Finite Group Databasebeta

← C3×D3×#929 #13174658

Subgroups — C3×D3×#929 #13174658

Order 1728.

1814 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C211yesmaximal, characteristic
3C3×#64138C211yesmaximal, characteristic, complemented
4C32×#929C211yesmaximal, characteristic, complemented
5C3×D3×#217C211yesmaximal, characteristic, complemented
6C3×#63966C211yesmaximal, characteristic, complemented
7C3×#63961C211yesmaximal, characteristic, complemented
8C3×D3×(C2×D3)⋊C4C212yesmaximal, complemented
9C3×#63905C212yesmaximal, complemented
10C3×D3×Dic3⋊C4C212yesmaximal, complemented
11C3×#63850C212yesmaximal, complemented
12C2×C3×#929—31nomaximal
13C3×D3×#123—31nomaximal
14D3×#929C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2211yescharacteristic
16C22×C3×D32C2211yescharacteristic
17C22×C33×C4C2211yescharacteristic, complemented
18C2×C3×#638C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic, complemented
21C2×C32×C4×D3—24no—
22C2×C32×C4×D3C2212yes—
23C2×C32×C4×D3C2212yescomplemented
24C3×D3×#67—24no—
25C2×C3×#626C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2212yes—
29C3×#3757C2211yescharacteristic, complemented
30C3×#3752C2212yescomplemented
31C3×#3750C2212yescomplemented
32C32×#217C2211yescharacteristic, complemented
33C32×(C2×D3)⋊C4C2212yescomplemented
34C32×Dic3⋊C4C2212yescomplemented
35C3×#3724C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C23×C32×C4—31no—
41C22×C3×#67—31no—
42C2×C3×D3×D4—31no—
43C22×C3×C4×D3—21no—
44C22×C3×C4×D3D311yescharacteristic, complemented
45C22×C3×C4×D3C2×C311yescharacteristic, complemented
46C2×D3×#67C2×C311yescharacteristic
47C32×#123—31no—
48#64138C2×C311yescharacteristic, complemented
49C2×C3×#217—31no—
50C3×#935—31no—
51C3×#929—21no—
52C3×#929—31no—
53C3×#929—31no—
54C3×#929—31no—
55C3×#929—31no—
56C3×#929—32no—
57C3×#929—32no—
58C3×#929—61no—
59C3×#929D311yescharacteristic, direct product factor
60C3×#929C2×C311yescharacteristic, complemented
61C2×C3×(C2×D3)⋊C4—32no—
62C2×C3×Dic3⋊C4—32no—
63C3×#894—32no—
64C3×D3×C4⋊C4—32no—
65C3×#886—31no—
66C3×#883—32no—
67C3×D3×C22⋊C4—32no—
68C3×D3×C22⋊C4—31no—
69D3×#217C2×C311yescharacteristic, complemented
70#63966C2×C311yescharacteristic, complemented
71#63961C2×C311yescharacteristic, complemented
72D3×(C2×D3)⋊C4C2×C312yescomplemented
73#63905C2×C312yescomplemented
74D3×Dic3⋊C4C2×C312yescomplemented
75#63850C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3—24no—
79C22×C32×D3D414yes—
80C22×C32×D3C2311yescharacteristic
81C22×C32×D3C2311yescharacteristic
82C22×C32×D3C2311yescharacteristic
83C2×C3×D32—22no—
84C2×C3×D32—24no—
85C2×C33×C4—22no—
86C2×C33×C4C2312yes—
87C3×#638—22no—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊Dic3C2312yes—
