Finite Group Databasebeta

← C3×#10596669 #13181544

Subgroups — C3×#10596669 #13181544

Order 1728.

3786 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C32×#235C212yesmaximal, complemented
3C3×#64330C214yesmaximal, complemented
4C3×#64308C212yesmaximal, complemented
5C3×#64307C214yesmaximal, complemented
6C3×#64306C214yesmaximal, complemented
7C3×D3×#235C218yesmaximal, complemented
8C3×#64298C212yesmaximal, complemented
9C3×#64297C214yesmaximal, complemented
10C3×#5964—32nomaximal
11#10596669C311yesmaximal, characteristic, direct product factor
12C22×C33×C4C2211yescharacteristic, complemented
13C2×C3×#638C2212yescomplemented
14C3×#3828C2214yescomplemented
15C3×#3828C2214yescomplemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C2×C3×C4×C3⋊D3C2212yescomplemented
18C2×C3×#634C2211yescharacteristic, complemented
19C2×C32×#67C2214yescomplemented
20C32×#235C2214yescomplemented
21C32×#235C2214yescomplemented
22C32×#235C2214yescomplemented
23C32×#235C2214yescomplemented
24C2×C32×D12C2212yescomplemented
25C2×C32×C4×D3C2214yescomplemented
26C2×C32×Dic6C2212yescomplemented
27C3×#3811C2218yescomplemented
28C3×D3×#67C22116yescomplemented
29C3×#3805C2218yescomplemented
30C3×#3804C22116yescomplemented
31C3×#3802C2214yescomplemented
32C3×D3×D12C2218yescomplemented
33C3×C4×D32C2218yescomplemented
34C3×#3799C2218yescomplemented
35C3×#3798C2218yescomplemented
36C3×#3797C2214yescomplemented
37C3×#3796C2218yescomplemented
38C3×#3795C2218yescomplemented
39C3×D3×Dic6C2218yescomplemented
40C2×C32×#41—32no—
41C2×#3828C2×C311yescharacteristic, complemented
42C3×#1010—34no—
43C3×#1010—34no—
44C3×#1009—34no—
45C3×#1009—34no—
46C3×D3×#41—38no—
47C3×D3×#41—38no—
48C3×#1007—34no—
49C3×#1004—38no—
50C3×#1004—34no—
51C2×C3×#235—22no—
52C2×C3×#235—32no—
53C2×C3×#235—38no—
54C2×C3×#235—61no—
55C2×C3×#235D312yescomplemented
56C2×C3×#235C2×C312yescomplemented
57#64330C2×C314yescomplemented
58#64308C2×C312yescomplemented
59#64307C2×C314yescomplemented
60#64306C2×C314yescomplemented
61D3×#235C2×C318yescomplemented
62#64298C2×C312yescomplemented
63#64297C2×C314yescomplemented
64C23×C33C2311yescharacteristic
65C22×C3×C3⋊D3C2312yes—
66C22×C32×D3C2314yes—
67C2×C3×D32C2318yes—
68C2×C33×C4C2312yes—
69C2×C33×C4C2312yes—
70C2×C33×C4C2311yescharacteristic
71C2×C33×C4C2311yescharacteristic
72C3×#638C2318yes—
73C2×C3×C3⋊Dic3C2312yes—
74C3×C4⋊(C3⋊D3)C2314yes—
75C3×C4×C3⋊D3C2314yes—
76C3×C4×C3⋊D3C2314yes—
77C3×#634C2314yes—
78C32×#67C2318yes—
79C32×#67C2318yes—
80C2×C32×Dic3C2314yes—
81C32×D12C2314yes—
82C32×D12C2314yes—
83C32×C4×D3C2318yes—
84C32×C4×D3C2318yes—
85C32×Dic6C2314yes—
86C32×Dic6C2314yes—
87C3×#627C2318yes—
88C3×#626C23116yes—
89C3×#625C2318yes—
90C3×#624C2318yes—
91C3×D3×Dic3C23116yes—
92C3×#585—91no—
93#5964—32no—
