Finite Group Databasebeta

← C3×C4×#937 #11801973

Subgroups — C3×C4×#937 #11801973

Order 1152.

2661 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×C32×C4×D4C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic
4C2×C3×C4×#67C212yesmaximal, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6C3×C4×#217C211yesmaximal, characteristic, complemented
7C3×#4989C212yesmaximal, complemented
8C3×#4956C212yesmaximal, complemented
9C3×#4955C211yesmaximal, characteristic, complemented
10C3×#4946C211yesmaximal, characteristic, complemented
11C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
12C3×C4×#120—31nomaximal
13C4×#937C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic, complemented
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×C4×D3—24no—
21C22×C3×C4×D3—28no—
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2212yes—
24C32×C4×D4—24no—
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic, complemented
28C2×C32×C42C2211yescharacteristic, complemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2212yescomplemented
32C3×#937C418yesdirect product factor
33C3×C4×#67—28no—
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2212yescomplemented
38C2×C3×C4×Dic3C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41C3×C3⋊#95C2212yescomplemented
42C24×C3×C4—31no—
43C23×C4×D3C2×C311yescharacteristic, complemented
44C2×C3×#120—31no—
45C2×C3×C4×D4—21no—
46C2×C3×C4×D4—32no—
47C2×C3×C4×D4D311yescharacteristic, complemented
48C2×C3×C4×D4C2×C311yescharacteristic, complemented
49C2×#937C2×C311yescharacteristic
50C2×C4×#67C2×C312yescomplemented
51C3×#386—31no—
52C3×#386—32no—
53C3×#385—32no—
54C3×#385—31no—
55C3×#379—31no—
56C3×C4×C22⋊C4—31no—
57C3×C4×C22⋊C4—32no—
58#5220C2×C311yescharacteristic, complemented
59C4×#217C2×C311yescharacteristic, complemented
60#4989C2×C312yescomplemented
61#4956C2×C312yescomplemented
62#4955C2×C311yescharacteristic, complemented
63#4946C2×C311yescharacteristic, complemented
64C4×(C2×D3)⋊C4C2×C312yescomplemented
65C24×C32C2311yescharacteristic
66C24×C32C2311yescharacteristic
67C23×C3×D3—22no—
68C23×C3×D3—22no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3C2×C414yescomplemented
72C23×C3×D3C2312yes—
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4C2×C414yescomplemented
76C22×C32×C4—24no—
77C22×C32×C4—22no—
78C22×C32×C4—24no—
79C22×C32×C4D414yescomplemented
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C2×C3×#67—24no—
86C2×C3×#67—24no—
87C2×C3×#67C2×C418yescomplemented
88C22×C3×Dic3—22no—
89C22×C3×Dic3—24no—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2312yes—
93C2×C3×C4×D3—232no—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3D418yescomplemented
100C32×C4⋊C4—22no—
101C32×C22⋊C4—22no—
102C32×C22⋊C4—22no—
103C32×C42—22no—
104C3×#217—22no—
105C3×#217—24no—
106C3×#217C2×C414yescomplemented
107C3×(C2×D3)⋊C4—24no—
108C3×(C2×D3)⋊C4—24no—
109C3×(C2×D3)⋊C4C2×C418yescomplemented
110C3×Dic3⋊C4—24no—
111C3×C4×Dic3—24no—
112C4×#120—31noSylow
113C25×C3—31no—
114C24×D3C22×C311yescharacteristic
115C22×C3×D4—21no—
116C22×C3×D4—32no—
117C22×C3×D4C2×D311yescharacteristic
