Finite Group Databasebeta

← C3×#10594979 #13174621

Subgroups — C3×#10594979 #13174621

Order 1728.

1354 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3752C211yesmaximal, characteristic, complemented
2C32×#930C211yesmaximal, characteristic, complemented
3C32×#924C211yesmaximal, characteristic, complemented
4C3×#63981C212yesmaximal, complemented
5C3×#67⋊Dic3C212yesmaximal, complemented
6C3×#63907C212yesmaximal, complemented
7C3×#63890C212yesmaximal, complemented
8C3×#63886C212yesmaximal, complemented
9C3×#63848C212yesmaximal, complemented
10C3×#5644—31nomaximal
11C3×#5617—31nomaximal
12#10594979C311yesmaximal, characteristic, direct product factor
13C23×C3×C3⋊D3C2211yescharacteristic
14C22×C33×C4C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C2×C32×#67C2212yes—
17C2×C32×D12C2211yescharacteristic, complemented
18C2×C32×Dic6C2211yescharacteristic, complemented
19C2×C3×#626C2212yes—
20C2×C3×#626C2212yes—
21C2×C3×D3×Dic3C2212yescomplemented
22C3×#3752C2212yes—
23C3×#3752C2212yes—
24C32×#217C2212yes—
25C32×(C2×D3)⋊C4C2212yescomplemented
26C32×C4⋊Dic3C2211yescharacteristic, complemented
27C32×C4⋊Dic3C2211yescharacteristic, complemented
28C32×Dic3⋊C4C2212yescomplemented
29C3×Dic3⋊Dic3C2212yescomplemented
30C3×#3722C2212yes—
31C3×#3722C2212yes—
32C3×(C2×D3)⋊Dic3C2212yescomplemented
33C3×Dic32C2212yescomplemented
34C32×C22⋊Q8—31no—
35C32×#121—31no—
36C2×#3752C2×C311yescharacteristic, complemented
37C3×#947—32no—
38C3×#939—32no—
39C3×#937—32no—
40C3×D4×Dic3—32no—
41C3×#930—21no—
42C3×#930D311yescharacteristic, complemented
43C3×#930C2×C311yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4—31no—
45C2×C3×(C2×D3)⋊C4—31no—
46C2×C3×(C2×D3)⋊C4—61no—
47C3×#924—21no—
48C3×#924D311yescharacteristic, complemented
49C3×#924C2×C311yescharacteristic, complemented
50C3×#898—32no—
51C3×#898—32no—
52C3×#895—32no—
53C3×#894—32no—
54C3×#886—32no—
55C3×#885—32no—
56C3×#882—32no—
57C3×#67⋊C4—32no—
58#63981C2×C312yescomplemented
59#67⋊Dic3C2×C312yescomplemented
60#63907C2×C312yescomplemented
61#63890C2×C312yescomplemented
62#63886C2×C312yescomplemented
63#63848C2×C312yescomplemented
64C23×C33C2311yescharacteristic
65C22×C3×C3⋊D3—22no—
66C22×C3×C3⋊D3—41no—
67C22×C3×C3⋊D3—41no—
68C22×C3×C3⋊D3C2312yes—
69C22×C32×D3C2312yes—
70C2×C33×C4—41no—
71C2×C33×C4C2311yescharacteristic
72C2×C33×C4C2311yescharacteristic
73C2×C3×C3⋊Dic3—41no—
74C2×C3×C3⋊Dic3C2312yes—
75C32×#67—24no—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78C2×C32×Dic3C2312yes—
79C32×D12—41no—
80C32×Dic6—41no—
81C3×#626—42no—
82C3×#626—42no—
83C3×D3×Dic3—42no—
84C3×#538—91no—
85#5644—31no—
86#5617—31no—
87C23×C3⋊D3C22×C311yescharacteristic
88C23×C3×D3—31no—
89C23×C3×D3—31no—
90C23×C3×D3—61no—
91C2×C32×Q8—31no—
92C2×C32×D4—32no—
93C2×C32×D4—31no—
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C22×C32×C4—41no—
98C22×C32×C4C2×D311yescharacteristic
99C22×C32×C4C2×D311yescharacteristic
