Finite Group Databasebeta

← C3×#74659 #11801988

Subgroups — C3×#74659 #11801988

Order 1152.

2591 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C212yesmaximal, complemented
5C32×#386C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7C3×#4956C212yesmaximal, complemented
8C3×#4955C211yesmaximal, characteristic, complemented
9C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
10C3×#4668C212yesmaximal, complemented
11C3×#4666C212yesmaximal, complemented
12C3×C4×#120—31nomaximal
13#74659C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic, complemented
20C22×C3×C4×D3—24no—
21C22×C3×C4×D3—28no—
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2212yes—
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yescomplemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic, complemented
29C3×#937C418yescomplemented
30C3×D4×Dic3—24no—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2212yescomplemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2212yescomplemented
38C3×#67⋊C4—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×#937C2×C311yescharacteristic
48C2×D4×Dic3C2×C311yescharacteristic, complemented
49C2×#67⋊C4C2×C312yescomplemented
50C3×#386—21no—
51C3×#386—32no—
52C3×#386D311yescharacteristic, complemented
53C3×#386C2×C311yescharacteristic, complemented
54C3×#385—31no—
55C3×#385—32no—
56C3×#379—31no—
57C3×C4×C22⋊C4—31no—
58C3×C4×C22⋊C4—32no—
59#5210C2×C311yescharacteristic, complemented
60#4956C2×C312yescomplemented
61#4955C2×C311yescharacteristic, complemented
62Dic3×C22⋊C4C2×C311yescharacteristic, complemented
63#4668C2×C312yescomplemented
64#4666C2×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—22no—
77C22×C32×C4—24no—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2312yes—
81C2×C3×#67—24no—
82C2×C3×#67—24no—
83C2×C3×#67C2×C418yescomplemented
84C22×C3×Dic3—24no—
85C22×C3×Dic3—24no—
86C22×C3×Dic3—22no—
87C22×C3×Dic3D414yescomplemented
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
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×C22⋊C4—22no—
101C32×C22⋊C4—24no—
102C3×#217—22no—
103C3×#217—22no—
104C3×#217C2×C414yescomplemented
105C3×(C2×D3)⋊C4—24no—
106C3×(C2×D3)⋊C4—24no—
107C3×(C2×D3)⋊C4C2×C418yescomplemented
108C3×C4⋊Dic3—22no—
109C3×Dic3⋊C4—24no—
110C3×C4×Dic3—24no—
111C3×C4×Dic3—22no—
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—31no—
121C23×C3×C4—32no—
122C23×C3×C4—31no—
123C23×C3×C4—32no—
124C23×C3×C4—64no—
125C23×C3×C4—68no—
126C23×C3×C4C2×D311yescharacteristic
127C23×C3×C4C22×C311yescharacteristic
128C22×#67C22×C312yes—
129C23×Dic3C22×C311yescharacteristic
130C23×Dic3C22×C311yescharacteristic, complemented
131C22×C4×D3—24no—
132C22×C4×D3—28no—
133C22×C4×D3C22×C312yes—
134C22×C4×D3C22×C312yes—
135C3×#120—38no—
136C3×C4×D4—68no—
137C3×C4×D4—64no—
138C2×C3×C4⋊C4—32no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—32no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—32no—
147C2×C3×C22⋊C4—32no—
148C2×C3×C22⋊C4C2×D311yescharacteristic
149C2×C3×C22⋊C4C2×D312yescomplemented
150C2×C3×C22⋊C4C22×C311yescharacteristic
151C2×C3×C22⋊C4C22×C312yescomplemented
152C2×C3×C42—32no—
153C2×C3×C42—31no—
154C2×#217C22×C311yescharacteristic
155C2×#217C22×C311yescharacteristic
156C2×#217C22×C311yescharacteristic, complemented
157#937C3×C418yescomplemented
158D4×Dic3—24no—
159C2×(C2×D3)⋊C4C22×C312yes—
160C2×(C2×D3)⋊C4C22×C312yes—
161C2×(C2×D3)⋊C4C22×C312yes—
