Finite Group Databasebeta

← C3×#10594382 #13173939

Subgroups — C3×#10594382 #13173939

Order 1728.

1424 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3796C211yesmaximal, characteristic, complemented
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#64106C211yesmaximal, characteristic, complemented
4C32×#895C211yesmaximal, characteristic, complemented
5C32×#887C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic, complemented
7C3×#63893C212yesmaximal, complemented
8C3×Dic3×D12C212yesmaximal, complemented
9C3×#63886C212yesmaximal, complemented
10C3×#63860C211yesmaximal, characteristic, complemented
11C3×#63852C212yesmaximal, complemented
12C3×#5598—31nomaximal
13C3×#5576—31nomaximal
14#10594382C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×D12C2212yes—
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×C3×#627C2212yes—
22C2×C3×#626C2212yes—
23C2×C3×#626C2211yescharacteristic
24C2×C3×D3×Dic3C2212yes—
25C2×C3×D3×Dic3C2212yes—
26C3×#3796—24no—
27C3×D3×Dic6—24no—
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2212yes—
30C3×C4⋊(C3⋊Dic3)C2212yes—
31C32×(C2×D3)⋊C4C2212yes—
32C32×Dic3⋊C4C2212yes—
33C32×C4×Dic3C2212yes—
34C32×C4×Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×#3722C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2212yes—
39C3×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×C3×#239—31no—
41C2×C3×D3×Q8—31no—
42C2×C3×#237—31no—
43C22×C3×Dic6—31no—
44C2×#3796C2×C311yescharacteristic, complemented
45C2×D3×Dic6C2×C311yescharacteristic, complemented
46C32×#121—31no—
47C32×C4×Q8—31no—
48#64106C2×C311yescharacteristic, complemented
49C3×#939—32no—
50C3×#936—31no—
51C3×D4×Dic3—32no—
52C3×C4×#67—31no—
53C3×#897—31no—
54C3×#897—31no—
55C3×#897—32no—
56C3×#897—61no—
57C3×#895—21no—
58C3×#895—32no—
59C3×#895D311yescharacteristic, complemented
60C3×#895C2×C311yescharacteristic, complemented
61C3×#887—21no—
62C3×#887D311yescharacteristic, complemented
63C3×#887C2×C311yescharacteristic, complemented
64C3×#885—32no—
65C3×#878—32no—
66C3×#875—31no—
67C3×#875—32no—
68C3×C4×D12—32no—
69C3×C4×D12—31no—
70C4×#626C2×C311yescharacteristic, complemented
71#63893C2×C312yescomplemented
72Dic3×D12C2×C312yescomplemented
73#63886C2×C312yescomplemented
74#63860C2×C311yescharacteristic, complemented
75#63852C2×C312yescomplemented
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C2×C33×C4C2312yes—
80C2×C33×C4C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C3×C4×C3⋊D3—22no—
84C3×#634—22no—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C32×D12—24no—
90C32×D12—22no—
91C32×C4×D3—22no—
92C32×Dic6D414yescomplemented
93C3×#627—24no—
94C3×#626—22no—
95C3×#626—24no—
96C3×D3×Dic3—24no—
97C3×D3×Dic3—24no—
98C3×#548—91no—
99#5598—31no—
100#5576—31no—
101C2×C32×Q8—31no—
102C2×C32×D4—32no—
103C2×C32×D4—31no—
104C22×C32×C4—31no—
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×#634C22×C311yescharacteristic
107C2×C3×#67—32no—
108C2×C3×#67—31no—