100C22×C32×C4C22×C311yescharacteristic
101C22×C3⋊Dic3C22×C311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—32no—
104C2×C3×#67—32no—
105C2×C3×#67C2×D312yes—
106C2×C3×#67C22×C312yes—
107C22×C3×Dic3—31no—
108C22×C3×Dic3—31no—
109C22×C3×Dic3—32no—
110C22×C3×Dic3—61no—
111C2×C3×D12—21no—
112C2×C3×D12—32no—
113C2×C3×D12—32no—
114C2×C3×D12C2×D311yescharacteristic, complemented
115C2×C3×D12C22×C311yescharacteristic, complemented
116C2×C3×C4×D3—32no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2×D311yescharacteristic, complemented
119C2×C3×Dic6C22×C311yescharacteristic, complemented
120C2×#626C22×C312yes—
121C2×#626C22×C312yes—
122C2×D3×Dic3C22×C312yescomplemented
123C32×C4⋊C4—31no—
124C32×C4⋊C4—32no—
125C32×C4⋊C4—31no—
126C32×C22⋊C4—32no—
127C32×C22⋊C4—32no—
128#3752C22×C312yes—
129#3752C22×C312yes—
130C3×#217—22no—
131C3×#217—32no—
132C3×#217C2×D312yes—
133C3×#217C22×C312yes—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—62no—
145C3×(C2×D3)⋊C4—62no—
146C3×(C2×D3)⋊C4C2×D312yescomplemented
147C3×(C2×D3)⋊C4C22×C312yescomplemented
148C3×C4⋊Dic3—21no—
149C3×C4⋊Dic3—21no—
150C3×C4⋊Dic3—32no—
151C3×C4⋊Dic3C2×D311yescharacteristic, complemented
152C3×C4⋊Dic3C2×D311yescharacteristic, complemented
153C3×C4⋊Dic3C22×C311yescharacteristic, complemented
154C3×C4⋊Dic3C22×C311yescharacteristic, complemented
155C3×Dic3⋊C4—22no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4C2×D312yescomplemented
158C3×Dic3⋊C4C22×C312yescomplemented
159C3×C4×Dic3—32no—
160C3×C4×Dic3—32no—
161Dic3⋊Dic3C22×C312yescomplemented
162#3722C22×C312yes—
163#3722C22×C312yes—
164(C2×D3)⋊Dic3C22×C312yescomplemented
165Dic32C22×C312yescomplemented
166C22×C33—21no—
167C22×C33—21no—
168C22×C33#4112yes—
169C22×C33C2411yescharacteristic
170C2×C3×C3⋊D3—22no—
171C2×C3×C3⋊D3—22no—
172C2×C3×C3⋊D3—22no—
173C2×C3×C3⋊D3—44no—
174C2×C32×D3—22no—
175C2×C32×D3—22no—
176C2×C32×D3—22no—
177C33×C4—21no—
178C33×C4—21no—
179C3×C3⋊Dic3—22no—
180C32×Dic3—22no—
181C32×Dic3—22no—
182C32×Dic3—22no—
183C3×#126—92no—
184C3×#124—92no—
185C3×#123—92no—
186C3×C22⋊Q8—31no—
187C3×C22⋊Q8—31no—
188C3×C22⋊Q8—61no—
189C3×#121—31no—
190C3×#121—31no—
191C3×#121—61no—
192C3×#121—92no—
193C3×#120—92no—
194C3×C4×D4—92no—
195C2×C3×C22⋊C4—91no—
196#947—32no—
197#939—32no—
198#937—32no—
199D4×Dic3—32no—
200#930C3×D311yescharacteristic, complemented
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—61no—
204#924C3×D311yescharacteristic, complemented
205#898—32no—
206#898—32no—
207#895—32no—
208#894—32no—
209#886—32no—
210#885—32no—
211#882—32no—
212#67⋊C4—32no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—32no—
217C23×C32—41no—
218C23×C32C22×D311yescharacteristic
219C23×C32C22×D311yescharacteristic
220C23×C32C23×C311yescharacteristic
221C22×C3⋊D3—22no—
222C22×C3⋊D3—41no—
223C22×C3⋊D3—41no—
224C22×C3⋊D3C23×C312yes—
225C22×C3×D3—22no—
226C22×C3×D3—32no—
227C22×C3×D3—32no—
228C22×C3×D3—62no—
229C22×C3×D3—64no—
230C22×C3×D3—62no—
