Finite Group Databasebeta

← C3×#10591316 #13158188

Subgroups — C3×#10591316 #13158188

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C2×C3×Dic32C211yesmaximal, characteristic, complemented
6C32×C3⋊#95C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#4951—31nomaximal
9C3×#4670—31nomaximal
10#10591316C311yesmaximal, characteristic, direct product factor
11C23×C32×D3C2211yescharacteristic
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C3×C4⋊(C3⋊Dic3)—22no—
19C32×(C2×D3)⋊C4C414yescomplemented
20C3×(C2×D3)⋊Dic3—22no—
21C3×(C2×D3)⋊Dic3—22no—
22C3×Dic32—22no—
23C2×C32×C22⋊C4—31no—
24C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
25C2×C3×#217—31no—
26C2×C3×#217—31no—
27C2×C3×(C2×D3)⋊C4—21no—
28C2×C3×(C2×D3)⋊C4—31no—
29C2×C3×(C2×D3)⋊C4—31no—
30C2×C3×(C2×D3)⋊C4D311yescharacteristic
31C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
32C2×C3×C4⋊Dic3—31no—
33C2×C3×C4⋊Dic3—31no—
34C2×C3×C4⋊Dic3—61no—
35C2×C3×C4×Dic3—31no—
36C2×C3×C4×Dic3—31no—
37C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
38C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
39C2×Dic32C2×C311yescharacteristic, complemented
40C32×#95—31no—
41C3×C3⋊#95—21no—
42C3×C3⋊#95—31no—
43C3×C3⋊#95—31no—
44C3×C3⋊#95D311yescharacteristic, complemented
45C3×C3⋊#95C2×C311yescharacteristic, complemented
46#63579C2×C311yescharacteristic, complemented
47C23×C33C2311yescharacteristic
48C22×C32×D3—21no—
49C22×C32×D3—21no—
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3C2×C412yes—
55C2×C33×C4—21no—
56C2×C33×C4—21no—
57C2×C33×C4C2×C412yes—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3D412yes—
64C2×C32×Dic3—21no—
65C2×C32×Dic3—21no—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3C2×C412yes—
72C2×C32×Dic3D412yes—
73C3×#388—91no—
74#4951—31no—
75#4670—31no—
76C24×C32—31no—
77C23×C3×D3—21no—
78C23×C3×D3C2×D311yescharacteristic
79C23×C3×D3C22×C311yescharacteristic
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C32×C4—41no—
87C22×C32×C4C2×D311yescharacteristic
88C22×C32×C4C2×D311yescharacteristic
89C22×C32×C4C22×C311yescharacteristic
90C22×C3⋊Dic3C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—61no—
100C22×C3×Dic3—61no—
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C22×C311yescharacteristic
105C22×C3×Dic3C22×C311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107C32×C22⋊C4—34no—
108C4⋊(C3⋊Dic3)—22no—
109C3×#217—62no—
110C3×#217—62no—
111C3×(C2×D3)⋊C4—24no—
112C3×(C2×D3)⋊C4—62no—
113C3×(C2×D3)⋊C4—62no—
114C3×(C2×D3)⋊C4Dic314yescomplemented
115C3×(C2×D3)⋊C4C3×C414yescomplemented
116C3×C4⋊Dic3—62no—
117C3×C4⋊Dic3—62no—
118C3×C4⋊Dic3—64no—
119C3×C4×Dic3—62no—
120C3×C4×Dic3—62no—
121(C2×D3)⋊Dic3—22no—
122(C2×D3)⋊Dic3—22no—
123Dic32—22no—
124C22×C33C22×C411yescharacteristic
125C22×C33C2×D411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C22×C33#4111yescharacteristic
128C22×C33#4111yescharacteristic
129C22×C33#4111yescharacteristic
130C22×C33#4111yescharacteristic
131C2×C32×D3—22no—
132C2×C32×D3—22no—
133C2×C32×D3—22no—
134C2×C32×D3—41no—
135C2×C32×D3—41no—
136C2×C32×D3—41no—
137C2×C32×D3—41no—
138C33×C4—22no—
139C3×C3⋊Dic3—22no—
140C3×C3⋊Dic3—41no—
141C32×Dic3—22no—
142C32×Dic3—22no—
143C32×Dic3—41no—
144C2×C3×C4⋊C4—91no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—61no—
148C2×C3×C22⋊C4—91no—
149C2×C3×C22⋊C4—91no—
150C2×C3×C42—91no—
151C2×#217—31no—
152C2×#217—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4C3×D311yescharacteristic
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—61no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C3×#95—31no—
162C3×#95—31no—
163C3×#95—61no—
164C3×#95—91no—
165C3⋊#95—31no—
166C3⋊#95—31no—
167C3⋊#95C3×D311yescharacteristic, complemented
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—32no—
