Finite Group Databasebeta

← C3×#80086 #11864402

Subgroups — C3×#80086 #11864402

Order 1152.

1545 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3C2×C3×#911C211yesmaximal, characteristic, complemented
4C3×#5607C211yesmaximal, characteristic, complemented
5C32×#449C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7C3×#5170C211yesmaximal, characteristic, complemented
8C3×#5158C211yesmaximal, characteristic, complemented
9C3×#5040C211yesmaximal, characteristic, complemented
10C3×#4806C211yesmaximal, characteristic, complemented
11C3×#4802C211yesmaximal, characteristic, complemented
12C3×#4781C211yesmaximal, characteristic, complemented
13C3×#4772C211yesmaximal, characteristic, complemented
14C3×#4738C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3010—31nomaximal
17#80086C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C3×#1010—24no—
20C3×#1010—24no—
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23C2×C3×#237—21no—
24C2×C3×#237—21no—
25C2×C3×#237C2211yescharacteristic
26C2×C3×#237C2211yescharacteristic, complemented
27C2×C3×D3×D4C2211yescharacteristic
28C2×C3×#235—21no—
29C2×C3×#235C2211yescharacteristic
30C22×C3×Dic6—21no—
31C22×C3×Dic6C2211yescharacteristic, complemented
32C2×C32×SD16C2211yescharacteristic
33C2×C32×D8C2211yescharacteristic
34C32×#121C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C3×#940—21no—
37C3×#938C2211yescharacteristic
38C3×#937—21no—
39C2×C3×#214C2211yescharacteristic
40C2×C3×#214C2211yescharacteristic
41C2×C3×#213C2211yescharacteristic
42C3×#930C2211yescharacteristic
43C3×D3×SD16—24no—
44C3×#911—24no—
45C2×C3×#204C2211yescharacteristic
46C2×C3×#204C2211yescharacteristic
47C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
48C2×C3×D3×C8C2211yescharacteristic
49C3×#895C2211yescharacteristic
50C3×#892C2211yescharacteristic
51C3×#885—21no—
52C3×#882—21no—
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C32×C22⋊C8C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
61C3×#816C2211yescharacteristic, complemented
62C3×#816C2211yescharacteristic, complemented
63C3×#810C2211yescharacteristic, complemented
64C3×#810C2211yescharacteristic, complemented
65C2×C3×2−1+4—31no—
66C2×#1010C2×C311yescharacteristic, complemented
67C2×C3×AGL(1,ℤ/8)—31no—
68C22×C3×SD16—31no—
69C3×#535—31no—
70C2×D3×SD16C2×C311yescharacteristic, complemented
71C2×#911C2×C311yescharacteristic, complemented
72#5607C2×C311yescharacteristic, complemented
73C3×#449—21no—
74C3×#449—31no—
75C3×#449—31no—
76C3×#449—31no—
77C3×#449D311yescharacteristic, complemented
78C3×#449C2×C311yescharacteristic, complemented
79C3×#448—31no—
80C3×#448—31no—
81C3×#448—31no—
82C3×#448—31no—
83C3×#419—31no—
84C3×#416—31no—
85C3×#408—31no—
86#5238C2×C311yescharacteristic, complemented
87#5170C2×C311yescharacteristic, complemented
88#5158C2×C311yescharacteristic, complemented
89#5040C2×C311yescharacteristic, complemented
90#4806C2×C311yescharacteristic, complemented
91#4802C2×C311yescharacteristic, complemented
92#4781C2×C311yescharacteristic, complemented
93#4772C2×C311yescharacteristic, complemented
94#4738C2×C311yescharacteristic, complemented
95#4727C2×C311yescharacteristic, complemented
96C23×C3×D3—21no—
97C32×#41—22no—
