Finite Group Databasebeta

← C2×C3×#5562 #11901467

Subgroups — C2×C3×#5562 #11901467

Order 1152.

2733 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×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×C3×#930C212yesmaximal, complemented
5C2×C3×#929C212yesmaximal, complemented
6C3×#5562C2116yesmaximal, direct product factor
7C2×C3×#895C211yesmaximal, characteristic, complemented
8C2×C3×#890C211yesmaximal, characteristic, complemented
9C2×C3×#884C212yesmaximal, complemented
10C2×C3×#883C212yesmaximal, complemented
11C2×C3×C4×D12C211yesmaximal, characteristic, complemented
12C2×C3×#872C211yesmaximal, characteristic, complemented
13C2×C3×#540—31nomaximal
14C2×#5562C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2212yes—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2212yes—
24C32×C4×D4C2218yescomplemented
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2212yes—
27C2×C32×C42C2211yescharacteristic
28C2×C3×#217C2212yes—
29C3×#940C2218yescomplemented
30C3×#938C2218yescomplemented
31C3×#930C22116yescomplemented
32C3×#929C22116yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×C4⋊Dic3C2212yes—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2212yes—
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#895C2218yescomplemented
44C3×#890C2218yescomplemented
45C3×#884C22116yescomplemented
46C3×#883C22116yescomplemented
47C3×C4×D12C2218yescomplemented
48C3×#872C2218yescomplemented
49C3×#540—316no—
50C2×C3×#127—31no—
51C2×C3×#125—31no—
52C2×C3×#123—32no—
53C2×C3×#123—32no—
54C2×C3×#121—31no—
55C2×C3×#121—32no—
56C2×C3×#121—31no—
57C2×C3×#121—32no—
58C2×C3×C4×D4—21no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4D311yescharacteristic, complemented
61C2×C3×C4×D4C2×C311yescharacteristic, complemented
62C2×C3×#117—31no—
63C2×#940C2×C311yescharacteristic, complemented
64C2×#938C2×C311yescharacteristic, complemented
65C2×#930C2×C312yescomplemented
66C2×#929C2×C312yescomplemented
67#5562C2×C3116yesdirect product factor
68C2×#895C2×C311yescharacteristic, complemented
69C2×#890C2×C311yescharacteristic, complemented
70C2×#884C2×C312yescomplemented
71C2×#883C2×C312yescomplemented
72C2×C4×D12C2×C311yescharacteristic, complemented
73C2×#872C2×C311yescharacteristic, complemented
74C24×C32C2312yes—
75C23×C3×D3C2311yescharacteristic
76C23×C3×D3C2312yes—
77C2×C32×D4—24no—
78C2×C32×D4C2314yes—
79C22×C32×C4—44no—
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2318yes—
84C22×C32×C4C2311yescharacteristic
85C2×C3×#67—44no—
86C2×C3×#67—44no—
87C2×C3×#67—44no—
88C2×C3×#67C2318yes—
89C2×C3×#67C2318yes—
90C2×C3×#67C2318yes—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2312yes—
95C2×C3×D12—24no—
96C2×C3×D12—44no—
97C2×C3×D12C2314yes—
98C2×C3×D12C2318yes—
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3—44no—
101C2×C3×C4×D3C2314yes—
102C2×C3×C4×D3C2318yes—
103C32×C4⋊C4C2314yes—
104C32×C22⋊C4C2318yes—
105C32×C42C2314yes—
106C3×#217C2318yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×(C2×D3)⋊C4C2314yes—
109C3×(C2×D3)⋊C4C2318yes—
110C3×(C2×D3)⋊C4C2314yes—
111C3×C4⋊Dic3C2318yes—
112C3×C4⋊Dic3C2314yes—
113C3×Dic3⋊C4C2314yes—
114C3×Dic3⋊C4C2318yes—
115C3×Dic3⋊C4C2314yes—
116C3×C4×Dic3C2314yes—
117C2×#540—31noSylow
118C22×C3×D4—21no—
119C22×C3×D4—32no—
