Finite Group Databasebeta

← C3×C4×#882 #11801985

Subgroups — C3×C4×#882 #11801985

Order 1152.

2577 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic
4C2×C3×C4×D12C212yesmaximal, complemented
5C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#4958C211yesmaximal, characteristic, complemented
7C3×#4955C211yesmaximal, characteristic, complemented
8C3×#4950C211yesmaximal, characteristic, complemented
9C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
10C3×#4668C212yesmaximal, complemented
11C3×#4665C212yesmaximal, complemented
12C3×C4×#120—31nomaximal
13C4×#882C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×D12C2212yes—
19C22×C3×C4×D3—24no—
20C22×C3×C4×D3—28no—
21C22×C3×C4×D3C2212yes—
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C42C2212yescomplemented
27C2×C3×#217C2211yescharacteristic
28C3×C4×#67—24no—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
33C2×C3×(C2×D3)⋊C4C2212yescomplemented
34C2×C3×C4⋊Dic3C2212yescomplemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C3×#882C418yesdirect product factor
38C3×C4×D12—28no—
39C32×#95C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41C3×C3⋊#95C2212yescomplemented
42C24×C3×C4—31no—
43C23×C4×D3C2×C311yescharacteristic, complemented
44C2×C3×#120—31no—
45C2×C3×C4×D4—31no—
46C2×C3×C4×D4—32no—
47C2×C4×#67C2×C311yescharacteristic, complemented
48C2×#882C2×C311yescharacteristic
49C2×C4×D12C2×C312yescomplemented
50C3×#386—31no—
51C3×#386—32no—
52C3×#385—31no—
53C3×#385—32no—
54C3×#379—31no—
55C3×C4×C22⋊C4—21no—
56C3×C4×C22⋊C4—32no—
57C3×C4×C22⋊C4D311yescharacteristic, complemented
58C3×C4×C22⋊C4C2×C311yescharacteristic, complemented
59#4958C2×C311yescharacteristic, complemented
60#4955C2×C311yescharacteristic, complemented
61#4950C2×C311yescharacteristic, complemented
62C4×(C2×D3)⋊C4C2×C312yescomplemented
63#4668C2×C312yescomplemented
64#4665C2×C312yescomplemented
65C24×C32C2311yescharacteristic
66C23×C3×D3—22no—
67C23×C3×D3—22no—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3C2×C414yescomplemented
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2312yes—
73C22×C32×C4—24no—
74C22×C32×C4D414yescomplemented
75C22×C32×C4C2312yes—
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C2×C3×#67—22no—
80C2×C3×#67—22no—
81C2×C3×#67C2×C414yescomplemented
82C22×C3×Dic3—22no—
83C22×C3×Dic3—24no—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C2×C3×D12—24no—
89C2×C3×D12—24no—
90C2×C3×D12C2×C418yescomplemented
91C2×C3×C4×D3—232no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—24no—
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×D3D418yescomplemented
100C32×C22⋊C4—22no—
101C32×C22⋊C4C2×C414yescomplemented
102C32×C42—24no—
103C3×#217—22no—
104C3×(C2×D3)⋊C4—24no—
105C3×(C2×D3)⋊C4—24no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—24no—
108C3×(C2×D3)⋊C4C2×C418yescomplemented
109C3×C4⋊Dic3—24no—
110C3×Dic3⋊C4—22no—
111C3×C4×Dic3—22no—
112C4×#120—31noSylow
113C25×C3—31no—
114C24×D3C22×C311yescharacteristic
115C22×C3×D4—31no—