98C32×#41—22no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4C2311yescharacteristic
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67D411yescharacteristic
112C2×C3×#67D411yescharacteristic
113C22×C3×Dic3—21no—
114C22×C3×Dic3—21no—
115C22×C3×Dic3—21no—
116C3×D3×Q8—22no—
117C3×D3×Q8—22no—
118C3×D3×Q8—22no—
119C3×D3×Q8D414yescomplemented
120C3×#237—28no—
121C3×#237—28no—
122C3×#237—22no—
123C3×#237—22no—
124C3×#237—22no—
125C3×#237D414yescomplemented
126C3×D3×D4—22no—
127C3×D3×D4—22no—
128C3×#235—28no—
129C3×#235—22no—
130C3×#235—22no—
131C2×C3×D12—21no—
132C2×C3×D12D411yescharacteristic
133C2×C3×D12C2311yescharacteristic
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6—28no—
139C2×C3×Dic6—21no—
140C2×C3×Dic6—21no—
141C2×C3×Dic6—21no—
142C2×C3×Dic6—22no—
143C2×C3×Dic6—22no—
144C2×C3×Dic6D411yescharacteristic
145C2×C3×Dic6C2311yescharacteristic
146C2×C3×Dic6C2311yescharacteristic
147C32×SD16—22no—
148C32×D8—22no—
149C2×C32×C8C2311yescharacteristic
150C2×C32×C8C2311yescharacteristic
151C32×C4⋊C4C2311yescharacteristic
152C32×C22⋊C4—21no—
153C3×#217—21no—
154C3×#215—22no—
155C3×#214—22no—
156C3×#214—22no—
157C3×#213—22no—
158C3×(C2×D3)⋊C4—21no—
159C3×(C2×D3)⋊C4—21no—
160C3×(C2×D3)⋊C4—21no—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4×Dic3—21no—
163C2×C3×C3⋊C8C2311yescharacteristic
164C2×C3×C3⋊C8C2311yescharacteristic
165C3×#204—22no—
166C3×#204—22no—
167C3×ΓL(1,𝔽25)—22no—
168C3×D3×C8—22no—
169#3010—31noSylow
170C3×2−1+4—64no—
171C3×2−1+4—64no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C2×C3×#41C2×D311yescharacteristic, complemented
180C2×C3×#41C22×C311yescharacteristic, complemented
181C22×C3×Q8—31no—
182C22×C3×Q8—31no—
183C22×C3×Q8—31no—
184C22×C3×Q8—61no—
185C22×C3×D4—31no—
186#1010—24no—
187#1010—24no—
188C2×D3×Q8C22×C311yescharacteristic
189C2×D3×Q8C22×C311yescharacteristic, complemented
190C2×#237—21no—
191C2×#237—21no—
192C2×#237C22×C311yescharacteristic
193C2×#237C22×C311yescharacteristic, complemented
194C2×D3×D4C22×C311yescharacteristic
195C2×#235—21no—
196C2×#235C22×C311yescharacteristic
197C22×Dic6—21no—
198C22×Dic6C22×C311yescharacteristic, complemented
199C3×AGL(1,ℤ/8)—64no—
200C2×C3×SD16—21no—
201C2×C3×SD16—31no—
202C2×C3×SD16—31no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16—64no—
207C2×C3×SD16C2×D311yescharacteristic
208C2×C3×SD16C22×C311yescharacteristic
209C2×C3×D8—21no—
210C2×C3×D8—31no—
211C2×C3×D8C2×D311yescharacteristic
212C2×C3×D8C22×C311yescharacteristic
213C2×C3×M16—31no—
214C22×C3×C8—31no—
215C3×#127—61no—
216C3×#124—61no—
217C3×#121—21no—
218C3×#121—31no—
219C3×#121—31no—
220C3×#121—31no—
221C3×#121C2×D311yescharacteristic
222C3×#121C22×C311yescharacteristic
223C3×#120—61no—
224C3×#120—61no—
225C3×#117—31no—
226C2×#215C22×C311yescharacteristic
227#940—21no—
228#938C22×C311yescharacteristic
229#937—21no—
230C2×#214C22×C311yescharacteristic
231C2×#214C22×C311yescharacteristic
232C2×#213C22×C311yescharacteristic
233#930C22×C311yescharacteristic
234D3×SD16—24no—
235#911—24no—
236C2×#204C22×C311yescharacteristic
237C2×#204C22×C311yescharacteristic
238C2×ΓL(1,𝔽25)C22×C311yescharacteristic
239C2×D3×C8C22×C311yescharacteristic
240#895C22×C311yescharacteristic
241#892C22×C311yescharacteristic
242#885—21no—
