Finite Group Databasebeta

← C2×A4×#214 #11923358

Subgroups — C2×A4×#214 #11923358

Order 1152.

854 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×A4C211yesmaximal, characteristic
2C2×A4×Dic6C211yesmaximal, characteristic, complemented
3A4×#214C214yesmaximal, direct product factor
4C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
5C23×#214C311yesmaximal, characteristic, complemented
6C2×A4×SD16—31nomaximal
7C23×C3×A4—21no—
8C3×D4×A4—21no—
9C3×D4×A4C2212yes—
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4—21no—
12A4×Dic6—21no—
13A4×Dic6C2212yescomplemented
14C2×C3×#214—41nomaximal
15A4×C3⋊C8C2212yescomplemented
16C23×C3×D4C2×C311yescharacteristic
17C23×Dic6C2×C311yescharacteristic, complemented
18C2×Q8×A4—31no—
19C2×D4×A4—21no—
20C2×D4×A4D311yescharacteristic
21C22×#214—31no—
22C22×#214—31no—
23C22×#214—31no—
24C22×#214—31no—
25C22×#214—34no—
26C22×#214C2×C314yescomplemented
27C23×C3⋊C8C2×C311yescharacteristic, complemented
28A4×SD16—34no—
29C2×C8×A4—31no—
30C22×C3×A4—22no—
31C22×C3×A4—42no—
32C22×C3×A4D411yescharacteristic
33C2×C32×D4—41no—
34C2×C3×Dic6—41no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37Dic3×A4—22no—
38C3×#214—44no—
39C2×C3×C3⋊C8—41no—
40C23×SD16—31noSylow
41C25×C3—21no—
42C23×A4—22no—
43C23×A4—21no—
44C22×C3×D4—21no—
45C22×C3×D4—31no—
46C22×C3×D4—31no—
47C22×C3×D4—32no—
48C22×C3×D4—61no—
49C22×C3×D4—61no—
50C22×C3×D4C22×C312yes—
51C23×C3×C4C22×C311yescharacteristic
52C23×Dic3—21no—
53C22×Dic6—21no—
54C22×Dic6—31no—
55C22×Dic6—31no—
56C22×Dic6—32no—
57C22×Dic6—61no—
58C22×Dic6—61no—
59C22×Dic6C22×C312yescomplemented
60Q8×A4—32no—
61Q8×A4—61no—
62D4×A4—22no—
63D4×A4—21no—
64D4×A4—22no—
65D4×A4C2×D312yes—
66C2×C4×A4—21no—
67C2×C4×A4—61no—
68C2×C4×A4C2×D311yescharacteristic
69C2×C3×SD16—121no—
70C2×#214—34no—
71C2×#214—34no—
72C2×#214—32no—
73C2×#214—34no—
74C2×#214—31no—
75C2×#214—31no—
76C2×#214—34no—
77C2×#214—34no—
78C2×#214—34no—
79C2×#214—34no—
80C2×#214—34no—
81C2×#214—31no—
82C2×#214A411yescharacteristic, direct product factor
83C22×C3⋊C8—31no—
84C22×C3⋊C8—31no—
85C22×C3⋊C8—32no—
86C22×C3⋊C8C22×C312yescomplemented
87C8×A4—32no—
88C23×C32—81no—
89C2×C3×A4—42no—
90C2×C3×A4SD1612yescomplemented
91C2×C3×A4C2×D411yescharacteristic
92C32×D4—42no—
93C32×D4—81no—
94C2×C32×C4—41no—
95C2×C3×Dic3—81no—
96C3×Dic6—42no—
97C3×Dic6—81no—
98C3×C3⋊C8—42no—
99C23×Q8—31no—
100C23×D4C3×D311yescharacteristic
101C22×SD16—34no—
102C22×SD16—91no—
103C22×SD16—91no—
104C22×SD16—94no—
105C22×SD16—91no—
106C22×SD16—91no—
107C23×C8—31no—
108C24×C3—22no—
109C24×C3—42no—
110C24×C3—61no—
111C24×C3—62no—
112C24×C3—61no—
113C24×C3—122no—
