Finite Group Databasebeta

← C2×C3×#64312 #13181548

Subgroups — C2×C3×#64312 #13181548

Order 1728.

4178 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×#237C212yesmaximal, complemented
3C2×C3×#3811C212yesmaximal, complemented
4C22×C3×#624C212yesmaximal, complemented
5C2×C3×#3804C214yesmaximal, complemented
6C3×#64312C2116yesmaximal, direct product factor
7C2×C3×C4×D32C211yesmaximal, characteristic, complemented
8C2×C3×#3799C212yesmaximal, complemented
9C2×C3×#3797C211yesmaximal, characteristic, complemented
10C2×C3×D3×#41—32nomaximal
11C2×#64312C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2212yes—
13C22×C3×D32C2211yescharacteristic
14C2×C33×D4C2211yescharacteristic, complemented
15C2×C3×#638C2212yescomplemented
16C3×D4×C3⋊D3C2218yescomplemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C32×#67C2214yescomplemented
20C22×C32×Dic3C2214yescomplemented
21C32×#237C22116yescomplemented
22C2×C32×C4×D3C2212yescomplemented
23C2×C32×Dic6C2212yescomplemented
24C3×#3811C22116yescomplemented
25C2×C3×#627C2212yescomplemented
26C2×C3×#626C2214yescomplemented
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2212yes—
29C2×C3×#624C22116yescomplemented
30C2×C3×#624C2214yescomplemented
31C3×#3804C22132yescomplemented
32C2×C3×D3×Dic3C2212yescomplemented
33C3×C4×D32C2218yescomplemented
34C3×#3799C22116yescomplemented
35C3×#3797C2218yescomplemented
36C2×C32×#41—32no—
37C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
38C3×D3×#41—332no—
39C2×C3×#239—32no—
40C2×C3×D3×Q8—32no—
41C2×C3×#237—22no—
42C2×C3×#237—34no—
43C2×C3×#237D312yescomplemented
44C2×C3×#237C2×C312yescomplemented
45C2×C3×D3×D4—32no—
46C2×C3×D3×D4—34no—
47C2×C3×D3×D4—61no—
48C2×C3×#235—34no—
49C2×C3×#235—32no—
50C22×C3×C4×D3—34no—
51C22×C3×C4×D3—32no—
52C2×#3811C2×C312yescomplemented
53C22×#624C2×C312yescomplemented
54C2×#3804C2×C314yescomplemented
55#64312C2×C3116yesdirect product factor
56C2×C4×D32C2×C311yescharacteristic, complemented
57C2×#3799C2×C312yescomplemented
58C2×#3797C2×C311yescharacteristic, complemented
59C23×C33C2312yes—
60C22×C3×C3⋊D3—28no—
61C22×C3×C3⋊D3C2312yes—
62C22×C3×C3⋊D3C2318yes—
63C22×C3×C3⋊D3C2311yescharacteristic
64C22×C32×D3C2312yes—
65C2×C3×D32—24no—
66C2×C3×D32C2314yes—
67C33×D4C2314yescomplemented
68C2×C33×C4C2311yescharacteristic
69C3×#638C2318yescomplemented
70C2×C3×C3⋊Dic3C2311yescharacteristic
71C3×C4⋊(C3⋊D3)C2314yescomplemented
72C3×C4×C3⋊D3C2314yes—
73C32×#67C23116yescomplemented
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2314yes—
76C2×C32×Dic3C23116yescomplemented
77C32×C4×D3C2318yescomplemented
78C32×Dic6C2318yescomplemented
79C3×#627C2318yescomplemented
80C3×#626C23116yescomplemented
81C3×#624C2318yes—
82C3×#624C2314yes—
