Finite Group Databasebeta

← C3×#10591335 #13158261

Subgroups — C3×#10591335 #13158261

Order 1728.

930 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
3C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
4C32×C3⋊#95C211yesmaximal, characteristic
5C32×C3⋊#95C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×#4655—31nomaximal
9C3×#4654—31nomaximal
10#10591335C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C32×Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C3×C4×C3⋊Dic3—22no—
19C3×Dic3⋊Dic3—22no—
20C3×Dic3⋊Dic3C414yescomplemented
21C2×C4×C3⋊Dic3C2×C311yescharacteristic
22C2×C3×C4⋊Dic3—31no—
23C2×C3×C4⋊Dic3—31no—
24C2×C3×Dic3⋊C4—31no—
25C2×C3×Dic3⋊C4—31no—
26C2×C3×C4×Dic3—31no—
27C2×C3×C4×Dic3—31no—
28C2×C3×C4×Dic3—61no—
29C2×Dic3⋊Dic3C2×C311yescharacteristic
30C2×Dic3⋊Dic3C2×C311yescharacteristic
31C32×#95—31no—
32C32×#95—31no—
33C3×C3⋊#95—21no—
34C3×C3⋊#95—21no—
35C3×C3⋊#95—31no—
36C3×C3⋊#95—31no—
37C3×C3⋊#95—31no—
38C3×C3⋊#95—31no—
39C3×C3⋊#95D311yescharacteristic
40C3×C3⋊#95D311yescharacteristic
41C3×C3⋊#95C2×C311yescharacteristic
42C3×C3⋊#95C2×C311yescharacteristic
43#63579C2×C311yescharacteristic
44#63579C2×C311yescharacteristic
45C23×C33C2311yescharacteristic
46C2×C33×C4—21no—
47C2×C33×C4—21no—
48C2×C33×C4Q812yes—
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3C2×C412yes—
54C2×C3×C3⋊Dic3D412yes—
55C2×C32×Dic3—21no—
56C2×C32×Dic3—21no—
57C2×C32×Dic3—21no—
58C2×C32×Dic3—21no—
59C2×C32×Dic3—21no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3—21no—
62C2×C32×Dic3—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3—21no—
65C2×C32×Dic3C2×C412yes—
66C2×C32×Dic3C2×C412yes—
67C3×#387—91no—
68#4655—31no—
69#4654—31no—
70C22×C32×C4—21no—
71C22×C32×C4—21no—
72C22×C32×C4—21no—
73C22×C32×C4—31no—
74C22×C32×C4—31no—
75C22×C32×C4—31no—
76C22×C32×C4—31no—
77C22×C32×C4—41no—
78C22×C32×C4C2×D311yescharacteristic
79C22×C32×C4C2×D311yescharacteristic
80C22×C32×C4C22×C311yescharacteristic
81C22×C3⋊Dic3C22×C311yescharacteristic
82C22×C3⋊Dic3C22×C311yescharacteristic
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—61no—
92C22×C3×Dic3—61no—
93C22×C3×Dic3C2×D311yescharacteristic
94C22×C3×Dic3C2×D311yescharacteristic
95C22×C3×Dic3C2×D311yescharacteristic
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C22×C311yescharacteristic
98C22×C3×Dic3C22×C311yescharacteristic
99C22×C3×Dic3C22×C311yescharacteristic
100C22×C3×Dic3C22×C311yescharacteristic
101C4×C3⋊Dic3—22no—
102C3×C4⋊Dic3—34no—
103C3×C4⋊Dic3—62no—
104C3×Dic3⋊C4—34no—
105C3×Dic3⋊C4—62no—
106C3×C4×Dic3—62no—
107C3×C4×Dic3—62no—
108C3×C4×Dic3—64no—
109Dic3⋊Dic3—22no—
110Dic3⋊Dic3C3×C414yescomplemented
111C22×C33C22×C411yescharacteristic
112C22×C33C2×D411yescharacteristic
113C22×C33C2×Q811yescharacteristic
114C22×C33#4111yescharacteristic
115C22×C33#4111yescharacteristic
116C22×C33#4111yescharacteristic
117C22×C33#4111yescharacteristic
118C33×C4—22no—
119C3×C3⋊Dic3—22no—
120C3×C3⋊Dic3—22no—
121C32×Dic3—22no—
122C32×Dic3—22no—
123C32×Dic3—41no—
124C32×Dic3—41no—
125C2×C3×C4⋊C4—91no—
126C2×C3×C4⋊C4—91no—
127C2×C3×C42—91no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—61no—
135C3×#95—31no—
136C3×#95—31no—
137C3×#95—31no—