114C24×C3C3×D411yescharacteristic
115C22×A4—24no—
116C22×A4—22no—
117C22×A4—21no—
118C22×A4—44no—
119C22×A4—42no—
120C22×A4#6711yescharacteristic
121C2×C3×Q8—121no—
122C2×C3×D4—32no—
123C2×C3×D4—32no—
124C2×C3×D4—32no—
125C2×C3×D4—32no—
126C2×C3×D4—31no—
127C2×C3×D4—41no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C2×C3×D4—61no—
132C2×C3×D4—64no—
133C2×C3×D4—61no—
134C2×C3×D4—62no—
135C2×C3×D4—61no—
136C2×C3×D4—62no—
137C2×C3×D4—81no—
138C2×C3×D4C2×A411yescharacteristic
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4C3×D411yescharacteristic
144C22×C3×C4C23×C311yescharacteristic
145C22×Dic3—22no—
146C22×Dic3—61no—
147C22×Dic3—62no—
148C22×Dic3—61no—
149C2×Dic6—32no—
150C2×Dic6—31no—
151C2×Dic6—32no—
152C2×Dic6—32no—
153C2×Dic6—32no—
154C2×Dic6—61no—
155C2×Dic6—61no—
156C2×Dic6—61no—
157C2×Dic6—64no—
158C2×Dic6—61no—
159C2×Dic6—62no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C2×Dic6—62no—
163C2×Dic6C2×A411yescharacteristic, complemented
164C4×A4—21no—
165C4×A4—21no—
166C4×A4—62no—
167C4×A4#6711yescharacteristic
168C4×A4C22×D311yescharacteristic
169C3×SD16—124no—
170C2×C3×C8—121no—
171#214—38no—
172#214—34no—
173#214—34no—
174#214—34no—
175#214C2×A414yesdirect product factor
176C2×C3⋊C8—32no—
177C2×C3⋊C8—31no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—32no—
180C2×C3⋊C8—32no—
181C2×C3⋊C8C2×A411yescharacteristic, complemented
182C22×C32—41no—
183C22×C32—82no—
184C22×C32—162no—
185C3×A4C2×SD1611yescharacteristic, complemented
186C32×C4—41no—
187C32×C4—41no—
188C3×Dic3—82no—
189C25—21no—
190C22×Q8—32no—
191C22×Q8—61no—
192C22×Q8—91no—
193C22×Q8—91no—
194C22×Q8—92no—
195C22×Q8—181no—
196C22×Q8—181no—
197C22×D4—21no—
198C22×D4—31no—
199C22×D4—31no—
200C22×D4—32no—
201C22×D4—61no—
202C22×D4—61no—
203C22×D4C2×C3×D312yes—
204C23×C4—61no—
205C23×C4C2×C3×D311yescharacteristic
206C2×SD16—31no—
207C2×SD16—91no—
208C2×SD16—94no—
209C2×SD16—94no—
210C2×SD16—91no—
211C2×SD16—94no—
212C2×SD16—94no—
213C2×SD16—94no—
214C2×SD16—92no—
215C2×SD16—91no—
216C2×SD16—94no—
217C2×SD16—94no—
218C2×SD16—94no—
219C22×C8—32no—
220C22×C8—91no—
221C22×C8—92no—
222C22×C8—91no—
223C23×C3—21no—
224C23×C3—31no—
225C23×C3—32no—
226C23×C3—31no—
227C23×C3—42no—
228C23×C3—62no—
229C23×C3—62no—
230C23×C3—62no—
231C23×C3—62no—
232C23×C3—61no—
233C23×C3—81no—
234C23×C3—82no—
235C23×C3—122no—
236C23×C3—122no—
237C23×C3—122no—
238C23×C3—124no—
239C23×C3—122no—
240C23×C3—122no—
241C23×C3—124no—
242C23×C3C3×SD1612yescomplemented
243C23×C3C2×C3×D411yescharacteristic
244C2×A4—22no—
245C2×A4—21no—
246C2×A4—44no—
247C2×A4—42no—
248C2×A4#21412yesdirect product factor
