Finite Group Databasebeta

← C2×C3×#5530 #11903096

Subgroups — C2×C3×#5530 #11903096

Order 1152.

2669 conjugacy classes of subgroups.

The subgroup lattice has 682 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, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C3×#5530C2116yesmaximal, direct product factor
5C2×C3×#895C211yesmaximal, characteristic, complemented
6C2×C3×#893C211yesmaximal, characteristic, complemented
7C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
8C2×C3×#890C211yesmaximal, characteristic, complemented
9C2×C3×#884C212yesmaximal, complemented
10C2×C3×#883C212yesmaximal, complemented
11C2×C3×#876C212yesmaximal, complemented
12C2×C3×C4×D12C212yesmaximal, complemented
13C2×C3×#553—31nomaximal
14C2×#5530C311yesmaximal, characteristic, direct product factor
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×D12C2212yes—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C22×C3×C4×D3C2212yes—
23C32×#117C2218yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2212yes—
27C2×C32×C42C2212yes—
28C2×C3×#217C2211yescharacteristic
29C3×#930C2218yescomplemented
30C3×C4×#67C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×C4⋊Dic3C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#895C2218yescomplemented
42C3×#893C2218yescomplemented
43C3×D3×C4⋊C4C2218yescomplemented
44C3×#890C2218yescomplemented
45C3×#884C22116yescomplemented
46C3×#883C22116yescomplemented
47C3×#876C22116yescomplemented
48C3×C4×D12C22116yescomplemented
49C3×#553—316no—
50C2×C3×#126—32no—
51C2×C3×#125—31no—
52C2×C3×#123—32no—
53C2×C3×#121—31no—
54C2×C3×#121—31no—
55C2×C3×#121—32no—
56C2×C3×C4×D4—31no—
57C2×C3×C4×D4—31no—
58C2×C3×C4×D4—32no—
59C2×C3×#117—21no—
60C2×C3×#117D311yescharacteristic, complemented
61C2×C3×#117C2×C311yescharacteristic, complemented
62C22×C3×C4⋊C4—31no—
63C2×#930C2×C311yescharacteristic, complemented
64C2×C4×#67C2×C311yescharacteristic, complemented
65#5530C2×C3116yesdirect product factor
66C2×#895C2×C311yescharacteristic, complemented
67C2×#893C2×C311yescharacteristic, complemented
68C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
69C2×#890C2×C311yescharacteristic, complemented
70C2×#884C2×C312yescomplemented
71C2×#883C2×C312yescomplemented
72C2×#876C2×C312yescomplemented
73C2×C4×D12C2×C312yescomplemented
74C24×C32C2311yescharacteristic
75C23×C3×D3C2312yes—
76C23×C3×D3C2311yescharacteristic
77C22×C32×C4—24no—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C2×C3×#67—24no—
84C2×C3×#67—44no—
85C2×C3×#67C2314yes—
86C2×C3×#67C2318yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C2×C3×D12—28no—
92C2×C3×D12—24no—
93C2×C3×D12C2318yes—
94C2×C3×D12C2314yes—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3—44no—
97C2×C3×C4×D3—44no—
98C2×C3×C4×D3C2314yes—
99C2×C3×C4×D3C2318yes—
100C2×C3×C4×D3C2318yes—
101C32×C4⋊C4C2314yes—
102C32×C4⋊C4C2314yes—
103C32×C22⋊C4C2318yes—
104C32×C42C2318yes—
105C3×#217C2314yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×(C2×D3)⋊C4C2314yes—
109C3×(C2×D3)⋊C4C2318yes—
110C3×C4⋊Dic3C2318yes—
111C3×C4⋊Dic3C2314yes—
112C3×Dic3⋊C4C2318yes—
113C3×Dic3⋊C4C2318yes—
114C3×Dic3⋊C4C2314yes—
115C3×C4×Dic3C2314yes—
116C2×#553—31noSylow
117C22×C3×D4—31no—
118C22×C3×D4—32no—
119C22×C3×D4—32no—