109C22×C3×Dic3—32no—
110C22×C3×Dic3—32no—
111C3×#239—64no—
112C3×D3×Q8—64no—
113C3×#237—64no—
114C2×C3×D12—21no—
115C2×C3×D12—22no—
116C2×C3×D12—31no—
117C2×C3×D12—32no—
118C2×C3×D12C2×D312yes—
119C2×C3×D12C2×D311yescharacteristic
120C2×C3×D12C22×C311yescharacteristic
121C2×C3×D12C22×C312yes—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3—32no—
124C2×C3×C4×D3—32no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—61no—
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×C4×D3C22×C311yescharacteristic
130C2×C3×Dic6—21no—
131C2×C3×Dic6—31no—
132C2×C3×Dic6—31no—
133C2×C3×Dic6—32no—
134C2×C3×Dic6—32no—
135C2×C3×Dic6—64no—
136C2×C3×Dic6—61no—
137C2×C3×Dic6C2×D311yescharacteristic
138C2×C3×Dic6C22×C311yescharacteristic
139C2×#627C22×C312yes—
140C2×#626C22×C312yes—
141C2×#626C22×C311yescharacteristic
142C2×D3×Dic3C22×C312yes—
143C2×D3×Dic3C22×C312yes—
144#3796—24no—
145D3×Dic6—24no—
146C32×C4⋊C4—21no—
147C32×C4⋊C4—21no—
148C32×C4⋊C4—21no—
149C32×C4⋊C4—32no—
150C32×C4⋊C4—41no—
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C4⋊C4C22×C311yescharacteristic
154C32×C22⋊C4—32no—
155C32×C42—32no—
156C32×C42—31no—
157#3752C22×C312yes—
158C4⋊(C3⋊Dic3)C22×C312yes—
159C3×#217—32no—
160C3×#217—32no—
161C3×#217—31no—
162C3×(C2×D3)⋊C4—22no—
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×(C2×D3)⋊C4—32no—
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—62no—
171C3×(C2×D3)⋊C4C2×D312yes—
172C3×(C2×D3)⋊C4C22×C312yes—
173C3×C4⋊Dic3—32no—
174C3×C4⋊Dic3—32no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—62no—
177C3×Dic3⋊C4—22no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4C2×D312yes—
180C3×Dic3⋊C4C22×C312yes—
181C3×C4×Dic3—22no—
182C3×C4×Dic3—21no—
183C3×C4×Dic3C2×D312yes—
184C3×C4×Dic3C2×D311yescharacteristic
185C3×C4×Dic3C22×C312yes—
186C3×C4×Dic3C22×C311yescharacteristic
187Dic3⋊Dic3C22×C311yescharacteristic
188#3722C22×C311yescharacteristic
189(C2×D3)⋊Dic3C22×C312yes—
190(C2×D3)⋊Dic3C22×C312yes—
191(C2×D3)⋊Dic3C22×C311yescharacteristic
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C32×D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3—22no—
199C2×C32×D3—22no—
200C2×C32×D3—22no—
201C2×C32×D3#4112yescomplemented
202C33×C4—22no—
203C33×C4C2×D412yes—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—22no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C32×Dic3C2×D414yes—
210C2×C3×#41—91no—
211C22×C3×Q8—91no—
212C2×#239—31no—
213C2×D3×Q8—31no—
214C2×#237—31no—
215C22×Dic6—31no—
216C3×#124—92no—
217C3×#124—91no—
218C3×C22⋊Q8—92no—
219C3×C22⋊Q8—91no—
220C3×#121—31no—
221C3×#121—31no—
222C3×#121—61no—
223C3×#121—92no—
224C3×C4×Q8—31no—
225C3×C4×Q8—31no—
226C3×C4×Q8—61no—
227C3×C4×D4—91no—
228C3×C4×D4—92no—
229#939—32no—
230#936—31no—
231D4×Dic3—32no—
232C4×#67—31no—
233#897—31no—
234#897—31no—
235#897—32no—
236#897—61no—
237#895—32no—
238#895C3×D311yescharacteristic, complemented
239#887C3×D311yescharacteristic, complemented
240#885—32no—
241#878—32no—
