Finite Group Databasebeta

← C2×C3×#5534 #11901631

Subgroups — C2×C3×#5534 #11901631

Order 1152.

2429 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C3×#5534C2116yesmaximal, direct product factor
5C2×C3×#898C212yesmaximal, complemented
6C2×C3×#896C212yesmaximal, complemented
7C2×C3×#885C212yesmaximal, complemented
8C2×C3×#883C212yesmaximal, complemented
9C2×C3×#875C211yesmaximal, characteristic, complemented
10C2×C3×C4×D12C211yesmaximal, characteristic, complemented
11C2×C3×#869C211yesmaximal, characteristic, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#542—31nomaximal
14C2×#5534C311yesmaximal, characteristic, direct product factor
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2212yes—
21C32×#117C2218yescomplemented
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic
28C2×C3×#217C2212yes—
29C3×#930C2218yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#924C2218yescomplemented
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×C4×Dic3C2212yes—
41C3×#898C22116yescomplemented
42C3×#896C22116yescomplemented
43C3×#885C22116yescomplemented
44C3×#883C22116yescomplemented
45C3×#875C2218yescomplemented
46C3×C4×D12C2218yescomplemented
47C3×#869C2218yescomplemented
48C3×C4×Dic6C2218yescomplemented
49C3×#542—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#126—32no—
52C2×C3×#124—32no—
53C2×C3×#124—31no—
54C2×C3×#123—32no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C22⋊Q8—32no—
57C2×C3×#121—31no—
58C2×C3×C4×Q8—31no—
59C2×C3×C4×D4—31no—
60C2×C3×#117—21no—
61C2×C3×#117D311yescharacteristic, complemented
62C2×C3×#117C2×C311yescharacteristic, complemented
63C2×#930C2×C311yescharacteristic
64C2×#924C2×C311yescharacteristic, complemented
65#5534C2×C3116yesdirect product factor
66C2×#898C2×C312yescomplemented
67C2×#896C2×C312yescomplemented
68C2×#885C2×C312yescomplemented
69C2×#883C2×C312yescomplemented
70C2×#875C2×C311yescharacteristic, complemented
71C2×C4×D12C2×C311yescharacteristic, complemented
72C2×#869C2×C311yescharacteristic, complemented
73C2×C4×Dic6C2×C311yescharacteristic, complemented
74C24×C32C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×C32×C4—24no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C2×C3×#67—44no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C2×C3×D12—24no—
90C2×C3×D12C2314yes—
91C2×C3×C4×D3—44no—
92C2×C3×C4×D3C2318yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6—44no—
95C2×C3×Dic6C2314yes—
96C2×C3×Dic6C2318yes—
97C32×C4⋊C4C2314yes—
98C32×C4⋊C4C2314yes—
99C32×C22⋊C4C2314yes—
100C32×C22⋊C4C2314yes—
101C32×C42C2314yes—
102C32×C42C2314yes—
103C3×#217C2318yes—
104C3×(C2×D3)⋊C4C2318yes—
105C3×(C2×D3)⋊C4C2318yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×C4⋊Dic3C2318yes—
109C3×C4⋊Dic3C2314yes—
110C3×C4⋊Dic3C2314yes—
111C3×Dic3⋊C4C2318yes—
112C3×Dic3⋊C4C2318yes—
113C3×C4×Dic3C2318yes—
114C2×#542—31noSylow
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×C3×D4—32no—
118C22×C3×D4—31no—
119C23×C3×C4—21no—
120C23×C3×C4—32no—
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C22×C311yescharacteristic
123C22×#67C22×C312yes—