94C32×#41—34no—
95C32×#41—34no—
96C32×#41—34no—
97C32×#41—34no—
98C2×C32×Q8—32no—
99C2×C32×D4—34no—
100C2×C32×D4—32no—
101C22×C32×C4—21no—
102C22×C32×C4—22no—
103C22×C32×C4—34no—
104C22×C32×C4—41no—
105C22×C32×C4C2×D312yescomplemented
106C22×C32×C4C22×C311yescharacteristic, complemented
107C2×#638C22×C312yescomplemented
108#3828C22×C314yescomplemented
109#3828C22×C314yescomplemented
110C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
111C2×C4×C3⋊D3C22×C312yescomplemented
112C2×#634C22×C311yescharacteristic, complemented
113C2×C3×#67—24no—
114C2×C3×#67—34no—
115C2×C3×#67—316no—
116C2×C3×#67—62no—
117C2×C3×#67C2×D314yescomplemented
118C2×C3×#67C22×C314yescomplemented
119C3×#239—38no—
120C3×#239—38no—
121C3×D3×Q8—38no—
122C3×D3×Q8—38no—
123C3×#237—316no—
124C3×#237—316no—
125C3×#237—38no—
126C3×#237—38no—
127C3×D3×D4—316no—
128C3×D3×D4—316no—
129C3×D3×D4—38no—
130C3×D3×D4—38no—
131C3×#235—24no—
132C3×#235—24no—
133C3×#235—24no—
134C3×#235—24no—
135C3×#235—34no—
136C3×#235—34no—
137C3×#235—34no—
138C3×#235—34no—
139C3×#235—316no—
140C3×#235—38no—
141C3×#235—316no—
142C3×#235—38no—
143C3×#235—64no—
144C3×#235—64no—
145C3×#235C2×D314yescomplemented
146C3×#235C2×D314yescomplemented
147C3×#235C2×D314yescomplemented
148C3×#235C2×D314yescomplemented
149C3×#235C22×C314yescomplemented
150C3×#235C22×C314yescomplemented
151C3×#235C22×C314yescomplemented
152C3×#235C22×C314yescomplemented
153C2×C3×D12—22no—
154C2×C3×D12—32no—
155C2×C3×D12—38no—
156C2×C3×D12—61no—
157C2×C3×D12C2×D312yescomplemented
158C2×C3×D12C22×C312yescomplemented
159C2×C3×C4×D3—24no—
160C2×C3×C4×D3—34no—
161C2×C3×C4×D3—316no—
162C2×C3×C4×D3—62no—
163C2×C3×C4×D3C2×D314yescomplemented
164C2×C3×C4×D3C22×C314yescomplemented
165C2×C3×Dic6—22no—
166C2×C3×Dic6—32no—
167C2×C3×Dic6—38no—
168C2×C3×Dic6—61no—
169C2×C3×Dic6C2×D312yescomplemented
170C2×C3×Dic6C22×C312yescomplemented
171#3811C22×C318yescomplemented
172D3×#67C22×C3116yescomplemented
173#3805C22×C318yescomplemented
174#3804C22×C3116yescomplemented
175#3802C22×C314yescomplemented
176D3×D12C22×C318yescomplemented
177C4×D32C22×C318yescomplemented
178#3799C22×C318yescomplemented
179#3798C22×C318yescomplemented
180#3797C22×C314yescomplemented
181#3796C22×C318yescomplemented
182#3795C22×C318yescomplemented
183D3×Dic6C22×C318yescomplemented
184C22×C33—41no—
185C22×C33C2412yes—
186C22×C33C2411yescharacteristic
187C2×C3×C3⋊D3—42no—
188C2×C3×C3⋊D3C2414yes—
189C2×C32×D3—44no—
190C2×C32×D3C2418yes—
191C3×D32—48no—
192C33×C4C2411yescharacteristic
193C33×C4C2412yes—
194C33×C4C2411yescharacteristic
195C3×C3⋊Dic3C2414yes—
196C32×Dic3C2418yes—
197C3×2−1+4—94no—
198C3×2−1+4—92no—
199C3×H(5,𝔽2)—94no—
200C3×H(5,𝔽2)—94no—
201C3×H(5,𝔽2)—92no—
202C2×C3×#41—32no—
203C2×C3×#41—32no—
204C2×C3×#41—62no—
