Finite Group Databasebeta

← C3×#10595215 #13174761

Subgroups — C3×#10595215 #13174761

Order 1728.

1830 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic
2C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#67⋊Dic3C212yesmaximal, complemented
5C3×Dic3×#67C212yesmaximal, complemented
6C3×D3×#217C212yesmaximal, complemented
7C2×C3×(C2×D3)⋊Dic3C212yesmaximal, complemented
8C3×#63898C211yesmaximal, characteristic, complemented
9C3×Dic3×D12C211yesmaximal, characteristic, complemented
10C3×#63855C211yesmaximal, characteristic, complemented
11C3×#63841C211yesmaximal, characteristic, complemented
12C3×#5798—31nomaximal
13C3×#5545—31nomaximal
14#10595215C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2212yes—
16C2×C33×D4C2211yescharacteristic
17C22×C3×C3⋊Dic3C2212yescomplemented
18C2×C32×#67C2212yes—
19C22×C32×Dic3C2212yescomplemented
20C32×D3×D4C418yescomplemented
21C2×C32×D12C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C3×D3×Dic3C2212yescomplemented
24C2×C3×D3×Dic3C2212yescomplemented
25C3×#3757C2212yescomplemented
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
27C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C32×#217C2212yescomplemented
29C32×C4⋊Dic3C2211yescharacteristic, complemented
30C32×C4×Dic3C2211yescharacteristic, complemented
31C3×Dic3⋊Dic3C2211yescharacteristic, complemented
32C3×Dic3⋊Dic3C2211yescharacteristic, complemented
33C3×(C2×D3)⋊Dic3C2211yescharacteristic
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×Dic32C2212yescomplemented
39C22×C32×D4—31no—
40C2×C3×D3×D4—21no—
41C2×C3×D3×D4D311yescharacteristic
42C2×C3×D3×D4C2×C311yescharacteristic
43C32×C4×D4—31no—
44D4×C3⋊Dic3C2×C311yescharacteristic, complemented
45C2×C3×#217—32no—
46C2×C3×#217—32no—
47C3×D4×Dic3—21no—
48C3×D4×Dic3—31no—
49C3×D4×Dic3—31no—
50C3×D4×Dic3—32no—
51C3×D4×Dic3—32no—
52C3×D4×Dic3—31no—
53C3×D4×Dic3—31no—
54C3×D4×Dic3—61no—
55C3×D4×Dic3D311yescharacteristic, complemented
56C3×D4×Dic3C2×C311yescharacteristic, complemented
57C3×C4×#67—32no—
58C2×C3×(C2×D3)⋊C4—32no—
59C3×#926—31no—
60C3×#926—31no—
61C3×#893—31no—
62C3×#892—31no—
63C3×#67⋊C4—32no—
64C3×D3×C22⋊C4—32no—
65C3×C4×D12—31no—
66C3×#872—31no—
67#67⋊Dic3C2×C312yescomplemented
68Dic3×#67C2×C312yescomplemented
69D3×#217C2×C312yescomplemented
70C2×(C2×D3)⋊Dic3C2×C312yescomplemented
71#63898C2×C311yescharacteristic, complemented
72Dic3×D12C2×C311yescharacteristic, complemented
73#63855C2×C311yescharacteristic, complemented
74#63841C2×C311yescharacteristic, complemented
75C23×C33C2312yes—
76C22×C32×D3—42no—
77C22×C32×D3—42no—
78C22×C32×D3C2×C418yescomplemented
79C22×C32×D3C2311yescharacteristic
80C22×C32×D3C2312yes—
81C33×D4C2×C414yescomplemented
82C2×C33×C4C2311yescharacteristic
83C2×C3×C3⋊Dic3—42no—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C32×#67C2×C418yescomplemented
88C2×C32×Dic3—42no—
89C2×C32×Dic3C2311yescharacteristic
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93C32×D12C2×C414yescomplemented
94C32×C4×D3C2×C414yescomplemented
95C3×D3×Dic3—42no—
96C3×D3×Dic3—42no—
97C3×#518—91no—
98#5798—31no—
99#5545—31no—
