Finite Group Databasebeta

← C2×C3×#4994 #11808258

Subgroups — C2×C3×#4994 #11808258

Order 1152.

2025 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
5C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4994C218yesmaximal, direct product factor
9C2×C3×#396—31nomaximal
10C2×#4994C311yesmaximal, characteristic, direct product factor
11C24×C3×D3C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×C32×C4⋊C4—24no—
19C2×C32×C4⋊C4C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—24no—
21C2×C3×(C2×D3)⋊C4—24no—
22C2×C3×(C2×D3)⋊C4—24no—
23C2×C3×(C2×D3)⋊C4C2214yes—
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×(C2×D3)⋊C4C2214yes—
26C2×C3×C4⋊Dic3—24no—
27C2×C3×C4⋊Dic3C2214yescomplemented
28C2×C3×Dic3⋊C4—24no—
29C2×C3×Dic3⋊C4C2214yescomplemented
30C3×C3⋊#95C2214yescomplemented
31C22×C3×C4⋊C4—21no—
32C22×C3×C4⋊C4—31no—
33C22×C3×C4⋊C4—31no—
34C22×C3×C4⋊C4D311yescharacteristic, complemented
35C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
36C22×C3×C22⋊C4—31no—
37C22×C3×C22⋊C4—31no—
38C22×C3×C22⋊C4—31no—
39C22×(C2×D3)⋊C4C2×C311yescharacteristic
40C22×(C2×D3)⋊C4C2×C311yescharacteristic
41C22×(C2×D3)⋊C4C2×C311yescharacteristic
42C22×C4⋊Dic3C2×C311yescharacteristic, complemented
43C22×Dic3⋊C4C2×C311yescharacteristic, complemented
44C3×#396—38no—
45C2×C3×#95—31no—
46C2×C3⋊#95C2×C311yescharacteristic, complemented
47#4994C2×C318yesdirect product factor
48C24×C32C2311yescharacteristic
49C23×C3×D3—22no—
50C23×C3×D3—22no—
51C23×C3×D3—22no—
52C23×C3×D3—22no—
53C23×C3×D3—22no—
54C23×C3×D3—22no—
55C23×C3×D3Q814yes—
56C23×C3×D3C2312yes—
57C22×C32×C4—22no—
58C22×C32×C4—22no—
59C22×C32×C4—22no—
60C22×C32×C4—22no—
61C22×C32×C4—22no—
62C22×C32×C4—22no—
63C22×C32×C4—22no—
64C22×C32×C4D414yes—
65C22×C32×C4D414yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2312yes—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3D414yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C32×C4⋊C4—28no—
82C3×(C2×D3)⋊C4—28no—
83C3×(C2×D3)⋊C4—28no—
84C3×(C2×D3)⋊C4—28no—
85C3×C4⋊Dic3—28no—
86C3×Dic3⋊C4—28no—
87C2×#396—31noSylow
88C25×C3—31no—
89C24×D3C22×C311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C23×C3×C4—31no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C2×D311yescharacteristic
99C23×C3×C4C22×C311yescharacteristic
100C23×C3×C4C22×C311yescharacteristic
101C23×C3×C4C22×C311yescharacteristic
102C23×Dic3C22×C311yescharacteristic
103C23×Dic3C22×C311yescharacteristic
104C23×Dic3C22×C311yescharacteristic
105C2×C3×C4⋊C4—28no—
106C2×C3×C4⋊C4—24no—
107C2×C3×C4⋊C4—24no—
108C2×C3×C4⋊C4—24no—
109C2×C3×C4⋊C4—34no—
110C2×C3×C4⋊C4—34no—
111C2×C3×C4⋊C4—64no—
112C2×C3×C4⋊C4—64no—
113C2×C3×C4⋊C4C2×D314yescomplemented
114C2×C3×C4⋊C4C22×C314yescomplemented
115C2×C3×C22⋊C4—34no—
116C2×C3×C22⋊C4—34no—
117C2×C3×C22⋊C4—34no—
118C2×C3×C22⋊C4—64no—
119C2×C3×C22⋊C4—64no—
120C2×C3×C22⋊C4—64no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4C22×C314yes—
125C2×(C2×D3)⋊C4C22×C314yes—
126C2×(C2×D3)⋊C4C22×C314yes—
127C2×C4⋊Dic3—24no—
128C2×C4⋊Dic3C22×C314yescomplemented
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4C22×C314yescomplemented
131C3×#95—34no—
132C3⋊#95C22×C314yescomplemented
133C23×C32C2×D412yes—
134C23×C32C2×D412yes—
135C23×C32C2×D412yes—
136C23×C32C2×Q812yes—
137C23×C32#4112yes—
138C23×C32#4112yes—
139C23×C32#4112yes—
140C23×C32C2411yescharacteristic
141C22×C3×D3—28no—
142C22×C3×D3—28no—
143C22×C3×D3—28no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—44no—
