Finite Group Databasebeta

← C2×C3×#10590397 #72269499

Subgroups — C2×C3×#10590397 #72269499

Order 3456.

4322 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#64308C211yesmaximal, characteristic, complemented
2C2×C3×#64083C211yesmaximal, characteristic, complemented
3C2×C3×#63825C212yesmaximal, complemented
4C2×C32×#805C212yesmaximal, complemented
5C2×C3×#63559C211yesmaximal, characteristic, complemented
6C3×#10590397C218yesmaximal, direct product factor
7C2×#10590397C311yesmaximal, characteristic, direct product factor
8C2×C3×#4822—32nomaximal
9C22×C3×C4⋊(C3⋊D3)—22no—
10C22×C3×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
12C2×C32×#235C2212yes—
13C2×C3×#3811—22no—
14C3×#64308—22no—
15C3×#64308—24no—
16C3×#64308C2214yescomplemented
17C2×C3×D3×D12—22no—
18C2×C3×#3799—22no—
19C2×C33×C42C2211yescharacteristic, complemented
20C3×#64083—22no—
21C3×#64083C2214yescomplemented
22C2×C32×#208C2212yescomplemented
23C2×C3×#3717—22no—
24C3×#63825—24no—
25C3×#63825C2218yescomplemented
26C2×C3×#3714—22no—
27C32×#805C2218yescomplemented
28C3×#63559C2214yescomplemented
29C2×C3×#1009—32no—
30C2×#64308C2×C311yescharacteristic, complemented
31C2×#64083C2×C311yescharacteristic, complemented
32C2×C3×#949—32no—
33C2×C3×#908—32no—
34C2×C3×#874—32no—
35C2×C3×#874—61no—
36C2×#63825C2×C312yescomplemented
37C2×C32×#104—32no—
38C2×C3×#823—32no—
39C2×C3×#805—22no—
40C2×C3×#805D312yescomplemented
41C2×C3×#805C2×C312yescomplemented
42C3×#4822—316no—
43C2×#63559C2×C311yescharacteristic, complemented
44#10590397C2×C318yesdirect product factor
45C23×C3×C3⋊D3—21no—
46C23×C3×C3⋊D3D412yes—
47C22×C3×D32—22no—
48C22×C33×C4—21no—
49C22×C33×C4C2311yescharacteristic
50C2×C3×C4⋊(C3⋊D3)—22no—
51C2×C3×C4⋊(C3⋊D3)—22no—
52C2×C3×C4⋊(C3⋊D3)—22no—
53C2×C3×C4⋊(C3⋊D3)—22no—
54C2×C3×C4⋊(C3⋊D3)—28no—
55C2×C3×C4⋊(C3⋊D3)—21no—
56C2×C3×C4⋊(C3⋊D3)—48no—
57C2×C3×C4⋊(C3⋊D3)D412yes—
58C2×C3×C4⋊(C3⋊D3)C2312yes—
59C2×C3×C4⋊(C3⋊D3)C2312yescomplemented
60C2×C32×#67—22no—
61C32×#235—22no—
62C32×#235—22no—
63C32×#235D414yescomplemented
64C32×#235C2314yes—
65C2×C32×D12D412yescomplemented
66C2×C32×C4×D3—22no—
67C2×C32×Dic6D412yescomplemented
68C3×#3811—28no—
69C3×#3811—28no—
70C2×C3×#626—24no—
71C2×C3×#624—22no—
72C3×D3×D12—28no—
73C3×D3×D12—28no—
74C3×#3799—28no—
75C3×#3799—28no—
76C33×C42—21no—
77C33×C42C2312yescomplemented
78C32×#208—22no—
79C32×#208C2314yescomplemented
80C2×C32×C3⋊C8—22no—
81C3×#3717—28no—
82C3×#3714—28no—
83C2×C3×#453—91no—
84C2×#4822—32no—
85C2×C32×#41—32no—
86C22×C4⋊(C3⋊D3)—22no—
87C22×C4⋊(C3⋊D3)C22×C311yescharacteristic
88C22×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
89C3×#1009—38no—
90C3×#1009—64no—
91C3×#1009—64no—
92C3×#1009—64no—
93C2×C3×#239—62no—
94C2×C3×D3×D4—64no—
95C2×C3×D3×D4—62no—
96C2×C3×#235—22no—
97C2×C3×#235—62no—
98C2×C3×#235C2×D312yes—
99C2×C3×#235C22×C312yes—
100C22×C3×D12—32no—
101C22×C3×D12—32no—
102C22×C3×D12—64no—
103C22×C3×D12—62no—
104C22×C3×D12—61no—
105C22×C3×D12—61no—
106C22×C3×D12—64no—
107C2×#3811—22no—
108#64308—22no—
109#64308—24no—
110#64308C22×C314yescomplemented
111C2×D3×D12—22no—
112C2×#3799—22no—
113C2×C32×M16—32no—
114C2×C32×C42—21no—
115C2×C32×C42—22no—
116C2×C32×C42—41no—
117C2×C32×C42C2×D312yescomplemented
118C2×C32×C42C22×C311yescharacteristic, complemented
119#64083—22no—