116C22×C3×D4—32no—
117C23×C3×C4—21no—
118C23×C3×C4—32no—
119C23×C3×C4—31no—
120C23×C3×C4—32no—
121C23×C3×C4—31no—
122C23×C3×C4—68no—
123C23×C3×C4—64no—
124C23×C3×C4C2×D311yescharacteristic
125C23×C3×C4C22×C311yescharacteristic
126C22×#67C22×C311yescharacteristic
127C23×Dic3C22×C311yescharacteristic
128C22×D12C22×C312yes—
129C22×C4×D3—24no—
130C22×C4×D3—28no—
131C22×C4×D3C22×C312yes—
132C22×C4×D3C22×C312yes—
133C22×C4×D3C22×C311yescharacteristic, complemented
134C3×#120—38no—
135C3×C4×D4—68no—
136C3×C4×D4—64no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—32no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—32no—
144C2×C3×C22⋊C4—32no—
145C2×C3×C22⋊C4—32no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C22⋊C4C2×D311yescharacteristic
149C2×C3×C22⋊C4C22×C311yescharacteristic
150C2×C3×C22⋊C4C22×C311yescharacteristic
151C2×C3×C42—22no—
152C2×C3×C42—31no—
153C2×C3×C42C2×D312yescomplemented
154C2×C3×C42C22×C312yescomplemented
155C2×#217C22×C311yescharacteristic
156C4×#67—24no—
157C2×(C2×D3)⋊C4C22×C312yes—
158C2×(C2×D3)⋊C4C22×C312yes—
159C2×(C2×D3)⋊C4C22×C312yes—
160C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
161C2×(C2×D3)⋊C4C22×C312yescomplemented
162C2×C4⋊Dic3C22×C312yescomplemented
163C2×Dic3⋊C4C22×C311yescharacteristic, complemented
164C2×C4×Dic3C22×C311yescharacteristic, complemented
165#882C3×C418yesdirect product factor
166C4×D12—28no—
167C3×#95—22no—
168C3×#95—32no—
169C3×#95—32no—
170C3×#95C2×D312yescomplemented
171C3×#95C22×C312yescomplemented
172C3⋊#95C22×C312yescomplemented
173C3⋊#95C22×C312yescomplemented
174C23×C32—22no—
175C23×C32—22no—
176C23×C32C22×C412yes—
177C23×C32C2×D412yes—
178C23×C32#4112yes—
179C23×C32C2411yescharacteristic
180C22×C3×D3—216no—
181C22×C3×D3—28no—
182C22×C3×D3—28no—
183C22×C3×D3—28no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—216no—
189C22×C3×D3—22no—
190C22×C3×D3—21no—
191C22×C3×D3—22no—
192C22×C3×D3—21no—
193C22×C3×D3C22×C414yes—
194C22×C3×D3C22×C412yescomplemented
195C22×C3×D3C2×D414yes—
196C22×C3×D3#4114yes—
197C2×C32×C4—22no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—28no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4C22×C414yescomplemented
205C2×C32×C4C2×D412yes—
206C2×C32×C4C2×D412yes—
207C2×C32×C4C2×D414yes—
208C3×#67—28no—
209C2×C3×Dic3—28no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3C22×C412yescomplemented
219C2×C3×Dic3C2×D414yes—
220C3×D12—216no—
221C3×C4×D3—216no—
222C3×C4×D3—216no—
223C3×C4×D3—44no—
224C24×C4—31no—
225C2×#120—31no—
226C2×C4×D4—31no—
227C2×C4×D4—32no—
228#386—31no—
229#386—32no—
230#385—31no—
231#385—32no—
232#379—31no—
233C4×C22⋊C4—32no—
234C4×C22⋊C4C3×D311yescharacteristic, complemented
235C24×C3—21no—
236C24×C3—32no—
237C24×C3—34no—
238C24×C3—31no—
239C24×C3—64no—
240C24×C3—64no—
241C24×C3—62no—
242C24×C3—62no—
243C24×C3C22×D311yescharacteristic
244C24×C3C23×C311yescharacteristic
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—24no—
248C23×D3—24no—
249C23×D3C2×C3×C414yescomplemented