242#875—31no—
243#875—32no—
244C4×D12—32no—
245C4×D12—31no—
246C23×C32—31no—
247C23×C32—32no—
248C22×C3⋊D3C23×C311yescharacteristic
249C22×C3×D3—21no—
250C22×C3×D3—22no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—61no—
254C22×C3×D3C22×D312yes—
255C22×C3×D3C22×D311yescharacteristic
256C22×C3×D3C23×C312yes—
257C22×C3×D3C23×C311yescharacteristic
258C32×Q8—34no—
259C32×D4—64no—
260C32×D4—62no—
261C2×C32×C4—21no—
262C2×C32×C4—22no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—22no—
266C2×C32×C4—22no—
267C2×C32×C4—32no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—41no—
272C2×C32×C4—42no—
273C2×C32×C4—62no—
274C2×C32×C4C22×D312yes—
275C2×C32×C4C22×D312yes—
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C23×C312yes—
279C2×C32×C4C23×C311yescharacteristic
280C2×C3⋊Dic3C23×C312yes—
281C2×C3⋊Dic3C23×C311yescharacteristic
282C4×C3⋊D3—22no—
283#634—22no—
284C3×#67—62no—
285C3×#67—64no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—61no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—64no—
297C2×C3×Dic3—64no—
298C2×C3×Dic3C22×D311yescharacteristic
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D311yescharacteristic
301C2×C3×Dic3C22×D312yes—
302C2×C3×Dic3C23×C311yescharacteristic
303C2×C3×Dic3C23×C311yescharacteristic
304C2×C3×Dic3C23×C311yescharacteristic
305C2×C3×Dic3C23×C312yes—
306C3×D12—24no—
307C3×D12—24no—
308C3×D12—22no—
309C3×D12—22no—
310C3×D12—42no—
311C3×D12—44no—
312C3×D12—64no—
313C3×D12—62no—
314C3×C4×D3—22no—
315C3×C4×D3—22no—
316C3×C4×D3—42no—
317C3×C4×D3—64no—
318C3×C4×D3—64no—
319C3×C4×D3—62no—
320C3×C4×D3—62no—
321C3×C4×D3—122no—
322C3×Dic6—24no—
323C3×Dic6—64no—
324C3×Dic6—62no—
325C3×Dic6—62no—
326C3×Dic6—64no—
327C3×Dic6—122no—
328C3×Dic6D1214yescomplemented
329C3×Dic6C3×D414yescomplemented
330#627—24no—
331#626—22no—
332#626—24no—
333D3×Dic3—24no—
334D3×Dic3—24no—
335#548—91noSylow
336C2×C33C22×D411yescharacteristic
337C2×C33C2×#4111yescharacteristic
338C2×C332−1+411yescharacteristic
339C3×C3⋊D3—41no—
340C32×D3—22no—
341C32×D3—42no—
342C3×#41—184no—
343C2×C3×Q8—31no—
344C2×C3×Q8—31no—
345C2×C3×Q8—61no—
346C2×C3×Q8—92no—
347C2×C3×Q8—91no—
348C2×C3×Q8—184no—
349C2×C3×D4—32no—
350C2×C3×D4—31no—
351C2×C3×D4—32no—
352C2×C3×D4—31no—
353C2×C3×D4—62no—
354C2×C3×D4—61no—
355C2×C3×D4—91no—
356C2×C3×D4—92no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—61no—
360C22×C3×C4—92no—
361C22×C3×C4—92no—
362C22×C3×C4—91no—
363C2×#67—32no—
364C2×#67—31no—
365C22×Dic3—32no—
366C22×Dic3—32no—
367#239—64no—
368D3×Q8—64no—
369#237—64no—
370C2×D12—31no—
371C2×D12—32no—
372C2×D12C2×C3×D312yes—
373C2×D12C2×C3×D311yescharacteristic
374C2×C4×D3—32no—
375C2×C4×D3—32no—
376C2×C4×D3—31no—
377C2×C4×D3—31no—
378C2×C4×D3—61no—
379C2×C4×D3C2×C3×D311yescharacteristic
380C2×Dic6—31no—
381C2×Dic6—31no—
382C2×Dic6—32no—
383C2×Dic6—32no—
384C2×Dic6—61no—
385C2×Dic6—64no—
386C2×Dic6C2×C3×D311yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—32no—