90C32×#67—22no—
91C2×C32×Dic3—22no—
92C2×C32×Dic3C2312yes—
93C2×C32×Dic3C2311yescharacteristic
94C2×C32×Dic3C2312yes—
95C32×C4×D3—24no—
96C32×C4×D3—24no—
97C3×#626—22no—
98C3×#625—22no—
99C3×D3×Dic3—22no—
100C3×D3×Dic3—24no—
101C2×C3×#123—91no—
102C2×#929—31no—
103D3×#123—31no—
104C24×C32—31no—
105C23×C3×D3—21no—
106C23×C3×D3—31no—
107C23×C3×D3—31no—
108C23×C3×D3C2×D311yescharacteristic
109C23×C3×D3C22×C311yescharacteristic
110C22×D32C22×C311yescharacteristic
111C2×C32×D4—31no—
112C22×C32×C4—21no—
113C22×C32×C4—21no—
114C22×C32×C4—21no—
115C22×C32×C4—31no—
116C22×C32×C4—32no—
117C22×C32×C4—32no—
118C22×C32×C4—41no—
119C22×C32×C4—64no—
120C22×C32×C4C2×D311yescharacteristic, complemented
121C22×C32×C4C2×D311yescharacteristic, complemented
122C22×C32×C4C22×C311yescharacteristic, complemented
123C2×#638C22×C311yescharacteristic
124C2×C3×#67—21no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C2×C3×#67—31no—
130C2×C3×#67—64no—
131C2×C3×#67—61no—
132C2×C3×#67C2×D311yescharacteristic
133C2×C3×#67C22×C311yescharacteristic
134C22×C3×Dic3—21no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—32no—
137C22×C3×Dic3C2×D311yescharacteristic, complemented
138C22×C3×Dic3C22×C311yescharacteristic, complemented
139C3×D3×D4—64no—
140C2×C3×D12—31no—
141C2×C3×C4×D3—28no—
142C2×C3×C4×D3—22no—
143C2×C3×C4×D3—22no—
144C2×C3×C4×D3—24no—
145C2×C3×C4×D3—24no—
146C2×C3×C4×D3—32no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3C2×D312yes—
149C2×C3×C4×D3C2×D312yescomplemented
150C2×C3×C4×D3C22×C312yes—
151C2×C3×C4×D3C22×C312yescomplemented
152D3×#67—24no—
153C2×#626C22×C311yescharacteristic
154C2×#625C22×C311yescharacteristic
155C2×D3×Dic3C22×C311yescharacteristic
156C2×D3×Dic3C22×C312yes—
157C32×C4⋊C4—32no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—32no—
160#3757C22×C311yescharacteristic, complemented
161#3752C22×C312yescomplemented
162#3750C22×C312yescomplemented
163C3×#217—21no—
164C3×#217—31no—
165C3×#217—31no—
166C3×#217—32no—
167C3×#217—32no—
168C3×#217—61no—
169C3×#217C2×D311yescharacteristic, complemented
170C3×#217C22×C311yescharacteristic, complemented
171C3×(C2×D3)⋊C4—22no—
172C3×(C2×D3)⋊C4—32no—
173C3×(C2×D3)⋊C4—32no—
174C3×(C2×D3)⋊C4—32no—
175C3×(C2×D3)⋊C4—32no—
176C3×(C2×D3)⋊C4—32no—
177C3×(C2×D3)⋊C4—32no—
178C3×(C2×D3)⋊C4—62no—
179C3×(C2×D3)⋊C4C2×D312yescomplemented
180C3×(C2×D3)⋊C4C22×C312yescomplemented
181C3×C4⋊Dic3—32no—
182C3×Dic3⋊C4—22no—
183C3×Dic3⋊C4—32no—
184C3×Dic3⋊C4—32no—
185C3×Dic3⋊C4—32no—
186C3×Dic3⋊C4—32no—
187C3×Dic3⋊C4—32no—
188C3×Dic3⋊C4—62no—
189C3×Dic3⋊C4C2×D312yescomplemented
190C3×Dic3⋊C4C22×C312yescomplemented
191#3724C22×C312yescomplemented
