Finite Group Databasebeta

← C2×C3×#63839 #13174634

Subgroups — C2×C3×#63839 #13174634

Order 1728.

1554 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×Dic6C211yesmaximal, characteristic
2C22×C3×#627C211yesmaximal, characteristic
3C2×C3×#3750C211yesmaximal, characteristic
4C2×C32×Dic3⋊C4C211yesmaximal, characteristic
5C2×C3×#3724C211yesmaximal, characteristic
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
7C2×C3×Dic32C211yesmaximal, characteristic
8C3×#63839C218yesmaximal, direct product factor
9C2×C3×#944—31nomaximal
10C2×C3×#888—31nomaximal
11C2×#63839C311yesmaximal, characteristic, direct product factor
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×C32×Dic6—24no—
20C2×C32×Dic6C2214yes—
21C2×C3×#627—24no—
22C2×C3×#627C2214yes—
23C3×#3750C2214yes—
24C32×Dic3⋊C4C2214yes—
25C3×#3724C2214yes—
26C3×Dic3⋊Dic3C2214yes—
27C3×Dic32C2214yes—
28C22×C32×Q8—31no—
29C22×C3×Dic6—21no—
30C22×C3×Dic6—31no—
31C22×C3×Dic6—31no—
32C22×C3×Dic6D311yescharacteristic
33C22×C3×Dic6C2×C311yescharacteristic
34C22×#627C2×C311yescharacteristic
35C2×C32×C4⋊C4—31no—
36C2×#3750C2×C311yescharacteristic
37C3×#944—38no—
38C2×C3×C4⋊Dic3—31no—
39C2×C3×Dic3⋊C4—21no—
40C2×C3×Dic3⋊C4—31no—
41C2×C3×Dic3⋊C4—31no—
42C2×C3×Dic3⋊C4—31no—
43C2×C3×Dic3⋊C4—31no—
44C2×C3×Dic3⋊C4—31no—
45C2×C3×Dic3⋊C4—61no—
46C2×C3×Dic3⋊C4D311yescharacteristic
47C2×C3×Dic3⋊C4C2×C311yescharacteristic
48C2×C3×C4×Dic3—31no—
49C2×C3×C4×Dic3—31no—
50C3×#888—38no—
51C2×#3724C2×C311yescharacteristic
52C2×Dic3⋊Dic3C2×C311yescharacteristic
53C2×Dic32C2×C311yescharacteristic
54#63839C2×C318yesdirect product factor
55C23×C33C2311yescharacteristic
56C2×C33×C4—22no—
57C2×C33×C4C2312yes—
58C2×C3×C3⋊Dic3—22no—
59C2×C3×C3⋊Dic3Q814yescomplemented
60C2×C3×C3⋊Dic3C2312yes—
61C2×C3×C3⋊Dic3C2312yes—
62C2×C32×Dic3—22no—
63C2×C32×Dic3—22no—
64C2×C32×Dic3D414yes—
65C2×C32×Dic3Q814yescomplemented
66C2×C32×Dic3C2312yes—
67C2×C32×Dic3C2312yes—
68C2×C32×Dic3C2312yes—
69C2×C32×Dic3C2312yes—
70C32×Dic6—28no—
71C3×#627—28no—
72C2×C3×C4⋊Q8—91no—
73C2×#944—31no—
74C2×#888—31no—
75C2×C32×Q8—34no—
76C2×C32×Q8—64no—
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4—31no—
81C22×C32×C4—31no—
82C22×C32×C4—31no—
83C22×C32×C4—31no—
84C22×C32×C4—41no—
85C22×C32×C4C2×D311yescharacteristic
86C22×C32×C4C2×D311yescharacteristic
87C22×C32×C4C22×C311yescharacteristic
88C22×C3⋊Dic3C22×C311yescharacteristic
89C22×C3⋊Dic3C22×C311yescharacteristic
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—61no—
99C22×C3×Dic3—61no—
100C22×C3×Dic3C2×D311yescharacteristic
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C22×C311yescharacteristic
105C22×C3×Dic3C22×C311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107C22×C3×Dic3C22×C311yescharacteristic
108C2×C3×Dic6—28no—
109C2×C3×Dic6—24no—
110C2×C3×Dic6—24no—
