Finite Group Databasebeta

← C3×#86467 #11901736

Subgroups — C3×#86467 #11901736

Order 1152.

2200 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#540C211yesmaximal, characteristic, complemented
2C3×#5719C211yesmaximal, characteristic, complemented
3C3×#5716C211yesmaximal, characteristic, complemented
4C3×#5698C211yesmaximal, characteristic, complemented
5C3×#5688C211yesmaximal, characteristic, complemented
6C3×#5660C214yesmaximal, complemented
7C3×#5649C214yesmaximal, complemented
8C3×#5613C214yesmaximal, complemented
9C3×#5606C212yesmaximal, complemented
10C3×#5603C212yesmaximal, complemented
11C3×#5600C214yesmaximal, complemented
12C3×#5561C212yesmaximal, complemented
13C3×C4×#237C212yesmaximal, complemented
14C3×D3×#117C211yesmaximal, characteristic, complemented
15C3×#5518C211yesmaximal, characteristic, complemented
16C3×#3455—31nomaximal
17#86467C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C32×#127C2211yescharacteristic, complemented
21C32×#125C2211yescharacteristic, complemented
22C32×#123C2214yescomplemented
23C32×#121C2214yes—
24C32×#121C2212yes—
25C32×C4×D4C2212yescomplemented
26C32×#117C2211yescharacteristic
27C3×#939C2214yes—
28C3×#938C2212yes—
29C3×#938C2214yes—
30C3×#937C2214yes—
31C3×#936C2214yes—
32C3×#936C2212yescomplemented
33C3×#935C2214yes—
34C3×#935C2214yescomplemented
35C3×D4×Dic3C2214yes—
36C3×D4×Dic3C2212yescomplemented
37C3×D4×Dic3C2214yescomplemented
38C3×#929C2214yes—
39C3×C4×#67C2214yes—
40C3×#926C2211yescharacteristic
41C3×#924C2212yes—
42C3×#924C2214yescomplemented
43C2×C3×C4×Dic3C2214yescomplemented
44C3×#898C2214yes—
45C3×#897C2212yes—
46C3×#896C2214yes—
47C3×#892C2212yes—
48C3×#892C2212yes—
49C3×D3×C4⋊C4C2212yes—
50C3×#890C2214yescomplemented
51C3×#889C2214yescomplemented
52C3×#888C2212yescomplemented
53C3×#887C2212yescomplemented
54C3×#887C2214yescomplemented
55C3×#885C2214yes—
56C3×#883C2214yes—
57C3×#67⋊C4C2214yes—
58C3×#67⋊C4C2214yes—
59C3×D3×C22⋊C4C2212yes—
60C3×#879C2214yes—
61C3×#879C2214yescomplemented
62C3×#879C2214yescomplemented
63C3×#878C2214yescomplemented
64C3×#877C2212yes—
65C3×#877C2214yescomplemented
66C3×#872C2211yescharacteristic
67C3×#872C2211yescharacteristic
68C3×C42×D3C2211yescharacteristic
69C3×C42×D3C2211yescharacteristic
70C3×#870C2211yescharacteristic, complemented
71C3×#869C2211yescharacteristic, complemented
72C3×C4×Dic6C2212yescomplemented
73C3×#542—32no—
74C3×#542—32no—
75C3×#541—31no—
76C3×#541—31no—
77C3×#540—21no—
78C3×#540—31no—
79C3×#540D311yescharacteristic, complemented
80C3×#540C2×C311yescharacteristic, complemented
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#5719C2×C311yescharacteristic, complemented
91#5716C2×C311yescharacteristic, complemented
92#5698C2×C311yescharacteristic, complemented
93#5688C2×C311yescharacteristic, complemented
94#5660C2×C314yescomplemented
95#5649C2×C314yescomplemented