162C2×C4⋊Dic3C22×C311yescharacteristic, complemented
163C2×Dic3⋊C4C22×C312yescomplemented
164C2×C4×Dic3C22×C311yescharacteristic, complemented
165C2×C4×Dic3C22×C312yescomplemented
166#67⋊C4—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×C32—21no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—21no—
180C23×C32C22×C412yes—
181C23×C32C22×C412yescomplemented
182C23×C32C2×D412yes—
183C23×C32#4112yes—
184C23×C32C2411yescharacteristic
185C22×C3×D3—216no—
186C22×C3×D3—28no—
187C22×C3×D3—28no—
188C22×C3×D3—28no—
189C22×C3×D3—22no—
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—216no—
194C22×C3×D3C22×C414yes—
195C22×C3×D3C2×D414yes—
196C22×C3×D3#4114yes—
197C32×D4—28no—
198C2×C32×C4—28no—
199C2×C32×C4—21no—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4C22×C412yescomplemented
207C2×C32×C4C2×D414yes—
208C3×#67—216no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—28no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—44no—
218C2×C3×Dic3C22×C414yescomplemented
219C2×C3×Dic3C2×D412yes—
220C2×C3×Dic3C2×D412yes—
221C2×C3×Dic3C2×D414yes—
222C3×C4×D3—216no—
223C3×C4×D3—216no—
224C24×C4—31no—
225C2×#120—31no—
226C2×C4×D4—31no—
227C2×C4×D4—32no—
228#386—32no—
229#386C3×D311yescharacteristic, complemented
230#385—31no—
231#385—32no—
232#379—31no—
233C4×C22⋊C4—31no—
234C4×C22⋊C4—32no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—32no—
238C24×C3—34no—
239C24×C3—64no—
240C24×C3—64no—
241C24×C3—62no—
242C24×C3—62no—
243C24×C3C22×D311yescharacteristic
244C24×C3C22×D311yescharacteristic
245C24×C3C23×C311yescharacteristic
246C24×C3C23×C311yescharacteristic
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—24no—
250C23×D3—24no—
251C23×D3C2×C3×C414yescomplemented
252C23×D3C23×C312yes—
253C2×C3×D4—22no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—22no—
257C2×C3×D4—24no—
258C2×C3×D4—38no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—64no—
262C2×C3×D4—64no—
263C2×C3×D4C4×D314yescomplemented
264C2×C3×D4C2×C3×C414yescomplemented
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—21no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—31no—
273C22×C3×C4—34no—
274C22×C3×C4—32no—
275C22×C3×C4—31no—
276C22×C3×C4—38no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—44no—
280C22×C3×C4—42no—
281C22×C3×C4—64no—
282C22×C3×C4—64no—
283C22×C3×C4—64no—
284C22×C3×C4—64no—
285C22×C3×C4—632no—
286C22×C3×C4—64no—
287C22×C3×C4—64no—
288C22×C3×C4—62no—
289C22×C3×C4—64no—
290C22×C3×C4C22×D312yes—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D312yes—
293C22×C3×C4C23×C312yes—
294C22×C3×C4C23×C311yescharacteristic
295C22×C3×C4C23×C312yes—
296C2×#67—24no—
297C2×#67—24no—
298C2×#67C2×C3×C418yescomplemented
299C22×Dic3—24no—
300C22×Dic3—24no—
301C22×Dic3—22no—
302C22×Dic3C3×D414yescomplemented
303C22×Dic3C23×C311yescharacteristic
304C22×Dic3C23×C311yescharacteristic
305C22×Dic3C23×C312yes—
306C22×Dic3C23×C311yescharacteristic
307C22×Dic3C23×C311yescharacteristic
308C2×C4×D3—232no—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×C4×D3—24no—
313C2×C4×D3—24no—
314C2×C4×D3C3×D418yescomplemented
315C3×C4⋊C4—62no—
316C3×C4⋊C4—64no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—34no—
322C3×C22⋊C4—38no—
323C3×C22⋊C4—44no—
324C3×C22⋊C4—42no—
325C3×C22⋊C4—64no—
326C3×C22⋊C4—64no—
327C3×C22⋊C4—62no—
328C3×C22⋊C4—62no—
329C3×C42—62no—
330C3×C42—64no—
331#217—22no—
332#217—22no—
333#217C2×C3×C414yescomplemented