100C24×C32—32no—
101C23×C3×D3—22no—
102C23×C3×D3C2×D312yes—
103C23×C3×D3C22×C312yes—
104C2×C32×D4—21no—
105C2×C32×D4—21no—
106C2×C32×D4—21no—
107C2×C32×D4—32no—
108C2×C32×D4—38no—
109C2×C32×D4—31no—
110C2×C32×D4—41no—
111C2×C32×D4C2×D311yescharacteristic
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C22×C311yescharacteristic
114C22×C32×C4—31no—
115C22×C32×C4—32no—
116C22×C3⋊Dic3C22×C312yescomplemented
117C2×C3×#67—22no—
118C2×C3×#67C2×D312yes—
119C2×C3×#67C22×C312yes—
120C22×C3×Dic3—22no—
121C22×C3×Dic3—32no—
122C22×C3×Dic3—32no—
123C22×C3×Dic3—32no—
124C22×C3×Dic3—32no—
125C22×C3×Dic3—62no—
126C22×C3×Dic3C2×D312yescomplemented
127C22×C3×Dic3C22×C312yescomplemented
128C3×D3×D4—28no—
129C3×D3×D4Dic318yescomplemented
130C3×D3×D4C3×C418yescomplemented
131C2×C3×D12—21no—
132C2×C3×D12C2×D311yescharacteristic
133C2×C3×D12C22×C311yescharacteristic
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×C4×D3C22×C311yescharacteristic
139C2×D3×Dic3C22×C312yescomplemented
140C2×D3×Dic3C22×C312yescomplemented
141C32×C4⋊C4—31no—
142C32×C22⋊C4—32no—
143C32×C42—31no—
144#3757C22×C312yescomplemented
145C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
146C4×C3⋊Dic3C22×C311yescharacteristic, complemented
147C3×#217—22no—
148C3×#217—32no—
149C3×#217—32no—
150C3×#217—32no—
151C3×#217—31no—
152C3×#217—31no—
153C3×#217—32no—
154C3×#217—32no—
155C3×#217—62no—
156C3×#217C2×D312yescomplemented
157C3×#217C22×C312yescomplemented
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—32no—
160C3×(C2×D3)⋊C4—32no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—32no—
163C3×C4⋊Dic3—21no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—31no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—61no—
169C3×C4⋊Dic3C2×D311yescharacteristic, complemented
170C3×C4⋊Dic3C22×C311yescharacteristic, complemented
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4—31no—
173C3×C4×Dic3—21no—
174C3×C4×Dic3—31no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—32no—
177C3×C4×Dic3—32no—
178C3×C4×Dic3—61no—
179C3×C4×Dic3C2×D311yescharacteristic, complemented
180C3×C4×Dic3C22×C311yescharacteristic, complemented
181Dic3⋊Dic3C22×C311yescharacteristic, complemented
182Dic3⋊Dic3C22×C311yescharacteristic, complemented
183(C2×D3)⋊Dic3C22×C312yes—
184(C2×D3)⋊Dic3C22×C311yescharacteristic
185(C2×D3)⋊Dic3C22×C311yescharacteristic
186(C2×D3)⋊Dic3C22×C312yescomplemented
187(C2×D3)⋊Dic3C22×C312yescomplemented
188Dic32C22×C312yescomplemented
189C22×C33—22no—
190C22×C33—22no—
191C22×C33C22×C414yes—
192C22×C33C2411yescharacteristic
193C2×C32×D3—21no—
194C2×C32×D3—21no—
195C2×C32×D3—22no—
196C2×C32×D3—22no—
197C2×C32×D3—48no—
198C2×C32×D3C22×C412yes—
199C2×C32×D3C22×C414yes—
200C33×C4C22×C412yes—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—22no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3—22no—
207C32×Dic3C22×C412yes—
208C22×C3×D4—31no—
209C22×C3×D4—31no—
210C22×C3×D4—61no—
211C2×D3×D4C3×D311yescharacteristic
212C3×C4×D4—31no—
213C3×C4×D4—31no—
214C3×C4×D4—61no—
215C3×C4×D4—91no—
216C3×C4×D4—92no—
217C3×C4×D4—91no—
218C3×C4×D4—92no—