120#64083C22×C314yescomplemented
121C3×#949—38no—
122C3×#949—64no—
123C2×C3×#215—62no—
124C2×C3×#213—62no—
125C2×C3×#208—22no—
126C2×C3×#208C2×D312yescomplemented
127C2×C3×#208C22×C312yescomplemented
128C3×#908—38no—
129C3×#908—64no—
130C2×C3×D24—62no—
131C2×C3×#204—62no—
132C3×#874—38no—
133C3×#874—64no—
134C3×#874—64no—
135C3×#874—64no—
136C2×#3717—22no—
137#63825—24no—
138#63825C22×C318yescomplemented
139C2×#3714—22no—
140C32×#104—38no—
141C3×#823—38no—
142C3×#805—28no—
143C3×#805C2×D318yescomplemented
144C3×#805C22×C318yescomplemented
145#63559C22×C314yescomplemented
146C23×C33C2×D411yescharacteristic
147C22×C3×C3⋊D3—22no—
148C22×C3×C3⋊D3—22no—
149C22×C3×C3⋊D3—22no—
150C22×C3×C3⋊D3—44no—
151C22×C3×C3⋊D3—44no—
152C22×C3×C3⋊D3—41no—
153C22×C3×C3⋊D3—41no—
154C22×C3×C3⋊D3C2×D414yes—
155C22×C32×D3—22no—
156C2×C3×D32—28no—
157C2×C3×D32—84no—
158C2×C33×C4—24no—
159C2×C33×C4—22no—
160C2×C33×C4C2×D411yescharacteristic
161C2×C33×C4C2×D412yes—
162C2×C33×C4C2×D412yes—
163C2×C33×C4C2411yescharacteristic
164C3×C4⋊(C3⋊D3)—24no—
165C3×C4⋊(C3⋊D3)—24no—
166C3×C4⋊(C3⋊D3)—24no—
167C3×C4⋊(C3⋊D3)—416no—
168C3×C4⋊(C3⋊D3)—42no—
169C32×#67—24no—
170C32×#67—24no—
171C2×C32×Dic3—22no—
172C32×D12—22no—
173C32×D12C2×D414yescomplemented
174C32×C4×D3—24no—
175C32×C4×D3—24no—
176C32×Dic6—22no—
177C32×Dic6C2×D414yescomplemented
178C3×#626—216no—
179C3×#624—28no—
180C32×C3⋊C8—24no—
181C2×C3×H(5,𝔽2)—91no—
182C2×#1009—32no—
183C2×C3×AGL(1,ℤ/8)—92no—
184C2×C3×#127—91no—
185C2×#949—32no—
186C2×#908—32no—
187C2×#874—32no—
188C2×#874—61no—
189C3×#453—98no—
190C2×C3×#104—32no—
191C2×C3×#104—32no—
192C2×C3×#104—62no—
193C2×C3×#100—91no—
194C2×#823—32no—
195C2×#805C3×D312yescomplemented
196#4822—316no—
197C23×C3⋊D3—21no—
198C23×C3⋊D3C3×D412yes—
199C23×C3×D3—34no—
200C23×C3×D3—64no—
201C23×C3×D3—62no—
202C23×C3×D3—62no—
203C23×C3×D3—62no—
204C22×D32—22no—
205C32×#41—34no—
206C32×#41—34no—
207C32×#41—62no—
208C32×#41—62no—
209C2×C32×Q8—32no—
210C2×C32×D4—32no—
211C2×C32×D4—62no—
212C22×C32×C4—22no—
213C22×C32×C4—21no—
214C22×C32×C4—22no—
215C22×C32×C4—22no—
216C22×C32×C4—21no—
217C22×C32×C4—42no—
218C22×C32×C4—41no—
219C22×C32×C4—42no—
220C22×C32×C4—62no—
221C22×C32×C4C22×D312yes—
222C22×C32×C4C23×C311yescharacteristic
223C2×C4⋊(C3⋊D3)—22no—
224C2×C4⋊(C3⋊D3)—22no—
225C2×C4⋊(C3⋊D3)—22no—
226C2×C4⋊(C3⋊D3)—22no—
227C2×C4⋊(C3⋊D3)—28no—
228C2×C4⋊(C3⋊D3)—21no—
229C2×C4⋊(C3⋊D3)—48no—
230C2×C4⋊(C3⋊D3)C3×D412yes—
231C2×C4⋊(C3⋊D3)C23×C312yes—
232C2×C4⋊(C3⋊D3)C23×C312yescomplemented
233C2×C3×#67—22no—
234C2×C3×#67—22no—
235C2×C3×#67—42no—
236C2×C3×#67—64no—
237C3×#239—68no—
238C3×#239—68no—
239C3×D3×D4—68no—
240C3×D3×D4—68no—
241C3×D3×D4—616no—
242C3×D3×D4—616no—
243C3×#235—22no—
244C3×#235—22no—
245C3×#235—22no—
246C3×#235—22no—
247C3×#235—24no—
248C3×#235—24no—
249C3×#235—42no—
250C3×#235—42no—
251C3×#235—68no—
252C3×#235—68no—
253C3×#235D1214yescomplemented
254C3×#235C3×D414yescomplemented
255C3×#235C22×D314yes—
256C3×#235C23×C314yes—
257C2×C3×D12—22no—
258C2×C3×D12—34no—
259C2×C3×D12—34no—
260C2×C3×D12—34no—
261C2×C3×D12—68no—
262C2×C3×D12—64no—
263C2×C3×D12—62no—
264C2×C3×D12—62no—
265C2×C3×D12—62no—
266C2×C3×D12—62no—
267C2×C3×D12—68no—
268C2×C3×D12—62no—
269C2×C3×D12—62no—
270C2×C3×D12—62no—
271C2×C3×D12—62no—
272C2×C3×D12—616no—
273C2×C3×D12—62no—
