Finite Group Databasebeta

← C3×#86495 #11901757

Subgroups — C3×#86495 #11901757

Order 1152.

2176 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#541C211yesmaximal, characteristic, complemented
2C3×#5731C211yesmaximal, characteristic, complemented
3C3×#5725C211yesmaximal, characteristic, complemented
4C3×#5706C214yesmaximal, complemented
5C3×#5704C214yesmaximal, complemented
6C3×#5697C211yesmaximal, characteristic, complemented
7C3×#5692C214yesmaximal, complemented
8C3×#5691C214yesmaximal, complemented
9C3×#5688C211yesmaximal, characteristic, complemented
10C3×#5643C212yesmaximal, complemented
11C3×#5627C212yesmaximal, complemented
12C3×#5582C212yesmaximal, complemented
13C3×C4×#239C212yesmaximal, complemented
14C3×#5535C211yesmaximal, characteristic, complemented
15C3×D3×#117C211yesmaximal, characteristic, complemented
16C3×#3455—31nomaximal
17#86495C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21C32×#126C2214yes—
22C32×#125C2211yescharacteristic, complemented
23C32×#125C2214yescomplemented
24C32×C22⋊Q8C2212yes—
25C32×C4×Q8C2212yescomplemented
26C32×#117C2211yescharacteristic
27C3×#947C2212yescomplemented
28C3×#946C2212yes—
29C3×Q8×Dic3C2212yescomplemented
30C3×#930C2212yes—
31C3×#926C2211yescharacteristic
32C3×#898C2214yes—
33C3×#898C2214yescomplemented
34C3×#897C2214yescomplemented
35C3×#896C2214yes—
36C3×#896C2214yescomplemented
37C3×#895C2212yes—
38C3×#895C2214yes—
39C3×#895C2214yes—
40C3×#894C2214yes—
41C3×#894C2214yes—
42C3×#894C2214yescomplemented
43C3×#894C2214yescomplemented
44C3×#893C2214yes—
45C3×#893C2214yes—
46C3×#893C2212yescomplemented
47C3×#893C2214yescomplemented
48C3×#892C2212yes—
49C3×#892C2212yes—
50C3×#892C2214yescomplemented
51C3×D3×C4⋊C4C2212yes—
52C3×#889C2214yescomplemented
53C3×#888C2212yescomplemented
54C3×#887C2214yescomplemented
55C3×#885C2214yes—
56C3×#884C2214yes—
57C3×#883C2214yes—
58C3×#882C2214yes—
59C3×#67⋊C4C2214yes—
60C3×D3×C22⋊C4C2212yes—
61C3×#877C2212yes—
62C3×#876C2214yescomplemented
63C3×#875C2214yes—
64C3×#874C2211yescharacteristic, complemented
65C3×C4×D12C2214yes—
66C3×C4×D12C2212yescomplemented
67C3×#872C2211yescharacteristic
68C3×#872C2211yescharacteristic
69C3×C42×D3C2211yescharacteristic
70C3×C42×D3C2211yescharacteristic
71C3×C42×D3C2214yescomplemented
72C3×#870C2211yescharacteristic, complemented
73C3×#542—32no—
74C3×#542—32no—
75C3×#541—21no—
76C3×#541—31no—
77C3×#541D311yescharacteristic, complemented
78C3×#541C2×C311yescharacteristic, complemented
79C3×#540—31no—
80C3×#540—31no—
81C3×#539—34no—
82C3×#538—34no—
83C3×#533—31no—
84C3×#532—31no—
85C3×#529—34no—
86C3×#529—34no—
87C3×#525—32no—
88C3×C4×#41—32no—
89C2×C3×#117—31no—
90#5731C2×C311yescharacteristic, complemented
91#5725C2×C311yescharacteristic, complemented
92#5706C2×C314yescomplemented
93#5704C2×C314yescomplemented
94#5697C2×C311yescharacteristic, complemented
95#5692C2×C314yescomplemented
