Finite Group Databasebeta

← C3×#10595295 #13174783

Subgroups — C3×#10595295 #13174783

Order 1728.

2134 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3811C212yesmaximal, complemented
2C2×C3×D3×#67C212yesmaximal, complemented
3C3×#64146C211yesmaximal, characteristic, complemented
4C32×#940C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6C3×#63970C212yesmaximal, complemented
7C3×#63958C212yesmaximal, complemented
8C3×#63922C212yesmaximal, complemented
9C3×#63880C212yesmaximal, complemented
10C3×#5717—31nomaximal
11C3×#5590—31nomaximal
12#10595295C311yesmaximal, characteristic, direct product factor
13C23×C3×C3⋊D3C2211yescharacteristic, complemented
14C23×C32×D3C2211yescharacteristic, complemented
15C22×C3×D32C2212yescomplemented
16C2×C33×D4C2211yescharacteristic, complemented
17C2×C3×#638C2212yescomplemented
18C2×C32×#67C2212yescomplemented
19C2×C32×#67C2212yescomplemented
20C2×C32×#67C2212yescomplemented
21C2×C32×D12C2211yescharacteristic, complemented
22C3×#3811—28no—
23C3×D3×#67—28no—
24C2×C3×#626C2212yes—
25C2×C3×#626C2212yescomplemented
26C2×C3×#625C2212yescomplemented
27C2×C3×#624C2212yescomplemented
28C2×C3×D3×Dic3C2212yescomplemented
29C3×#3757C2211yescharacteristic, complemented
30C3×#3752C2212yescomplemented
31C32×#217C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2212yescomplemented
33C32×C4×Dic3C2211yescharacteristic, complemented
34C3×Dic3⋊Dic3C2212yescomplemented
35C3×(C2×D3)⋊Dic3C2212yescomplemented
36C22×C3×#67—32no—
37C2×C3×D3×D4—32no—
38C2×C3×D3×D4—32no—
39C2×C3×D3×D4—32no—
40C2×#3811C2×C312yescomplemented
41C2×D3×#67C2×C312yescomplemented
42C32×#127—31no—
43C32×#120—31no—
44#64146C2×C311yescharacteristic, complemented
45C3×#940—21no—
46C3×#940D311yescharacteristic, complemented
47C3×#940C2×C311yescharacteristic, complemented
48C3×#939—32no—
49C3×#938—32no—
50C3×#938—32no—
51C3×#937—21no—
52C3×#937—31no—
53C3×#937—31no—
54C3×#937—32no—
55C3×#937—61no—
56C3×#937D311yescharacteristic, complemented
57C3×#937C2×C311yescharacteristic, complemented
58C3×#884—32no—
59C3×#882—32no—
60C3×#67⋊C4—32no—
61C3×C4×D12—32no—
62#63970C2×C312yescomplemented
63#63958C2×C312yescomplemented
64#63922C2×C312yescomplemented
65#63880C2×C312yescomplemented
66C23×C33C2311yescharacteristic
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3—24no—
69C22×C3×C3⋊D3—41no—
70C22×C3×C3⋊D3C2312yes—
71C22×C32×D3—24no—
72C22×C32×D3—41no—
73C22×C32×D3C2312yes—
74C22×C32×D3C2312yes—
75C2×C3×D32—24no—
76C2×C3×D32—24no—
77C2×C3×D32—42no—
78C33×D4—41no—
79C2×C33×C4C2311yescharacteristic
80C3×#638—24no—
81C2×C3×C3⋊Dic3C2312yes—
82C32×#67—24no—
83C32×#67—24no—
84C32×#67—24no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C32×D12—41no—