250C23×D3C23×C311yescharacteristic
251C23×D3C23×C312yes—
252C2×C3×D4—34no—
253C2×C3×D4—38no—
254C2×C3×D4—64no—
255C2×C3×D4—64no—
256C2×C3×D4—62no—
257C2×C3×D4—62no—
258C22×C3×C4—24no—
259C22×C3×C4—24no—
260C22×C3×C4—24no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—31no—
266C22×C3×C4—32no—
267C22×C3×C4—38no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—44no—
271C22×C3×C4—64no—
272C22×C3×C4—64no—
273C22×C3×C4—632no—
274C22×C3×C4—64no—
275C22×C3×C4—62no—
276C22×C3×C4—64no—
277C22×C3×C4—64no—
278C22×C3×C4—64no—
279C22×C3×C4—62no—
280C22×C3×C4—64no—
281C22×C3×C4D1214yescomplemented
282C22×C3×C4C3×D414yescomplemented
283C22×C3×C4C22×D312yes—
284C22×C3×C4C22×D312yes—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C23×C312yes—
288C22×C3×C4C23×C312yes—
289C22×C3×C4C23×C311yescharacteristic
290C22×C3×C4C23×C311yescharacteristic
291C2×#67—22no—
292C2×#67—22no—
293C2×#67C2×C3×C414yescomplemented
294C22×Dic3—22no—
295C22×Dic3—24no—
296C22×Dic3C23×C311yescharacteristic
297C22×Dic3C23×C311yescharacteristic
298C22×Dic3C23×C311yescharacteristic
299C22×Dic3C23×C312yes—
300C2×D12—24no—
301C2×D12—24no—
302C2×D12C2×C3×C418yescomplemented
303C2×C4×D3—232no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—24no—
310C2×C4×D3—22no—
311C2×C4×D3C3×D418yescomplemented
312C3×C4⋊C4—64no—
313C3×C4⋊C4—62no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—38no—
319C3×C22⋊C4—64no—
320C3×C22⋊C4—64no—
321C3×C22⋊C4—64no—
322C3×C22⋊C4—62no—
323C3×C22⋊C4—62no—
324C3×C22⋊C4C4×D314yescomplemented
325C3×C22⋊C4C2×C3×C414yescomplemented
326C3×C42—24no—
327C3×C42—24no—
328C3×C42—44no—
329C3×C42—62no—
330#217—22no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—22no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4C2×C3×C418yescomplemented
336C4⋊Dic3—24no—
337Dic3⋊C4—22no—
338C4×Dic3—22no—
339C22×C32—24no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—24no—
343C22×C32C4×D414yescomplemented
344C22×C32C23×C411yescharacteristic
345C22×C32C22×D411yescharacteristic
346C22×C32C22×D412yes—
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4112yes—
349C2×C3×D3—232no—
350C2×C3×D3—24no—
351C2×C3×D3—24no—
352C2×C3×D3—24no—
353C2×C3×D3—24no—
354C2×C3×D3—24no—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—22no—
358C2×C3×D3—41no—
359C2×C3×D3—41no—
360C2×C3×D3—42no—
361C2×C3×D3C4×D418yescomplemented
362C32×C4—24no—
363C32×C4—22no—
364C32×C4—42no—
365C32×C4#12014yescomplemented
366C3×Dic3—22no—
367C3×Dic3—24no—
368C3×Dic3—41no—
369C3×Dic3—41no—
370C25—31no—
371C22×D4—31no—
372C22×D4—32no—
373C23×C4—32no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—32no—
377C23×C4—68no—
378C23×C4—64no—
379C23×C4C2×C3×D311yescharacteristic
380#120—38no—
381C4×D4—68no—
382C4×D4—64no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—32no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4C2×C3×D311yescharacteristic
392C2×C22⋊C4C2×C3×D311yescharacteristic
393C2×C42—31no—
394C2×C42C2×C3×D312yescomplemented
395#95—32no—
396#95—32no—
397#95C2×C3×D312yescomplemented