219C3×C4×D4—91no—
220C3×#117—91no—
221C3×#117—91no—
222C2×C3×C22⋊C4—92no—
223C2×C3×C22⋊C4—92no—
224C2×#217—32no—
225C2×#217—32no—
226D4×Dic3—31no—
227D4×Dic3—31no—
228D4×Dic3—32no—
229D4×Dic3—32no—
230D4×Dic3—31no—
231D4×Dic3—31no—
232D4×Dic3—61no—
233D4×Dic3C3×D311yescharacteristic, complemented
234C4×#67—32no—
235C2×(C2×D3)⋊C4—32no—
236#926—31no—
237#926—31no—
238#893—31no—
239#892—31no—
240#67⋊C4—32no—
241D3×C22⋊C4—32no—
242C4×D12—31no—
243#872—31no—
244C23×C32—22no—
245C23×C32—22no—
246C23×C32—22no—
247C23×C32—31no—
248C23×C32—32no—
249C23×C32—38no—
250C23×C32—42no—
251C23×C32—122no—
252C23×C32—122no—
253C23×C32C22×D312yes—
254C23×C32C22×D312yes—
255C23×C32C23×C312yes—
256C22×C3×D3—28no—
257C22×C3×D3—21no—
258C22×C3×D3—22no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3C2×Dic318yescomplemented
266C22×C3×D3C2×C3×C418yescomplemented
267C22×C3×D3C22×D311yescharacteristic
268C22×C3×D3C22×D312yes—
269C22×C3×D3C23×C311yescharacteristic
270C22×C3×D3C23×C312yes—
271C32×D4—24no—
272C32×D4—24no—
273C32×D4—24no—
274C32×D4—38no—
275C32×D4—34no—
276C32×D4—44no—
277C32×D4C4×D314yescomplemented
278C32×D4C2×Dic314yescomplemented
279C32×D4C2×C3×C414yescomplemented
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—31no—
284C2×C32×C4—34no—
285C2×C32×C4—32no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4—41no—
289C2×C32×C4—122no—
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C23×C311yescharacteristic
293C2×C3⋊Dic3—42no—
294C2×C3⋊Dic3C23×C312yes—
295C2×C3⋊Dic3C23×C311yescharacteristic
296C2×C3⋊Dic3C23×C311yescharacteristic
297C3×#67—28no—
298C3×#67C2×Dic318yescomplemented
299C3×#67C2×C3×C418yescomplemented
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—32no—
310C2×C3×Dic3—42no—
311C2×C3×Dic3—42no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3—122no—
317C2×C3×Dic3—122no—
318C2×C3×Dic3—122no—
319C2×C3×Dic3—122no—
320C2×C3×Dic3—124no—
321C2×C3×Dic3C22×D312yes—
322C2×C3×Dic3C22×D311yescharacteristic
323C2×C3×Dic3C22×D311yescharacteristic
324C2×C3×Dic3C22×D311yescharacteristic
325C2×C3×Dic3C23×C312yes—
326C2×C3×Dic3C23×C311yescharacteristic
327C2×C3×Dic3C23×C311yescharacteristic
328C2×C3×Dic3C23×C311yescharacteristic
329C3×D12—24no—
330C3×D12C2×Dic314yescomplemented
331C3×D12C2×C3×C414yescomplemented
332C3×C4×D3—24no—
333C3×C4×D3—122no—
334C3×C4×D3—122no—
335C3×C4×D3C2×Dic314yescomplemented
336C3×C4×D3C2×C3×C414yescomplemented
337D3×Dic3—42no—
338D3×Dic3—42no—
339#518—91noSylow
340C2×C33—24no—
341C2×C33C23×C411yescharacteristic
342C2×C33H(5,𝔽2)11yescharacteristic
343C2×C33H(5,𝔽2)11yescharacteristic
344C32×D3—22no—
345C32×D3—24no—
346C24×C3—32no—
347C24×C3—32no—
348C24×C3—62no—
349C23×D3C2×C3×D312yes—
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—21no—
353C2×C3×D4—32no—
354C2×C3×D4—32no—
355C2×C3×D4—38no—
356C2×C3×D4—38no—
357C2×C3×D4—31no—
358C2×C3×D4—31no—
359C2×C3×D4—41no—
360C2×C3×D4—61no—
361C2×C3×D4—68no—
362C2×C3×D4—62no—
363C2×C3×D4D3211yescharacteristic
364C2×C3×D4C2×C3×D311yescharacteristic
365C2×C3×D4C2×C3×D311yescharacteristic
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—32no—
