Finite Group Databasebeta

← C3×#74010 #11805407

Subgroups — C3×#74010 #11805407

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C212yesmaximal
5C32×#380C211yesmaximal, characteristic, complemented
6C3×#4987C211yesmaximal, characteristic, complemented
7C3×#4975C211yesmaximal, characteristic, complemented
8C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
9C3×#4946C212yesmaximal, complemented
10C3×#4668C212yesmaximal, complemented
11C3×#4647C212yesmaximal, complemented
12C3×D4×C4⋊C4—31nomaximal
13#74010C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×C3×C4×D3C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2212yes—
22C2×C3×#217C2211yescharacteristic
23C3×C4×#67C418yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×C4⋊Dic3—24no—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2212yes—
35C2×C3×C4×Dic3C2211yescharacteristic
36C3×D3×C4⋊C4—24no—
37C3×#67⋊C4—28no—
38C32×#95C2212yes—
39C3×C3⋊#95C2212yes—
40C3×C3⋊#95C2212yes—
41C2×C3×C4×D4—31no—
42C2×C3×C4×D4—32no—
43C22×C3×C4⋊C4—31no—
44C22×C3×C4⋊C4—31no—
45C2×C4×#67C2×C311yescharacteristic
46C22×C4⋊Dic3C2×C311yescharacteristic, complemented
47C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
48C2×#67⋊C4C2×C312yes—
49C3×#389—32no—
50C3×#385—32no—
51C3×#385—32no—
52C3×#384—31no—
53C3×#380—21no—
54C3×#380—31no—
55C3×#380D311yescharacteristic, complemented
56C3×#380C2×C311yescharacteristic, complemented
57C3×C4×C4⋊C4—31no—
58#4987C2×C311yescharacteristic, complemented
59#4975C2×C311yescharacteristic, complemented
60Dic3×C4⋊C4C2×C311yescharacteristic, complemented
61#4946C2×C312yescomplemented
62#4668C2×C312yescomplemented
63#4647C2×C312yescomplemented
64C24×C32C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4—22no—
67C22×C32×C4—22no—
68C22×C32×C4C2×C414yescomplemented
69C22×C32×C4C2312yes—
70C22×C32×C4C2312yes—
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67C2×C414yes—
74C2×C3×#67D414yes—
75C2×C3×#67Q814yes—
76C22×C3×Dic3—24no—
77C22×C3×Dic3—24no—
78C22×C3×Dic3—42no—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3—24no—
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3—42no—
89C2×C3×C4×D3C2×C414yescomplemented
90C32×C4⋊C4—22no—
91C32×C4⋊C4—22no—
92C32×C22⋊C4—24no—
93C3×#217C2×C414yescomplemented
94C3×(C2×D3)⋊C4—24no—
95C3×(C2×D3)⋊C4C2×C414yescomplemented
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3—24no—
98C3×C4⋊Dic3D414yescomplemented
99C3×Dic3⋊C4—24no—
100C3×Dic3⋊C4—24no—
101C3×Dic3⋊C4—42no—
102C3×Dic3⋊C4C2×C414yescomplemented
103C3×C4×Dic3—24no—
104C3×C4×Dic3C2×C414yescomplemented
105D4×C4⋊C4—31noSylow
106C22×C3×D4—31no—
107C23×C3×C4—21no—
108C23×C3×C4—31no—
109C23×C3×C4—32no—
110C23×C3×C4—32no—
111C23×C3×C4C2×D311yescharacteristic
112C23×C3×C4C22×C311yescharacteristic
113C22×#67C22×C311yescharacteristic
114C23×Dic3C22×C312yes—
115C22×C4×D3C22×C312yes—
116C22×C4×D3C22×C311yescharacteristic
117C3×C4×D4—38no—
118C3×C4×D4—68no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—32no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C4⋊C4—64no—
129C2×C3×C4⋊C4—64no—
130C2×C3×C4⋊C4C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C4⋊C4C22×C311yescharacteristic