120C22×C3×D4—31no—
121C23×C3×C4—21no—
122C23×C3×C4—31no—
123C23×C3×C4—32no—
124C23×C3×C4—32no—
125C23×C3×C4C2×D311yescharacteristic
126C23×C3×C4C22×C311yescharacteristic
127C22×#67C22×C311yescharacteristic
128C22×#67C22×C312yes—
129C22×D12C22×C312yes—
130C22×D12C22×C311yescharacteristic
131C22×C4×D3C22×C311yescharacteristic
132C22×C4×D3C22×C312yes—
133C22×C4×D3C22×C312yes—
134C3×#126—316no—
135C3×#125—38no—
136C3×#123—316no—
137C3×#121—38no—
138C3×#121—38no—
139C3×#121—316no—
140C3×C4×D4—38no—
141C3×C4×D4—38no—
142C3×C4×D4—316no—
143C3×#117—28no—
144C3×#117C2×D318yescomplemented
145C3×#117C22×C318yescomplemented
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—32no—
153C2×C3×C4⋊C4—38no—
154C2×C3×C4⋊C4C2×D311yescharacteristic
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C22×C311yescharacteristic
157C2×C3×C4⋊C4C22×C311yescharacteristic
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—32no—
162C2×C3×C22⋊C4—32no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C22⋊C4C2×D312yes—
165C2×C3×C22⋊C4C22×C312yes—
166C2×C3×C42—22no—
167C2×C3×C42—31no—
168C2×C3×C42C2×D312yes—
169C2×C3×C42C22×C312yes—
170C2×#217C22×C311yescharacteristic
171#930C22×C318yescomplemented
172C4×#67C22×C318yescomplemented
173C2×(C2×D3)⋊C4C22×C311yescharacteristic
174C2×(C2×D3)⋊C4C22×C312yes—
175C2×(C2×D3)⋊C4C22×C312yes—
176C2×(C2×D3)⋊C4C22×C312yes—
177C2×C4⋊Dic3C22×C312yes—
178C2×C4⋊Dic3C22×C311yescharacteristic
179C2×Dic3⋊C4C22×C311yescharacteristic
180C2×Dic3⋊C4C22×C312yes—
181C2×Dic3⋊C4C22×C312yes—
182C2×C4×Dic3C22×C311yescharacteristic
183#895C22×C318yescomplemented
184#893C22×C318yescomplemented
185D3×C4⋊C4C22×C318yescomplemented
186#890C22×C318yescomplemented
187#884C22×C3116yescomplemented
188#883C22×C3116yescomplemented
189#876C22×C3116yescomplemented
190C4×D12C22×C3116yescomplemented
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32C2412yes—
195C23×C32C2411yescharacteristic
196C22×C3×D3—22no—
197C22×C3×D3—22no—
198C22×C3×D3—24no—
199C22×C3×D3—24no—
200C22×C3×D3—24no—
201C22×C3×D3#4114yes—
202C22×C3×D3C2414yes—
203C22×C3×D3C2412yes—
204C2×C32×C4—22no—
205C2×C32×C4—28no—
206C2×C32×C4—24no—
207C2×C32×C4—24no—
208C2×C32×C4#4114yes—
209C2×C32×C4C2414yes—
210C2×C32×C4C2412yes—
211C2×C32×C4C2414yes—
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×Dic3C2412yes—
220C2×C3×Dic3C2412yes—
221C2×C3×Dic3C2412yes—
222C2×C3×Dic3C2414yes—
223C3×D12—216no—
224C3×D12—28no—
225C3×C4×D3—28no—
226C3×C4×D3—48no—
227C3×C4×D3—48no—
228#553—316no—
229C2×#126—32no—
230C2×#125—31no—
231C2×#123—32no—
232C2×#121—31no—
233C2×#121—31no—
234C2×#121—32no—
235C2×C4×D4—31no—
236C2×C4×D4—31no—
237C2×C4×D4—32no—
238C2×#117C3×D311yescharacteristic, complemented
239C22×C4⋊C4—31no—
240C24×C3—21no—
241C24×C3—31no—
242C24×C3—32no—
243C24×C3C22×D311yescharacteristic
244C24×C3C23×C311yescharacteristic
245C23×D3C23×C312yes—
246C23×D3C23×C311yescharacteristic
247C2×C3×D4—34no—
248C2×C3×D4—38no—
249C2×C3×D4—38no—
250C2×C3×D4—34no—
251C2×C3×D4—68no—
252C2×C3×D4—64no—
253C2×C3×D4—64no—
254C2×C3×D4—124no—
255C22×C3×C4—28no—
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—24no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—32no—
267C22×C3×C4—34no—
268C22×C3×C4—38no—
269C22×C3×C4—38no—