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4C2×C3×C418yescomplemented
337C4⋊Dic3—22no—
338Dic3⋊C4—24no—
339C4×Dic3—24no—
340C4×Dic3—22no—
341C22×C32—24no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—24no—
345C22×C32—24no—
346C22×C32—22no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32—42no—
350C22×C32C4×D414yescomplemented
351C22×C32C23×C411yescharacteristic
352C22×C32C22×D412yes—
353C22×C32C22×D411yescharacteristic
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4112yes—
356C2×C3×D3—232no—
357C2×C3×D3—24no—
358C2×C3×D3—24no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3C4×D418yescomplemented
364C32×C4—22no—
365C32×C4—24no—
366C32×C4—42no—
367C3×Dic3—24no—
368C3×Dic3—22no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3#12014yescomplemented
372C25—31no—
373C22×D4—32no—
374C22×D4C2×C3×D311yescharacteristic
375C23×C4—31no—
376C23×C4—32no—
377C23×C4—31no—
378C23×C4—32no—
379C23×C4—64no—
380C23×C4—68no—
381C23×C4C2×C3×D311yescharacteristic
382#120—38no—
383C4×D4—68no—
384C4×D4—64no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—31no—
391C2×C22⋊C4—32no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4C2×C3×D311yescharacteristic
394C2×C22⋊C4C2×C3×D312yescomplemented
395C2×C42—32no—
396C2×C42—31no—
397#95—32no—
398#95—32no—
399#95C2×C3×D312yescomplemented
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—34no—
418C23×C3—34no—
419C23×C3—34no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—42no—
426C23×C3—616no—
427C23×C3—68no—
428C23×C3—68no—
429C23×C3—616no—
430C23×C3—68no—
431C23×C3—62no—
432C23×C3—62no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3C2×C4×D312yes—
436C23×C3C2×C4×D312yescomplemented
437C23×C3D3×D412yes—
438C23×C3#23712yes—
439C23×C3C22×C3×C412yes—
440C23×C3C22×C3×C412yescomplemented
441C23×C3C2×C3×D412yes—
442C23×C3C3×#4112yes—
443C23×C3C23×D311yescharacteristic
444C23×C3C24×C311yescharacteristic
445C22×D3—28no—
446C22×D3—216no—
447C22×D3—28no—
448C22×D3—28no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—216no—
454C22×D3C22×C3×C414yes—
455C22×D3C2×C3×D414yes—
456C22×D3C3×#4114yes—
457C3×D4—28no—
458C3×D4—28no—
459C3×D4—48no—
460C3×D4—616no—
461C2×C3×C4—28no—
462C2×C3×C4—28no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—32no—
480C2×C3×C4—34no—
481C2×C3×C4—34no—
482C2×C3×C4—32no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—48no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—616no—
492C2×C3×C4—616no—
493C2×C3×C4—68no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—124no—
502C2×C3×C4C2×C4×D312yescomplemented
503C2×C3×C4D3×D414yes—
504C2×C3×C4C22×C3×C412yescomplemented
505C2×C3×C4C2×C3×D414yes—
506#67—216no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—28no—
511C2×Dic3—21no—
512C2×Dic3—22no—
513C2×Dic3—21no—
514C2×Dic3—22no—
515C2×Dic3—44no—
516C2×Dic3C22×C3×C414yescomplemented
517C2×Dic3C2×C3×D412yes—
518C2×Dic3C2×C3×D412yes—
519C2×Dic3C2×C3×D414yes—
520C4×D3—216no—
521C4×D3—216no—
522C2×C32—24no—
523C2×C32—42no—
524C2×C32C2×C4×D411yescharacteristic
525C2×C32C2×C4×D412yes—
526C2×C32C2×#12011yescharacteristic
527C2×C32#52511yescharacteristic
528C2×C32#52512yes—
529C3×D3—28no—
530C24—32no—
531C24—34no—
532C24—64no—
533C24—64no—
534C24—62no—
535C24—62no—
536C24C22×C3×D311yescharacteristic
537C24C22×C3×D311yescharacteristic
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—38no—
541C2×D4—64no—
542C2×D4—64no—
543C2×D4C3×C4×D314yescomplemented
