Finite Group Databasebeta

← C2×C3×#63964 #13175114

Subgroups — C2×C3×#63964 #13175114

Order 1728.

1922 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×Dic3C211yesmaximal, characteristic
2C22×C3×#627C211yesmaximal, characteristic, complemented
3C2×C3×#3757C211yesmaximal, characteristic
4C2×C32×#217C211yesmaximal, characteristic
5C2×C3×#3724C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63964C218yesmaximal, direct product factor
9C2×C3×#924—31nomaximal
10C2×C3×#878—31nomaximal
11C2×#63964C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3—24no—
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2214yes—
18C22×C32×Dic3C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C2×C3×#627—24no—
22C2×C3×#627C2214yescomplemented
23C3×#3757C2214yes—
24C32×#217C2214yes—
25C3×#3724C2214yescomplemented
26C3×Dic3⋊Dic3C2214yescomplemented
27C3×Dic3⋊Dic3C2214yescomplemented
28C23×C32×C4—31no—
29C23×C3×Dic3—21no—
30C23×C3×Dic3D311yescharacteristic
31C23×C3×Dic3C2×C311yescharacteristic
32C22×C3×Dic6—31no—
33C22×C3×Dic6—31no—
34C22×#627C2×C311yescharacteristic, complemented
35C2×C32×C22⋊C4—31no—
36C2×#3757C2×C311yescharacteristic
37C2×C3×#217—21no—
38C2×C3×#217—31no—
39C2×C3×#217—31no—
40C2×C3×#217—61no—
41C2×C3×#217D311yescharacteristic
42C2×C3×#217C2×C311yescharacteristic
43C2×C3×C4⋊Dic3—31no—
44C2×C3×C4⋊Dic3—31no—
45C3×#924—38no—
46C2×C3×Dic3⋊C4—31no—
47C2×C3×Dic3⋊C4—31no—
48C2×C3×Dic3⋊C4—31no—
49C2×C3×Dic3⋊C4—31no—
50C3×#878—38no—
51C2×#3724C2×C311yescharacteristic, complemented
52C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
53C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
54#63964C2×C318yesdirect product factor
55C23×C33—22no—
56C23×C33—22no—
57C23×C33Q814yescomplemented
58C23×C33C2312yes—
59C23×C33C2311yescharacteristic
60C2×C3×C3⋊Dic3—22no—
61C2×C3×C3⋊Dic3—22no—
62C2×C3×C3⋊Dic3C2312yes—
63C2×C3×C3⋊Dic3C2312yes—
64C2×C32×Dic3—22no—
65C2×C32×Dic3—22no—
66C2×C32×Dic3—22no—
67C2×C32×Dic3—28no—
68C2×C32×Dic3D414yes—
69C2×C32×Dic3C2312yes—
70C2×C32×Dic3C2312yes—
71C2×C32×Dic3C2312yes—
72C2×C32×Dic3C2312yes—
73C3×#627—28no—
74C2×C3×C22⋊Q8—91no—
75C2×#924—31no—
76C2×#878—31no—
77C24×C32—21no—
78C24×C32—21no—
79C24×C32—21no—
80C24×C32—41no—
81C24×C32C2×D311yescharacteristic
82C24×C32C2×D311yescharacteristic
83C24×C32C22×C311yescharacteristic
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C22×C32×C4—34no—
89C22×C32×C4—64no—
90C22×C3⋊Dic3C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C22×C3×Dic3—28no—
93C22×C3×Dic3—24no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—24no—
97C22×C3×Dic3—24no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—61no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3C2×D314yes—
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C2×D311yescharacteristic
110C22×C3×Dic3C2×D311yescharacteristic
111C22×C3×Dic3C22×C311yescharacteristic
112C22×C3×Dic3C22×C311yescharacteristic
113C22×C3×Dic3C22×C314yes—
114C22×C3×Dic3C22×C311yescharacteristic
115C22×C3×Dic3C22×C311yescharacteristic
116C2×C3×Dic6—34no—
117C2×C3×Dic6—34no—
118C2×C3×Dic6—64no—
119C2×C3×Dic6—64no—
120C2×#627—24no—
121C2×#627C22×C314yescomplemented
122C32×C22⋊C4—34no—
123#3757C22×C314yes—