96#5613C2×C314yescomplemented
97#5606C2×C312yescomplemented
98#5603C2×C312yescomplemented
99#5600C2×C314yescomplemented
100#5561C2×C312yescomplemented
101C4×#237C2×C312yescomplemented
102D3×#117C2×C311yescharacteristic, complemented
103#5518C2×C311yescharacteristic, complemented
104C23×C3×D3C2311yescharacteristic
105C2×C32×D4C2312yes—
106C2×C32×D4C2314yes—
107C2×C32×D4C2314yes—
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2314yes—
110C2×C3×#67C2314yes—
111C2×C3×#67C2314yes—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2314yes—
114C22×C3×Dic3C2314yes—
115C3×#237—28no—
116C2×C3×C4×D3—24no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2312yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×Dic6C2312yes—
124C2×C3×Dic6C2314yes—
125C32×C4⋊C4C2312yes—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2312yes—
128C32×C22⋊C4C2312yes—
129C32×C22⋊C4C2314yes—
130C32×C22⋊C4C2314yes—
131C32×C42C2311yescharacteristic
132C32×C42C2311yescharacteristic
133C3×#217C2312yes—
134C3×#217C2314yes—
135C3×#217C2314yes—
136C3×#217C2314yes—
137C3×#217C2314yes—
138C3×#217C2314yes—
139C3×(C2×D3)⋊C4C2312yes—
140C3×(C2×D3)⋊C4C2312yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2312yes—
144C3×C4⋊Dic3C2314yes—
145C3×C4⋊Dic3C2314yes—
146C3×C4⋊Dic3C2312yes—
147C3×Dic3⋊C4C2312yes—
148C3×Dic3⋊C4C2312yes—
149C3×Dic3⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×C4×Dic3C2312yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2314yes—
157C3×C4×Dic3C2314yes—
158C3×C4×Dic3C2314yes—
159C3×C4×Dic3C2311yescharacteristic
160C3×C4×Dic3C2311yescharacteristic
161#3455—31noSylow
162C2×C3×#41—32no—
163C23×C3×C4—31no—
164C2×#237C22×C312yes—
165C22×C4×D3C22×C311yescharacteristic
166C3×C4⋊Q8—32no—
167C3×C4⋊Q8—31no—
168C3×#127—21no—
169C3×#127C2×D311yescharacteristic, complemented
170C3×#127C22×C311yescharacteristic, complemented
171C3×#126—34no—
172C3×#126—34no—
173C3×#126—34no—
174C3×#126—34no—
175C3×#125—21no—
176C3×#125—34no—
177C3×#125—34no—
178C3×#125—31no—
179C3×#125C2×D311yescharacteristic, complemented
180C3×#125C22×C311yescharacteristic, complemented
181C3×#124—34no—
182C3×#124—32no—
183C3×#124—34no—
184C3×#123—24no—
185C3×#123—34no—
186C3×#123—34no—
187C3×#123—34no—
188C3×#123—34no—
189C3×#123C2×D314yescomplemented
190C3×#123C22×C314yescomplemented
191C3×C22⋊Q8—32no—
192C3×C22⋊Q8—34no—
193C3×C22⋊Q8—34no—
194C3×C22⋊Q8—32no—
195C3×C22⋊Q8—34no—
196C3×#121—22no—
197C3×#121—24no—
198C3×#121—32no—
199C3×#121—34no—
200C3×#121—34no—
201C3×#121C2×D312yes—
202C3×#121C2×D314yes—
203C3×#121C22×C314yes—
204C3×#121C22×C312yes—
205C3×#120—34no—
206C3×C4×Q8—32no—
207C3×C4×Q8—34no—
208C3×C4×Q8—32no—
209C3×C4×D4—22no—
210C3×C4×D4—34no—
211C3×C4×D4—32no—
212C3×C4×D4—34no—
213C3×C4×D4—34no—
214C3×C4×D4—34no—
215C3×C4×D4—34no—
216C3×C4×D4C2×D312yescomplemented
217C3×C4×D4C22×C312yescomplemented
218C3×#117—21no—