391C3×C4⋊C4—32no—
392C3×C4⋊C4—41no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—91no—
395C3×C4⋊C4—92no—
396C3×C4⋊C4D3211yescharacteristic
397C3×C4⋊C4C2×C3×D311yescharacteristic
398C3×C4⋊C4C2×C3×D311yescharacteristic
399C3×C22⋊C4—32no—
400C3×C22⋊C4—32no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—91no—
403C3×C22⋊C4—91no—
404C3×C22⋊C4—92no—
405C3×C22⋊C4—92no—
406C3×C22⋊C4—92no—
407C3×C42—32no—
408C3×C42—31no—
409C3×C42—32no—
410C3×C42—31no—
411C3×C42—61no—
412C3×C42—62no—
413#217—32no—
414#217—32no—
415#217—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—32no—
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—32no—
420(C2×D3)⋊C4—32no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—62no—
424(C2×D3)⋊C4C2×C3×D312yes—
425C4⋊Dic3—32no—
426C4⋊Dic3—32no—
427C4⋊Dic3—31no—
428C4⋊Dic3—62no—
429Dic3⋊C4—31no—
430Dic3⋊C4C2×C3×D312yes—
431C4×Dic3C2×C3×D312yes—
432C4×Dic3C2×C3×D311yescharacteristic
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—32no—
437C22×C32—41no—
438C22×C32—61no—
439C22×C32—61no—
440C22×C32—62no—
441C22×C32—62no—
442C22×C32—62no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C24×C311yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—42no—
463C2×C3×D3—42no—
464C2×C3×D3—42no—
465C2×C3×D3—62no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—121no—
473C2×C3×D3—121no—
474C2×C3×D3#23712yescomplemented
475C2×C3×D3C3×#4112yescomplemented
476C32×C4—22no—
477C32×C4—22no—
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—34no—
483C32×C4—42no—
484C32×C4—42no—
485C32×C4—42no—
486C32×C4—42no—
487C32×C4—61no—
488C32×C4—61no—
489C32×C4—61no—
490C32×C4—82no—
491C32×C4C2×D1212yes—
492C32×C4D3×D412yes—
493C32×C4C2×C3×D412yes—
494C3⋊Dic3—21no—
495C3⋊Dic3—22no—
496C3×Dic3—22no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—21no—
501C3×Dic3—21no—
502C3×Dic3—21no—
503C3×Dic3—24no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—62no—
507C3×Dic3—61no—
508C3×Dic3—62no—
509C3×Dic3—61no—
510C3×Dic3—122no—
511C3×Dic3—121no—
512C3×Dic3C2×D1214yes—
513C3×Dic3C2×C3×D414yes—
514C2×#41—91no—
515C22×Q8—91no—
516#124—92no—
517#124—91no—
518C22⋊Q8—92no—
519C22⋊Q8—91no—
520#121—31no—
521#121—92no—
522C4×Q8—31no—
523C4×D4—91no—
524C4×D4—92no—
525C33#54811yescharacteristic, complemented, Sylow
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—32no—
529C23×C3—32no—
530C23×C3—61no—
531C23×C3—62no—
532C23×C3—91no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—61no—
536C22×D3C22×C3×D312yes—
537C22×D3C22×C3×D311yescharacteristic
538C3×Q8—34no—
539C3×Q8—34no—
540C3×Q8—64no—
541C3×Q8—184no—
542C3×Q8—182no—
543C3×D4—64no—
544C3×D4—64no—
545C3×D4—62no—
546C3×D4—62no—
547C3×D4—122no—
548C3×D4—124no—
549C3×D4—184no—
550C3×D4—182no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—42no—
567C2×C3×C4—61no—
568C2×C3×C4—62no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—92no—
574C2×C3×C4—91no—
575C2×C3×C4—122no—
576C2×C3×C4—184no—