118C22×C3×D4C22×C311yescharacteristic
119C23×C3×C4—21no—
120C23×C3×C4—21no—
121C23×C3×C4—32no—
122C23×C3×C4—31no—
123C23×C3×C4—32no—
124C23×C3×C4—68no—
125C23×C3×C4—64no—
126C23×C3×C4C2×D311yescharacteristic
127C23×C3×C4C2×D311yescharacteristic, complemented
128C23×C3×C4C22×C311yescharacteristic
129C23×C3×C4C22×C311yescharacteristic, complemented
130C22×#67C22×C312yes—
131C23×Dic3C22×C311yescharacteristic
132C22×C4×D3—24no—
133C22×C4×D3—28no—
134C22×C4×D3C22×C312yes—
135C22×C4×D3C22×C312yes—
136C3×#120—38no—
137C3×C4×D4—28no—
138C3×C4×D4—24no—
139C3×C4×D4—24no—
140C3×C4×D4—68no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
144C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—32no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—32no—
151C2×C3×C22⋊C4—32no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4C2×D311yescharacteristic
154C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
155C2×C3×C22⋊C4C22×C311yescharacteristic
156C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
157C2×C3×C42—21no—
158C2×C3×C42—32no—
159C2×C3×C42C2×D311yescharacteristic, complemented
160C2×C3×C42C22×C311yescharacteristic, complemented
161C2×#217C22×C311yescharacteristic
162C2×#217C22×C311yescharacteristic
163C2×#217C22×C312yescomplemented
164#937C3×C418yesdirect product factor
165C4×#67—28no—
166C2×(C2×D3)⋊C4C22×C312yes—
167C2×(C2×D3)⋊C4C22×C312yes—
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×Dic3⋊C4C22×C312yescomplemented
170C2×C4×Dic3C22×C312yescomplemented
171C3×#95—32no—
172C3×#95—32no—
173C3×#95—32no—
174C3⋊#95C22×C312yescomplemented
175C3⋊#95C22×C312yescomplemented
176C3⋊#95C22×C312yescomplemented
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32—22no—
182C23×C32—22no—
183C23×C32C22×C412yes—
184C23×C32C22×C412yescomplemented
185C23×C32C2×D412yes—
186C23×C32#4112yes—
187C23×C32C2411yescharacteristic
188C22×C3×D3—216no—
189C22×C3×D3—28no—
190C22×C3×D3—28no—
191C22×C3×D3—28no—
192C22×C3×D3—22no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—216no—
197C22×C3×D3C22×C414yes—
198C22×C3×D3C2×D414yes—
199C22×C3×D3#4114yes—
200C32×D4—28no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—28no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—44no—
210C2×C32×C4C22×C412yescomplemented
211C2×C32×C4C2×D414yes—
212C2×C32×C4C2×D412yes—
213C2×C32×C4C2×D412yes—
214C3×#67—216no—
215C2×C3×Dic3—28no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C22×C414yescomplemented
224C2×C3×Dic3C2×D414yes—
225C3×C4×D3—216no—
226C3×C4×D3—216no—
227C24×C4—31no—
228C2×#120—31no—
229C2×C4×D4—32no—
230C2×C4×D4C3×D311yescharacteristic, complemented
231#386—31no—
232#386—32no—
233#385—32no—
234#385—31no—
235#379—31no—
236C4×C22⋊C4—31no—
237C4×C22⋊C4—32no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—32no—
241C24×C3—34no—
242C24×C3—64no—
243C24×C3—64no—
244C24×C3—62no—
245C24×C3—62no—
246C24×C3C22×D311yescharacteristic
247C24×C3C22×D311yescharacteristic
248C24×C3C23×C311yescharacteristic
249C24×C3C23×C311yescharacteristic
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—24no—
253C23×D3—24no—
254C23×D3C2×C3×C414yescomplemented