219C3×#117—31no—
220C3×#117—32no—
221C3×#117—32no—
222C3×#117—32no—
223C3×#117—34no—
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—34no—
231C2×C3×C42—31no—
232C2×C3×C42—31no—
233#939C22×C314yes—
234#938C22×C314yes—
235#938C22×C312yes—
236#937C22×C314yes—
237#936C22×C314yes—
238#936C22×C312yescomplemented
239#935C22×C314yes—
240#935C22×C314yescomplemented
241D4×Dic3C22×C314yes—
242D4×Dic3C22×C314yescomplemented
243D4×Dic3C22×C312yescomplemented
244#929C22×C314yes—
245C4×#67C22×C314yes—
246#926C22×C311yescharacteristic
247#924C22×C312yes—
248#924C22×C314yescomplemented
249C2×C4×Dic3C22×C314yescomplemented
250#898C22×C314yes—
251#897C22×C312yes—
252#896C22×C314yes—
253#892C22×C312yes—
254#892C22×C312yes—
255D3×C4⋊C4C22×C312yes—
256#890C22×C314yescomplemented
257#889C22×C314yescomplemented
258#888C22×C312yescomplemented
259#887C22×C314yescomplemented
260#887C22×C312yescomplemented
261#885C22×C314yes—
262#883C22×C314yes—
263#67⋊C4C22×C314yes—
264#67⋊C4C22×C314yes—
265D3×C22⋊C4C22×C312yes—
266#879C22×C314yes—
267#879C22×C314yescomplemented
268#879C22×C314yescomplemented
269#878C22×C314yescomplemented
270#877C22×C312yes—
271#877C22×C314yescomplemented
272#872C22×C311yescharacteristic
273#872C22×C311yescharacteristic
274C42×D3C22×C311yescharacteristic
275C42×D3C22×C311yescharacteristic
276#870C22×C311yescharacteristic, complemented
277#869C22×C311yescharacteristic, complemented
278C4×Dic6C22×C312yescomplemented
279C23×C32C2411yescharacteristic
280C23×C32C2414yes—
281C22×C3×D3—22no—
282C22×C3×D3—42no—
283C22×C3×D3C2411yescharacteristic
284C22×C3×D3C2411yescharacteristic
285C32×D4—24no—
286C32×D4—44no—
287C32×D4—44no—
288C2×C32×C4—22no—
289C2×C32×C4—44no—
290C2×C32×C4C2412yes—
291C2×C32×C4C2414yes—
292C2×C32×C4C2412yes—
293C2×C32×C4C2411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295C3×#67—28no—
296C3×#67—44no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—28no—
299C2×C3×Dic3—44no—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2414yes—
302C2×C3×Dic3C2414yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2411yescharacteristic
306C3×C4×D3—22no—
307C3×C4×D3—22no—
308C3×C4×D3—22no—
309C3×C4×D3—42no—
310C3×C4×D3—42no—
311C3×C4×D3#4114yes—
312C3×Dic6—24no—
313C3×Dic6—44no—
314#542—32no—
315#542—32no—
316#541—31no—
317#541—31no—
318#540—31no—
319#540C3×D311yescharacteristic, complemented
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—32no—
333C2×C3×Q8—34no—
334C2×C3×D4—22no—
335C2×C3×D4—24no—
336C2×C3×D4—24no—
337C2×C3×D4—34no—
338C2×C3×D4—34no—
339C2×C3×D4C22×D312yes—
340C2×C3×D4C22×D314yes—
341C2×C3×D4C22×D314yes—
342C2×C3×D4C23×C312yes—
343C2×C3×D4C23×C314yes—
344C2×C3×D4C23×C314yes—
345C22×C3×C4—21no—
346C22×C3×C4—24no—
347C22×C3×C4—31no—
348C22×C3×C4—34no—
349C22×C3×C4—31no—
350C22×C3×C4—34no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—32no—
355C22×C3×C4—32no—