172C23×C32—41no—
173C23×C32—61no—
174C23×C32—61no—
175C23×C32—61no—
176C23×C32—61no—
177C23×C32—61no—
178C23×C32—61no—
179C23×C32C22×D311yescharacteristic
180C23×C32C22×D311yescharacteristic
181C23×C32C23×C311yescharacteristic
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—21no—
189C22×C3×D3—21no—
190C22×C3×D3—21no—
191C22×C3×D3—21no—
192C22×C3×D3—21no—
193C22×C3×D3—21no—
194C22×C3×D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3—22no—
197C22×C3×D3—41no—
198C22×C3×D3—41no—
199C22×C3×D3—41no—
200C22×C3×D3—41no—
201C22×C3×D3C2×Dic312yes—
202C22×C3×D3C2×C3×C412yes—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—22no—
214C2×C32×C4—32no—
215C2×C32×C4—32no—
216C2×C32×C4—42no—
217C2×C32×C4—41no—
218C2×C32×C4—41no—
219C2×C32×C4—41no—
220C2×C32×C4—41no—
221C2×C32×C4—42no—
222C2×C32×C4—42no—
223C2×C32×C4—61no—
224C2×C32×C4—61no—
225C2×C32×C4—61no—
226C2×C32×C4—61no—
227C2×C32×C4—61no—
228C2×C32×C4—61no—
229C2×C32×C4—61no—
230C2×C32×C4C4×D312yes—
231C2×C32×C4C2×Dic312yes—
232C2×C32×C4C2×C3×C412yes—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C3×D412yes—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—32no—
257C2×C3×Dic3—32no—
258C2×C3×Dic3—41no—
259C2×C3×Dic3—41no—
260C2×C3×Dic3—41no—
261C2×C3×Dic3—41no—
262C2×C3×Dic3—41no—
263C2×C3×Dic3—41no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—121no—
277C2×C3×Dic3—121no—
278C2×C3×Dic3—121no—
279C2×C3×Dic3—121no—
280C2×C3×Dic3D1212yes—
281C2×C3×Dic3C2×Dic312yes—
282C2×C3×Dic3C2×C3×C412yes—
283C2×C3×Dic3C3×D412yes—
284#388—91noSylow
285C2×C33#11711yescharacteristic
286C2×C33C4×D411yescharacteristic
287C2×C33C4×D411yescharacteristic
288C2×C33#12111yescharacteristic
289C2×C33#12311yescharacteristic
290C2×C33#12411yescharacteristic
291C2×C33#12611yescharacteristic
292C32×D3—42no—
293C24×C3—31no—
294C24×C3—31no—
295C24×C3—61no—
296C23×D3C2×C3×D311yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—41no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C22×C3×C4D3211yescharacteristic
313C22×C3×C4C2×C3×D311yescharacteristic
314C22×C3×C4C2×C3×D311yescharacteristic
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3C2×C3×D311yescharacteristic
322C22×Dic3C2×C3×D311yescharacteristic
323C22×Dic3C2×C3×D311yescharacteristic
324C3×C4⋊C4—182no—
325C3×C22⋊C4—34no—
326C3×C22⋊C4—34no—
327C3×C22⋊C4—64no—
328C3×C22⋊C4—182no—
329C3×C22⋊C4—182no—
330C3×C42—182no—
331#217—62no—
332#217—62no—
333(C2×D3)⋊C4—62no—
334(C2×D3)⋊C4—62no—
335(C2×D3)⋊C4C3×Dic314yescomplemented
336C4⋊Dic3—62no—
337C4⋊Dic3—62no—
338C4⋊Dic3—64no—
339C4×Dic3—62no—
340C4×Dic3—62no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—41no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32—62no—
370C22×C32—62no—
371C22×C32—62no—
372C22×C32—121no—
373C22×C32—121no—
374C22×C32—121no—
375C22×C32—121no—
376C22×C32C2×C4×D311yescharacteristic
377C22×C32C2×D1211yescharacteristic
378C22×C32#23511yescharacteristic
379C22×C32#23511yescharacteristic
380C22×C32#23511yescharacteristic
381C22×C32D3×D411yescharacteristic
382C22×C32D3×D411yescharacteristic
383C22×C32D3×D411yescharacteristic
384C22×C32#23711yescharacteristic
385C22×C32#23711yescharacteristic
386C22×C32#23711yescharacteristic
387C22×C32#23711yescharacteristic
388C22×C32#23911yescharacteristic
389C22×C32C22×Dic311yescharacteristic
390C22×C32C22×C3×C411yescharacteristic
391C22×C32C2×C3×D411yescharacteristic
392C22×C32C2×C3×D411yescharacteristic
393C22×C32C3×#4111yescharacteristic
394C22×C32C3×#4111yescharacteristic
395C22×C32C3×#4111yescharacteristic
396C22×C32C3×#4111yescharacteristic
397C2×C3×D3—24no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—42no—
405C2×C3×D3—42no—
406C2×C3×D3—42no—
407C2×C3×D3—42no—
408C2×C3×D3—42no—
