Finite Group Databasebeta

← C2×A4×C4⋊Dic3 #11923345

Subgroups — C2×A4×C4⋊Dic3 #11923345

Order 1152.

1190 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 195 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2C22×Dic3×A4C212yesmaximal
3A4×C4⋊Dic3C214yesmaximal, direct product factor
4C23×C4⋊Dic3C311yesmaximal, characteristic, complemented
5C2×A4×C4⋊C4—31nomaximal
6C23×C3×A4C2211yescharacteristic
7C2×C3×C4×A4C414yescomplemented
8C2×C3×C4×A4C2212yes—
9C2×Dic3×A4—24no—
10C2×Dic3×A4C2214yes—
11C2×C3×C4⋊Dic3—41nomaximal
12C24×C3×C4C2×C311yescharacteristic
13C24×Dic3C2×C312yes—
14C22×C4×A4—21no—
15C22×C4×A4—32no—
16C22×C4×A4D311yescharacteristic
17C22×C4⋊Dic3—31no—
18C22×C4⋊Dic3—31no—
19C22×C4⋊Dic3—32no—
20C22×C4⋊Dic3—34no—
21C22×C4⋊Dic3C2×C314yescomplemented
22A4×C4⋊C4—34no—
23C22×C3×A4C2×C412yes—
24C22×C3×A4D412yes—
25C22×C3×A4Q812yes—
26C22×C3×A4C2311yescharacteristic
27C22×C32×C4—41no—
28C22×C3×Dic3—42no—
29C3×C4×A4C2×C414yescomplemented
30Dic3×A4—24no—
31C3×C4⋊Dic3—44no—
32C23×C4⋊C4—31noSylow
33C25×C3C22×C311yescharacteristic
34C23×A4—21no—
35C23×A4C2×D311yescharacteristic
36C23×C3×C4—31no—
37C23×C3×C4—34no—
38C23×C3×C4—31no—
39C23×C3×C4—32no—
40C23×C3×C4C3×C414yescomplemented
41C23×C3×C4C22×C312yes—
42C23×Dic3—24no—
43C23×Dic3—32no—
44C23×Dic3—32no—
45C23×Dic3—34no—
46C23×Dic3—64no—
47C23×Dic3C22×C314yes—
48C2×C4×A4—24no—
49C2×C4×A4—22no—
50C2×C4×A4—34no—
51C2×C4×A4—64no—
52C2×C4×A4Dic314yescomplemented
53C2×C4×A4C2×D312yes—
54C2×C3×C4⋊C4—121no—
55C2×C4⋊Dic3—32no—
56C2×C4⋊Dic3—34no—
57C2×C4⋊Dic3—38no—
58C2×C4⋊Dic3—31no—
59C2×C4⋊Dic3—32no—
60C2×C4⋊Dic3—34no—
61C2×C4⋊Dic3—34no—
62C2×C4⋊Dic3—34no—
63C2×C4⋊Dic3—38no—
64C2×C4⋊Dic3A411yescharacteristic, direct product factor
65C23×C32—41no—
66C2×C3×A4C4⋊C414yescomplemented
67C2×C3×A4C22×C411yescharacteristic
68C2×C3×A4C2×D411yescharacteristic
69C2×C3×A4C2×Q811yescharacteristic
70C2×C32×C4—44no—
71C2×C32×C4—42no—
72C2×C3×Dic3—44no—
73C2×C3×Dic3—84no—
74C24×C4—32no—
75C24×C4C3×D311yescharacteristic
76C22×C4⋊C4—34no—
77C22×C4⋊C4—91no—
78C22×C4⋊C4—94no—
79C22×C4⋊C4—92no—
80C22×C4⋊C4—91no—
81C24×C3—32no—
82C24×C3—31no—
83C24×C3—32no—
84C24×C3—32no—
85C24×C3—31no—
86C24×C3C2×C3×C412yes—
87C24×C3C3×D412yes—
88C24×C3C3×Q812yes—
89C24×C3C23×C311yescharacteristic
90C22×A4—22no—
91C22×A4—22no—
92C22×A4—22no—
93C22×A4—21no—
94C22×A4Dic612yes—
95C22×A4D1212yes—
96C22×A4C2×Dic312yes—
97C22×A4C22×D311yescharacteristic
98C22×C3×C4—32no—
99C22×C3×C4—34no—