192Dic3⋊Dic3C22×C312yescomplemented
193#3722C22×C312yescomplemented
194(C2×D3)⋊Dic3C22×C312yescomplemented
195(C2×D3)⋊Dic3C22×C312yescomplemented
196C22×C33—22no—
197C22×C33C2×D412yes—
198C22×C33C2411yescharacteristic
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—22no—
201C2×C32×D3—22no—
202C2×C32×D3—28no—
203C2×C32×D3—21no—
204C2×C32×D3—22no—
205C2×C32×D3C2×D412yes—
206C2×C32×D3C2×D412yes—
207C2×C32×D3#4114yes—
208C3×D32—44no—
209C33×C4—22no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—22no—
212C32×Dic3—22no—
213C32×Dic3—21no—
214C32×Dic3—22no—
215C22×C3×D4—91no—
216C23×C3×C4—31no—
217C23×C3×C4—31no—
218C23×C3×C4—61no—
219C22×#67—31no—
220C2×D3×D4—31no—
221C22×C4×D3C3×D311yescharacteristic, complemented
222C3×#123—31no—
223C3×#123—31no—
224C3×#123—61no—
225C3×#123—92no—
226C3×#123—91no—
227C3×#123—92no—
228C3×#123—91no—
229C3×#123—91no—
230C2×C3×C4⋊C4—92no—
231C2×C3×C22⋊C4—92no—
232C2×C3×C22⋊C4—91no—
233C2×#217—31no—
234#935—31no—
235#929—31no—
236#929—31no—
237#929—31no—
238#929—31no—
239#929—32no—
240#929—32no—
241#929—61no—
242#929C3×D311yescharacteristic, direct product factor
243C2×(C2×D3)⋊C4—32no—
244C2×Dic3⋊C4—32no—
245#894—32no—
246D3×C4⋊C4—32no—
247#886—31no—
248#883—32no—
249D3×C22⋊C4—31no—
250D3×C22⋊C4—32no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32—31no—
255C23×C32—34no—
256C23×C32—31no—
257C23×C32—31no—
258C23×C32—41no—
259C23×C32—64no—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C23×C32C23×C311yescharacteristic
263C22×C3⋊D3C23×C311yescharacteristic
264C22×C3×D3—28no—
265C22×C3×D3—24no—
266C22×C3×D3—24no—
267C22×C3×D3—24no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—61no—
274C22×C3×D3—64no—
275C22×C3×D3—62no—
276C22×C3×D3—64no—
277C22×C3×D3—62no—
278C22×C3×D3#6714yes—
279C22×C3×D3C3×D414yes—
280C22×C3×D3C22×D311yescharacteristic
281C22×C3×D3C22×D311yescharacteristic
282C22×C3×D3C22×D311yescharacteristic
283C22×C3×D3C23×C311yescharacteristic
284C22×C3×D3C23×C311yescharacteristic
285C22×C3×D3C23×C311yescharacteristic
286C2×D32—22no—
287C2×D32—24no—
288C32×D4—62no—
289C2×C32×C4—22no—
290C2×C32×C4—24no—
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4—22no—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4—32no—
297C2×C32×C4—31no—
298C2×C32×C4—32no—
299C2×C32×C4—42no—
300C2×C32×C4—42no—
301C2×C32×C4—42no—
302C2×C32×C4—44no—
303C2×C32×C4—64no—
304C2×C32×C4—64no—
305C2×C32×C4—62no—
306C2×C32×C4C22×D312yes—
307C2×C32×C4C22×D312yes—
308C2×C32×C4C23×C312yes—
309#638—22no—
310C2×C3⋊Dic3C23×C312yes—
311C2×C3⋊Dic3C23×C311yescharacteristic
312C3×#67—22no—
313C3×#67—22no—
314C3×#67—42no—
315C3×#67—62no—
316C3×#67—62no—
317C3×#67—62no—
318C3×#67—62no—
