Finite Group Databasebeta

← C2×C3×#5614 #11903105

Subgroups — C2×C3×#5614 #11903105

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic, complemented
3C2×C3×#938C212yesmaximal, complemented
4C2×C3×#935C212yesmaximal, complemented
5C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
6C2×C3×C4×#67C211yesmaximal, characteristic, complemented
7C2×C3×#926C211yesmaximal, characteristic, complemented
8C3×#5614C2116yesmaximal, direct product factor
9C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#890C211yesmaximal, characteristic, complemented
11C2×C3×#67⋊C4C212yesmaximal, complemented
12C2×C3×#879C212yesmaximal, complemented
13C2×C3×#553—31nomaximal
14C2×#5614C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C22×C32×D4C2212yes—
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2212yes—
20C23×C3×Dic3C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C32×#121C2218yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2212yes—
29C2×C3×#217C2212yes—
30C3×#938C22116yescomplemented
31C3×#938C2218yescomplemented
32C3×#935C22116yescomplemented
33C3×D4×Dic3C2218yescomplemented
34C3×C4×#67C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×#926C2218yescomplemented
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2212yes—
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2212yes—
41C2×C3×Dic3⋊C4C2212yes—
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2212yes—
45C3×D3×C4⋊C4C2218yescomplemented
46C3×#890C2218yescomplemented
47C3×#67⋊C4C22116yescomplemented
48C3×#879C22116yescomplemented
49C3×#553—316no—
50C2×C3×#126—32no—
51C2×C3×#125—31no—
52C2×C3×#123—32no—
53C2×C3×#121—21no—
54C2×C3×#121—32no—
55C2×C3×#121—31no—
56C2×C3×#121D311yescharacteristic, complemented
57C2×C3×#121C2×C311yescharacteristic, complemented
58C2×C3×C4×D4—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—32no—
61C2×C3×#117—31no—
62C22×C3×C4⋊C4—31no—
63C2×#938C2×C312yescomplemented
64C2×#938C2×C311yescharacteristic, complemented
65C2×#935C2×C312yescomplemented
66C2×D4×Dic3C2×C311yescharacteristic, complemented
67C2×C4×#67C2×C311yescharacteristic, complemented
68C2×#926C2×C311yescharacteristic, complemented
69#5614C2×C3116yesdirect product factor
70C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
71C2×#890C2×C311yescharacteristic, complemented
72C2×#67⋊C4C2×C312yescomplemented
73C2×#879C2×C312yescomplemented
74C24×C32C2311yescharacteristic
75C24×C32C2312yes—
76C23×C3×D3C2311yescharacteristic
77C2×C32×D4—24no—
78C2×C32×D4—44no—
79C2×C32×D4C2314yes—
80C2×C32×D4C2318yes—
81C22×C32×C4—24no—
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2312yes—
84C22×C32×C4C2314yes—
85C22×C32×C4C2311yescharacteristic
86C2×C3×#67—24no—
87C2×C3×#67—28no—
88C2×C3×#67C2318yes—
89C2×C3×#67C2314yes—
90C22×C3×Dic3—44no—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2318yes—
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3—44no—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2318yes—
101C32×C4⋊C4C2314yes—
102C32×C22⋊C4C2318yes—
103C3×#217C2318yes—
104C3×#217C2318yes—
105C3×#217C2318yes—
106C3×#217C2314yes—
107C3×(C2×D3)⋊C4C2314yes—
108C3×C4⋊Dic3C2318yes—
109C3×C4⋊Dic3C2314yes—
110C3×C4⋊Dic3C2314yes—
111C3×Dic3⋊C4C2314yes—
112C3×Dic3⋊C4C2318yes—
113C3×Dic3⋊C4C2318yes—
114C3×C4×Dic3C2318yes—
115C3×C4×Dic3C2314yes—
116C2×#553—31noSylow
117C22×C3×D4—21no—
118C22×C3×D4—22no—