83C3×#624C23116yescomplemented
84C3×D3×Dic3C2318yescomplemented
85C22×C3×#41—91no—
86C2×D3×#41—32no—
87C23×C3⋊D3C22×C312yes—
88C23×C3×D3—34no—
89C23×C3×D3—32no—
90C23×C3×D3—62no—
91C22×D32C22×C311yescharacteristic
92C32×#41—316no—
93C2×C32×Q8—32no—
94C2×C32×D4—21no—
95C2×C32×D4—22no—
96C2×C32×D4—34no—
97C2×C32×D4—41no—
98C2×C32×D4C2×D312yescomplemented
99C2×C32×D4C22×C311yescharacteristic, complemented
100C22×C32×C4—34no—
101C22×C32×C4—32no—
102C2×#638C22×C312yescomplemented
103D4×C3⋊D3C22×C318yescomplemented
104C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×C3×#67—24no—
107C2×C3×#67—34no—
108C2×C3×#67—34no—
109C2×C3×#67—62no—
110C2×C3×#67C2×D314yescomplemented
111C2×C3×#67C22×C314yescomplemented
112C22×C3×Dic3—24no—
113C22×C3×Dic3—32no—
114C22×C3×Dic3C2×D314yescomplemented
115C22×C3×Dic3C22×C314yescomplemented
116C3×#239—316no—
117C3×D3×Q8—316no—
118C3×#237—216no—
119C3×#237—332no—
120C3×#237C2×D3116yescomplemented
121C3×#237C22×C3116yescomplemented
122C3×D3×D4—316no—
123C3×D3×D4—332no—
124C3×D3×D4—68no—
125C3×#235—332no—
126C3×#235—316no—
127C2×C3×D12—34no—
128C2×C3×D12—32no—
129C2×C3×D12—61no—
130C2×C3×C4×D3—22no—
131C2×C3×C4×D3—32no—
132C2×C3×C4×D3—32no—
133C2×C3×C4×D3—32no—
134C2×C3×C4×D3—34no—
135C2×C3×C4×D3—34no—
136C2×C3×C4×D3—34no—
137C2×C3×C4×D3—332no—
138C2×C3×C4×D3—316no—
139C2×C3×C4×D3—61no—
140C2×C3×C4×D3C2×D312yescomplemented
141C2×C3×C4×D3C22×C312yescomplemented
142C2×C3×Dic6—22no—
143C2×C3×Dic6—34no—
144C2×C3×Dic6C2×D312yescomplemented
145C2×C3×Dic6C22×C312yescomplemented
146#3811C22×C3116yescomplemented
147C2×#627C22×C312yescomplemented
148C2×#626C22×C314yescomplemented
149C2×#624C22×C312yes—
150C2×#624C22×C311yescharacteristic
151C2×#624C22×C3116yescomplemented
152C2×#624C22×C314yescomplemented
153#3804C22×C3132yescomplemented
154C2×D3×Dic3C22×C312yescomplemented
155C4×D32C22×C318yescomplemented
156#3799C22×C3116yescomplemented
157#3797C22×C318yescomplemented
158C22×C33—24no—
159C22×C33C2414yes—
160C22×C33C2411yescharacteristic
161C2×C3×C3⋊D3—24no—
162C2×C3×C3⋊D3—216no—
163C2×C3×C3⋊D3#4114yescomplemented
164C2×C3×C3⋊D3C2414yes—
165C2×C3×C3⋊D3C2412yes—
166C2×C32×D3—24no—
167C2×C32×D3C2414yes—
168C3×D32—28no—
169C33×C4C2412yes—
170C3×C3⋊Dic3C2412yes—
171C32×Dic3C2414yes—
172C32×Dic3C2418yes—
173C2×C3×#41—32no—
174C2×C3×#41—32no—
175C2×C3×#41—62no—
176C2×C3×#41—94no—
177C2×C3×#41—92no—
178C2×C3×#41—916no—
179C22×C3×Q8—91no—
180C22×C3×D4—92no—
181C22×C3×D4—91no—
182C23×C3×C4—92no—
183C23×C3×C4—91no—
184D3×#41—332no—
185C2×#239—32no—
186C2×D3×Q8—32no—
187C2×#237—34no—
188C2×#237C3×D312yescomplemented
189C2×D3×D4—32no—
190C2×D3×D4—34no—
191C2×D3×D4—61no—
192C2×#235—34no—
193C2×#235—32no—
194C22×C4×D3—34no—
195C22×C4×D3—32no—
196C23×C32—22no—