231C22×C3×D3—62no—
232C22×C3×D3—121no—
233C22×C3×D3—121no—
234C22×C3×D3—121no—
235C22×C3×D3—121no—
236C22×C3×D3—122no—
237C22×C3×D3—122no—
238C22×C3×D3C22×D312yes—
239C22×C3×D3C23×C312yes—
240C32×Q8—121no—
241C32×D4—64no—
242C32×D4—121no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—32no—
250C2×C32×C4—32no—
251C2×C32×C4—32no—
252C2×C32×C4—41no—
253C2×C32×C4—41no—
254C2×C32×C4—41no—
255C2×C32×C4—41no—
256C2×C32×C4—41no—
257C2×C32×C4—42no—
258C2×C32×C4—42no—
259C2×C32×C4—42no—
260C2×C32×C4—44no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C23×C311yescharacteristic
266C2×C32×C4C23×C311yescharacteristic
267C2×C3⋊Dic3—41no—
268C2×C3⋊Dic3C23×C312yes—
269C3×#67—24no—
270C3×#67—24no—
271C3×#67—44no—
272C3×#67—122no—
273C3×#67—122no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—122no—
281C2×C3×Dic3—121no—
282C2×C3×Dic3—121no—
283C2×C3×Dic3—122no—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C23×C312yes—
288C2×C3×Dic3C23×C312yes—
289C2×C3×Dic3C23×C312yes—
290C3×D12—41no—
291C3×D12—41no—
292C3×D12—42no—
293C3×D12—122no—
294C3×D12—122no—
295C3×C4×D3—122no—
296C3×Dic6—41no—
297C3×Dic6—41no—
298C3×Dic6—42no—
299#626—42no—
300#626—42no—
301D3×Dic3—42no—
302#538—91noSylow
303C2×C33—22no—
304C2×C33C2×#4111yescharacteristic
305C2×C33H(5,𝔽2)11yescharacteristic
306C2×C33H(5,𝔽2)11yescharacteristic
307C3×C3⋊D3—42no—
308C32×D3—42no—
309C24×C3—91no—
310C23×D3—31no—
311C23×D3—31no—
312C23×D3—61no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×D4—32no—
317C2×C3×D4—32no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—61no—
321C2×C3×D4—62no—
322C2×C3×D4—92no—
323C2×C3×D4—92no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—41no—
328C22×C3×C4—92no—
329C22×C3×C4—91no—
330C22×C3×C4D3211yescharacteristic
331C22×C3×C4C2×C3×D311yescharacteristic
332C22×C3×C4C2×C3×D311yescharacteristic
333C2×#67—32no—
334C2×#67—32no—
335C2×#67C2×C3×D312yes—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—32no—
339C22×Dic3—61no—
340C2×D12—32no—
341C2×D12—32no—
342C2×D12C2×C3×D311yescharacteristic, complemented
343C2×C4×D3—32no—
344C2×Dic6C2×C3×D311yescharacteristic, complemented
345C3×C4⋊C4—32no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—32no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—62no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—92no—
355C3×C22⋊C4—32no—
356C3×C22⋊C4—32no—
357C3×C22⋊C4—32no—
358C3×C22⋊C4—32no—
359C3×C22⋊C4—62no—
360C3×C22⋊C4—62no—
361C3×C22⋊C4—92no—
362C3×C22⋊C4—92no—
363C3×C22⋊C4—92no—
364C3×C22⋊C4—92no—
365C3×C22⋊C4—92no—
366C3×C42—92no—
367#217—32no—
368#217C2×C3×D312yes—
369(C2×D3)⋊C4—32no—
370(C2×D3)⋊C4—32no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—32no—
373(C2×D3)⋊C4—32no—
374(C2×D3)⋊C4—32no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4—32no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4C2×C3×D312yescomplemented
381C4⋊Dic3—32no—
382C4⋊Dic3C2×C3×D311yescharacteristic, complemented