138C3×#95—31no—
139C3×#95—61no—
140C3×#95—61no—
141C3×#95—91no—
142C3×#95—91no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C3⋊#95—31no—
146C3⋊#95—31no—
147C3⋊#95C3×D311yescharacteristic
148C3⋊#95C3×D311yescharacteristic
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—41no—
153C23×C32C22×D311yescharacteristic
154C23×C32C22×D311yescharacteristic
155C23×C32C23×C311yescharacteristic
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4—32no—
168C2×C32×C4—32no—
169C2×C32×C4—42no—
170C2×C32×C4—41no—
171C2×C32×C4—41no—
172C2×C32×C4—41no—
173C2×C32×C4—41no—
174C2×C32×C4—42no—
175C2×C32×C4—42no—
176C2×C32×C4—61no—
177C2×C32×C4—61no—
178C2×C32×C4—61no—
179C2×C32×C4—61no—
180C2×C32×C4—61no—
181C2×C32×C4—61no—
182C2×C32×C4—61no—
183C2×C32×C4—61no—
184C2×C32×C4—61no—
185C2×C32×C4—61no—
186C2×C32×C4Dic612yes—
187C2×C32×C4Dic612yes—
188C2×C32×C4C3×Q812yes—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C2×C3×C412yes—
194C2×C3⋊Dic3C3×D412yes—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—32no—
220C2×C3×Dic3—32no—
221C2×C3×Dic3—32no—
222C2×C3×Dic3—32no—
223C2×C3×Dic3—41no—
224C2×C3×Dic3—41no—
225C2×C3×Dic3—41no—
226C2×C3×Dic3—41no—
227C2×C3×Dic3—41no—
228C2×C3×Dic3—41no—
229C2×C3×Dic3—41no—
230C2×C3×Dic3—41no—
231C2×C3×Dic3—62no—
232C2×C3×Dic3—62no—
233C2×C3×Dic3—62no—
234C2×C3×Dic3—62no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—61no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3C4×D312yes—
246C2×C3×Dic3C4×D312yes—
247C2×C3×Dic3C2×C3×C412yes—
248C2×C3×Dic3C2×C3×C412yes—
249#387—91noSylow
250C2×C33#11711yescharacteristic
251C2×C33C4×D411yescharacteristic
252C2×C33C4×Q811yescharacteristic
253C2×C33C22⋊Q811yescharacteristic
254C2×C33#12311yescharacteristic
255C2×C33#12511yescharacteristic
256C2×C33#12611yescharacteristic
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—41no—
269C22×C3×C4—61no—
270C22×C3×C4—61no—
271C22×C3×C4—61no—
272C22×C3×C4—61no—
273C22×C3×C4—91no—
274C22×C3×C4—91no—
275C22×C3×C4D3211yescharacteristic
276C22×C3×C4C2×C3×D311yescharacteristic
277C22×C3×C4C2×C3×D311yescharacteristic
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—61no—
283C22×Dic3—61no—
284C22×Dic3C2×C3×D311yescharacteristic
285C22×Dic3C2×C3×D311yescharacteristic
286C22×Dic3C2×C3×D311yescharacteristic
287C22×Dic3C2×C3×D311yescharacteristic
288C3×C4⋊C4—94no—
289C3×C4⋊C4—182no—
290C3×C42—182no—
291C4⋊Dic3—34no—
292C4⋊Dic3—62no—
293Dic3⋊C4—34no—
294Dic3⋊C4—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3—64no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32C2×Dic611yescharacteristic
327C22×C32C2×Dic611yescharacteristic
328C22×C32C2×C4×D311yescharacteristic
329C22×C32C2×C4×D311yescharacteristic
330C22×C32#23511yescharacteristic
331C22×C32#23511yescharacteristic
332C22×C32D3×D411yescharacteristic
333C22×C32D3×D411yescharacteristic
334C22×C32#23711yescharacteristic
335C22×C32#23711yescharacteristic
336C22×C32#23711yescharacteristic
337C22×C32#23711yescharacteristic
338C22×C32#23911yescharacteristic
339C22×C32#23911yescharacteristic
340C22×C32C22×C3×C411yescharacteristic
341C22×C32C2×C3×D411yescharacteristic
342C22×C32C2×C3×Q811yescharacteristic
343C22×C32C3×#4111yescharacteristic