96#5691C2×C314yescomplemented
97#5688C2×C311yescharacteristic, complemented
98#5643C2×C312yescomplemented
99#5627C2×C312yescomplemented
100#5582C2×C312yescomplemented
101C4×#239C2×C312yescomplemented
102#5535C2×C311yescharacteristic, complemented
103D3×#117C2×C311yescharacteristic, complemented
104C23×C3×D3C2311yescharacteristic
105C2×C32×Q8C2312yes—
106C22×C32×C4C2311yescharacteristic
107C2×C3×#67C2314yes—
108C22×C3×Dic3C2311yescharacteristic
109C3×#239—28no—
110C2×C3×D12C2314yes—
111C2×C3×D12C2312yes—
112C2×C3×D12C2314yes—
113C2×C3×D12C2314yes—
114C2×C3×C4×D3—24no—
115C2×C3×C4×D3C2314yes—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2312yes—
120C2×C3×C4×D3C2312yes—
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2314yes—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6C2314yes—
125C32×C4⋊C4C2314yes—
126C32×C4⋊C4C2312yes—
127C32×C4⋊C4C2314yes—
128C32×C4⋊C4C2312yes—
129C32×C4⋊C4C2314yes—
130C32×C4⋊C4C2314yes—
131C32×C22⋊C4C2312yes—
132C32×C22⋊C4C2314yes—
133C32×C42C2311yescharacteristic
134C32×C42C2311yescharacteristic
135C32×C42C2314yes—
136C3×#217C2312yes—
137C3×(C2×D3)⋊C4C2312yes—
138C3×(C2×D3)⋊C4C2312yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×C4⋊Dic3C2314yes—
148C3×C4⋊Dic3C2312yes—
149C3×C4⋊Dic3C2312yes—
150C3×Dic3⋊C4C2312yes—
151C3×Dic3⋊C4C2312yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2314yes—
158C3×C4×Dic3C2314yes—
159C3×C4×Dic3C2311yescharacteristic
160C3×C4×Dic3C2311yescharacteristic
161#3455—31noSylow
162C2×C3×#41—32no—
163C23×C3×C4—31no—
164C2×#239C22×C312yes—
165C22×C4×D3C22×C311yescharacteristic
166C3×C4⋊Q8—21no—
167C3×C4⋊Q8—32no—
168C3×C4⋊Q8C2×D311yescharacteristic, complemented
169C3×C4⋊Q8C22×C311yescharacteristic, complemented
170C3×#127—31no—
171C3×#126—24no—
172C3×#126—34no—
173C3×#126—34no—
174C3×#126—34no—
175C3×#126C2×D314yes—
176C3×#126C22×C314yes—
177C3×#125—24no—
178C3×#125—21no—
179C3×#125—34no—
180C3×#125—31no—
181C3×#125C2×D314yescomplemented
182C3×#125C2×D311yescharacteristic, complemented
183C3×#125C22×C311yescharacteristic, complemented
184C3×#125C22×C314yescomplemented
185C3×#124—32no—
186C3×#124—34no—
187C3×#124—34no—
188C3×#123—34no—
189C3×#123—34no—
190C3×#123—34no—
191C3×#123—34no—
192C3×#123—34no—
193C3×C22⋊Q8—22no—
194C3×C22⋊Q8—32no—
195C3×C22⋊Q8—34no—
196C3×C22⋊Q8—34no—
197C3×C22⋊Q8—34no—
198C3×C22⋊Q8C2×D312yes—
199C3×C22⋊Q8C22×C312yes—
200C3×#121—32no—
201C3×#121—32no—
202C3×#121—34no—
203C3×#121—34no—
204C3×#121—34no—
205C3×#120—34no—
206C3×C4×Q8—22no—
207C3×C4×Q8—32no—
208C3×C4×Q8—34no—
209C3×C4×Q8C2×D312yescomplemented
210C3×C4×Q8C22×C312yescomplemented
211C3×C4×D4—34no—
212C3×C4×D4—34no—
213C3×C4×D4—32no—
214C3×C4×D4—34no—
215C3×C4×D4—34no—
216C3×C4×D4—34no—
217C3×C4×D4—32no—
218C3×#117—21no—
219C3×#117—31no—
220C3×#117—32no—
221C3×#117—32no—
222C3×#117—34no—
223C3×#117—32no—
224C3×#117—31no—
225C3×#117—31no—
226C3×#117C2×D311yescharacteristic
