4C2×D3211yescharacteristic
663C3×D4C22×C3×D311yescharacteristic
664C3×D4C22×C3×D311yescharacteristic
665C2×C3×C4—22no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—42no—
675C2×C3×C4—41no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—92no—
679C2×C3×C4—121no—
680C2×C3×C4—182no—
681C2×C3×C4—182no—
682C2×C3×C4C2×D3211yescharacteristic
683C2×C3×C4C22×C3×D311yescharacteristic
684C2×C3×C4C22×C3×D311yescharacteristic
685#67—21no—
686#67—32no—
687#67—32no—
688#67—62no—
689#67—62no—
690#67—62no—
691#67—62no—
692#67—62no—
693#67—62no—
694#67—64no—
695C2×Dic3—62no—
696D12—21no—
697D12—32no—
698D12—32no—
699D12—31no—
700D12—31no—
701D12—61no—
702D12—62no—
703D12—62no—
704D12—62no—
705D12—62no—
706D12—64no—
707D12—62no—
708D12—61no—
709D12—61no—
710D12C22×C3×D312yes—
711D12C22×C3×D311yescharacteristic
712C4×D3—21no—
713C4×D3—32no—
714C4×D3—32no—
715C4×D3—62no—
716C4×D3—62no—
717C4×D3—62no—
718C4×D3—62no—
719C4×D3—64no—
720Dic6—31no—
721Dic6—31no—
722Dic6—61no—
723Dic6C22×C3×D311yescharacteristic
724C3×C8—31no—
725C3×C8—31no—
726C3×C8—32no—
727C3×C8—31no—
728C3×C8—32no—
729C3×C8—31no—
730C3×C8—61no—
731C3×C8—61no—
732C3×C8—62no—
733C3⋊C8C22×C3×D311yescharacteristic
734C3⋊C8C22×C3×D312yes—
735C3⋊C8C22×C3×D311yescharacteristic
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—41no—
743C2×C32—41no—
744C2×C32—41no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—42no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—81no—
751C2×C32—81no—
752C2×C32—81no—
753C2×C32—82no—
754C2×C32—122no—
755C2×C32—121no—
756C2×C32C2×D3×D411yescharacteristic
757C2×C32C2×D3×D411yescharacteristic
758C2×C32C22×C3×D411yescharacteristic
759C3⋊D3—22no—
760C3⋊D3—42no—
761C3×D3—41no—
762C3×D3—42no—
763C3×D3—41no—
764C3×D3—42no—
765C3×D3—62no—
766C3×D3—62no—
767C3×D3—81no—
768C3×D3—82no—
769C3×D3—122no—
770C3×D3—124no—
771C3×D3—122no—
772C3×D3—122no—
773#41—31no—
774#41—91no—
775#41—92no—
776#41—92no—
777#41—181no—
778#41—181no—
779#41C3×D3211yescharacteristic, complemented
780C2×D4—31no—
781C2×D4—92no—
782C2×D4—92no—
783C2×D4—91no—
784C2×D4—181no—
785C2×D4—181no—
786C2×D4—182no—
787C2×D4—182no—
788Q16—31no—
789SD16—31no—
790SD16—32no—
791SD16—31no—
792SD16—92no—
793D8—31no—
794D8—32no—
795D8—92no—
796D8—92no—
797D8—92no—
798M16—31no—
799M16—92no—
800C2×C8—31no—
801C2×C8—92no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—42no—
812C22×C3—41no—
813C22×C3—61no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—61no—
817C22×C3—92no—
818C22×C3—121no—
819C22×C3—122no—
820C22×C3—182no—
821C22×C3—241no—
822C22×C3—241no—
823C22×C3—242no—
824C22×C3—721no—
825C22×C3—722no—
826C22×C3—722no—
827C22×C3#381111yescharacteristic
828C22×C3C3×D3×D411yescharacteristic
829C22×C3C3×D3×D411yescharacteristic
830C2×D3—21no—
831C2×D3—22no—
832C2×D3—32no—
833C2×D3—32no—
834C2×D3—62no—
835C2×D3—64no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—81no—
839C2×D3—242no—
840C2×D3—242no—
841C2×D3—242no—
842C2×D3—242no—
843C2×D3—241no—
844C2×D3—241no—
845C2×D3—242no—
846C2×D3—244no—
847C3×C4—22no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—21no—
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—41no—
858C3×C4—41no—
859C3×C4—42no—
860C3×C4—41no—
861C3×C4—41no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—92no—
865C3×C4—121no—
866C3×C4#381111yescharacteristic
867C3×C4C3×D3×D411yescharacteristic
868C3×C4C3×D3×D411yescharacteristic
869C3×C4C22×D3211yescharacteristic
870C3×C4C23×C3×D311yescharacteristic
871C3×C4C23×C3×D311yescharacteristic
872Dic3—21no—
873Dic3—32no—
874Dic3—32no—
875Dic3—62no—
876C32—21no—
877C32—21no—
878C32—21no—
879C32—41no—
880C32#576911yescharacteristic, complemented
881C32#577411yescharacteristic, complemented
882C32C3×#57611yescharacteristic, complemented
883C23—61no—
884C23—182no—
885C23—182no—
886C23—181no—
887Q8—31no—
888Q8—91no—
889Q8C2×C3×D3211yescharacteristic
890D4—21no—
891D4—32no—
892D4—31no—
893D4—61no—
894D4—61no—
895D4—92no—
896D4—92no—
897D4—91no—
898D4—182no—
899D4—182no—
900D4—182no—
901D4—182no—
902D4—181no—
903D4C2×C3×D3211yescharacteristic