151C22×C3×D3—44no—
152C22×C3×D3—44no—
153C22×C3×D3—44no—
154C22×C3×D3C2×Q814yes—
155C2×C32×C4—28no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—28no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—44no—
165C2×C32×C4C2×D414yes—
166C2×C32×C4C2×D414yes—
167C2×C3×Dic3—28no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—44no—
177C2×C3×Dic3—44no—
178C2×C3×Dic3C2×D414yes—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4C3×D311yescharacteristic, complemented
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185#396—38no—
186C2×#95—31no—
187C24×C3—21no—
188C24×C3—34no—
189C24×C3—32no—
190C24×C3—62no—
191C24×C3—62no—
192C24×C3—62no—
193C24×C3—62no—
194C24×C3—62no—
195C24×C3—62no—
196C24×C3C22×D311yescharacteristic
197C24×C3C23×C311yescharacteristic
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—22no—
202C23×D3—22no—
203C23×D3—22no—
204C23×D3C3×Q814yes—
205C23×D3C23×C312yes—
206C22×C3×C4—24no—
207C22×C3×C4—24no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—24no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—24no—
224C22×C3×C4—24no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—34no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—42no—
236C22×C3×C4—62no—
237C22×C3×C4—62no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4—62no—
241C22×C3×C4—62no—
242C22×C3×C4—62no—
243C22×C3×C4—62no—
244C22×C3×C4D1214yes—
245C22×C3×C4#6714yes—
246C22×C3×C4C3×D414yes—
247C22×C3×C4C3×D414yes—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C23×C312yes—
252C22×C3×C4C23×C312yes—
253C22×C3×C4C23×C312yes—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3C3×D414yes—
263C22×Dic3C23×C312yes—
264C22×Dic3C23×C312yes—
265C22×Dic3C23×C312yes—
266C3×C4⋊C4—216no—
267C3×C4⋊C4—28no—
268C3×C4⋊C4—28no—
269C3×C4⋊C4—68no—
270C3×C4⋊C4—68no—
271C3×C22⋊C4—68no—
272C3×C22⋊C4—68no—
273C3×C22⋊C4—68no—
274(C2×D3)⋊C4—28no—
275(C2×D3)⋊C4—28no—
276(C2×D3)⋊C4—28no—
277C4⋊Dic3—28no—
278Dic3⋊C4—28no—
279C22×C32#12114yes—
280C22×C32#12114yes—
281C22×C32#12114yes—
282C22×C32C22⋊Q814yes—
283C22×C32C22⋊Q814yes—
284C22×C32C22⋊Q814yes—
285C22×C32#12614yes—
286C22×C32C22×D411yescharacteristic
287C22×C32C22×D411yescharacteristic
288C22×C32C22×D411yescharacteristic
289C22×C32C22×Q811yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C22×C32C2×#4111yescharacteristic
292C22×C32C2×#4111yescharacteristic
293C2×C3×D3—24no—
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3—42no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C2×C3×D3—42no—
300C2×C3×D3—416no—
301C32×C4—24no—
302C32×C4—24no—
303C32×C4—42no—
304C3×Dic3—24no—
305C3×Dic3—42no—
306C3×Dic3—42no—
307C25—31no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4C2×C3×D311yescharacteristic
312C23×C4C2×C3×D311yescharacteristic
313C23×C4C2×C3×D311yescharacteristic
314C2×C4⋊C4—24no—
315C2×C4⋊C4—34no—
316C2×C4⋊C4—34no—
317C2×C4⋊C4—64no—
318C2×C4⋊C4—64no—
319C2×C4⋊C4C2×C3×D314yescomplemented
320C2×C22⋊C4—34no—
321C2×C22⋊C4—34no—
322C2×C22⋊C4—34no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326#95—34no—
327C23×C3—21no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—34no—
336C23×C3—68no—
337C23×C3—68no—
338C23×C3—68no—
339C23×C3—62no—
340C23×C3—62no—
341C23×C3—62no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—62no—
345C23×C3—124no—
346C23×C3—124no—
347C23×C3—124no—
348C23×C3—124no—
349C23×C3C2×D1212yes—
350C23×C3#23512yes—