274C2×C3×D12—62no—
275C2×C3×D12—62no—
276C2×C3×D12—616no—
277C2×C3×D12—62no—
278C2×C3×D12—62no—
279C2×C3×D12—122no—
280C2×C3×D12—122no—
281C2×C3×D12—122no—
282C2×C3×D12—122no—
283C2×C3×D12—1216no—
284C2×C3×D12—1216no—
285C2×C3×D12D1212yescomplemented
286C2×C3×D12C3×D412yescomplemented
287C2×C3×C4×D3—22no—
288C2×C3×C4×D3—22no—
289C2×C3×C4×D3—42no—
290C2×C3×C4×D3—64no—
291C2×C3×Dic6—22no—
292C2×C3×Dic6D1212yescomplemented
293C2×C3×Dic6C3×D412yescomplemented
294#3811—28no—
295#3811—28no—
296C2×#626—24no—
297C2×#624—22no—
298D3×D12—28no—
299D3×D12—28no—
300#3799—28no—
301#3799—28no—
302C32×M16—34no—
303C32×M16—62no—
304C2×C32×C8—62no—
305C32×C42—22no—
306C32×C42—22no—
307C32×C42—22no—
308C32×C42—21no—
309C32×C42—24no—
310C32×C42—42no—
311C32×C42—42no—
312C32×C42—42no—
313C32×C42C22×D314yescomplemented
314C32×C42C23×C312yescomplemented
315C3×#215—68no—
316C3×#213—68no—
317C3×#208—22no—
318C3×#208—22no—
319C3×#208—24no—
320C3×#208—42no—
321C3×#208C22×D314yescomplemented
322C3×#208C23×C314yescomplemented
323C2×C3×C3⋊C8—22no—
324C2×C3×C3⋊C8—22no—
325C2×C3×C3⋊C8—42no—
326C3×D24—68no—
327C3×#204—68no—
328#3717—28no—
329#3714—28no—
330C2×#453—91noSylow
331C22×C33—22no—
332C22×C33#12011yescharacteristic
333C22×C33#12011yescharacteristic
334C22×C33C22×D411yescharacteristic
335C2×C3×C3⋊D3—24no—
336C2×C3×C3⋊D3—44no—
337C2×C3×C3⋊D3—44no—
338C2×C3×C3⋊D3—44no—
339C2×C3×C3⋊D3—42no—
340C2×C3×C3⋊D3—82no—
341C2×C3×C3⋊D3—82no—
342C2×C3×C3⋊D3—82no—
343C2×C32×D3—24no—
344C2×C32×D3—44no—
345C3×D32—88no—
346C33×C4—24no—
347C33×C4#12012yes—
348C33×C4C22×D412yes—
349C32×Dic3—24no—
350C3×H(5,𝔽2)—94no—
351C3×H(5,𝔽2)—182no—
352C3×H(5,𝔽2)—184no—
353C2×C3×#41—32no—
354C2×C3×#41—32no—
355C2×C3×#41—62no—
356C2×C3×#41—182no—
357C22×C3×D4—91no—
358C22×C3×D4—91no—
359C22×C3×D4—182no—
360C22×C3×D4—182no—
361C22×C3×D4—182no—
362#1009—38no—
363#1009—64no—
364#1009—64no—
365#1009—64no—
366C2×#239—62no—
367C2×D3×D4—62no—
368C2×D3×D4—64no—
369C2×#235—62no—
370C2×#235C2×C3×D312yes—
371C22×D12—32no—
372C22×D12—32no—
373C22×D12—61no—
374C22×D12—61no—
375C22×D12—62no—
376C22×D12—64no—
377C22×D12—64no—
378C3×AGL(1,ℤ/8)—98no—
379C3×AGL(1,ℤ/8)—184no—
380C2×C3×SD16—182no—
381C2×C3×D8—182no—
382C2×C3×M16—32no—
383C2×C3×M16—32no—
384C2×C3×M16—62no—
385C3×#127—94no—
386C3×#127—182no—
387C2×C3×C42—21no—
388C2×C3×C42—22no—
389C2×C3×C42—41no—
390C2×C3×C42D3211yescharacteristic, complemented
391C2×C3×C42C2×C3×D312yescomplemented
392#949—38no—
393#949—64no—
394C2×#215—62no—
395C2×#213—62no—
396C2×#208C2×C3×D312yescomplemented
397#908—38no—
398#908—64no—
399C2×D24—62no—
400C2×#204—62no—
401#874—38no—
402#874—64no—
403#874—64no—
404#874—64no—
405C3×#104—38no—
406C3×#104—38no—
407C3×#104—68no—
408C3×#100—94no—
409#823—38no—
410#805C2×C3×D318yescomplemented
411C23×C32—21no—
412C23×C32—22no—
413C23×C32—41no—
414C23×C32—62no—
415C23×C32D3×D412yes—
416C23×C32C2×C3×D411yescharacteristic
417C22×C3⋊D3—22no—
418C22×C3⋊D3—22no—
419C22×C3⋊D3—22no—
420C22×C3⋊D3—44no—
421C22×C3⋊D3—44no—
422C22×C3⋊D3—41no—
423C22×C3⋊D3—41no—
424C22×C3⋊D3C2×C3×D414yes—
425C22×C3×D3—22no—
426C22×C3×D3—22no—
427C22×C3×D3—38no—
428C22×C3×D3—42no—
429C22×C3×D3—64no—
430C22×C3×D3—616no—
431C22×C3×D3—64no—
432C22×C3×D3—64no—
433C22×C3×D3—64no—
434C22×C3×D3—64no—
435C22×C3×D3—122no—