227C3×#117C22×C311yescharacteristic
228C2×C3×C4⋊C4—32no—
229C2×C3×C22⋊C4—32no—
230C2×C3×C42—31no—
231C2×C3×C42—31no—
232C2×C3×C42—34no—
233#947C22×C312yescomplemented
234#946C22×C312yes—
235Q8×Dic3C22×C312yescomplemented
236#930C22×C312yes—
237#926C22×C311yescharacteristic
238#898C22×C314yes—
239#898C22×C314yescomplemented
240#897C22×C314yescomplemented
241#896C22×C314yes—
242#896C22×C314yescomplemented
243#895C22×C314yes—
244#895C22×C314yes—
245#895C22×C312yes—
246#894C22×C314yes—
247#894C22×C314yes—
248#894C22×C314yescomplemented
249#894C22×C314yescomplemented
250#893C22×C314yes—
251#893C22×C314yes—
252#893C22×C312yescomplemented
253#893C22×C314yescomplemented
254#892C22×C312yes—
255#892C22×C312yes—
256#892C22×C314yescomplemented
257D3×C4⋊C4C22×C312yes—
258#889C22×C314yescomplemented
259#888C22×C312yescomplemented
260#887C22×C314yescomplemented
261#885C22×C314yes—
262#884C22×C314yes—
263#883C22×C314yes—
264#882C22×C314yes—
265#67⋊C4C22×C314yes—
266D3×C22⋊C4C22×C312yes—
267#877C22×C312yes—
268#876C22×C314yescomplemented
269#875C22×C314yes—
270#874C22×C311yescharacteristic, complemented
271C4×D12C22×C314yes—
272C4×D12C22×C312yescomplemented
273#872C22×C311yescharacteristic
274#872C22×C311yescharacteristic
275C42×D3C22×C311yescharacteristic
276C42×D3C22×C311yescharacteristic
277C42×D3C22×C314yescomplemented
278#870C22×C311yescharacteristic, complemented
279C23×C32C2411yescharacteristic
280C22×C3×D3—22no—
281C22×C3×D3—42no—
282C22×C3×D3C2411yescharacteristic
283C22×C3×D3C2414yes—
284C22×C3×D3C2411yescharacteristic
285C32×Q8—24no—
286C2×C32×C4—22no—
287C2×C32×C4C2412yes—
288C2×C32×C4C2414yes—
289C2×C32×C4C2412yes—
290C2×C32×C4C2414yes—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2411yescharacteristic
293C3×#67—44no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2414yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2411yescharacteristic
299C2×C3×Dic3C2411yescharacteristic
300C3×D12—28no—
301C3×D12—24no—
302C3×D12—44no—
303C3×D12—44no—
304C3×C4×D3—22no—
305C3×C4×D3—22no—
306C3×C4×D3—22no—
307C3×C4×D3—28no—
308C3×C4×D3—42no—
309C3×C4×D3—44no—
310C3×C4×D3—44no—
311C3×C4×D3—42no—
312C3×C4×D3#4114yes—
313C3×Dic6—44no—
314#542—32no—
315#542—32no—
316#541—31no—
317#541C3×D311yescharacteristic, complemented
318#540—31no—
319#540—31no—
320#539—34no—
321#538—34no—
322#533—31no—
323#532—31no—
324#529—34no—
325#529—34no—
326#525—32no—
327C4×#41—32no—
328C2×#117—31no—
329C24×C3—31no—
330C23×D3C23×C311yescharacteristic
331C3×#41—68no—
332C2×C3×Q8—22no—
333C2×C3×Q8—34no—
334C2×C3×Q8C22×D312yes—
335C2×C3×Q8C23×C312yes—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4—32no—
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C22×C3×C4—21no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—34no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—32no—
349C22×C3×C4—32no—