111C2×C3×Dic6—24no—
112C2×C3×Dic6—34no—
113C2×C3×Dic6—34no—
114C2×C3×Dic6—64no—
115C2×C3×Dic6—64no—
116C2×C3×Dic6C2×D314yes—
117C2×C3×Dic6C22×C314yes—
118C2×#627—24no—
119C2×#627C22×C314yes—
120C32×C4⋊C4—34no—
121#3750C22×C314yes—
122C3×C4⋊Dic3—34no—
123C3×Dic3⋊C4—24no—
124C3×Dic3⋊C4—34no—
125C3×Dic3⋊C4—34no—
126C3×Dic3⋊C4—34no—
127C3×Dic3⋊C4—34no—
128C3×Dic3⋊C4—34no—
129C3×Dic3⋊C4—64no—
130C3×Dic3⋊C4C2×D314yes—
131C3×Dic3⋊C4C22×C314yes—
132C3×C4×Dic3—34no—
133C3×C4×Dic3—34no—
134#3724C22×C314yes—
135Dic3⋊Dic3C22×C314yes—
136Dic32C22×C314yes—
137C22×C33C2×D412yes—
138C22×C33C2×Q812yes—
139C22×C33C2×Q812yes—
140C22×C33C2411yescharacteristic
141C33×C4—22no—
142C3×C3⋊Dic3—22no—
143C3×C3⋊Dic3C2×Q814yescomplemented
144C32×Dic3—22no—
145C32×Dic3—22no—
146C32×Dic3C2×D414yes—
147C32×Dic3C2×Q814yescomplemented
148C22×C3×Q8—31no—
149C22×C3×Q8—31no—
150C22×C3×Q8—61no—
151C22×C3×Q8—91no—
152C22×Dic6—31no—
153C22×Dic6—31no—
154C22×Dic6C3×D311yescharacteristic
155C3×C4⋊Q8—98no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—61no—
159C2×C3×C4⋊C4—91no—
160C2×C3×C4⋊C4—91no—
161C2×C3×C4⋊C4—91no—
162C2×C3×C42—91no—
163#944—38no—
164C2×C4⋊Dic3—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—61no—
171C2×Dic3⋊C4C3×D311yescharacteristic
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174#888—38no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—41no—
179C23×C32C22×D311yescharacteristic
180C23×C32C22×D311yescharacteristic
181C23×C32C23×C311yescharacteristic
182C32×Q8—68no—
183C2×C32×C4—22no—
184C2×C32×C4—24no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—34no—
191C2×C32×C4—34no—
192C2×C32×C4—32no—
193C2×C32×C4—32no—
194C2×C32×C4—32no—
195C2×C32×C4—32no—
196C2×C32×C4—42no—
197C2×C32×C4—42no—
198C2×C32×C4—42no—
199C2×C32×C4—44no—
200C2×C32×C4—62no—
201C2×C32×C4—62no—
202C2×C32×C4C22×D312yes—
203C2×C32×C4C22×D312yes—
204C2×C32×C4C23×C312yes—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3C3×Q814yescomplemented
207C2×C3⋊Dic3C23×C312yes—
208C2×C3⋊Dic3C23×C312yes—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—24no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—34no—
221C2×C3×Dic3—34no—
222C2×C3×Dic3—32no—
223C2×C3×Dic3—32no—
224C2×C3×Dic3—32no—
225C2×C3×Dic3—32no—
226C2×C3×Dic3—42no—
227C2×C3×Dic3—62no—
228C2×C3×Dic3—64no—
229C2×C3×Dic3—62no—
230C2×C3×Dic3—62no—
231C2×C3×Dic3—62no—
232C2×C3×Dic3—122no—
233C2×C3×Dic3Dic614yescomplemented
234C2×C3×Dic3#6714yes—
235C2×C3×Dic3C3×D414yes—
236C2×C3×Dic3C3×Q814yescomplemented
237C2×C3×Dic3C22×D312yes—
238C2×C3×Dic3C22×D312yes—
239C2×C3×Dic3C22×D312yes—
240C2×C3×Dic3C22×D312yes—
241C2×C3×Dic3C23×C312yes—
242C2×C3×Dic3C23×C312yes—
243C2×C3×Dic3C23×C312yes—
244C2×C3×Dic3C23×C312yes—
245C3×Dic6—216no—
246C3×Dic6—28no—
247C3×Dic6—28no—
248C3×Dic6—68no—
249C3×Dic6—68no—
250#627—28no—
