Finite Group Databasebeta

← C2×A4×#208 #11923341

Subgroups — C2×A4×#208 #11923341

Order 1152.

854 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 147 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
2A4×#208C214yesmaximal, direct product factor
3C2×A4×C3⋊C8C212yesmaximal, complemented
4C23×#208C311yesmaximal, characteristic, complemented
5C2×A4×M16—31nomaximal
6C23×C3×A4C411yescharacteristic
7C2×C3×C4×A4C412yes—
8C2×C3×C4×A4C411yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3×C4×A4C2212yes—
11C2×C3×#208—41nomaximal
12A4×C3⋊C8C2214yescomplemented
13C24×C3×C4C2×C311yescharacteristic
14C22×C4×A4—21no—
15C22×C4×A4D311yescharacteristic
16C22×#208—31no—
17C22×#208—32no—
18C22×#208—31no—
19C22×#208—34no—
20C22×#208C2×C314yescomplemented
21C23×C3⋊C8C2×C312yescomplemented
22A4×M16—34no—
23C2×C8×A4—32no—
24C22×C3×A4—22no—
25C22×C3×A4C2×C412yes—
26C22×C3×A4C2×C411yescharacteristic
27C22×C32×C4—41no—
28C3×C4×A4C2×C411yescharacteristic
29C3×C4×A4C2×C412yes—
30C3×C4×A4C2311yescharacteristic
31C3×#208—44no—
32C2×C3×C3⋊C8—42no—
33C23×M16—31noSylow
34C25×C3C3×C411yescharacteristic
35C23×A4—21no—
36C23×A4Dic311yescharacteristic
37C23×C3×C4—31no—
38C23×C3×C4—31no—
39C23×C3×C4—31no—
40C23×C3×C4—32no—
41C23×C3×C4—31no—
42C23×C3×C4—32no—
43C23×C3×C4C3×C412yes—
44C23×C3×C4C3×C411yescharacteristic
45C23×C3×C4C22×C311yescharacteristic
46C23×C3×C4C22×C312yes—
47C2×C4×A4—22no—
48C2×C4×A4—21no—
49C2×C4×A4—22no—
50C2×C4×A4—21no—
51C2×C4×A4Dic312yes—
52C2×C4×A4Dic311yescharacteristic
53C2×C4×A4C2×D311yescharacteristic
54C2×C4×A4C2×D312yes—
55C2×C3×M16—121no—
56C2×#208—34no—
57C2×#208—38no—
58C2×#208—32no—
59C2×#208—31no—
60C2×#208—34no—
61C2×#208—34no—
62C2×#208—38no—
63C2×#208—34no—
64C2×#208—32no—
65C2×#208A411yescharacteristic, direct product factor
66C22×C3⋊C8—32no—
67C22×C3⋊C8—32no—
68C22×C3⋊C8—34no—
69C22×C3⋊C8C22×C314yescomplemented
70C8×A4—34no—
71C23×C32—41no—
72C2×C3×A4—22no—
73C2×C3×A4M1612yescomplemented
74C2×C3×A4C22×C411yescharacteristic
75C2×C32×C4—41no—
76C2×C32×C4—42no—
77C2×C32×C4—41no—
78C2×C32×C4—42no—
79C3×C3⋊C8—44no—
80C24×C4C3×D311yescharacteristic
81C22×M16—34no—
82C22×M16—91no—
83C22×M16—92no—
84C22×M16—94no—
85C22×M16—91no—
86C23×C8—32no—
87C24×C3—22no—
88C24×C3—32no—
89C24×C3—31no—
90C24×C3—31no—
91C24×C3—62no—
92C24×C3C2×C3×C412yes—
93C24×C3C2×C3×C411yescharacteristic
94C22×A4—24no—
95C22×A4—22no—
96C22×A4—22no—
97C22×A4—21no—
98C22×A4C2×Dic312yes—
99C22×A4C2×Dic311yescharacteristic
100C22×C3×C4—32no—
101C22×C3×C4—34no—
102C22×C3×C4—32no—
103C22×C3×C4—32no—
104C22×C3×C4—34no—
105C22×C3×C4—31no—
106C22×C3×C4—32no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—32no—
110C22×C3×C4—31no—
111C22×C3×C4—32no—
112C22×C3×C4—31no—
113C22×C3×C4—32no—
114C22×C3×C4—31no—
115C22×C3×C4—32no—
116C22×C3×C4—31no—
117C22×C3×C4—32no—
118C22×C3×C4—32no—
119C22×C3×C4—32no—
120C22×C3×C4—32no—
121C22×C3×C4—31no—
122C22×C3×C4—32no—
123C22×C3×C4—31no—
124C22×C3×C4—32no—
125C22×C3×C4—41no—
126C22×C3×C4—81no—
127C22×C3×C4C2×C3×C411yescharacteristic
