Finite Group Databasebeta

← C2×C3×#5618 #11903120

Subgroups — C2×C3×#5618 #11903120

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×#939C212yesmaximal, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
5C2×C3×D4×Dic3C212yesmaximal, complemented
6C2×C3×C4×#67C211yesmaximal, characteristic, complemented
7C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#5618C2116yesmaximal, direct product factor
9C2×C3×#892C211yesmaximal, characteristic, complemented
10C2×C3×#890C211yesmaximal, characteristic, complemented
11C2×C3×#886C212yesmaximal, complemented
12C2×C3×#879C212yesmaximal, complemented
13C2×C3×#553—31nomaximal
14C2×#5618C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C22×C32×D4C2212yes—
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2212yes—
20C23×C3×Dic3C2212yes—
21C23×C3×Dic3C2212yes—
22C22×C3×C4×D3C2211yescharacteristic
23C32×#121C2218yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yes—
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2212yes—
28C2×C3×#217C2212yes—
29C3×#939C22116yescomplemented
30C3×#938C2218yescomplemented
31C3×D4×Dic3C22116yescomplemented
32C3×D4×Dic3C2218yescomplemented
33C3×C4×#67C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×C4⋊Dic3C2212yes—
37C2×C3×C4⋊Dic3C2212yes—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×C4⋊Dic3C2218yescomplemented
41C2×C3×Dic3⋊C4C2212yes—
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2212yes—
45C3×#892C2218yescomplemented
46C3×#890C2218yescomplemented
47C3×#886C22116yescomplemented
48C3×#879C22116yescomplemented
49C3×#553—316no—
50C2×C3×#126—32no—
51C2×C3×#125—31no—
52C2×C3×#123—32no—
53C2×C3×#121—21no—
54C2×C3×#121—31no—
55C2×C3×#121—32no—
56C2×C3×#121D311yescharacteristic, complemented
57C2×C3×#121C2×C311yescharacteristic, complemented
58C2×C3×C4×D4—32no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—31no—
61C2×C3×#117—31no—
62C22×C3×C4⋊C4—31no—
63C2×#939C2×C312yescomplemented
64C2×#938C2×C311yescharacteristic, complemented
65C2×D4×Dic3C2×C312yescomplemented
66C2×D4×Dic3C2×C311yescharacteristic, complemented
67C2×C4×#67C2×C311yescharacteristic, complemented
68C22×C4⋊Dic3C2×C311yescharacteristic, complemented
69#5618C2×C3116yesdirect product factor
70C2×#892C2×C311yescharacteristic, complemented
71C2×#890C2×C311yescharacteristic, complemented
72C2×#886C2×C312yescomplemented
73C2×#879C2×C312yescomplemented
74C24×C32C2312yes—
75C24×C32C2311yescharacteristic
76C23×C3×D3C2311yescharacteristic
77C2×C32×D4—28no—
78C2×C32×D4—24no—
79C2×C32×D4C2314yes—
80C2×C32×D4C2318yes—
81C22×C32×C4—24no—
82C22×C32×C4C2312yes—
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2314yes—
85C22×C32×C4C2311yescharacteristic
86C2×C3×#67—24no—
87C2×C3×#67—44no—
88C2×C3×#67C2314yes—
89C2×C3×#67C2318yes—
90C22×C3×Dic3—44no—
91C22×C3×Dic3—44no—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2318yes—
98C22×C3×Dic3C2318yes—
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3C2314yes—
101C32×C4⋊C4C2314yes—
102C32×C22⋊C4C2318yes—
103C3×#217C2318yes—
104C3×#217C2318yes—
105C3×#217C2314yes—
106C3×(C2×D3)⋊C4C2314yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×C4⋊Dic3C2318yes—