350C22×C3×C4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—64no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C23×C311yescharacteristic
355C2×#67C23×C314yes—
356C22×Dic3C23×C311yescharacteristic
357#239—28no—
358C2×D12C23×C314yes—
359C2×D12C23×C312yes—
360C2×D12C23×C314yes—
361C2×D12C23×C314yes—
362C2×C4×D3—24no—
363C2×C4×D3C23×C314yes—
364C2×C4×D3C23×C311yescharacteristic
365C2×C4×D3C23×C311yescharacteristic
366C2×C4×D3C23×C311yescharacteristic
367C2×C4×D3C23×C312yes—
368C2×C4×D3C23×C312yes—
369C2×C4×D3C23×C314yes—
370C2×C4×D3C23×C314yes—
371C2×C4×D3C23×C311yescharacteristic
372C2×Dic6C23×C314yes—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—24no—
376C3×C4⋊C4—24no—
377C3×C4⋊C4—24no—
378C3×C4⋊C4—24no—
379C3×C4⋊C4—32no—
380C3×C4⋊C4—32no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—32no—
385C3×C4⋊C4—32no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4C22×D312yes—
388C3×C4⋊C4C22×D312yes—
389C3×C4⋊C4C22×D314yes—
390C3×C4⋊C4C22×D314yes—
391C3×C4⋊C4C22×D314yes—
392C3×C4⋊C4C22×D314yes—
393C3×C4⋊C4C23×C314yes—
394C3×C4⋊C4C23×C312yes—
395C3×C4⋊C4C23×C314yes—
396C3×C4⋊C4C23×C312yes—
397C3×C4⋊C4C23×C314yes—
398C3×C4⋊C4C23×C314yes—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—24no—
401C3×C22⋊C4—32no—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—32no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4C22×D312yes—
413C3×C22⋊C4C22×D314yes—
414C3×C22⋊C4C23×C312yes—
415C3×C22⋊C4C23×C314yes—
416C3×C42—21no—
417C3×C42—21no—
418C3×C42—24no—
419C3×C42—32no—
420C3×C42—32no—
421C3×C42—34no—
422C3×C42—31no—
423C3×C42—31no—
424C3×C42—34no—
425C3×C42C22×D311yescharacteristic
426C3×C42C22×D311yescharacteristic
427C3×C42C22×D314yes—
428C3×C42C23×C311yescharacteristic
429C3×C42C23×C311yescharacteristic
430C3×C42C23×C314yes—
431#217C23×C312yes—
432(C2×D3)⋊C4C23×C312yes—
433(C2×D3)⋊C4C23×C312yes—
434(C2×D3)⋊C4C23×C314yes—
435(C2×D3)⋊C4C23×C314yes—
436(C2×D3)⋊C4C23×C314yes—
437(C2×D3)⋊C4C23×C314yes—
438(C2×D3)⋊C4C23×C314yes—
439(C2×D3)⋊C4C23×C314yes—
440(C2×D3)⋊C4C23×C314yes—
441(C2×D3)⋊C4C23×C314yes—
442C4⋊Dic3C23×C312yes—
443C4⋊Dic3C23×C314yes—
444C4⋊Dic3C23×C312yes—
445Dic3⋊C4C23×C314yes—
446Dic3⋊C4C23×C312yes—
447Dic3⋊C4C23×C312yes—
448Dic3⋊C4C23×C314yes—
449Dic3⋊C4C23×C314yes—
450C4×Dic3C23×C312yes—
451C4×Dic3C23×C311yescharacteristic
452C4×Dic3C23×C311yescharacteristic
453C4×Dic3C23×C312yes—
454C4×Dic3C23×C314yes—
455C4×Dic3C23×C314yes—
456C22×C32—21no—
457C22×C32—22no—
458C22×C32C2511yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—22no—
465C2×C3×D3—44no—
466C2×C3×D3C2×#4112yes—
467C32×C4—21no—
468C32×C4—24no—
469C32×C4—24no—
470C32×C4—22no—
471C32×C4—22no—
472C32×C4C2×#4112yes—
473C3×Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—24no—
476C3×Dic3—22no—
477C3×Dic3C2×#4112yes—
478C2×#41—32no—
479C23×C4—31no—
480C4⋊Q8—32no—
481C4⋊Q8C2×C3×D311yescharacteristic, complemented
482#127—31no—
483#126—34no—
484#126—34no—
485#126—34no—
486#126C2×C3×D314yes—
