Finite Group Databasebeta

← C3×D3×#394 #11808132

Subgroups — C3×D3×#394 #11808132

Order 1152.

2623 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×D3×C22⋊C4C212yesmaximal, complemented
4C2×C3×D3×C22⋊C4C212yesmaximal, complemented
5C32×#394C211yesmaximal, characteristic, complemented
6C3×#5222C211yesmaximal, characteristic, complemented
7C3×#4991C211yesmaximal, characteristic, complemented
8C3×#4961C212yesmaximal, complemented
9C3×#4959C212yesmaximal, complemented
10C3×#4672C211yesmaximal, characteristic, complemented
11C3×D3×#95C211yesmaximal, characteristic, complemented
12C2×C3×#394—31nomaximal
13D3×#394C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2212yes—
15C22×C32×D4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C2×C3×D3×D4—24no—
18C2×C3×D3×D4—28no—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2212yescomplemented
26C2×C32×C22⋊C4C2212yescomplemented
27C2×C3×#217C2212yescomplemented
28C2×C3×#217C2212yescomplemented
29C2×C3×(C2×D3)⋊C4C2212yescomplemented
30C2×C3×(C2×D3)⋊C4C2212yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C3×D3×C4⋊C4—24no—
37C3×D3×C22⋊C4—28no—
38C3×D3×C22⋊C4—28no—
39C32×#95C2211yescharacteristic, complemented
40C3×C3⋊#95C2212yescomplemented
41C3×C3⋊#95C2211yescharacteristic, complemented
42C23×C3×D4—31no—
43C22×D3×D4C2×C311yescharacteristic
44C22×C3×C4⋊C4—31no—
45C22×C3×C22⋊C4—32no—
46C22×C3×C22⋊C4—32no—
47C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
48C2×D3×C22⋊C4C2×C312yescomplemented
49C2×D3×C22⋊C4C2×C312yescomplemented
50C3×#394—21no—
51C3×#394—31no—
52C3×#394—31no—
53C3×#394—32no—
54C3×#394—32no—
55C3×#394—31no—
56C3×#394D311yescharacteristic, direct product factor
57C3×#394C2×C311yescharacteristic, complemented
58C2×C3×#95—31no—
59#5222C2×C311yescharacteristic, complemented
60#4991C2×C311yescharacteristic, complemented
61#4961C2×C312yescomplemented
62#4959C2×C312yescomplemented
63#4672C2×C311yescharacteristic, complemented
64D3×#95C2×C311yescharacteristic, complemented
65C24×C32C2312yes—
66C23×C3×D3—24no—
67C23×C3×D3—24no—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3—24no—
72C23×C3×D3D418yes—
73C23×C3×D3C2312yes—
74C23×C3×D3C2311yescharacteristic
75C2×C32×D4—24no—
76C2×C32×D4—22no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C2×C3×#67—24no—
82C2×C3×#67—24no—
83C2×C3×#67—24no—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C3×D3×D4—232no—
89C2×C3×D12—24no—
90C2×C3×D12—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3—22no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3D414yes—
100C2×C3×C4×D3D414yescomplemented
101C32×C4⋊C4—22no—
102C32×C22⋊C4—24no—
103C32×C22⋊C4—24no—
104C3×#217—24no—
105C3×#217—24no—
106C3×(C2×D3)⋊C4—24no—
107C3×(C2×D3)⋊C4—24no—
108C3×(C2×D3)⋊C4—24no—
109C3×(C2×D3)⋊C4—24no—
110C3×C4⋊Dic3—22no—
111C3×Dic3⋊C4—22no—
112C3×Dic3⋊C4—22no—
113C2×#394—31noSylow
114C25×C3—32no—
115C24×D3C22×C312yes—
116C22×C3×D4—21no—
117C22×C3×D4—32no—
118C22×C3×D4—31no—
119C22×C3×D4—64no—
120C22×C3×D4—68no—
121C22×C3×D4C2×D311yescharacteristic
122C22×C3×D4C22×C311yescharacteristic
123C23×C3×C4—31no—
124C23×C3×C4—31no—
125C23×C3×C4—32no—
126C23×C3×C4—31no—
127C22×#67C22×C312yes—
128C2×D3×D4—28no—
129C2×D3×D4—24no—
130C22×D12C22×C311yescharacteristic
131C22×C4×D3C22×C312yes—
132C22×C4×D3C22×C311yescharacteristic
133C22×C4×D3C22×C311yescharacteristic
134C22×C4×D3C22×C311yescharacteristic