409C2×C3×D3—42no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—22no—
419C32×C4—24no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—42no—
423C32×C4—42no—
424C32×C4—44no—
425C32×C4—62no—
426C32×C4—62no—
427C32×C4—121no—
428C3⋊Dic3—22no—
429C3⋊Dic3—41no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—42no—
435C3×Dic3—42no—
436C3×Dic3—42no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—62no—
440C3×Dic3—62no—
441C3×Dic3—122no—
442C3×Dic3—122no—
443C3×Dic3—121no—
444C3×Dic3—121no—
445C2×C4⋊C4—91no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C42—91no—
450#95—31no—
451#95—91no—
452C33#38811yescharacteristic, complemented, Sylow
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—32no—
457C23×C3—32no—
458C23×C3—41no—
459C23×C3—62no—
460C23×C3—62no—
461C23×C3—62no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—121no—
475C23×C3—121no—
476C23×C3—121no—
477C23×C3—121no—
478C23×C3C2×D3211yescharacteristic
479C23×C3C22×C3×D311yescharacteristic
480C23×C3C22×C3×D311yescharacteristic
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3C2×C3×Dic312yes—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—62no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—92no—
528C2×C3×C4—121no—
529C2×C3×C4—121no—
530C2×C3×C4—121no—
531C2×C3×C4—121no—
532C2×C3×C4—121no—
533C2×C3×C4—121no—
534C2×C3×C4—181no—
535C2×C3×C4—181no—
536C2×C3×C4—181no—
537C2×C3×C4—181no—
538C2×C3×C4—181no—
539C2×C3×C4D3×Dic312yes—
540C2×C3×C4C3×C4×D312yes—
541C2×C3×C4C2×C3×Dic312yes—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—62no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—62no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3C3×D1212yes—
568C2×Dic3C2×C3×Dic312yes—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
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—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—41no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—41no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32—122no—
598C2×C32C4×D1211yescharacteristic
599C2×C32#87911yescharacteristic
600C2×C32#67⋊C411yescharacteristic
601C2×C32#88311yescharacteristic
602C2×C32#88411yescharacteristic
603C2×C32#88511yescharacteristic
604C2×C32#88511yescharacteristic
605C2×C32#88611yescharacteristic
606C2×C32#89211yescharacteristic
607C2×C32#89511yescharacteristic
608C2×C32#89811yescharacteristic
609C2×C32#92611yescharacteristic
610C2×C32D4×Dic311yescharacteristic
611C2×C32D4×Dic311yescharacteristic
612C2×C32C3×#11711yescharacteristic
613C2×C32C3×C4×D411yescharacteristic
614C2×C32C3×C4×D411yescharacteristic
615C2×C32C3×#12111yescharacteristic
616C2×C32C3×#12311yescharacteristic
617C2×C32C3×#12411yescharacteristic
618C2×C32C3×#12611yescharacteristic
619C3×D3—44no—
620C3×D3—42no—
621C3×D3—42no—
622C24—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—91no—
627C22×C4—91no—
628C22×C4C3×D3211yescharacteristic
629C4⋊C4—182no—
630C22⋊C4—34no—
631C22⋊C4—182no—
632C22⋊C4—182no—
633C42—182no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—64no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—62no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—122no—
670C22×C3—122no—
671C22×C3—122no—
672C22×C3—122no—
673C22×C3—122no—
674C22×C3—122no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3#379511yescharacteristic
684C22×C3#379511yescharacteristic
685C22×C3#379911yescharacteristic
686C22×C3D3×D1211yescharacteristic
687C22×C3C2×D3×Dic311yescharacteristic
688C22×C3#380511yescharacteristic
689C22×C3#381111yescharacteristic
690C22×C3C2×C3×C4×D311yescharacteristic
691C22×C3C2×C3×D1211yescharacteristic
692C22×C3C3×#23511yescharacteristic
693C22×C3C3×#23511yescharacteristic
694C22×C3C3×#23511yescharacteristic
695C22×C3C3×D3×D411yescharacteristic