356C22×C3×C4—64no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D314yes—
359C22×C3×C4C23×C311yescharacteristic
360C22×C3×C4C23×C314yes—
361C2×#67C23×C314yes—
362C2×#67C23×C314yes—
363C22×Dic3C23×C311yescharacteristic
364C22×Dic3C23×C314yes—
365C22×Dic3C23×C314yes—
366#237—28no—
367C2×C4×D3—24no—
368C2×C4×D3C23×C311yescharacteristic
369C2×C4×D3C23×C311yescharacteristic
370C2×C4×D3C23×C311yescharacteristic
371C2×C4×D3C23×C312yes—
372C2×C4×D3C23×C312yes—
373C2×C4×D3C23×C311yescharacteristic
374C2×Dic6C23×C312yes—
375C2×Dic6C23×C314yes—
376C3×C4⋊C4—22no—
377C3×C4⋊C4—22no—
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—34no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—32no—
387C3×C4⋊C4—32no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4C22×D312yes—
391C3×C4⋊C4C22×D312yes—
392C3×C4⋊C4C22×D314yes—
393C3×C4⋊C4C23×C312yes—
394C3×C4⋊C4C23×C314yes—
395C3×C4⋊C4C23×C312yes—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—24no—
398C3×C22⋊C4—24no—
399C3×C22⋊C4—32no—
400C3×C22⋊C4—34no—
401C3×C22⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—32no—
406C3×C22⋊C4—32no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4C22×D312yes—
410C3×C22⋊C4C22×D314yes—
411C3×C22⋊C4C22×D314yes—
412C3×C22⋊C4C23×C312yes—
413C3×C22⋊C4C23×C314yes—
414C3×C22⋊C4C23×C314yes—
415C3×C42—21no—
416C3×C42—21no—
417C3×C42—32no—
418C3×C42—32no—
419C3×C42—34no—
420C3×C42—31no—
421C3×C42—31no—
422C3×C42—34no—
423C3×C42—34no—
424C3×C42C22×D311yescharacteristic
425C3×C42C22×D311yescharacteristic
426C3×C42C23×C311yescharacteristic
427C3×C42C23×C311yescharacteristic
428#217C23×C312yes—
429#217C23×C314yes—
430#217C23×C314yes—
431#217C23×C314yes—
432#217C23×C314yes—
433#217C23×C314yes—
434(C2×D3)⋊C4C23×C312yes—
435(C2×D3)⋊C4C23×C312yes—
436(C2×D3)⋊C4C23×C314yes—
437(C2×D3)⋊C4C23×C314yes—
438C4⋊Dic3C23×C312yes—
439C4⋊Dic3C23×C314yes—
440C4⋊Dic3C23×C312yes—
441C4⋊Dic3C23×C314yes—
442Dic3⋊C4C23×C314yes—
443Dic3⋊C4C23×C314yes—
444Dic3⋊C4C23×C312yes—
445Dic3⋊C4C23×C312yes—
446Dic3⋊C4C23×C314yes—
447Dic3⋊C4C23×C314yes—
448Dic3⋊C4C23×C314yes—
449C4×Dic3C23×C314yes—
450C4×Dic3C23×C311yescharacteristic
451C4×Dic3C23×C311yescharacteristic
452C4×Dic3C23×C312yes—
453C4×Dic3C23×C312yes—
454C4×Dic3C23×C314yes—
455C4×Dic3C23×C314yes—
456C22×C32—24no—
457C22×C32—21no—
458C22×C32—24no—
459C22×C32—24no—
460C22×C32—22no—
461C22×C32C2511yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—44no—
466C2×C3×D3C2×#4112yes—
467C32×C4—21no—
468C32×C4—24no—
469C32×C4—22no—
470C32×C4—22no—
471C32×C4C2×#4112yes—
472C3×Dic3—24no—
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⋊Q8—31no—
482#127C2×C3×D311yescharacteristic, complemented
483#126—34no—
484#126—34no—
485#126—34no—
486#126—34no—
487#125—34no—
488#125—34no—
489#125—31no—
490#125C2×C3×D311yescharacteristic, complemented
491#124—34no—
492#124—32no—
493#124—34no—
494#123—34no—