205C2×C3×#41—98no—
206C2×C3×#41—94no—
207C2×C3×#41—91no—
208#1010—34no—
209#1010—34no—
210#1009—34no—
211#1009—34no—
212D3×#41—38no—
213D3×#41—38no—
214#1007—34no—
215#1004—38no—
216#1004—34no—
217C2×#235—32no—
218C2×#235—38no—
219C2×#235—61no—
220C2×#235C3×D312yescomplemented
221C23×C32—21no—
222C23×C32—22no—
223C23×C32—34no—
224C23×C32—41no—
225C23×C32C22×D312yes—
226C23×C32C23×C311yescharacteristic
227C22×C3⋊D3C23×C312yes—
228C22×C3×D3—24no—
229C22×C3×D3—34no—
230C22×C3×D3—316no—
231C22×C3×D3—62no—
232C22×C3×D3C22×D314yes—
233C22×C3×D3C23×C314yes—
234C2×D32C23×C318yes—
235C32×Q8—34no—
236C32×Q8—34no—
237C32×D4—38no—
238C32×D4—38no—
239C32×D4—34no—
240C32×D4—34no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—22no—
244C2×C32×C4—22no—
245C2×C32×C4—22no—
246C2×C32×C4—22no—
247C2×C32×C4—22no—
248C2×C32×C4—22no—
249C2×C32×C4—22no—
250C2×C32×C4—22no—
251C2×C32×C4—34no—
252C2×C32×C4—38no—
253C2×C32×C4—38no—
254C2×C32×C4—42no—
255C2×C32×C4—42no—
256C2×C32×C4—41no—
257C2×C32×C4—41no—
258C2×C32×C4C22×D312yes—
259C2×C32×C4C22×D312yes—
260C2×C32×C4C22×D312yes—
261C2×C32×C4C22×D312yes—
262C2×C32×C4C22×D312yes—
263C2×C32×C4C22×D312yes—
264C2×C32×C4C23×C312yes—
265C2×C32×C4C23×C312yes—
266C2×C32×C4C23×C311yescharacteristic
267C2×C32×C4C23×C311yescharacteristic
268#638C23×C318yes—
269C2×C3⋊Dic3C23×C312yes—
270C4⋊(C3⋊D3)C23×C314yes—
271C4×C3⋊D3C23×C314yes—
272C4×C3⋊D3C23×C314yes—
273#634C23×C314yes—
274C3×#67—28no—
275C3×#67—28no—
276C3×#67—38no—
277C3×#67—38no—
278C3×#67—316no—
279C3×#67—316no—
280C3×#67—68no—
281C3×#67C22×D318yes—
282C3×#67C22×D318yes—
283C3×#67C23×C318yes—
284C3×#67C23×C318yes—
285C2×C3×Dic3—24no—
286C2×C3×Dic3—34no—
287C2×C3×Dic3—316no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3C22×D314yes—
290C2×C3×Dic3C23×C314yes—
291C3×D12—24no—
292C3×D12—24no—
293C3×D12—316no—
294C3×D12—34no—
295C3×D12—34no—
296C3×D12—64no—
297C3×D12C22×D314yes—
298C3×D12C22×D314yes—
299C3×D12C23×C314yes—
300C3×D12C23×C314yes—
301C3×C4×D3—28no—
302C3×C4×D3—28no—
303C3×C4×D3—316no—
304C3×C4×D3—38no—
305C3×C4×D3—38no—
306C3×C4×D3—316no—
307C3×C4×D3—64no—
308C3×C4×D3—64no—
309C3×C4×D3C22×D318yes—
310C3×C4×D3C22×D318yes—
311C3×C4×D3C23×C318yes—
312C3×C4×D3C23×C318yes—
313C3×Dic6—24no—
314C3×Dic6—24no—
315C3×Dic6—34no—
316C3×Dic6—34no—
317C3×Dic6—316no—
318C3×Dic6—64no—
319C3×Dic6C22×D314yes—
320C3×Dic6C22×D314yes—
321C3×Dic6C23×C314yes—
322C3×Dic6C23×C314yes—
323#627C23×C318yes—
324#626C23×C3116yes—
325#625C23×C318yes—
326#624C23×C318yes—
327D3×Dic3C23×C3116yes—
328#585—91noSylow
329C2×C33—22no—
330C2×C33—21no—
331C2×C33C2511yescharacteristic
332C3×C3⋊D3—24no—
333C32×D3—28no—
334C3×#41—34no—
335C3×#41—34no—
336C3×#41—34no—
337C3×#41—34no—
338C3×#41—34no—
339C3×#41—34no—
340C3×#41—34no—
341C3×#41—34no—
342C3×#41—64no—