120C22×C3×D4—32no—
121C22×C3×D4—32no—
122C22×C3×D4—31no—
123C22×C3×D4—32no—
124C22×C3×D4C2×D311yescharacteristic
125C22×C3×D4C22×C311yescharacteristic
126C23×C3×C4—22no—
127C23×C3×C4—31no—
128C23×C3×C4—32no—
129C23×C3×C4C2×D312yes—
130C23×C3×C4C22×C312yes—
131C22×#67C22×C312yes—
132C22×#67C22×C312yes—
133C22×#67C22×C312yes—
134C22×D12C22×C311yescharacteristic
135C22×D12C22×C312yes—
136C22×C4×D3C22×C311yescharacteristic
137C22×C4×D3C22×C312yes—
138C3×#127—38no—
139C3×#125—38no—
140C3×#123—316no—
141C3×#123—316no—
142C3×#121—38no—
143C3×#121—316no—
144C3×#121—38no—
145C3×#121—316no—
146C3×C4×D4—28no—
147C3×C4×D4—38no—
148C3×C4×D4C2×D318yescomplemented
149C3×C4×D4C22×C318yescomplemented
150C3×#117—38no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—32no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—32no—
157C2×C3×C4⋊C4C2×D311yescharacteristic
158C2×C3×C4⋊C4C22×C311yescharacteristic
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C22⋊C4—32no—
165C2×C3×C22⋊C4C2×D312yes—
166C2×C3×C22⋊C4C22×C312yes—
167C2×C3×C42—21no—
168C2×C3×C42—31no—
169C2×C3×C42C2×D311yescharacteristic
170C2×C3×C42C22×C311yescharacteristic
171C2×#217C22×C312yes—
172#940C22×C318yescomplemented
173#938C22×C318yescomplemented
174#930C22×C3116yescomplemented
175#929C22×C3116yescomplemented
176C2×(C2×D3)⋊C4C22×C311yescharacteristic
177C2×(C2×D3)⋊C4C22×C311yescharacteristic
178C2×(C2×D3)⋊C4C22×C312yes—
179C2×(C2×D3)⋊C4C22×C312yes—
180C2×C4⋊Dic3C22×C311yescharacteristic
181C2×C4⋊Dic3C22×C312yes—
182C2×Dic3⋊C4C22×C311yescharacteristic
183C2×Dic3⋊C4C22×C311yescharacteristic
184C2×Dic3⋊C4C22×C312yes—
185C2×C4×Dic3C22×C311yescharacteristic
186#895C22×C318yescomplemented
187#890C22×C318yescomplemented
188#884C22×C3116yescomplemented
189#883C22×C3116yescomplemented
190C4×D12C22×C318yescomplemented
191#872C22×C318yescomplemented
192C23×C32—24no—
193C23×C32—24no—
194C23×C32—24no—
195C23×C32C2414yes—
196C23×C32C2411yescharacteristic
197C22×C3×D3—22no—
198C22×C3×D3—24no—
199C22×C3×D3—24no—
200C22×C3×D3—22no—
201C22×C3×D3—24no—
202C22×C3×D3—22no—
203C22×C3×D3C2412yes—
204C22×C3×D3C2414yes—
205C32×D4—28no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—24no—
209C2×C32×C4—48no—
210C2×C32×C4#4114yes—
211C2×C32×C4C2414yes—
212C2×C32×C4C2412yes—
213C2×C32×C4C2412yes—
214C2×C32×C4C2412yes—
215C3×#67—48no—
216C3×#67—48no—
217C3×#67—48no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—24no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3C2412yes—
223C2×C3×Dic3C2412yes—
224C2×C3×Dic3C2412yes—
225C2×C3×Dic3C2414yes—
226C3×D12—28no—
227C3×D12—48no—
228C3×C4×D3—28no—
229C3×C4×D3—48no—
230#540—316no—
231C2×#127—31no—
232C2×#125—31no—
233C2×#123—32no—
234C2×#123—32no—
235C2×#121—31no—
236C2×#121—32no—
237C2×#121—31no—
238C2×#121—32no—
239C2×C4×D4—31no—
240C2×C4×D4C3×D311yescharacteristic, complemented
241C2×#117—31no—
242C24×C3—22no—
243C24×C3—31no—
244C24×C3—32no—
245C24×C3C22×D312yes—
246C24×C3C23×C312yes—
247C23×D3C23×C311yescharacteristic
248C23×D3C23×C312yes—
249C2×C3×D4—28no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—38no—
254C2×C3×D4—38no—
255C2×C3×D4—38no—
256C2×C3×D4—34no—
257C2×C3×D4—38no—
258C2×C3×D4—64no—
259C2×C3×D4—124no—
260C2×C3×D4—124no—
261C2×C3×D4—124no—
262C2×C3×D4—124no—
263C2×C3×D4C22×D314yes—