124C3×#217—24no—
125C3×#217—34no—
126C3×#217—34no—
127C3×#217—64no—
128C3×#217C2×D314yes—
129C3×#217C22×C314yes—
130C3×C4⋊Dic3—34no—
131C3×C4⋊Dic3—34no—
132C3×Dic3⋊C4—34no—
133C3×Dic3⋊C4—34no—
134C3×Dic3⋊C4—34no—
135C3×Dic3⋊C4—34no—
136#3724C22×C314yescomplemented
137Dic3⋊Dic3C22×C314yescomplemented
138Dic3⋊Dic3C22×C314yescomplemented
139C22×C33—28no—
140C22×C33—22no—
141C22×C33—22no—
142C22×C33C2×D412yes—
143C22×C33C2×Q812yes—
144C22×C33C2×Q814yescomplemented
145C22×C33#4112yes—
146C22×C33C2411yescharacteristic
147C3×C3⋊Dic3—22no—
148C3×C3⋊Dic3—22no—
149C32×Dic3—22no—
150C32×Dic3—22no—
151C32×Dic3—22no—
152C32×Dic3C2×D414yes—
153C22×C3×Q8—91no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C23×C3×C4—61no—
157C23×Dic3C3×D311yescharacteristic
158C22×Dic6—31no—
159C22×Dic6—31no—
160C3×C22⋊Q8—98no—
161C2×C3×C4⋊C4—91no—
162C2×C3×C4⋊C4—91no—
163C2×C3×C4⋊C4—91no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—61no—
167C2×C3×C22⋊C4—91no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—61no—
171C2×#217C3×D311yescharacteristic
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174#924—38no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179#878—38no—
180C23×C32—22no—
181C23×C32—22no—
182C23×C32—24no—
183C23×C32—24no—
184C23×C32—22no—
185C23×C32—22no—
186C23×C32—22no—
187C23×C32—22no—
188C23×C32—24no—
189C23×C32—24no—
190C23×C32—24no—
191C23×C32—22no—
192C23×C32—21no—
193C23×C32—22no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—22no—
197C23×C32—44no—
198C23×C32—41no—
199C23×C32—42no—
200C23×C32—42no—
201C23×C32—42no—
202C23×C32—42no—
203C23×C32—42no—
204C23×C32—44no—
205C23×C32—44no—
206C23×C32Dic614yescomplemented
207C23×C32Dic614yescomplemented
208C23×C32C3×Q814yescomplemented
209C23×C32C22×D312yes—
210C23×C32C22×D312yes—
211C23×C32C22×D311yescharacteristic
212C23×C32C22×D311yescharacteristic
213C23×C32C23×C312yes—
214C23×C32C23×C311yescharacteristic
215C2×C32×C4—34no—
216C2×C32×C4—32no—
217C2×C32×C4—32no—
218C2×C32×C4—32no—
219C2×C32×C4—32no—
220C2×C32×C4—68no—
221C2×C32×C4—62no—
222C2×C32×C4—62no—
223C2×C32×C4—62no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3C23×C312yes—
227C2×C3⋊Dic3C23×C312yes—
228C2×C3×Dic3—24no—
229C2×C3×Dic3—216no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—28no—
237C2×C3×Dic3—28no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—32no—
244C2×C3×Dic3—32no—
245C2×C3×Dic3—32no—
246C2×C3×Dic3—32no—
247C2×C3×Dic3—42no—
248C2×C3×Dic3—42no—
249C2×C3×Dic3—62no—
250C2×C3×Dic3—62no—
251C2×C3×Dic3—62no—
252C2×C3×Dic3—62no—
253C2×C3×Dic3—62no—
254C2×C3×Dic3—62no—
255C2×C3×Dic3—122no—
256C2×C3×Dic3—122no—
257C2×C3×Dic3#6714yes—
258C2×C3×Dic3C3×D414yes—
259C2×C3×Dic3C22×D312yes—
260C2×C3×Dic3C22×D312yes—
261C2×C3×Dic3C22×D312yes—
262C2×C3×Dic3C22×D312yes—
263C2×C3×Dic3C23×C312yes—
264C2×C3×Dic3C23×C312yes—
265C2×C3×Dic3C23×C312yes—
266C2×C3×Dic3C23×C312yes—
267C3×Dic6—68no—
268C3×Dic6—68no—
269#627—28no—
270C2×C22⋊Q8—91noSylow
271C2×C33—24no—
272C2×C33C22⋊Q814yescomplemented
273C2×C33C22×D411yescharacteristic
274C2×C33C22×Q811yescharacteristic
275C2×C33C2×#4111yescharacteristic
276C24×C3—21no—
277C24×C3—21no—
278C24×C3—21no—
279C24×C3—41no—
280C24×C3D3211yescharacteristic