243#882—21no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103—31no—
249C3×#103—31no—
250C3×#103C2×D311yescharacteristic, complemented
251C3×#103C22×C311yescharacteristic, complemented
252C3×#102—21no—
253C3×#102—31no—
254C3×#102C2×D311yescharacteristic, complemented
255C3×#102C22×C311yescharacteristic, complemented
256C3×C22⋊C8—21no—
257C3×C22⋊C8—31no—
258C3×C22⋊C8—31no—
259C3×C22⋊C8—31no—
260C3×C22⋊C8C2×D311yescharacteristic, complemented
261C3×C22⋊C8C22×C311yescharacteristic, complemented
262#835C22×C311yescharacteristic, complemented
263#832C22×C311yescharacteristic, complemented
264#830C22×C311yescharacteristic, complemented
265(C2×D3)⋊C8C22×C311yescharacteristic, complemented
266(C2×D3)⋊C8C22×C311yescharacteristic, complemented
267#816C22×C311yescharacteristic, complemented
268#816C22×C311yescharacteristic, complemented
269#810C22×C311yescharacteristic, complemented
270#810C22×C311yescharacteristic, complemented
271C23×C32—21no—
272C23×C32—21no—
273C23×C32C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—42no—
276C22×C3×D3—81no—
277C22×C3×D3—81no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C32×Q8—21no—
281C32×Q8C2×D412yes—
282C32×D4—24no—
283C32×D4—21no—
284C32×D4—21no—
285C32×D4—21no—
286C32×D4—81no—
287C32×D4C2×D412yes—
288C2×C32×C4—24no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2×D411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295C3×#67—24no—
296C3×#67—22no—
297C3×#67—24no—
298C3×#67—22no—
299C3×#67—42no—
300C3×#67—81no—
301C3×#67—81no—
302C2×C3×Dic3—24no—
303C2×C3×Dic3—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—24no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—22no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—81no—
314C3×C4×D3—24no—
315C3×C4×D3—24no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—24no—
321C3×Dic6—24no—
322C3×Dic6—21no—
323C3×Dic6—21no—
324C3×Dic6—22no—
325C3×Dic6—24no—
326C3×Dic6C2×D412yes—
327C3×Dic6C2×D412yes—
328C32×C8—21no—
329C32×C8—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C2×2−1+4—31no—
333C2×AGL(1,ℤ/8)—31no—
334C22×SD16—31no—
335#535—31no—
336#449—31no—
337#449—31no—
338#449—31no—
339#449C3×D311yescharacteristic, complemented
340#448—31no—
341#448—31no—
342#448—31no—
343#448—31no—
344#419—31no—
345#416—31no—
346#408—31no—
347C24×C3—61no—
348C23×D3—21no—
349C3×#41—22no—
350C3×#41—22no—
351C3×#41—22no—
352C3×#41—22no—
353C3×#41—34no—
354C3×#41—42no—
355C3×#41—42no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—68no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—68no—
362C3×#41—68no—
363C3×#41—62no—
364C2×C3×Q8—21no—
365C2×C3×Q8—31no—
366C2×C3×Q8—34no—
367C2×C3×Q8—31no—
368C2×C3×Q8—31no—
369C2×C3×Q8—61no—
370C2×C3×Q8—61no—
371C2×C3×Q8—62no—
372C2×C3×Q8—62no—
373C2×C3×Q8—68no—
374C2×C3×Q8—62no—
375C2×C3×Q8—62no—
376C2×C3×Q8—62no—
377C2×C3×Q8—61no—
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×Q8C23×C311yescharacteristic
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—21no—
384C2×C3×D4—21no—
385C2×C3×D4—21no—
386C2×C3×D4—31no—
387C2×C3×D4—31no—
388C2×C3×D4—31no—
389C2×C3×D4—31no—
390C2×C3×D4—41no—
391C2×C3×D4—41no—
392C2×C3×D4—61no—
393C2×C3×D4—62no—
394C2×C3×D4—62no—
395C2×C3×D4—61no—
396C2×C3×D4—61no—
397C2×C3×D4—61no—
398C2×C3×D4—61no—