436C22×C3×D3—122no—
437C22×C3×D3—128no—
438C22×C3×D3—128no—
439C22×C3×D3—128no—
440C22×C3×D3—128no—
441C22×C3×D3—122no—
442C22×C3×D3—122no—
443C22×C3×D3—122no—
444C22×C3×D3—122no—
445C22×C3×D3—248no—
446C2×D32—28no—
447C2×D32—84no—
448C32×Q8—34no—
449C32×Q8—62no—
450C32×D4—34no—
451C32×D4—64no—
452C32×D4—64no—
453C32×D4—62no—
454C2×C32×C4—24no—
455C2×C32×C4—22no—
456C2×C32×C4—24no—
457C2×C32×C4—28no—
458C2×C32×C4—28no—
459C2×C32×C4—24no—
460C2×C32×C4—21no—
461C2×C32×C4—22no—
462C2×C32×C4—22no—
463C2×C32×C4—22no—
464C2×C32×C4—21no—
465C2×C32×C4—22no—
466C2×C32×C4—22no—
467C2×C32×C4—22no—
468C2×C32×C4—22no—
469C2×C32×C4—22no—
470C2×C32×C4—41no—
471C2×C32×C4—42no—
472C2×C32×C4—42no—
473C2×C32×C4—41no—
474C2×C32×C4—44no—
475C2×C32×C4—44no—
476C2×C32×C4—48no—
477C2×C32×C4—48no—
478C2×C32×C4—62no—
479C2×C32×C4—64no—
480C2×C32×C4—64no—
481C2×C32×C4C2×D1212yes—
482C2×C32×C4C2×D1212yes—
483C2×C32×C4D3×D412yes—
484C2×C32×C4D3×D412yes—
485C2×C32×C4D3×D412yes—
486C2×C32×C4C2×C3×D412yes—
487C2×C32×C4C2×C3×D412yes—
488C2×C32×C4C2×C3×D411yescharacteristic
489C2×C32×C4C23×D312yes—
490C2×C32×C4C24×C311yescharacteristic
491C4⋊(C3⋊D3)—24no—
492C4⋊(C3⋊D3)—24no—
493C4⋊(C3⋊D3)—24no—
494C4⋊(C3⋊D3)—416no—
495C4⋊(C3⋊D3)—42no—
496C3×#67—24no—
497C3×#67—24no—
498C3×#67—24no—
499C3×#67—24no—
500C3×#67—44no—
501C3×#67—44no—
502C3×#67—616no—
503C2×C3×Dic3—22no—
504C2×C3×Dic3—22no—
505C2×C3×Dic3—42no—
506C3×D12—22no—
507C3×D12—22no—
508C3×D12—24no—
509C3×D12—42no—
510C3×D12—616no—
511C3×D12—64no—
512C3×D12—64no—
513C3×D12—64no—
514C3×D12—64no—
515C3×D12—64no—
516C3×D12—64no—
517C3×D12—124no—
518C3×D12—124no—
519C3×D12—124no—
520C3×D12—1232no—
521C3×D12—1232no—
522C3×D12—124no—
523C3×D12—122no—
524C3×D12—122no—
525C3×D12C2×D1214yescomplemented
526C3×D12C2×C3×D414yescomplemented
527C3×C4×D3—24no—
528C3×C4×D3—24no—
529C3×C4×D3—24no—
530C3×C4×D3—24no—
531C3×C4×D3—44no—
532C3×C4×D3—44no—
533C3×C4×D3—616no—
534C3×Dic6—22no—
535C3×Dic6—22no—
536C3×Dic6—24no—
537C3×Dic6—42no—
538C3×Dic6C2×D1214yescomplemented
539C3×Dic6C2×C3×D414yescomplemented
540#626—216no—
541#624—28no—
542C32×C8—64no—
543C3×C3⋊C8—24no—
544C3×C3⋊C8—24no—
545C3×C3⋊C8—44no—
546C2×H(5,𝔽2)—91no—
547C2×AGL(1,ℤ/8)—92no—
548C2×#127—91no—
549#453—98no—
550C2×#104—32no—
551C2×#100—91no—
552C2×C33—21no—
553C2×C33—21no—
554C2×C33#45312yescomplemented
555C2×C33C2×#12011yescharacteristic
556C3×C3⋊D3—44no—
557C3×C3⋊D3—82no—
558C32×D3—44no—
559C24×C3—92no—
560C24×C3—182no—
561C24×C3—181no—
562C23×D3—34no—
563C23×D3—62no—
564C23×D3—64no—
565C23×D3—62no—
566C23×D3—62no—
567C3×#41—34no—
568C3×#41—34no—
569C3×#41—34no—
570C3×#41—34no—
571C3×#41—64no—
572C3×#41—64no—
573C3×#41—62no—
574C3×#41—62no—
575C3×#41—62no—
576C3×#41—62no—
577C3×#41—122no—
578C3×#41—122no—
579C3×#41—188no—
580C3×#41—188no—
581C2×C3×Q8—32no—
582C2×C3×Q8—32no—
583C2×C3×Q8—62no—
584C2×C3×D4—32no—
585C2×C3×D4—32no—
586C2×C3×D4—62no—
587C2×C3×D4—62no—
588C2×C3×D4—62no—
589C2×C3×D4—92no—
590C2×C3×D4—92no—
591C2×C3×D4—92no—
592C2×C3×D4—122no—
593C2×C3×D4—188no—
594C2×C3×D4—188no—
595C2×C3×D4—188no—
596C2×C3×D4—184no—
597C2×C3×D4—188no—
598C2×C3×D4—188no—
599C2×C3×D4—182no—
600C2×C3×D4—182no—
601C2×C3×D4—182no—
602C2×C3×D4—182no—
603C2×C3×D4—181no—
604C2×C3×D4—368no—
605C22×C3×C4—22no—
606C22×C3×C4—21no—
607C22×C3×C4—22no—