487#125—34no—
488#125—31no—
489#125C2×C3×D314yescomplemented
490#125C2×C3×D311yescharacteristic, complemented
491#124—32no—
492#124—34no—
493#124—34no—
494#123—34no—
495#123—34no—
496#123—34no—
497#123—34no—
498#123—34no—
499C22⋊Q8—32no—
500C22⋊Q8—34no—
501C22⋊Q8—34no—
502C22⋊Q8—34no—
503C22⋊Q8C2×C3×D312yes—
504#121—32no—
505#121—32no—
506#121—34no—
507#121—34no—
508#121—34no—
509#120—34no—
510C4×Q8—32no—
511C4×Q8—34no—
512C4×Q8C2×C3×D312yescomplemented
513C4×D4—34no—
514C4×D4—32no—
515C4×D4—34no—
516C4×D4—34no—
517C4×D4—34no—
518C4×D4—34no—
519C4×D4—32no—
520#117—31no—
521#117—32no—
522#117—32no—
523#117—34no—
524#117—32no—
525#117—31no—
526#117—31no—
527#117C2×C3×D311yescharacteristic
528C2×C4⋊C4—32no—
529C2×C22⋊C4—32no—
530C2×C42—31no—
531C2×C42—31no—
532C2×C42—34no—
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—34no—
537C23×C3—62no—
538C23×C3—122no—
539C23×C3C23×D311yescharacteristic
540C23×C3C24×C311yescharacteristic
541C22×D3—22no—
542C22×D3—42no—
543C22×D3C24×C311yescharacteristic
544C22×D3C24×C314yes—
545C22×D3C24×C311yescharacteristic
546C3×Q8—24no—
547C3×Q8—24no—
548C3×Q8—44no—
549C3×Q8—124no—
550C3×D4—68no—
551C3×D4—64no—
552C3×D4—124no—
553C3×D4—124no—
554C3×D4—124no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—24no—
560C2×C3×C4—22no—
561C2×C3×C4—24no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—34no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—34no—
568C2×C3×C4—31no—
569C2×C3×C4—42no—
570C2×C3×C4—62no—
571C2×C3×C4—68no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—122no—
576C2×C3×C4—124no—
577C2×C3×C4—122no—
578C2×C3×C4—124no—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D314yes—
581C2×C3×C4C23×D314yes—
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C24×C312yes—
586C2×C3×C4C24×C314yes—
587C2×C3×C4C24×C312yes—
588C2×C3×C4C24×C314yes—
589C2×C3×C4C24×C311yescharacteristic
590C2×C3×C4C24×C311yescharacteristic
591#67—44no—
592C2×Dic3—22no—
593C2×Dic3C24×C312yes—
594C2×Dic3C24×C314yes—
595C2×Dic3C24×C312yes—
596C2×Dic3C24×C311yescharacteristic
597C2×Dic3C24×C311yescharacteristic
598D12—28no—
599D12—24no—
600D12—44no—
601D12—44no—
602C4×D3—22no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—28no—
606C4×D3—42no—
607C4×D3—44no—
608C4×D3—44no—
609C4×D3—42no—
610C4×D3C3×#4114yes—
611Dic6—44no—
612C2×C32—41no—
613C2×C32C22×#4111yescharacteristic
614C2×C32#58512yes—
615C3×D3—22no—
616C3×D3—44no—
617C3×D3—41no—
618C24—31no—
619#41—68no—
620C2×Q8—34no—
621C2×Q8C22×C3×D312yes—
622C2×D4—34no—
623C2×D4—34no—
624C2×D4—32no—
625C2×D4—34no—
626C2×D4—34no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—34no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—32no—
634C22×C4—32no—
635C22×C4—34no—
636C22×C4—34no—
637C22×C4—64no—
638C22×C4C22×C3×D311yescharacteristic
639C4⋊C4—32no—
640C4⋊C4—32no—
641C4⋊C4—32no—
642C4⋊C4—32no—
643C4⋊C4—34no—
644C4⋊C4—34no—
645C4⋊C4—34no—