88C3×#626—24no—
89C3×#626D418yescomplemented
90C3×#625—24no—
91C3×#624—24no—
92C3×D3×Dic3—24no—
93C3×D42—91no—
94#5717—31no—
95#5590—31no—
96C24×C32—31no—
97C23×C3⋊D3C22×C311yescharacteristic, complemented
98C23×C3×D3—21no—
99C23×C3×D3—31no—
100C23×C3×D3—31no—
101C23×C3×D3—32no—
102C23×C3×D3—32no—
103C23×C3×D3—61no—
104C23×C3×D3C2×D311yescharacteristic, complemented
105C23×C3×D3C22×C311yescharacteristic, complemented
106C22×D32C22×C312yescomplemented
107C2×C32×D4—21no—
108C2×C32×D4—21no—
109C2×C32×D4—21no—
110C2×C32×D4—32no—
111C2×C32×D4—32no—
112C2×C32×D4—32no—
113C2×C32×D4—31no—
114C2×C32×D4—41no—
115C2×C32×D4C2×D311yescharacteristic, complemented
116C2×C32×D4C2×D311yescharacteristic, complemented
117C2×C32×D4C22×C311yescharacteristic, complemented
118C2×#638C22×C312yescomplemented
119C2×C3×#67—22no—
120C2×C3×#67—22no—
121C2×C3×#67—22no—
122C2×C3×#67—32no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C2×C3×#67—32no—
127C2×C3×#67—32no—
128C2×C3×#67—68no—
129C2×C3×#67—62no—
130C2×C3×#67C2×D312yescomplemented
131C2×C3×#67C2×D312yescomplemented
132C2×C3×#67C2×D312yescomplemented
133C2×C3×#67C22×C312yescomplemented
134C2×C3×#67C22×C312yescomplemented
135C2×C3×#67C22×C312yescomplemented
136C22×C3×Dic3—32no—
137C3×D3×D4—68no—
138C3×D3×D4—68no—
139C3×D3×D4—68no—
140C2×C3×D12—21no—
141C2×C3×D12—32no—
142C2×C3×D12—32no—
143C2×C3×D12C2×D311yescharacteristic, complemented
144C2×C3×D12C22×C311yescharacteristic, complemented
145C2×C3×C4×D3—32no—
146C2×C3×C4×D3—32no—
147C2×C3×C4×D3—32no—
148#3811—28no—
149D3×#67—28no—
150C2×#626C22×C312yes—
151C2×#626C22×C312yescomplemented
152C2×#625C22×C312yescomplemented
153C2×#624C22×C312yescomplemented
154C2×D3×Dic3C22×C312yescomplemented
155C32×C22⋊C4—31no—
156C32×C22⋊C4—32no—
157C32×C42—31no—
158#3757C22×C311yescharacteristic, complemented
159#3752C22×C312yescomplemented
160C3×#217—21no—
161C3×#217—31no—
162C3×#217—31no—
163C3×#217—32no—
164C3×#217—61no—
165C3×#217C2×D311yescharacteristic, complemented
166C3×#217C22×C311yescharacteristic, complemented
167C3×(C2×D3)⋊C4—22no—
168C3×(C2×D3)⋊C4—32no—
169C3×(C2×D3)⋊C4—32no—
170C3×(C2×D3)⋊C4—32no—
171C3×(C2×D3)⋊C4—62no—
172C3×(C2×D3)⋊C4C2×D312yescomplemented
173C3×(C2×D3)⋊C4C22×C312yescomplemented
174C3×C4⋊Dic3—32no—
175C3×Dic3⋊C4—32no—
176C3×C4×Dic3—21no—
177C3×C4×Dic3C2×D311yescharacteristic, complemented
178C3×C4×Dic3C22×C311yescharacteristic, complemented
179Dic3⋊Dic3C22×C312yescomplemented
180(C2×D3)⋊Dic3C22×C312yescomplemented
181C22×C33—22no—
182C22×C33—22no—
183C22×C33—21no—
184C22×C33—21no—
185C22×C33C2411yescharacteristic
186C2×C3×C3⋊D3—22no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—44no—