128C22×C3×C4C2×C3×C412yes—
129C22×C3×C4C2×A411yescharacteristic
130C22×C3×C4C23×C311yescharacteristic
131C4×A4—22no—
132C4×A4—21no—
133C4×A4—21no—
134C4×A4C2×Dic311yescharacteristic
135C4×A4C2×Dic312yes—
136C4×A4C22×D311yescharacteristic
137C3×M16—124no—
138C2×C3×C8—122no—
139#208—38no—
140#208—34no—
141#208—38no—
142#208C2×A414yesdirect product factor
143C2×C3⋊C8—34no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—34no—
146C2×C3⋊C8—34no—
147C2×C3⋊C8—34no—
148C2×C3⋊C8C2×A412yescomplemented
149C22×C32—41no—
150C22×C32—42no—
151C22×C32—82no—
152C3×A4C2×M1611yescharacteristic, complemented
153C32×C4—41no—
154C32×C4—42no—
155C32×C4—41no—
156C25C3×Dic311yescharacteristic
157C23×C4—31no—
158C23×C4—32no—
159C23×C4—31no—
160C23×C4—31no—
161C23×C4—31no—
162C23×C4—32no—
163C23×C4C3×Dic312yes—
164C23×C4C3×Dic311yescharacteristic
165C23×C4C2×C3×D311yescharacteristic
166C23×C4C2×C3×D312yes—
167C2×M16—31no—
168C2×M16—92no—
169C2×M16—94no—
170C2×M16—94no—
171C2×M16—98no—
172C2×M16—94no—
173C2×M16—92no—
174C2×M16—91no—
175C2×M16—98no—
176C2×M16—94no—
177C22×C8—34no—
178C22×C8—92no—
179C22×C8—94no—
180C22×C8—92no—
181C23×C3—22no—
182C23×C3—31no—
183C23×C3—32no—
184C23×C3—31no—
185C23×C3—32no—
186C23×C3—32no—
187C23×C3—32no—
188C23×C3—31no—
189C23×C3—32no—
190C23×C3—41no—
191C23×C3—62no—
192C23×C3—62no—
193C23×C3—62no—
194C23×C3—64no—
195C23×C3—62no—
196C23×C3—62no—
197C23×C3—64no—
198C23×C3—81no—
199C23×C3C3×M1612yescomplemented
200C23×C3C4×A411yescharacteristic
201C23×C3C22×C3×C411yescharacteristic
202C2×A4—24no—
203C2×A4—22no—
204C2×A4—22no—
205C2×A4—21no—
206C2×A4#20812yesdirect product factor
207C2×A4C22×Dic311yescharacteristic
208C2×C3×C4—32no—
209C2×C3×C4—32no—
210C2×C3×C4—34no—
211C2×C3×C4—34no—
212C2×C3×C4—32no—
213C2×C3×C4—32no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—32no—
218C2×C3×C4—32no—
219C2×C3×C4—32no—
220C2×C3×C4—32no—
221C2×C3×C4—31no—
222C2×C3×C4—32no—
223C2×C3×C4—31no—
224C2×C3×C4—31no—
225C2×C3×C4—32no—
226C2×C3×C4—31no—
227C2×C3×C4—32no—
228C2×C3×C4—31no—
229C2×C3×C4—42no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—42no—
233C2×C3×C4—82no—
234C2×C3×C4—81no—
235C2×C3×C4—81no—
236C2×C3×C4—82no—
237C2×C3×C4C4×A412yes—
238C2×C3×C4C4×A411yescharacteristic
239C2×C3×C4C22×A412yes—
240C2×C3×C4C22×A411yescharacteristic
241C3×C8—124no—
242C3⋊C8—34no—
243C3⋊C8C22×A414yescomplemented
244C2×C32—41no—
245C2×C32—42no—
246C2×C32—82no—
247C24—22no—
248C24—32no—
249C24—31no—
250C24—31no—
251C24—62no—
252C24C2×C3×Dic312yes—
253C24C2×C3×Dic311yescharacteristic
254C22×C4—32no—
255C22×C4—34no—
256C22×C4—32no—
257C22×C4—32no—
258C22×C4—34no—
259C22×C4—31no—
260C22×C4—32no—
261C22×C4—32no—
262C22×C4—31no—
263C22×C4—31no—
264C22×C4—31no—
265C22×C4—32no—
266C22×C4—32no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—32no—
270C22×C4—31no—
271C22×C4—32no—
272C22×C4—32no—
273C22×C4—32no—
274C22×C4—32no—
275C22×C4—31no—
276C22×C4—32no—
277C22×C4—31no—
278C22×C4—32no—
279C22×C4C2×C3×Dic311yescharacteristic