344C22×C32C3×#4111yescharacteristic
345C22×C32C3×#4111yescharacteristic
346C22×C32C3×#4111yescharacteristic
347C32×C4—22no—
348C32×C4—24no—
349C32×C4—22no—
350C32×C4—22no—
351C32×C4—42no—
352C32×C4—42no—
353C32×C4—44no—
354C32×C4—62no—
355C32×C4—62no—
356C32×C4—121no—
357C32×C4—121no—
358C3⋊Dic3—22no—
359C3⋊Dic3—22no—
360C3×Dic3—22no—
361C3×Dic3—22no—
362C3×Dic3—22no—
363C3×Dic3—22no—
364C3×Dic3—42no—
365C3×Dic3—42no—
366C3×Dic3—42no—
367C3×Dic3—42no—
368C3×Dic3—41no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—64no—
373C3×Dic3—64no—
374C3×Dic3—62no—
375C3×Dic3—62no—
376C3×Dic3—62no—
377C3×Dic3—62no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4—91no—
380C2×C42—91no—
381#95—31no—
382#95—31no—
383#95—91no—
384#95—91no—
385C33#38711yescharacteristic, complemented, Sylow
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—41no—
390C23×C3C2×D3211yescharacteristic
391C23×C3C22×C3×D311yescharacteristic
392C23×C3C22×C3×D311yescharacteristic
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—32no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—92no—
440C2×C3×C4—92no—
441C2×C3×C4—121no—
442C2×C3×C4—121no—
443C2×C3×C4—121no—
444C2×C3×C4—121no—
445C2×C3×C4—121no—
446C2×C3×C4—121no—
447C2×C3×C4—121no—
448C2×C3×C4—121no—
449C2×C3×C4—181no—
450C2×C3×C4—181no—
451C2×C3×C4—181no—
452C2×C3×C4—181no—
453C2×C3×C4#62712yes—
454C2×C3×C4C3×Dic612yes—
455C2×C3×C4C3×Dic612yes—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—32no—
467C2×Dic3—32no—
468C2×Dic3—32no—
469C2×Dic3—32no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3C3×C4×D312yes—
485C2×Dic3C3×C4×D312yes—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—41no—
508C2×C32—41no—
509C2×C32—41no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32—41no—
513C2×C32—41no—
514C2×C32C4×Dic611yescharacteristic
515C2×C32C4×Dic611yescharacteristic
516C2×C32#87711yescharacteristic
517C2×C32#87811yescharacteristic
518C2×C32#87811yescharacteristic
519C2×C32#87911yescharacteristic
520C2×C32#67⋊C411yescharacteristic
521C2×C32#88311yescharacteristic
522C2×C32#89011yescharacteristic
523C2×C32#89011yescharacteristic
524C2×C32#89211yescharacteristic
525C2×C32#89311yescharacteristic
526C2×C32#89411yescharacteristic
527C2×C32#89811yescharacteristic
528C2×C32C3×#11711yescharacteristic
529C2×C32C3×C4×D411yescharacteristic
530C2×C32C3×C4×Q811yescharacteristic
531C2×C32C3×C22⋊Q811yescharacteristic
532C2×C32C3×#12311yescharacteristic
533C2×C32C3×#12511yescharacteristic
534C2×C32C3×#12611yescharacteristic
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4C3×D3211yescharacteristic
542C4⋊C4—94no—
543C4⋊C4—182no—
544C42—182no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3#379611yescharacteristic
574C22×C3#379611yescharacteristic
575C22×C3#379811yescharacteristic
576C22×C3C4×D3211yescharacteristic
577C22×C3#380511yescharacteristic
578C22×C3C2×#62711yescharacteristic
579C22×C3#381111yescharacteristic
580C22×C3C2×C3×Dic611yescharacteristic
581C22×C3C2×C3×Dic611yescharacteristic
582C22×C3C2×C3×C4×D311yescharacteristic
583C22×C3C2×C3×C4×D311yescharacteristic
584C22×C3C3×#23511yescharacteristic
585C22×C3C3×#23511yescharacteristic
586C22×C3C3×D3×D411yescharacteristic