319C3×#67—62no—
320C3×#67—122no—
321C2×C3×Dic3—24no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—32no—
330C2×C3×Dic3—32no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—62no—
333C2×C3×Dic3—64no—
334C2×C3×Dic3—62no—
335C2×C3×Dic3C22×D311yescharacteristic
336C2×C3×Dic3C22×D312yes—
337C2×C3×Dic3C22×D312yes—
338C2×C3×Dic3C23×C312yes—
339C2×C3×Dic3C23×C312yes—
340C2×C3×Dic3C23×C311yescharacteristic
341C3×D12—62no—
342C3×C4×D3—28no—
343C3×C4×D3—28no—
344C3×C4×D3—24no—
345C3×C4×D3—24no—
346C3×C4×D3—24no—
347C3×C4×D3—24no—
348C3×C4×D3—64no—
349C3×C4×D3—62no—
350#626—22no—
351#625—22no—
352D3×Dic3—22no—
353D3×Dic3—24no—
354C2×#123—91noSylow
355C2×C33—22no—
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4112yes—
358C3×C3⋊D3—41no—
359C32×D3—22no—
360C32×D3—41no—
361C32×D3#12314yescomplemented
362C24×C3—31no—
363C24×C3—31no—
364C24×C3—61no—
365C24×C3—91no—
366C23×D3—31no—
367C23×D3—31no—
368C23×D3C2×C3×D311yescharacteristic
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—61no—
372C2×C3×D4—91no—
373C2×C3×D4—91no—
374C2×C3×D4—91no—
375C2×C3×D4—184no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—32no—
382C22×C3×C4—32no—
383C22×C3×C4—32no—
384C22×C3×C4—32no—
385C22×C3×C4—41no—
386C22×C3×C4—62no—
387C22×C3×C4—62no—
388C22×C3×C4—61no—
389C22×C3×C4—64no—
390C22×C3×C4—64no—
391C22×C3×C4—68no—
392C22×C3×C4—92no—
393C22×C3×C4—91no—
394C22×C3×C4D3211yescharacteristic, complemented
395C22×C3×C4C2×C3×D311yescharacteristic, complemented
396C22×C3×C4C2×C3×D311yescharacteristic, complemented
397C2×#67—31no—
398C2×#67—31no—
399C2×#67—31no—
400C2×#67—31no—
401C2×#67—31no—
402C2×#67—61no—
403C2×#67—64no—
404C2×#67C2×C3×D311yescharacteristic
405C22×Dic3—31no—
406C22×Dic3—32no—
407C22×Dic3C2×C3×D311yescharacteristic, complemented
408D3×D4—64no—
409C2×D12—31no—
410C2×C4×D3—24no—
411C2×C4×D3—32no—
412C2×C4×D3—31no—
413C2×C4×D3C2×C3×D312yes—
414C2×C4×D3C2×C3×D312yescomplemented
415C3×C4⋊C4—32no—
416C3×C4⋊C4—32no—
417C3×C4⋊C4—62no—
418C3×C4⋊C4—92no—
419C3×C4⋊C4—92no—
420C3×C4⋊C4—92no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—32no—
424C3×C22⋊C4—32no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—92no—
428C3×C22⋊C4—92no—
429C3×C22⋊C4—92no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—92no—
432#217—31no—
433#217—31no—
434#217—32no—
435#217—32no—
436#217—61no—
437#217C2×C3×D311yescharacteristic, complemented
438(C2×D3)⋊C4—32no—
439(C2×D3)⋊C4—32no—
440(C2×D3)⋊C4—32no—
441(C2×D3)⋊C4—32no—
442(C2×D3)⋊C4—32no—
443(C2×D3)⋊C4—32no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4C2×C3×D312yescomplemented
446C4⋊Dic3—32no—
447Dic3⋊C4—32no—
448Dic3⋊C4—32no—
449Dic3⋊C4—32no—
450Dic3⋊C4—32no—
451Dic3⋊C4—32no—