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—64no—
140C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
141C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—32no—
145C2×C3×C22⋊C4—32no—
146C2×C3×C22⋊C4—32no—
147C2×C3×C22⋊C4—32no—
148C2×C3×C22⋊C4—32no—
149C2×C3×C22⋊C4—32no—
150C2×C3×C22⋊C4—68no—
151C2×C3×C22⋊C4—68no—
152C2×C3×C22⋊C4C2×D312yescomplemented
153C2×C3×C22⋊C4C2×D312yescomplemented
154C2×C3×C22⋊C4C22×C312yescomplemented
155C2×C3×C22⋊C4C22×C312yescomplemented
156C2×#217C22×C312yescomplemented
157C2×#217C22×C312yescomplemented
158C2×(C2×D3)⋊C4C22×C312yescomplemented
159C2×(C2×D3)⋊C4C22×C312yescomplemented
160C2×(C2×D3)⋊C4C22×C312yescomplemented
161C2×(C2×D3)⋊C4C22×C312yescomplemented
162C2×C4⋊Dic3C22×C311yescharacteristic, complemented
163C2×Dic3⋊C4C22×C311yescharacteristic, complemented
164C2×Dic3⋊C4C22×C311yescharacteristic, complemented
165D3×C4⋊C4—24no—
166D3×C22⋊C4—28no—
167D3×C22⋊C4—28no—
168C3×#95—21no—
169C3×#95—32no—
170C3×#95—31no—
171C3×#95C2×D311yescharacteristic, complemented
172C3×#95C22×C311yescharacteristic, complemented
173C3⋊#95C22×C312yescomplemented
174C3⋊#95C22×C311yescharacteristic, complemented
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32C2×D414yes—
182C23×C32C2411yescharacteristic
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—216no—
190C22×C3×D3—216no—
191C22×C3×D3—216no—
192C22×C3×D3—48no—
193C22×C3×D3—48no—
194C22×C3×D3—48no—
195C22×C3×D3—48no—
196C22×C3×D3C2×D414yes—
197C22×C3×D3C2×D414yes—
198C22×C3×D3C2×D412yes—
199C22×C3×D3C2×D412yes—
200C22×C3×D3#4112yes—
201C22×C3×D3#4114yes—
202C32×D4—28no—
203C2×C32×C4—21no—
204C2×C32×C4—22no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4C2×D412yes—
212C2×C32×C4C2×D412yescomplemented
213C3×#67—216no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3C2×D412yes—
223C2×C3×Dic3C2×D412yescomplemented
224C3×D12—28no—
225C3×C4×D3—28no—
226C3×C4×D3—28no—
227C3×C4×D3—44no—
228C3×C4×D3—48no—
229C23×D4—31no—
230C22×C4⋊C4—31no—
231C22×C22⋊C4—32no—
232C22×C22⋊C4—32no—
233#394—31no—
234#394—31no—
235#394—32no—
236#394—32no—
237#394—31no—
238#394C3×D311yescharacteristic, direct product factor
239C2×#95—31no—
240C24×C3—22no—
241C24×C3—31no—
242C24×C3—38no—
243C24×C3—32no—
244C24×C3—64no—
245C24×C3—64no—
246C24×C3—64no—
247C24×C3—64no—
248C24×C3—64no—
249C24×C3—64no—
250C24×C3C22×D312yes—
251C24×C3C23×C312yes—
252C23×D3—24no—
253C23×D3—24no—
254C23×D3—24no—
255C23×D3—24no—
256C23×D3—24no—
257C23×D3—24no—
258C23×D3C3×D418yes—
259C23×D3C23×C312yes—
260C23×D3C23×C311yescharacteristic
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4—42no—
266C2×C3×D4—44no—
267C2×C3×D4—64no—
268C2×C3×D4—64no—
269C2×C3×D4—632no—
270C2×C3×D4—64no—
271C2×C3×D4—64no—
272C2×C3×D4—62no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—22no—
276C22×C3×C4—21no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—34no—
280C22×C3×C4—34no—
281C22×C3×C4—32no—
282C22×C3×C4—31no—
283C22×C3×C4—62no—
284C22×C3×C4—62no—
285C22×C3×C4—64no—
286C22×C3×C4—64no—
287C22×C3×C4—64no—
288C22×C3×C4—64no—
289C22×C3×C4—62no—
290C22×C3×C4—64no—
291C22×C3×C4C22×D312yes—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C23×C312yes—
296C22×C3×C4C23×C311yescharacteristic
297C22×C3×C4C23×C311yescharacteristic
298C22×C3×C4C23×C311yescharacteristic
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C22×Dic3C23×C312yes—