369C22×C3×C4—32no—
370C22×C3×C4—61no—
371C22×C3×C4—62no—
372C22×C3×C4—92no—
373C22×C3×C4—92no—
374C22×C3×C4—92no—
375C2×#67C2×C3×D312yes—
376C22×Dic3—32no—
377C22×Dic3—32no—
378C22×Dic3—32no—
379C22×Dic3—32no—
380C22×Dic3—62no—
381C22×Dic3C2×C3×D312yescomplemented
382D3×D4C3×Dic318yescomplemented
383C2×D12C2×C3×D311yescharacteristic
384C2×C4×D3—32no—
385C2×C4×D3—32no—
386C2×C4×D3C2×C3×D311yescharacteristic
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C4⋊C4—91no—
393C3×C22⋊C4—32no—
394C3×C22⋊C4—32no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—92no—
399C3×C22⋊C4—92no—
400C3×C22⋊C4—92no—
401C3×C22⋊C4—92no—
402C3×C42—31no—
403C3×C42—31no—
404C3×C42—61no—
405C3×C42—92no—
406C3×C42—91no—
407#217—32no—
408#217—32no—
409#217—32no—
410#217—31no—
411#217—31no—
412#217—32no—
413#217—32no—
414#217—62no—
415#217C2×C3×D312yescomplemented
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—32no—
420(C2×D3)⋊C4—32no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3C2×C3×D311yescharacteristic, complemented
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—32no—
432C4×Dic3—32no—
433C4×Dic3—61no—
434C4×Dic3C2×C3×D311yescharacteristic, complemented
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—24no—
445C22×C32—24no—
446C22×C32—24no—
447C22×C32—32no—
448C22×C32—34no—
449C22×C32—41no—
450C22×C32—44no—
451C22×C32—42no—
452C22×C32—42no—
453C22×C32—42no—
454C22×C32—42no—
455C22×C32—42no—
456C22×C32—42no—
457C22×C32—61no—
458C22×C32—61no—
459C22×C32—62no—
460C22×C32—62no—
461C22×C32—82no—
462C22×C32—82no—
463C22×C32—128no—
464C22×C32C2×C4×D314yes—
465C22×C32C22×Dic314yes—
466C22×C32C22×C3×C414yes—
467C22×C32C23×D311yescharacteristic
468C22×C32C23×D311yescharacteristic
469C22×C32C24×C311yescharacteristic
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—21no—
479C2×C3×D3—21no—
480C2×C3×D3—22no—
481C2×C3×D3—24no—
482C2×C3×D3—42no—
483C2×C3×D3—42no—
484C2×C3×D3—48no—
485C2×C3×D3—48no—
486C2×C3×D3—416no—
487C2×C3×D3C22×Dic312yes—
488C2×C3×D3C22×Dic314yes—
489C2×C3×D3C22×C3×C412yes—
490C2×C3×D3C22×C3×C414yes—
491C32×C4—22no—
492C32×C4—22no—
493C32×C4—22no—
494C32×C4—32no—
495C32×C4—42no—
496C32×C4—61no—
497C32×C4—61no—
498C32×C4—62no—
499C32×C4C2×C4×D312yes—
500C32×C4C22×Dic312yes—
501C32×C4C22×C3×C412yes—
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—21no—
507C3×Dic3—22no—
508C3×Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3—22no—
511C3×Dic3—21no—
512C3×Dic3—22no—
513C3×Dic3—41no—
514C3×Dic3—42no—
515C3×Dic3—62no—
516C3×Dic3—61no—
517C3×Dic3—62no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—62no—
522C3×Dic3—121no—
523C3×Dic3—122no—
524C3×Dic3C22×Dic312yes—
525C3×Dic3C22×C3×C412yes—
526C22×D4—31no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—92no—
530C4×D4—91no—
531C4×D4—92no—
532C4×D4—91no—
533#117—91no—
534#117—91no—
535C2×C22⋊C4—92no—
536C2×C22⋊C4—92no—
537C33#51811yescharacteristic, complemented, Sylow
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—31no—
542C23×C3—32no—
543C23×C3—31no—
544C23×C3—32no—
545C23×C3—38no—
546C23×C3—38no—
547C23×C3—42no—
548C23×C3—61no—