119C22×C3×D4—31no—
120C22×C3×D4—32no—
121C22×C3×D4C2×D311yescharacteristic
122C22×C3×D4C2×D312yes—
123C22×C3×D4C22×C311yescharacteristic
124C22×C3×D4C22×C312yes—
125C23×C3×C4—21no—
126C23×C3×C4—32no—
127C23×C3×C4—31no—
128C23×C3×C4—32no—
129C23×C3×C4C2×D311yescharacteristic
130C23×C3×C4C22×C311yescharacteristic
131C22×#67C22×C312yes—
132C22×#67C22×C311yescharacteristic
133C23×Dic3C22×C312yes—
134C22×C4×D3C22×C311yescharacteristic
135C22×C4×D3C22×C312yes—
136C3×#126—316no—
137C3×#125—38no—
138C3×#123—316no—
139C3×#121—28no—
140C3×#121—316no—
141C3×#121—38no—
142C3×#121C2×D318yescomplemented
143C3×#121C22×C318yescomplemented
144C3×C4×D4—38no—
145C3×C4×D4—38no—
146C3×C4×D4—316no—
147C3×#117—38no—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4—32no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—32no—
155C2×C3×C4⋊C4—38no—
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C4⋊C4C22×C311yescharacteristic
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—32no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4C2×D312yes—
165C2×C3×C22⋊C4C22×C312yes—
166C2×C3×C42—32no—
167C2×C3×C42—31no—
168C2×#217C22×C312yes—
169C2×#217C22×C312yes—
170C2×#217C22×C312yes—
171C2×#217C22×C311yescharacteristic
172#938C22×C3116yescomplemented
173#938C22×C318yescomplemented
174#935C22×C3116yescomplemented
175D4×Dic3C22×C318yescomplemented
176C4×#67C22×C318yescomplemented
177C2×(C2×D3)⋊C4C22×C311yescharacteristic
178#926C22×C318yescomplemented
179C2×C4⋊Dic3C22×C312yes—
180C2×C4⋊Dic3C22×C311yescharacteristic
181C2×C4⋊Dic3C22×C311yescharacteristic
182C2×Dic3⋊C4C22×C311yescharacteristic
183C2×Dic3⋊C4C22×C312yes—
184C2×Dic3⋊C4C22×C312yes—
185C2×C4×Dic3C22×C312yes—
186C2×C4×Dic3C22×C311yescharacteristic
187D3×C4⋊C4C22×C318yescomplemented
188#890C22×C318yescomplemented
189#67⋊C4C22×C3116yescomplemented
190#879C22×C3116yescomplemented
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—24no—
194C23×C32—22no—
195C23×C32—24no—
196C23×C32—24no—
197C23×C32C2412yes—
198C23×C32C2414yes—
199C23×C32C2411yescharacteristic
200C22×C3×D3—22no—
201C22×C3×D3—22no—
202C22×C3×D3#4114yes—
203C22×C3×D3C2412yes—
204C32×D4—28no—
205C32×D4—48no—
206C2×C32×C4—22no—
207C2×C32×C4—24no—
208C2×C32×C4—28no—
209C2×C32×C4#4114yes—
210C2×C32×C4C2412yes—
211C2×C32×C4C2414yes—
212C2×C32×C4C2412yes—
213C3×#67—216no—
214C3×#67—28no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—24no—
218C2×C3×Dic3—24no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—48no—
221C2×C3×Dic3C2412yes—
222C2×C3×Dic3C2414yes—
223C2×C3×Dic3C2412yes—
224C2×C3×Dic3C2414yes—
225C2×C3×Dic3C2412yes—
226C3×C4×D3—28no—
227C3×C4×D3—48no—
228#553—316no—
229C2×#126—32no—
230C2×#125—31no—
231C2×#123—32no—
232C2×#121—32no—
233C2×#121—31no—
234C2×#121C3×D311yescharacteristic, complemented
235C2×C4×D4—31no—
236C2×C4×D4—31no—
237C2×C4×D4—32no—
238C2×#117—31no—
239C22×C4⋊C4—31no—
240C24×C3—21no—
241C24×C3—22no—
242C24×C3—31no—
243C24×C3C22×D311yescharacteristic
244C24×C3C22×D312yes—
245C24×C3C23×C311yescharacteristic
246C24×C3C23×C312yes—
247C23×D3C23×C311yescharacteristic
248C2×C3×D4—24no—
249C2×C3×D4—24no—
250C2×C3×D4—24no—
251C2×C3×D4—28no—
252C2×C3×D4—34no—
253C2×C3×D4—38no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C2×C3×D4—44no—
257C2×C3×D4—48no—
258C2×C3×D4—64no—
259C2×C3×D4—68no—
260C2×C3×D4C22×D314yes—
261C2×C3×D4C22×D318yes—