249C2×A4C2×#6711yescharacteristic
250C3×Q8—122no—
251C3×Q8—241no—
252C3×D4—21no—
253C3×D4—32no—
254C3×D4—42no—
255C3×D4—62no—
256C3×D4—62no—
257C3×D4—62no—
258C3×D4—62no—
259C3×D4—61no—
260C3×D4—81no—
261C3×D4—82no—
262C3×D4—82no—
263C3×D4C22×A412yes—
264C2×C3×C4—32no—
265C2×C3×C4—31no—
266C2×C3×C4—31no—
267C2×C3×C4—31no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—41no—
273C2×C3×C4—81no—
274C2×C3×C4—241no—
275C2×C3×C4C22×A411yescharacteristic
276C2×Dic3—21no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—61no—
281C2×Dic3—62no—
282Dic6—21no—
283Dic6—32no—
284Dic6—62no—
285Dic6—62no—
286Dic6—62no—
287Dic6—61no—
288Dic6—62no—
289Dic6C22×A412yescomplemented
290C3×C8—122no—
291C3⋊C8—32no—
292C3⋊C8C22×A412yescomplemented
293C2×C32—41no—
294C2×C32—42no—
295C2×C32—162no—
296C24—22no—
297C24—42no—
298C24—61no—
299C24—62no—
300C24—61no—
301C24—122no—
302C24C3×#6711yescharacteristic
303C2×Q8—31no—
304C2×Q8—92no—
305C2×Q8—92no—
306C2×Q8—92no—
307C2×Q8—92no—
308C2×Q8—91no—
309C2×Q8—181no—
310C2×Q8—181no—
311C2×Q8—181no—
312C2×Q8—182no—
313C2×Q8—181no—
314C2×Q8—182no—
315C2×Q8—181no—
316C2×Q8—184no—
317C2×Q8—181no—
318C2×D4—32no—
319C2×D4—32no—
320C2×D4—32no—
321C2×D4—32no—
322C2×D4—31no—
323C2×D4—61no—
324C2×D4—61no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—64no—
328C2×D4—61no—
329C2×D4—62no—
330C2×D4—61no—
331C2×D4—62no—
332C2×D4D3×A411yescharacteristic
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—62no—
338C22×C4—181no—
339C22×C4—182no—
340C22×C4—181no—
341C22×C4C3×#6711yescharacteristic
342C22×C4C22×C3×D311yescharacteristic
343SD16—34no—
344SD16—94no—
345SD16—94no—
346SD16—98no—
347SD16—94no—
348C2×C8—31no—
349C2×C8—92no—
350C2×C8—92no—
351C2×C8—92no—
352C2×C8—91no—
353C2×C8—92no—
354C22×C3—22no—
355C22×C3—32no—
356C22×C3—31no—
357C22×C3—32no—
358C22×C3—31no—
359C22×C3—31no—
360C22×C3—32no—
361C22×C3—32no—
362C22×C3—42no—
363C22×C3—41no—
364C22×C3—62no—
365C22×C3—82no—
366C22×C3—84no—
367C22×C3—81no—
368C22×C3—122no—
369C22×C3—122no—
370C22×C3—124no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3—124no—
374C22×C3—122no—
375C22×C3—162no—
376C22×C3—164no—
377C22×C3C2×C3×SD1611yescharacteristic, complemented
378C22×C3D4×A411yescharacteristic
379A4—21no—
380A4C2×#21411yescharacteristic, direct product factor
381C3×C4—31no—
382C3×C4—31no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—81no—
386C3×C4—81no—
387C3×C4—242no—
388C3×C4D4×A411yescharacteristic
389C3×C4C23×A411yescharacteristic
390Dic3—22no—
391Dic3—62no—
392C32—41noSylow
393C23—21no—
394C23—31no—
395C23—32no—
396C23—31no—
397C23—42no—
398C23—62no—
399C23—62no—
400C23—62no—