495#123—34no—
496#123—34no—
497#123—34no—
498#123C2×C3×D314yescomplemented
499C22⋊Q8—32no—
500C22⋊Q8—34no—
501C22⋊Q8—32no—
502C22⋊Q8—34no—
503C22⋊Q8—34no—
504#121—32no—
505#121—34no—
506#121—34no—
507#121C2×C3×D312yes—
508#121C2×C3×D314yes—
509#120—34no—
510C4×Q8—32no—
511C4×Q8—34no—
512C4×Q8—32no—
513C4×D4—32no—
514C4×D4—34no—
515C4×D4—34no—
516C4×D4—34no—
517C4×D4—34no—
518C4×D4—34no—
519C4×D4C2×C3×D312yescomplemented
520#117—31no—
521#117—32no—
522#117—32no—
523#117—32no—
524#117—34no—
525#117—31no—
526#117—31no—
527#117C2×C3×D311yescharacteristic
528C2×C4⋊C4—32no—
529C2×C22⋊C4—32no—
530C2×C42—34no—
531C2×C42—31no—
532C2×C42—31no—
533C23×C3—21no—
534C23×C3—24no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—62no—
538C23×C3—122no—
539C23×C3C23×D311yescharacteristic
540C23×C3C23×D314yes—
541C23×C3C24×C311yescharacteristic
542C23×C3C24×C314yes—
543C22×D3—22no—
544C22×D3—42no—
545C22×D3C24×C311yescharacteristic
546C22×D3C24×C311yescharacteristic
547C3×Q8—64no—
548C3×Q8—124no—
549C3×D4—24no—
550C3×D4—24no—
551C3×D4—44no—
552C3×D4—44no—
553C3×D4—44no—
554C3×D4—44no—
555C3×D4—44no—
556C3×D4—68no—
557C3×D4—84no—
558C3×D4—84no—
559C3×D4—124no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—21no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—24no—
567C2×C3×C4—31no—
568C2×C3×C4—34no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—34no—
572C2×C3×C4—34no—
573C2×C3×C4—31no—
574C2×C3×C4—42no—
575C2×C3×C4—44no—
576C2×C3×C4—44no—
577C2×C3×C4—62no—
578C2×C3×C4—62no—
579C2×C3×C4—62no—
580C2×C3×C4—68no—
581C2×C3×C4—62no—
582C2×C3×C4—84no—
583C2×C3×C4—122no—
584C2×C3×C4—122no—
585C2×C3×C4—124no—
586C2×C3×C4C23×D312yes—
587C2×C3×C4C23×D314yes—
588C2×C3×C4C23×D312yes—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C24×C312yes—
592C2×C3×C4C24×C314yes—
593C2×C3×C4C24×C312yes—
594C2×C3×C4C24×C311yescharacteristic
595C2×C3×C4C24×C311yescharacteristic
596#67—28no—
597#67—44no—
598C2×Dic3—22no—
599C2×Dic3—28no—
600C2×Dic3—44no—
601C2×Dic3C24×C312yes—
602C2×Dic3C24×C314yes—
603C2×Dic3C24×C314yes—
604C2×Dic3C24×C312yes—
605C2×Dic3C24×C311yescharacteristic
606C2×Dic3C24×C311yescharacteristic
607C4×D3—22no—
608C4×D3—22no—
609C4×D3—22no—
610C4×D3—42no—
611C4×D3—42no—
612C4×D3C3×#4114yes—
613Dic6—24no—
614Dic6—44no—
615C2×C32—41no—
616C2×C32—44no—
617C2×C32C22×#4111yescharacteristic
618C2×C32#58512yes—
619C3×D3—22no—
620C3×D3—41no—
621C24—31no—
622#41—68no—
623C2×Q8—32no—
624C2×Q8—34no—
625C2×D4—34no—
626C2×D4—34no—
627C2×D4C22×C3×D312yes—
628C2×D4C22×C3×D314yes—
629C2×D4C22×C3×D314yes—
630C22×C4—31no—
631C22×C4—34no—
632C22×C4—31no—
633C22×C4—34no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—64no—
640C22×C4C22×C3×D311yescharacteristic
641C22×C4C22×C3×D314yes—
642C4⋊C4—32no—
643C4⋊C4—32no—
644C4⋊C4—32no—
645C4⋊C4—32no—
646C4⋊C4—34no—
647C4⋊C4—34no—
648C4⋊C4—34no—
649C4⋊C4—34no—
650C4⋊C4—34no—