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—34no—
407C23×C3—34no—
408C23×C3—34no—
409C23×C3—32no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—616no—
413C23×C3—68no—
414C23×C3—68no—
415C23×C3—616no—
416C23×C3—68no—
417C23×C3—62no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3—61no—
422C23×C3—61no—
423C23×C3—62no—
424C23×C3—62no—
425C23×C3C2×C4×D312yes—
426C23×C3C2×D1212yes—
427C23×C3#23512yes—
428C23×C3C22×C3×C412yes—
429C23×C3C2×C3×D412yes—
430C23×C3C3×#4112yes—
431C23×C3C23×D311yescharacteristic
432C23×C3C24×C311yescharacteristic
433C22×D3—28no—
434C22×D3—216no—
435C22×D3—28no—
436C22×D3—28no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—216no—
442C22×D3—22no—
443C22×D3—21no—
444C22×D3—22no—
445C22×D3—21no—
446C22×D3C22×C3×C414yes—
447C22×D3C22×C3×C412yescomplemented
448C22×D3C2×C3×D414yes—
449C22×D3C3×#4114yes—
450C3×D4—616no—
451C3×D4—68no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—28no—
459C2×C3×C4—28no—
460C2×C3×C4—24no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—24no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—24no—
471C2×C3×C4—32no—
472C2×C3×C4—34no—
473C2×C3×C4—48no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
479C2×C3×C4—616no—
480C2×C3×C4—68no—
481C2×C3×C4—61no—
482C2×C3×C4—62no—
483C2×C3×C4—61no—
484C2×C3×C4—62no—
485C2×C3×C4—616no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—124no—
491C2×C3×C4C2×C4×D314yescomplemented
492C2×C3×C4C2×D1212yes—
493C2×C3×C4C2×D1212yes—
494C2×C3×C4D3×D414yes—
495C2×C3×C4C22×C3×C414yescomplemented
496C2×C3×C4C2×C3×D412yes—
497C2×C3×C4C2×C3×D412yes—
498C2×C3×C4C2×C3×D414yes—
499#67—28no—
500C2×Dic3—28no—
501C2×Dic3—21no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3C22×C3×C412yescomplemented
510C2×Dic3C2×C3×D414yes—
511D12—216no—
512C4×D3—216no—
513C4×D3—216no—
514C4×D3—44no—
515C2×C32—24no—
516C2×C32C2×C4×D411yescharacteristic
517C2×C32C2×C4×D412yes—
518C2×C32C2×#12011yescharacteristic
519C2×C32#52511yescharacteristic
520C2×C32#52512yes—
521C3×D3—28no—
522C3×D3—42no—
523C24—32no—
524C24—31no—
525C24—34no—
526C24—64no—
527C24—64no—
528C24—62no—
529C24—62no—
530C24C22×C3×D311yescharacteristic
531C2×D4—34no—
532C2×D4—38no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—62no—
536C2×D4—62no—
537C22×C4—24no—
538C22×C4—31no—
539C22×C4—32no—
540C22×C4—38no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—632no—
546C22×C4—64no—
547C22×C4—62no—
548C22×C4—64no—
549C22×C4—64no—
550C22×C4—64no—
551C22×C4—62no—
552C22×C4—64no—
553C22×C4C3×D1214yescomplemented
554C22×C4C22×C3×D312yes—
555C22×C4C22×C3×D312yes—
556C22×C4C22×C3×D311yescharacteristic
557C22×C4C22×C3×D311yescharacteristic
558C4⋊C4—64no—
559C4⋊C4—62no—
560C22⋊C4—22no—
561C22⋊C4—38no—
562C22⋊C4—64no—
563C22⋊C4—64no—
564C22⋊C4—64no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4C3×C4×D314yescomplemented
568C42—24no—
569C42—62no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—24no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—24no—