549C23×C3—62no—
550C23×C3—68no—
551C23×C3—122no—
552C23×C3—122no—
553C23×C3—122no—
554C23×C3—122no—
555C23×C3—124no—
556C23×C3—124no—
557C23×C3C2×D3212yes—
558C23×C3C22×C3×D312yes—
559C23×C3C22×C3×D312yes—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3C2×C3×Dic318yescomplemented
563C22×D3C22×C3×D311yescharacteristic
564C22×D3C22×C3×D312yes—
565C3×D4—24no—
566C3×D4—24no—
567C3×D4—24no—
568C3×D4—38no—
569C3×D4—38no—
570C3×D4—34no—
571C3×D4—34no—
572C3×D4—44no—
573C3×D4—64no—
574C3×D4—68no—
575C3×D4D3×Dic314yescomplemented
576C3×D4C3×C4×D314yescomplemented
577C3×D4C2×C3×Dic314yescomplemented
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—34no—
584C2×C3×C4—34no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—41no—
592C2×C3×C4—64no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—62no—
597C2×C3×C4—91no—
598C2×C3×C4—91no—
599C2×C3×C4—92no—
600C2×C3×C4—122no—
601C2×C3×C4—122no—
602C2×C3×C4—124no—
603C2×C3×C4—362no—
604C2×C3×C4—362no—
605C2×C3×C4—362no—
606C2×C3×C4C2×D3211yescharacteristic
607C2×C3×C4C22×C3×D311yescharacteristic
608C2×C3×C4C22×C3×D311yescharacteristic
609#67C2×C3×Dic318yescomplemented
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—32no—
613C2×Dic3—31no—
614C2×Dic3—32no—
615C2×Dic3—31no—
616C2×Dic3—42no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—62no—
620C2×Dic3—122no—
621C2×Dic3—122no—
622C2×Dic3—122no—
623C2×Dic3—122no—
624C2×Dic3—124no—
625C2×Dic3C22×C3×D312yes—
626C2×Dic3C22×C3×D311yescharacteristic
627C2×Dic3C22×C3×D311yescharacteristic
628C2×Dic3C22×C3×D311yescharacteristic
629D12C2×C3×Dic314yescomplemented
630C4×D3—122no—
631C4×D3—122no—
632C4×D3C2×C3×Dic314yescomplemented
633C2×C32—24no—
634C2×C32—24no—
635C2×C32—24no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—21no—
645C2×C32—41no—
646C2×C32—41no—
647C2×C32—41no—
648C2×C32—44no—
649C2×C32—44no—
650C2×C32—44no—
651C2×C32—62no—
652C2×C32—64no—
653C2×C32—84no—
654C2×C32C22×C4×D311yescharacteristic
655C2×C32#100411yescharacteristic
656C2×C32#100411yescharacteristic
657C2×C32#100411yescharacteristic
658C2×C32#100911yescharacteristic
659C2×C32C23×Dic311yescharacteristic
660C2×C32C23×C3×C411yescharacteristic
661C2×C32C3×H(5,𝔽2)11yescharacteristic
662C2×C32C3×H(5,𝔽2)11yescharacteristic
663C3×D3—24no—
664C3×D3—22no—
665C3×D3—24no—
666C3×D3—22no—
667C3×D3—24no—
668C3×D3—44no—
669C24—32no—
670C2×D4—32no—
671C2×D4—38no—
672C2×D4—31no—
673C2×D4C3×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—32no—
676C22×C4—92no—
677C22×C4—92no—
678C22×C4—92no—
679C4⋊C4—31no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C4⋊C4—91no—
683C22⋊C4—32no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—92no—
687C22⋊C4—92no—
688C22⋊C4—92no—
689C22⋊C4—92no—
690C42—31no—
691C42—92no—
692C42—91no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—24no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—32no—
706C22×C3—34no—
707C22×C3—32no—
708C22×C3—34no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—44no—
717C22×C3—62no—
718C22×C3—64no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—61no—