608C22×C3×C4—22no—
609C22×C3×C4—21no—
610C22×C3×C4—42no—
611C22×C3×C4—42no—
612C22×C3×C4—41no—
613C22×C3×C4—62no—
614C22×C3×C4—62no—
615C22×C3×C4—122no—
616C22×C3×C4—182no—
617C22×C3×C4C2×D3211yescharacteristic
618C22×C3×C4C22×C3×D312yes—
619C2×#67—22no—
620C2×#67—64no—
621#239—68no—
622#239—68no—
623D3×D4—68no—
624D3×D4—68no—
625D3×D4—616no—
626D3×D4—616no—
627#235—22no—
628#235—22no—
629#235—68no—
630#235—68no—
631#235C3×D1214yescomplemented
632#235C22×C3×D314yes—
633C2×D12—34no—
634C2×D12—34no—
635C2×D12—34no—
636C2×D12—62no—
637C2×D12—62no—
638C2×D12—62no—
639C2×D12—68no—
640C2×D12—64no—
641C2×D12—62no—
642C2×D12—62no—
643C2×D12—62no—
644C2×D12—62no—
645C2×D12—68no—
646C2×D12—62no—
647C2×D12—62no—
648C2×D12—62no—
649C2×D12—62no—
650C2×D12—616no—
651C2×D12—616no—
652C2×D12—62no—
653C2×D12—62no—
654C2×D12—122no—
655C2×D12—122no—
656C2×D12—122no—
657C2×D12—122no—
658C2×D12—1216no—
659C2×D12—1216no—
660C2×D12C3×D1212yescomplemented
661C2×C4×D3—22no—
662C2×C4×D3—64no—
663C2×Dic6C3×D1212yescomplemented
664C3×SD16—188no—
665C3×D8—188no—
666C3×M16—34no—
667C3×M16—34no—
668C3×M16—64no—
669C3×M16—62no—
670C3×M16—62no—
671C3×M16—122no—
672C2×C3×C8—62no—
673C2×C3×C8—62no—
674C2×C3×C8—122no—
675C3×C42—22no—
676C3×C42—21no—
677C3×C42—22no—
678C3×C42—22no—
679C3×C42—24no—
680C3×C42—42no—
681C3×C42—42no—
682C3×C42—42no—
683C3×C42C2×D3212yescomplemented
684C3×C42C22×C3×D314yescomplemented
685#215—68no—
686#213—68no—
687#208—22no—
688#208C22×C3×D314yescomplemented
689C2×C3⋊C8—22no—
690D24—68no—
691#204—68no—
692C22×C32—22no—
693C22×C32—24no—
694C22×C32—24no—
695C22×C32—22no—
696C22×C32—22no—
697C22×C32—21no—
698C22×C32—22no—
699C22×C32—21no—
700C22×C32—21no—
701C22×C32—41no—
702C22×C32—41no—
703C22×C32—41no—
704C22×C32—44no—
705C22×C32—44no—
706C22×C32—64no—
707C22×C32—124no—
708C22×C32#88212yes—
709C22×C32#88212yes—
710C22×C32C3×#12011yescharacteristic
711C22×C32C3×#12011yescharacteristic
712C22×C32C2×D3×D412yes—
713C22×C32C22×C3×D411yescharacteristic
714C2×C3⋊D3—24no—
715C2×C3⋊D3—44no—
716C2×C3⋊D3—44no—
717C2×C3⋊D3—42no—
718C2×C3⋊D3—44no—
719C2×C3⋊D3—82no—
720C2×C3⋊D3—82no—
721C2×C3⋊D3—82no—
722C2×C3×D3—24no—
723C2×C3×D3—24no—
724C2×C3×D3—44no—
725C2×C3×D3—44no—
726C2×C3×D3—44no—
727C2×C3×D3—68no—
728C2×C3×D3—84no—
729C2×C3×D3—124no—
730C2×C3×D3—128no—
731C2×C3×D3—128no—
732C2×C3×D3—128no—
733C2×C3×D3—128no—
734C2×C3×D3—128no—
735C2×C3×D3—124no—
736C2×C3×D3—124no—
737C2×C3×D3—244no—
738C2×C3×D3—2416no—
739C2×C3×D3—244no—
740C2×C3×D3—244no—
741C2×C3×D3—244no—
742C2×C3×D3—244no—
743C2×C3×D3—244no—
744C2×C3×D3—244no—
745D32—88no—
746C32×C4—24no—
747C32×C4—28no—
748C32×C4—28no—
749C32×C4—22no—
750C32×C4—22no—
751C32×C4—22no—
752C32×C4—22no—
753C32×C4—22no—
754C32×C4—22no—
755C32×C4—42no—
756C32×C4—42no—
757C32×C4—48no—
758C32×C4—48no—
759C32×C4—64no—
760C32×C4#88212yes—
761C32×C4#88212yes—
762C32×C4C3×#12012yes—
763C32×C4C22×D1212yes—
764C32×C4C2×D3×D412yes—
765C32×C4C22×C3×D412yes—
766C3×Dic3—24no—
767C3×Dic3—24no—
768C3×Dic3—44no—
769H(5,𝔽2)—94no—
770H(5,𝔽2)—182no—
771H(5,𝔽2)—184no—
772C2×#41—32no—
773C2×#41—182no—
774C22×D4—91no—
775C22×D4—91no—
776C22×D4—182no—
777C22×D4—182no—
778C22×D4—182no—
779AGL(1,ℤ/8)—98no—
780AGL(1,ℤ/8)—184no—
781C2×SD16—182no—
782C2×D8—182no—
783C2×M16—32no—
784#127—94no—
785#127—182no—