264C2×C3×D4C23×C314yes—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—22no—
269C22×C3×C4—28no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—32no—
274C22×C3×C4—34no—
275C22×C3×C4—38no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4—48no—
279C22×C3×C4—64no—
280C22×C3×C4—124no—
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D312yes—
284C22×C3×C4C22×D318yes—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C23×C312yes—
287C22×C3×C4C23×C311yescharacteristic
288C22×C3×C4C23×C311yescharacteristic
289C22×C3×C4C23×C318yes—
290C22×C3×C4C23×C311yescharacteristic
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67C23×C318yes—
295C2×#67C23×C318yes—
296C2×#67C23×C318yes—
297C22×Dic3C23×C311yescharacteristic
298C22×Dic3C23×C311yescharacteristic
299C22×Dic3C23×C311yescharacteristic
300C22×Dic3C23×C312yes—
301C2×D12—24no—
302C2×D12—44no—
303C2×D12C23×C314yes—
304C2×D12C23×C318yes—
305C2×C4×D3—24no—
306C2×C4×D3—44no—
307C2×C4×D3C23×C314yes—
308C2×C4×D3C23×C318yes—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—34no—
311C3×C4⋊C4—34no—
312C3×C4⋊C4—38no—
313C3×C4⋊C4—34no—
314C3×C4⋊C4—38no—
315C3×C4⋊C4C22×D314yes—
316C3×C4⋊C4C23×C314yes—
317C3×C22⋊C4—28no—
318C3×C22⋊C4—38no—
319C3×C22⋊C4—34no—
320C3×C22⋊C4—34no—
321C3×C22⋊C4—38no—
322C3×C22⋊C4—38no—
323C3×C22⋊C4C22×D318yes—
324C3×C22⋊C4C23×C318yes—
325C3×C42—24no—
326C3×C42—34no—
327C3×C42C22×D314yes—
328C3×C42C23×C314yes—
329#217C23×C318yes—
330(C2×D3)⋊C4C23×C314yes—
331(C2×D3)⋊C4C23×C314yes—
332(C2×D3)⋊C4C23×C318yes—
333(C2×D3)⋊C4C23×C318yes—
334C4⋊Dic3C23×C314yes—
335C4⋊Dic3C23×C318yes—
336Dic3⋊C4C23×C314yes—
337Dic3⋊C4C23×C314yes—
338Dic3⋊C4C23×C318yes—
339C4×Dic3C23×C314yes—
340C22×C32—24no—
341C22×C32—24no—
342C22×C32—24no—
343C22×C32—48no—
344C22×C32C2×#4112yes—
345C22×C32H(5,𝔽2)12yes—
346C22×C32H(5,𝔽2)12yes—
347C22×C32C2511yescharacteristic
348C2×C3×D3—22no—
349C2×C3×D3—24no—
350C2×C3×D3—24no—
351C2×C3×D3—22no—
352C2×C3×D3—24no—
353C2×C3×D3—22no—
354C2×C3×D3—44no—
355C2×C3×D3—48no—
356C32×C4—22no—
357C32×C4—22no—
358C32×C4—24no—
359C32×C4C2×#4114yes—
360C3×Dic3—22no—
361C3×Dic3—24no—
362C3×Dic3—22no—
363C3×Dic3—22no—
364C22×D4—32no—
365C22×D4—32no—
366C22×D4—32no—
367C22×D4—31no—
368C22×D4—32no—
369C22×D4C2×C3×D311yescharacteristic
370C23×C4—31no—
371C23×C4—32no—
372C23×C4C2×C3×D312yes—
373#127—38no—
374#125—38no—
375#123—316no—
376#123—316no—
377#121—38no—
378#121—316no—
379#121—38no—
380#121—316no—
381C4×D4—38no—
382C4×D4C2×C3×D318yescomplemented
383#117—38no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4C2×C3×D311yescharacteristic
390C2×C22⋊C4—32no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4C2×C3×D312yes—
396C2×C42—31no—
397C2×C42C2×C3×D311yescharacteristic
398C23×C3—28no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—24no—
405C23×C3—21no—
406C23×C3—24no—
407C23×C3—32no—
408C23×C3—34no—
409C23×C3—44no—
410C23×C3—44no—
411C23×C3—62no—
412C23×C3—64no—
413C23×C3—62no—
414C23×C3—64no—
415C23×C3—64no—
416C23×C3—62no—
417C23×C3C23×D314yes—
418C23×C3C23×D311yescharacteristic
419C23×C3C24×C314yes—
420C23×C3C24×C311yescharacteristic
421C22×D3—22no—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—22no—
425C22×D3—24no—
426C22×D3—22no—
427C22×D3C24×C312yes—
428C22×D3C24×C314yes—