109C3×C4⋊Dic3C2318yes—
110C3×C4⋊Dic3C2314yes—
111C3×C4⋊Dic3C2314yes—
112C3×Dic3⋊C4C2314yes—
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×D312yes—
122C22×C3×D4C2×D311yescharacteristic
123C22×C3×D4C22×C311yescharacteristic
124C22×C3×D4C22×C312yes—
125C23×C3×C4—21no—
126C23×C3×C4—32no—
127C23×C3×C4—32no—
128C23×C3×C4—31no—
129C23×C3×C4C2×D311yescharacteristic
130C23×C3×C4C22×C311yescharacteristic
131C22×#67C22×C311yescharacteristic
132C22×#67C22×C312yes—
133C23×Dic3C22×C312yes—
134C23×Dic3C22×C312yes—
135C22×C4×D3C22×C311yescharacteristic
136C3×#126—316no—
137C3×#125—38no—
138C3×#123—316no—
139C3×#121—28no—
140C3×#121—38no—
141C3×#121—316no—
142C3×#121C2×D318yescomplemented
143C3×#121C22×C318yescomplemented
144C3×C4×D4—316no—
145C3×C4×D4—38no—
146C3×C4×D4—38no—
147C3×#117—38no—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—32no—
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—31no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—32no—
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×C311yescharacteristic
171#939C22×C3116yescomplemented
172#938C22×C318yescomplemented
173D4×Dic3C22×C3116yescomplemented
174D4×Dic3C22×C318yescomplemented
175C4×#67C22×C318yescomplemented
176C2×(C2×D3)⋊C4C22×C311yescharacteristic
177C2×(C2×D3)⋊C4C22×C312yes—
178C2×C4⋊Dic3C22×C312yes—
179C2×C4⋊Dic3C22×C312yes—
180C2×C4⋊Dic3C22×C311yescharacteristic
181C2×C4⋊Dic3C22×C311yescharacteristic
182C2×C4⋊Dic3C22×C318yescomplemented
183C2×Dic3⋊C4C22×C311yescharacteristic
184C2×Dic3⋊C4C22×C312yes—
185C2×C4×Dic3C22×C312yes—
186C2×C4×Dic3C22×C311yescharacteristic
187#892C22×C318yescomplemented
188#890C22×C318yescomplemented
189#886C22×C3116yescomplemented
190#879C22×C3116yescomplemented
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—24no—
194C23×C32—24no—
195C23×C32—24no—
196C23×C32#4114yes—
197C23×C32C2414yes—
198C23×C32C2412yes—
199C23×C32C2411yescharacteristic
200C22×C3×D3—22no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3C2412yes—
204C32×D4—216no—
205C32×D4—28no—
206C2×C32×C4—22no—
207C2×C32×C4—24no—
208C2×C32×C4—28no—
209C2×C32×C4#4114yes—
210C2×C32×C4C2414yes—
211C2×C32×C4C2412yes—
212C2×C32×C4C2412yes—
213C3×#67—28no—
214C3×#67—48no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—24no—
219C2×C3×Dic3—24no—
220C2×C3×Dic3—48no—
221C2×C3×Dic3—48no—
222C2×C3×Dic3C2412yes—
223C2×C3×Dic3C2412yes—
224C2×C3×Dic3C2414yes—
225C2×C3×Dic3C2412yes—
226C2×C3×Dic3C2414yes—
227C3×C4×D3—28no—
228#553—316no—
229C2×#126—32no—
230C2×#125—31no—
231C2×#123—32no—
232C2×#121—31no—
233C2×#121—32no—
234C2×#121C3×D311yescharacteristic, complemented
235C2×C4×D4—32no—
236C2×C4×D4—31no—
237C2×C4×D4—31no—
238C2×#117—31no—
239C22×C4⋊C4—31no—
240C24×C3—21no—
241C24×C3—22no—
242C24×C3—31no—
243C24×C3C22×D312yes—
244C24×C3C22×D311yescharacteristic
245C24×C3C23×C312yes—
246C24×C3C23×C311yescharacteristic
247C23×D3C23×C311yescharacteristic
248C2×C3×D4—28no—
249C2×C3×D4—28no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—28no—
254C2×C3×D4—34no—
255C2×C3×D4—38no—
256C2×C3×D4—44no—
257C2×C3×D4—48no—
258C2×C3×D4—64no—
259C2×C3×D4—124no—
260C2×C3×D4C22×D318yes—
261C2×C3×D4C22×D314yes—