133C2×C3×C4⋊C4C22×C311yescharacteristic
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4C2×D312yes—
139C2×C3×C22⋊C4C22×C312yes—
140C2×C3×C42—31no—
141C2×C3×C42—32no—
142C2×#217C22×C311yescharacteristic
143C4×#67C3×C418yescomplemented
144C2×(C2×D3)⋊C4C22×C312yes—
145C2×(C2×D3)⋊C4C22×C311yescharacteristic
146C2×C4⋊Dic3—24no—
147C2×C4⋊Dic3C22×C312yes—
148C2×C4⋊Dic3C22×C311yescharacteristic
149C2×C4⋊Dic3C22×C311yescharacteristic
150C2×Dic3⋊C4C22×C312yes—
151C2×Dic3⋊C4C22×C312yes—
152C2×Dic3⋊C4C22×C312yes—
153C2×Dic3⋊C4C22×C311yescharacteristic
154C2×C4×Dic3C22×C312yes—
155C2×C4×Dic3C22×C311yescharacteristic
156D3×C4⋊C4—24no—
157#67⋊C4—28no—
158C3×#95—22no—
159C3×#95—32no—
160C3×#95—32no—
161C3×#95C2×D312yes—
162C3×#95C22×C312yes—
163C3⋊#95C22×C312yes—
164C3⋊#95C22×C312yes—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32C22×C412yes—
170C23×C32C2×D412yes—
171C23×C32C2×Q812yes—
172C23×C32C2411yescharacteristic
173C22×C3×D3—21no—
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C22×C412yes—
178C22×C3×D3C2×D412yes—
179C22×C3×D3C2×Q812yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—28no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C2×D412yes—
192C2×C32×C4#4112yes—
193C3×#67C4⋊C4116yescomplemented
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—48no—
204C2×C3×Dic3C22×C412yes—
205C2×C3×Dic3C22×C412yes—
206C2×C3×Dic3C22×C412yes—
207C2×C3×Dic3C2×D414yes—
208C2×C3×Dic3C2×D412yes—
209C2×C3×Dic3C2×Q812yes—
210C3×C4×D3—28no—
211C3×C4×D3—48no—
212C2×C4×D4—31no—
213C2×C4×D4—32no—
214C22×C4⋊C4—31no—
215C22×C4⋊C4—31no—
216#389—32no—
217#385—32no—
218#385—32no—
219#384—31no—
220#380—31no—
221#380C3×D311yescharacteristic, complemented
222C4×C4⋊C4—31no—
223C24×C3—21no—
224C24×C3—31no—
225C24×C3C22×D311yescharacteristic
226C24×C3C23×C311yescharacteristic
227C23×D3C23×C311yescharacteristic
228C2×C3×D4—34no—
229C2×C3×D4—34no—
230C2×C3×D4—34no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—24no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—34no—
245C22×C3×C4—32no—
246C22×C3×C4—42no—
247C22×C3×C4—42no—
248C22×C3×C4—64no—
249C22×C3×C4—64no—
250C22×C3×C4—64no—
251C22×C3×C4—62no—
252C22×C3×C4—62no—
253C22×C3×C4—64no—
254C22×C3×C4—122no—
255C22×C3×C4—122no—
256C22×C3×C4C4×D314yescomplemented
257C22×C3×C4C2×C3×C414yescomplemented
258C22×C3×C4C22×D312yes—
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C23×C312yes—
263C22×C3×C4C23×C312yes—
264C22×C3×C4C23×C311yescharacteristic
265C22×C3×C4C23×C311yescharacteristic
266C2×#67C2×C3×C414yes—
267C2×#67C3×D414yes—
268C2×#67C3×Q814yes—
269C22×Dic3—24no—
270C22×Dic3—24no—
271C22×Dic3—42no—
272C22×Dic3C23×C312yes—
273C22×Dic3C23×C311yescharacteristic
274C22×Dic3C23×C311yescharacteristic
275C22×Dic3C23×C312yes—
276C22×Dic3C23×C311yescharacteristic
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3—24no—
280C2×C4×D3—24no—
281C2×C4×D3—42no—
282C2×C4×D3C2×C3×C414yescomplemented
283C3×C4⋊C4—22no—
284C3×C4⋊C4—22no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—34no—
289C3×C4⋊C4—42no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4—64no—
292C3×C4⋊C4—64no—
293C3×C4⋊C4—64no—
294C3×C4⋊C4—62no—
295C3×C4⋊C4—122no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—34no—