343C3×#41—64no—
344C3×#41—64no—
345C3×#41—64no—
346C3×#41—98no—
347C3×#41—916no—
348C3×#41—98no—
349C3×#41—98no—
350C3×#41—98no—
351C3×#41—98no—
352C3×#41—94no—
353C3×#41—94no—
354C2×C3×Q8—32no—
355C2×C3×Q8—32no—
356C2×C3×Q8—62no—
357C2×C3×Q8—98no—
358C2×C3×Q8—94no—
359C2×C3×Q8—91no—
360C2×C3×D4—34no—
361C2×C3×D4—34no—
362C2×C3×D4—32no—
363C2×C3×D4—32no—
364C2×C3×D4—62no—
365C2×C3×D4—64no—
366C2×C3×D4—98no—
367C2×C3×D4—98no—
368C2×C3×D4—94no—
369C2×C3×D4—916no—
370C2×C3×D4—92no—
371C2×C3×D4—91no—
372C22×C3×C4—21no—
373C22×C3×C4—22no—
374C22×C3×C4—34no—
375C22×C3×C4—34no—
376C22×C3×C4—41no—
377C22×C3×C4—64no—
378C22×C3×C4—98no—
379C22×C3×C4—92no—
380C22×C3×C4D3211yescharacteristic, complemented
381C22×C3×C4C2×C3×D312yescomplemented
382C2×#67—34no—
383C2×#67—316no—
384C2×#67—62no—
385C2×#67C2×C3×D314yescomplemented
386#239—38no—
387#239—38no—
388D3×Q8—38no—
389D3×Q8—38no—
390#237—316no—
391#237—316no—
392#237—38no—
393#237—38no—
394D3×D4—316no—
395D3×D4—316no—
396D3×D4—38no—
397D3×D4—38no—
398#235—34no—
399#235—34no—
400#235—34no—
401#235—34no—
402#235—316no—
403#235—38no—
404#235—316no—
405#235—38no—
406#235—64no—
407#235—64no—
408#235C2×C3×D314yescomplemented
409#235C2×C3×D314yescomplemented
410#235C2×C3×D314yescomplemented
411#235C2×C3×D314yescomplemented
412C2×D12—32no—
413C2×D12—38no—
414C2×D12—61no—
415C2×D12C2×C3×D312yescomplemented
416C2×C4×D3—34no—
417C2×C4×D3—316no—
418C2×C4×D3—62no—
419C2×C4×D3C2×C3×D314yescomplemented
420C2×Dic6—32no—
421C2×Dic6—38no—
422C2×Dic6—61no—
423C2×Dic6C2×C3×D312yescomplemented
424C22×C32—21no—
425C22×C32—22no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—38no—
430C22×C32—41no—
431C22×C32—42no—
432C22×C32—42no—
433C22×C32—41no—
434C22×C32—42no—
435C22×C32—44no—
436C22×C32—44no—
437C22×C32—124no—
438C22×C32C23×D312yes—
439C22×C32C23×D312yes—
440C22×C32C23×D312yes—
441C22×C32C24×C312yes—
442C22×C32C24×C311yescharacteristic
443C2×C3⋊D3—42no—
444C2×C3⋊D3C24×C314yes—
445C2×C3×D3—28no—
446C2×C3×D3—38no—
447C2×C3×D3—44no—
448C2×C3×D3—44no—
449C2×C3×D3—48no—
450C2×C3×D3—64no—
451C2×C3×D3—1216no—
452C2×C3×D3—124no—
453C2×C3×D3—124no—
454C2×C3×D3C23×D318yes—
455C2×C3×D3C24×C318yes—
456D32—48no—
457C32×C4—22no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—38no—
465C32×C4—42no—
466C32×C4—41no—
467C32×C4—41no—
468C32×C4C23×D312yes—
469C32×C4C23×D312yes—
470C32×C4C23×D312yes—
471C32×C4C23×D312yes—
472C32×C4C24×C311yescharacteristic
473C32×C4C24×C312yes—
474C32×C4C24×C311yescharacteristic
475C3⋊Dic3C24×C314yes—
476C3×Dic3—28no—
477C3×Dic3—38no—
478C3×Dic3—64no—
479C3×Dic3C23×D318yes—
480C3×Dic3C24×C318yes—
4812−1+4—94no—
4822−1+4—92no—
483H(5,𝔽2)—94no—
484H(5,𝔽2)—94no—
485H(5,𝔽2)—92no—
486C2×#41—32no—
487C2×#41—98no—
488C2×#41—94no—
489C2×#41—91no—