189C2×C3×C3⋊D3C2×D414yescomplemented
190C2×C32×D3—22no—
191C2×C32×D3—22no—
192C2×C32×D3—22no—
193C2×C32×D3—22no—
194C2×C32×D3—22no—
195C2×C32×D3—44no—
196C2×C32×D3C2×D414yescomplemented
197C3×D32—48no—
198C33×C4—21no—
199C3×C3⋊Dic3—22no—
200C32×Dic3—22no—
201C32×Dic3C2×D414yescomplemented
202C22×C3×D4—92no—
203C22×C3×D4—92no—
204C22×#67—32no—
205C2×D3×D4—32no—
206C2×D3×D4—32no—
207C2×D3×D4—32no—
208C3×#127—31no—
209C3×#127—31no—
210C3×#127—61no—
211C3×#121—92no—
212C3×#121—92no—
213C3×#120—31no—
214C3×#120—31no—
215C3×#120—61no—
216C3×#120—92no—
217C3×#120—91no—
218C3×C4×D4—92no—
219#940C3×D311yescharacteristic, complemented
220#939—32no—
221#938—32no—
222#938—32no—
223#937—31no—
224#937—31no—
225#937—32no—
226#937—61no—
227#937C3×D311yescharacteristic, complemented
228#884—32no—
229#882—32no—
230#67⋊C4—32no—
231C4×D12—32no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—32no—
239C23×C32—32no—
240C23×C32—41no—
241C23×C32—41no—
242C23×C32—64no—
243C23×C32—121no—
244C23×C32C22×D311yescharacteristic
245C23×C32C22×D311yescharacteristic
246C23×C32C22×D311yescharacteristic
247C23×C32C22×D311yescharacteristic
248C23×C32C23×C311yescharacteristic
249C23×C32C23×C311yescharacteristic
250C22×C3⋊D3—24no—
251C22×C3⋊D3—41no—
252C22×C3⋊D3C23×C312yes—
253C22×C3×D3—24no—
254C22×C3×D3—24no—
255C22×C3×D3—22no—
256C22×C3×D3—22no—
257C22×C3×D3—32no—
258C22×C3×D3—32no—
259C22×C3×D3—44no—
260C22×C3×D3—41no—
261C22×C3×D3—41no—
262C22×C3×D3—42no—
263C22×C3×D3—62no—
264C22×C3×D3—64no—
265C22×C3×D3—64no—
266C22×C3×D3—64no—
267C22×C3×D3—64no—
268C22×C3×D3—64no—
269C22×C3×D3—64no—
270C22×C3×D3—124no—
271C22×C3×D3—122no—
272C22×C3×D3—122no—
273C22×C3×D3—121no—
274C22×C3×D3—121no—
275C22×C3×D3—122no—
276C22×C3×D3C22×D312yes—
277C22×C3×D3C22×D312yes—
278C22×C3×D3C23×C312yes—
279C22×C3×D3C23×C312yes—
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—42no—
283C32×D4—41no—
284C32×D4—41no—
285C32×D4—41no—
286C32×D4—42no—
287C32×D4—42no—
288C32×D4—42no—
289C32×D4—44no—
290C32×D4—64no—
291C32×D4—64no—
292C32×D4—64no—
293C32×D4—121no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—32no—
298C2×C32×C4—32no—
299C2×C32×C4—41no—
300C2×C32×C4C22×D311yescharacteristic
301C2×C32×C4C22×D311yescharacteristic
302C2×C32×C4C23×C311yescharacteristic
303#638—24no—
304C2×C3⋊Dic3C23×C312yes—
305C3×#67—24no—
306C3×#67—24no—
307C3×#67—24no—
308C3×#67—24no—
309C3×#67—24no—
310C3×#67—24no—
311C3×#67—38no—
312C3×#67—44no—
313C3×#67—44no—
314C3×#67—44no—
315C3×#67—64no—
316C3×#67—64no—
317C3×#67—64no—
318C3×#67—64no—
319C3×#67—64no—
320C3×#67—124no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—32no—
324C2×C3×Dic3—32no—
325C2×C3×Dic3—62no—
326C2×C3×Dic3—64no—
