Finite Group Databasebeta

← C3×#10591319 #13158237

Subgroups — C3×#10591319 #13158237

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 870 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×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#3724C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#4994—31nomaximal
9C3×#4948—31nomaximal
10#10591319C311yesmaximal, 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)⋊C4—22no—
20C32×Dic3⋊C4—22no—
21C3×#3724—22no—
22C3×(C2×D3)⋊Dic3—22no—
23C3×(C2×D3)⋊Dic3—22no—
24C2×C32×C4⋊C4—31no—
25C2×C32×C22⋊C4—31no—
26C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
27C2×C3×#217—31no—
28C2×C3×#217—31no—
29C2×C3×(C2×D3)⋊C4—21no—
30C2×C3×(C2×D3)⋊C4—31no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×(C2×D3)⋊C4D311yescharacteristic
33C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
34C2×C3×C4⋊Dic3—31no—
35C2×C3×C4⋊Dic3—31no—
36C2×C3×C4⋊Dic3—61no—
37C2×C3×Dic3⋊C4—21no—
38C2×C3×Dic3⋊C4—31no—
39C2×C3×Dic3⋊C4—31no—
40C2×C3×Dic3⋊C4D311yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
42C2×#3724C2×C311yescharacteristic, complemented
43C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
44C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
45C3×C3⋊#95—31no—
46C3×C3⋊#95—31no—
47#63579C2×C311yescharacteristic, complemented
48C23×C33C2311yescharacteristic
49C22×C32×D3—21no—
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3—21no—
55C22×C32×D3Q812yes—
56C2×C33×C4—21no—
57C2×C33×C4—21no—
58C2×C33×C4D412yes—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3D412yes—
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×Dic3—21no—
72C2×C32×Dic3—21no—
73C2×C32×Dic3D412yes—
74C3×#396—91no—
75#4994—31no—
76#4948—31no—
77C24×C32—31no—
78C23×C3×D3—21no—
79C23×C3×D3C2×D311yescharacteristic
80C23×C3×D3C22×C311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—21no—
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C32×C4—31no—
87C22×C32×C4—41no—
88C22×C32×C4C2×D311yescharacteristic
89C22×C32×C4C2×D311yescharacteristic
90C22×C32×C4C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C22×C3⋊Dic3C22×C311yescharacteristic
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—61no—
101C22×C3×Dic3—61no—
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C22×C311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107C22×C3×Dic3C22×C311yescharacteristic
108C32×C4⋊C4—62no—
109C32×C22⋊C4—62no—
110C4⋊(C3⋊Dic3)—22no—
111C3×#217—62no—
112C3×#217—62no—
113C3×(C2×D3)⋊C4—24no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—62no—
117C3×(C2×D3)⋊C4—62no—
118C3×C4⋊Dic3—62no—
119C3×C4⋊Dic3—62no—
120C3×C4⋊Dic3—64no—
121C3×Dic3⋊C4—24no—
122C3×Dic3⋊C4—22no—
123C3×Dic3⋊C4—22no—
124C3×Dic3⋊C4—62no—
125C3×Dic3⋊C4—62no—
126#3724—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129C22×C33C2×D411yescharacteristic
130C22×C33C2×D411yescharacteristic
131C22×C33C2×D411yescharacteristic
132C22×C33C2×Q811yescharacteristic
133C22×C33#4111yescharacteristic
134C22×C33#4111yescharacteristic
135C22×C33#4111yescharacteristic
136C2×C32×D3—22no—
137C2×C32×D3—22no—
138C2×C32×D3—22no—
139C2×C32×D3—41no—
140C2×C32×D3—41no—
141C2×C32×D3—41no—
142C2×C32×D3—41no—
143C33×C4—22no—
144C3×C3⋊Dic3—22no—
145C3×C3⋊Dic3—41no—
146C32×Dic3—22no—
147C32×Dic3—41no—
148C32×Dic3—41no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—61no—
152C2×C3×C4⋊C4—91no—
153C2×C3×C4⋊C4—91no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—61no—
157C2×C3×C22⋊C4—91no—
158C2×C3×C22⋊C4—91no—
159C2×#217—31no—
160C2×#217—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4C3×D311yescharacteristic
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—61no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4C3×D311yescharacteristic, complemented
170C3×#95—91no—