299C3×C22⋊C4—34no—
300C3×C22⋊C4—44no—
301C3×C22⋊C4—64no—
302C3×C42—34no—
303C3×C42—64no—
304#217C2×C3×C414yescomplemented
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4C2×C3×C414yescomplemented
307C4⋊Dic3—22no—
308C4⋊Dic3—24no—
309C4⋊Dic3C3×D414yescomplemented
310Dic3⋊C4—24no—
311Dic3⋊C4—24no—
312Dic3⋊C4—42no—
313Dic3⋊C4C2×C3×C414yescomplemented
314C4×Dic3—24no—
315C4×Dic3C2×C3×C414yescomplemented
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—22no—
322C22×C32C2×C4⋊C414yescomplemented
323C22×C32C23×C411yescharacteristic
324C22×C32C22×D411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C22×Q811yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32H(5,𝔽2)11yescharacteristic
329C22×C322−1+411yescharacteristic
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3C2×C4⋊C414yescomplemented
337C32×C4—22no—
338C32×C4—42no—
339C32×C4—42no—
340C32×C4C4×D414yescomplemented
341C3×Dic3—22no—
342C3×Dic3—22no—
343C3×Dic3—24no—
344C3×Dic3—42no—
345C3×Dic3C2×C4⋊C414yescomplemented
346C22×D4—31no—
347C23×C4—31no—
348C23×C4—32no—
349C23×C4—32no—
350C23×C4C2×C3×D311yescharacteristic
351C4×D4—38no—
352C4×D4—68no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—64no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4C2×C3×D311yescharacteristic
363C2×C4⋊C4C2×C3×D311yescharacteristic
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—32no—
367C2×C22⋊C4C2×C3×D312yes—
368C2×C42—31no—
369C2×C42—32no—
370#95—32no—
371#95—32no—
372#95C2×C3×D312yes—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—32no—
386C23×C3—32no—
387C23×C3—32no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—61no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3C2×C4×D312yes—
397C23×C3D3×D412yes—
398C23×C3D3×Q812yes—
399C23×C3C22×C3×C412yes—
400C23×C3C2×C3×D412yes—
401C23×C3C2×C3×Q812yes—
402C23×C3C23×D311yescharacteristic
403C23×C3C24×C311yescharacteristic
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3C22×C3×C412yes—
409C22×D3C2×C3×D412yes—
410C22×D3C2×C3×Q812yes—
411C3×D4—316no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—28no—
417C2×C3×C4—28no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—32no—
437C2×C3×C4—32no—
438C2×C3×C4—32no—
439C2×C3×C4—34no—
440C2×C3×C4—48no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—62no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—62no—
454C2×C3×C4—61no—
455C2×C3×C4—68no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—128no—
460C2×C3×C4—128no—
461C2×C3×C4C2×C4×D312yes—
462C2×C3×C4C2×C4×D312yes—
463C2×C3×C4D3×D412yes—
464C2×C3×C4#23712yes—
465C2×C3×C4C22×C3×C412yes—
466C2×C3×C4C22×C3×C412yes—
467C2×C3×C4C2×C3×D412yes—
468C2×C3×C4C3×#4112yes—
469#67C3×C4⋊C4116yescomplemented
470C2×Dic3—22no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—48no—
480C2×Dic3C22×C3×C412yes—
481C2×Dic3C22×C3×C412yes—
482C2×Dic3C22×C3×C412yes—
483C2×Dic3C2×C3×D414yes—
484C2×Dic3C2×C3×D412yes—
485C2×Dic3C2×C3×Q812yes—
486C4×D3—28no—
487C4×D3—48no—
488C2×C32—24no—
489C2×C32C22×C4⋊C411yescharacteristic
490C2×C32C2×C4×D411yescharacteristic
491C2×C32#52011yescharacteristic
492C2×C32D4211yescharacteristic
493C2×C32#54711yescharacteristic