100C22×C3×C4—38no—
101C22×C3×C4—31no—
102C22×C3×C4—34no—
103C22×C3×C4—34no—
104C22×C3×C4—32no—
105C22×C3×C4—32no—
106C22×C3×C4—32no—
107C22×C3×C4—34no—
108C22×C3×C4—38no—
109C22×C3×C4—34no—
110C22×C3×C4—41no—
111C22×C3×C4—81no—
112C22×C3×C4—122no—
113C22×C3×C4C2×C3×C414yescomplemented
114C22×C3×C4C2×A411yescharacteristic
115C22×Dic3—24no—
116C22×Dic3—34no—
117C22×Dic3—32no—
118C22×Dic3—34no—
119C22×Dic3—34no—
120C22×Dic3—34no—
121C22×Dic3—64no—
122C22×Dic3—64no—
123C22×Dic3—68no—
124C22×Dic3—68no—
125C22×Dic3—64no—
126C22×Dic3—64no—
127C22×Dic3—64no—
128C22×Dic3C2×A412yes—
129C4×A4—24no—
130C4×A4—64no—
131C4×A4C2×Dic314yescomplemented
132C3×C4⋊C4—124no—
133C4⋊Dic3—38no—
134C4⋊Dic3—34no—
135C4⋊Dic3—38no—
136C4⋊Dic3C2×A414yesdirect product factor
137C22×C32—42no—
138C22×C32—42no—
139C22×C32—42no—
140C22×C32—41no—
141C3×A4C2×C4⋊C411yescharacteristic, complemented
142C32×C4—44no—
143C3×Dic3—84no—
144C25C2×C3×D311yescharacteristic
145C23×C4—31no—
146C23×C4—31no—
147C23×C4—32no—
148C23×C4—34no—
149C23×C4—34no—
150C23×C4—64no—
151C23×C4—92no—
152C23×C4—94no—
153C23×C4—92no—
154C23×C4—184no—
155C23×C4C3×Dic314yescomplemented
156C23×C4C2×C3×D312yes—
157C2×C4⋊C4—31no—
158C2×C4⋊C4—94no—
159C2×C4⋊C4—94no—
160C2×C4⋊C4—92no—
161C2×C4⋊C4—98no—
162C2×C4⋊C4—92no—
163C2×C4⋊C4—94no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4—98no—
166C2×C4⋊C4—94no—
167C23×C3—32no—
168C23×C3—31no—
169C23×C3—32no—
170C23×C3—31no—
171C23×C3—34no—
172C23×C3—34no—
173C23×C3—32no—
174C23×C3—34no—
175C23×C3—31no—
176C23×C3—32no—
177C23×C3—32no—
178C23×C3—32no—
179C23×C3—38no—
180C23×C3—32no—
181C23×C3—32no—
182C23×C3—32no—
183C23×C3—32no—
184C23×C3—32no—
185C23×C3—32no—
186C23×C3—31no—
187C23×C3—31no—
188C23×C3—41no—
189C23×C3—81no—
190C23×C3C3×C4⋊C414yescomplemented
191C23×C3C22×C3×C411yescharacteristic
192C23×C3C2×C3×D411yescharacteristic
193C23×C3C2×C3×Q811yescharacteristic
194C23×C3C22×A411yescharacteristic
195C2×A4—24no—
196C2×A4—21no—
197C2×A4—21no—
198C2×A4—21no—
199C2×A4C4⋊Dic314yesdirect product factor
200C2×A4C2×Dic611yescharacteristic
201C2×A4C2×D1211yescharacteristic
202C2×A4C22×Dic311yescharacteristic
203C2×C3×C4—38no—
204C2×C3×C4—34no—
205C2×C3×C4—34no—
206C2×C3×C4—32no—
207C2×C3×C4—34no—
208C2×C3×C4—38no—
209C2×C3×C4—34no—
210C2×C3×C4—34no—
211C2×C3×C4—42no—
212C2×C3×C4—44no—
213C2×C3×C4—82no—
214C2×C3×C4—84no—
215C2×C3×C4—124no—
216C2×C3×C4—244no—
217C2×C3×C4C4×A414yescomplemented
218C2×C3×C4C22×A412yes—
219C2×Dic3—24no—