401C23—62no—
402C23—61no—
403C23—122no—
404C23—122no—
405C23—122no—
406C23—124no—
407C23—122no—
408C23—122no—
409C23—124no—
410C23C3×#21412yescomplemented
411C23C2×C3×#6711yescharacteristic
412Q8—32no—
413Q8—61no—
414Q8—92no—
415Q8—182no—
416Q8—182no—
417Q8—182no—
418Q8—182no—
419Q8—181no—
420D4—21no—
421D4—32no—
422D4—62no—
423D4—62no—
424D4—62no—
425D4—62no—
426D4—61no—
427D4C2×D3×A412yes—
428C2×C4—32no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—61no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—181no—
441C2×C4—182no—
442C2×C4C2×D3×A411yescharacteristic
443C8—32no—
444C8—92no—
445C2×C3—32no—
446C2×C3—31no—
447C2×C3—31no—
448C2×C3—42no—
449C2×C3—41no—
450C2×C3—42no—
451C2×C3—81no—
452C2×C3—82no—
453C2×C3—122no—
454C2×C3—162no—
455C2×C3—164no—
456C2×C3A4×SD1612yescomplemented
457C2×C3C2×D4×A411yescharacteristic
458C22—22no—
459C22—32no—
460C22—31no—
461C22—32no—
462C22—31no—
463C22—31no—
464C22—32no—
465C22—32no—
466C22—42no—
467C22—62no—
468C22—122no—
469C22—122no—
470C22—124no—
471C22—122no—
472C22—122no—
473C22—124no—
474C22—122no—
475C22C2×C3×#21411yescharacteristic, complemented
476C22A4×#6711yescharacteristic
477C4—31no—
478C4—31no—
479C4—62no—
480C4—182no—
481C4A4×#6711yescharacteristic
482C4C22×D3×A411yescharacteristic
483C3—41no—
484C3—81no—
485C3C2×A4×SD1611yescharacteristic, complemented
486C2—31no—
487C2—32no—
488C2—31no—
489C2—42no—
490C2—122no—
491C2A4×#21412yesdirect product factor
492C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC22A4×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC4C22×D3×A4
FittingC23×C3×D4C2×C3
socleC24×C3C3×D4
prime radicalC2×C3×D4×A4C2
hypercenterC2×D4D3×A4
hypocenterC22×C3C2×C3×SD16
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic6C2semidirect
3. A4×#214C2direct (N × H)
4. C2×A4×C3⋊C8C2semidirect
5. C23×#214C3semidirect
13. A4×Dic6C22semidirect
15. A4×C3⋊C8C22semidirect
17. C23×Dic6C2×C3semidirect
26. C22×#214C2×C3semidirect
27. C23×C3⋊C8C2×C3semidirect
59. C22×Dic6C22×C3semidirect
82. C2×#214A4direct (N × H)
86. C22×C3⋊C8C22×C3semidirect
90. C2×C3×A4SD16semidirect
163. C2×Dic6C2×A4semidirect
175. #214C2×A4direct (N × H)
181. C2×C3⋊C8C2×A4semidirect
185. C3×A4C2×SD16semidirect
242. C23×C3C3×SD16semidirect
248. C2×A4#214direct (N × H)
289. Dic6C22×A4semidirect
292. C3⋊C8C22×A4semidirect
377. C22×C3C2×C3×SD16semidirect
380. A4C2×#214direct (N × H)
410. C23C3×#214semidirect
456. C2×C3A4×SD16semidirect
475. C22C2×C3×#214semidirect
485. C3C2×A4×SD16semidirect
491. C2A4×#214direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×A4×Dic62
A4×#2142
C2×A4×C3⋊C82
C23×#2143
C2×A4×SD163
C2×C3×#2144