399C2×C3×D4—61no—
400C2×C3×D4C22×D311yescharacteristic
401C2×C3×D4C22×D311yescharacteristic
402C2×C3×D4C23×C311yescharacteristic
403C2×C3×D4C23×C311yescharacteristic
404C22×C3×C4—21no—
405C22×C3×C4—21no—
406C22×C3×C4—21no—
407C22×C3×C4—31no—
408C22×C3×C4—31no—
409C22×C3×C4—41no—
410C22×C3×C4—61no—
411C22×C3×C4—61no—
412C22×C3×C4—61no—
413C22×C3×C4—61no—
414C22×C3×C4—61no—
415C22×C3×C4C22×D311yescharacteristic
416C22×C3×C4C23×C311yescharacteristic
417C2×#67—21no—
418C2×#67—21no—
419C2×#67—21no—
420C2×#67—21no—
421C2×#67—21no—
422C2×#67C3×D411yescharacteristic
423C2×#67C3×D411yescharacteristic
424C22×Dic3—21no—
425C22×Dic3—21no—
426C22×Dic3—21no—
427D3×Q8—22no—
428D3×Q8—22no—
429D3×Q8—22no—
430D3×Q8C3×D414yescomplemented
431#237—28no—
432#237—28no—
433#237—22no—
434#237—22no—
435#237—22no—
436#237C3×D414yescomplemented
437D3×D4—22no—
438D3×D4—22no—
439#235—28no—
440#235—22no—
441#235—22no—
442C2×D12—21no—
443C2×D12C3×D411yescharacteristic
444C2×D12C23×C311yescharacteristic
445C2×C4×D3—21no—
446C2×C4×D3—21no—
447C2×C4×D3C23×C311yescharacteristic
448C2×C4×D3C23×C311yescharacteristic
449C2×Dic6—28no—
450C2×Dic6—21no—
451C2×Dic6—21no—
452C2×Dic6—21no—
453C2×Dic6—22no—
454C2×Dic6—22no—
455C2×Dic6C3×D411yescharacteristic
456C2×Dic6C23×C311yescharacteristic
457C2×Dic6C23×C311yescharacteristic
458C3×SD16—22no—
459C3×SD16—22no—
460C3×SD16—42no—
461C3×SD16—62no—
462C3×SD16—62no—
463C3×SD16—62no—
464C3×SD16—62no—
465C3×SD16—62no—
466C3×D8—22no—
467C3×D8—22no—
468C3×D8—42no—
469C3×D8—62no—
470C3×M16—62no—
471C2×C3×C8—21no—
472C2×C3×C8—21no—
473C2×C3×C8—31no—
474C2×C3×C8—31no—
475C2×C3×C8—62no—
476C2×C3×C8C22×D311yescharacteristic
477C2×C3×C8C22×D311yescharacteristic
478C2×C3×C8C23×C311yescharacteristic
479C2×C3×C8C23×C311yescharacteristic
480C3×C4⋊C4—21no—
481C3×C4⋊C4—31no—
482C3×C4⋊C4C22×D311yescharacteristic
483C3×C4⋊C4C23×C311yescharacteristic
484C3×C22⋊C4—21no—
485C3×C22⋊C4—21no—
486C3×C22⋊C4—41no—
487C3×C22⋊C4—61no—
488C3×C22⋊C4—61no—
489C3×C22⋊C4—61no—
490C3×C22⋊C4—61no—
491C3×C42—61no—
492#217—21no—
493#215—22no—
494#214—22no—
495#214—22no—
496#213—22no—
497(C2×D3)⋊C4—21no—
498(C2×D3)⋊C4—21no—
499(C2×D3)⋊C4—21no—
500C4⋊Dic3C23×C311yescharacteristic
501C4×Dic3—21no—
502C2×C3⋊C8C23×C311yescharacteristic
503C2×C3⋊C8C23×C311yescharacteristic
504#204—22no—
505#204—22no—
506ΓL(1,𝔽25)—22no—
507D3×C8—22no—
508C22×C32—21no—
509C22×C32—22no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—41no—
513C22×C32—41no—
514C22×C32—41no—
515C22×C32—41no—
516C22×C32—41no—
517C22×C32C22×D411yescharacteristic
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—84no—
527C2×C3×D3#12012yes—
528C32×C4—21no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3×Dic3—21no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3#12012yes—
5382−1+4—64no—
5392−1+4—64no—
540C2×#41—31no—
541C2×#41—31no—
542C2×#41—31no—
543C2×#41—61no—
544C2×#41—61no—
545C2×#41—61no—
546C2×#41C2×C3×D311yescharacteristic, complemented
547C22×Q8—31no—
548C22×Q8—31no—
549C22×Q8—31no—
550C22×Q8—61no—
551C22×D4—31no—
552AGL(1,ℤ/8)—64no—
553C2×SD16—31no—
554C2×SD16—31no—
555C2×SD16—31no—
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—64no—
559C2×SD16C2×C3×D311yescharacteristic
560C2×D8—31no—
561C2×D8C2×C3×D311yescharacteristic