646C4⋊C4—34no—
647C4⋊C4C22×C3×D312yes—
648C4⋊C4C22×C3×D312yes—
649C4⋊C4C22×C3×D314yes—
650C4⋊C4C22×C3×D314yes—
651C4⋊C4C22×C3×D314yes—
652C4⋊C4C22×C3×D314yes—
653C22⋊C4—32no—
654C22⋊C4—32no—
655C22⋊C4—32no—
656C22⋊C4—34no—
657C22⋊C4—34no—
658C22⋊C4—34no—
659C22⋊C4—34no—
660C22⋊C4—34no—
661C22⋊C4—34no—
662C22⋊C4—34no—
663C22⋊C4—34no—
664C22⋊C4C22×C3×D312yes—
665C22⋊C4C22×C3×D314yes—
666C42—32no—
667C42—32no—
668C42—34no—
669C42—31no—
670C42—31no—
671C42—34no—
672C42C22×C3×D311yescharacteristic
673C42C22×C3×D311yescharacteristic
674C42C22×C3×D314yes—
675C22×C3—21no—
676C22×C3—22no—
677C22×C3—21no—
678C22×C3—22no—
679C22×C3—21no—
680C22×C3—32no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—62no—
684C22×C3—61no—
685C22×C3—64no—
686C22×C3—64no—
687C22×C3—64no—
688C22×C3—62no—
689C22×C3—124no—
690C22×C3C24×D311yescharacteristic
691C22×C3C25×C311yescharacteristic
692C2×D3—22no—
693C2×D3—21no—
694C2×D3—24no—
695C2×D3—24no—
696C2×D3—24no—
697C2×D3—22no—
698C2×D3—44no—
699C2×D3C2×C3×#4112yes—
700C3×C4—21no—
701C3×C4—24no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—24no—
705C3×C4—21no—
706C3×C4—24no—
707C3×C4—24no—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—22no—
711C3×C4—32no—
712C3×C4—41no—
713C3×C4—44no—
714C3×C4—42no—
715C3×C4—42no—
716C3×C4—44no—
717C3×C4—61no—
718C3×C4—62no—
719C3×C4—64no—
720C3×C4—62no—
721C3×C4D3×#4112yes—
722C3×C4C2×C3×#4112yes—
723Dic3—21no—
724Dic3—22no—
725Dic3—24no—
726Dic3—22no—
727Dic3C2×C3×#4112yes—
728C32#345511yescharacteristic, complemented, Sylow
729C23—31no—
730C23—31no—
731C23—34no—
732C23—62no—
733C23—122no—
734C23C23×C3×D311yescharacteristic
735Q8—24no—
736Q8—124no—
737D4—68no—
738D4—64no—
739D4—124no—
740D4—124no—
741D4—124no—
742C2×C4—22no—
743C2×C4—31no—
744C2×C4—34no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—34no—
748C2×C4—31no—
749C2×C4—62no—
750C2×C4—68no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—122no—
755C2×C4—124no—
756C2×C4—122no—
757C2×C4—124no—
758C2×C4C23×C3×D312yes—
759C2×C4C23×C3×D314yes—
760C2×C4C23×C3×D314yes—
761C2×C4C23×C3×D312yes—
762C2×C4C23×C3×D311yescharacteristic
763C2×C4C23×C3×D311yescharacteristic
764C2×C3—21no—
765C2×C3—22no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—62no—
769C2×C3—81no—
770C2×C3—121no—
771C2×C3—124no—
772C2×C3C2×D3×#4111yescharacteristic
773C2×C3#596812yes—
774C2×C3C22×C3×#4111yescharacteristic
775C2×C3C3×#58512yes—
776D3—22no—
777D3—41no—
778D3—44no—
779C22—21no—
780C22—22no—
781C22—32no—
782C22—62no—
783C22—61no—
784C22—64no—
785C22—64no—
786C22—64no—
787C22—62no—
788C22—124no—
789C22C24×C3×D311yescharacteristic
790C4—21no—
791C4—24no—
792C4—22no—
793C4—22no—
794C4—24no—
795C4—32no—
796C4—61no—
797C4—62no—
798C4—64no—
799C4—62no—
800C4C3×D3×#4112yes—
801C3—21no—
802C3#8649511yescharacteristic, direct product factor
803C3C3×#345511yescharacteristic, complemented
804C2—41no—
805C2—62no—
806C2—121no—