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—31no—
547C22×C4—32no—
548C22×C4—31no—
549C22×C4—34no—
550C22×C4—38no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—64no—
556C22×C4—64no—
557C22×C4—632no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—62no—
561C22×C4—64no—
562C22×C4C22×C3×D312yes—
563C22×C4C22×C3×D311yescharacteristic
564C22×C4C22×C3×D312yes—
565C4⋊C4—62no—
566C4⋊C4—64no—
567C22⋊C4—22no—
568C22⋊C4—24no—
569C22⋊C4—34no—
570C22⋊C4—38no—
571C22⋊C4—64no—
572C22⋊C4—64no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C42—62no—
576C42—64no—
577C22×C3—22no—
578C22×C3—24no—
579C22×C3—22no—
580C22×C3—24no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—24no—
584C22×C3—24no—
585C22×C3—22no—
586C22×C3—24no—
587C22×C3—24no—
588C22×C3—22no—
589C22×C3—24no—
590C22×C3—21no—
591C22×C3—22no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—22no—
595C22×C3—38no—
596C22×C3—42no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—44no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—41no—
607C22×C3—42no—
608C22×C3—632no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—64no—
613C22×C3—64no—
614C22×C3—64no—
615C22×C3—81no—
616C22×C3—82no—
617C22×C3—81no—
618C22×C3#67⋊C414yescomplemented
619C22×C3C3×C4×D414yescomplemented
620C22×C3C22×C4×D311yescharacteristic
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D412yes—
623C22×C3C2×#23711yescharacteristic
624C22×C3D3×#4112yes—
625C22×C3C23×C3×C411yescharacteristic
626C22×C3C22×C3×D412yes—
627C22×C3C22×C3×D411yescharacteristic
628C22×C3C2×C3×#4111yescharacteristic
629C22×C3C2×C3×#4112yes—
630C2×D3—232no—
631C2×D3—24no—
632C2×D3—24no—
633C2×D3—24no—
634C2×D3—24no—
635C2×D3—24no—
636C2×D3—24no—
637C2×D3C3×C4×D418yescomplemented
638C3×C4—22no—
639C3×C4—24no—
640C3×C4—22no—
641C3×C4—24no—
642C3×C4—34no—
643C3×C4—44no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—64no—
648C3×C4—62no—
649C3×C4—82no—
650C3×C4—121no—
651C3×C4—121no—
652Dic3—24no—
653Dic3—22no—
654Dic3—41no—
655Dic3—41no—
656Dic3C3×#12014yescomplemented
657C32C4×#12011yescharacteristic, complemented, Sylow
658C23—22no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—34no—
665C23—34no—
666C23—34no—
667C23—616no—
668C23—68no—
669C23—616no—
670C23—68no—
671C23—68no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23C2×C3×C4×D312yes—
677C23C2×C3×C4×D312yescomplemented
678C23C3×D3×D412yes—
679C23C3×#23712yes—
680C23C23×C3×D311yescharacteristic
681D4—28no—
682D4—616no—
683C2×C4—28no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—34no—
692C2×C4—32no—
693C2×C4—34no—
694C2×C4—32no—
695C2×C4—616no—
696C2×C4—616no—
697C2×C4—68no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—61no—
702C2×C4—62no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—124no—
706C2×C4C2×C3×C4×D312yescomplemented
707C2×C4C3×D3×D414yes—
708C2×C3—24no—
709C2×C3—24no—
710C2×C3—22no—
711C2×C3—21no—
712C2×C3—22no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—44no—
716C2×C3—42no—
717C2×C3—42no—
718C2×C3—68no—
719C2×C3—82no—
720C2×C3C2×#67⋊C411yescharacteristic
721C2×C3C4×D3×D412yes—
722C2×C3D3×#12011yescharacteristic
723C2×C3#560612yes—
724C2×C3#565611yescharacteristic
725C2×C3C2×C3×C4×D412yes—
726C2×C3C2×C3×C4×D411yescharacteristic
727C2×C3C2×C3×#12011yescharacteristic
728C2×C3C3×#52512yes—
729C2×C3C3×#52511yescharacteristic
730D3—28no—
731C22—24no—
732C22—22no—
733C22—24no—
734C22—22no—
735C22—24no—
736C22—22no—