262C2×C3×D4C23×C314yes—
263C2×C3×D4C23×C318yes—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—22no—
269C22×C3×C4—24no—
270C22×C3×C4—32no—
271C22×C3×C4—31no—
272C22×C3×C4—32no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—38no—
276C22×C3×C4—34no—
277C22×C3×C4—38no—
278C22×C3×C4—44no—
279C22×C3×C4—64no—
280C22×C3×C4—124no—
281C22×C3×C4—124no—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D312yes—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C23×C311yescharacteristic
287C22×C3×C4C23×C312yes—
288C22×C3×C4C23×C314yes—
289C22×C3×C4C23×C311yescharacteristic
290C2×#67—28no—
291C2×#67—24no—
292C2×#67C23×C318yes—
293C2×#67C23×C314yes—
294C22×Dic3—44no—
295C22×Dic3C23×C311yescharacteristic
296C22×Dic3C23×C312yes—
297C22×Dic3C23×C311yescharacteristic
298C22×Dic3C23×C312yes—
299C22×Dic3C23×C311yescharacteristic
300C22×Dic3C23×C318yes—
301C2×C4×D3—24no—
302C2×C4×D3—44no—
303C2×C4×D3C23×C314yes—
304C2×C4×D3C23×C318yes—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—38no—
307C3×C4⋊C4—38no—
308C3×C4⋊C4—34no—
309C3×C4⋊C4—34no—
310C3×C4⋊C4—34no—
311C3×C4⋊C4—38no—
312C3×C4⋊C4C22×D314yes—
313C3×C4⋊C4C23×C314yes—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—38no—
316C3×C22⋊C4—38no—
317C3×C22⋊C4—34no—
318C3×C22⋊C4—38no—
319C3×C22⋊C4—34no—
320C3×C22⋊C4C22×D318yes—
321C3×C22⋊C4C23×C318yes—
322C3×C42—38no—
323C3×C42—34no—
324#217C23×C318yes—
325#217C23×C318yes—
326#217C23×C318yes—
327#217C23×C314yes—
328(C2×D3)⋊C4C23×C314yes—
329C4⋊Dic3C23×C318yes—
330C4⋊Dic3C23×C314yes—
331C4⋊Dic3C23×C314yes—
332Dic3⋊C4C23×C314yes—
333Dic3⋊C4C23×C318yes—
334Dic3⋊C4C23×C318yes—
335C4×Dic3C23×C318yes—
336C4×Dic3C23×C314yes—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—24no—
340C22×C32—22no—
341C22×C32—24no—
342C22×C32—24no—
343C22×C32—44no—
344C22×C32—48no—
345C22×C32C2×#4112yes—
346C22×C32C2×#4112yes—
347C22×C32H(5,𝔽2)12yes—
348C22×C32C2511yescharacteristic
349C2×C3×D3—28no—
350C2×C3×D3—22no—
351C2×C3×D3—22no—
352C2×C3×D3C2×#4114yes—
353C32×C4—22no—
354C32×C4—24no—
355C32×C4C2×#4114yes—
356C3×Dic3—22no—
357C3×Dic3—24no—
358C3×Dic3—22no—
359C3×Dic3—24no—
360C3×Dic3—22no—
361C22×D4—31no—
362C22×D4—32no—
363C22×D4C2×C3×D311yescharacteristic
364C22×D4C2×C3×D312yes—
365C23×C4—32no—
366C23×C4—31no—
367C23×C4—32no—
368C23×C4C2×C3×D311yescharacteristic
369#126—316no—
370#125—38no—
371#123—316no—
372#121—316no—
373#121—38no—
374#121C2×C3×D318yescomplemented
375C4×D4—38no—
376C4×D4—38no—
377C4×D4—316no—
378#117—38no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—38no—
386C2×C4⋊C4C2×C3×D311yescharacteristic
387C2×C22⋊C4—32no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4C2×C3×D312yes—
393C2×C42—32no—
394C2×C42—31no—
395C23×C3—24no—
396C23×C3—22no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—24no—
402C23×C3—22no—
403C23×C3—24no—
404C23×C3—22no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3—24no—
411C23×C3—34no—
412C23×C3—32no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—44no—
416C23×C3—44no—
417C23×C3—44no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3C23×D312yes—
421C23×C3C23×D314yes—
422C23×C3C23×D311yescharacteristic
423C23×C3C24×C312yes—
424C23×C3C24×C314yes—
425C23×C3C24×C311yescharacteristic
426C22×D3—22no—
427C22×D3—22no—
428C22×D3C3×#4114yes—
429C22×D3C24×C312yes—
430C3×D4—28no—
431C3×D4—28no—
432C3×D4—48no—
433C3×D4—48no—