786C2×C42C3×D3211yescharacteristic, complemented
787#104—38no—
788#100—94no—
789C33C2×#45311yescharacteristic, complemented, Sylow
790C23×C3—21no—
791C23×C3—22no—
792C23×C3—41no—
793C23×C3—62no—
794C23×C3—62no—
795C23×C3—94no—
796C23×C3—122no—
797C23×C3—188no—
798C23×C3—182no—
799C23×C3—182no—
800C23×C3—182no—
801C23×C3—364no—
802C23×C3—364no—
803C23×C3—361no—
804C23×C3—361no—
805C23×C3—724no—
806C23×C3#381111yescharacteristic
807C23×C3C3×D3×D412yes—
808C22×D3—22no—
809C22×D3—38no—
810C22×D3—64no—
811C22×D3—616no—
812C22×D3—64no—
813C22×D3—64no—
814C22×D3—64no—
815C22×D3—64no—
816C22×D3—122no—
817C22×D3—122no—
818C22×D3—128no—
819C22×D3—128no—
820C22×D3—128no—
821C22×D3—128no—
822C22×D3—122no—
823C22×D3—122no—
824C22×D3—122no—
825C22×D3—122no—
826C22×D3—248no—
827C3×Q8—34no—
828C3×Q8—34no—
829C3×Q8—64no—
830C3×Q8—62no—
831C3×Q8—62no—
832C3×Q8—122no—
833C3×D4—34no—
834C3×D4—34no—
835C3×D4—64no—
836C3×D4—64no—
837C3×D4—64no—
838C3×D4—64no—
839C3×D4—64no—
840C3×D4—62no—
841C3×D4—62no—
842C3×D4—122no—
843C3×D4—124no—
844C3×D4—124no—
845C3×D4—1816no—
846C3×D4—184no—
847C3×D4—184no—
848C3×D4—184no—
849C3×D4—3616no—
850C3×D4—362no—
851C2×C3×C4—24no—
852C2×C3×C4—24no—
853C2×C3×C4—28no—
854C2×C3×C4—28no—
855C2×C3×C4—22no—
856C2×C3×C4—24no—
857C2×C3×C4—22no—
858C2×C3×C4—21no—
859C2×C3×C4—22no—
860C2×C3×C4—22no—
861C2×C3×C4—22no—
862C2×C3×C4—22no—
863C2×C3×C4—22no—
864C2×C3×C4—22no—
865C2×C3×C4—22no—
866C2×C3×C4—21no—
867C2×C3×C4—44no—
868C2×C3×C4—44no—
869C2×C3×C4—48no—
870C2×C3×C4—48no—
871C2×C3×C4—41no—
872C2×C3×C4—42no—
873C2×C3×C4—42no—
874C2×C3×C4—41no—
875C2×C3×C4—62no—
876C2×C3×C4—62no—
877C2×C3×C4—64no—
878C2×C3×C4—64no—
879C2×C3×C4—64no—
880C2×C3×C4—64no—
881C2×C3×C4—124no—
882C2×C3×C4—124no—
883C2×C3×C4—122no—
884C2×C3×C4—188no—
885C2×C3×C4D3×D1212yes—
886C2×C3×C4D3×D1212yes—
887C2×C3×C4#381111yescharacteristic
888C2×C3×C4C2×C3×D1212yes—
889C2×C3×C4C2×C3×D1212yes—
890C2×C3×C4C3×D3×D412yes—
891C2×C3×C4C3×D3×D412yes—
892C2×C3×C4C3×D3×D412yes—
893C2×C3×C4C22×D3211yescharacteristic
894C2×C3×C4C23×C3×D312yes—
895#67—24no—
896#67—24no—
897#67—616no—
898C2×Dic3—22no—
899D12—22no—
900D12—616no—
901D12—64no—
902D12—64no—
903D12—64no—
904D12—64no—
905D12—64no—
906D12—64no—
907D12—124no—
908D12—124no—
909D12—124no—
910D12—1232no—
911D12—1232no—
912D12—124no—
913D12—122no—
914D12—122no—
915D12C2×C3×D1214yescomplemented
916C4×D3—24no—
917C4×D3—24no—
918C4×D3—616no—
919Dic6—22no—
920Dic6C2×C3×D1214yescomplemented
921C3×C8—64no—
922C3×C8—64no—
923C3×C8—124no—
924C3⋊C8—24no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—22no—
928C2×C32—22no—
929C2×C32—22no—
930C2×C32—22no—
931C2×C32—22no—
932C2×C32—24no—
933C2×C32—22no—
934C2×C32—21no—
935C2×C32—41no—
936C2×C32—42no—
937C2×C32—42no—
938C2×C32—42no—
939C2×C32—42no—
940C2×C32—42no—
941C2×C32—124no—
942C2×C32#482214yescomplemented
943C2×C32C3×#45312yescomplemented
944C2×C32C2×#88212yes—
945C2×C32C2×C3×#12011yescharacteristic
946C3⋊D3—44no—
947C3⋊D3—82no—
948C3×D3—44no—
949C3×D3—44no—
950C3×D3—84no—
951C3×D3—128no—
952C3×D3—244no—
953C3×D3—244no—
954C3×D3—244no—
955C24—92no—
956C24—182no—
957C24—181no—
958#41—34no—
959#41—34no—
960#41—62no—
961#41—62no—
962#41—188no—
963#41—188no—
964C2×Q8—32no—
965C2×D4—32no—
966C2×D4—62no—
967C2×D4—92no—
968C2×D4—92no—