429C3×D4—216no—
430C3×D4—28no—
431C3×D4—28no—
432C3×D4—68no—
433C3×D4—128no—
434C3×D4—128no—
435C3×D4—128no—
436C3×D4—128no—
437C2×C3×C4—24no—
438C2×C3×C4—22no—
439C2×C3×C4—24no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—24no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—34no—
453C2×C3×C4—42no—
454C2×C3×C4—44no—
455C2×C3×C4—48no—
456C2×C3×C4—48no—
457C2×C3×C4—416no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—64no—
461C2×C3×C4—62no—
462C2×C3×C4—68no—
463C2×C3×C4—128no—
464C2×C3×C4#23514yes—
465C2×C3×C4C3×#4114yes—
466C2×C3×C4C23×D312yes—
467C2×C3×C4C23×D312yes—
468C2×C3×C4C23×D314yes—
469C2×C3×C4C23×D312yes—
470C2×C3×C4C24×C314yes—
471C2×C3×C4C24×C312yes—
472C2×C3×C4C24×C312yes—
473C2×C3×C4C24×C312yes—
474#67—48no—
475#67—48no—
476#67—48no—
477C2×Dic3—22no—
478C2×Dic3—24no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3C24×C312yes—
482C2×Dic3C24×C312yes—
483C2×Dic3C24×C312yes—
484C2×Dic3C24×C314yes—
485D12—28no—
486D12—48no—
487C4×D3—28no—
488C4×D3—48no—
489C2×C32—44no—
490C2×C32#54014yescomplemented
491C2×C32C22×#4111yescharacteristic
492C2×C32C2×H(5,𝔽2)11yescharacteristic
493C2×C32C2×H(5,𝔽2)11yescharacteristic
494C3×D3—42no—
495C3×D3—44no—
496C24—31no—
497C24—32no—
498C24C22×C3×D312yes—
499C2×D4—24no—
500C2×D4—38no—
501C2×D4—38no—
502C2×D4—38no—
503C2×D4—34no—
504C2×D4—38no—
505C2×D4—64no—
506C2×D4—124no—
507C2×D4—124no—
508C2×D4—124no—
509C2×D4—124no—
510C2×D4C22×C3×D314yes—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—32no—
515C22×C4—34no—
516C22×C4—38no—
517C22×C4—44no—
518C22×C4—64no—
519C22×C4—124no—
520C22×C4C22×C3×D311yescharacteristic
521C22×C4C22×C3×D311yescharacteristic
522C22×C4C22×C3×D312yes—
523C22×C4C22×C3×D318yes—
524C22×C4C22×C3×D311yescharacteristic
525C4⋊C4—34no—
526C4⋊C4—34no—
527C4⋊C4—34no—
528C4⋊C4—38no—
529C4⋊C4—38no—
530C4⋊C4C22×C3×D314yes—
531C22⋊C4—38no—
532C22⋊C4—34no—
533C22⋊C4—34no—
534C22⋊C4—38no—
535C22⋊C4—38no—
536C22⋊C4C22×C3×D318yes—
537C42—34no—
538C42C22×C3×D314yes—
539C22×C3—28no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—21no—
550C22×C3—44no—
551C22×C3—44no—
552C22×C3—416no—
553C22×C3—48no—
554C22×C3—48no—
555C22×C3—62no—
556C22×C3—64no—
557C22×C3—62no—
558C22×C3—64no—
559C22×C3—64no—
560C22×C3—62no—
561C22×C3—124no—
562C22×C3—128no—
563C22×C3C2×#23512yes—
564C22×C3#100412yes—
565C22×C3#100912yes—
566C22×C3C2×C3×#4112yes—
567C22×C3C3×H(5,𝔽2)12yes—
568C22×C3C3×H(5,𝔽2)12yes—
569C22×C3C24×D311yescharacteristic
570C22×C3C25×C311yescharacteristic
571C2×D3—22no—
572C2×D3—24no—
573C2×D3—24no—
574C2×D3—22no—
575C2×D3—24no—
576C2×D3—22no—
577C2×D3—44no—
578C2×D3—48no—
579C3×C4—24no—
580C3×C4—22no—
581C3×C4—24no—
582C3×C4—22no—
583C3×C4—22no—
584C3×C4—24no—
585C3×C4—22no—
586C3×C4—24no—
587C3×C4—44no—
588C3×C4—42no—
589C3×C4—62no—
590C3×C4—62no—
591C3×C4—64no—
592C3×C4—62no—
593C3×C4C2×#23514yes—
594C3×C4C2×C3×#4114yes—
595Dic3—22no—
596Dic3—24no—
597Dic3—22no—
598Dic3—22no—
599C32C2×#54011yescharacteristic, complemented, Sylow
600C23—24no—
601C23—24no—
602C23—24no—
603C23—32no—
604C23—34no—
605C23—62no—
606C23—64no—
607C23—62no—
608C23—64no—
609C23—64no—
610C23—62no—
611C23C23×C3×D314yes—
612C23C23×C3×D311yescharacteristic
613D4—28no—
614D4—68no—
615D4—128no—
616D4—128no—
617D4—128no—