171C3⋊#95—31no—
172C3⋊#95—31no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—32no—
177C23×C32—41no—
178C23×C32—61no—
179C23×C32—61no—
180C23×C32—61no—
181C23×C32—61no—
182C23×C32—61no—
183C23×C32—61no—
184C23×C32C22×D311yescharacteristic
185C23×C32C22×D311yescharacteristic
186C23×C32C23×C311yescharacteristic
187C22×C3×D3—22no—
188C22×C3×D3—22no—
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—21no—
197C22×C3×D3—21no—
198C22×C3×D3—21no—
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—22no—
202C22×C3×D3—41no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3—41no—
206C22×C3×D3Dic612yes—
207C22×C3×D3C3×Q812yes—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—22no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4—32no—
220C2×C32×C4—42no—
221C2×C32×C4—41no—
222C2×C32×C4—41no—
223C2×C32×C4—41no—
224C2×C32×C4—41no—
225C2×C32×C4—42no—
226C2×C32×C4—42no—
227C2×C32×C4—61no—
228C2×C32×C4—61no—
229C2×C32×C4—61no—
230C2×C32×C4—61no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C32×C4—61no—
234C2×C32×C4—61no—
235C2×C32×C4#6712yes—
236C2×C32×C4#6712yes—
237C2×C32×C4C3×D412yes—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C3×D412yes—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—41no—
268C2×C3×Dic3—41no—
269C2×C3×Dic3—41no—
270C2×C3×Dic3—41no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—121no—
284C2×C3×Dic3—121no—
285C2×C3×Dic3—121no—
286C2×C3×Dic3—121no—
287C2×C3×Dic3D1212yes—
288C2×C3×Dic3C3×D412yes—
289#396—91noSylow
290C2×C33#12111yescharacteristic
291C2×C33#12111yescharacteristic
292C2×C33#12111yescharacteristic
293C2×C33C22⋊Q811yescharacteristic
294C2×C33C22⋊Q811yescharacteristic
295C2×C33C22⋊Q811yescharacteristic
296C2×C33#12611yescharacteristic
297C32×D3—42no—
298C24×C3—31no—
299C24×C3—31no—
300C24×C3—61no—
301C23×D3C2×C3×D311yescharacteristic
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—41no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—91no—
316C22×C3×C4—91no—
317C22×C3×C4D3211yescharacteristic
318C22×C3×C4C2×C3×D311yescharacteristic
319C22×C3×C4C2×C3×D311yescharacteristic
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3C2×C3×D311yescharacteristic
327C22×Dic3C2×C3×D311yescharacteristic
328C22×Dic3C2×C3×D311yescharacteristic
329C3×C4⋊C4—64no—
330C3×C4⋊C4—62no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—182no—
333C3×C4⋊C4—182no—
334C3×C22⋊C4—64no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—182no—
338C3×C22⋊C4—182no—
339#217—62no—
340#217—62no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344C4⋊Dic3—62no—
345C4⋊Dic3—62no—
346C4⋊Dic3—64no—
347Dic3⋊C4—22no—
348Dic3⋊C4—62no—
349Dic3⋊C4—62no—
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—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—41no—
372C22×C32—41no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32—62no—
379C22×C32—62no—
380C22×C32—62no—
381C22×C32—121no—
382C22×C32—121no—
383C22×C32—121no—
384C22×C32—121no—
385C22×C32C2×Dic611yescharacteristic
386C22×C32C2×D1211yescharacteristic
387C22×C32#23511yescharacteristic
388C22×C32#23511yescharacteristic
389C22×C32D3×D411yescharacteristic
390C22×C32D3×D411yescharacteristic
391C22×C32D3×D411yescharacteristic
392C22×C32#23711yescharacteristic
393C22×C32#23711yescharacteristic
394C22×C32#23711yescharacteristic
395C22×C32D3×Q811yescharacteristic
396C22×C32#23911yescharacteristic
397C22×C32C2×#6711yescharacteristic
398C22×C32C2×#6711yescharacteristic
399C22×C32C2×C3×D411yescharacteristic
400C22×C32C2×C3×D411yescharacteristic
401C22×C32C2×C3×D411yescharacteristic
402C22×C32C2×C3×Q811yescharacteristic
403C22×C32C3×#4111yescharacteristic
404C22×C32C3×#4111yescharacteristic
405C22×C32C3×#4111yescharacteristic
406C2×C3×D3—24no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—22no—