562C2×M16—31no—
563C22×C8—31no—
564#127—61no—
565#124—61no—
566#121—31no—
567#121—31no—
568#121—31no—
569#121C2×C3×D311yescharacteristic
570#120—61no—
571#120—61no—
572#117—31no—
573#103—31no—
574#103—31no—
575#103—31no—
576#103—31no—
577#103—31no—
578#103C2×C3×D311yescharacteristic, complemented
579#102—31no—
580#102C2×C3×D311yescharacteristic, complemented
581C22⋊C8—31no—
582C22⋊C8—31no—
583C22⋊C8—31no—
584C22⋊C8C2×C3×D311yescharacteristic, complemented
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—31no—
591C23×C3—31no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—61no—
595C23×C3—122no—
596C23×C3—241no—
597C23×C3—241no—
598C23×C3D3×D411yescharacteristic
599C23×C3C2×C3×D411yescharacteristic
600C22×D3—21no—
601C22×D3—42no—
602C22×D3—81no—
603C22×D3—81no—
604C22×D3C2×C3×D411yescharacteristic
605C22×D3C2×C3×D411yescharacteristic
606C3×Q8—21no—
607C3×Q8—21no—
608C3×Q8—22no—
609C3×Q8—32no—
610C3×Q8—32no—
611C3×Q8—41no—
612C3×Q8—62no—
613C3×Q8—64no—
614C3×Q8—64no—
615C3×Q8—64no—
616C3×Q8—61no—
617C3×Q8—61no—
618C3×Q8D3×D412yes—
619C3×Q8C2×C3×D412yes—
620C3×D4—24no—
621C3×D4—24no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—22no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—44no—
633C3×D4—62no—
634C3×D4—62no—
635C3×D4—62no—
636C3×D4—64no—
637C3×D4—64no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—81no—
641C3×D4—81no—
642C3×D4—82no—
643C3×D4—122no—
644C3×D4—241no—
645C3×D4—241no—
646C3×D4—241no—
647C3×D4D3×D412yes—
648C3×D4C2×C3×D412yes—
649C2×C3×C4—24no—
650C2×C3×C4—24no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—31no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—31no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—44no—
669C2×C3×C4—41no—
670C2×C3×C4—64no—
671C2×C3×C4—64no—
672C2×C3×C4—64no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4D3×D411yescharacteristic
681C2×C3×C4C2×C3×D411yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C24×C311yescharacteristic
684#67—24no—
685#67—22no—
686#67—24no—
687#67—22no—
688#67—42no—
689#67—81no—
690#67—81no—
691C2×Dic3—24no—
692C2×Dic3—24no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—24no—
696C2×Dic3—21no—
697C2×Dic3C2×C3×D411yescharacteristic
698C2×Dic3C2×C3×D411yescharacteristic
699D12—22no—
700D12—21no—
701D12—21no—
702D12—81no—
703C4×D3—24no—
704C4×D3—24no—
705C4×D3—21no—
706C4×D3—21no—
707C4×D3C2×C3×D412yes—
708C4×D3C2×C3×D412yes—
709Dic6—24no—
710Dic6—24no—
711Dic6—21no—
712Dic6—21no—
713Dic6—22no—
714Dic6—24no—
715Dic6C2×C3×D412yes—
716Dic6C2×C3×D412yes—
717C3×C8—21no—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—21no—
721C3×C8—41no—
722C3×C8—41no—
723C3×C8—61no—
724C3×C8—61no—
725C3⋊C8—21no—
726C3⋊C8—21no—
727C2×C32—41no—
728C2×C32—42no—
729C2×C32—81no—
730C2×C32C2×#12011yescharacteristic
731C2×C32#57711yescharacteristic
732C2×C32#57711yescharacteristic
733C3×D3—22no—
734C3×D3—41no—
735C3×D3—81no—
736C24—61no—
737#41—22no—
738#41—22no—
739#41—34no—
740#41—62no—
741#41—62no—
742#41—68no—
743#41—62no—
744#41—62no—
745#41—68no—
746#41—68no—
747#41—62no—
748C2×Q8—31no—
749C2×Q8—34no—
750C2×Q8—31no—
751C2×Q8—31no—
752C2×Q8—61no—
753C2×Q8—61no—
754C2×Q8—62no—
755C2×Q8—62no—
756C2×Q8—68no—
757C2×Q8—62no—
758C2×Q8—62no—
759C2×Q8—62no—