303C22×Dic3C23×C311yescharacteristic
304C22×Dic3C23×C311yescharacteristic
305C22×Dic3C23×C311yescharacteristic
306D3×D4—232no—
307C2×D12—24no—
308C2×D12—22no—
309C2×C4×D3—22no—
310C2×C4×D3—24no—
311C2×C4×D3—22no—
312C2×C4×D3—24no—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—22no—
316C2×C4×D3—24no—
317C2×C4×D3C3×D414yes—
318C2×C4×D3C3×D414yescomplemented
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—42no—
322C3×C4⋊C4—62no—
323C3×C4⋊C4—62no—
324C3×C4⋊C4—62no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—44no—
330C3×C22⋊C4—44no—
331C3×C22⋊C4—64no—
332C3×C22⋊C4—64no—
333C3×C22⋊C4—64no—
334C3×C22⋊C4—64no—
335C3×C22⋊C4—64no—
336C3×C22⋊C4—64no—
337#217—24no—
338#217—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—24no—
343C4⋊Dic3—22no—
344Dic3⋊C4—22no—
345Dic3⋊C4—22no—
346C22×C32—24no—
347C22×C32—24no—
348C22×C32—24no—
349C22×C32—42no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—42no—
353C22×C32C22×D412yes—
354C22×C32C22×D411yescharacteristic
355C22×C32C22×D411yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C22×C32C2×#4112yes—
358C2×C3×D3—24no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3—42no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C2×C3×D3—42no—
365C2×C3×D3—432no—
366C2×C3×D3#12014yes—
367C2×C3×D3#12114yes—
368C2×C3×D3#12118yes—
369C2×C3×D3#12318yes—
370C2×C3×D3#12414yes—
371C32×C4—22no—
372C32×C4—22no—
373C32×C4—41no—
374C32×C4—42no—
375C3×Dic3—22no—
376C3×Dic3—22no—
377C3×Dic3—41no—
378C3×Dic3—42no—
379C25—32no—
380C22×D4—32no—
381C22×D4—31no—
382C22×D4—64no—
383C22×D4—68no—
384C22×D4C2×C3×D311yescharacteristic
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—32no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—64no—
393C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—32no—
400C2×C22⋊C4—68no—
401C2×C22⋊C4—68no—
402C2×C22⋊C4C2×C3×D312yescomplemented
403C2×C22⋊C4C2×C3×D312yescomplemented
404#95—32no—
405#95—31no—
406#95C2×C3×D311yescharacteristic, complemented
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—21no—
420C23×C3—24no—
421C23×C3—32no—
422C23×C3—32no—
423C23×C3—34no—
424C23×C3—32no—
425C23×C3—34no—
426C23×C3—34no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—616no—
434C23×C3—616no—
435C23×C3—616no—
436C23×C3—62no—
437C23×C3—62no—
438C23×C3—62no—
439C23×C3—62no—
440C23×C3—62no—
441C23×C3—62no—
442C23×C3—128no—
443C23×C3—128no—
444C23×C3—128no—
445C23×C3—128no—
446C23×C3D3×D414yes—
447C23×C3C2×C3×D414yes—
448C23×C3C23×D311yescharacteristic
449C23×C3C24×C311yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—216no—
457C22×D3—216no—
458C22×D3—216no—
459C22×D3—48no—
460C22×D3—48no—
461C22×D3—48no—
462C22×D3—48no—
463C22×D3C2×C3×D414yes—
464C22×D3C2×C3×D414yes—
465C22×D3C2×C3×D412yes—
466C22×D3C2×C3×D412yes—
467C22×D3C3×#4112yes—
468C22×D3C3×#4114yes—
469C3×D4—28no—
470C3×D4—28no—
471C3×D4—48no—
472C3×D4—68no—
473C3×D4—616no—
474C2×C3×C4—21no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4—68no—
503C2×C3×C4—68no—
504C2×C3×C4—61no—
505C2×C3×C4—62no—
506C2×C3×C4—61no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—61no—
511C2×C3×C4—62no—
512C2×C3×C4—124no—
513C2×C3×C4—128no—
514C2×C3×C4D3×D412yes—
515C2×C3×C4D3×D412yescomplemented
516C2×C3×C4C2×C3×D412yes—
517C2×C3×C4C2×C3×D412yescomplemented
518#67—216no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3C2×C3×D412yes—