577C2×C3×C4—184no—
578C2×C3×C4—182no—
579C2×C3×C4C2×D3212yes—
580C2×C3×C4C2×D3211yescharacteristic
581C2×C3×C4C22×C3×D312yes—
582C2×C3×C4C22×C3×D312yes—
583C2×C3×C4C22×C3×D311yescharacteristic
584C2×C3×C4C22×C3×D311yescharacteristic
585#67—62no—
586#67—64no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—61no—
592C2×Dic3—62no—
593C2×Dic3—64no—
594C2×Dic3—64no—
595C2×Dic3C22×C3×D311yescharacteristic
596C2×Dic3C22×C3×D311yescharacteristic
597C2×Dic3C22×C3×D311yescharacteristic
598C2×Dic3C22×C3×D312yes—
599D12—24no—
600D12—22no—
601D12—64no—
602D12—62no—
603C4×D3—22no—
604C4×D3—64no—
605C4×D3—64no—
606C4×D3—62no—
607C4×D3—62no—
608C4×D3—122no—
609Dic6—64no—
610Dic6—62no—
611Dic6—62no—
612Dic6—64no—
613Dic6—122no—
614Dic6C3×D1214yescomplemented
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—41no—
625C2×C32—41no—
626C2×C32—41no—
627C2×C32—62no—
628C2×C32—122no—
629C2×C32C22×D1211yescharacteristic
630C2×C32C2×D3×D411yescharacteristic
631C2×C32C2×#23711yescharacteristic
632C2×C32#100711yescharacteristic
633C2×C32D3×#4111yescharacteristic
634C2×C32#101011yescharacteristic
635C2×C32C22×C3×D411yescharacteristic
636C2×C32C2×C3×#4111yescharacteristic
637C2×C32C3×2−1+411yescharacteristic
638C3⋊D3—41no—
639C3×D3—22no—
640C3×D3—22no—
641C3×D3—42no—
642C3×D3—42no—
643C3×D3—42no—
644C3×D3—82no—
645C3×D3—122no—
646C3×D3—121no—
647C3×D3—121no—
648#41—184no—
649C2×Q8—31no—
650C2×Q8—92no—
651C2×Q8—91no—
652C2×Q8—184no—
653C2×D4—32no—
654C2×D4—31no—
655C2×D4—91no—
656C2×D4—92no—
657C22×C4—31no—
658C22×C4—92no—
659C22×C4—92no—
660C22×C4—91no—
661C4⋊C4—32no—
662C4⋊C4—91no—
663C4⋊C4—92no—
664C4⋊C4C3×D3211yescharacteristic
665C22⋊C4—32no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—92no—
669C22⋊C4—92no—
670C22⋊C4—92no—
671C42—32no—
672C42—31no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—32no—
677C22×C3—32no—
678C22×C3—41no—
679C22×C3—62no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—62no—
685C22×C3—62no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—122no—
693C22×C3—122no—
694C22×C3—122no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3C22×D3211yescharacteristic
699C22×C3C23×C3×D311yescharacteristic
700C22×C3C23×C3×D311yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—62no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3C3×#23712yescomplemented
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—34no—
723C3×C4—34no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—64no—
729C3×C4—62no—
730C3×C4—61no—
731C3×C4—61no—
732C3×C4—61no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—82no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4—181no—
740C3×C4—182no—
741C3×C4D3×D1212yes—
742C3×C4C2×C3×D1212yes—
743C3×C4C3×D3×D412yes—
744Dic3—21no—
745Dic3—21no—
746Dic3—21no—
747Dic3—62no—
748Dic3—61no—
749Dic3—62no—
750Dic3—61no—
751Dic3—122no—
752Dic3—121no—
753Dic3C2×C3×D1214yes—
754C32—21no—
755C32—21no—
756C32—21no—
757C32—41no—