490C33#58511yescharacteristic, complemented, Sylow
491C23×C3—22no—
492C23×C3—21no—
493C23×C3—34no—
494C23×C3—34no—
495C23×C3—41no—
496C23×C3—64no—
497C23×C3—98no—
498C23×C3—92no—
499C23×C3C2×D3211yescharacteristic
500C23×C3C22×C3×D312yes—
501C22×D3—34no—
502C22×D3—316no—
503C22×D3—62no—
504C22×D3C22×C3×D314yes—
505C3×Q8—34no—
506C3×Q8—34no—
507C3×Q8—34no—
508C3×Q8—34no—
509C3×Q8—64no—
510C3×Q8—64no—
511C3×Q8—98no—
512C3×Q8—94no—
513C3×D4—38no—
514C3×D4—38no—
515C3×D4—38no—
516C3×D4—38no—
517C3×D4—34no—
518C3×D4—34no—
519C3×D4—34no—
520C3×D4—34no—
521C3×D4—64no—
522C3×D4—64no—
523C3×D4—68no—
524C3×D4—68no—
525C3×D4—916no—
526C3×D4—98no—
527C3×D4—98no—
528C3×D4—94no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—38no—
542C2×C3×C4—38no—
543C2×C3×C4—38no—
544C2×C3×C4—38no—
545C2×C3×C4—42no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—41no—
549C2×C3×C4—68no—
550C2×C3×C4—68no—
551C2×C3×C4—64no—
552C2×C3×C4—98no—
553C2×C3×C4—916no—
554C2×C3×C4—92no—
555C2×C3×C4—94no—
556C2×C3×C4—94no—
557C2×C3×C4C2×D3212yes—
558C2×C3×C4C2×D3211yescharacteristic
559C2×C3×C4C2×D3212yes—
560C2×C3×C4C2×D3211yescharacteristic
561C2×C3×C4C22×C3×D312yes—
562C2×C3×C4C22×C3×D312yes—
563C2×C3×C4C22×C3×D312yes—
564C2×C3×C4C22×C3×D312yes—
565C2×C3×C4C22×C3×D312yes—
566C2×C3×C4C22×C3×D312yes—
567#67—38no—
568#67—38no—
569#67—316no—
570#67—316no—
571#67—68no—
572#67C22×C3×D318yes—
573#67C22×C3×D318yes—
574C2×Dic3—34no—
575C2×Dic3—316no—
576C2×Dic3—62no—
577C2×Dic3C22×C3×D314yes—
578D12—316no—
579D12—34no—
580D12—34no—
581D12—64no—
582D12C22×C3×D314yes—
583D12C22×C3×D314yes—
584C4×D3—316no—
585C4×D3—38no—
586C4×D3—38no—
587C4×D3—316no—
588C4×D3—64no—
589C4×D3—64no—
590C4×D3C22×C3×D318yes—
591C4×D3C22×C3×D318yes—
592Dic6—34no—
593Dic6—34no—
594Dic6—316no—
595Dic6—64no—
596Dic6C22×C3×D314yes—
597Dic6C22×C3×D314yes—
598C2×C32—22no—
599C2×C32—21no—
600C2×C32—24no—
601C2×C32—22no—
602C2×C32—22no—
603C2×C32—22no—
604C2×C32—22no—
605C2×C32—21no—
606C2×C32—22no—
607C2×C32—41no—
608C2×C32—42no—
609C2×C32—42no—
610C2×C32—42no—
611C2×C32—42no—
612C2×C32—44no—
613C2×C32—68no—
614C2×C32C24×D312yes—
615C2×C32C25×C311yescharacteristic
616C3⋊D3—24no—
617C3×D3—28no—
618C3×D3—28no—
619C3×D3—48no—
620C3×D3—68no—
621C3×D3—124no—
622#41—34no—
623#41—34no—
624#41—34no—
625#41—34no—
626#41—98no—
627#41—916no—
628#41—98no—
629#41—98no—
630#41—98no—
631#41—98no—
632#41—94no—
633#41—94no—
634C2×Q8—32no—
635C2×Q8—98no—
636C2×Q8—94no—
637C2×Q8—91no—
638C2×D4—34no—
639C2×D4—32no—
640C2×D4—98no—
641C2×D4—98no—
642C2×D4—94no—
643C2×D4—916no—
644C2×D4—92no—
645C2×D4—91no—
646C22×C4—34no—
647C22×C4—98no—
648C22×C4—92no—
649C22×C4C3×D3211yescharacteristic, complemented
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—38no—