197C23×C32—24no—
198C23×C32—32no—
199C23×C32—42no—
200C23×C32C22×D314yes—
201C23×C32C23×C312yes—
202C22×C3⋊D3—28no—
203C22×C3⋊D3C23×C312yes—
204C22×C3⋊D3C23×C318yes—
205C22×C3⋊D3C23×C311yescharacteristic
206C22×C3×D3—22no—
207C22×C3×D3—32no—
208C22×C3×D3—34no—
209C22×C3×D3—316no—
210C22×C3×D3—38no—
211C22×C3×D3—61no—
212C22×C3×D3—62no—
213C22×C3×D3—68no—
214C22×C3×D3—68no—
215C22×C3×D3—616no—
216C22×C3×D3—128no—
217C22×C3×D3C22×D312yes—
218C22×C3×D3C23×C312yes—
219C2×D32—24no—
220C2×D32C23×C314yes—
221C32×Q8—38no—
222C32×D4—24no—
223C32×D4—28no—
224C32×D4—316no—
225C32×D4—44no—
226C32×D4C22×D318yescomplemented
227C32×D4C23×C314yescomplemented
228C2×C32×C4—21no—
229C2×C32×C4—22no—
230C2×C32×C4—34no—
231C2×C32×C4—32no—
232C2×C32×C4—316no—
233C2×C32×C4—38no—
234C2×C32×C4—41no—
235C2×C32×C4C22×D312yes—
236C2×C32×C4C23×C311yescharacteristic
237#638C23×C318yescomplemented
238C2×C3⋊Dic3C23×C311yescharacteristic
239C4⋊(C3⋊D3)C23×C314yescomplemented
240C4×C3⋊D3C23×C314yes—
241C3×#67—216no—
242C3×#67—316no—
243C3×#67—316no—
244C3×#67—68no—
245C3×#67C22×D3116yescomplemented
246C3×#67C23×C3116yescomplemented
247C2×C3×Dic3—24no—
248C2×C3×Dic3—22no—
249C2×C3×Dic3—216no—
250C2×C3×Dic3—32no—
251C2×C3×Dic3—38no—
252C2×C3×Dic3—61no—
253C2×C3×Dic3C22×D314yes—
254C2×C3×Dic3C22×D312yes—
255C2×C3×Dic3C22×D3116yescomplemented
256C2×C3×Dic3C23×C312yes—
257C2×C3×Dic3C23×C314yes—
258C2×C3×Dic3C23×C3116yescomplemented
259C3×D12—316no—
260C3×D12—38no—
261C3×D12—64no—
262C3×C4×D3—28no—
263C3×C4×D3—38no—
264C3×C4×D3—38no—
265C3×C4×D3—38no—
266C3×C4×D3—316no—
267C3×C4×D3—316no—
268C3×C4×D3—316no—
269C3×C4×D3—64no—
270C3×C4×D3C22×D318yescomplemented
271C3×C4×D3C23×C318yescomplemented
272C3×Dic6—28no—
273C3×Dic6—316no—
274C3×Dic6C22×D318yescomplemented
275C3×Dic6C23×C318yescomplemented
276#627C23×C318yescomplemented
277#626C23×C3116yescomplemented
278#624C23×C318yes—
279#624C23×C314yes—
280#624C23×C3116yescomplemented
281D3×Dic3C23×C318yescomplemented
282C22×#41—91noSylow
283C2×C33—24no—
284C2×C33C2×#4112yescomplemented
285C2×C33C2511yescharacteristic
286C3×C3⋊D3—24no—
287C3×C3⋊D3C2×#4114yescomplemented
288C32×D3—24no—
289C24×C3—91no—
290C24×C3—92no—
291C23×D3—34no—
292C23×D3—32no—
293C23×D3—62no—
294C3×#41—316no—
295C3×#41—316no—
296C3×#41—616no—
297C3×#41—932no—
298C3×#41—916no—
299C2×C3×Q8—32no—
300C2×C3×Q8—32no—
301C2×C3×Q8—62no—
302C2×C3×Q8—92no—
303C2×C3×Q8—98no—
304C2×C3×D4—21no—
305C2×C3×D4—22no—
306C2×C3×D4—34no—
307C2×C3×D4—34no—
308C2×C3×D4—41no—
309C2×C3×D4—64no—
310C2×C3×D4—94no—
311C2×C3×D4—916no—
312C2×C3×D4—92no—
313C2×C3×D4—98no—
314C2×C3×D4—91no—
315C2×C3×D4D3211yescharacteristic, complemented
316C2×C3×D4C2×C3×D312yescomplemented
317C22×C3×C4—34no—
318C22×C3×C4—34no—