618D4—128no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—32no—
623C2×C4—32no—
624C2×C4—32no—
625C2×C4—34no—
626C2×C4—48no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—64no—
630C2×C4—62no—
631C2×C4—68no—
632C2×C4—128no—
633C2×C4C3×#23514yes—
634C2×C4C23×C3×D312yes—
635C2×C4C23×C3×D312yes—
636C2×C4C23×C3×D314yes—
637C2×C4C23×C3×D312yes—
638C2×C3—24no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—48no—
643C2×C3—44no—
644C2×C3—44no—
645C2×C3—122no—
646C2×C3—124no—
647C2×C3#556214yesdirect product factor
648C2×C3C3×#54014yescomplemented
649C2×C3C22×#23511yescharacteristic
650C2×C3C2×#100411yescharacteristic
651C2×C3C2×#100911yescharacteristic
652C2×C3C22×C3×#4111yescharacteristic
653C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
654C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
655D3—42no—
656D3—44no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—48no—
661C22—62no—
662C22—64no—
663C22—62no—
664C22—64no—
665C22—64no—
666C22—62no—
667C22—124no—
668C22—128no—
669C22C2×C3×#23512yes—
670C22C3×#100412yes—
671C22C3×#100912yes—
672C22C24×C3×D311yescharacteristic
673C4—22no—
674C4—24no—
675C4—22no—
676C4—62no—
677C4—62no—
678C4—64no—
679C4—62no—
680C4C2×C3×#23514yes—
681C3—21no—
682C3C2×#556211yescharacteristic, direct product factor
683C3C2×C3×#54011yescharacteristic, complemented
684C2—44no—
685C2—122no—
686C2—124no—
687C2C3×#556214yesdirect product factor
688C2C22×C3×#23511yescharacteristic
689C2C2×C3×#100411yescharacteristic
690C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#540
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×#930C2semidirect
5. C2×C3×#929C2semidirect
6. C3×#5562C2direct (N × H)
7. C2×C3×#895C2semidirect
8. C2×C3×#890C2semidirect
9. C2×C3×#884C2semidirect
10. C2×C3×#883C2semidirect
11. C2×C3×C4×D12C2semidirect
12. C2×C3×#872C2semidirect
14. C2×#5562C3direct (N × H)
24. C32×C4×D4C22semidirect
29. C3×#940C22semidirect
30. C3×#938C22semidirect
31. C3×#930C22semidirect
32. C3×#929C22semidirect
43. C3×#895C22semidirect
44. C3×#890C22semidirect
45. C3×#884C22semidirect
46. C3×#883C22semidirect
47. C3×C4×D12C22semidirect
48. C3×#872C22semidirect
60. C2×C3×C4×D4D3semidirect
61. C2×C3×C4×D4C2×C3semidirect
63. C2×#940C2×C3semidirect
64. C2×#938C2×C3semidirect
65. C2×#930C2×C3semidirect
66. C2×#929C2×C3semidirect
67. #5562C2×C3direct (N × H)
68. C2×#895C2×C3semidirect
69. C2×#890C2×C3semidirect
70. C2×#884C2×C3semidirect
71. C2×#883C2×C3semidirect
72. C2×C4×D12C2×C3semidirect
73. C2×#872C2×C3semidirect
148. C3×C4×D4C2×D3semidirect
149. C3×C4×D4C22×C3semidirect
172. #940C22×C3semidirect
173. #938C22×C3semidirect
174. #930C22×C3semidirect
175. #929C22×C3semidirect
186. #895C22×C3semidirect
187. #890C22×C3semidirect
188. #884C22×C3semidirect
189. #883C22×C3semidirect
190. C4×D12C22×C3semidirect
191. #872C22×C3semidirect
240. C2×C4×D4C3×D3semidirect
382. C4×D4C2×C3×D3semidirect
490. C2×C32#540semidirect
599. C32C2×#540semidirect
647. C2×C3#5562direct (N × H)
648. C2×C3C3×#540semidirect
682. C3C2×#5562direct (N × H)
683. C3C2×C3×#540semidirect
687. C2C3×#5562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9402
C2×C3×#9382
C2×C3×#9302
C2×C3×#9292
C3×#55622
C2×C3×#8952
C2×C3×#8902
C2×C3×#8842
C2×C3×#8832
C2×C3×C4×D122
C2×C3×#8722
C2×C3×#5403
C2×#55623