327C2×C3×Dic3C22×D312yes—
328C2×C3×Dic3C22×D312yes—
329C2×C3×Dic3C23×C312yes—
330C2×C3×Dic3C23×C312yes—
331C3×D12—38no—
332C3×D12—41no—
333C3×D12—41no—
334C3×D12—42no—
335C3×D12—64no—
336C3×C4×D3—64no—
337C3×C4×D3—64no—
338C3×C4×D3—64no—
339#626—24no—
340#626C3×D418yescomplemented
341#625—24no—
342#624—24no—
343D3×Dic3—24no—
344D42—91noSylow
345C2×C33—41no—
346C2×C33—41no—
347C2×C33C22×D412yes—
348C2×C33H(5,𝔽2)11yescharacteristic
349C3×C3⋊D3—24no—
350C32×D3—24no—
351C32×D3—42no—
352C24×C3—31no—
353C24×C3—31no—
354C24×C3—61no—
355C24×C3—92no—
356C24×C3—91no—
357C23×D3—31no—
358C23×D3—31no—
359C23×D3—32no—
360C23×D3—32no—
361C23×D3—61no—
362C23×D3C2×C3×D311yescharacteristic, complemented
363C2×C3×D4—21no—
364C2×C3×D4—21no—
365C2×C3×D4—21no—
366C2×C3×D4—32no—
367C2×C3×D4—32no—
368C2×C3×D4—32no—
369C2×C3×D4—32no—
370C2×C3×D4—32no—
371C2×C3×D4—32no—
372C2×C3×D4—31no—
373C2×C3×D4—31no—
374C2×C3×D4—41no—
375C2×C3×D4—61no—
376C2×C3×D4—62no—
377C2×C3×D4—62no—
378C2×C3×D4—62no—
379C2×C3×D4—92no—
380C2×C3×D4—92no—
381C2×C3×D4—92no—
382C2×C3×D4—92no—
383C2×C3×D4—188no—
384C2×C3×D4—188no—
385C2×C3×D4D3211yescharacteristic, complemented
386C2×C3×D4C2×C3×D311yescharacteristic, complemented
387C2×C3×D4C2×C3×D311yescharacteristic, complemented
388C22×C3×C4—92no—
389C22×C3×C4—92no—
390C2×#67—32no—
391C2×#67—32no—
392C2×#67—32no—
393C2×#67—32no—
394C2×#67—32no—
395C2×#67—32no—
396C2×#67—62no—
397C2×#67—68no—
398C2×#67C2×C3×D312yescomplemented
399C2×#67C2×C3×D312yescomplemented
400C2×#67C2×C3×D312yescomplemented
401C22×Dic3—32no—
402D3×D4—68no—
403D3×D4—68no—
404D3×D4—68no—
405C2×D12—32no—
406C2×D12—32no—
407C2×D12C2×C3×D311yescharacteristic, complemented
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—32no—
411C3×C4⋊C4—92no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—32no—
415C3×C22⋊C4—32no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—61no—
418C3×C22⋊C4—92no—
419C3×C22⋊C4—91no—
420C3×C22⋊C4—92no—
421C3×C42—31no—
422C3×C42—31no—
423C3×C42—61no—
424#217—31no—
425#217—31no—
426#217—32no—
427#217—61no—
428#217C2×C3×D311yescharacteristic, complemented
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—32no—
431(C2×D3)⋊C4—32no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4C2×C3×D312yescomplemented
434C4⋊Dic3—32no—
435Dic3⋊C4—32no—
436C4×Dic3C2×C3×D311yescharacteristic, complemented
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—34no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—42no—
461C22×C32—42no—
462C22×C32—42no—
463C22×C32—42no—
464C22×C32—42no—
465C22×C32—42no—
466C22×C32—42no—
467C22×C32—42no—
468C22×C32—62no—
469C22×C32—62no—
470C22×C32—62no—
471C22×C32—62no—
472C22×C32—62no—
473C22×C32—82no—