651C4⋊C4—34no—
652C4⋊C4—34no—
653C4⋊C4C22×C3×D312yes—
654C4⋊C4C22×C3×D312yes—
655C4⋊C4C22×C3×D314yes—
656C22⋊C4—32no—
657C22⋊C4—34no—
658C22⋊C4—34no—
659C22⋊C4—34no—
660C22⋊C4—34no—
661C22⋊C4—34no—
662C22⋊C4—32no—
663C22⋊C4—32no—
664C22⋊C4—34no—
665C22⋊C4—34no—
666C22⋊C4C22×C3×D312yes—
667C22⋊C4C22×C3×D314yes—
668C22⋊C4C22×C3×D314yes—
669C42—32no—
670C42—32no—
671C42—34no—
672C42—31no—
673C42—31no—
674C42—34no—
675C42—34no—
676C42C22×C3×D311yescharacteristic
677C42C22×C3×D311yescharacteristic
678C22×C3—21no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—22no—
683C22×C3—24no—
684C22×C3—21no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—32no—
690C22×C3—41no—
691C22×C3—44no—
692C22×C3—44no—
693C22×C3—44no—
694C22×C3—42no—
695C22×C3—62no—
696C22×C3—61no—
697C22×C3—62no—
698C22×C3—124no—
699C22×C3C24×D311yescharacteristic
700C22×C3C25×C311yescharacteristic
701C2×D3—22no—
702C2×D3—21no—
703C2×D3—22no—
704C2×D3—44no—
705C2×D3C2×C3×#4112yes—
706C3×C4—21no—
707C3×C4—22no—
708C3×C4—24no—
709C3×C4—22no—
710C3×C4—21no—
711C3×C4—24no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—32no—
716C3×C4—41no—
717C3×C4—42no—
718C3×C4—44no—
719C3×C4—42no—
720C3×C4—61no—
721C3×C4—64no—
722C3×C4—62no—
723C3×C4—64no—
724C3×C4—62no—
725C3×C4D3×#4112yes—
726C3×C4C2×C3×#4112yes—
727Dic3—24no—
728Dic3—21no—
729Dic3—22no—
730Dic3—24no—
731Dic3—22no—
732Dic3C2×C3×#4112yes—
733C32#345511yescharacteristic, complemented, Sylow
734C23—31no—
735C23—31no—
736C23—62no—
737C23—122no—
738C23C23×C3×D311yescharacteristic
739C23C23×C3×D314yes—
740Q8—64no—
741Q8—124no—
742D4—24no—
743D4—44no—
744D4—44no—
745D4—68no—
746D4—124no—
747C2×C4—22no—
748C2×C4—31no—
749C2×C4—34no—
750C2×C4—32no—
751C2×C4—32no—
752C2×C4—34no—
753C2×C4—34no—
754C2×C4—31no—
755C2×C4—44no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—68no—
760C2×C4—62no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—124no—
764C2×C4C23×C3×D312yes—
765C2×C4C23×C3×D314yes—
766C2×C4C23×C3×D312yes—
767C2×C4C23×C3×D311yescharacteristic
768C2×C4C23×C3×D311yescharacteristic
769C2×C3—21no—
770C2×C3—22no—
771C2×C3—41no—
772C2×C3—44no—
773C2×C3—41no—
774C2×C3—44no—
775C2×C3—62no—
776C2×C3—81no—
777C2×C3—84no—
778C2×C3—121no—
779C2×C3C2×D3×#4111yescharacteristic
780C2×C3#596612yes—
781C2×C3C22×C3×#4111yescharacteristic
782C2×C3C3×#58512yes—
783D3—22no—
784D3—41no—
785C22—21no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—22no—
790C22—32no—
791C22—62no—
792C22—61no—
793C22—62no—
794C22—124no—
795C22C24×C3×D311yescharacteristic
796C4—21no—
797C4—22no—
798C4—24no—
799C4—22no—
800C4—32no—
801C4—61no—
802C4—64no—
803C4—62no—
804C4—64no—
805C4—62no—
806C4C3×D3×#4112yes—
807C3—21no—
808C3#8646711yescharacteristic, direct product factor
809C3C3×#345511yescharacteristic, complemented
810C2—41no—
811C2—44no—
812C2—62no—
813C2—121no—
814C2C2×C3×D3×#4111yescharacteristic