434C3×D4—48no—
435C3×D4—416no—
436C3×D4—68no—
437C3×D4—616no—
438C2×C3×C4—22no—
439C2×C3×C4—24no—
440C2×C3×C4—22no—
441C2×C3×C4—24no—
442C2×C3×C4—28no—
443C2×C3×C4—28no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—34no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—34no—
452C2×C3×C4—32no—
453C2×C3×C4—48no—
454C2×C3×C4—42no—
455C2×C3×C4—44no—
456C2×C3×C4—62no—
457C2×C3×C4—64no—
458C2×C3×C4—62no—
459C2×C3×C4—64no—
460C2×C3×C4—62no—
461C2×C3×C4—68no—
462C2×C3×C4—128no—
463C2×C3×C4—128no—
464C2×C3×C4#23714yes—
465C2×C3×C4C3×#4114yes—
466C2×C3×C4C23×D312yes—
467C2×C3×C4C23×D314yes—
468C2×C3×C4C23×D312yes—
469C2×C3×C4C24×C312yes—
470C2×C3×C4C24×C314yes—
471C2×C3×C4C24×C312yes—
472#67—216no—
473#67—28no—
474C2×Dic3—22no—
475C2×Dic3—24no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—22no—
479C2×Dic3—48no—
480C2×Dic3C24×C312yes—
481C2×Dic3C24×C314yes—
482C2×Dic3C24×C312yes—
483C2×Dic3C24×C314yes—
484C2×Dic3C24×C312yes—
485C4×D3—28no—
486C4×D3—48no—
487C2×C32—42no—
488C2×C32—44no—
489C2×C32#55314yescomplemented
490C2×C32C22×#4111yescharacteristic
491C2×C32C22×#4111yescharacteristic
492C2×C32C2×H(5,𝔽2)11yescharacteristic
493C3×D3—24no—
494C24—31no—
495C24C22×C3×D311yescharacteristic
496C24C22×C3×D312yes—
497C2×D4—24no—
498C2×D4—34no—
499C2×D4—38no—
500C2×D4—44no—
501C2×D4—64no—
502C2×D4—68no—
503C2×D4C22×C3×D314yes—
504C2×D4C22×C3×D318yes—
505C22×C4—24no—
506C22×C4—32no—
507C22×C4—31no—
508C22×C4—32no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—38no—
512C22×C4—34no—
513C22×C4—38no—
514C22×C4—64no—
515C22×C4—124no—
516C22×C4—124no—
517C22×C4C22×C3×D311yescharacteristic
518C22×C4C22×C3×D312yes—
519C22×C4C22×C3×D314yes—
520C22×C4C22×C3×D311yescharacteristic
521C4⋊C4—34no—
522C4⋊C4—38no—
523C4⋊C4—34no—
524C4⋊C4—38no—
525C4⋊C4—34no—
526C4⋊C4—38no—
527C4⋊C4C22×C3×D314yes—
528C22⋊C4—38no—
529C22⋊C4—38no—
530C22⋊C4—34no—
531C22⋊C4—38no—
532C22⋊C4—34no—
533C22⋊C4C22×C3×D318yes—
534C42—38no—
535C42—34no—
536C22×C3—24no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—24no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—24no—
543C22×C3—22no—
544C22×C3—24no—
545C22×C3—22no—
546C22×C3—24no—
547C22×C3—24no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—21no—
553C22×C3—34no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—48no—
560C22×C3—44no—
561C22×C3—48no—
562C22×C3—44no—
563C22×C3—48no—
564C22×C3—62no—
565C22×C3—62no—
566C22×C3—68no—
567C22×C3—88no—
568C22×C3C2×#23712yes—
569C22×C3#100412yes—
570C22×C3D3×#4112yes—
571C22×C3C2×C3×#4112yes—
572C22×C3C2×C3×#4112yes—
573C22×C3C3×H(5,𝔽2)12yes—
574C22×C3C24×D311yescharacteristic
575C22×C3C25×C311yescharacteristic
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—28no—
579C2×D3C2×C3×#4114yes—
580C3×C4—22no—
581C3×C4—24no—
582C3×C4—22no—
583C3×C4—24no—
584C3×C4—24no—
585C3×C4—42no—
586C3×C4—44no—
587C3×C4—62no—
588C3×C4—64no—
589C3×C4—62no—
590C3×C4—64no—
591C3×C4—62no—
592C3×C4C2×#23714yes—
593C3×C4C2×C3×#4114yes—
594Dic3—22no—
595Dic3—24no—
596Dic3—22no—
597Dic3—24no—
598Dic3—22no—
599C32C2×#55311yescharacteristic, complemented, Sylow
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—34no—
607C23—32no—
608C23—62no—
609C23—62no—
610C23C23×C3×D312yes—
611C23C23×C3×D314yes—
612C23C23×C3×D311yescharacteristic
613D4—28no—
614D4—48no—
615D4—68no—
616D4—616no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—28no—