656C22×C3—38no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—42no—
663C22×C3—41no—
664C22×C3—68no—
665C22×C3—94no—
666C22×C3—124no—
667C22×C3—124no—
668C22×C3—128no—
669C22×C3—362no—
670C22×C3—368no—
671C22×C3C22×D3212yes—
672C22×C3C22×D3211yescharacteristic
673C22×C3C23×C3×D312yes—
674C22×C3C23×C3×D312yes—
675C22×C3C23×C3×D312yes—
676C2×D3—38no—
677C2×D3—44no—
678C2×D3—64no—
679C2×D3—1216no—
680C2×D3—124no—
681C2×D3—124no—
682C2×D3C23×C3×D318yes—
683C3×C4—22no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—22no—
690C3×C4—38no—
691C3×C4—38no—
692C3×C4—41no—
693C3×C4—42no—
694C3×C4—41no—
695C3×C4—68no—
696C3×C4—94no—
697C3×C4C22×D3212yes—
698C3×C4C22×D3211yescharacteristic
699C3×C4C22×D3211yescharacteristic
700C3×C4C23×C3×D312yes—
701C3×C4C23×C3×D312yes—
702C3×C4C23×C3×D312yes—
703C3×C4C23×C3×D312yes—
704Dic3—38no—
705Dic3—64no—
706Dic3C23×C3×D318yes—
707C32—21no—
708C32—22no—
709C32—41no—
710C32#596412yescomplemented
711C32C3×#58511yescharacteristic, complemented
712C23—34no—
713C23—98no—
714C23—92no—
715C23C2×C3×D3211yescharacteristic
716Q8—34no—
717Q8—34no—
718Q8—98no—
719Q8—94no—
720D4—38no—
721D4—38no—
722D4—34no—
723D4—34no—
724D4—916no—
725D4—98no—
726D4—98no—
727D4—94no—
728C2×C4—34no—
729C2×C4—38no—
730C2×C4—38no—
731C2×C4—98no—
732C2×C4—916no—
733C2×C4—92no—
734C2×C4—94no—
735C2×C4—94no—
736C2×C4C2×C3×D3212yes—
737C2×C4C2×C3×D3211yescharacteristic
738C2×C4C2×C3×D3212yes—
739C2×C4C2×C3×D3211yescharacteristic
740C2×C3—22no—
741C2×C3—24no—
742C2×C3—22no—
743C2×C3—21no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—22no—
747C2×C3—21no—
748C2×C3—22no—
749C2×C3—42no—
750C2×C3—42no—
751C2×C3—42no—
752C2×C3—44no—
753C2×C3—42no—
754C2×C3—41no—
755C2×C3—68no—
756C2×C3—68no—
757C2×C3—128no—
758C2×C3—184no—
759C2×C3C23×D3211yescharacteristic
760C2×C3C24×C3×D312yes—
761D3—28no—
762D3—68no—
763D3—124no—
764C22—38no—
765C22—41no—
766C22—94no—
767C22—124no—
768C22—362no—
769C22—368no—
770C22C22×C3×D3212yes—
771C22C22×C3×D3211yescharacteristic
772C4—38no—
773C4—94no—
774C4C22×C3×D3211yescharacteristic
775C4C22×C3×D3212yes—
776C4C22×C3×D3211yescharacteristic
777C3—21no—
778C3—22no—
779C3—41no—
780C3#1059666911yescharacteristic, direct product factor
781C3C3×#596412yescomplemented
782C2—22no—
783C2—21no—
784C2—68no—
785C2—184no—
786C2C23×C3×D3211yescharacteristic
subgroupG/H
centerC3×C4C22×D32
commutator, cosocleC2×C32C25×C3
FrattiniC2C23×C3×D32
FittingC22×C33×C4C22
socleC2×C33C25
hypercenterC22×C3×C4D32
hypocenterC32C3×#585
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C32×#235C2semidirect
3. C3×#64330C2semidirect
4. C3×#64308C2semidirect
5. C3×#64307C2semidirect
6. C3×#64306C2semidirect
7. C3×D3×#235C2semidirect
8. C3×#64298C2semidirect
9. C3×#64297C2semidirect
11. #10596669C3direct (N × H)
12. C22×C33×C4C22semidirect