255C23×D3C23×C312yes—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—24no—
263C2×C3×D4—38no—
264C2×C3×D4—64no—
265C2×C3×D4—64no—
266C2×C3×D4C4×D314yescomplemented
267C2×C3×D4C2×C3×C414yescomplemented
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4—24no—
272C22×C3×C4—22no—
273C22×C3×C4—24no—
274C22×C3×C4—22no—
275C22×C3×C4—24no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—32no—
282C22×C3×C4—32no—
283C22×C3×C4—38no—
284C22×C3×C4—32no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—64no—
288C22×C3×C4—64no—
289C22×C3×C4—632no—
290C22×C3×C4—64no—
291C22×C3×C4—62no—
292C22×C3×C4—64no—
293C22×C3×C4—64no—
294C22×C3×C4—64no—
295C22×C3×C4#6714yescomplemented
296C22×C3×C4C3×D414yescomplemented
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C23×C311yescharacteristic
303C22×C3×C4C23×C311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C22×C3×C4C23×C311yescharacteristic
306C22×C3×C4C23×C311yescharacteristic
307C2×#67—24no—
308C2×#67—24no—
309C2×#67C2×C3×C418yescomplemented
310C22×Dic3—22no—
311C22×Dic3—24no—
312C22×Dic3C23×C312yes—
313C22×Dic3C23×C312yes—
314C22×Dic3C23×C312yes—
315C2×C4×D3—232no—
316C2×C4×D3—24no—
317C2×C4×D3—24no—
318C2×C4×D3—24no—
319C2×C4×D3—24no—
320C2×C4×D3—24no—
321C2×C4×D3C3×D418yescomplemented
322C3×C4⋊C4—24no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—64no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—22no—
329C3×C22⋊C4—22no—
330C3×C22⋊C4—22no—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—38no—
334C3×C22⋊C4—64no—
335C3×C22⋊C4—64no—
336C3×C22⋊C4—64no—
337C3×C22⋊C4—62no—
338C3×C42—24no—
339C3×C42—22no—
340C3×C42—22no—
341C3×C42—64no—
342#217—22no—
343#217—24no—
344#217C2×C3×C414yescomplemented
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4C2×C3×C418yescomplemented
348Dic3⋊C4—24no—
349C4×Dic3—24no—
350C22×C32—22no—
351C22×C32—24no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—24no—
355C22×C32—24no—
356C22×C32—41no—
357C22×C32—42no—
358C22×C32—41no—
359C22×C32C4×D414yescomplemented
360C22×C32C23×C411yescharacteristic
361C22×C32C22×D412yes—
362C22×C32C22×D411yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C22×C32C2×#4112yes—
365C2×C3×D3—232no—
366C2×C3×D3—24no—
367C2×C3×D3—24no—
368C2×C3×D3—24no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—24no—
372C2×C3×D3C4×D418yescomplemented
373C32×C4—22no—
374C32×C4—22no—
375C32×C4—41no—
376C32×C4—41no—
377C32×C4#12014yescomplemented
378C3×Dic3—24no—
379C3×Dic3—24no—
380C3×Dic3—42no—
381C25—31no—
382C22×D4—32no—
383C22×D4C2×C3×D311yescharacteristic
384C23×C4—32no—
385C23×C4—31no—
386C23×C4—32no—
387C23×C4—68no—
388C23×C4—64no—
389C23×C4C2×C3×D311yescharacteristic
390C23×C4C2×C3×D311yescharacteristic, complemented
391#120—38no—
392C4×D4—24no—
393C4×D4—68no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
396C2×C22⋊C4—31no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—32no—
402C2×C22⋊C4C2×C3×D311yescharacteristic
403C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
404C2×C42—32no—
405C2×C42C2×C3×D311yescharacteristic, complemented
406#95—32no—
407#95—32no—