220C2×Dic3—34no—
221C2×Dic3—64no—
222C2×Dic3—68no—
223C2×Dic3—64no—
224C2×Dic3—68no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3C22×A414yes—
229C2×C32—41no—
230C2×C32—41no—
231C2×C32—41no—
232C2×C32—44no—
233C24—31no—
234C24—32no—
235C24—32no—
236C24—32no—
237C24—31no—
238C24C3×Dic612yes—
239C24C3×D1212yes—
240C24C2×C3×Dic312yes—
241C24C22×C3×D311yescharacteristic
242C22×C4—32no—
243C22×C4—34no—
244C22×C4—38no—
245C22×C4—31no—
246C22×C4—32no—
247C22×C4—32no—
248C22×C4—34no—
249C22×C4—34no—
250C22×C4—32no—
251C22×C4—34no—
252C22×C4—38no—
253C22×C4—34no—
254C22×C4—32no—
255C22×C4—64no—
256C22×C4—94no—
257C22×C4—94no—
258C22×C4—94no—
259C22×C4—92no—
260C22×C4—94no—
261C22×C4—184no—
262C22×C4—184no—
263C22×C4—188no—
264C22×C4—188no—
265C22×C4—184no—
266C22×C4—184no—
267C22×C4—184no—
268C22×C4C2×C3×Dic314yescomplemented
269C22×C4D3×A411yescharacteristic
270C4⋊C4—34no—
271C4⋊C4—98no—
272C4⋊C4—98no—
273C4⋊C4—94no—
274C22×C3—34no—
275C22×C3—31no—
276C22×C3—31no—
277C22×C3—31no—
278C22×C3—34no—
279C22×C3—32no—
280C22×C3—34no—
281C22×C3—34no—
282C22×C3—32no—
283C22×C3—31no—
284C22×C3—31no—
285C22×C3—32no—
286C22×C3—31no—
287C22×C3—31no—
288C22×C3—32no—
289C22×C3—31no—
290C22×C3—31no—
291C22×C3—34no—
292C22×C3—34no—
293C22×C3—34no—
294C22×C3—34no—
295C22×C3—42no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—41no—
299C22×C3—82no—
300C22×C3—82no—
301C22×C3—82no—
302C22×C3—81no—
303C22×C3C2×C3×C4⋊C411yescharacteristic, complemented
304C22×C3C2×C4×A412yes—
305C22×C3D4×A412yes—
306C22×C3Q8×A412yes—
307C22×C3C23×A411yescharacteristic
308A4—21no—
309A4C2×C4⋊Dic311yescharacteristic, direct product factor
310C3×C4—34no—
311C3×C4—44no—
312C3×C4—84no—
313C3×C4—244no—
314C3×C4C2×C4×A414yescomplemented
315Dic3—24no—
316Dic3—64no—
317C32—41noSylow
318C23—32no—
319C23—31no—
320C23—32no—
321C23—31no—
322C23—32no—
323C23—34no—
324C23—34no—
325C23—34no—
326C23—31no—
327C23—32no—
328C23—32no—
329C23—38no—
330C23—32no—
331C23—32no—
332C23—32no—
333C23—32no—
334C23—32no—
335C23—32no—
336C23—32no—
337C23—31no—
338C23—31no—
339C23C3×C4⋊Dic314yescomplemented
340C23C2×C3×Dic611yescharacteristic
341C23C2×C3×D1211yescharacteristic
342C23C22×C3×Dic311yescharacteristic
343C23C2×D3×A411yescharacteristic
344C2×C4—38no—
345C2×C4—34no—
346C2×C4—34no—
347C2×C4—32no—
348C2×C4—34no—
349C2×C4—34no—
350C2×C4—38no—
351C2×C4—34no—
352C2×C4—34no—
353C2×C4—64no—
354C2×C4—94no—
355C2×C4—184no—
356C2×C4—184no—
357C2×C4—188no—