383C4⋊Dic3C2×C3×D311yescharacteristic, complemented
384Dic3⋊C4—32no—
385Dic3⋊C4C2×C3×D312yescomplemented
386C4×Dic3—32no—
387C4×Dic3—32no—
388C22×C32—21no—
389C22×C32—21no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—42no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—42no—
409C22×C32—42no—
410C22×C32—62no—
411C22×C32—62no—
412C22×C32—62no—
413C22×C32#23712yes—
414C22×C32#23912yes—
415C22×C32C3×#4112yes—
416C22×C32C23×D311yescharacteristic
417C22×C32C23×D311yescharacteristic
418C22×C32C24×C311yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3—44no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—42no—
430C2×C3×D3—42no—
431C2×C3×D3—42no—
432C2×C3×D3—64no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—62no—
438C2×C3×D3—62no—
439C2×C3×D3—122no—
440C2×C3×D3—122no—
441C2×C3×D3—128no—
442C2×C3×D3—124no—
443C2×C3×D3—124no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—22no—
447C32×C4—22no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—41no—
453C32×C4—41no—
454C32×C4—41no—
455C32×C4—41no—
456C32×C4—42no—
457C32×C4—42no—
458C32×C4—62no—
459C32×C4—62no—
460C32×C4—62no—
461C3⋊Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—42no—
469C3×Dic3—42no—
470C3×Dic3—42no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—122no—
474#126—92no—
475#124—92no—
476#123—92no—
477C22⋊Q8—31no—
478#121—31no—
479#121—92no—
480#120—92no—
481C4×D4—92no—
482C2×C22⋊C4—91no—
483C33#53811yescharacteristic, complemented, Sylow
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—32no—
488C23×C3—32no—
489C23×C3—41no—
490C23×C3—62no—
491C23×C3—92no—
492C23×C3—182no—
493C23×C3—361no—
494C23×C3—361no—
495C23×C3C2×D3211yescharacteristic
496C23×C3C22×C3×D311yescharacteristic
497C23×C3C22×C3×D311yescharacteristic
498C22×D3—32no—
499C22×D3—32no—
500C22×D3—62no—
501C22×D3—64no—
502C22×D3—62no—
503C22×D3—62no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—121no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3C22×C3×D312yes—
511C3×Q8—121no—
512C3×Q8—121no—
513C3×Q8—122no—
514C3×D4—64no—
515C3×D4—64no—
516C3×D4—124no—
517C3×D4—121no—
518C3×D4—121no—
519C3×D4—122no—
520C3×D4—362no—
521C3×D4—362no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—42no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—44no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—62no—
546C2×C3×C4—92no—
547C2×C3×C4—362no—
548C2×C3×C4—361no—
549C2×C3×C4C2×D3211yescharacteristic
550C2×C3×C4C2×D3211yescharacteristic
551C2×C3×C4C22×C3×D311yescharacteristic
552C2×C3×C4C22×C3×D311yescharacteristic
553C2×C3×C4C22×C3×D311yescharacteristic
554C2×C3×C4C22×C3×D311yescharacteristic
555#67—24no—
556#67—122no—
557#67—122no—
558C2×Dic3—32no—
559C2×Dic3—32no—
560C2×Dic3—62no—
561C2×Dic3—122no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3C22×C3×D312yes—
566C2×Dic3C22×C3×D312yes—
567C2×Dic3C22×C3×D312yes—
568D12—41no—
569D12—122no—
570D12—122no—
571C4×D3—122no—
572Dic6—41no—