351C23×C3D3×D412yes—
352C23×C3#23712yes—
353C23×C3D3×Q812yes—
354C23×C3#23912yes—
355C23×C3C2×#6712yes—
356C23×C3C2×C3×D412yes—
357C23×C3C2×C3×D412yes—
358C23×C3C2×C3×D412yes—
359C23×C3C2×C3×Q812yes—
360C23×C3C3×#4112yes—
361C23×C3C3×#4112yes—
362C23×C3C3×#4112yes—
363C23×C3C23×D311yescharacteristic
364C23×C3C24×C311yescharacteristic
365C22×D3—28no—
366C22×D3—28no—
367C22×D3—28no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—44no—
375C22×D3—44no—
376C22×D3—44no—
377C22×D3—44no—
378C22×D3C2×C3×Q814yes—
379C2×C3×C4—24no—
380C2×C3×C4—216no—
381C2×C3×C4—24no—
382C2×C3×C4—28no—
383C2×C3×C4—28no—
384C2×C3×C4—28no—
385C2×C3×C4—28no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—34no—
404C2×C3×C4—48no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—48no—
410C2×C3×C4—44no—
411C2×C3×C4—44no—
412C2×C3×C4—68no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—124no—
422C2×C3×C4—124no—
423C2×C3×C4C2×D1214yes—
424C2×C3×C4C2×#6714yes—
425C2×C3×C4C2×C3×D414yes—
426C2×C3×C4C2×C3×D414yes—
427C2×Dic3—28no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—44no—
437C2×Dic3—44no—
438C2×Dic3C2×C3×D414yes—
439C2×C32#39618yescomplemented
440C2×C32C2×#12111yescharacteristic
441C2×C32C2×#12111yescharacteristic
442C2×C32C2×#12111yescharacteristic
443C2×C32C2×C22⋊Q811yescharacteristic
444C2×C32C2×C22⋊Q811yescharacteristic
445C2×C32C2×C22⋊Q811yescharacteristic
446C2×C32C2×#12611yescharacteristic
447C3×D3—44no—
448C24—32no—
449C24—34no—
450C24—62no—
451C24—62no—
452C24—62no—
453C24—62no—
454C24—62no—
455C24—62no—
456C24C22×C3×D311yescharacteristic
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—32no—
465C22×C4—34no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—62no—
469C22×C4—62no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4C3×D1214yes—
477C22×C4C3×#6714yes—
478C22×C4C22×C3×D312yes—
479C22×C4C22×C3×D312yes—
480C22×C4C22×C3×D312yes—
481C4⋊C4—28no—
482C4⋊C4—68no—
483C4⋊C4—68no—
484C22⋊C4—68no—
485C22⋊C4—68no—
486C22⋊C4—68no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—24no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—64no—
502C22×C3—64no—
503C22×C3—64no—
504C22×C3—1216no—
505C22×C3—122no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3#89514yes—
510C22×C3#89614yes—
511C22×C3#89714yes—
512C22×C3#89814yes—
513C22×C3#93014yes—
514C22×C3#93914yes—
515C22×C3#94614yes—
516C22×C3C3×#12114yes—
517C22×C3C3×#12114yes—
518C22×C3C3×#12114yes—
519C22×C3C3×C22⋊Q814yes—
520C22×C3C3×C22⋊Q814yes—
521C22×C3C3×C22⋊Q814yes—
522C22×C3C3×#12614yes—
523C22×C3C22×D1211yescharacteristic
524C22×C3C2×#23511yescharacteristic
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C2×#23711yescharacteristic
527C22×C3C2×D3×Q811yescharacteristic
528C22×C3C2×#23911yescharacteristic
529C22×C3C22×#6711yescharacteristic
530C22×C3C22×C3×D411yescharacteristic
531C22×C3C22×C3×D411yescharacteristic
532C22×C3C22×C3×D411yescharacteristic
533C22×C3C22×C3×Q811yescharacteristic
534C22×C3C2×C3×#4111yescharacteristic
535C22×C3C2×C3×#4111yescharacteristic
536C22×C3C2×C3×#4111yescharacteristic
537C2×D3—24no—
538C2×D3—24no—
539C2×D3—24no—
540C2×D3—416no—
541C2×D3—42no—
542C2×D3—42no—
543C2×D3—42no—
544C2×D3—42no—
545C3×C4—28no—
546C3×C4—24no—
547C3×C4—24no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—44no—
551C3×C4—44no—
552C3×C4—42no—
553C3×C4—42no—
554C3×C4—64no—
555C3×C4—122no—
556C3×C4—122no—
557Dic3—24no—
558Dic3—42no—
559Dic3—42no—