408#95—32no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—21no—
419C23×C3—22no—
420C23×C3—21no—
421C23×C3—22no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—34no—
429C23×C3—34no—
430C23×C3—34no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—616no—
436C23×C3—68no—
437C23×C3—616no—
438C23×C3—68no—
439C23×C3—68no—
440C23×C3—62no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3C2×C4×D312yes—
445C23×C3C2×C4×D312yescomplemented
446C23×C3#23512yes—
447C23×C3C2×#6712yes—
448C23×C3C22×C3×C412yes—
449C23×C3C22×C3×C412yescomplemented
450C23×C3C2×C3×D412yes—
451C23×C3C3×#4112yes—
452C23×C3C23×D311yescharacteristic
453C23×C3C24×C311yescharacteristic
454C22×D3—28no—
455C22×D3—216no—
456C22×D3—28no—
457C22×D3—28no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—216no—
463C22×D3C22×C3×C414yes—
464C22×D3C2×C3×D414yes—
465C22×D3C3×#4114yes—
466C3×D4—216no—
467C3×D4—28no—
468C3×D4—28no—
469C3×D4—616no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—21no—
478C2×C3×C4—28no—
479C2×C3×C4—28no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—24no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—48no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—48no—
501C2×C3×C4—44no—
502C2×C3×C4—44no—
503C2×C3×C4—616no—
504C2×C3×C4—68no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—616no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4C2×C4×D312yescomplemented
514C2×C3×C4D3×D414yes—
515C2×C3×C4C2×#6712yes—
516C2×C3×C4C2×#6712yes—
517C2×C3×C4C22×C3×C412yescomplemented
518C2×C3×C4C2×C3×D414yes—
519C2×C3×C4C2×C3×D412yes—
520C2×C3×C4C2×C3×D412yes—
521#67—216no—
522C2×Dic3—28no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3C22×C3×C414yescomplemented
531C2×Dic3C2×C3×D414yes—
532C4×D3—216no—
533C4×D3—216no—
534C2×C32—24no—
535C2×C32—42no—
536C2×C32C2×C4×D411yescharacteristic
537C2×C32C2×C4×D412yes—
538C2×C32C2×#12011yescharacteristic
539C2×C32#52512yes—
540C2×C32#52511yescharacteristic
541C3×D3—28no—
542C24—32no—
543C24—34no—
544C24—64no—
545C24—64no—
546C24—62no—
547C24—62no—
548C24C22×C3×D311yescharacteristic
549C24C22×C3×D311yescharacteristic
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—38no—
553C2×D4—64no—
554C2×D4—64no—
555C2×D4C3×C4×D314yescomplemented
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—38no—
562C22×C4—32no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—632no—
566C22×C4—64no—
567C22×C4—62no—
568C22×C4—64no—
569C22×C4—64no—
570C22×C4—64no—
571C22×C4C3×#6714yescomplemented
572C22×C4C22×C3×D311yescharacteristic
573C22×C4C22×C3×D311yescharacteristic
574C22×C4C22×C3×D311yescharacteristic
575C22×C4C22×C3×D311yescharacteristic
576C22×C4C22×C3×D311yescharacteristic
577C4⋊C4—22no—
578C4⋊C4—64no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—34no—
582C22⋊C4—38no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C22⋊C4—64no—
586C22⋊C4—62no—
587C42—22no—
588C42—64no—
589C22×C3—22no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—22no—
593C22×C3—24no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—22no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—24no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—38no—