270C22×C3×C4—64no—
271C22×C3×C4—124no—
272C22×C3×C4—124no—
273C22×C3×C4C22×D314yes—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D312yes—
276C22×C3×C4C22×D312yes—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C23×C312yes—
279C22×C3×C4C23×C311yescharacteristic
280C22×C3×C4C23×C312yes—
281C22×C3×C4C23×C314yes—
282C22×C3×C4C23×C311yescharacteristic
283C2×#67—24no—
284C2×#67—44no—
285C2×#67C23×C314yes—
286C2×#67C23×C318yes—
287C22×Dic3C23×C311yescharacteristic
288C22×Dic3C23×C311yescharacteristic
289C22×Dic3C23×C311yescharacteristic
290C22×Dic3C23×C312yes—
291C2×D12—28no—
292C2×D12—24no—
293C2×D12C23×C318yes—
294C2×D12C23×C314yes—
295C2×C4×D3—24no—
296C2×C4×D3—44no—
297C2×C4×D3—44no—
298C2×C4×D3C23×C314yes—
299C2×C4×D3C23×C318yes—
300C2×C4×D3C23×C318yes—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—24no—
303C3×C4⋊C4—38no—
304C3×C4⋊C4—34no—
305C3×C4⋊C4—38no—
306C3×C4⋊C4—34no—
307C3×C4⋊C4—38no—
308C3×C4⋊C4C22×D314yes—
309C3×C4⋊C4C22×D314yes—
310C3×C4⋊C4C23×C314yes—
311C3×C4⋊C4C23×C314yes—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—34no—
314C3×C22⋊C4—34no—
315C3×C22⋊C4—38no—
316C3×C22⋊C4—38no—
317C3×C22⋊C4—38no—
318C3×C22⋊C4C22×D318yes—
319C3×C22⋊C4C23×C318yes—
320C3×C42—28no—
321C3×C42—34no—
322C3×C42C22×D318yes—
323C3×C42C23×C318yes—
324#217C23×C314yes—
325(C2×D3)⋊C4C23×C314yes—
326(C2×D3)⋊C4C23×C318yes—
327(C2×D3)⋊C4C23×C318yes—
328(C2×D3)⋊C4C23×C318yes—
329C4⋊Dic3C23×C318yes—
330C4⋊Dic3C23×C314yes—
331Dic3⋊C4C23×C314yes—
332Dic3⋊C4C23×C318yes—
333Dic3⋊C4C23×C318yes—
334C4×Dic3C23×C314yes—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—22no—
338C22×C32—44no—
339C22×C32C2×#4112yes—
340C22×C32C2×#4112yes—
341C22×C32H(5,𝔽2)12yes—
342C22×C32C2511yescharacteristic
343C2×C3×D3—28no—
344C2×C3×D3—22no—
345C2×C3×D3—22no—
346C2×C3×D3—24no—
347C2×C3×D3—24no—
348C2×C3×D3—24no—
349C2×C3×D3—48no—
350C2×C3×D3C2×#4114yes—
351C32×C4—22no—
352C32×C4—24no—
353C32×C4—24no—
354C32×C4C2×#4114yes—
355C3×Dic3—22no—
356C3×Dic3—22no—
357C3×Dic3—22no—
358C3×Dic3—24no—
359C22×D4—31no—
360C22×D4—32no—
361C22×D4—32no—
362C22×D4—31no—
363C23×C4—31no—
364C23×C4—32no—
365C23×C4—32no—
366C23×C4C2×C3×D311yescharacteristic
367#126—316no—
368#125—38no—
369#123—316no—
370#121—38no—
371#121—38no—
372#121—316no—
373C4×D4—38no—
374C4×D4—38no—
375C4×D4—316no—
376#117C2×C3×D318yescomplemented
377C2×C4⋊C4—31no—
378C2×C4⋊C4—32no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—38no—
383C2×C4⋊C4C2×C3×D311yescharacteristic
384C2×C4⋊C4C2×C3×D311yescharacteristic
385C2×C22⋊C4—31no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4C2×C3×D312yes—
391C2×C42—31no—
392C2×C42C2×C3×D312yes—
393C23×C3—24no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—34no—
403C23×C3—32no—
404C23×C3—34no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—62no—
408C23×C3—62no—
409C23×C3—64no—
410C23×C3—64no—
411C23×C3—64no—
412C23×C3C23×D312yes—
413C23×C3C23×D311yescharacteristic
414C23×C3C24×C312yes—
415C23×C3C24×C311yescharacteristic
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—24no—
419C22×D3—24no—
420C22×D3—24no—
421C22×D3C3×#4114yes—
422C22×D3C24×C314yes—
423C22×D3C24×C312yes—
424C3×D4—616no—
425C3×D4—68no—
426C3×D4—68no—
427C3×D4—128no—
428C2×C3×C4—24no—
429C2×C3×C4—216no—