723C22×C3—62no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—61no—
727C22×C3—62no—
728C22×C3—61no—
729C22×C3—82no—
730C22×C3—82no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—128no—
734C22×C3—128no—
735C22×C3—1216no—
736C22×C3C2×D3×Dic314yes—
737C22×C3C2×C3×C4×D314yes—
738C22×C3C22×C3×Dic314yes—
739C22×C3C22×D3211yescharacteristic
740C22×C3C23×C3×D311yescharacteristic
741C22×C3C23×C3×D311yescharacteristic
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—48no—
747C2×D3C22×C3×Dic312yes—
748C2×D3C22×C3×Dic314yes—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—32no—
753C3×C4—32no—
754C3×C4—42no—
755C3×C4—62no—
756C3×C4—62no—
757C3×C4—61no—
758C3×C4—62no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—62no—
762C3×C4—61no—
763C3×C4—122no—
764C3×C4—121no—
765C3×C4—181no—
766C3×C4—181no—
767C3×C4—182no—
768C3×C4C2×D3×Dic312yes—
769C3×C4C2×C3×C4×D312yes—
770C3×C4C22×C3×Dic312yes—
771Dic3—21no—
772Dic3—22no—
773Dic3—21no—
774Dic3—62no—
775Dic3—61no—
776Dic3—62no—
777Dic3—61no—
778Dic3—61no—
779Dic3—61no—
780Dic3—62no—
781Dic3—122no—
782Dic3—121no—
783Dic3C22×C3×Dic312yes—
784C32—21no—
785C32—21no—
786C32—21no—
787C32—41no—
788C32#554511yescharacteristic, complemented
789C32#579811yescharacteristic, complemented
790C32C3×#51811yescharacteristic, complemented
791C23—31no—
792C23—32no—
793C23—38no—
794C23—122no—
795C23—122no—
796C23C2×C3×D3212yes—
797D4—38no—
798D4—34no—
799D4C3×D3×Dic314yescomplemented
800C2×C4—31no—
801C2×C4—34no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—32no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—92no—
808C2×C4—122no—
809C2×C4—362no—
810C2×C4—362no—
811C2×C4—362no—
812C2×C4C2×C3×D3211yescharacteristic
813C2×C3—24no—
814C2×C3—24no—
815C2×C3—24no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—44no—
826C2×C3—44no—
827C2×C3—44no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—64no—
832C2×C3—62no—
833C2×C3—64no—
834C2×C3—62no—
835C2×C3—64no—
836C2×C3—84no—
837C2×C3—124no—
838C2×C3#6431311yescharacteristic
839C2×C3#6431411yescharacteristic
840C2×C3C22×D3×Dic311yescharacteristic
841C2×C3C22×C3×C4×D311yescharacteristic
842C2×C3C3×#100411yescharacteristic
843C2×C3C3×#100411yescharacteristic
844C2×C3C3×#100411yescharacteristic
845C2×C3C3×#100911yescharacteristic
846C2×C3C23×C3×Dic311yescharacteristic
847D3—22no—
848D3—24no—
849C22—22no—
850C22—22no—
851C22—32no—
852C22—34no—
853C22—62no—
854C22—61no—
855C22—62no—
856C22—61no—
857C22—128no—
858C22C2×C3×D3×Dic314yes—
859C22C22×C3×D3211yescharacteristic
860C4—32no—
861C4—61no—
862C4—62no—
863C4—61no—
864C4—181no—
865C4—181no—
866C4—182no—
867C4C2×C3×D3×Dic312yes—
868C3—21no—
869C3—21no—
870C3—21no—
871C3—41no—
872C3#1059521511yescharacteristic, direct product factor
873C3C3×#554511yescharacteristic, complemented
874C3C3×#579811yescharacteristic, complemented
875C2—24no—
876C2—62no—
877C2—64no—
878C2C3×#6431311yescharacteristic
879C2C3×#6431411yescharacteristic
880C2C22×C3×D3×Dic311yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC2×C32×D3×D4C2
cosocleC22×C32C24×C3
hypercenterC2×C3×D4D32
hypocenterC32C3×#518