412C2×C3×D3—22no—
413C2×C3×D3—42no—
414C2×C3×D3—42no—
415C2×C3×D3—42no—
416C2×C3×D3—42no—
417C2×C3×D3—42no—
418C2×C3×D3—42no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C32×C4—22no—
428C32×C4—24no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—42no—
432C32×C4—42no—
433C32×C4—44no—
434C32×C4—62no—
435C32×C4—121no—
436C32×C4—121no—
437C3⋊Dic3—22no—
438C3⋊Dic3—41no—
439C3×Dic3—24no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—42no—
443C3×Dic3—42no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—122no—
451C3×Dic3—122no—
452C3×Dic3—121no—
453C3×Dic3—121no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C22⋊C4—31no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460#95—91no—
461C33#39611yescharacteristic, complemented, Sylow
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—32no—
466C23×C3—32no—
467C23×C3—41no—
468C23×C3—62no—
469C23×C3—62no—
470C23×C3—62no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—121no—
484C23×C3—121no—
485C23×C3—121no—
486C23×C3—121no—
487C23×C3C2×D3211yescharacteristic
488C23×C3C22×C3×D311yescharacteristic
489C23×C3C22×C3×D311yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3C3×Dic612yes—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—62no—
525C2×C3×C4—62no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—92no—
539C2×C3×C4—121no—
540C2×C3×C4—121no—
541C2×C3×C4—121no—
542C2×C3×C4—121no—
543C2×C3×C4—181no—
544C2×C3×C4—181no—
545C2×C3×C4—181no—
546C2×C3×C4—181no—
547C2×C3×C4—181no—
548C2×C3×C4#62512yes—
549C2×C3×C4C3×#6712yes—
550C2×C3×C4C3×#6712yes—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—62no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—62no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3C3×D1212yes—
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—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—41no—
600C2×C32—41no—
601C2×C32—41no—
602C2×C32—41no—
603C2×C32—41no—
604C2×C32—41no—
605C2×C32—41no—
606C2×C32—122no—
607C2×C32#87811yescharacteristic
608C2×C32#87811yescharacteristic
609C2×C32#87911yescharacteristic
610C2×C32#88411yescharacteristic
611C2×C32#89511yescharacteristic
612C2×C32#89611yescharacteristic
613C2×C32#89711yescharacteristic
614C2×C32#89811yescharacteristic
615C2×C32#92411yescharacteristic
616C2×C32#93011yescharacteristic
617C2×C32#93811yescharacteristic
618C2×C32#93911yescharacteristic
619C2×C32#93911yescharacteristic
620C2×C32#94611yescharacteristic
621C2×C32C3×#12111yescharacteristic
622C2×C32C3×#12111yescharacteristic
623C2×C32C3×#12111yescharacteristic
624C2×C32C3×C22⋊Q811yescharacteristic
625C2×C32C3×C22⋊Q811yescharacteristic
626C2×C32C3×C22⋊Q811yescharacteristic
627C2×C32C3×#12611yescharacteristic
628C3×D3—44no—
629C3×D3—42no—
630C3×D3—42no—
631C24—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—91no—
636C22×C4—91no—
637C22×C4C3×D3211yescharacteristic
638C4⋊C4—62no—
639C4⋊C4—182no—
640C4⋊C4—182no—
641C22⋊C4—62no—
642C22⋊C4—182no—
643C22⋊C4—182no—
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—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—64no—
673C22×C3—62no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—122no—
680C22×C3—122no—
681C22×C3—122no—
682C22×C3—122no—
683C22×C3—122no—
684C22×C3—122no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3D3×Dic611yescharacteristic
694C22×C3#379511yescharacteristic
695C22×C3#379911yescharacteristic
696C22×C3D3×D1211yescharacteristic
697C22×C3#380511yescharacteristic
698C22×C3C2×#62511yescharacteristic
699C22×C3#381111yescharacteristic
700C22×C3C2×C3×Dic611yescharacteristic
701C22×C3C2×C3×D1211yescharacteristic
702C22×C3C3×#23511yescharacteristic
703C22×C3C3×#23511yescharacteristic
704C22×C3C3×D3×D411yescharacteristic
705C22×C3C3×D3×D411yescharacteristic