251C2×C4⋊Q8—91noSylow
252C2×C33C4⋊Q814yescomplemented
253C2×C33C22×D411yescharacteristic
254C2×C33C22×Q811yescharacteristic
255C2×C33C22×Q811yescharacteristic
256C2×C3×Q8—34no—
257C2×C3×Q8—34no—
258C2×C3×Q8—64no—
259C2×C3×Q8—64no—
260C2×C3×Q8—64no—
261C2×C3×Q8—68no—
262C2×C3×Q8—94no—
263C2×C3×Q8—184no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—41no—
276C22×C3×C4—61no—
277C22×C3×C4—61no—
278C22×C3×C4—61no—
279C22×C3×C4—61no—
280C22×C3×C4—91no—
281C22×C3×C4—91no—
282C22×C3×C4D3211yescharacteristic
283C22×C3×C4C2×C3×D311yescharacteristic
284C22×C3×C4C2×C3×D311yescharacteristic
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3C2×C3×D311yescharacteristic
292C22×Dic3C2×C3×D311yescharacteristic
293C22×Dic3C2×C3×D311yescharacteristic
294C22×Dic3C2×C3×D311yescharacteristic
295C2×Dic6—24no—
296C2×Dic6—34no—
297C2×Dic6—34no—
298C2×Dic6—64no—
299C2×Dic6—64no—
300C2×Dic6C2×C3×D314yes—
301C3×C4⋊C4—34no—
302C3×C4⋊C4—34no—
303C3×C4⋊C4—64no—
304C3×C4⋊C4—94no—
305C3×C4⋊C4—94no—
306C3×C4⋊C4—94no—
307C3×C42—94no—
308C4⋊Dic3—34no—
309Dic3⋊C4—34no—
310Dic3⋊C4—34no—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—34no—
314Dic3⋊C4—64no—
315Dic3⋊C4C2×C3×D314yes—
316C4×Dic3—34no—
317C4×Dic3—34no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—42no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—41no—
334C22×C32C2×Dic612yes—
335C22×C32D3×D412yes—
336C22×C32D3×Q812yes—
337C22×C32D3×Q812yes—
338C22×C32D3×Q812yes—
339C22×C32C2×#6712yes—
340C22×C32C2×C3×D412yes—
341C22×C32C2×C3×Q812yes—
342C22×C32C2×C3×Q812yes—
343C22×C32C23×D311yescharacteristic
344C22×C32C23×D311yescharacteristic
345C22×C32C24×C311yescharacteristic
346C32×C4—22no—
347C32×C4—24no—
348C32×C4—22no—
349C32×C4—22no—
350C32×C4—34no—
351C32×C4—34no—
352C32×C4—42no—
353C32×C4—42no—
354C32×C4—44no—
355C32×C4—62no—
356C32×C4—62no—
357C3⋊Dic3—22no—
358C3⋊Dic3C2×C3×Q814yescomplemented
359C3×Dic3—24no—
360C3×Dic3—22no—
361C3×Dic3—22no—
362C3×Dic3—22no—
363C3×Dic3—22no—
364C3×Dic3—24no—
365C3×Dic3—24no—
366C3×Dic3—34no—
367C3×Dic3—34no—
368C3×Dic3—42no—
369C3×Dic3—64no—
370C3×Dic3—62no—
371C3×Dic3—62no—
372C3×Dic3—122no—
373C3×Dic3C2×Dic614yescomplemented
374C3×Dic3C2×#6714yes—
375C3×Dic3C2×C3×D414yes—
376C3×Dic3C2×C3×Q814yescomplemented
377C22×Q8—31no—
378C22×Q8—91no—
379C4⋊Q8—98no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C42—91no—
385C33C2×C4⋊Q811yescharacteristic, complemented, Sylow
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—41no—
390C23×C3C2×D3211yescharacteristic
391C23×C3C22×C3×D311yescharacteristic
392C23×C3C22×C3×D311yescharacteristic
393C3×Q8—68no—
394C3×Q8—68no—
395C3×Q8—616no—
396C3×Q8—188no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—32no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—34no—
409C2×C3×C4—34no—
410C2×C3×C4—34no—
411C2×C3×C4—34no—