430C2×C3×C4—22no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—22no—
435C2×C3×C4—24no—
436C2×C3×C4—28no—
437C2×C3×C4—28no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—34no—
447C2×C3×C4—44no—
448C2×C3×C4—44no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—64no—
453C2×C3×C4—68no—
454C2×C3×C4—128no—
455C2×C3×C4—128no—
456C2×C3×C4#23514yes—
457C2×C3×C4C3×#4114yes—
458C2×C3×C4C23×D312yes—
459C2×C3×C4C23×D314yes—
460C2×C3×C4C23×D314yes—
461C2×C3×C4C23×D312yes—
462C2×C3×C4C24×C314yes—
463C2×C3×C4C24×C312yes—
464C2×C3×C4C24×C314yes—
465C2×C3×C4C24×C312yes—
466#67—28no—
467#67—48no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—24no—
472C2×Dic3C24×C312yes—
473C2×Dic3C24×C312yes—
474C2×Dic3C24×C312yes—
475C2×Dic3C24×C314yes—
476D12—216no—
477D12—28no—
478C4×D3—28no—
479C4×D3—48no—
480C4×D3—48no—
481C2×C32—42no—
482C2×C32#55314yescomplemented
483C2×C32C22×#4111yescharacteristic
484C2×C32C22×#4111yescharacteristic
485C2×C32C2×H(5,𝔽2)11yescharacteristic
486C3×D3—24no—
487C3×D3—44no—
488C24—31no—
489C24—32no—
490C24C22×C3×D311yescharacteristic
491C2×D4—34no—
492C2×D4—38no—
493C2×D4—38no—
494C2×D4—34no—
495C2×D4—68no—
496C2×D4—64no—
497C2×D4—64no—
498C2×D4—124no—
499C22×C4—24no—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—32no—
504C22×C4—34no—
505C22×C4—38no—
506C22×C4—38no—
507C22×C4—64no—
508C22×C4—124no—
509C22×C4—124no—
510C22×C4C22×C3×D311yescharacteristic
511C22×C4C22×C3×D312yes—
512C22×C4C22×C3×D312yes—
513C22×C4C22×C3×D314yes—
514C22×C4C22×C3×D311yescharacteristic
515C4⋊C4—34no—
516C4⋊C4—38no—
517C4⋊C4—38no—
518C4⋊C4—34no—
519C4⋊C4—38no—
520C4⋊C4C22×C3×D314yes—
521C4⋊C4C22×C3×D314yes—
522C22⋊C4—34no—
523C22⋊C4—34no—
524C22⋊C4—38no—
525C22⋊C4—38no—
526C22⋊C4—38no—
527C22⋊C4C22×C3×D318yes—
528C42—34no—
529C42C22×C3×D318yes—
530C22×C3—24no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—21no—
541C22×C3—34no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—48no—
545C22×C3—44no—
546C22×C3—44no—
547C22×C3—62no—
548C22×C3—62no—
549C22×C3—68no—
550C22×C3—64no—
551C22×C3—64no—
552C22×C3—64no—
553C22×C3—128no—
554C22×C3C2×#23512yes—
555C22×C3D3×#4112yes—
556C22×C3#100912yes—
557C22×C3C2×C3×#4112yes—
558C22×C3C2×C3×#4112yes—
559C22×C3C3×H(5,𝔽2)12yes—
560C22×C3C24×D311yescharacteristic
561C22×C3C25×C311yescharacteristic
562C2×D3—22no—
563C2×D3—22no—
564C2×D3—28no—
565C2×D3—24no—
566C2×D3—24no—
567C2×D3—24no—
568C2×D3—48no—
569C2×D3C2×C3×#4114yes—
570C3×C4—24no—
571C3×C4—22no—
572C3×C4—24no—
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—22no—
576C3×C4—24no—
577C3×C4—24no—
578C3×C4—44no—
579C3×C4—44no—
580C3×C4—62no—
581C3×C4—62no—
582C3×C4—62no—
583C3×C4—64no—
584C3×C4C2×#23514yes—
585C3×C4C2×C3×#4114yes—
586Dic3—22no—
587Dic3—22no—
588Dic3—22no—
589Dic3—24no—
590C32C2×#55311yescharacteristic, complemented, Sylow
591C23—22no—
592C23—22no—
593C23—22no—
594C23—34no—
595C23—32no—
596C23—34no—
597C23—62no—
598C23—62no—
599C23—64no—
600C23—64no—
601C23—64no—
602C23C23×C3×D312yes—
603C23C23×C3×D311yescharacteristic
604D4—616no—
605D4—68no—
606D4—68no—
607D4—128no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—28no—
612C2×C4—32no—
613C2×C4—32no—
614C2×C4—32no—
615C2×C4—34no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—64no—