815C2C3×#596612yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#540C2
socleC22×C32C25
hypercenterC3×#540D3
hypocenterC3C3×#3455
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#540

Complements

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

NH ≅ G/Ntype
1. C32×#540C2semidirect
2. C3×#5719C2semidirect
3. C3×#5716C2semidirect
4. C3×#5698C2semidirect
5. C3×#5688C2semidirect
6. C3×#5660C2semidirect
7. C3×#5649C2semidirect
8. C3×#5613C2semidirect
9. C3×#5606C2semidirect
10. C3×#5603C2semidirect
11. C3×#5600C2semidirect
12. C3×#5561C2semidirect
13. C3×C4×#237C2semidirect
14. C3×D3×#117C2semidirect
15. C3×#5518C2semidirect
17. #86467C3direct (N × H)
20. C32×#127C22semidirect
21. C32×#125C22semidirect
22. C32×#123C22semidirect
25. C32×C4×D4C22semidirect
32. C3×#936C22semidirect
34. C3×#935C22semidirect
36. C3×D4×Dic3C22semidirect
37. C3×D4×Dic3C22semidirect
42. C3×#924C22semidirect
43. C2×C3×C4×Dic3C22semidirect
50. C3×#890C22semidirect
51. C3×#889C22semidirect
52. C3×#888C22semidirect
53. C3×#887C22semidirect
54. C3×#887C22semidirect
61. C3×#879C22semidirect
62. C3×#879C22semidirect
63. C3×#878C22semidirect
65. C3×#877C22semidirect
70. C3×#870C22semidirect
71. C3×#869C22semidirect
72. C3×C4×Dic6C22semidirect
79. C3×#540D3semidirect
80. C3×#540C2×C3semidirect
90. #5719C2×C3semidirect
91. #5716C2×C3semidirect
92. #5698C2×C3semidirect
93. #5688C2×C3semidirect
94. #5660C2×C3semidirect
95. #5649C2×C3semidirect
96. #5613C2×C3semidirect
97. #5606C2×C3semidirect
98. #5603C2×C3semidirect
99. #5600C2×C3semidirect
100. #5561C2×C3semidirect
101. C4×#237C2×C3semidirect
102. D3×#117C2×C3semidirect
103. #5518C2×C3semidirect
169. C3×#127C2×D3semidirect
170. C3×#127C22×C3semidirect
179. C3×#125C2×D3semidirect
180. C3×#125C22×C3semidirect
189. C3×#123C2×D3semidirect
190. C3×#123C22×C3semidirect
216. C3×C4×D4C2×D3semidirect
217. C3×C4×D4C22×C3semidirect
238. #936C22×C3semidirect
240. #935C22×C3semidirect
242. D4×Dic3C22×C3semidirect
243. D4×Dic3C22×C3semidirect
248. #924C22×C3semidirect
249. C2×C4×Dic3C22×C3semidirect
256. #890C22×C3semidirect
257. #889C22×C3semidirect
258. #888C22×C3semidirect
259. #887C22×C3semidirect
260. #887C22×C3semidirect
267. #879C22×C3semidirect
268. #879C22×C3semidirect
269. #878C22×C3semidirect
271. #877C22×C3semidirect
276. #870C22×C3semidirect
277. #869C22×C3semidirect
278. C4×Dic6C22×C3semidirect
319. #540C3×D3semidirect
482. #127C2×C3×D3semidirect
490. #125C2×C3×D3semidirect
498. #123C2×C3×D3semidirect
519. C4×D4C2×C3×D3semidirect
733. C32#3455semidirect
808. C3#86467direct (N × H)
809. C3C3×#3455semidirect

Maximal subgroups

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

subgroupindex
C32×#5402
C3×#57192
C3×#57162
C3×#56982
C3×#56882
C3×#56602
C3×#56492
C3×#56132
C3×#56062
C3×#56032
C3×#56002
C3×#55612
C3×C4×#2372
C3×D3×#1172
C3×#55182
C3×#34553
#864673