587C22×C3C3×D3×D411yescharacteristic
588C22×C3C3×#23711yescharacteristic
589C22×C3C3×#23711yescharacteristic
590C22×C3C3×#23711yescharacteristic
591C22×C3C3×#23711yescharacteristic
592C22×C3C3×#23911yescharacteristic
593C22×C3C3×#23911yescharacteristic
594C3×C4—24no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—42no—
599C3×C4—42no—
600C3×C4—44no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—62no—
604C3×C4—62no—
605C3×C4—122no—
606C3×C4—122no—
607C3×C4—122no—
608C3×C4—122no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—182no—
614C3×C4—182no—
615Dic3—22no—
616Dic3—22no—
617Dic3—41no—
618Dic3—41no—
619Dic3—64no—
620Dic3—64no—
621Dic3—62no—
622Dic3—62no—
623Dic3—62no—
624Dic3—62no—
625C32—21no—
626C32—21no—
627C32—21no—
628C32—41no—
629C32#465411yescharacteristic, complemented
630C32#465511yescharacteristic, complemented
631C32C3×#38711yescharacteristic, complemented
632C23C2×C3×D3211yescharacteristic
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—92no—
648C2×C4—92no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4C3×#62712yes—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—41no—
680C2×C3—41no—
681C2×C3—41no—
682C2×C3#6385311yescharacteristic
683C2×C3#6386211yescharacteristic
684C2×C3#6387211yescharacteristic
685C2×C3#6387811yescharacteristic
686C2×C3#6388111yescharacteristic
687C2×C3C4×#62711yescharacteristic
688C2×C3#6398211yescharacteristic
689C2×C3C3×C4×Dic611yescharacteristic
690C2×C3C3×C4×Dic611yescharacteristic
691C2×C3C3×#87711yescharacteristic
692C2×C3C3×#87811yescharacteristic
693C2×C3C3×#87811yescharacteristic
694C2×C3C3×#87911yescharacteristic
695C2×C3C3×#67⋊C411yescharacteristic
696C2×C3C3×#88311yescharacteristic
697C2×C3C3×#89011yescharacteristic
698C2×C3C3×#89011yescharacteristic
699C2×C3C3×#89211yescharacteristic
700C2×C3C3×#89311yescharacteristic
701C2×C3C3×#89411yescharacteristic
702C2×C3C3×#89811yescharacteristic
703C22C3×#379611yescharacteristic
704C22C3×#379611yescharacteristic
705C22C3×#379811yescharacteristic
706C22C3×C4×D3211yescharacteristic
707C22C3×#380511yescharacteristic
708C22C2×C3×#62711yescharacteristic
709C22C3×#381111yescharacteristic
710C4—22no—
711C4—62no—
712C4—62no—
713C4—121no—
714C4—121no—
715C4—182no—
716C4—182no—
717C3—21no—
718C3—21no—
719C3—21no—
720C3—41no—
721C3#1059133511yescharacteristic, direct product factor
722C3C3×#465411yescharacteristic, complemented
723C3C3×#465511yescharacteristic, complemented
724C2C3×#6385311yescharacteristic
725C2C3×#6386211yescharacteristic
726C2C3×#6387211yescharacteristic
727C2C3×#6387811yescharacteristic
728C2C3×#6388111yescharacteristic
729C2C3×C4×#62711yescharacteristic
730C2C3×#6398211yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#387
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
10. #10591335C3direct (N × H)
20. C3×Dic3⋊Dic3C4semidirect
110. Dic3⋊Dic3C3×C4semidirect
385. C33#387semidirect
629. C32#4654semidirect
630. C32#4655semidirect
631. C32C3×#387semidirect
721. C3#10591335direct (N × H)
722. C3C3×#4654semidirect
723. C3C3×#4655semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C3⋊Dic32
C2×C3×Dic3⋊Dic32
C32×C3⋊#952
C3×#635792
C3×#46553
C3×#46543
#105913353