319C22×C3×C4—32no—
320C22×C3×C4—32no—
321C22×C3×C4—62no—
322C22×C3×C4—64no—
323C22×C3×C4—91no—
324C22×C3×C4—92no—
325C22×C3×C4—916no—
326C22×C3×C4—94no—
327C22×C3×C4—98no—
328C22×C3×C4—92no—
329C22×C3×C4—91no—
330C2×#67—34no—
331C2×#67—34no—
332C2×#67—62no—
333C2×#67C2×C3×D314yescomplemented
334C22×Dic3—32no—
335C22×Dic3C2×C3×D314yescomplemented
336#239—316no—
337D3×Q8—316no—
338#237—332no—
339#237C2×C3×D3116yescomplemented
340D3×D4—316no—
341D3×D4—332no—
342D3×D4—68no—
343#235—332no—
344#235—316no—
345C2×D12—34no—
346C2×D12—32no—
347C2×D12—61no—
348C2×C4×D3—32no—
349C2×C4×D3—32no—
350C2×C4×D3—32no—
351C2×C4×D3—34no—
352C2×C4×D3—34no—
353C2×C4×D3—34no—
354C2×C4×D3—332no—
355C2×C4×D3—316no—
356C2×C4×D3—61no—
357C2×C4×D3C2×C3×D312yescomplemented
358C2×Dic6—34no—
359C2×Dic6C2×C3×D312yescomplemented
360C22×C32—28no—
361C22×C32—24no—
362C22×C32—24no—
363C22×C32—21no—
364C22×C32—22no—
365C22×C32—28no—
366C22×C32—34no—
367C22×C32—41no—
368C22×C32—44no—
369C22×C32—44no—
370C22×C32—48no—
371C22×C32—64no—
372C22×C32—84no—
373C22×C32C23×D318yes—
374C22×C32C23×D312yes—
375C22×C32C24×C314yes—
376C22×C32C24×C311yescharacteristic
377C2×C3⋊D3—24no—
378C2×C3⋊D3—216no—
379C2×C3⋊D3C3×#4114yescomplemented
380C2×C3⋊D3C24×C314yes—
381C2×C3⋊D3C24×C312yes—
382C2×C3×D3—24no—
383C2×C3×D3—24no—
384C2×C3×D3—24no—
385C2×C3×D3—38no—
386C2×C3×D3—34no—
387C2×C3×D3—38no—
388C2×C3×D3—44no—
389C2×C3×D3—64no—
390C2×C3×D3—62no—
391C2×C3×D3—64no—
392C2×C3×D3—616no—
393C2×C3×D3—632no—
394C2×C3×D3—68no—
395C2×C3×D3—1216no—
396C2×C3×D3—124no—
397C2×C3×D3C23×D314yes—
398C2×C3×D3C24×C314yes—
399D32—28no—
400C32×C4—22no—
401C32×C4—24no—
402C32×C4—38no—
403C32×C4—34no—
404C32×C4—42no—
405C32×C4C23×D314yes—
406C32×C4C24×C312yes—
407C3⋊Dic3C24×C312yes—
408C3×Dic3—28no—
409C3×Dic3—24no—
410C3×Dic3—34no—
411C3×Dic3—62no—
412C3×Dic3C23×D318yes—
413C3×Dic3C23×D314yes—
414C3×Dic3C24×C314yes—
415C3×Dic3C24×C318yes—
416C2×#41—32no—
417C2×#41—94no—
418C2×#41—92no—
419C2×#41—916no—
420C22×Q8—91no—
421C22×D4—92no—
422C22×D4—91no—
423C23×C4—92no—
424C23×C4—91no—
425C33C22×#4111yescharacteristic, complemented, Sylow
426C23×C3—24no—
427C23×C3—22no—
428C23×C3—32no—
429C23×C3—32no—
430C23×C3—42no—
431C23×C3—62no—
432C23×C3—94no—
433C23×C3—91no—
434C23×C3—98no—
435C23×C3—92no—
436C23×C3—188no—
437C23×C3—184no—
438C23×C3C2×D3212yes—
439C23×C3C22×C3×D314yes—
440C22×D3—32no—
441C22×D3—34no—
442C22×D3—316no—
443C22×D3—38no—
444C22×D3—61no—
445C22×D3—62no—
446C22×D3—68no—
447C22×D3—68no—
448C22×D3—616no—
449C22×D3—128no—
450C22×D3C22×C3×D312yes—
451C3×Q8—38no—
452C3×Q8—38no—
453C3×Q8—68no—
454C3×Q8—98no—
455C3×D4—28no—
456C3×D4—24no—
457C3×D4—316no—
458C3×D4—316no—
459C3×D4—44no—
460C3×D4—616no—
461C3×D4—916no—
462C3×D4—98no—