452Dic3⋊C4—62no—
453Dic3⋊C4C2×C3×D312yescomplemented
454C22×C32—22no—
455C22×C32—24no—
456C22×C32—22no—
457C22×C32—22no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—32no—
465C22×C32—34no—
466C22×C32—32no—
467C22×C32—42no—
468C22×C32—41no—
469C22×C32—42no—
470C22×C32—42no—
471C22×C32—44no—
472C22×C32—68no—
473C22×C32—62no—
474C22×C32—62no—
475C22×C32—61no—
476C22×C32D3×D412yes—
477C22×C32C2×#6712yes—
478C22×C32C2×C3×D412yes—
479C22×C32C23×D311yescharacteristic
480C22×C32C23×D311yescharacteristic
481C22×C32C24×C311yescharacteristic
482C2×C3⋊D3—21no—
483C2×C3⋊D3—22no—
484C2×C3×D3—24no—
485C2×C3×D3—216no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—28no—
489C2×C3×D3—28no—
490C2×C3×D3—21no—
491C2×C3×D3—22no—
492C2×C3×D3—21no—
493C2×C3×D3—22no—
494C2×C3×D3—24no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—41no—
498C2×C3×D3—42no—
499C2×C3×D3—62no—
500C2×C3×D3—61no—
501C2×C3×D3—62no—
502C2×C3×D3—61no—
503C2×C3×D3—121no—
504C2×C3×D3—122no—
505C2×C3×D3—124no—
506C2×C3×D3—124no—
507C2×C3×D3#23514yes—
508C2×C3×D3C2×#6712yes—
509C2×C3×D3C2×#6712yes—
510C2×C3×D3C2×C3×D412yes—
511C2×C3×D3C2×C3×D412yes—
512C2×C3×D3C3×#4114yes—
513D32—44no—
514C32×C4—22no—
515C32×C4—24no—
516C32×C4—22no—
517C32×C4—22no—
518C32×C4—42no—
519C32×C4—42no—
520C32×C4—44no—
521C32×C4—62no—
522C32×C4—62no—
523C32×C4—61no—
524C3⋊Dic3—21no—
525C3⋊Dic3—22no—
526C3×Dic3—24no—
527C3×Dic3—21no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—21no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—42no—
534C3×Dic3—41no—
535C3×Dic3—62no—
536C3×Dic3—61no—
537C3×Dic3—62no—
538C3×Dic3—61no—
539C3×Dic3—122no—
540C3×Dic3—121no—
541C22×D4—91no—
542C23×C4—31no—
543#123—31no—
544#123—92no—
545#123—91no—
546#123—92no—
547#123—91no—
548#123—91no—
549C2×C4⋊C4—92no—
550C2×C22⋊C4—92no—
551C2×C22⋊C4—91no—
552C33C2×#12311yescharacteristic, complemented, Sylow
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—31no—
557C23×C3—31no—
558C23×C3—31no—
559C23×C3—31no—
560C23×C3—34no—
561C23×C3—34no—
562C23×C3—31no—
563C23×C3—31no—
564C23×C3—41no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—64no—
568C23×C3—61no—
569C23×C3—64no—
570C23×C3—64no—
571C23×C3—68no—
572C23×C3—91no—
573C23×C3—182no—
574C23×C3—184no—
575C23×C3C2×D3211yescharacteristic
576C23×C3C22×C3×D311yescharacteristic
577C23×C3C22×C3×D311yescharacteristic
578C22×D3—24no—
579C22×D3—31no—
580C22×D3—31no—
581C22×D3—61no—
582C22×D3—62no—
583C22×D3—64no—
584C22×D3—64no—
585C22×D3—62no—
586C22×D3C3×#6714yes—
587C22×D3C22×C3×D311yescharacteristic
588C22×D3C22×C3×D311yescharacteristic
589C22×D3C22×C3×D311yescharacteristic
590C3×D4—62no—
591C3×D4—62no—
592C3×D4—122no—
593C3×D4—182no—