494C2×C32D4×Q811yescharacteristic
495C2×C32#55411yescharacteristic
496C3×D3—24no—
497C24—31no—
498C24C22×C3×D311yescharacteristic
499C2×D4—34no—
500C2×D4—34no—
501C2×D4—34no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—32no—
508C22×C4—34no—
509C22×C4—32no—
510C22×C4—64no—
511C22×C4—64no—
512C22×C4—64no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—64no—
516C22×C4—122no—
517C22×C4—122no—
518C22×C4C3×C4×D314yescomplemented
519C22×C4C22×C3×D312yes—
520C22×C4C22×C3×D312yes—
521C22×C4C22×C3×D311yescharacteristic
522C22×C4C22×C3×D311yescharacteristic
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—34no—
526C4⋊C4—34no—
527C4⋊C4—64no—
528C4⋊C4—64no—
529C4⋊C4—64no—
530C4⋊C4—62no—
531C4⋊C4—122no—
532C22⋊C4—24no—
533C22⋊C4—34no—
534C22⋊C4—34no—
535C22⋊C4—64no—
536C42—34no—
537C42—64no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—24no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—34no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—62no—
566C22×C3—62no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—62no—
570C22×C3—62no—
571C22×C3D3×C4⋊C414yescomplemented
572C22×C3C2×C3×C4⋊C414yescomplemented
573C22×C3C22×C4×D311yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C2×D3×D411yescharacteristic
576C22×C3C2×#23711yescharacteristic
577C22×C3C2×D3×Q811yescharacteristic
578C22×C3#100911yescharacteristic
579C22×C3#101011yescharacteristic
580C22×C3C23×C3×C411yescharacteristic
581C22×C3C22×C3×D411yescharacteristic
582C22×C3C22×C3×D411yescharacteristic
583C22×C3C22×C3×Q811yescharacteristic
584C22×C3C2×C3×#4111yescharacteristic
585C22×C3C3×H(5,𝔽2)11yescharacteristic
586C22×C3C3×2−1+411yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3C2×C3×C4⋊C414yescomplemented
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—24no—
597C3×C4—34no—
598C3×C4—42no—
599C3×C4—42no—
600C3×C4—42no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—62no—
604C3×C4—62no—
605C3×C4—64no—
606C3×C4—82no—
607C3×C4—82no—
608C3×C4—122no—
609C3×C4#67⋊C414yescomplemented
610C3×C4C3×C4×D414yescomplemented
611Dic3—22no—
612Dic3—22no—
613Dic3—24no—
614Dic3—42no—
615Dic3C2×C3×C4⋊C414yescomplemented
616C32D4×C4⋊C411yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—32no—
622C23—32no—
623C23—32no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23C2×C3×C4×D312yes—
629C23C3×D3×D412yes—
630C23C3×D3×Q812yes—
631C23C23×C3×D311yescharacteristic
632D4—316no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—28no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—32no—
643C2×C4—32no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—32no—
647C2×C4—34no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—62no—
653C2×C4—61no—
654C2×C4—68no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—128no—
659C2×C4—128no—
660C2×C4C2×C3×C4×D312yes—
661C2×C4C2×C3×C4×D312yes—
662C2×C4C3×D3×D412yes—
663C2×C4C3×#23712yes—
664C2×C3—24no—
665C2×C3—24no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—44no—
674C2×C3—64no—
675C2×C3C2×#67⋊C411yescharacteristic
676C2×C3C2×D3×C4⋊C411yescharacteristic
677C2×C3#552311yescharacteristic
678C2×C3#560911yescharacteristic
679C2×C3#561111yescharacteristic