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—31no—
271C22×C3×C4—31no—
272C22×C3×C4—32no—
273C22×C3×C4—31no—
274C22×C3×C4—32no—
275C22×C3×C4—38no—
276C22×C3×C4—38no—
277C22×C3×C4—34no—
278C22×C3×C4—44no—
279C22×C3×C4—64no—
280C22×C3×C4—124no—
281C22×C3×C4—124no—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D312yes—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C23×C312yes—
287C22×C3×C4C23×C311yescharacteristic
288C22×C3×C4C23×C314yes—
289C22×C3×C4C23×C311yescharacteristic
290C2×#67—24no—
291C2×#67—44no—
292C2×#67C23×C314yes—
293C2×#67C23×C318yes—
294C22×Dic3—44no—
295C22×Dic3—44no—
296C22×Dic3C23×C311yescharacteristic
297C22×Dic3C23×C311yescharacteristic
298C22×Dic3C23×C312yes—
299C22×Dic3C23×C311yescharacteristic
300C22×Dic3C23×C312yes—
301C22×Dic3C23×C318yes—
302C22×Dic3C23×C318yes—
303C2×C4×D3—24no—
304C2×C4×D3C23×C314yes—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—34no—
307C3×C4⋊C4—38no—
308C3×C4⋊C4—34no—
309C3×C4⋊C4—34no—
310C3×C4⋊C4—38no—
311C3×C4⋊C4—38no—
312C3×C4⋊C4C22×D314yes—
313C3×C4⋊C4C23×C314yes—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—34no—
316C3×C22⋊C4—38no—
317C3×C22⋊C4—38no—
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×C314yes—
327(C2×D3)⋊C4C23×C314yes—
328(C2×D3)⋊C4C23×C318yes—
329C4⋊Dic3C23×C318yes—
330C4⋊Dic3C23×C318yes—
331C4⋊Dic3C23×C314yes—
332C4⋊Dic3C23×C314yes—
333Dic3⋊C4C23×C314yes—
334Dic3⋊C4C23×C318yes—
335C4×Dic3C23×C318yes—
336C4×Dic3C23×C314yes—
337C22×C32—28no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—24no—
341C22×C32—24no—
342C22×C32—24no—
343C22×C32—48no—
344C22×C32C2×#4114yes—
345C22×C32C2×#4112yes—
346C22×C32C2×#4112yes—
347C22×C32H(5,𝔽2)12yes—
348C22×C32C2511yescharacteristic
349C2×C3×D3—22no—
350C2×C3×D3—22no—
351C2×C3×D3—22no—
352C2×C3×D3—44no—
353C32×C4—22no—
354C32×C4—24no—
355C32×C4C2×#4114yes—
356C3×Dic3—22no—
357C3×Dic3—22no—
358C3×Dic3—22no—
359C3×Dic3—24no—
360C3×Dic3—24no—
361C22×D4—31no—
362C22×D4—32no—
363C22×D4C2×C3×D312yes—
364C22×D4C2×C3×D311yescharacteristic
365C23×C4—32no—
366C23×C4—32no—
367C23×C4—31no—
368C23×C4C2×C3×D311yescharacteristic
369#126—316no—
370#125—38no—
371#123—316no—
372#121—38no—
373#121—316no—
374#121C2×C3×D318yescomplemented
375C4×D4—316no—
376C4×D4—38no—
377C4×D4—38no—
378#117—38no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—38no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4C2×C3×D311yescharacteristic
387C2×C22⋊C4—31no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4C2×C3×D312yes—
393C2×C42—32no—
394C2×C42—31no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—24no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—32no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—44no—
413C23×C3—44no—
414C23×C3—44no—
415C23×C3—62no—
416C23×C3—62no—
417C23×C3—62no—
418C23×C3#23714yes—
419C23×C3C3×#4114yes—
420C23×C3C23×D314yes—
421C23×C3C23×D312yes—
422C23×C3C23×D311yescharacteristic
423C23×C3C24×C314yes—
424C23×C3C24×C312yes—
425C23×C3C24×C311yescharacteristic
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3C24×C312yes—
430C3×D4—216no—
431C3×D4—216no—
432C3×D4—28no—
433C3×D4—28no—
434C3×D4—48no—
435C3×D4—416no—
436C3×D4—68no—
437C3×D4—128no—