594C3×D4—182no—
595C3×D4—182no—
596C2×C3×C4—24no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—32no—
604C2×C3×C4—32no—
605C2×C3×C4—31no—
606C2×C3×C4—32no—
607C2×C3×C4—31no—
608C2×C3×C4—32no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—44no—
612C2×C3×C4—42no—
613C2×C3×C4—62no—
614C2×C3×C4—62no—
615C2×C3×C4—61no—
616C2×C3×C4—64no—
617C2×C3×C4—64no—
618C2×C3×C4—64no—
619C2×C3×C4—64no—
620C2×C3×C4—68no—
621C2×C3×C4—68no—
622C2×C3×C4—64no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—92no—
626C2×C3×C4—91no—
627C2×C3×C4—184no—
628C2×C3×C4—182no—
629C2×C3×C4C2×D3212yes—
630C2×C3×C4C22×C3×D312yes—
631C2×C3×C4C22×C3×D312yes—
632#67—22no—
633#67—62no—
634#67—62no—
635#67—62no—
636#67—62no—
637#67—62no—
638#67—122no—
639C2×Dic3—22no—
640C2×Dic3—31no—
641C2×Dic3—31no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—61no—
645C2×Dic3—62no—
646C2×Dic3—64no—
647C2×Dic3—62no—
648C2×Dic3C22×C3×D311yescharacteristic
649C2×Dic3C22×C3×D312yes—
650C2×Dic3C22×C3×D312yes—
651D12—62no—
652C4×D3—24no—
653C4×D3—24no—
654C4×D3—64no—
655C4×D3—62no—
656C2×C32—22no—
657C2×C32—24no—
658C2×C32—22no—
659C2×C32—22no—
660C2×C32—22no—
661C2×C32—21no—
662C2×C32—22no—
663C2×C32—21no—
664C2×C32—22no—
665C2×C32—21no—
666C2×C32—34no—
667C2×C32—41no—
668C2×C32—42no—
669C2×C32—42no—
670C2×C32—42no—
671C2×C32—44no—
672C2×C32—62no—
673C2×C32—121no—
674C2×C32C2×#23512yes—
675C2×C32C2×D3×D411yescharacteristic
676C2×C32D3×#4112yes—
677C2×C32C22×#6711yescharacteristic
678C2×C32C22×C3×D411yescharacteristic
679C2×C32C2×C3×#4112yes—
680C3⋊D3—41no—
681C3×D3—24no—
682C3×D3—22no—
683C3×D3—22no—
684C3×D3—24no—
685C3×D3—41no—
686C3×D3—41no—
687C3×D3—81no—
688C3×D3—121no—
689C3×D3—121no—
690C3×D3—241no—
691C3×D3#92914yesdirect product factor
692C3×D3C3×#12314yescomplemented
693C24—31no—
694C24—91no—
695C2×D4—31no—
696C2×D4—91no—
697C2×D4—91no—
698C2×D4—91no—
699C2×D4—184no—
700C22×C4—31no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—64no—
704C22×C4—92no—
705C22×C4—91no—
706C22×C4C3×D3211yescharacteristic, complemented
707C4⋊C4—32no—
708C4⋊C4—92no—
709C4⋊C4—92no—
710C4⋊C4—92no—
711C22⋊C4—31no—
712C22⋊C4—32no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4—92no—
716C22⋊C4—91no—
717C22⋊C4—92no—
718C22×C3—24no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—34no—
729C22×C3—32no—
730C22×C3—32no—
731C22×C3—34no—
732C22×C3—32no—
733C22×C3—32no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—44no—
737C22×C3—41no—
738C22×C3—42no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—64no—
742C22×C3—68no—
743C22×C3—68no—
744C22×C3—616no—
745C22×C3—64no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—62no—
749C22×C3—61no—