124C22×D12C22×C311yescharacteristic
125C22×C4×D3C22×C312yes—
126C22×Dic6C22×C311yescharacteristic
127C22×Dic6C22×C312yes—
128C3×C4⋊Q8—38no—
129C3×#126—316no—
130C3×#124—316no—
131C3×#124—38no—
132C3×#123—316no—
133C3×C22⋊Q8—38no—
134C3×C22⋊Q8—316no—
135C3×#121—38no—
136C3×C4×Q8—38no—
137C3×C4×D4—38no—
138C3×#117—28no—
139C3×#117C2×D318yescomplemented
140C3×#117C22×C318yescomplemented
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—32no—
144C2×C3×C4⋊C4—32no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C22×C311yescharacteristic
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C22⋊C4—32no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4—32no—
158C2×C3×C22⋊C4—32no—
159C2×C3×C22⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4C22×C311yescharacteristic
162C2×C3×C22⋊C4C22×C311yescharacteristic
163C2×C3×C42—21no—
164C2×C3×C42—21no—
165C2×C3×C42—32no—
166C2×C3×C42C2×D311yescharacteristic
167C2×C3×C42C2×D311yescharacteristic
168C2×C3×C42C22×C311yescharacteristic
169C2×C3×C42C22×C311yescharacteristic
170C2×#217C22×C312yes—
171#930C22×C318yes—
172C2×(C2×D3)⋊C4C22×C312yes—
173C2×(C2×D3)⋊C4C22×C312yes—
174C2×(C2×D3)⋊C4C22×C312yes—
175C2×(C2×D3)⋊C4C22×C312yes—
176C2×C4⋊Dic3C22×C311yescharacteristic
177C2×C4⋊Dic3C22×C311yescharacteristic
178C2×C4⋊Dic3C22×C312yes—
179#924C22×C318yescomplemented
180C2×Dic3⋊C4C22×C312yes—
181C2×Dic3⋊C4C22×C312yes—
182C2×C4×Dic3C22×C312yes—
183#898C22×C3116yescomplemented
184#896C22×C3116yescomplemented
185#885C22×C3116yescomplemented
186#883C22×C3116yescomplemented
187#875C22×C318yescomplemented
188C4×D12C22×C318yescomplemented
189#869C22×C318yescomplemented
190C4×Dic6C22×C318yescomplemented
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32C2412yes—
195C23×C32C2411yescharacteristic
196C22×C3×D3—24no—
197C22×C3×D3—24no—
198C22×C3×D3—24no—
199C22×C3×D3C2414yes—
200C2×C32×C4—22no—
201C2×C32×C4—28no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4#4114yes—
207C2×C32×C4C2412yes—
208C2×C32×C4C2412yes—
209C2×C32×C4C2412yes—
210C2×C32×C4C2412yes—
211C2×C32×C4C2412yes—
212C2×C32×C4C2412yes—
213C3×#67—48no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—24no—
216C2×C3×Dic3—24no—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2414yes—
220C3×D12—28no—
221C3×C4×D3—48no—
222C3×Dic6—28no—
223C3×Dic6—48no—
224#542—316no—
225C2×C4⋊Q8—31no—
226C2×#126—32no—
227C2×#124—32no—
228C2×#124—31no—
229C2×#123—32no—
230C2×C22⋊Q8—31no—
231C2×C22⋊Q8—32no—
232C2×#121—31no—
233C2×C4×Q8—31no—
234C2×C4×D4—31no—
235C2×#117C3×D311yescharacteristic, complemented
236C24×C3—21no—
237C24×C3—32no—
238C24×C3C22×D311yescharacteristic
239C24×C3C23×C311yescharacteristic
240C23×D3C23×C312yes—
241C2×C3×Q8—34no—
242C2×C3×Q8—38no—
243C2×C3×Q8—64no—
244C2×C3×Q8—124no—
245C2×C3×D4—38no—
246C2×C3×D4—34no—
247C2×C3×D4—64no—
248C2×C3×D4—124no—
249C22×C3×C4—28no—
250C22×C3×C4—24no—
251C22×C3×C4—24no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—24no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—32no—
260C22×C3×C4—32no—
261C22×C3×C4—32no—
262C22×C3×C4—38no—
263C22×C3×C4—124no—