474C22×C32—82no—
475C22×C32—124no—
476C22×C32C23×D311yescharacteristic
477C22×C32C23×D311yescharacteristic
478C22×C32C24×C311yescharacteristic
479C2×C3⋊D3—22no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—44no—
482C2×C3⋊D3C2×C3×D414yescomplemented
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—24no—
494C2×C3×D3—34no—
495C2×C3×D3—34no—
496C2×C3×D3—42no—
497C2×C3×D3—42no—
498C2×C3×D3—42no—
499C2×C3×D3—42no—
500C2×C3×D3—42no—
501C2×C3×D3—44no—
502C2×C3×D3—44no—
503C2×C3×D3—48no—
504C2×C3×D3—64no—
505C2×C3×D3—62no—
506C2×C3×D3—62no—
507C2×C3×D3—62no—
508C2×C3×D3—62no—
509C2×C3×D3—122no—
510C2×C3×D3—122no—
511C2×C3×D3—128no—
512C2×C3×D3—128no—
513C2×C3×D3—124no—
514C2×C3×D3—124no—
515C2×C3×D3—128no—
516C2×C3×D3D3×D414yescomplemented
517C2×C3×D3C2×C3×D414yescomplemented
518D32—48no—
519C32×C4—21no—
520C32×C4—22no—
521C32×C4—21no—
522C32×C4—21no—
523C32×C4—34no—
524C32×C4—41no—
525C32×C4—41no—
526C32×C4—42no—
527C32×C4—62no—
528C3⋊Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—24no—
532C3×Dic3—42no—
533C3×Dic3—62no—
534C3×Dic3—62no—
535C3×Dic3—122no—
536C3×Dic3D3×D414yescomplemented
537C3×Dic3C2×C3×D414yescomplemented
538C22×D4—92no—
539C22×D4—92no—
540#127—31no—
541#121—92no—
542#121—92no—
543#120—31no—
544#120—92no—
545#120—91no—
546C4×D4—92no—
547C33D4211yescharacteristic, complemented, Sylow
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—32no—
555C23×C3—32no—
556C23×C3—32no—
557C23×C3—32no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—62no—
561C23×C3—62no—
562C23×C3—64no—
563C23×C3—64no—
564C23×C3—92no—
565C23×C3—124no—
566C23×C3—121no—
567C23×C3—121no—
568C23×C3—122no—
569C23×C3—184no—
570C23×C3—184no—
571C23×C3—184no—
572C23×C3—361no—
573C23×C3—362no—
574C23×C3C2×D3211yescharacteristic
575C23×C3C2×D3211yescharacteristic
576C23×C3C22×C3×D311yescharacteristic
577C23×C3C22×C3×D311yescharacteristic
578C23×C3C22×C3×D311yescharacteristic
579C23×C3C22×C3×D311yescharacteristic
580C22×D3—24no—
581C22×D3—32no—
582C22×D3—32no—
583C22×D3—41no—
584C22×D3—62no—
585C22×D3—64no—
586C22×D3—64no—
587C22×D3—64no—
588C22×D3—64no—
589C22×D3—64no—
590C22×D3—64no—
591C22×D3—124no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—121no—
595C22×D3—121no—
596C22×D3—122no—
597C22×D3C22×C3×D312yes—
598C22×D3C22×C3×D312yes—
599C3×D4—41no—
600C3×D4—41no—
601C3×D4—41no—
602C3×D4—42no—
603C3×D4—42no—
604C3×D4—42no—
605C3×D4—44no—
606C3×D4—64no—
607C3×D4—64no—
608C3×D4—64no—
609C3×D4—64no—
610C3×D4—64no—
611C3×D4—64no—
612C3×D4—98no—
613C3×D4—124no—
614C3×D4—124no—
615C3×D4—124no—
616C3×D4—121no—
617C3×D4—121no—
618C3×D4—122no—
619C3×D4—184no—
620C3×D4—184no—
621C3×D4—184no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—32no—