281C24×C3C2×C3×D311yescharacteristic
282C24×C3C2×C3×D311yescharacteristic
283C2×C3×Q8—94no—
284C2×C3×Q8—184no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—34no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—34no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C22×C3×C4—64no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—64no—
301C22×C3×C4—64no—
302C22×C3×C4—68no—
303C22×C3×C4—91no—
304C22×C3×C4—91no—
305C22×Dic3—24no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3C2×C3×D314yes—
313C22×Dic3C2×C3×D311yescharacteristic
314C22×Dic3C2×C3×D311yescharacteristic
315C22×Dic3C2×C3×D311yescharacteristic
316C22×Dic3C2×C3×D311yescharacteristic
317C2×Dic6—34no—
318C2×Dic6—34no—
319C2×Dic6—64no—
320C2×Dic6—64no—
321C3×C4⋊C4—94no—
322C3×C4⋊C4—94no—
323C3×C4⋊C4—94no—
324C3×C22⋊C4—34no—
325C3×C22⋊C4—34no—
326C3×C22⋊C4—64no—
327C3×C22⋊C4—94no—
328#217—34no—
329#217—34no—
330#217—64no—
331#217C2×C3×D314yes—
332C4⋊Dic3—34no—
333C4⋊Dic3—34no—
334Dic3⋊C4—34no—
335Dic3⋊C4—34no—
336Dic3⋊C4—34no—
337Dic3⋊C4—34no—
338C22×C32—28no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—24no—
342C22×C32—216no—
343C22×C32—24no—
344C22×C32—28no—
345C22×C32—28no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—22no—
349C22×C32—22no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—24no—
356C22×C32—22no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32—24no—
360C22×C32—24no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—42no—
366C22×C32—42no—
367C22×C32—44no—
368C22×C32—42no—
369C22×C32—41no—
370C22×C32—48no—
371C22×C32—42no—
372C22×C32—42no—
373C22×C32—42no—
374C22×C32—42no—
375C22×C32—48no—
376C22×C32—44no—
377C22×C32—416no—
378C22×C32—44no—
379C22×C32C2×Dic612yes—
380C22×C32C2×Dic612yes—
381C22×C32C2×Dic614yescomplemented
382C22×C32C2×Dic614yescomplemented
383C22×C32#23512yes—
384C22×C32D3×D412yes—
385C22×C32#23712yes—
386C22×C32C2×#6712yes—
387C22×C32C2×C3×D412yes—
388C22×C32C2×C3×Q812yes—
389C22×C32C2×C3×Q814yescomplemented
390C22×C32C3×#4112yes—
391C22×C32C23×D311yescharacteristic
392C22×C32C23×D311yescharacteristic
393C22×C32C24×C311yescharacteristic
394C32×C4—34no—
395C32×C4—62no—
396C32×C4—62no—
397C32×C4—62no—
398C3⋊Dic3—22no—
399C3⋊Dic3—22no—
400C3×Dic3—24no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—24no—
408C3×Dic3—42no—
409C3×Dic3—42no—
410C3×Dic3—62no—
411C3×Dic3—62no—
412C3×Dic3—62no—
413C3×Dic3—62no—
414C3×Dic3—122no—
415C3×Dic3—122no—
416C3×Dic3C2×#6714yes—
417C3×Dic3C2×C3×D414yes—
418C22×Q8—91no—
419C23×C4—31no—
420C22⋊Q8—98no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—91no—
426C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
427C23×C3—24no—
428C23×C3—24no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—42no—
448C23×C3—44no—
449C23×C3—44no—
450C23×C3—44no—
451C23×C3—42no—
452C23×C3—41no—
453C23×C3#62714yescomplemented
454C23×C3C3×Dic614yescomplemented
455C23×C3C3×Dic614yescomplemented
456C23×C3C2×D3212yes—
457C23×C3C2×D3211yescharacteristic
458C23×C3C22×C3×D312yes—
459C23×C3C22×C3×D312yes—
460C23×C3C22×C3×D311yescharacteristic
461C23×C3C22×C3×D311yescharacteristic
462C3×Q8—188no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—34no—