904C2×C4—21no—
905C2×C4—61no—
906C2×C4—92no—
907C2×C4—182no—
908C2×C4—182no—
909C2×C4C2×C3×D3211yescharacteristic
910C8—31no—
911C8—31no—
912C8—32no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—42no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3—81no—
930C2×C3—82no—
931C2×C3—122no—
932C2×C3—121no—
933C2×C3—122no—
934C2×C3—121no—
935C2×C3—182no—
936C2×C3—242no—
937C2×C3—241no—
938C2×C3—362no—
939C2×C3C2×#381111yescharacteristic
940C2×C3C2×C3×D3×D411yescharacteristic
941C2×C3C2×C3×D3×D411yescharacteristic
942D3—41no—
943D3—42no—
944D3—62no—
945D3—62no—
946D3—122no—
947D3—124no—
948D3—122no—
949D3—122no—
950C22—21no—
951C22—61no—
952C22—62no—
953C22—92no—
954C22—182no—
955C22—241no—
956C22—721no—
957C22—722no—
958C22—722no—
959C22C3×#381111yescharacteristic
960C4—21no—
961C4—61no—
962C4—92no—
963C4C3×#381111yescharacteristic
964C4C22×C3×D3211yescharacteristic
965C3—21no—
966C3—21no—
967C3—21no—
968C3—41no—
969C3#1059546111yescharacteristic, direct product factor
970C3C3×#576911yescharacteristic, complemented
971C3C3×#577411yescharacteristic, complemented
972C2—21no—
973C2—41no—
974C2—122no—
975C2—121no—
976C2—182no—
977C2—362no—
978C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3C2×#3811
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#576
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×#64366C2semidirect
2. C3×#64307C2semidirect
3. C32×#950C2semidirect
4. C32×#949C2semidirect
5. C3×#63950C2semidirect
6. C3×#63941C2semidirect
7. C3×#63937C2semidirect
8. C3×#63926C2semidirect
9. C3×#63825C2semidirect
10. C2×C3×#3714C2semidirect
11. C3×#63817C2semidirect
14. #10595461C3direct (N × H)
15. C33×#41C22semidirect
16. C3×#3832C22semidirect
18. C3×D4×C3⋊D3C22semidirect
22. C2×C3×C4⋊(C3⋊D3)C22semidirect
23. C32×#235C22semidirect
24. C2×C32×D12C22semidirect
26. C3×#3802C22semidirect
28. C3×#3796C22semidirect
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×#3717C22semidirect
39. C3×#3714C22semidirect
40. C3×#3714C22semidirect
41. C3×#3714C22semidirect
42. C3×#3712C22semidirect
43. C3×#3710C22semidirect
44. #64366C2×C3semidirect
50. #64307C2×C3semidirect
54. C3×#950D3semidirect
55. C3×#950C2×C3semidirect
58. C3×#949D3semidirect
59. C3×#949C2×C3semidirect
73. #63950C2×C3semidirect
74. #63941C2×C3semidirect
75. #63937C2×C3semidirect
76. #63926C2×C3semidirect
77. #63825C2×C3semidirect
78. C2×#3714C2×C3semidirect
79. #63817C2×C3semidirect
118. C32×#41C2×D3semidirect
119. C32×#41C2×D3semidirect
120. C32×#41C22×C3semidirect
122. #3832C22×C3semidirect
124. D4×C3⋊D3C22×C3semidirect
128. C2×C4⋊(C3⋊D3)C22×C3semidirect
154. C3×#235C2×D3semidirect
155. C3×#235C22×C3semidirect
164. C2×C3×D12C2×D3semidirect
165. C2×C3×D12C22×C3semidirect
167. #3802C22×C3semidirect
169. #3796C22×C3semidirect
180. C3×#216C2×D3semidirect
181. C3×#216C22×C3semidirect
185. C3×#215C2×D3semidirect
186. C3×#215C2×D3semidirect
187. C3×#215C22×C3semidirect
188. C3×#215C22×C3semidirect
190. C3×#214C2×D3semidirect
191. 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. #3717C22×C3semidirect
216. #3714C22×C3semidirect
217. #3714C22×C3semidirect
218. #3714C22×C3semidirect
219. #3712C22×C3semidirect
220. #3710C22×C3semidirect
256. #950C3×D3semidirect
258. #949C3×D3semidirect
423. C3×#41D32semidirect
424. C3×#41C2×C3×D3semidirect
425. C3×#41C2×C3×D3semidirect
460. #235C2×C3×D3semidirect
468. C2×D12C2×C3×D3semidirect
499. #216C2×C3×D3semidirect
501. #215C2×C3×D3semidirect
502. #215C2×C3×D3semidirect
503. #214C2×C3×D3semidirect
507. #213C2×C3×D3semidirect
508. #213C2×C3×D3semidirect
509. #208C2×C3×D3semidirect
510. C2×C3⋊C8C2×C3×D3semidirect
604. C33#576semidirect
779. #41C3×D32semidirect
880. C32#5769semidirect
881. C32#5774semidirect
882. C32C3×#576semidirect
969. C3#10595461direct (N × H)
970. C3C3×#5769semidirect
971. C3C3×#5774semidirect

Maximal subgroups

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

subgroupindex
C3×#643662
C3×#643072
C32×#9502
C32×#9492
C3×#639502
C3×#639412
C3×#639372
C3×#639262
C3×#638252
C2×C3×#37142
C3×#638172
C3×#57743
C3×#57693
#105954613