629C2×C3×C4—41no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—92no—
633C2×C3×C4—184no—
634C2×C3×C4—184no—
635C2×C3×C4C2×D3211yescharacteristic
636C2×C3×C4C22×C3×D311yescharacteristic
637C2×C3×C4C22×C3×D311yescharacteristic
638#67—24no—
639#67—24no—
640#67—24no—
641#67—38no—
642#67—64no—
643#67—64no—
644#67—64no—
645#67—64no—
646#67—64no—
647#67—124no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—62no—
651C2×Dic3—64no—
652C2×Dic3C22×C3×D312yes—
653C2×Dic3C22×C3×D312yes—
654D12—38no—
655D12—41no—
656D12—64no—
657C4×D3—64no—
658C4×D3—64no—
659C4×D3—64no—
660C2×C32—22no—
661C2×C32—21no—
662C2×C32—22no—
663C2×C32—22no—
664C2×C32—21no—
665C2×C32—21no—
666C2×C32—42no—
667C2×C32—41no—
668C2×C32—41no—
669C2×C32—41no—
670C2×C32—42no—
671C2×C32—42no—
672C2×C32—41no—
673C2×C32—41no—
674C2×C32—41no—
675C2×C32—41no—
676C2×C32—64no—
677C2×C32—81no—
678C2×C32—81no—
679C2×C32—81no—
680C2×C32—81no—
681C2×C32—82no—
682C2×C32—82no—
683C2×C32—122no—
684C2×C32C2×D3×D412yes—
685C2×C32C2×D3×D412yes—
686C2×C32#100411yescharacteristic
687C2×C32#100411yescharacteristic
688C2×C32C22×C3×D412yes—
689C2×C32C3×H(5,𝔽2)11yescharacteristic
690C3⋊D3—24no—
691C3×D3—24no—
692C3×D3—24no—
693C3×D3—44no—
694C3×D3—42no—
695C3×D3—42no—
696C3×D3—64no—
697C3×D3—64no—
698C3×D3—82no—
699C3×D3—124no—
700C24—31no—
701C24—92no—
702C24—91no—
703C2×D4—32no—
704C2×D4—32no—
705C2×D4—32no—
706C2×D4—31no—
707C2×D4—92no—
708C2×D4—92no—
709C2×D4—92no—
710C2×D4—92no—
711C2×D4—188no—
712C2×D4—188no—
713C2×D4C3×D3211yescharacteristic, complemented
714C22×C4—92no—
715C22×C4—92no—
716C4⋊C4—92no—
717C22⋊C4—31no—
718C22⋊C4—32no—
719C22⋊C4—92no—
720C22⋊C4—91no—
721C22⋊C4—92no—
722C42—31no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—34no—
741C22×C3—34no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—41no—
755C22×C3—64no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—82no—
767C22×C3—82no—
768C22×C3—94no—
769C22×C3—122no—
770C22×C3—122no—
771C22×C3—122no—
772C22×C3—122no—
773C22×C3—122no—
774C22×C3—124no—
775C22×C3—124no—
776C22×C3—128no—
777C22×C3—182no—
778C22×C3—182no—
779C22×C3—364no—
780C22×C3—368no—
781C22×C3C22×D3211yescharacteristic
782C22×C3C23×C3×D311yescharacteristic
783C22×C3C23×C3×D311yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—34no—
790C2×D3—34no—
791C2×D3—44no—
792C2×D3—64no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—122no—
798C2×D3—122no—
799C2×D3—128no—
800C2×D3—128no—
801C2×D3—124no—
802C2×D3—124no—
803C2×D3—128no—
804C2×D3C3×D3×D414yescomplemented
805C3×C4—22no—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—34no—
810C3×C4—34no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4—42no—