264C22×C3×C4C22×D314yes—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C22×D311yescharacteristic
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C23×C311yescharacteristic
272C22×C3×C4C23×C311yescharacteristic
273C22×C3×C4C23×C311yescharacteristic
274C22×C3×C4C23×C314yes—
275C22×C3×C4C23×C311yescharacteristic
276C22×C3×C4C23×C311yescharacteristic
277C22×C3×C4C23×C311yescharacteristic
278C2×#67—44no—
279C2×#67C23×C318yes—
280C22×Dic3C23×C312yes—
281C22×Dic3C23×C312yes—
282C22×Dic3C23×C312yes—
283C2×D12—24no—
284C2×D12C23×C314yes—
285C2×C4×D3—44no—
286C2×C4×D3C23×C318yes—
287C2×Dic6—24no—
288C2×Dic6—44no—
289C2×Dic6C23×C314yes—
290C2×Dic6C23×C318yes—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—38no—
294C3×C4⋊C4—38no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—38no—
298C3×C4⋊C4C22×D314yes—
299C3×C4⋊C4C22×D314yes—
300C3×C4⋊C4C23×C314yes—
301C3×C4⋊C4C23×C314yes—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—38no—
305C3×C22⋊C4—38no—
306C3×C22⋊C4—38no—
307C3×C22⋊C4—38no—
308C3×C22⋊C4—38no—
309C3×C22⋊C4C22×D314yes—
310C3×C22⋊C4C22×D314yes—
311C3×C22⋊C4C23×C314yes—
312C3×C22⋊C4C23×C314yes—
313C3×C42—24no—
314C3×C42—24no—
315C3×C42—38no—
316C3×C42C22×D314yes—
317C3×C42C22×D314yes—
318C3×C42C23×C314yes—
319C3×C42C23×C314yes—
320#217C23×C318yes—
321(C2×D3)⋊C4C23×C318yes—
322(C2×D3)⋊C4C23×C318yes—
323(C2×D3)⋊C4C23×C318yes—
324(C2×D3)⋊C4C23×C318yes—
325C4⋊Dic3C23×C314yes—
326C4⋊Dic3C23×C314yes—
327C4⋊Dic3C23×C318yes—
328Dic3⋊C4C23×C318yes—
329Dic3⋊C4C23×C318yes—
330C4×Dic3C23×C318yes—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—44no—
335C22×C32C2×#4112yes—
336C22×C32H(5,𝔽2)12yes—
337C22×C322−1+412yes—
338C22×C32C2511yescharacteristic
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—24no—
342C2×C3×D3—48no—
343C32×C4—22no—
344C32×C4—22no—
345C32×C4—22no—
346C32×C4—22no—
347C32×C4—22no—
348C32×C4C2×#4114yes—
349C3×Dic3—24no—
350C3×Dic3—24no—
351C3×Dic3—24no—
352C22×Q8—31no—
353C22×Q8—32no—
354C22×D4—32no—
355C22×D4—31no—
356C23×C4—32no—
357C23×C4C2×C3×D311yescharacteristic
358C4⋊Q8—38no—
359#126—316no—
360#124—316no—
361#124—38no—
362#123—316no—
363C22⋊Q8—38no—
364C22⋊Q8—316no—
365#121—38no—
366C4×Q8—38no—
367C4×D4—38no—
368#117C2×C3×D318yescomplemented
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4C2×C3×D311yescharacteristic
375C2×C4⋊C4C2×C3×D311yescharacteristic
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—32no—
380C2×C22⋊C4—32no—
381C2×C22⋊C4C2×C3×D311yescharacteristic
382C2×C22⋊C4C2×C3×D311yescharacteristic
383C2×C42—32no—
384C2×C42C2×C3×D311yescharacteristic
385C2×C42C2×C3×D311yescharacteristic
386C23×C3—24no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—22no—
395C23×C3—34no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—64no—
399C23×C3—64no—
400C23×C3—64no—
401C23×C3C23×D312yes—
402C23×C3C23×D311yescharacteristic
403C23×C3C24×C312yes—
404C23×C3C24×C311yescharacteristic
405C22×D3—24no—
406C22×D3—24no—
407C22×D3—24no—
408C22×D3C24×C314yes—
409C3×Q8—68no—
410C3×Q8—128no—
411C3×D4—68no—
412C3×D4—128no—
413C2×C3×C4—24no—