466C2×C3×C4—34no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—32no—
473C2×C3×C4—62no—
474C2×C3×C4—64no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—68no—
479C2×C3×C4—68no—
480C2×C3×C4—616no—
481C2×C3×C4—64no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4—92no—
489C2×C3×C4—92no—
490C2×C3×C4—122no—
491C2×C3×C4—122no—
492C2×C3×C4—182no—
493C2×C3×C4—182no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—28no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—122no—
509C2×Dic3—122no—
510C2×Dic3C3×#6714yes—
511C2×Dic3C22×C3×D312yes—
512C2×Dic3C22×C3×D312yes—
513C2×Dic3C22×C3×D312yes—
514C2×Dic3C22×C3×D312yes—
515Dic6—68no—
516Dic6—68no—
517C2×C32—24no—
518C2×C32—28no—
519C2×C32—24no—
520C2×C32—24no—
521C2×C32—24no—
522C2×C32—24no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—24no—
533C2×C32—44no—
534C2×C32—41no—
535C2×C32—41no—
536C2×C32—41no—
537C2×C32—44no—
538C2×C32—44no—
539C2×C32—48no—
540C2×C32#87814yescomplemented
541C2×C32#92414yescomplemented
542C2×C32C3×C22⋊Q814yescomplemented
543C2×C32C22×Dic611yescharacteristic
544C2×C32C22×Dic611yescharacteristic
545C2×C32C2×#23511yescharacteristic
546C2×C32C2×D3×D411yescharacteristic
547C2×C32C2×#23711yescharacteristic
548C2×C32C22×#6711yescharacteristic
549C2×C32C22×C3×D411yescharacteristic
550C2×C32C22×C3×Q811yescharacteristic
551C2×C32C2×C3×#4111yescharacteristic
552C24C3×D3211yescharacteristic
553C2×Q8—94no—
554C2×Q8—184no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—34no—
560C22×C4—64no—
561C22×C4—91no—
562C22×C4—91no—
563C4⋊C4—94no—
564C4⋊C4—94no—
565C4⋊C4—94no—
566C22⋊C4—34no—
567C22⋊C4—94no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—216no—
571C22×C3—28no—
572C22×C3—28no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—28no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—48no—
600C22×C3—48no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—416no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—44no—
608C22×C3—42no—
609C22×C3#380412yes—
610C22×C3C2×#62712yes—
611C22×C3C2×#62714yescomplemented
612C22×C3D3×#6712yes—
613C22×C3C2×C3×Dic612yes—
614C22×C3C2×C3×Dic612yes—
615C22×C3C2×C3×Dic614yescomplemented
616C22×C3C2×C3×Dic614yescomplemented
617C22×C3C3×#23512yes—
618C22×C3C3×D3×D412yes—
619C22×C3C3×#23712yes—
620C22×C3C2×C3×#6712yes—
621C22×C3C22×D3211yescharacteristic
622C22×C3C23×C3×D311yescharacteristic
623C22×C3C23×C3×D311yescharacteristic
624C3×C4—34no—
625C3×C4—34no—
626C3×C4—64no—
627C3×C4—64no—
628C3×C4—62no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—122no—
635C3×C4—122no—
636C3×C4—182no—
637C3×C4—182no—
638Dic3—22no—
639Dic3—22no—
640Dic3—22no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3—122no—
647Dic3C2×C3×#6714yes—
648C32—21no—
649C32—21no—
650C32—21no—
651C32—41no—
652C32C2×#87811yescharacteristic, complemented
653C32C2×#92411yescharacteristic, complemented
654C32C2×C3×C22⋊Q811yescharacteristic, complemented
655C23—22no—
656C23—22no—
657C23C3×#62714yescomplemented
658C23C2×C3×D3212yes—
659C23C2×C3×D3211yescharacteristic
660Q8—188no—
661C2×C4—32no—
662C2×C4—34no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—68no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—92no—