814C3×C4—64no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—122no—
818C3×C4—182no—
819Dic3—22no—
820Dic3—62no—
821Dic3—62no—
822Dic3—122no—
823Dic3C3×D3×D414yescomplemented
824C32—21no—
825C32—21no—
826C32—21no—
827C32—41no—
828C32#559011yescharacteristic, complemented
829C32#571711yescharacteristic, complemented
830C32C3×D4211yescharacteristic, complemented
831C23—32no—
832C23—32no—
833C23—64no—
834C23—92no—
835C23—121no—
836C23—184no—
837C23—184no—
838C23—184no—
839C23—361no—
840C23—362no—
841C23C2×C3×D3211yescharacteristic
842C23C2×C3×D3211yescharacteristic
843D4—41no—
844D4—64no—
845D4—64no—
846D4—64no—
847D4—98no—
848D4—121no—
849D4—184no—
850D4—184no—
851D4—184no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—92no—
855C2×C4—184no—
856C2×C4—184no—
857C2×C4C2×C3×D3211yescharacteristic
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—22no—
862C2×C3—22no—
863C2×C3—22no—
864C2×C3—42no—
865C2×C3—42no—
866C2×C3—41no—
867C2×C3—41no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—41no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—42no—
874C2×C3—64no—
875C2×C3—64no—
876C2×C3—81no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—81no—
880C2×C3—82no—
881C2×C3—82no—
882C2×C3—124no—
883C2×C3—122no—
884C2×C3—122no—
885C2×C3—184no—
886C2×C3—242no—
887C2×C3D32×D412yes—
888C2×C3#6433011yescharacteristic
889C2×C3C2×C3×D3×D412yes—
890C2×C3C2×C3×D3×D412yes—
891C2×C3C3×#100411yescharacteristic
892C2×C3C3×#100411yescharacteristic
893D3—24no—
894D3—42no—
895D3—64no—
896D3—64no—
897D3—124no—
898C22—21no—
899C22—21no—
900C22—22no—
901C22—22no—
902C22—34no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—94no—
909C22—124no—
910C22—182no—
911C22—182no—
912C22—364no—
913C22—368no—
914C22C22×C3×D3211yescharacteristic
915C4—21no—
916C4—34no—
917C4—62no—
918C4—182no—
919C3—21no—
920C3—21no—
921C3—21no—
922C3—41no—
923C3#1059529511yescharacteristic, direct product factor
924C3C3×#559011yescharacteristic, complemented
925C3C3×#571711yescharacteristic, complemented
926C2—41no—
927C2—41no—
928C2—64no—
929C2—122no—
930C2—184no—
931C2C3×D32×D412yes—
932C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×D42
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3811C2semidirect
2. C2×C3×D3×#67C2semidirect
3. C3×#64146C2semidirect
4. C32×#940C2semidirect
5. C32×#937C2semidirect
6. C3×#63970C2semidirect
7. C3×#63958C2semidirect
8. C3×#63922C2semidirect
9. C3×#63880C2semidirect
12. #10595295C3direct (N × H)
13. C23×C3×C3⋊D3C22semidirect
14. C23×C32×D3C22semidirect
15. C22×C3×D32C22semidirect
16. C2×C33×D4C22semidirect
17. C2×C3×#638C22semidirect
18. C2×C32×#67C22semidirect
19. C2×C32×#67C22semidirect
20. C2×C32×#67C22semidirect