680C2×C3#563211yescharacteristic
681C2×C3#563511yescharacteristic
682C2×C3C22×C3×C4⋊C411yescharacteristic
683C2×C3C2×C3×C4×D411yescharacteristic
684C2×C3C3×#52011yescharacteristic
685C2×C3C3×D4211yescharacteristic
686C2×C3C3×#54711yescharacteristic
687C2×C3C3×D4×Q811yescharacteristic
688C2×C3C3×#55411yescharacteristic
689D3—24no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—34no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—62no—
701C22—62no—
702C22—62no—
703C22C3×D3×C4⋊C414yescomplemented
704C22C22×C3×C4×D311yescharacteristic
705C22C2×C3×D3×D411yescharacteristic
706C22C2×C3×D3×D411yescharacteristic
707C22C2×C3×#23711yescharacteristic
708C22C2×C3×D3×Q811yescharacteristic
709C22C3×#100911yescharacteristic
710C22C3×#101011yescharacteristic
711C4—22no—
712C4—34no—
713C4—42no—
714C4—42no—
715C4—62no—
716C4—64no—
717C4—62no—
718C4—122no—
719C4C3×#67⋊C414yescomplemented
720C3—21no—
721C3#7401011yescharacteristic, direct product factor
722C3C3×D4×C4⋊C411yescharacteristic, complemented
723C2—24no—
724C2—64no—
725C2C2×C3×#67⋊C411yescharacteristic
726C2C2×C3×D3×C4⋊C411yescharacteristic
727C2C3×#552311yescharacteristic
728C2C3×#560911yescharacteristic
729C2C3×#561111yescharacteristic
730C2C3×#563211yescharacteristic
731C2C3×#563511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#380C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC3×#380D3
hypocenterC3C3×D4×C4⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
5. C32×#380C2semidirect
6. C3×#4987C2semidirect
7. C3×#4975C2semidirect
8. C3×Dic3×C4⋊C4C2semidirect
9. C3×#4946C2semidirect
10. C3×#4668C2semidirect
11. C3×#4647C2semidirect
13. #74010C3direct (N × H)
23. C3×C4×#67C4semidirect
46. C22×C4⋊Dic3C2×C3semidirect
47. C2×D3×C4⋊C4C2×C3semidirect
55. C3×#380D3semidirect
56. C3×#380C2×C3semidirect
58. #4987C2×C3semidirect
59. #4975C2×C3semidirect
60. Dic3×C4⋊C4C2×C3semidirect
61. #4946C2×C3semidirect
62. #4668C2×C3semidirect
63. #4647C2×C3semidirect
68. C22×C32×C4C2×C4semidirect
89. C2×C3×C4×D3C2×C4semidirect
93. C3×#217C2×C4semidirect
95. C3×(C2×D3)⋊C4C2×C4semidirect
98. C3×C4⋊Dic3D4semidirect
102. C3×Dic3⋊C4C2×C4semidirect
104. C3×C4×Dic3C2×C4semidirect
143. C4×#67C3×C4semidirect
193. C3×#67C4⋊C4semidirect
221. #380C3×D3semidirect
256. C22×C3×C4C4×D3semidirect
257. C22×C3×C4C2×C3×C4semidirect
282. C2×C4×D3C2×C3×C4semidirect
304. #217C2×C3×C4semidirect
306. (C2×D3)⋊C4C2×C3×C4semidirect
309. C4⋊Dic3C3×D4semidirect
313. Dic3⋊C4C2×C3×C4semidirect
315. C4×Dic3C2×C3×C4semidirect
322. C22×C32C2×C4⋊C4semidirect
336. C2×C3×D3C2×C4⋊C4semidirect
340. C32×C4C4×D4semidirect
345. C3×Dic3C2×C4⋊C4semidirect
469. #67C3×C4⋊C4semidirect
518. C22×C4C3×C4×D3semidirect
571. C22×C3D3×C4⋊C4semidirect
572. C22×C3C2×C3×C4⋊C4semidirect
593. C2×D3C2×C3×C4⋊C4semidirect
609. C3×C4#67⋊C4semidirect
610. C3×C4C3×C4×D4semidirect
615. Dic3C2×C3×C4⋊C4semidirect
616. C32D4×C4⋊C4semidirect
703. C22C3×D3×C4⋊C4semidirect
719. C4C3×#67⋊C4semidirect
721. C3#74010direct (N × H)
722. C3C3×D4×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C22×C3×C4⋊Dic32
C2×C3×D3×C4⋊C42
C2×C3×#67⋊C42
C32×#3802
C3×#49872
C3×#49752
C3×Dic3×C4⋊C42
C3×#49462
C3×#46682
C3×#46472
C3×D4×C4⋊C43
#740103