584C22×C3—38no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—632no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—64no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—62no—
597C22×C3—64no—
598C22×C3—121no—
599C22×C3—121no—
600C22×C3—122no—
601C22×C3C4×D1214yescomplemented
602C22×C3C3×C4×D414yescomplemented
603C22×C3C22×C4×D311yescharacteristic
604C22×C3C22×D1211yescharacteristic
605C22×C3C2×#23511yescharacteristic
606C22×C3C2×D3×D412yes—
607C22×C3D3×#4112yes—
608C22×C3C23×C3×C411yescharacteristic
609C22×C3C22×C3×D411yescharacteristic
610C22×C3C22×C3×D412yes—
611C22×C3C2×C3×#4111yescharacteristic
612C22×C3C2×C3×#4112yes—
613C2×D3—232no—
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—22no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—42no—
625C2×D3C3×C4×D418yescomplemented
626C3×C4—22no—
627C3×C4—24no—
628C3×C4—24no—
629C3×C4—22no—
630C3×C4—24no—
631C3×C4—42no—
632C3×C4—44no—
633C3×C4—44no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—62no—
637C3×C4—64no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4#88214yesdirect product factor
641C3×C4C3×#12014yescomplemented
642Dic3—22no—
643Dic3—24no—
644Dic3—41no—
645Dic3—41no—
646C32C4×#12011yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—34no—
650C23—34no—
651C23—34no—
652C23—32no—
653C23—616no—
654C23—68no—
655C23—68no—
656C23—616no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—68no—
662C23—61no—
663C23—61no—
664C23—62no—
665C23—62no—
666C23C2×C3×C4×D312yes—
667C23C2×C3×D1212yes—
668C23C3×#23512yes—
669C23C23×C3×D311yescharacteristic
670D4—616no—
671D4—68no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—32no—
680C2×C4—34no—
681C2×C4—616no—
682C2×C4—68no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—616no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—124no—
693C2×C4C2×C3×C4×D314yescomplemented
694C2×C4C2×C3×D1212yes—
695C2×C4C2×C3×D1212yes—
696C2×C4C3×D3×D414yes—
697C2×C3—24no—
698C2×C3—24no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—22no—
702C2×C3—22no—
703C2×C3—21no—
704C2×C3—44no—
705C2×C3—68no—
706C2×C3—122no—
707C2×C3C2×C4×D1211yescharacteristic
708C2×C3C2×#88211yescharacteristic
709C2×C3#552411yescharacteristic
710C2×C3C4×D3×D412yes—
711C2×C3#554712yes—
712C2×C3C2×C3×C4×D412yes—
713C2×C3C2×C3×C4×D411yescharacteristic
714C2×C3C2×C3×#12011yescharacteristic
715C2×C3C3×#52511yescharacteristic
716C2×C3C3×#52512yes—
717D3—28no—
718D3—42no—
719C22—22no—
720C22—22no—
721C22—24no—
722C22—24no—
723C22—38no—
724C22—632no—
725C22—64no—
726C22—64no—
727C22—64no—
728C22—64no—
729C22—64no—
730C22—64no—
731C22—64no—
732C22—62no—
733C22—121no—
734C22—121no—
735C22—122no—
736C22C3×C4×D1214yescomplemented
737C22C22×C3×C4×D311yescharacteristic
738C22C22×C3×D1211yescharacteristic
739C22C2×C3×#23511yescharacteristic
740C22C2×C3×D3×D412yes—
741C22C3×D3×#4112yes—
742C4—22no—
743C4—24no—
744C4—42no—
745C4—64no—
746C4—62no—
747C4—121no—
748C4—121no—
749C4C3×#88214yesdirect product factor
750C3—21no—