414C2×C3×C4—216no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—28no—
426C2×C3×C4—28no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—34no—
435C2×C3×C4—34no—
436C2×C3×C4—34no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—64no—
442C2×C3×C4—64no—
443C2×C3×C4—64no—
444C2×C3×C4—128no—
445C2×C3×C4#23514yes—
446C2×C3×C4C3×#4114yes—
447C2×C3×C4C23×D312yes—
448C2×C3×C4C23×D312yes—
449C2×C3×C4C23×D312yes—
450C2×C3×C4C23×D312yes—
451C2×C3×C4C23×D312yes—
452C2×C3×C4C23×D312yes—
453C2×C3×C4C24×C312yes—
454C2×C3×C4C24×C312yes—
455C2×C3×C4C24×C312yes—
456C2×C3×C4C24×C312yes—
457C2×C3×C4C24×C312yes—
458C2×C3×C4C24×C312yes—
459#67—48no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3C24×C314yes—
464C2×Dic3C24×C314yes—
465C2×Dic3C24×C314yes—
466D12—28no—
467C4×D3—48no—
468Dic6—28no—
469Dic6—48no—
470C2×C32—42no—
471C2×C32#54214yescomplemented
472C2×C32C22×#4111yescharacteristic
473C2×C32C2×H(5,𝔽2)11yescharacteristic
474C2×C32C2×2−1+411yescharacteristic
475C3×D3—44no—
476C24—32no—
477C24C22×C3×D311yescharacteristic
478C2×Q8—34no—
479C2×Q8—38no—
480C2×Q8—64no—
481C2×Q8—124no—
482C2×D4—38no—
483C2×D4—34no—
484C2×D4—64no—
485C2×D4—124no—
486C22×C4—24no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—38no—
491C22×C4—124no—
492C22×C4C22×C3×D311yescharacteristic
493C22×C4C22×C3×D311yescharacteristic
494C22×C4C22×C3×D311yescharacteristic
495C22×C4C22×C3×D311yescharacteristic
496C22×C4C22×C3×D311yescharacteristic
497C22×C4C22×C3×D314yes—
498C22×C4C22×C3×D311yescharacteristic
499C4⋊C4—34no—
500C4⋊C4—34no—
501C4⋊C4—38no—
502C4⋊C4—38no—
503C4⋊C4—38no—
504C4⋊C4C22×C3×D314yes—
505C4⋊C4C22×C3×D314yes—
506C22⋊C4—38no—
507C22⋊C4—38no—
508C22⋊C4—38no—
509C22⋊C4—38no—
510C22⋊C4—38no—
511C22⋊C4C22×C3×D314yes—
512C22⋊C4C22×C3×D314yes—
513C42—38no—
514C42C22×C3×D314yes—
515C42C22×C3×D314yes—
516C22×C3—24no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—21no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—48no—
530C22×C3—44no—
531C22×C3—44no—
532C22×C3—64no—
533C22×C3—64no—
534C22×C3—64no—
535C22×C3—128no—
536C22×C3C2×#23512yes—
537C22×C3#100912yes—
538C22×C3#101012yes—
539C22×C3C2×C3×#4112yes—
540C22×C3C3×H(5,𝔽2)12yes—
541C22×C3C3×2−1+412yes—
542C22×C3C24×D311yescharacteristic
543C22×C3C25×C311yescharacteristic
544C2×D3—24no—
545C2×D3—24no—
546C2×D3—24no—
547C2×D3—48no—
548C3×C4—24no—
549C3×C4—22no—
550C3×C4—22no—
551C3×C4—22no—
552C3×C4—22no—
553C3×C4—22no—
554C3×C4—22no—
555C3×C4—22no—
556C3×C4—22no—
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—24no—
560C3×C4—42no—
561C3×C4—42no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—64no—
565C3×C4—64no—
566C3×C4—64no—
567C3×C4C2×#23514yes—
568C3×C4C2×C3×#4114yes—
569Dic3—24no—
570Dic3—24no—
571Dic3—24no—
572C32C2×#54211yescharacteristic, complemented, Sylow
573C23—22no—
574C23—22no—
575C23—22no—
576C23—34no—
577C23—64no—
578C23—64no—
579C23—64no—
580C23C23×C3×D312yes—
581C23C23×C3×D311yescharacteristic
582Q8—68no—
583Q8—128no—
584D4—68no—
585D4—128no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—28no—
592C2×C4—34no—
593C2×C4—34no—