737C22—38no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—632no—
742C22—64no—
743C22—64no—
744C22—64no—
745C22—64no—
746C22—64no—
747C22—64no—
748C22C3×#67⋊C414yescomplemented
749C22C22×C3×C4×D311yescharacteristic
750C22C2×C3×D3×D412yes—
751C22C2×C3×D3×D411yescharacteristic
752C22C2×C3×#23711yescharacteristic
753C22C3×D3×#4112yes—
754C4—24no—
755C4—22no—
756C4—34no—
757C4—42no—
758C4—64no—
759C4—62no—
760C4—121no—
761C4—121no—
762C3—21no—
763C3#7465911yescharacteristic, direct product factor
764C3C3×C4×#12011yescharacteristic, complemented
765C2—24no—
766C2—42no—
767C2—68no—
768C2C2×C3×#67⋊C411yescharacteristic
769C2C3×C4×D3×D412yes—
770C2C3×D3×#12011yescharacteristic
771C2C3×#560612yes—
772C2C3×#565611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC2×C3×#937C2
cosocleC23×C3C24×C3
hypercenterC3×#386D3
hypocenterC3C3×C4×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×C3×#67⋊C4C2semidirect
5. C32×#386C2semidirect
6. C3×#5210C2semidirect
7. C3×#4956C2semidirect
8. C3×#4955C2semidirect
9. C3×Dic3×C22⋊C4C2semidirect
10. C3×#4668C2semidirect
11. C3×#4666C2semidirect
13. #74659C3direct (N × H)
19. C23×C3×Dic3C22semidirect
25. C2×C32×C22⋊C4C22semidirect
28. C2×C3×#217C22semidirect
29. C3×#937C4semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
37. C2×C3×C4×Dic3C22semidirect
39. C32×#95C22semidirect
40. C3×C3⋊#95C22semidirect
41. C3×C3⋊#95C22semidirect
43. C23×C4×D3C2×C3semidirect
48. C2×D4×Dic3C2×C3semidirect
49. C2×#67⋊C4C2×C3semidirect
52. C3×#386D3semidirect
53. C3×#386C2×C3semidirect
59. #5210C2×C3semidirect
60. #4956C2×C3semidirect
61. #4955C2×C3semidirect
62. Dic3×C22⋊C4C2×C3semidirect
63. #4668C2×C3semidirect
64. #4666C2×C3semidirect
71. C23×C3×D3C2×C4semidirect
75. C2×C32×D4C2×C4semidirect
83. C2×C3×#67C2×C4semidirect
87. C22×C3×Dic3D4semidirect
99. C2×C3×C4×D3D4semidirect
104. C3×#217C2×C4semidirect
107. C3×(C2×D3)⋊C4C2×C4semidirect
130. C23×Dic3C22×C3semidirect
149. C2×C3×C22⋊C4C2×D3semidirect
151. C2×C3×C22⋊C4C22×C3semidirect
156. C2×#217C22×C3semidirect
157. #937C3×C4semidirect
162. C2×C4⋊Dic3C22×C3semidirect
163. C2×Dic3⋊C4C22×C3semidirect
164. C2×C4×Dic3C22×C3semidirect
165. C2×C4×Dic3C22×C3semidirect
170. C3×#95C2×D3semidirect
171. C3×#95C22×C3semidirect
172. C3⋊#95C22×C3semidirect
173. C3⋊#95C22×C3semidirect
181. C23×C32C22×C4semidirect
206. C2×C32×C4C22×C4semidirect
218. C2×C3×Dic3C22×C4semidirect
229. #386C3×D3semidirect
251. C23×D3C2×C3×C4semidirect
263. C2×C3×D4C4×D3semidirect
264. C2×C3×D4C2×C3×C4semidirect
298. C2×#67C2×C3×C4semidirect
302. C22×Dic3C3×D4semidirect
314. C2×C4×D3C3×D4semidirect
333. #217C2×C3×C4semidirect
336. (C2×D3)⋊C4C2×C3×C4semidirect
350. C22×C32C4×D4semidirect
363. C2×C3×D3C4×D4semidirect
371. C3×Dic3#120semidirect
394. C2×C22⋊C4C2×C3×D3semidirect
399. #95C2×C3×D3semidirect
436. C23×C3C2×C4×D3semidirect
440. C23×C3C22×C3×C4semidirect
502. C2×C3×C4C2×C4×D3semidirect
504. C2×C3×C4C22×C3×C4semidirect
516. C2×Dic3C22×C3×C4semidirect
543. C2×D4C3×C4×D3semidirect
618. C22×C3#67⋊C4semidirect
619. C22×C3C3×C4×D4semidirect
637. C2×D3C3×C4×D4semidirect
656. Dic3C3×#120semidirect
657. C32C4×#120semidirect
677. C23C2×C3×C4×D3semidirect
706. C2×C4C2×C3×C4×D3semidirect
748. C22C3×#67⋊C4semidirect
763. C3#74659direct (N × H)
764. 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×#9372
C2×C3×D4×Dic32
C2×C3×#67⋊C42
C32×#3862
C3×#52102
C3×#49562
C3×#49552
C3×Dic3×C22⋊C42
C3×#46682
C3×#46662
C3×C4×#1203
#746593