760C2×Q8—61no—
761C2×Q8C22×C3×D311yescharacteristic
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—31no—
765C2×D4—31no—
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—61no—
769C2×D4—62no—
770C2×D4—62no—
771C2×D4—61no—
772C2×D4—61no—
773C2×D4—61no—
774C2×D4—61no—
775C2×D4—61no—
776C2×D4C22×C3×D311yescharacteristic
777C2×D4C22×C3×D311yescharacteristic
778C22×C4—21no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4C22×C3×D311yescharacteristic
787SD16—22no—
788SD16—62no—
789SD16—62no—
790SD16—62no—
791SD16—62no—
792SD16—62no—
793D8—22no—
794D8—62no—
795M16—62no—
796C2×C8—31no—
797C2×C8—31no—
798C2×C8—62no—
799C2×C8C22×C3×D311yescharacteristic
800C2×C8C22×C3×D311yescharacteristic
801C4⋊C4—31no—
802C4⋊C4C22×C3×D311yescharacteristic
803C22⋊C4—21no—
804C22⋊C4—61no—
805C22⋊C4—61no—
806C22⋊C4—61no—
807C22⋊C4—61no—
808C42—61no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—22no—
815C22×C3—21no—
816C22×C3—22no—
817C22×C3—21no—
818C22×C3—32no—
819C22×C3—42no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—61no—
834C22×C3—61no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—61no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—81no—
842C22×C3—81no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—244no—
847C22×C3C2×D3×D411yescharacteristic
848C22×C3C22×C3×D411yescharacteristic
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—21no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—84no—
858C2×D3C3×#12012yes—
859C3×C4—21no—
860C3×C4—22no—
861C3×C4—21no—
862C3×C4—22no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—32no—
866C3×C4—41no—
867C3×C4—42no—
868C3×C4—41no—
869C3×C4—41no—
870C3×C4—61no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4—81no—
874C3×C4—121no—
875C3×C4C2×D3×D411yescharacteristic
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C22×C3×D411yescharacteristic
878C3×C4C22×C3×D411yescharacteristic
879Dic3—21no—
880Dic3—22no—
881Dic3—22no—
882Dic3—41no—
883Dic3C3×#12012yes—
884C32#301011yescharacteristic, complemented, Sylow
885C23—21no—
886C23—21no—
887C23—31no—
888C23—31no—
889C23—61no—
890C23—122no—
891C23—241no—
892C23—241no—
893C23C3×D3×D411yescharacteristic
894Q8—21no—
895Q8—32no—
896Q8—32no—
897Q8—62no—
898Q8—64no—
899Q8—64no—
900Q8—64no—
901Q8—61no—
902Q8—61no—
903Q8C3×D3×D412yes—
904D4—24no—
905D4—21no—
906D4—21no—
907D4—21no—
908D4—62no—
909D4—62no—
910D4—62no—
911D4—64no—
912D4—64no—
913D4—61no—
914D4—61no—
915D4—81no—
916D4—122no—
917D4—241no—
918D4—241no—
919D4—241no—
920D4C3×D3×D412yes—
921C2×C4—24no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—31no—
927C2×C4—32no—
928C2×C4—32no—
929C2×C4—31no—
930C2×C4—64no—
931C2×C4—64no—
932C2×C4—64no—
933C2×C4—64no—
934C2×C4—64no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4C3×D3×D411yescharacteristic
941C2×C4C23×C3×D311yescharacteristic
942C8—21no—
943C8—21no—
944C8—61no—
945C8—61no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—41no—
950C2×C3—42no—
951C2×C3—41no—
952C2×C3—42no—
953C2×C3—62no—
954C2×C3—81no—
955C2×C3—82no—
956C2×C3—81no—
957C2×C3—81no—
958C2×C3—121no—
959C2×C3—161no—
960C2×C3—241no—
961C2×C3D3×#12011yescharacteristic
962C2×C3#577011yescharacteristic
963C2×C3#577511yescharacteristic
964C2×C3C2×C3×#12011yescharacteristic