463C3×D4—94no—
464C3×D4C2×D3214yescomplemented
465C3×D4C22×C3×D318yescomplemented
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—316no—
469C2×C3×C4—32no—
470C2×C3×C4—34no—
471C2×C3×C4—34no—
472C2×C3×C4—32no—
473C2×C3×C4—316no—
474C2×C3×C4—38no—
475C2×C3×C4—38no—
476C2×C3×C4—41no—
477C2×C3×C4—68no—
478C2×C3×C4—62no—
479C2×C3×C4—64no—
480C2×C3×C4—616no—
481C2×C3×C4—94no—
482C2×C3×C4—98no—
483C2×C3×C4—916no—
484C2×C3×C4—98no—
485C2×C3×C4—91no—
486C2×C3×C4—94no—
487C2×C3×C4C2×D3211yescharacteristic
488C2×C3×C4C22×C3×D312yes—
489#67—316no—
490#67—316no—
491#67—68no—
492#67C22×C3×D3116yescomplemented
493C2×Dic3—32no—
494C2×Dic3—38no—
495C2×Dic3—61no—
496C2×Dic3C22×C3×D314yes—
497C2×Dic3C22×C3×D312yes—
498C2×Dic3C22×C3×D3116yescomplemented
499D12—316no—
500D12—38no—
501D12—64no—
502C4×D3—38no—
503C4×D3—38no—
504C4×D3—38no—
505C4×D3—316no—
506C4×D3—316no—
507C4×D3—316no—
508C4×D3—64no—
509C4×D3C22×C3×D318yescomplemented
510Dic6—316no—
511Dic6C22×C3×D318yescomplemented
512C2×C32—28no—
513C2×C32—24no—
514C2×C32—22no—
515C2×C32—24no—
516C2×C32—21no—
517C2×C32—22no—
518C2×C32—42no—
519C2×C32—41no—
520C2×C32—44no—
521C2×C32—48no—
522C2×C32—64no—
523C2×C32—84no—
524C2×C32D3×#4114yescomplemented
525C2×C32C2×C3×#4112yescomplemented
526C2×C32C24×D312yes—
527C2×C32C25×C311yescharacteristic
528C3⋊D3—24no—
529C3⋊D3C2×C3×#4114yescomplemented
530C3×D3—24no—
531C3×D3—24no—
532C3×D3—38no—
533C3×D3—44no—
534C3×D3—64no—
535C3×D3—68no—
536C3×D3—124no—
537C24—91no—
538C24—92no—
539#41—316no—
540#41—932no—
541#41—916no—
542C2×Q8—32no—
543C2×Q8—92no—
544C2×Q8—98no—
545C2×D4—34no—
546C2×D4—94no—
547C2×D4—916no—
548C2×D4—92no—
549C2×D4—98no—
550C2×D4—91no—
551C2×D4C3×D3211yescharacteristic, complemented
552C22×C4—34no—
553C22×C4—32no—
554C22×C4—91no—
555C22×C4—92no—
556C22×C4—94no—
557C22×C4—916no—
558C22×C4—98no—
559C22×C4—92no—
560C22×C4—91no—
561C22×C3—24no—
562C22×C3—28no—
563C22×C3—21no—
564C22×C3—22no—
565C22×C3—24no—
566C22×C3—28no—
567C22×C3—34no—
568C22×C3—34no—
569C22×C3—44no—
570C22×C3—48no—
571C22×C3—41no—
572C22×C3—44no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—84no—
577C22×C3—94no—
578C22×C3—92no—
579C22×C3—94no—
580C22×C3—124no—
581C22×C3—1816no—
582C22×C3—188no—
583C22×C3—184no—
584C22×C3C22×D3214yes—
585C22×C3C22×D3211yescharacteristic
586C22×C3C23×C3×D318yes—
587C22×C3C23×C3×D312yes—
588C2×D3—24no—
589C2×D3—38no—
590C2×D3—34no—
591C2×D3—38no—
592C2×D3—62no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—616no—
596C2×D3—632no—
597C2×D3—68no—
598C2×D3—1216no—
599C2×D3—124no—
600C2×D3C23×C3×D314yes—
601C3×C4—22no—
602C3×C4—24no—
603C3×C4—34no—
604C3×C4—38no—
605C3×C4—38no—
606C3×C4—34no—
607C3×C4—42no—
608C3×C4—64no—
609C3×C4—68no—
610C3×C4—92no—