573C2×C32—22no—
574C2×C32—24no—
575C2×C32—22no—
576C2×C32—22no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32—41no—
589C2×C32—42no—
590C2×C32—42no—
591C2×C32—44no—
592C2×C32—122no—
593C2×C32C2×#23711yescharacteristic
594C2×C32#100411yescharacteristic
595C2×C32#100411yescharacteristic
596C2×C32C2×#23911yescharacteristic
597C2×C32#100911yescharacteristic
598C2×C32#100911yescharacteristic
599C2×C32C2×C3×#4111yescharacteristic
600C2×C32C3×H(5,𝔽2)11yescharacteristic
601C2×C32C3×H(5,𝔽2)11yescharacteristic
602C3⋊D3—42no—
603C3×D3—42no—
604C3×D3—42no—
605C3×D3—82no—
606C3×D3—124no—
607C3×D3—122no—
608C3×D3—122no—
609C24—91no—
610C2×Q8—31no—
611C2×D4—32no—
612C2×D4—31no—
613C2×D4—92no—
614C2×D4—92no—
615C22×C4—92no—
616C22×C4—91no—
617C22×C4C3×D3211yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—32no—
620C4⋊C4—31no—
621C4⋊C4—92no—
622C22⋊C4—32no—
623C22⋊C4—32no—
624C22⋊C4—92no—
625C22⋊C4—92no—
626C22⋊C4—92no—
627C22⋊C4—92no—
628C22⋊C4—92no—
629C42—92no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—42no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—42no—
652C22×C3—62no—
653C22×C3—62no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—122no—
659C22×C3—122no—
660C22×C3—122no—
661C22×C3—182no—
662C22×C3—182no—
663C22×C3—182no—
664C22×C3—364no—
665C22×C3#379612yes—
666C22×C3C3×#23712yes—
667C22×C3C3×#23912yes—
668C22×C3C22×D3211yescharacteristic
669C22×C3C23×C3×D311yescharacteristic
670C22×C3C23×C3×D311yescharacteristic
671C2×D3—22no—
672C2×D3—22no—
673C2×D3—22no—
674C2×D3—64no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—62no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—122no—
682C2×D3—122no—
683C2×D3—128no—
684C2×D3—124no—
685C2×D3—124no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—62no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—62no—
704C3×C4—62no—
705C3×C4—62no—
706C3×C4—122no—
707C3×C4—122no—
708C3×C4—122no—
709C3×C4—182no—
710Dic3—22no—
711Dic3—22no—
712Dic3—22no—
713Dic3—62no—
714Dic3—62no—
715Dic3—122no—
716C32—21no—
717C32—21no—
718C32—21no—
719C32—41no—
720C32#561711yescharacteristic, complemented
721C32#564411yescharacteristic, complemented
722C32C3×#53811yescharacteristic, complemented
723C23—32no—
724C23—92no—
725C23—182no—
726C23—361no—
727C23—361no—
728C23C2×C3×D3211yescharacteristic
729Q8—121no—
730D4—64no—
731D4—121no—
732D4—362no—
733D4—362no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—41no—
738C2×C4—92no—
739C2×C4—362no—
740C2×C4—361no—
741C2×C4C2×C3×D3211yescharacteristic
742C2×C4C2×C3×D3211yescharacteristic
743C2×C3—24no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—22no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—42no—
757C2×C3—42no—
758C2×C3—44no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—122no—
763C2×C3—122no—
764C2×C3—242no—
765C2×C3—362no—
766C2×C3C2×#379611yescharacteristic
767C2×C3#6430811yescharacteristic
768C2×C3#6433011yescharacteristic