609C22×C3—42no—
610C22×C3—44no—
611C22×C3—44no—
612C22×C3—42no—
613C22×C3—44no—
614C22×C3—42no—
615C22×C3—44no—
616C22×C3—42no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—632no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—64no—
629C22×C3—64no—
630C22×C3C4×#6714yescomplemented
631C22×C3C3×C4×D414yescomplemented
632C22×C3C22×C4×D311yescharacteristic
633C22×C3C2×#23511yescharacteristic
634C22×C3C2×D3×D412yes—
635C22×C3D3×#4112yes—
636C22×C3C22×#6711yescharacteristic
637C22×C3C23×C3×C411yescharacteristic
638C22×C3C22×C3×D412yes—
639C22×C3C22×C3×D411yescharacteristic
640C22×C3C2×C3×#4111yescharacteristic
641C22×C3C2×C3×#4112yes—
642C2×D3—232no—
643C2×D3—24no—
644C2×D3—24no—
645C2×D3—24no—
646C2×D3—24no—
647C2×D3—24no—
648C2×D3—24no—
649C2×D3C3×C4×D418yescomplemented
650C3×C4—24no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—24no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—64no—
664C3×C4—64no—
665C3×C4—122no—
666C3×C4#93714yesdirect product factor
667C3×C4C3×#12014yescomplemented
668Dic3—24no—
669Dic3—24no—
670Dic3—42no—
671C32C4×#12011yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—34no—
679C23—34no—
680C23—34no—
681C23—616no—
682C23—68no—
683C23—616no—
684C23—68no—
685C23—68no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23C2×C3×C4×D312yes—
691C23C2×C3×C4×D312yescomplemented
692C23C3×#23512yes—
693C23C2×C3×#6712yes—
694C23C23×C3×D311yescharacteristic
695D4—28no—
696D4—616no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—34no—
706C2×C4—34no—
707C2×C4—44no—
708C2×C4—616no—
709C2×C4—68no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—616no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4C2×C3×C4×D312yescomplemented
719C2×C4C3×D3×D414yes—
720C2×C4C2×C3×#6712yes—
721C2×C4C2×C3×#6712yes—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—22no—
727C2×C3—22no—
728C2×C3—21no—
729C2×C3—44no—
730C2×C3—44no—
731C2×C3—42no—
732C2×C3—42no—
733C2×C3—68no—
734C2×C3C4×D3×D412yes—
735C2×C3#554712yes—
736C2×C3C2×C4×#6711yescharacteristic
737C2×C3C2×#93711yescharacteristic
738C2×C3#582811yescharacteristic
739C2×C3C2×C3×C4×D411yescharacteristic
740C2×C3C2×C3×C4×D412yes—
741C2×C3C2×C3×#12011yescharacteristic
742C2×C3C3×#52512yes—
743C2×C3C3×#52511yescharacteristic
744D3—28no—
745C22—22no—
746C22—24no—
747C22—24no—
748C22—22no—
749C22—22no—
750C22—24no—
751C22—38no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—632no—
756C22—64no—
757C22—64no—
758C22—64no—
759C22—64no—
760C22—64no—
761C22—64no—
762C22C3×C4×#6714yescomplemented
763C22C22×C3×C4×D311yescharacteristic
764C22C2×C3×#23511yescharacteristic
765C22C2×C3×D3×D412yes—
766C22C3×D3×#4112yes—
767C22C22×C3×#6711yescharacteristic
768C4—22no—
769C4—22no—
770C4—41no—
771C4—41no—
772C4—64no—
773C4—64no—
774C4—122no—
775C4C3×#93714yesdirect product factor
776C3—21no—
777C3C4×#93711yescharacteristic, direct product factor
778C3C3×C4×#12011yescharacteristic, complemented
779C2—24no—
780C2—42no—
781C2—68no—
782C2C3×C4×D3×D412yes—
783C2C3×#554712yes—
784C2C2×C3×C4×#6711yescharacteristic