750C22×C3—62no—
751C22×C3—61no—
752C22×C3—121no—
753C22×C3—122no—
754C22×C3—182no—
755C22×C3—181no—
756C22×C3—364no—
757C22×C3D3×#6712yes—
758C22×C3C3×D3×D412yes—
759C22×C3C2×C3×#6712yes—
760C22×C3C22×D3211yescharacteristic
761C22×C3C23×C3×D311yescharacteristic
762C22×C3C23×C3×D311yescharacteristic
763C2×D3—22no—
764C2×D3—28no—
765C2×D3—21no—
766C2×D3—22no—
767C2×D3—62no—
768C2×D3—61no—
769C2×D3—62no—
770C2×D3—61no—
771C2×D3—121no—
772C2×D3—122no—
773C2×D3—124no—
774C2×D3—124no—
775C2×D3C3×#23514yes—
776C2×D3C2×C3×#6712yes—
777C2×D3C2×C3×#6712yes—
778C3×C4—24no—
779C3×C4—22no—
780C3×C4—22no—
781C3×C4—22no—
782C3×C4—42no—
783C3×C4—42no—
784C3×C4—44no—
785C3×C4—64no—
786C3×C4—62no—
787C3×C4—62no—
788C3×C4—61no—
789C3×C4—62no—
790C3×C4—62no—
791C3×C4—61no—
792C3×C4—121no—
793C3×C4—122no—
794C3×C4—182no—
795C3×C4—181no—
796Dic3—21no—
797Dic3—22no—
798Dic3—22no—
799Dic3—62no—
800Dic3—61no—
801Dic3—62no—
802Dic3—61no—
803Dic3—121no—
804Dic3—122no—
805C32—21no—
806C32—21no—
807C32—21no—
808C32—41no—
809C32D3×#12311yescharacteristic, complemented
810C32C2×#92911yescharacteristic, complemented
811C32C2×C3×#12311yescharacteristic, complemented
812C23—31no—
813C23—31no—
814C23—34no—
815C23—31no—
816C23—64no—
817C23—91no—
818C23—182no—
819C23—184no—
820C23C2×C3×D3211yescharacteristic
821D4—62no—
822D4—182no—
823D4—182no—
824D4—182no—
825C2×C4—22no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—31no—
829C2×C4—64no—
830C2×C4—64no—
831C2×C4—62no—
832C2×C4—92no—
833C2×C4—91no—
834C2×C4—182no—
835C2×C4—184no—
836C2×C4C2×C3×D3212yes—
837C2×C3—24no—
838C2×C3—22no—
839C2×C3—22no—
840C2×C3—22no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—22no—
845C2×C3—22no—
846C2×C3—22no—
847C2×C3—34no—
848C2×C3—34no—
849C2×C3—42no—
850C2×C3—42no—
851C2×C3—44no—
852C2×C3—41no—
853C2×C3—42no—
854C2×C3—64no—
855C2×C3—64no—
856C2×C3—62no—
857C2×C3—62no—
858C2×C3—121no—
859C2×C3—121no—
860C2×C3—241no—
861C2×C3—361no—
862C2×C3D3×#23512yes—
863C2×C3C2×D3×#6711yescharacteristic
864C2×C3C2×C3×#23512yes—
865C2×C3C2×C3×D3×D411yescharacteristic
866C2×C3C3×D3×#4112yes—
867C2×C3C22×C3×#6711yescharacteristic
868D3—22no—
869D3—41no—
870D3—121no—
871D3—121no—
872D3—241no—
873D3C3×#92914yesdirect product factor
874C22—22no—
875C22—32no—
876C22—34no—
877C22—32no—
878C22—68no—
879C22—62no—
880C22—61no—
881C22—62no—
882C22—181no—
883C22—182no—
884C22—364no—
885C22C3×D3×#6712yes—
886C22C22×C3×D3211yescharacteristic
887C4—22no—
888C4—62no—
889C4—61no—
890C4—62no—
891C4—181no—
892C4—182no—
893C3—21no—
894C3—21no—
895C3—21no—
896C3—41no—
897C3D3×#92911yescharacteristic, direct product factor
898C3C3×D3×#12311yescharacteristic, complemented