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×C3⋊Dic3C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#67⋊Dic3C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×D3×#217C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. C3×#63898C2semidirect
9. C3×Dic3×D12C2semidirect
10. C3×#63855C2semidirect
11. C3×#63841C2semidirect
14. #10595215C3direct (N × H)
17. C22×C3×C3⋊Dic3C22semidirect
19. C22×C32×Dic3C22semidirect
20. C32×D3×D4C4semidirect
23. C2×C3×D3×Dic3C22semidirect
24. C2×C3×D3×Dic3C22semidirect
25. C3×#3757C22semidirect
26. C3×C4⋊(C3⋊Dic3)C22semidirect
27. C3×C4×C3⋊Dic3C22semidirect
28. C32×#217C22semidirect
29. C32×C4⋊Dic3C22semidirect
30. C32×C4×Dic3C22semidirect
31. C3×Dic3⋊Dic3C22semidirect
32. C3×Dic3⋊Dic3C22semidirect
36. C3×(C2×D3)⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×Dic32C22semidirect
44. D4×C3⋊Dic3C2×C3semidirect
55. C3×D4×Dic3D3semidirect
56. C3×D4×Dic3C2×C3semidirect
67. #67⋊Dic3C2×C3semidirect
68. Dic3×#67C2×C3semidirect
69. D3×#217C2×C3semidirect
70. C2×(C2×D3)⋊Dic3C2×C3semidirect
71. #63898C2×C3semidirect
72. Dic3×D12C2×C3semidirect
73. #63855C2×C3semidirect
74. #63841C2×C3semidirect
78. C22×C32×D3C2×C4semidirect
81. C33×D4C2×C4semidirect
87. C32×#67C2×C4semidirect
93. C32×D12C2×C4semidirect
94. C32×C4×D3C2×C4semidirect
116. C22×C3⋊Dic3C22×C3semidirect
126. C22×C3×Dic3C2×D3semidirect
127. C22×C3×Dic3C22×C3semidirect
129. C3×D3×D4Dic3semidirect
130. C3×D3×D4C3×C4semidirect
139. C2×D3×Dic3C22×C3semidirect
140. C2×D3×Dic3C22×C3semidirect
144. #3757C22×C3semidirect
145. C4⋊(C3⋊Dic3)C22×C3semidirect
146. C4×C3⋊Dic3C22×C3semidirect
156. C3×#217C2×D3semidirect
157. C3×#217C22×C3semidirect
169. C3×C4⋊Dic3C2×D3semidirect
170. C3×C4⋊Dic3C22×C3semidirect
179. C3×C4×Dic3C2×D3semidirect
180. C3×C4×Dic3C22×C3semidirect
181. Dic3⋊Dic3C22×C3semidirect
182. Dic3⋊Dic3C22×C3semidirect
186. (C2×D3)⋊Dic3C22×C3semidirect
187. (C2×D3)⋊Dic3C22×C3semidirect
188. Dic32C22×C3semidirect
233. D4×Dic3C3×D3semidirect
265. C22×C3×D3C2×Dic3semidirect
266. C22×C3×D3C2×C3×C4semidirect
277. C32×D4C4×D3semidirect
278. C32×D4C2×Dic3semidirect
279. C32×D4C2×C3×C4semidirect
298. C3×#67C2×Dic3semidirect
299. C3×#67C2×C3×C4semidirect
330. C3×D12C2×Dic3semidirect
331. C3×D12C2×C3×C4semidirect
335. C3×C4×D3C2×Dic3semidirect
336. C3×C4×D3C2×C3×C4semidirect
381. C22×Dic3C2×C3×D3semidirect
382. D3×D4C3×Dic3semidirect
415. #217C2×C3×D3semidirect
426. C4⋊Dic3C2×C3×D3semidirect
434. C4×Dic3C2×C3×D3semidirect
537. C33#518semidirect
562. C22×D3C2×C3×Dic3semidirect
575. C3×D4D3×Dic3semidirect
576. C3×D4C3×C4×D3semidirect
577. C3×D4C2×C3×Dic3semidirect
609. #67C2×C3×Dic3semidirect
629. D12C2×C3×Dic3semidirect
632. C4×D3C2×C3×Dic3semidirect
788. C32#5545semidirect
789. C32#5798semidirect
790. C32C3×#518semidirect
799. D4C3×D3×Dic3semidirect
872. C3#10595215direct (N × H)
873. C3C3×#5545semidirect
874. C3C3×#5798semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C3×D4×C3⋊Dic32
C32×D4×Dic32
C3×#67⋊Dic32
C3×Dic3×#672
C3×D3×#2172
C2×C3×(C2×D3)⋊Dic32
C3×#638982
C3×Dic3×D122
C3×#638552
C3×#638412
C3×#57983
C3×#55453
#105952153