969C2×D4—92no—
970C2×D4—188no—
971C2×D4—188no—
972C2×D4—188no—
973C2×D4—184no—
974C2×D4—188no—
975C2×D4—188no—
976C2×D4—182no—
977C2×D4—182no—
978C2×D4—182no—
979C2×D4—182no—
980C2×D4—181no—
981C2×D4—368no—
982C22×C4—21no—
983C22×C4—62no—
984C22×C4—182no—
985C22×C4C2×C3×D3211yescharacteristic
986SD16—188no—
987D8—188no—
988M16—34no—
989M16—62no—
990C2×C8—62no—
991C42—21no—
992C42C2×C3×D3212yescomplemented
993C22×C3—24no—
994C22×C3—24no—
995C22×C3—22no—
996C22×C3—21no—
997C22×C3—22no—
998C22×C3—22no—
999C22×C3—21no—
1000C22×C3—21no—
1001C22×C3—22no—
1002C22×C3—44no—
1003C22×C3—44no—
1004C22×C3—41no—
1005C22×C3—41no—
1006C22×C3—41no—
1007C22×C3—64no—
1008C22×C3—64no—
1009C22×C3—124no—
1010C22×C3—124no—
1011C22×C3—124no—
1012C22×C3—184no—
1013C22×C3—244no—
1014C22×C3—364no—
1015C22×C3—364no—
1016C22×C3—364no—
1017C22×C3—362no—
1018C22×C3—722no—
1019C22×C3—722no—
1020C22×C3—728no—
1021C22×C3—722no—
1022C22×C3#6392311yescharacteristic
1023C22×C3#6392311yescharacteristic
1024C22×C3C3×#88212yes—
1025C22×C3C3×#88212yes—
1026C22×C3C2×#381111yescharacteristic
1027C22×C3C2×C3×D3×D412yes—
1028C2×D3—24no—
1029C2×D3—44no—
1030C2×D3—68no—
1031C2×D3—124no—
1032C2×D3—128no—
1033C2×D3—128no—
1034C2×D3—128no—
1035C2×D3—128no—
1036C2×D3—128no—
1037C2×D3—124no—
1038C2×D3—124no—
1039C2×D3—244no—
1040C2×D3—2416no—
1041C2×D3—244no—
1042C2×D3—244no—
1043C2×D3—244no—
1044C2×D3—244no—
1045C2×D3—244no—
1046C2×D3—244no—
1047C3×C4—28no—
1048C3×C4—28no—
1049C3×C4—24no—
1050C3×C4—22no—
1051C3×C4—22no—
1052C3×C4—22no—
1053C3×C4—22no—
1054C3×C4—22no—
1055C3×C4—22no—
1056C3×C4—48no—
1057C3×C4—48no—
1058C3×C4—42no—
1059C3×C4—42no—
1060C3×C4—64no—
1061C3×C4—64no—
1062C3×C4—124no—
1063C3×C4#6392312yes—
1064C3×C4C3×#88212yes—
1065C3×C4C3×#88212yes—
1066C3×C4C2×D3×D1212yes—
1067C3×C4C22×C3×D1212yes—
1068C3×C4C2×C3×D3×D412yes—
1069Dic3—24no—
1070C32—22no—
1071C32—21no—
1072C32—41no—
1073C32C2×#482212yescomplemented
1074C32C2×C3×#45311yescharacteristic, complemented
1075C23—62no—
1076C23—94no—
1077C23—188no—
1078C23—182no—
1079C23—182no—
1080C23—182no—
1081C23—364no—
1082C23—364no—
1083C23—361no—
1084C23—361no—
1085C23—724no—
1086C23C3×#381111yescharacteristic
1087Q8—34no—
1088Q8—62no—
1089D4—34no—
1090D4—64no—
1091D4—64no—
1092D4—62no—
1093D4—1816no—
1094D4—184no—
1095D4—184no—
1096D4—184no—
1097D4—3616no—
1098D4—362no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—62no—
1102C2×C4—64no—
1103C2×C4—64no—
1104C2×C4—188no—
1105C2×C4C3×D3×D1212yes—
1106C2×C4C3×D3×D1212yes—
1107C2×C4C3×#381111yescharacteristic
1108C2×C4C22×C3×D3211yescharacteristic
1109C8—64no—
1110C2×C3—22no—
1111C2×C3—22no—
1112C2×C3—22no—
1113C2×C3—22no—
1114C2×C3—21no—
1115C2×C3—21no—
1116C2×C3—22no—
1117C2×C3—24no—
1118C2×C3—22no—
1119C2×C3—21no—
1120C2×C3—42no—
1121C2×C3—42no—
1122C2×C3—42no—
1123C2×C3—42no—
1124C2×C3—42no—
1125C2×C3—41no—
1126C2×C3—124no—
1127C2×C3—124no—
1128C2×C3—244no—
1129C2×C3—364no—
1130C2×C3—722no—
1131C2×C3#1059039712yesdirect product factor
1132C2×C3C3×#482214yescomplemented
1133C2×C3C2×#6392311yescharacteristic
1134C2×C3C2×C3×#88212yes—
1135D3—44no—
1136D3—128no—
1137D3—244no—
1138D3—244no—
1139D3—244no—
1140C22—22no—
1141C22—64no—
1142C22—124no—
1143C22—184no—
1144C22—364no—
1145C22—364no—
1146C22—364no—
1147C22—362no—
1148C22—722no—
1149C22—722no—