21. C2×C32×D12C22semidirect
25. C2×C3×#626C22semidirect
26. C2×C3×#625C22semidirect
27. C2×C3×#624C22semidirect
28. C2×C3×D3×Dic3C22semidirect
29. C3×#3757C22semidirect
30. C3×#3752C22semidirect
31. C32×#217C22semidirect
32. C32×(C2×D3)⋊C4C22semidirect
33. C32×C4×Dic3C22semidirect
34. C3×Dic3⋊Dic3C22semidirect
35. C3×(C2×D3)⋊Dic3C22semidirect
40. C2×#3811C2×C3semidirect
41. C2×D3×#67C2×C3semidirect
44. #64146C2×C3semidirect
46. C3×#940D3semidirect
47. C3×#940C2×C3semidirect
56. C3×#937D3semidirect
57. C3×#937C2×C3semidirect
62. #63970C2×C3semidirect
63. #63958C2×C3semidirect
64. #63922C2×C3semidirect
65. #63880C2×C3semidirect
89. C3×#626D4semidirect
97. C23×C3⋊D3C22×C3semidirect
104. C23×C3×D3C2×D3semidirect
105. C23×C3×D3C22×C3semidirect
106. C22×D32C22×C3semidirect
115. C2×C32×D4C2×D3semidirect
116. C2×C32×D4C2×D3semidirect
117. C2×C32×D4C22×C3semidirect
118. C2×#638C22×C3semidirect
130. C2×C3×#67C2×D3semidirect
131. C2×C3×#67C2×D3semidirect
132. C2×C3×#67C2×D3semidirect
133. C2×C3×#67C22×C3semidirect
134. C2×C3×#67C22×C3semidirect
135. C2×C3×#67C22×C3semidirect
143. C2×C3×D12C2×D3semidirect
144. C2×C3×D12C22×C3semidirect
151. C2×#626C22×C3semidirect
152. C2×#625C22×C3semidirect
153. C2×#624C22×C3semidirect
154. C2×D3×Dic3C22×C3semidirect
158. #3757C22×C3semidirect
159. #3752C22×C3semidirect
165. C3×#217C2×D3semidirect
166. C3×#217C22×C3semidirect
172. C3×(C2×D3)⋊C4C2×D3semidirect
173. C3×(C2×D3)⋊C4C22×C3semidirect
177. C3×C4×Dic3C2×D3semidirect
178. C3×C4×Dic3C22×C3semidirect
179. Dic3⋊Dic3C22×C3semidirect
180. (C2×D3)⋊Dic3C22×C3semidirect
189. C2×C3×C3⋊D3C2×D4semidirect
196. C2×C32×D3C2×D4semidirect
201. C32×Dic3C2×D4semidirect
219. #940C3×D3semidirect
227. #937C3×D3semidirect
340. #626C3×D4semidirect
362. C23×D3C2×C3×D3semidirect
385. C2×C3×D4D32semidirect
386. C2×C3×D4C2×C3×D3semidirect
387. C2×C3×D4C2×C3×D3semidirect
398. C2×#67C2×C3×D3semidirect
399. C2×#67C2×C3×D3semidirect
400. C2×#67C2×C3×D3semidirect
407. C2×D12C2×C3×D3semidirect
428. #217C2×C3×D3semidirect
433. (C2×D3)⋊C4C2×C3×D3semidirect
436. C4×Dic3C2×C3×D3semidirect
482. C2×C3⋊D3C2×C3×D4semidirect
516. C2×C3×D3D3×D4semidirect
517. C2×C3×D3C2×C3×D4semidirect
536. C3×Dic3D3×D4semidirect
537. C3×Dic3C2×C3×D4semidirect
547. C33D42semidirect
713. C2×D4C3×D32semidirect
804. C2×D3C3×D3×D4semidirect
823. Dic3C3×D3×D4semidirect
828. C32#5590semidirect
829. C32#5717semidirect
830. C32C3×D42semidirect
923. C3#10595295direct (N × H)
924. C3C3×#5590semidirect
925. C3C3×#5717semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38112
C2×C3×D3×#672
C3×#641462
C32×#9402
C32×#9372
C3×#639702
C3×#639582
C3×#639222
C3×#638802
C3×#57173
C3×#55903
#105952953