785C2C2×C3×#93711yescharacteristic
786C2C3×#582811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#937C2
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×C4×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
2. C2×C32×C4×D4C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C3×#5220C2semidirect
6. C3×C4×#217C2semidirect
7. C3×#4989C2semidirect
8. C3×#4956C2semidirect
9. C3×#4955C2semidirect
10. C3×#4946C2semidirect
11. C3×C4×(C2×D3)⋊C4C2semidirect
13. C4×#937C3direct (N × H)
17. C23×C32×C4C22semidirect
25. C2×C32×C4⋊C4C22semidirect
27. C2×C32×C22⋊C4C22semidirect
28. C2×C32×C42C22semidirect
31. C2×C3×#217C22semidirect
32. C3×#937C4direct (N × H)
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
39. C3×C3⋊#95C22semidirect
40. C3×C3⋊#95C22semidirect
41. C3×C3⋊#95C22semidirect
43. C23×C4×D3C2×C3semidirect
47. C2×C3×C4×D4D3semidirect
48. C2×C3×C4×D4C2×C3semidirect
50. C2×C4×#67C2×C3semidirect
58. #5220C2×C3semidirect
59. C4×#217C2×C3semidirect
60. #4989C2×C3semidirect
61. #4956C2×C3semidirect
62. #4955C2×C3semidirect
63. #4946C2×C3semidirect
64. C4×(C2×D3)⋊C4C2×C3semidirect
71. C23×C3×D3C2×C4semidirect
75. C2×C32×D4C2×C4semidirect
79. C22×C32×C4D4semidirect
87. C2×C3×#67C2×C4semidirect
99. C2×C3×C4×D3D4semidirect
106. C3×#217C2×C4semidirect
109. C3×(C2×D3)⋊C4C2×C4semidirect
127. C23×C3×C4C2×D3semidirect
129. C23×C3×C4C22×C3semidirect
143. C2×C3×C4⋊C4C2×D3semidirect
144. C2×C3×C4⋊C4C22×C3semidirect
154. C2×C3×C22⋊C4C2×D3semidirect
156. C2×C3×C22⋊C4C22×C3semidirect
159. C2×C3×C42C2×D3semidirect
160. C2×C3×C42C22×C3semidirect
163. C2×#217C22×C3semidirect
164. #937C3×C4direct (N × H)
169. C2×Dic3⋊C4C22×C3semidirect
170. C2×C4×Dic3C22×C3semidirect
174. C3⋊#95C22×C3semidirect
175. C3⋊#95C22×C3semidirect
176. C3⋊#95C22×C3semidirect
184. C23×C32C22×C4semidirect
210. C2×C32×C4C22×C4semidirect
223. C2×C3×Dic3C22×C4semidirect
230. C2×C4×D4C3×D3semidirect
254. C23×D3C2×C3×C4semidirect
266. C2×C3×D4C4×D3semidirect
267. C2×C3×D4C2×C3×C4semidirect
295. C22×C3×C4#67semidirect
296. C22×C3×C4C3×D4semidirect
309. C2×#67C2×C3×C4semidirect
321. C2×C4×D3C3×D4semidirect
344. #217C2×C3×C4semidirect
347. (C2×D3)⋊C4C2×C3×C4semidirect
359. C22×C32C4×D4semidirect
372. C2×C3×D3C4×D4semidirect
377. C32×C4#120semidirect
390. C23×C4C2×C3×D3semidirect
395. C2×C4⋊C4C2×C3×D3semidirect
403. C2×C22⋊C4C2×C3×D3semidirect
405. C2×C42C2×C3×D3semidirect
445. C23×C3C2×C4×D3semidirect
449. C23×C3C22×C3×C4semidirect
513. C2×C3×C4C2×C4×D3semidirect
517. C2×C3×C4C22×C3×C4semidirect
530. C2×Dic3C22×C3×C4semidirect
555. C2×D4C3×C4×D3semidirect
571. C22×C4C3×#67semidirect
630. C22×C3C4×#67semidirect
631. C22×C3C3×C4×D4semidirect
649. C2×D3C3×C4×D4semidirect
666. C3×C4#937direct (N × H)
667. C3×C4C3×#120semidirect
671. C32C4×#120semidirect
691. C23C2×C3×C4×D3semidirect
718. C2×C4C2×C3×C4×D3semidirect
762. C22C3×C4×#67semidirect
775. C4C3×#937direct (N × H)
777. C3C4×#937direct (N × H)
778. 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×C32×C4×D42
C2×C3×#9372
C2×C3×C4×#672
C3×#52202
C3×C4×#2172
C3×#49892
C3×#49562
C3×#49552
C3×#49462
C3×C4×(C2×D3)⋊C42
C3×C4×#1203
C4×#9373