528C2×Dic3C2×C3×D412yescomplemented
529D12—28no—
530C4×D3—28no—
531C4×D3—28no—
532C4×D3—44no—
533C4×D3—48no—
534C2×C32—44no—
535C2×C32C2×#12011yescharacteristic
536C2×C32C2×#12111yescharacteristic
537C2×C32C2×#12112yes—
538C2×C32C2×#12312yes—
539C2×C32C2×#12411yescharacteristic
540C3×D3—44no—
541C3×D3#39418yesdirect product factor
542C24—31no—
543C24—32no—
544C24—38no—
545C24—64no—
546C24—64no—
547C24—64no—
548C24—64no—
549C24—64no—
550C24—64no—
551C24C22×C3×D312yes—
552C2×D4—24no—
553C2×D4—22no—
554C2×D4—64no—
555C2×D4—64no—
556C2×D4—632no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—62no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—34no—
563C22×C4—34no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—62no—
567C22×C4—64no—
568C22×C4—62no—
569C22×C4—64no—
570C22×C4—64no—
571C22×C4—64no—
572C22×C4—62no—
573C22×C4—64no—
574C22×C4C22×C3×D312yes—
575C22×C4C22×C3×D311yescharacteristic
576C22×C4C22×C3×D311yescharacteristic
577C22×C4C22×C3×D311yescharacteristic
578C4⋊C4—22no—
579C4⋊C4—62no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—64no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C22⋊C4—64no—
589C22⋊C4—64no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—22no—
599C22×C3—21no—
600C22×C3—22no—
601C22×C3—38no—
602C22×C3—34no—
603C22×C3—34no—
604C22×C3—34no—
605C22×C3—38no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—64no—
618C22×C3—64no—
619C22×C3—64no—
620C22×C3—82no—
621C22×C3—82no—
622C22×C3—82no—
623C22×C3—82no—
624C22×C3—1232no—
625C22×C3—122no—
626C22×C3—122no—
627C22×C3—122no—
628C22×C3—122no—
629C22×C3C2×D3×D412yes—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C22×C3D3×#4111yescharacteristic
633C22×C3D3×#4112yes—
634C22×C3C22×C3×D412yes—
635C22×C3C22×C3×D411yescharacteristic
636C22×C3C22×C3×D411yescharacteristic
637C22×C3C2×C3×#4111yescharacteristic
638C22×C3C2×C3×#4112yes—
639C2×D3—24no—
640C2×D3—24no—
641C2×D3—24no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C2×D3—42no—
646C2×D3—432no—
647C2×D3C3×#12014yes—
648C2×D3C3×#12114yes—
649C2×D3C3×#12118yes—
650C2×D3C3×#12318yes—
651C2×D3C3×#12414yes—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—81no—
665C3×C4—82no—
666C3×C4—121no—
667C3×C4—122no—
668Dic3—22no—
669Dic3—22no—
670Dic3—41no—
671Dic3—42no—
672C32C2×#39411yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—32no—
680C23—32no—
681C23—34no—
682C23—32no—
683C23—34no—
684C23—34no—
685C23—616no—
686C23—616no—
687C23—616no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—62no—
692C23—62no—
693C23—62no—
694C23—128no—
695C23—128no—
696C23—128no—
697C23—128no—
698C23C3×D3×D414yes—
699C23C23×C3×D311yescharacteristic
700D4—28no—
701D4—68no—
702D4—616no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—68no—
714C2×C4—68no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—61no—
722C2×C4—62no—
723C2×C4—124no—
724C2×C4—128no—
725C2×C4C3×D3×D412yes—
726C2×C4C3×D3×D412yescomplemented
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—21no—
732C2×C3—38no—
733C2×C3—44no—
734C2×C3—44no—
735C2×C3—84no—
736C2×C3—124no—
737C2×C3D3×#12011yescharacteristic
738C2×C3D3×#12111yescharacteristic
739C2×C3D3×#12112yes—
740C2×C3D3×#12312yes—
741C2×C3D3×#12411yescharacteristic
742C2×C3C2×C3×#12011yescharacteristic
743C2×C3C2×C3×#12111yescharacteristic
744C2×C3C2×C3×#12112yes—
745C2×C3C2×C3×#12312yes—