671C2×C4—92no—
672C2×C4—182no—
673C2×C4—182no—
674C2×C3—28no—
675C2×C3—24no—
676C2×C3—24no—
677C2×C3—24no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—24no—
688C2×C3—24no—
689C2×C3—24no—
690C2×C3—44no—
691C2×C3—44no—
692C2×C3—48no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—44no—
697C2×C3#6396414yesdirect product factor
698C2×C3C3×#87814yescomplemented
699C2×C3C3×#92414yescomplemented
700C2×C3C2×#380411yescharacteristic
701C2×C3C22×#62711yescharacteristic
702C2×C3C2×D3×#6711yescharacteristic
703C2×C3C22×C3×Dic611yescharacteristic
704C2×C3C22×C3×Dic611yescharacteristic
705C2×C3C2×C3×#23511yescharacteristic
706C2×C3C2×C3×D3×D411yescharacteristic
707C2×C3C2×C3×#23711yescharacteristic
708C2×C3C22×C3×#6711yescharacteristic
709C22—22no—
710C22—22no—
711C22—28no—
712C22C3×#380412yes—
713C22C2×C3×#62712yes—
714C22C2×C3×#62714yescomplemented
715C22C3×D3×#6712yes—
716C22C22×C3×D3211yescharacteristic
717C4—34no—
718C4—62no—
719C4—62no—
720C4—62no—
721C4—182no—
722C4—182no—
723C3—21no—
724C3—21no—
725C3—21no—
726C3—41no—
727C3C2×#6396411yescharacteristic, direct product factor
728C3C2×C3×#87811yescharacteristic, complemented
729C3C2×C3×#92411yescharacteristic, complemented
730C2—24no—
731C2C3×#6396414yesdirect product factor
732C2C2×C3×#380411yescharacteristic
733C2C22×C3×#62711yescharacteristic
734C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
Fitting, prime radicalC24×C33C22
socleC23×C33C23
hypercenterC24×C3D32
hypocenterC32C2×C3×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
2. C22×C3×#627C2semidirect
5. C2×C3×#3724C2semidirect
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C2×C3×Dic3⋊Dic3C2semidirect
8. C3×#63964C2direct (N × H)
11. C2×#63964C3direct (N × H)
22. C2×C3×#627C22semidirect
25. C3×#3724C22semidirect
26. C3×Dic3⋊Dic3C22semidirect
27. C3×Dic3⋊Dic3C22semidirect
34. C22×#627C2×C3semidirect
51. C2×#3724C2×C3semidirect
52. C2×Dic3⋊Dic3C2×C3semidirect
53. C2×Dic3⋊Dic3C2×C3semidirect
54. #63964C2×C3direct (N × H)
57. C23×C33Q8semidirect
121. C2×#627C22×C3semidirect
136. #3724C22×C3semidirect
137. Dic3⋊Dic3C22×C3semidirect
138. Dic3⋊Dic3C22×C3semidirect
144. C22×C33C2×Q8semidirect
206. C23×C32Dic6semidirect
207. C23×C32Dic6semidirect
208. C23×C32C3×Q8semidirect
272. C2×C33C22⋊Q8semidirect
381. C22×C32C2×Dic6semidirect
382. C22×C32C2×Dic6semidirect
389. C22×C32C2×C3×Q8semidirect
426. C33C2×C22⋊Q8semidirect
453. C23×C3#627semidirect
454. C23×C3C3×Dic6semidirect
455. C23×C3C3×Dic6semidirect
540. C2×C32#878semidirect
541. C2×C32#924semidirect
542. C2×C32C3×C22⋊Q8semidirect
611. C22×C3C2×#627semidirect
615. C22×C3C2×C3×Dic6semidirect
616. C22×C3C2×C3×Dic6semidirect
652. C32C2×#878semidirect
653. C32C2×#924semidirect
654. C32C2×C3×C22⋊Q8semidirect
657. C23C3×#627semidirect
697. C2×C3#63964direct (N × H)
698. C2×C3C3×#878semidirect
699. C2×C3C3×#924semidirect
714. C22C2×C3×#627semidirect
727. C3C2×#63964direct (N × H)
728. C3C2×C3×#878semidirect
729. C3C2×C3×#924semidirect
731. C2C3×#63964direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×Dic32
C22×C3×#6272
C2×C3×#37572
C2×C32×#2172
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C3×#639642
C2×C3×#9243
C2×C3×#8783
C2×#639643