751C3C4×#88211yescharacteristic, direct product factor
752C3C3×C4×#12011yescharacteristic, complemented
753C2—24no—
754C2—68no—
755C2—122no—
756C2C2×C3×C4×D1211yescharacteristic
757C2C2×C3×#88211yescharacteristic
758C2C3×#552411yescharacteristic
759C2C3×C4×D3×D412yes—
760C2C3×#554712yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC2×C3×#882C2
cosocleC23×C3C24×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×C4×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
2. C2×C3×C4×#67C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C32×C4×C22⋊C4C2semidirect
6. C3×#4958C2semidirect
7. C3×#4955C2semidirect
8. C3×#4950C2semidirect
9. C3×C4×(C2×D3)⋊C4C2semidirect
10. C3×#4668C2semidirect
11. C3×#4665C2semidirect
13. C4×#882C3direct (N × H)
23. C22×C3×C4×D3C22semidirect
26. C2×C32×C42C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
37. C3×#882C4direct (N × H)
39. C32×#95C22semidirect
40. C3×C3⋊#95C22semidirect
41. C3×C3⋊#95C22semidirect
43. C23×C4×D3C2×C3semidirect
47. C2×C4×#67C2×C3semidirect
49. C2×C4×D12C2×C3semidirect
57. C3×C4×C22⋊C4D3semidirect
58. C3×C4×C22⋊C4C2×C3semidirect
59. #4958C2×C3semidirect
60. #4955C2×C3semidirect
61. #4950C2×C3semidirect
62. C4×(C2×D3)⋊C4C2×C3semidirect
63. #4668C2×C3semidirect
64. #4665C2×C3semidirect
70. C23×C3×D3C2×C4semidirect
74. C22×C32×C4D4semidirect
81. C2×C3×#67C2×C4semidirect
90. C2×C3×D12C2×C4semidirect
99. C2×C3×C4×D3D4semidirect
101. C32×C22⋊C4C2×C4semidirect
108. C3×(C2×D3)⋊C4C2×C4semidirect
133. C22×C4×D3C22×C3semidirect
153. C2×C3×C42C2×D3semidirect
154. C2×C3×C42C22×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×C4×Dic3C22×C3semidirect
165. #882C3×C4direct (N × H)
170. C3×#95C2×D3semidirect
171. C3×#95C22×C3semidirect
172. C3⋊#95C22×C3semidirect
173. C3⋊#95C22×C3semidirect
194. C22×C3×D3C22×C4semidirect
204. C2×C32×C4C22×C4semidirect
218. C2×C3×Dic3C22×C4semidirect
234. C4×C22⋊C4C3×D3semidirect
249. C23×D3C2×C3×C4semidirect
281. C22×C3×C4D12semidirect
282. C22×C3×C4C3×D4semidirect
293. C2×#67C2×C3×C4semidirect
302. C2×D12C2×C3×C4semidirect
311. C2×C4×D3C3×D4semidirect
324. C3×C22⋊C4C4×D3semidirect
325. C3×C22⋊C4C2×C3×C4semidirect
335. (C2×D3)⋊C4C2×C3×C4semidirect
343. C22×C32C4×D4semidirect
361. C2×C3×D3C4×D4semidirect
365. C32×C4#120semidirect
394. C2×C42C2×C3×D3semidirect
397. #95C2×C3×D3semidirect
447. C22×D3C22×C3×C4semidirect
491. C2×C3×C4C2×C4×D3semidirect
495. C2×C3×C4C22×C3×C4semidirect
509. C2×Dic3C22×C3×C4semidirect
553. C22×C4C3×D12semidirect
567. C22⋊C4C3×C4×D3semidirect
601. C22×C3C4×D12semidirect
602. C22×C3C3×C4×D4semidirect
625. C2×D3C3×C4×D4semidirect
640. C3×C4#882direct (N × H)
641. C3×C4C3×#120semidirect
646. C32C4×#120semidirect
693. C2×C4C2×C3×C4×D3semidirect
736. C22C3×C4×D12semidirect
749. C4C3×#882direct (N × H)
751. C3C4×#882direct (N × H)
752. C3C3×C4×#120semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×C3×C4×#672
C2×C3×#8822
C2×C3×C4×D122
C32×C4×C22⋊C42
C3×#49582
C3×#49552
C3×#49502
C3×C4×(C2×D3)⋊C42
C3×#46682
C3×#46652
C3×C4×#1203
C4×#8823