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—32no—
449C2×C3×C4—32no—
450C2×C3×C4—34no—
451C2×C3×C4—32no—
452C2×C3×C4—34no—
453C2×C3×C4—48no—
454C2×C3×C4—42no—
455C2×C3×C4—44no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—64no—
459C2×C3×C4—62no—
460C2×C3×C4—64no—
461C2×C3×C4—68no—
462C2×C3×C4—128no—
463C2×C3×C4—128no—
464C2×C3×C4#23714yes—
465C2×C3×C4C3×#4114yes—
466C2×C3×C4C23×D314yes—
467C2×C3×C4C23×D312yes—
468C2×C3×C4C23×D312yes—
469C2×C3×C4C24×C314yes—
470C2×C3×C4C24×C312yes—
471C2×C3×C4C24×C312yes—
472#67—28no—
473#67—48no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—48no—
480C2×Dic3—48no—
481C2×Dic3C24×C312yes—
482C2×Dic3C24×C312yes—
483C2×Dic3C24×C314yes—
484C2×Dic3C24×C312yes—
485C2×Dic3C24×C314yes—
486C4×D3—28no—
487C2×C32—24no—
488C2×C32—44no—
489C2×C32#55314yescomplemented
490C2×C32C22×#4111yescharacteristic
491C2×C32C22×#4111yescharacteristic
492C2×C32C2×H(5,𝔽2)11yescharacteristic
493C3×D3—42no—
494C24—31no—
495C24C22×C3×D312yes—
496C24C22×C3×D311yescharacteristic
497C2×D4—28no—
498C2×D4—24no—
499C2×D4—34no—
500C2×D4—38no—
501C2×D4—64no—
502C2×D4—124no—
503C2×D4C22×C3×D318yes—
504C2×D4C22×C3×D314yes—
505C22×C4—24no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—32no—
509C22×C4—31no—
510C22×C4—32no—
511C22×C4—38no—
512C22×C4—38no—
513C22×C4—34no—
514C22×C4—64no—
515C22×C4—124no—
516C22×C4—124no—
517C22×C4C22×C3×D312yes—
518C22×C4C22×C3×D311yescharacteristic
519C22×C4C22×C3×D314yes—
520C22×C4C22×C3×D311yescharacteristic
521C4⋊C4—34no—
522C4⋊C4—34no—
523C4⋊C4—38no—
524C4⋊C4—38no—
525C4⋊C4—34no—
526C4⋊C4—38no—
527C4⋊C4C22×C3×D314yes—
528C22⋊C4—34no—
529C22⋊C4—38no—
530C22⋊C4—38no—
531C22⋊C4—38no—
532C22⋊C4—34no—
533C22⋊C4C22×C3×D318yes—
534C42—38no—
535C42—34no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—28no—
541C22×C3—28no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—24no—
547C22×C3—24no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—24no—
551C22×C3—22no—
552C22×C3—21no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—48no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—48no—
560C22×C3—48no—
561C22×C3—62no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—88no—
565C22×C3—124no—
566C22×C3C2×#23714yes—
567C22×C3C2×#23712yes—
568C22×C3C2×#23712yes—
569C22×C3#100912yes—
570C22×C3C2×C3×#4114yes—
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—22no—
579C2×D3—44no—
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—62no—
589C3×C4—64no—
590C3×C4—62no—
591C3×C4—64no—
592C3×C4C2×#23714yes—
593C3×C4C2×C3×#4114yes—
594Dic3—22no—
595Dic3—22no—
596Dic3—22no—
597Dic3—24no—
598Dic3—24no—
599C32C2×#55311yescharacteristic, complemented, Sylow
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—32no—
606C23—62no—
607C23—62no—
608C23—62no—
609C23C3×#23714yes—
610C23C23×C3×D314yes—
611C23C23×C3×D312yes—
612C23C23×C3×D311yescharacteristic
613D4—216no—
614D4—28no—
615D4—68no—
616D4—128no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—28no—
620C2×C4—32no—
621C2×C4—32no—
622C2×C4—34no—
623C2×C4—32no—
624C2×C4—34no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—64no—
628C2×C4—62no—
629C2×C4—64no—
630C2×C4—68no—