620C2×C4—34no—
621C2×C4—32no—
622C2×C4—34no—
623C2×C4—32no—
624C2×C4—32no—
625C2×C4—62no—
626C2×C4—64no—
627C2×C4—62no—
628C2×C4—64no—
629C2×C4—62no—
630C2×C4—68no—
631C2×C4—128no—
632C2×C4—128no—
633C2×C4C3×#23714yes—
634C2×C4C23×C3×D312yes—
635C2×C4C23×C3×D314yes—
636C2×C4C23×C3×D312yes—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—24no—
641C2×C3—44no—
642C2×C3—42no—
643C2×C3—44no—
644C2×C3—42no—
645C2×C3—44no—
646C2×C3—64no—
647C2×C3—84no—
648C2×C3#561414yesdirect product factor
649C2×C3C3×#55314yescomplemented
650C2×C3C22×#23711yescharacteristic
651C2×C3C2×#100411yescharacteristic
652C2×C3C2×D3×#4111yescharacteristic
653C2×C3C22×C3×#4111yescharacteristic
654C2×C3C22×C3×#4111yescharacteristic
655C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
656D3—24no—
657C22—22no—
658C22—24no—
659C22—24no—
660C22—22no—
661C22—22no—
662C22—24no—
663C22—34no—
664C22—44no—
665C22—48no—
666C22—62no—
667C22—62no—
668C22—68no—
669C22C2×C3×#23712yes—
670C22C3×#100412yes—
671C22C3×D3×#4112yes—
672C22C24×C3×D311yescharacteristic
673C4—22no—
674C4—24no—
675C4—62no—
676C4—64no—
677C4—62no—
678C4—64no—
679C4—62no—
680C4C2×C3×#23714yes—
681C3—21no—
682C3C2×#561411yescharacteristic, direct product factor
683C3C2×C3×#55311yescharacteristic, complemented
684C2—42no—
685C2—44no—
686C2—64no—
687C2C3×#561414yesdirect product factor
688C2C22×C3×#23711yescharacteristic
689C2C2×C3×#100411yescharacteristic
690C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#553
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×C3×#938C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×#935C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×C3×C4×#67C2semidirect
7. C2×C3×#926C2semidirect
8. C3×#5614C2direct (N × H)
9. C2×C3×D3×C4⋊C4C2semidirect
10. C2×C3×#890C2semidirect
11. C2×C3×#67⋊C4C2semidirect
12. C2×C3×#879C2semidirect
14. C2×#5614C3direct (N × H)
23. C32×#121C22semidirect
30. C3×#938C22semidirect
31. C3×#938C22semidirect
32. C3×#935C22semidirect
33. C3×D4×Dic3C22semidirect
34. C3×C4×#67C22semidirect
36. C3×#926C22semidirect
45. C3×D3×C4⋊C4C22semidirect
46. C3×#890C22semidirect
47. C3×#67⋊C4C22semidirect
48. C3×#879C22semidirect
56. C2×C3×#121D3semidirect
57. C2×C3×#121C2×C3semidirect
63. C2×#938C2×C3semidirect
64. C2×#938C2×C3semidirect
65. C2×#935C2×C3semidirect
66. C2×D4×Dic3C2×C3semidirect
67. C2×C4×#67C2×C3semidirect
68. C2×#926C2×C3semidirect
69. #5614C2×C3direct (N × H)
70. C2×D3×C4⋊C4C2×C3semidirect
71. C2×#890C2×C3semidirect
72. C2×#67⋊C4C2×C3semidirect
73. C2×#879C2×C3semidirect
142. C3×#121C2×D3semidirect
143. C3×#121C22×C3semidirect
172. #938C22×C3semidirect
173. #938C22×C3semidirect
174. #935C22×C3semidirect
175. D4×Dic3C22×C3semidirect
176. C4×#67C22×C3semidirect
178. #926C22×C3semidirect
187. D3×C4⋊C4C22×C3semidirect
188. #890C22×C3semidirect
189. #67⋊C4C22×C3semidirect
190. #879C22×C3semidirect
234. C2×#121C3×D3semidirect
374. #121C2×C3×D3semidirect
489. C2×C32#553semidirect
599. C32C2×#553semidirect
648. C2×C3#5614direct (N × H)
649. C2×C3C3×#553semidirect
682. C3C2×#5614direct (N × H)
683. C3C2×C3×#553semidirect
687. C2C3×#5614direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×#9382
C2×C3×#9352
C2×C3×D4×Dic32
C2×C3×C4×#672
C2×C3×#9262
C3×#56142
C2×C3×D3×C4⋊C42
C2×C3×#8902
C2×C3×#67⋊C42
C2×C3×#8792
C2×C3×#5533
C2×#56143