706C22×C3C3×D3×D411yescharacteristic
707C22×C3C3×#23711yescharacteristic
708C22×C3C3×#23711yescharacteristic
709C22×C3C3×#23711yescharacteristic
710C22×C3C3×D3×Q811yescharacteristic
711C22×C3C3×#23911yescharacteristic
712C22×C3C2×C3×#6711yescharacteristic
713C22×C3C2×C3×#6711yescharacteristic
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C3×C4—24no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—44no—
728C3×C4—64no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—122no—
732C3×C4—122no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—121no—
737C3×C4—182no—
738C3×C4—361no—
739Dic3—22no—
740Dic3—41no—
741Dic3—41no—
742Dic3—62no—
743Dic3—62no—
744Dic3—122no—
745Dic3—122no—
746Dic3—121no—
747Dic3—121no—
748C32—21no—
749C32—21no—
750C32—21no—
751C32—41no—
752C32#494811yescharacteristic, complemented
753C32#499411yescharacteristic, complemented
754C32C3×#39611yescharacteristic, complemented
755C23—32no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23C2×C3×D3211yescharacteristic
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—32no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—92no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4C3×#62512yes—
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—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—41no—
805C2×C3—41no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3—41no—
809C2×C3—124no—
810C2×C3—122no—
811C2×C3—122no—
812C2×C3#6385611yescharacteristic
813C2×C3#6386111yescharacteristic
814C2×C3#6389311yescharacteristic
815C2×C3#6389611yescharacteristic
816C2×C3#6390811yescharacteristic
817C2×C3#6391011yescharacteristic
818C2×C3#6398011yescharacteristic
819C2×C3C3×#87811yescharacteristic
820C2×C3C3×#87811yescharacteristic
821C2×C3C3×#87911yescharacteristic
822C2×C3C3×#88411yescharacteristic
823C2×C3C3×#89511yescharacteristic
824C2×C3C3×#89611yescharacteristic
825C2×C3C3×#89711yescharacteristic
826C2×C3C3×#89811yescharacteristic
827C2×C3C3×#92411yescharacteristic
828C2×C3C3×#93011yescharacteristic
829C2×C3C3×#93811yescharacteristic
830C2×C3C3×#93911yescharacteristic
831C2×C3C3×#93911yescharacteristic
832C2×C3C3×#94611yescharacteristic
833D3—42no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22C3×D3×Dic611yescharacteristic
842C22C3×#379511yescharacteristic
843C22C3×#379911yescharacteristic
844C22C3×D3×D1211yescharacteristic
845C22C3×#380511yescharacteristic
846C22C2×C3×#62511yescharacteristic
847C22C3×#381111yescharacteristic
848C4—22no—
849C4—62no—
850C4—121no—
851C4—121no—
852C4—182no—
853C4—361no—
854C3—21no—
855C3—21no—
856C3—21no—
857C3—41no—
858C3#1059131911yescharacteristic, direct product factor
859C3C3×#494811yescharacteristic, complemented
860C3C3×#499411yescharacteristic, complemented
861C2—122no—
862C2C3×#6385611yescharacteristic
863C2C3×#6386111yescharacteristic
864C2C3×#6389311yescharacteristic
865C2C3×#6389611yescharacteristic
866C2C3×#6390811yescharacteristic
867C2C3×#6391011yescharacteristic
868C2C3×#6398011yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
hypercenterC22×C3×C4D32
hypocenterC32C3×#396
LCSG ▷ C23×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
3. C2×C32×Dic3⋊C4C2semidirect
4. C2×C3×#3724C2semidirect
7. C3×#63579C2semidirect
10. #10591319C3direct (N × H)
26. C2×C4⋊(C3⋊Dic3)C2×C3semidirect
40. C2×C3×Dic3⋊C4D3semidirect
41. C2×C3×Dic3⋊C4C2×C3semidirect
42. C2×#3724C2×C3semidirect
47. #63579C2×C3semidirect
169. C2×Dic3⋊C4C3×D3semidirect
461. C33#396semidirect
752. C32#4948semidirect
753. C32#4994semidirect
754. C32C3×#396semidirect
858. C3#10591319direct (N × H)
859. C3C3×#4948semidirect
860. C3C3×#4994semidirect

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×C32×Dic3⋊C42
C2×C3×#37242
C2×C3×(C2×D3)⋊Dic32
C3×#635792
C3×#49943
C3×#49483
#105913193