746C2×C3C2×C3×#12411yescharacteristic
747D3—44no—
748D3C3×#39418yesdirect product factor
749C22—24no—
750C22—24no—
751C22—24no—
752C22—34no—
753C22—34no—
754C22—38no—
755C22—38no—
756C22—34no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—64no—
762C22—64no—
763C22—64no—
764C22—1232no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22C2×C3×D3×D412yes—
770C22C2×C3×D3×D411yescharacteristic
771C22C2×C3×D3×D411yescharacteristic
772C22C3×D3×#4111yescharacteristic
773C22C3×D3×#4112yes—
774C4—22no—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—62no—
779C4—62no—
780C4—121no—
781C4—122no—
782C3—21no—
783C3D3×#39411yescharacteristic, direct product factor
784C3C2×C3×#39411yescharacteristic, complemented
785C2—38no—
786C2—44no—
787C2—124no—
788C2C3×D3×#12011yescharacteristic
789C2C3×D3×#12111yescharacteristic
790C2C3×D3×#12112yes—
791C2C3×D3×#12312yes—
792C2C3×D3×#12411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#394C2
socleC23×C32C24
prime radicalC22×C3×D3×D4C2
hypercenterC3×#394D3
hypocenterC3C2×C3×#394
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C4⋊C4C2semidirect
3. C2×C3×D3×C22⋊C4C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C32×#394C2semidirect
6. C3×#5222C2semidirect
7. C3×#4991C2semidirect
8. C3×#4961C2semidirect
9. C3×#4959C2semidirect
10. C3×#4672C2semidirect
11. C3×D3×#95C2semidirect
13. D3×#394C3direct (N × H)
24. C2×C32×C4⋊C4C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×C32×C22⋊C4C22semidirect
27. C2×C3×#217C22semidirect
28. C2×C3×#217C22semidirect
29. C2×C3×(C2×D3)⋊C4C22semidirect
30. C2×C3×(C2×D3)⋊C4C22semidirect
31. C2×C3×(C2×D3)⋊C4C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
39. C32×#95C22semidirect
40. C3×C3⋊#95C22semidirect
41. C3×C3⋊#95C22semidirect
47. C2×D3×C4⋊C4C2×C3semidirect
48. C2×D3×C22⋊C4C2×C3semidirect
49. C2×D3×C22⋊C4C2×C3semidirect
56. C3×#394D3direct (N × H)
57. C3×#394C2×C3semidirect
59. #5222C2×C3semidirect
60. #4991C2×C3semidirect
61. #4961C2×C3semidirect
62. #4959C2×C3semidirect
63. #4672C2×C3semidirect
64. D3×#95C2×C3semidirect
100. C2×C3×C4×D3D4semidirect
140. C2×C3×C4⋊C4C2×D3semidirect
141. C2×C3×C4⋊C4C22×C3semidirect
152. C2×C3×C22⋊C4C2×D3semidirect
153. C2×C3×C22⋊C4C2×D3semidirect
154. C2×C3×C22⋊C4C22×C3semidirect
155. C2×C3×C22⋊C4C22×C3semidirect
156. C2×#217C22×C3semidirect
157. C2×#217C22×C3semidirect
158. C2×(C2×D3)⋊C4C22×C3semidirect
159. C2×(C2×D3)⋊C4C22×C3semidirect
160. C2×(C2×D3)⋊C4C22×C3semidirect
161. C2×(C2×D3)⋊C4C22×C3semidirect
162. C2×C4⋊Dic3C22×C3semidirect
163. C2×Dic3⋊C4C22×C3semidirect
164. C2×Dic3⋊C4C22×C3semidirect
171. C3×#95C2×D3semidirect
172. C3×#95C22×C3semidirect
173. C3⋊#95C22×C3semidirect
174. C3⋊#95C22×C3semidirect
212. C2×C32×C4C2×D4semidirect
223. C2×C3×Dic3C2×D4semidirect
238. #394C3×D3direct (N × H)
318. C2×C4×D3C3×D4semidirect
393. C2×C4⋊C4C2×C3×D3semidirect
402. C2×C22⋊C4C2×C3×D3semidirect
403. C2×C22⋊C4C2×C3×D3semidirect
406. #95C2×C3×D3semidirect
515. C2×C3×C4D3×D4semidirect
517. C2×C3×C4C2×C3×D4semidirect
528. C2×Dic3C2×C3×D4semidirect
541. C3×D3#394direct (N × H)
672. C32C2×#394semidirect
726. C2×C4C3×D3×D4semidirect
748. D3C3×#394direct (N × H)
783. C3D3×#394direct (N × H)
784. C3C2×C3×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×C3×D3×C4⋊C42
C2×C3×D3×C22⋊C42
C32×#3942
C3×#52222
C3×#49912
C3×#49612
C3×#49592
C3×#46722
C3×D3×#952
C2×C3×#3943
D3×#3943