412C2×C3×C4—32no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—32no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—44no—
419C2×C3×C4—42no—
420C2×C3×C4—62no—
421C2×C3×C4—64no—
422C2×C3×C4—62no—
423C2×C3×C4—64no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—64no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—92no—
432C2×C3×C4—94no—
433C2×C3×C4—92no—
434C2×C3×C4—122no—
435C2×C3×C4—182no—
436C2×C3×C4C2×D3212yes—
437C2×C3×C4C22×C3×D312yes—
438C2×C3×C4C22×C3×D312yes—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—34no—
444C2×Dic3—34no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—64no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—122no—
453C2×Dic3C3×Dic614yescomplemented
454C2×Dic3C3×#6714yes—
455C2×Dic3C22×C3×D312yes—
456C2×Dic3C22×C3×D312yes—
457C2×Dic3C22×C3×D312yes—
458C2×Dic3C22×C3×D312yes—
459Dic6—28no—
460Dic6—68no—
461Dic6—68no—
462C2×C32—24no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—24no—
466C2×C32—21no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32—21no—
471C2×C32—21no—
472C2×C32—24no—
473C2×C32—21no—
474C2×C32—44no—
475C2×C32—41no—
476C2×C32—41no—
477C2×C32—41no—
478C2×C32#88814yescomplemented
479C2×C32#94414yescomplemented
480C2×C32C3×C4⋊Q814yescomplemented
481C2×C32C22×Dic611yescharacteristic
482C2×C32C2×D3×D411yescharacteristic
483C2×C32C2×D3×Q811yescharacteristic
484C2×C32C2×D3×Q811yescharacteristic
485C2×C32C2×D3×Q811yescharacteristic
486C2×C32C22×#6711yescharacteristic
487C2×C32C22×C3×D411yescharacteristic
488C2×C32C22×C3×Q811yescharacteristic
489C2×C32C22×C3×Q811yescharacteristic
490C2×Q8—34no—
491C2×Q8—64no—
492C2×Q8—94no—
493C2×Q8—184no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—91no—
499C22×C4—91no—
500C22×C4C3×D3211yescharacteristic
501C4⋊C4—34no—
502C4⋊C4—94no—
503C4⋊C4—94no—
504C4⋊C4—94no—
505C42—94no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—41no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3D3×Dic612yes—
523C22×C3#379712yes—
524C22×C3D3×#6712yes—
525C22×C3C2×C3×Dic612yes—
526C22×C3C3×D3×D412yes—
527C22×C3C3×D3×Q812yes—
528C22×C3C3×D3×Q812yes—
529C22×C3C3×D3×Q812yes—
530C22×C3C2×C3×#6712yes—
531C22×C3C22×D3211yescharacteristic
532C22×C3C23×C3×D311yescharacteristic
533C22×C3C23×C3×D311yescharacteristic
534C3×C4—24no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—34no—
539C3×C4—34no—
540C3×C4—34no—
541C3×C4—34no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—44no—
545C3×C4—64no—
546C3×C4—64no—
547C3×C4—64no—
548C3×C4—62no—
549C3×C4—62no—
550C3×C4—62no—
551C3×C4—62no—
552C3×C4—94no—
553C3×C4—122no—
554C3×C4—182no—
555Dic3—22no—
556Dic3—22no—
557Dic3—34no—
558Dic3—34no—
559Dic3—64no—
560Dic3—62no—
561Dic3—62no—
562Dic3—122no—
563Dic3C2×C3×Dic614yescomplemented
564Dic3C2×C3×#6714yes—
565C32—21no—
566C32—21no—