899C3C2×C3×#92911yescharacteristic, complemented
900C2—22no—
901C2—34no—
902C2—62no—
903C2—121no—
904C2—361no—
905C2C3×D3×#23512yes—
906C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC2×C3×D3×#67C2
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4×D3C2semidirect
3. C3×#64138C2semidirect
4. C32×#929C2semidirect
5. C3×D3×#217C2semidirect
6. C3×#63966C2semidirect
7. C3×#63961C2semidirect
8. C3×D3×(C2×D3)⋊C4C2semidirect
9. C3×#63905C2semidirect
10. C3×D3×Dic3⋊C4C2semidirect
11. C3×#63850C2semidirect
14. D3×#929C3direct (N × H)
17. C22×C33×C4C22semidirect
20. C22×C32×Dic3C22semidirect
23. C2×C32×C4×D3C22semidirect
29. C3×#3757C22semidirect
30. C3×#3752C22semidirect
31. C3×#3750C22semidirect
32. C32×#217C22semidirect
33. C32×(C2×D3)⋊C4C22semidirect
34. C32×Dic3⋊C4C22semidirect
35. C3×#3724C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C22×C3×C4×D3D3semidirect
45. C22×C3×C4×D3C2×C3semidirect
48. #64138C2×C3semidirect
59. C3×#929D3direct (N × H)
60. C3×#929C2×C3semidirect
69. D3×#217C2×C3semidirect
70. #63966C2×C3semidirect
71. #63961C2×C3semidirect
72. D3×(C2×D3)⋊C4C2×C3semidirect
73. #63905C2×C3semidirect
74. D3×Dic3⋊C4C2×C3semidirect
75. #63850C2×C3semidirect
120. C22×C32×C4C2×D3semidirect
121. C22×C32×C4C2×D3semidirect
122. C22×C32×C4C22×C3semidirect
137. C22×C3×Dic3C2×D3semidirect
138. C22×C3×Dic3C22×C3semidirect
149. C2×C3×C4×D3C2×D3semidirect
151. C2×C3×C4×D3C22×C3semidirect
160. #3757C22×C3semidirect
161. #3752C22×C3semidirect
162. #3750C22×C3semidirect
169. C3×#217C2×D3semidirect
170. C3×#217C22×C3semidirect
179. C3×(C2×D3)⋊C4C2×D3semidirect
180. C3×(C2×D3)⋊C4C22×C3semidirect
189. C3×Dic3⋊C4C2×D3semidirect
190. C3×Dic3⋊C4C22×C3semidirect
191. #3724C22×C3semidirect
192. Dic3⋊Dic3C22×C3semidirect
193. #3722C22×C3semidirect
194. (C2×D3)⋊Dic3C22×C3semidirect
195. (C2×D3)⋊Dic3C22×C3semidirect
221. C22×C4×D3C3×D3semidirect
242. #929C3×D3direct (N × H)
361. C32×D3#123semidirect
394. C22×C3×C4D32semidirect
395. C22×C3×C4C2×C3×D3semidirect
396. C22×C3×C4C2×C3×D3semidirect
407. C22×Dic3C2×C3×D3semidirect
414. C2×C4×D3C2×C3×D3semidirect
437. #217C2×C3×D3semidirect
445. (C2×D3)⋊C4C2×C3×D3semidirect
453. Dic3⋊C4C2×C3×D3semidirect
552. C33C2×#123semidirect
691. C3×D3#929direct (N × H)
692. C3×D3C3×#123semidirect
706. C22×C4C3×D32semidirect
809. C32D3×#123semidirect
810. C32C2×#929semidirect
811. C32C2×C3×#123semidirect
873. D3C3×#929direct (N × H)
897. C3D3×#929direct (N × H)
898. C3C3×D3×#123semidirect
899. C3C2×C3×#929semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×C3×D3×#672
C3×#641382
C32×#9292
C3×D3×#2172
C3×#639662
C3×#639612
C3×D3×(C2×D3)⋊C42
C3×#639052
C3×D3×Dic3⋊C42
C3×#638502
C2×C3×#9293
C3×D3×#1233
D3×#9293