965C2×C3C3×#57711yescharacteristic
966C2×C3C3×#57711yescharacteristic
967D3—22no—
968D3—41no—
969D3—81no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—22no—
974C22—32no—
975C22—41no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—61no—
981C22—61no—
982C22—61no—
983C22—61no—
984C22—61no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—244no—
989C22C2×C3×D3×D411yescharacteristic
990C4—21no—
991C4—22no—
992C4—32no—
993C4—41no—
994C4—61no—
995C4—62no—
996C4—62no—
997C4—121no—
998C4C2×C3×D3×D411yescharacteristic
999C4C2×C3×D3×D411yescharacteristic
1000C3—21no—
1001C3#8008611yescharacteristic, direct product factor
1002C3C3×#301011yescharacteristic, complemented
1003C2—41no—
1004C2—42no—
1005C2—62no—
1006C2—81no—
1007C2—121no—
1008C2—241no—
1009C2C3×D3×#12011yescharacteristic
1010C2C3×#577011yescharacteristic
1011C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3010
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. C2×C3×#911C2semidirect
4. C3×#5607C2semidirect
5. C32×#449C2semidirect
6. C3×#5238C2semidirect
7. C3×#5170C2semidirect
8. C3×#5158C2semidirect
9. C3×#5040C2semidirect
10. C3×#4806C2semidirect
11. C3×#4802C2semidirect
12. C3×#4781C2semidirect
13. C3×#4772C2semidirect
14. C3×#4738C2semidirect
15. C3×#4727C2semidirect
17. #80086C3direct (N × H)
18. C2×C32×#41C22semidirect
22. C2×C3×D3×Q8C22semidirect
26. C2×C3×#237C22semidirect
31. C22×C3×Dic6C22semidirect
53. C32×#103C22semidirect
54. C32×#102C22semidirect
55. C32×C22⋊C8C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. C3×(C2×D3)⋊C8C22semidirect
60. C3×(C2×D3)⋊C8C22semidirect
61. C3×#816C22semidirect
62. C3×#816C22semidirect
63. C3×#810C22semidirect
64. C3×#810C22semidirect
66. C2×#1010C2×C3semidirect
70. C2×D3×SD16C2×C3semidirect
71. C2×#911C2×C3semidirect
72. #5607C2×C3semidirect
77. C3×#449D3semidirect
78. C3×#449C2×C3semidirect
86. #5238C2×C3semidirect
87. #5170C2×C3semidirect
88. #5158C2×C3semidirect
89. #5040C2×C3semidirect
90. #4806C2×C3semidirect
91. #4802C2×C3semidirect
92. #4781C2×C3semidirect
93. #4772C2×C3semidirect
94. #4738C2×C3semidirect
95. #4727C2×C3semidirect
119. C3×D3×Q8D4semidirect
125. C3×#237D4semidirect
179. C2×C3×#41C2×D3semidirect
180. C2×C3×#41C22×C3semidirect
189. C2×D3×Q8C22×C3semidirect
193. C2×#237C22×C3semidirect
198. C22×Dic6C22×C3semidirect
250. C3×#103C2×D3semidirect
251. C3×#103C22×C3semidirect
254. C3×#102C2×D3semidirect
255. C3×#102C22×C3semidirect
260. C3×C22⋊C8C2×D3semidirect
261. C3×C22⋊C8C22×C3semidirect
262. #835C22×C3semidirect
263. #832C22×C3semidirect
264. #830C22×C3semidirect
265. (C2×D3)⋊C8C22×C3semidirect
266. (C2×D3)⋊C8C22×C3semidirect
267. #816C22×C3semidirect
268. #816C22×C3semidirect
269. #810C22×C3semidirect
270. #810C22×C3semidirect
339. #449C3×D3semidirect
430. D3×Q8C3×D4semidirect
436. #237C3×D4semidirect
546. C2×#41C2×C3×D3semidirect
578. #103C2×C3×D3semidirect
580. #102C2×C3×D3semidirect
584. C22⋊C8C2×C3×D3semidirect
884. C32#3010semidirect
1001. C3#80086direct (N × H)
1002. C3C3×#3010semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×D3×SD162
C2×C3×#9112
C3×#56072
C32×#4492
C3×#52382
C3×#51702
C3×#51582
C3×#50402
C3×#48062
C3×#48022
C3×#47812
C3×#47722
C3×#47382
C3×#47272
C3×#30103
#800863