1150C22—728no—
1151C22—722no—
1152C22C3×#6392311yescharacteristic
1153C22C3×#6392311yescharacteristic
1154C22C2×C3×#381111yescharacteristic
1155C4—24no—
1156C4—64no—
1157C4C3×#6392312yes—
1158C4C2×C3×D3×D1212yes—
1159C3—21no—
1160C3—22no—
1161C3—41no—
1162C3C2×C3×#482212yescomplemented
1163C3C2×#1059039711yescharacteristic, direct product factor
1164C2—21no—
1165C2—21no—
1166C2—124no—
1167C2—364no—
1168C2—722no—
1169C2C3×#1059039712yesdirect product factor
1170C2C2×C3×#6392311yescharacteristic
subgroupG/H
centerC22×C3#63923
commutator, cosocleC2×C32×C4C24×C3
FrattiniC2×C4C22×C3×D32
FittingC2×C33×C42C22
socleC22×C33#120
hypercenterC2×C3×C42D32
hypocenterC32C2×C3×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#64308C2semidirect
2. C2×C3×#64083C2semidirect
3. C2×C3×#63825C2semidirect
4. C2×C32×#805C2semidirect
5. C2×C3×#63559C2semidirect
6. C3×#10590397C2direct (N × H)
7. C2×#10590397C3direct (N × H)
11. C22×C3×C4⋊(C3⋊D3)C22semidirect
16. C3×#64308C22semidirect
19. C2×C33×C42C22semidirect
21. C3×#64083C22semidirect
22. C2×C32×#208C22semidirect
25. C3×#63825C22semidirect
27. C32×#805C22semidirect
28. C3×#63559C22semidirect
30. C2×#64308C2×C3semidirect
31. C2×#64083C2×C3semidirect
36. C2×#63825C2×C3semidirect
40. C2×C3×#805D3semidirect
41. C2×C3×#805C2×C3semidirect
43. C2×#63559C2×C3semidirect
44. #10590397C2×C3direct (N × H)
59. C2×C3×C4⋊(C3⋊D3)C23semidirect
63. C32×#235D4semidirect
65. C2×C32×D12D4semidirect
67. C2×C32×Dic6D4semidirect
77. C33×C42C23semidirect
79. C32×#208C23semidirect
88. C22×C4⋊(C3⋊D3)C22×C3semidirect
110. #64308C22×C3semidirect
117. C2×C32×C42C2×D3semidirect
118. C2×C32×C42C22×C3semidirect
120. #64083C22×C3semidirect
126. C2×C3×#208C2×D3semidirect
127. C2×C3×#208C22×C3semidirect
138. #63825C22×C3semidirect
143. C3×#805C2×D3semidirect
144. C3×#805C22×C3semidirect
145. #63559C22×C3semidirect
173. C32×D12C2×D4semidirect
177. C32×Dic6C2×D4semidirect
195. C2×#805C3×D3semidirect
232. C2×C4⋊(C3⋊D3)C23×C3semidirect
253. C3×#235D12semidirect
254. C3×#235C3×D4semidirect
285. C2×C3×D12D12semidirect
286. C2×C3×D12C3×D4semidirect
292. C2×C3×Dic6D12semidirect
293. C2×C3×Dic6C3×D4semidirect
313. C32×C42C22×D3semidirect
314. C32×C42C23×C3semidirect
321. C3×#208C22×D3semidirect
322. C3×#208C23×C3semidirect
390. C2×C3×C42D32semidirect
391. C2×C3×C42C2×C3×D3semidirect
396. C2×#208C2×C3×D3semidirect
410. #805C2×C3×D3semidirect
525. C3×D12C2×D12semidirect
526. C3×D12C2×C3×D4semidirect
538. C3×Dic6C2×D12semidirect
539. C3×Dic6C2×C3×D4semidirect
554. C2×C33#453semidirect
631. #235C3×D12semidirect
660. C2×D12C3×D12semidirect
663. C2×Dic6C3×D12semidirect
683. C3×C42C2×D32semidirect
684. C3×C42C22×C3×D3semidirect
688. #208C22×C3×D3semidirect
786. C2×C42C3×D32semidirect
789. C33C2×#453semidirect
915. D12C2×C3×D12semidirect
920. Dic6C2×C3×D12semidirect
942. C2×C32#4822semidirect
943. C2×C32C3×#453semidirect
992. C42C2×C3×D32semidirect
1073. C32C2×#4822semidirect
1074. C32C2×C3×#453semidirect
1131. C2×C3#10590397direct (N × H)
1132. C2×C3C3×#4822semidirect
1162. C3C2×C3×#4822semidirect
1163. C3C2×#10590397direct (N × H)
1169. C2C3×#10590397direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#643082
C2×C3×#640832
C2×C3×#638252
C2×C32×#8052
C2×C3×#635592
C3×#105903972
C2×#105903973
C2×C3×#48223