631C2×C4—128no—
632C2×C4—128no—
633C2×C4C3×#23714yes—
634C2×C4C23×C3×D314yes—
635C2×C4C23×C3×D312yes—
636C2×C4C23×C3×D312yes—
637C2×C3—24no—
638C2×C3—24no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—24no—
643C2×C3—44no—
644C2×C3—44no—
645C2×C3—44no—
646C2×C3—84no—
647C2×C3—122no—
648C2×C3#561814yesdirect product factor
649C2×C3C3×#55314yescomplemented
650C2×C3C22×#23711yescharacteristic
651C2×C3C22×#23711yescharacteristic
652C2×C3C2×#100911yescharacteristic
653C2×C3C22×C3×#4111yescharacteristic
654C2×C3C22×C3×#4111yescharacteristic
655C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
656D3—42no—
657C22—22no—
658C22—22no—
659C22—28no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—48no—
664C22—62no—
665C22—62no—
666C22—62no—
667C22—124no—
668C22C2×C3×#23714yes—
669C22C2×C3×#23712yes—
670C22C2×C3×#23712yes—
671C22C3×#100912yes—
672C22C24×C3×D311yescharacteristic
673C4—22no—
674C4—24no—
675C4—62no—
676C4—62no—
677C4—64no—
678C4—62no—
679C4—64no—
680C4C2×C3×#23714yes—
681C3—21no—
682C3C2×#561811yescharacteristic, direct product factor
683C3C2×C3×#55311yescharacteristic, complemented
684C2—24no—
685C2—44no—
686C2—122no—
687C2C3×#561814yesdirect product factor
688C2C22×C3×#23711yescharacteristic
689C2C22×C3×#23711yescharacteristic
690C2C2×C3×#100911yescharacteristic
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×#939C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×D4×Dic3C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×C3×C4×#67C2semidirect
7. C22×C3×C4⋊Dic3C2semidirect
8. C3×#5618C2direct (N × H)
9. C2×C3×#892C2semidirect
10. C2×C3×#890C2semidirect
11. C2×C3×#886C2semidirect
12. C2×C3×#879C2semidirect
14. C2×#5618C3direct (N × H)
23. C32×#121C22semidirect
29. C3×#939C22semidirect
30. C3×#938C22semidirect
31. C3×D4×Dic3C22semidirect
32. C3×D4×Dic3C22semidirect
33. C3×C4×#67C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
45. C3×#892C22semidirect
46. C3×#890C22semidirect
47. C3×#886C22semidirect
48. C3×#879C22semidirect
56. C2×C3×#121D3semidirect
57. C2×C3×#121C2×C3semidirect
63. C2×#939C2×C3semidirect
64. C2×#938C2×C3semidirect
65. C2×D4×Dic3C2×C3semidirect
66. C2×D4×Dic3C2×C3semidirect
67. C2×C4×#67C2×C3semidirect
68. C22×C4⋊Dic3C2×C3semidirect
69. #5618C2×C3direct (N × H)
70. C2×#892C2×C3semidirect
71. C2×#890C2×C3semidirect
72. C2×#886C2×C3semidirect
73. C2×#879C2×C3semidirect
142. C3×#121C2×D3semidirect
143. C3×#121C22×C3semidirect
171. #939C22×C3semidirect
172. #938C22×C3semidirect
173. D4×Dic3C22×C3semidirect
174. D4×Dic3C22×C3semidirect
175. C4×#67C22×C3semidirect
182. C2×C4⋊Dic3C22×C3semidirect
187. #892C22×C3semidirect
188. #890C22×C3semidirect
189. #886C22×C3semidirect
190. #879C22×C3semidirect
234. C2×#121C3×D3semidirect
374. #121C2×C3×D3semidirect
489. C2×C32#553semidirect
599. C32C2×#553semidirect
648. C2×C3#5618direct (N × H)
649. C2×C3C3×#553semidirect
682. C3C2×#5618direct (N × H)
683. C3C2×C3×#553semidirect
687. C2C3×#5618direct (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×#9392
C2×C3×#9382
C2×C3×D4×Dic32
C2×C3×C4×#672
C22×C3×C4⋊Dic32
C3×#56182
C2×C3×#8922
C2×C3×#8902
C2×C3×#8862
C2×C3×#8792
C2×C3×#5533
C2×#56183