358C2×C4—188no—
359C2×C4—184no—
360C2×C4—184no—
361C2×C4—184no—
362C2×C4Dic3×A414yescomplemented
363C2×C4C2×D3×A412yes—
364C2×C3—34no—
365C2×C3—31no—
366C2×C3—31no—
367C2×C3—31no—
368C2×C3—31no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—44no—
372C2×C3—41no—
373C2×C3—81no—
374C2×C3—81no—
375C2×C3—84no—
376C2×C3—81no—
377C2×C3A4×C4⋊C414yescomplemented
378C2×C3C22×C4×A411yescharacteristic
379C2×C3C2×D4×A411yescharacteristic
380C2×C3C2×Q8×A411yescharacteristic
381C22—34no—
382C22—31no—
383C22—31no—
384C22—31no—
385C22—34no—
386C22—32no—
387C22—34no—
388C22—34no—
389C22—31no—
390C22—32no—
391C22—31no—
392C22—31no—
393C22—32no—
394C22—31no—
395C22—34no—
396C22—34no—
397C22—34no—
398C22—34no—
399C22—31no—
400C22—32no—
401C22—31no—
402C22C2×C3×C4⋊Dic311yescharacteristic, complemented
403C22A4×Dic612yes—
404C22A4×D1212yes—
405C22C2×Dic3×A412yes—
406C22C22×D3×A411yescharacteristic
407C4—34no—
408C4—64no—
409C4—184no—
410C4C2×Dic3×A414yescomplemented
411C3—41no—
412C3—81no—
413C3C2×A4×C4⋊C411yescharacteristic, complemented
414C2—31no—
415C2—34no—
416C2—31no—
417C2—31no—
418C2—31no—
419C2A4×C4⋊Dic314yesdirect product factor
420C2C2×A4×Dic611yescharacteristic
421C2C2×A4×D1211yescharacteristic
422C2C22×Dic3×A411yescharacteristic
subgroupG/H
centerC23C2×D3×A4
commutatorC23×C3C22×C3×C4
FrattiniC22C22×D3×A4
FittingC24×C3×C4C2×C3
socleC25×C3C22×C3
prime radicalC23×C3×A4C22
cosocleC24×C3C23×C3
hypercenterC22×C4D3×A4
hypocenterC22×C3C2×C3×C4⋊C4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. A4×C4⋊Dic3C2direct (N × H)
4. C23×C4⋊Dic3C3semidirect
7. C2×C3×C4×A4C4semidirect
21. C22×C4⋊Dic3C2×C3semidirect
29. C3×C4×A4C2×C4semidirect
40. C23×C3×C4C3×C4semidirect
52. C2×C4×A4Dic3semidirect
64. C2×C4⋊Dic3A4direct (N × H)
66. C2×C3×A4C4⋊C4semidirect
113. C22×C3×C4C2×C3×C4semidirect
131. C4×A4C2×Dic3semidirect
136. C4⋊Dic3C2×A4direct (N × H)
141. C3×A4C2×C4⋊C4semidirect
155. C23×C4C3×Dic3semidirect
190. C23×C3C3×C4⋊C4semidirect
199. C2×A4C4⋊Dic3direct (N × H)
217. C2×C3×C4C4×A4semidirect
268. C22×C4C2×C3×Dic3semidirect
303. C22×C3C2×C3×C4⋊C4semidirect
309. A4C2×C4⋊Dic3direct (N × H)
314. C3×C4C2×C4×A4semidirect
339. C23C3×C4⋊Dic3semidirect
362. C2×C4Dic3×A4semidirect
377. C2×C3A4×C4⋊C4semidirect
402. C22C2×C3×C4⋊Dic3semidirect
410. C4C2×Dic3×A4semidirect
413. C3C2×A4×C4⋊C4semidirect
419. C2A4×C4⋊Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C22×Dic3×A42
A4×C4⋊Dic32
C23×C4⋊Dic33
C2×A4×C4⋊C43
C2×C3×C4⋊Dic34