769C2×C3C2×C3×#23711yescharacteristic
770C2×C3C3×#100411yescharacteristic
771C2×C3C3×#100411yescharacteristic
772C2×C3C2×C3×#23911yescharacteristic
773C2×C3C3×#100911yescharacteristic
774C2×C3C3×#100911yescharacteristic
775D3—42no—
776D3—124no—
777D3—122no—
778D3—122no—
779C22—21no—
780C22—21no—
781C22—62no—
782C22—62no—
783C22—62no—
784C22—182no—
785C22—182no—
786C22—182no—
787C22—364no—
788C22C3×#379612yes—
789C22C22×C3×D3211yescharacteristic
790C4—21no—
791C4—21no—
792C4—62no—
793C4—62no—
794C4—62no—
795C4—182no—
796C3—21no—
797C3—21no—
798C3—21no—
799C3—41no—
800C3#1059497911yescharacteristic, direct product factor
801C3C3×#561711yescharacteristic, complemented
802C3C3×#564411yescharacteristic, complemented
803C2—22no—
804C2—122no—
805C2—362no—
806C2C2×C3×#379611yescharacteristic
807C2C3×#6430811yescharacteristic
808C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#538
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. C2×C3×#3752C2semidirect
2. C32×#930C2semidirect
3. C32×#924C2semidirect
4. C3×#63981C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. C3×#63907C2semidirect
7. C3×#63890C2semidirect
8. C3×#63886C2semidirect
9. C3×#63848C2semidirect
12. #10594979C3direct (N × H)
17. C2×C32×D12C22semidirect
18. C2×C32×Dic6C22semidirect
21. C2×C3×D3×Dic3C22semidirect
25. C32×(C2×D3)⋊C4C22semidirect
26. C32×C4⋊Dic3C22semidirect
27. C32×C4⋊Dic3C22semidirect
28. C32×Dic3⋊C4C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
32. C3×(C2×D3)⋊Dic3C22semidirect
33. C3×Dic32C22semidirect
36. C2×#3752C2×C3semidirect
42. C3×#930D3semidirect
43. C3×#930C2×C3semidirect
48. C3×#924D3semidirect
49. C3×#924C2×C3semidirect
58. #63981C2×C3semidirect
59. #67⋊Dic3C2×C3semidirect
60. #63907C2×C3semidirect
61. #63890C2×C3semidirect
62. #63886C2×C3semidirect
63. #63848C2×C3semidirect
114. C2×C3×D12C2×D3semidirect
115. C2×C3×D12C22×C3semidirect
118. C2×C3×Dic6C2×D3semidirect
119. C2×C3×Dic6C22×C3semidirect
122. C2×D3×Dic3C22×C3semidirect
146. C3×(C2×D3)⋊C4C2×D3semidirect
147. C3×(C2×D3)⋊C4C22×C3semidirect
151. C3×C4⋊Dic3C2×D3semidirect
152. C3×C4⋊Dic3C2×D3semidirect
153. C3×C4⋊Dic3C22×C3semidirect
154. C3×C4⋊Dic3C22×C3semidirect
157. C3×Dic3⋊C4C2×D3semidirect
158. C3×Dic3⋊C4C22×C3semidirect
161. Dic3⋊Dic3C22×C3semidirect
164. (C2×D3)⋊Dic3C22×C3semidirect
165. Dic32C22×C3semidirect
200. #930C3×D3semidirect
204. #924C3×D3semidirect
342. C2×D12C2×C3×D3semidirect
344. C2×Dic6C2×C3×D3semidirect
380. (C2×D3)⋊C4C2×C3×D3semidirect
382. C4⋊Dic3C2×C3×D3semidirect
383. C4⋊Dic3C2×C3×D3semidirect
385. Dic3⋊C4C2×C3×D3semidirect
483. C33#538semidirect
720. C32#5617semidirect
721. C32#5644semidirect
722. C32C3×#538semidirect
800. C3#10594979direct (N × H)
801. C3C3×#5617semidirect
802. C3C3×#5644semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37522
C32×#9302
C32×#9242
C3×#639812
C3×#67⋊Dic32
C3×#639072
C3×#638902
C3×#638862
C3×#638482
C3×#56443
C3×#56173
#105949793