594C2×C4—34no—
595C2×C4—64no—
596C2×C4—64no—
597C2×C4—64no—
598C2×C4—128no—
599C2×C4C3×#23514yes—
600C2×C4C23×C3×D312yes—
601C2×C4C23×C3×D312yes—
602C2×C4C23×C3×D312yes—
603C2×C4C23×C3×D312yes—
604C2×C4C23×C3×D312yes—
605C2×C4C23×C3×D312yes—
606C2×C3—24no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—44no—
611C2×C3—42no—
612C2×C3—42no—
613C2×C3—124no—
614C2×C3#553414yesdirect product factor
615C2×C3C3×#54214yescomplemented
616C2×C3C22×#23511yescharacteristic
617C2×C3C2×#100911yescharacteristic
618C2×C3C2×#101011yescharacteristic
619C2×C3C22×C3×#4111yescharacteristic
620C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
621C2×C3C2×C3×2−1+411yescharacteristic
622D3—44no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—44no—
627C22—64no—
628C22—64no—
629C22—64no—
630C22—128no—
631C22C2×C3×#23512yes—
632C22C3×#100912yes—
633C22C3×#101012yes—
634C22C24×C3×D311yescharacteristic
635C4—22no—
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—64no—
641C4—64no—
642C4—64no—
643C4C2×C3×#23514yes—
644C3—21no—
645C3C2×#553411yescharacteristic, direct product factor
646C3C2×C3×#54211yescharacteristic, complemented
647C2—42no—
648C2—124no—
649C2C3×#553414yesdirect product factor
650C2C22×C3×#23511yescharacteristic
651C2C2×C3×#100911yescharacteristic
652C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC2×C3×#117D3
hypocenterC3C2×C3×#542
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
3. C2×C3×#924C2semidirect
4. C3×#5534C2direct (N × H)
5. C2×C3×#898C2semidirect
6. C2×C3×#896C2semidirect
7. C2×C3×#885C2semidirect
8. C2×C3×#883C2semidirect
9. C2×C3×#875C2semidirect
10. C2×C3×C4×D12C2semidirect
11. C2×C3×#869C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5534C3direct (N × H)
21. C32×#117C22semidirect
37. C3×#924C22semidirect
41. C3×#898C22semidirect
42. C3×#896C22semidirect
43. C3×#885C22semidirect
44. C3×#883C22semidirect
45. C3×#875C22semidirect
46. C3×C4×D12C22semidirect
47. C3×#869C22semidirect
48. C3×C4×Dic6C22semidirect
61. C2×C3×#117D3semidirect
62. C2×C3×#117C2×C3semidirect
64. C2×#924C2×C3semidirect
65. #5534C2×C3direct (N × H)
66. C2×#898C2×C3semidirect
67. C2×#896C2×C3semidirect
68. C2×#885C2×C3semidirect
69. C2×#883C2×C3semidirect
70. C2×#875C2×C3semidirect
71. C2×C4×D12C2×C3semidirect
72. C2×#869C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
139. C3×#117C2×D3semidirect
140. C3×#117C22×C3semidirect
179. #924C22×C3semidirect
183. #898C22×C3semidirect
184. #896C22×C3semidirect
185. #885C22×C3semidirect
186. #883C22×C3semidirect
187. #875C22×C3semidirect
188. C4×D12C22×C3semidirect
189. #869C22×C3semidirect
190. C4×Dic6C22×C3semidirect
235. C2×#117C3×D3semidirect
368. #117C2×C3×D3semidirect
471. C2×C32#542semidirect
572. C32C2×#542semidirect
614. C2×C3#5534direct (N × H)
615. C2×C3C3×#542semidirect
645. C3C2×#5534direct (N × H)
646. C3C2×C3×#542semidirect
649. C2C3×#5534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C3×#9302
C2×C3×#9242
C3×#55342
C2×C3×#8982
C2×C3×#8962
C2×C3×#8852
C2×C3×#8832
C2×C3×#8752
C2×C3×C4×D122
C2×C3×#8692
C2×C3×C4×Dic62
C2×C3×#5423
C2×#55343