611C3×C4C22×D3212yes—
612C3×C4C23×C3×D314yes—
613Dic3—34no—
614Dic3—62no—
615Dic3C23×C3×D318yes—
616Dic3C23×C3×D314yes—
617C32—21no—
618C32—22no—
619C32—41no—
620C32C2×D3×#4112yescomplemented
621C32C22×C3×#4111yescharacteristic, complemented
622C23—32no—
623C23—94no—
624C23—91no—
625C23—98no—
626C23—92no—
627C23—188no—
628C23—184no—
629C23C2×C3×D3212yes—
630Q8—38no—
631Q8—98no—
632D4—316no—
633D4—916no—
634D4—98no—
635D4—94no—
636D4C2×C3×D3214yescomplemented
637C2×C4—32no—
638C2×C4—34no—
639C2×C4—316no—
640C2×C4—38no—
641C2×C4—94no—
642C2×C4—98no—
643C2×C4—916no—
644C2×C4—98no—
645C2×C4—91no—
646C2×C4—94no—
647C2×C4C2×C3×D3211yescharacteristic
648C2×C3—24no—
649C2×C3—28no—
650C2×C3—21no—
651C2×C3—22no—
652C2×C3—22no—
653C2×C3—24no—
654C2×C3—44no—
655C2×C3—48no—
656C2×C3—41no—
657C2×C3—42no—
658C2×C3—64no—
659C2×C3—64no—
660C2×C3—84no—
661C2×C3—94no—
662C2×C3—124no—
663C2×C3—184no—
664C2×C3#6431212yesdirect product factor
665C2×C3C3×D3×#4114yescomplemented
666C2×C3C23×D3211yescharacteristic
667C2×C3C24×C3×D312yes—
668D3—24no—
669D3—38no—
670D3—64no—
671D3—68no—
672D3—124no—
673C22—24no—
674C22—34no—
675C22—64no—
676C22—92no—
677C22—94no—
678C22—94no—
679C22—1816no—
680C22—188no—
681C22—184no—
682C22C22×C3×D3214yes—
683C22C22×C3×D3211yescharacteristic
684C4—34no—
685C4—38no—
686C4—92no—
687C4C22×C3×D3212yes—
688C3—21no—
689C3—22no—
690C3—41no—
691C3C2×#6431211yescharacteristic, direct product factor
692C3C2×C3×D3×#4112yescomplemented
693C2—24no—
694C2—64no—
695C2—94no—
696C2—184no—
697C2C3×#6431212yesdirect product factor
698C2C23×C3×D3211yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC2×C32C25×C3
FrattiniC2C23×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C22×C3×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×C32×#237C2semidirect
3. C2×C3×#3811C2semidirect
4. C22×C3×#624C2semidirect
5. C2×C3×#3804C2semidirect
6. C3×#64312C2direct (N × H)
7. C2×C3×C4×D32C2semidirect
8. C2×C3×#3799C2semidirect
9. C2×C3×#3797C2semidirect
11. C2×#64312C3direct (N × H)
14. C2×C33×D4C22semidirect
15. C2×C3×#638C22semidirect
16. C3×D4×C3⋊D3C22semidirect
17. C2×C3×C4⋊(C3⋊D3)C22semidirect
19. C2×C32×#67C22semidirect
20. C22×C32×Dic3C22semidirect
21. C32×#237C22semidirect
22. C2×C32×C4×D3C22semidirect
23. C2×C32×Dic6C22semidirect
24. C3×#3811C22semidirect
25. C2×C3×#627C22semidirect
26. C2×C3×#626C22semidirect
29. C2×C3×#624C22semidirect
30. C2×C3×#624C22semidirect
31. C3×#3804C22semidirect
32. C2×C3×D3×Dic3C22semidirect
33. C3×C4×D32C22semidirect
34. C3×#3799C22semidirect
35. C3×#3797C22semidirect
37. C2×D4×C3⋊D3C2×C3semidirect
43. C2×C3×#237D3semidirect
44. C2×C3×#237C2×C3semidirect
52. C2×#3811C2×C3semidirect
53. C22×#624C2×C3semidirect
54. C2×#3804C2×C3semidirect