758C32#557611yescharacteristic, complemented
759C32#559811yescharacteristic, complemented
760C32C3×#54811yescharacteristic, complemented
761C23—31no—
762C23—32no—
763C23—91no—
764Q8—34no—
765Q8—184no—
766Q8—182no—
767D4—64no—
768D4—62no—
769D4—184no—
770D4—182no—
771C2×C4—32no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—62no—
776C2×C4—92no—
777C2×C4—91no—
778C2×C4—184no—
779C2×C4—184no—
780C2×C4—182no—
781C2×C4C2×C3×D3212yes—
782C2×C4C2×C3×D3211yescharacteristic
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—62no—
796C2×C3—62no—
797C2×C3—122no—
798C2×C3—122no—
799C2×C3—122no—
800C2×C3—242no—
801C2×C3—361no—
802C2×C3C2×D3×D1211yescharacteristic
803C2×C3D3×#23711yescharacteristic
804C2×C3#6431511yescharacteristic
805C2×C3C22×C3×D1211yescharacteristic
806C2×C3C2×C3×D3×D411yescharacteristic
807C2×C3C2×C3×#23711yescharacteristic
808C2×C3C3×#100711yescharacteristic
809C2×C3C3×D3×#4111yescharacteristic
810C2×C3C3×#101011yescharacteristic
811D3—22no—
812D3—42no—
813D3—122no—
814D3—121no—
815D3—121no—
816C22—32no—
817C22—61no—
818C22—61no—
819C22—62no—
820C22—62no—
821C22—62no—
822C22—181no—
823C22—181no—
824C22—181no—
825C22C22×C3×D3211yescharacteristic
826C4—22no—
827C4—34no—
828C4—61no—
829C4—61no—
830C4—61no—
831C4—181no—
832C4—182no—
833C4C3×D3×D1212yes—
834C3—21no—
835C3—21no—
836C3—21no—
837C3—41no—
838C3#1059438211yescharacteristic, direct product factor
839C3C3×#557611yescharacteristic, complemented
840C3C3×#559811yescharacteristic, complemented
841C2—62no—
842C2—122no—
843C2—361no—
844C2C2×C3×D3×D1211yescharacteristic
845C2C3×D3×#23711yescharacteristic
846C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3796C2semidirect
2. C2×C3×D3×Dic6C2semidirect
3. C3×#64106C2semidirect
4. C32×#895C2semidirect
5. C32×#887C2semidirect
6. C3×C4×#626C2semidirect
7. C3×#63893C2semidirect
8. C3×Dic3×D12C2semidirect
9. C3×#63886C2semidirect
10. C3×#63860C2semidirect
11. C3×#63852C2semidirect
14. #10594382C3direct (N × H)
44. C2×#3796C2×C3semidirect
45. C2×D3×Dic6C2×C3semidirect
48. #64106C2×C3semidirect
59. C3×#895D3semidirect
60. C3×#895C2×C3semidirect
62. C3×#887D3semidirect
63. C3×#887C2×C3semidirect
70. C4×#626C2×C3semidirect
71. #63893C2×C3semidirect
72. Dic3×D12C2×C3semidirect
73. #63886C2×C3semidirect
74. #63860C2×C3semidirect
75. #63852C2×C3semidirect
92. C32×Dic6D4semidirect
201. C2×C32×D3#41semidirect
238. #895C3×D3semidirect
239. #887C3×D3semidirect
328. C3×Dic6D12semidirect
329. C3×Dic6C3×D4semidirect
474. C2×C3×D3#237semidirect
475. C2×C3×D3C3×#41semidirect
525. C33#548semidirect
614. Dic6C3×D12semidirect
715. C2×D3C3×#237semidirect
758. C32#5576semidirect
759. C32#5598semidirect
760. C32C3×#548semidirect
838. C3#10594382direct (N × H)
839. C3C3×#5576semidirect
840. C3C3×#5598semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37962
C2×C3×D3×Dic62
C3×#641062
C32×#8952
C32×#8872
C3×C4×#6262
C3×#638932
C3×Dic3×D122
C3×#638862
C3×#638602
C3×#638522
C3×#55983
C3×#55763
#105943823