13. C2×C3×#638C22semidirect
14. C3×#3828C22semidirect
15. C3×#3828C22semidirect
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C2×C3×C4×C3⋊D3C22semidirect
18. C2×C3×#634C22semidirect
19. C2×C32×#67C22semidirect
20. C32×#235C22semidirect
21. C32×#235C22semidirect
22. C32×#235C22semidirect
23. C32×#235C22semidirect
24. C2×C32×D12C22semidirect
25. C2×C32×C4×D3C22semidirect
26. C2×C32×Dic6C22semidirect
27. C3×#3811C22semidirect
28. C3×D3×#67C22semidirect
29. C3×#3805C22semidirect
30. C3×#3804C22semidirect
31. C3×#3802C22semidirect
32. C3×D3×D12C22semidirect
33. C3×C4×D32C22semidirect
34. C3×#3799C22semidirect
35. C3×#3798C22semidirect
36. C3×#3797C22semidirect
37. C3×#3796C22semidirect
38. C3×#3795C22semidirect
39. C3×D3×Dic6C22semidirect
41. C2×#3828C2×C3semidirect
55. C2×C3×#235D3semidirect
56. C2×C3×#235C2×C3semidirect
57. #64330C2×C3semidirect
58. #64308C2×C3semidirect
59. #64307C2×C3semidirect
60. #64306C2×C3semidirect
61. D3×#235C2×C3semidirect
62. #64298C2×C3semidirect
63. #64297C2×C3semidirect
105. C22×C32×C4C2×D3semidirect
106. C22×C32×C4C22×C3semidirect
107. C2×#638C22×C3semidirect
108. #3828C22×C3semidirect
109. #3828C22×C3semidirect
110. C2×C4⋊(C3⋊D3)C22×C3semidirect
111. C2×C4×C3⋊D3C22×C3semidirect
112. C2×#634C22×C3semidirect
117. C2×C3×#67C2×D3semidirect
118. C2×C3×#67C22×C3semidirect
145. C3×#235C2×D3semidirect
146. C3×#235C2×D3semidirect
147. C3×#235C2×D3semidirect
148. C3×#235C2×D3semidirect
149. C3×#235C22×C3semidirect
150. C3×#235C22×C3semidirect
151. C3×#235C22×C3semidirect
152. C3×#235C22×C3semidirect
157. C2×C3×D12C2×D3semidirect
158. C2×C3×D12C22×C3semidirect
163. C2×C3×C4×D3C2×D3semidirect
164. C2×C3×C4×D3C22×C3semidirect
169. C2×C3×Dic6C2×D3semidirect
170. C2×C3×Dic6C22×C3semidirect
171. #3811C22×C3semidirect
172. D3×#67C22×C3semidirect
173. #3805C22×C3semidirect
174. #3804C22×C3semidirect
175. #3802C22×C3semidirect
176. D3×D12C22×C3semidirect
177. C4×D32C22×C3semidirect
178. #3799C22×C3semidirect
179. #3798C22×C3semidirect
180. #3797C22×C3semidirect
181. #3796C22×C3semidirect
182. #3795C22×C3semidirect
183. D3×Dic6C22×C3semidirect
220. C2×#235C3×D3semidirect
380. C22×C3×C4D32semidirect
381. C22×C3×C4C2×C3×D3semidirect
385. C2×#67C2×C3×D3semidirect
408. #235C2×C3×D3semidirect
409. #235C2×C3×D3semidirect
410. #235C2×C3×D3semidirect
411. #235C2×C3×D3semidirect
415. C2×D12C2×C3×D3semidirect
419. C2×C4×D3C2×C3×D3semidirect
423. C2×Dic6C2×C3×D3semidirect
490. C33#585semidirect
649. C22×C4C3×D32semidirect
710. C32#5964semidirect
711. C32C3×#585semidirect
780. C3#10596669direct (N × H)
781. C3C3×#5964semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C32×#2352
C3×#643302
C3×#643082
C3×#643072
C3×#643062
C3×D3×#2352
C3×#642982
C3×#642972
C3×#59643
#105966693