560C32C2×#39611yescharacteristic, complemented, Sylow
561C23—34no—
562C23—68no—
563C23—68no—
564C23—68no—
565C23—62no—
566C23—62no—
567C23—62no—
568C23—62no—
569C23—62no—
570C23—62no—
571C23—124no—
572C23—124no—
573C23—124no—
574C23—124no—
575C23C2×C3×D1212yes—
576C23C3×#23512yes—
577C23C3×D3×D412yes—
578C23C3×#23712yes—
579C23C3×D3×Q812yes—
580C23C3×#23912yes—
581C23C2×C3×#6712yes—
582C23C23×C3×D311yescharacteristic
583C2×C4—28no—
584C2×C4—28no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—34no—
593C2×C4—44no—
594C2×C4—68no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—124no—
604C2×C4—124no—
605C2×C4C2×C3×D1214yes—
606C2×C4C2×C3×#6714yes—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—28no—
615C2×C3—124no—
616C2×C3#499418yesdirect product factor
617C2×C3C3×#39618yescomplemented
618C2×C3C2×#89511yescharacteristic
619C2×C3C2×#89611yescharacteristic
620C2×C3C2×#89711yescharacteristic
621C2×C3C2×#89811yescharacteristic
622C2×C3C2×#93011yescharacteristic
623C2×C3C2×#93911yescharacteristic
624C2×C3C2×#94611yescharacteristic
625C2×C3C2×C3×#12111yescharacteristic
626C2×C3C2×C3×#12111yescharacteristic
627C2×C3C2×C3×#12111yescharacteristic
628C2×C3C2×C3×C22⋊Q811yescharacteristic
629C2×C3C2×C3×C22⋊Q811yescharacteristic
630C2×C3C2×C3×C22⋊Q811yescharacteristic
631C2×C3C2×C3×#12611yescharacteristic
632D3—44no—
633C22—64no—
634C22—64no—
635C22—64no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22—122no—
640C22—1216no—
641C22C3×#89514yes—
642C22C3×#89614yes—
643C22C3×#89714yes—
644C22C3×#89814yes—
645C22C3×#93014yes—
646C22C3×#93914yes—
647C22C3×#94614yes—
648C22C22×C3×D1211yescharacteristic
649C22C2×C3×#23511yescharacteristic
650C22C2×C3×D3×D411yescharacteristic
651C22C2×C3×#23711yescharacteristic
652C22C2×C3×D3×Q811yescharacteristic
653C22C2×C3×#23911yescharacteristic
654C22C22×C3×#6711yescharacteristic
655C4—24no—
656C4—24no—
657C4—42no—
658C4—64no—
659C4—122no—
660C4—122no—
661C3—21no—
662C3C2×#499411yescharacteristic, direct product factor
663C3C2×C3×#39611yescharacteristic, complemented
664C2—124no—
665C2C3×#499418yesdirect product factor
666C2C2×C3×#89511yescharacteristic
667C2C2×C3×#89611yescharacteristic
668C2C2×C3×#89711yescharacteristic
669C2C2×C3×#89811yescharacteristic
670C2C2×C3×#93011yescharacteristic
671C2C2×C3×#93911yescharacteristic
672C2C2×C3×#94611yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC22×C32×C4⋊C4C2
socleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4⋊C4C2semidirect
5. C22×C3×C4⋊Dic3C2semidirect
6. C22×C3×Dic3⋊C4C2semidirect
7. C2×C3×C3⋊#95C2semidirect
8. C3×#4994C2direct (N × H)
10. C2×#4994C3direct (N × H)
19. C2×C32×C4⋊C4C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
29. C2×C3×Dic3⋊C4C22semidirect
30. C3×C3⋊#95C22semidirect
34. C22×C3×C4⋊C4D3semidirect
35. C22×C3×C4⋊C4C2×C3semidirect
42. C22×C4⋊Dic3C2×C3semidirect
43. C22×Dic3⋊C4C2×C3semidirect
46. C2×C3⋊#95C2×C3semidirect
47. #4994C2×C3direct (N × H)
113. C2×C3×C4⋊C4C2×D3semidirect
114. C2×C3×C4⋊C4C22×C3semidirect
128. C2×C4⋊Dic3C22×C3semidirect
130. C2×Dic3⋊C4C22×C3semidirect
132. C3⋊#95C22×C3semidirect
181. C22×C4⋊C4C3×D3semidirect
319. C2×C4⋊C4C2×C3×D3semidirect
439. C2×C32#396semidirect
560. C32C2×#396semidirect
616. C2×C3#4994direct (N × H)
617. C2×C3C3×#396semidirect
662. C3C2×#4994direct (N × H)
663. C3C2×C3×#396semidirect
665. C2C3×#4994direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C3×#49942
C2×C3×#3963
C2×#49943