620C2×C4—68no—
621C2×C4—128no—
622C2×C4—128no—
623C2×C4C3×#23514yes—
624C2×C4C23×C3×D312yes—
625C2×C4C23×C3×D314yes—
626C2×C4C23×C3×D314yes—
627C2×C4C23×C3×D312yes—
628C2×C3—24no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—44no—
633C2×C3—42no—
634C2×C3—42no—
635C2×C3—64no—
636C2×C3—124no—
637C2×C3#553014yesdirect product factor
638C2×C3C3×#55314yescomplemented
639C2×C3C22×#23511yescharacteristic
640C2×C3C2×D3×#4111yescharacteristic
641C2×C3C2×#100911yescharacteristic
642C2×C3C22×C3×#4111yescharacteristic
643C2×C3C22×C3×#4111yescharacteristic
644C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
645D3—24no—
646D3—44no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—34no—
651C22—44no—
652C22—68no—
653C22—62no—
654C22—62no—
655C22—64no—
656C22—64no—
657C22—64no—
658C22—128no—
659C22C2×C3×#23512yes—
660C22C3×D3×#4112yes—
661C22C3×#100912yes—
662C22C24×C3×D311yescharacteristic
663C4—22no—
664C4—24no—
665C4—24no—
666C4—62no—
667C4—62no—
668C4—62no—
669C4—64no—
670C4C2×C3×#23514yes—
671C3—21no—
672C3C2×#553011yescharacteristic, direct product factor
673C3C2×C3×#55311yescharacteristic, complemented
674C2—42no—
675C2—64no—
676C2—124no—
677C2C3×#553014yesdirect product factor
678C2C22×C3×#23511yescharacteristic
679C2C2×C3×D3×#4111yescharacteristic
680C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
hypercenterC2×C3×#117D3
hypocenterC3C2×C3×#553
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
2. C2×C3×#930C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C3×#5530C2direct (N × H)
5. C2×C3×#895C2semidirect
6. C2×C3×#893C2semidirect
7. C2×C3×D3×C4⋊C4C2semidirect
8. C2×C3×#890C2semidirect
9. C2×C3×#884C2semidirect
10. C2×C3×#883C2semidirect
11. C2×C3×#876C2semidirect
12. C2×C3×C4×D12C2semidirect
14. C2×#5530C3direct (N × H)
23. C32×#117C22semidirect
29. C3×#930C22semidirect
30. C3×C4×#67C22semidirect
41. C3×#895C22semidirect
42. C3×#893C22semidirect
43. C3×D3×C4⋊C4C22semidirect
44. C3×#890C22semidirect
45. C3×#884C22semidirect
46. C3×#883C22semidirect
47. C3×#876C22semidirect
48. C3×C4×D12C22semidirect
60. C2×C3×#117D3semidirect
61. C2×C3×#117C2×C3semidirect
63. C2×#930C2×C3semidirect
64. C2×C4×#67C2×C3semidirect
65. #5530C2×C3direct (N × H)
66. C2×#895C2×C3semidirect
67. C2×#893C2×C3semidirect
68. C2×D3×C4⋊C4C2×C3semidirect
69. C2×#890C2×C3semidirect
70. C2×#884C2×C3semidirect
71. C2×#883C2×C3semidirect
72. C2×#876C2×C3semidirect
73. C2×C4×D12C2×C3semidirect
144. C3×#117C2×D3semidirect
145. C3×#117C22×C3semidirect
171. #930C22×C3semidirect
172. C4×#67C22×C3semidirect
183. #895C22×C3semidirect
184. #893C22×C3semidirect
185. D3×C4⋊C4C22×C3semidirect
186. #890C22×C3semidirect
187. #884C22×C3semidirect
188. #883C22×C3semidirect
189. #876C22×C3semidirect
190. C4×D12C22×C3semidirect
238. C2×#117C3×D3semidirect
376. #117C2×C3×D3semidirect
482. C2×C32#553semidirect
590. C32C2×#553semidirect
637. C2×C3#5530direct (N × H)
638. C2×C3C3×#553semidirect
672. C3C2×#5530direct (N × H)
673. C3C2×C3×#553semidirect
677. C2C3×#5530direct (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×C4×#672
C3×#55302
C2×C3×#8952
C2×C3×#8932
C2×C3×D3×C4⋊C42
C2×C3×#8902
C2×C3×#8842
C2×C3×#8832
C2×C3×#8762
C2×C3×C4×D122
C2×C3×#5533
C2×#55303