807C2—124no—
808C2C2×C3×D3×#4111yescharacteristic
809C2C3×#596812yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#541C2
socleC22×C32C25
hypercenterC3×#541D3
hypocenterC3C3×#3455
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#541

Complements

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

NH ≅ G/Ntype
1. C32×#541C2semidirect
2. C3×#5731C2semidirect
3. C3×#5725C2semidirect
4. C3×#5706C2semidirect
5. C3×#5704C2semidirect
6. C3×#5697C2semidirect
7. C3×#5692C2semidirect
8. C3×#5691C2semidirect
9. C3×#5688C2semidirect
10. C3×#5643C2semidirect
11. C3×#5627C2semidirect
12. C3×#5582C2semidirect
13. C3×C4×#239C2semidirect
14. C3×#5535C2semidirect
15. C3×D3×#117C2semidirect
17. #86495C3direct (N × H)
20. C32×C4⋊Q8C22semidirect
22. C32×#125C22semidirect
23. C32×#125C22semidirect
25. C32×C4×Q8C22semidirect
27. C3×#947C22semidirect
29. C3×Q8×Dic3C22semidirect
33. C3×#898C22semidirect
34. C3×#897C22semidirect
36. C3×#896C22semidirect
42. C3×#894C22semidirect
43. C3×#894C22semidirect
46. C3×#893C22semidirect
47. C3×#893C22semidirect
50. C3×#892C22semidirect
52. C3×#889C22semidirect
53. C3×#888C22semidirect
54. C3×#887C22semidirect
62. C3×#876C22semidirect
64. C3×#874C22semidirect
66. C3×C4×D12C22semidirect
71. C3×C42×D3C22semidirect
72. C3×#870C22semidirect
77. C3×#541D3semidirect
78. C3×#541C2×C3semidirect
90. #5731C2×C3semidirect
91. #5725C2×C3semidirect
92. #5706C2×C3semidirect
93. #5704C2×C3semidirect
94. #5697C2×C3semidirect
95. #5692C2×C3semidirect
96. #5691C2×C3semidirect
97. #5688C2×C3semidirect
98. #5643C2×C3semidirect
99. #5627C2×C3semidirect
100. #5582C2×C3semidirect
101. C4×#239C2×C3semidirect
102. #5535C2×C3semidirect
103. D3×#117C2×C3semidirect
168. C3×C4⋊Q8C2×D3semidirect
169. C3×C4⋊Q8C22×C3semidirect
181. C3×#125C2×D3semidirect
182. C3×#125C2×D3semidirect
183. C3×#125C22×C3semidirect
184. C3×#125C22×C3semidirect
209. C3×C4×Q8C2×D3semidirect
210. C3×C4×Q8C22×C3semidirect
233. #947C22×C3semidirect
235. Q8×Dic3C22×C3semidirect
239. #898C22×C3semidirect
240. #897C22×C3semidirect
242. #896C22×C3semidirect
248. #894C22×C3semidirect
249. #894C22×C3semidirect
252. #893C22×C3semidirect
253. #893C22×C3semidirect
256. #892C22×C3semidirect
258. #889C22×C3semidirect
259. #888C22×C3semidirect
260. #887C22×C3semidirect
268. #876C22×C3semidirect
270. #874C22×C3semidirect
272. C4×D12C22×C3semidirect
277. C42×D3C22×C3semidirect
278. #870C22×C3semidirect
317. #541C3×D3semidirect
481. C4⋊Q8C2×C3×D3semidirect
489. #125C2×C3×D3semidirect
490. #125C2×C3×D3semidirect
512. C4×Q8C2×C3×D3semidirect
728. C32#3455semidirect
802. C3#86495direct (N × H)
803. C3C3×#3455semidirect

Maximal subgroups

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

subgroupindex
C32×#5412
C3×#57312
C3×#57252
C3×#57062
C3×#57042
C3×#56972
C3×#56922
C3×#56912
C3×#56882
C3×#56432
C3×#56272
C3×#55822
C3×C4×#2392
C3×#55352
C3×D3×#1172
C3×#34553
#864953