55. #64312C2×C3direct (N × H)
56. C2×C4×D32C2×C3semidirect
57. C2×#3799C2×C3semidirect
58. C2×#3797C2×C3semidirect
67. C33×D4C23semidirect
69. C3×#638C23semidirect
71. C3×C4⋊(C3⋊D3)C23semidirect
73. C32×#67C23semidirect
76. C2×C32×Dic3C23semidirect
77. C32×C4×D3C23semidirect
78. C32×Dic6C23semidirect
79. C3×#627C23semidirect
80. C3×#626C23semidirect
83. C3×#624C23semidirect
84. C3×D3×Dic3C23semidirect
98. C2×C32×D4C2×D3semidirect
99. C2×C32×D4C22×C3semidirect
102. C2×#638C22×C3semidirect
103. D4×C3⋊D3C22×C3semidirect
104. C2×C4⋊(C3⋊D3)C22×C3semidirect
110. C2×C3×#67C2×D3semidirect
111. C2×C3×#67C22×C3semidirect
114. C22×C3×Dic3C2×D3semidirect
115. C22×C3×Dic3C22×C3semidirect
120. C3×#237C2×D3semidirect
121. C3×#237C22×C3semidirect
140. C2×C3×C4×D3C2×D3semidirect
141. C2×C3×C4×D3C22×C3semidirect
144. C2×C3×Dic6C2×D3semidirect
145. C2×C3×Dic6C22×C3semidirect
146. #3811C22×C3semidirect
147. C2×#627C22×C3semidirect
148. C2×#626C22×C3semidirect
151. C2×#624C22×C3semidirect
152. C2×#624C22×C3semidirect
153. #3804C22×C3semidirect
154. C2×D3×Dic3C22×C3semidirect
155. C4×D32C22×C3semidirect
156. #3799C22×C3semidirect
157. #3797C22×C3semidirect
163. C2×C3×C3⋊D3#41semidirect
188. C2×#237C3×D3semidirect
226. C32×D4C22×D3semidirect
227. C32×D4C23×C3semidirect
237. #638C23×C3semidirect
239. C4⋊(C3⋊D3)C23×C3semidirect
245. C3×#67C22×D3semidirect
246. C3×#67C23×C3semidirect
255. C2×C3×Dic3C22×D3semidirect
258. C2×C3×Dic3C23×C3semidirect
270. C3×C4×D3C22×D3semidirect
271. C3×C4×D3C23×C3semidirect
274. C3×Dic6C22×D3semidirect
275. C3×Dic6C23×C3semidirect
276. #627C23×C3semidirect
277. #626C23×C3semidirect
280. #624C23×C3semidirect
281. D3×Dic3C23×C3semidirect
284. C2×C33C2×#41semidirect
287. C3×C3⋊D3C2×#41semidirect
315. C2×C3×D4D32semidirect
316. C2×C3×D4C2×C3×D3semidirect
333. C2×#67C2×C3×D3semidirect
335. C22×Dic3C2×C3×D3semidirect
339. #237C2×C3×D3semidirect
357. C2×C4×D3C2×C3×D3semidirect
359. C2×Dic6C2×C3×D3semidirect
379. C2×C3⋊D3C3×#41semidirect
425. C33C22×#41semidirect
464. C3×D4C2×D32semidirect
465. C3×D4C22×C3×D3semidirect
492. #67C22×C3×D3semidirect
498. C2×Dic3C22×C3×D3semidirect
509. C4×D3C22×C3×D3semidirect
511. Dic6C22×C3×D3semidirect
524. C2×C32D3×#41semidirect
525. C2×C32C2×C3×#41semidirect
529. C3⋊D3C2×C3×#41semidirect
551. C2×D4C3×D32semidirect
620. C32C2×D3×#41semidirect
621. C32C22×C3×#41semidirect
636. D4C2×C3×D32semidirect
664. C2×C3#64312direct (N × H)
665. C2×C3C3×D3×#41semidirect
691. C3C2×#64312direct (N × H)
692. C3C2×C3×D3×#41semidirect
697. C2C3×#64312direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C32×#2372
C2×C3×#38112
C22×C3×#6242
C2×C3×#38042
C3×#643122
C2×C3×C4×D322
C2×C3×#37992
C2×C3×#37972
C2×C3×D3×#413
C2×#643123