696C22×C3C3×D3×D411yescharacteristic
697C22×C3C3×D3×D411yescharacteristic
698C22×C3C3×#23711yescharacteristic
699C22×C3C3×#23711yescharacteristic
700C22×C3C3×#23711yescharacteristic
701C22×C3C3×#23711yescharacteristic
702C22×C3C3×#23911yescharacteristic
703C22×C3C22×C3×Dic311yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C3×C4—24no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—42no—
716C3×C4—42no—
717C3×C4—44no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—122no—
723C3×C4—122no—
724C3×C4—122no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4—182no—
728C3×C4—361no—
729Dic3—22no—
730Dic3—22no—
731Dic3—41no—
732Dic3—62no—
733Dic3—62no—
734Dic3—122no—
735Dic3—122no—
736Dic3—121no—
737Dic3—121no—
738C32—21no—
739C32—21no—
740C32—21no—
741C32—41no—
742C32#467011yescharacteristic, complemented
743C32#495111yescharacteristic, complemented
744C32C3×#38811yescharacteristic, complemented
745C23—32no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23C2×C3×D3211yescharacteristic
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—92no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4C3×D3×Dic312yes—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—41no—
798C2×C3—41no—
799C2×C3—124no—
800C2×C3—122no—
801C2×C3—122no—
802C2×C3#6384111yescharacteristic
803C2×C3#6386111yescharacteristic
804C2×C3#6389111yescharacteristic
805C2×C3Dic3×D1211yescharacteristic
806C2×C3#6391011yescharacteristic
807C2×C3#6391311yescharacteristic
808C2×C3#67⋊Dic311yescharacteristic
809C2×C3C3×C4×D1211yescharacteristic
810C2×C3C3×#87911yescharacteristic
811C2×C3C3×#67⋊C411yescharacteristic
812C2×C3C3×#88311yescharacteristic
813C2×C3C3×#88411yescharacteristic
814C2×C3C3×#88511yescharacteristic
815C2×C3C3×#88511yescharacteristic
816C2×C3C3×#88611yescharacteristic
817C2×C3C3×#89211yescharacteristic
818C2×C3C3×#89511yescharacteristic
819C2×C3C3×#89811yescharacteristic
820C2×C3C3×#92611yescharacteristic
821C2×C3C3×D4×Dic311yescharacteristic
822C2×C3C3×D4×Dic311yescharacteristic
823D3—42no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22C3×#379511yescharacteristic
832C22C3×#379511yescharacteristic
833C22C3×#379911yescharacteristic
834C22C3×D3×D1211yescharacteristic
835C22C2×C3×D3×Dic311yescharacteristic
836C22C3×#380511yescharacteristic
837C22C3×#381111yescharacteristic
838C4—22no—
839C4—62no—
840C4—62no—
841C4—121no—
842C4—182no—
843C4—361no—
844C3—21no—
845C3—21no—
846C3—21no—
847C3—41no—
848C3#1059131611yescharacteristic, direct product factor
849C3C3×#467011yescharacteristic, complemented
850C3C3×#495111yescharacteristic, complemented
851C2—122no—
852C2C3×#6384111yescharacteristic
853C2C3×#6386111yescharacteristic
854C2C3×#6389111yescharacteristic
855C2C3×Dic3×D1211yescharacteristic
856C2C3×#6391011yescharacteristic
857C2C3×#6391311yescharacteristic
858C2C3×#67⋊Dic311yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#388
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4⋊(C3⋊Dic3)C2semidirect
5. C2×C3×Dic32C2semidirect
6. C32×C3⋊#95C2semidirect
7. C3×#63579C2semidirect
10. #10591316C3direct (N × H)
19. C32×(C2×D3)⋊C4C4semidirect
24. C2×C4⋊(C3⋊Dic3)C2×C3semidirect
39. C2×Dic32C2×C3semidirect
44. C3×C3⋊#95D3semidirect
45. C3×C3⋊#95C2×C3semidirect
46. #63579C2×C3semidirect
114. C3×(C2×D3)⋊C4Dic3semidirect
115. C3×(C2×D3)⋊C4C3×C4semidirect
167. C3⋊#95C3×D3semidirect
335. (C2×D3)⋊C4C3×Dic3semidirect
452. C33#388semidirect
742. C32#4670semidirect
743. C32#4951semidirect
744. C32C3×#388semidirect
848. C3#10591316direct (N × H)
849. C3C3×#4670semidirect
850. C3C3×#4951semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4⋊(C3⋊Dic3)2
C2×C32×(C2×D3)⋊C42
C2×C3×(C2×D3)⋊Dic32
C2×C3×Dic322
C32×C3⋊#952
C3×#635792
C3×#49513
C3×#46703
#105913163