567C32—21no—
568C32—41no—
569C32C2×#88811yescharacteristic, complemented
570C32C2×#94411yescharacteristic, complemented
571C32C2×C3×C4⋊Q811yescharacteristic, complemented
572C23C2×C3×D3211yescharacteristic
573Q8—68no—
574Q8—188no—
575C2×C4—22no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—34no—
579C2×C4—34no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—92no—
585C2×C4—94no—
586C2×C4—92no—
587C2×C4—182no—
588C2×C4C2×C3×D3212yes—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—24no—
593C2×C3—24no—
594C2×C3—24no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—41no—
602C2×C3—44no—
603C2×C3—41no—
604C2×C3—41no—
605C2×C3#6383914yesdirect product factor
606C2×C3C3×#88814yescomplemented
607C2×C3C3×#94414yescomplemented
608C2×C3C2×D3×Dic611yescharacteristic
609C2×C3C2×#379711yescharacteristic
610C2×C3C2×D3×#6711yescharacteristic
611C2×C3C22×C3×Dic611yescharacteristic
612C2×C3C2×C3×D3×D411yescharacteristic
613C2×C3C2×C3×D3×Q811yescharacteristic
614C2×C3C2×C3×D3×Q811yescharacteristic
615C2×C3C2×C3×D3×Q811yescharacteristic
616C2×C3C22×C3×#6711yescharacteristic
617C22C3×D3×Dic612yes—
618C22C3×#379712yes—
619C22C3×D3×#6712yes—
620C22C22×C3×D3211yescharacteristic
621C4—22no—
622C4—34no—
623C4—34no—
624C4—62no—
625C4—62no—
626C4—94no—
627C4—182no—
628C3—21no—
629C3—21no—
630C3—21no—
631C3—41no—
632C3C2×#6383911yescharacteristic, direct product factor
633C3C2×C3×#88811yescharacteristic, complemented
634C3C2×C3×#94411yescharacteristic, complemented
635C2C3×#6383914yesdirect product factor
636C2C2×C3×D3×Dic611yescharacteristic
637C2C2×C3×#379711yescharacteristic
638C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×C4⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
8. C3×#63839C2direct (N × H)
11. C2×#63839C3direct (N × H)
54. #63839C2×C3direct (N × H)
59. C2×C3×C3⋊Dic3Q8semidirect
65. C2×C32×Dic3Q8semidirect
143. C3×C3⋊Dic3C2×Q8semidirect
147. C32×Dic3C2×Q8semidirect
206. C2×C3⋊Dic3C3×Q8semidirect
233. C2×C3×Dic3Dic6semidirect
236. C2×C3×Dic3C3×Q8semidirect
252. C2×C33C4⋊Q8semidirect
358. C3⋊Dic3C2×C3×Q8semidirect
373. C3×Dic3C2×Dic6semidirect
376. C3×Dic3C2×C3×Q8semidirect
385. C33C2×C4⋊Q8semidirect
453. C2×Dic3C3×Dic6semidirect
478. C2×C32#888semidirect
479. C2×C32#944semidirect
480. C2×C32C3×C4⋊Q8semidirect
563. Dic3C2×C3×Dic6semidirect
569. C32C2×#888semidirect
570. C32C2×#944semidirect
571. C32C2×C3×C4⋊Q8semidirect
605. C2×C3#63839direct (N × H)
606. C2×C3C3×#888semidirect
607. C2×C3C3×#944semidirect
632. C3C2×#63839direct (N × H)
633. C3C2×C3×#888semidirect
634. C3C2×C3×#944semidirect
635. C2C3×#63839direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×Dic62
C22×C3×#6272
C2×C3×#37502
C2×C32×Dic3⋊C42
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C2×C3×Dic322
C3×#638392
C2×C3×#9443
C2×C3×#8883
C2×#638393