280C22×C4C2×C3×Dic312yes—
281C22×C4D3×A411yescharacteristic
282C22×C4C22×C3×D311yescharacteristic
283M16—34no—
284M16—98no—
285M16—98no—
286M16—94no—
287C2×C8—32no—
288C2×C8—94no—
289C2×C8—94no—
290C2×C8—94no—
291C2×C8—92no—
292C2×C8—94no—
293C22×C3—22no—
294C22×C3—32no—
295C22×C3—31no—
296C22×C3—32no—
297C22×C3—31no—
298C22×C3—31no—
299C22×C3—32no—
300C22×C3—32no—
301C22×C3—32no—
302C22×C3—41no—
303C22×C3—42no—
304C22×C3—62no—
305C22×C3—64no—
306C22×C3—62no—
307C22×C3—62no—
308C22×C3—62no—
309C22×C3—64no—
310C22×C3—62no—
311C22×C3—82no—
312C22×C3—84no—
313C22×C3—82no—
314C22×C3—81no—
315C22×C3C2×C3×M1611yescharacteristic, complemented
316C22×C3C2×C4×A412yes—
317C22×C3C2×C4×A411yescharacteristic
318A4—21no—
319A4C2×#20811yescharacteristic, direct product factor
320C3×C4—31no—
321C3×C4—31no—
322C3×C4—32no—
323C3×C4—42no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—82no—
327C3×C4—81no—
328C3×C4—81no—
329C3×C4C2×C4×A412yes—
330C3×C4C2×C4×A411yescharacteristic
331C3×C4C23×A411yescharacteristic
332C32—41noSylow
333C23—22no—
334C23—31no—
335C23—32no—
336C23—31no—
337C23—32no—
338C23—32no—
339C23—32no—
340C23—32no—
341C23—31no—
342C23—62no—
343C23—62no—
344C23—62no—
345C23—64no—
346C23—62no—
347C23—62no—
348C23—64no—
349C23C3×#20812yescomplemented
350C23Dic3×A411yescharacteristic
351C23C22×C3×Dic311yescharacteristic
352C2×C4—32no—
353C2×C4—32no—
354C2×C4—34no—
355C2×C4—34no—
356C2×C4—32no—
357C2×C4—32no—
358C2×C4—31no—
359C2×C4—31no—
360C2×C4—32no—
361C2×C4—31no—
362C2×C4—32no—
363C2×C4—32no—
364C2×C4—32no—
365C2×C4—31no—
366C2×C4—32no—
367C2×C4—31no—
368C2×C4—31no—
369C2×C4—32no—
370C2×C4—31no—
371C2×C4—32no—
372C2×C4—31no—
373C2×C4Dic3×A411yescharacteristic
374C2×C4Dic3×A412yes—
375C2×C4C2×D3×A412yes—
376C2×C4C2×D3×A411yescharacteristic
377C8—34no—
378C8—94no—
379C2×C3—22no—
380C2×C3—32no—
381C2×C3—31no—
382C2×C3—31no—
383C2×C3—41no—
384C2×C3—42no—
385C2×C3—62no—
386C2×C3—82no—
387C2×C3—84no—
388C2×C3—81no—
389C2×C3—82no—
390C2×C3A4×M1612yescomplemented
391C2×C3C22×C4×A411yescharacteristic
392C22—22no—
393C22—32no—
394C22—31no—
395C22—32no—
396C22—31no—
397C22—31no—
398C22—32no—
399C22—32no—
400C22—32no—
401C22—62no—
402C22—62no—
403C22—64no—
404C22—62no—
405C22—62no—
406C22—64no—
407C22—62no—
408C22C2×C3×#20811yescharacteristic, complemented
409C22C2×Dic3×A412yes—
410C22C2×Dic3×A411yescharacteristic
411C4—31no—
412C4—32no—
413C4—31no—
414C4C2×Dic3×A412yes—
415C4C2×Dic3×A411yescharacteristic
416C4C22×D3×A411yescharacteristic
417C3—41no—
418C3—81no—
419C3C2×A4×M1611yescharacteristic, complemented
420C2—22no—
421C2—31no—
422C2—32no—
423C2—31no—
424C2—62no—
425C2A4×#20812yesdirect product factor
426C2C22×Dic3×A411yescharacteristic
subgroupG/H
centerC2×C4C2×D3×A4
commutatorC23×C3C22×C3×C4
FrattiniC4C22×D3×A4
FittingC24×C3×C4C2×C3
socleC24×C3C2×C3×C4
prime radicalC23×C3×A4C4
cosocleC22×C3×C4C23×C3
hypercenterC22×C4D3×A4
hypocenterC22×C3C2×C3×M16
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. A4×#208C2direct (N × H)
3. C2×A4×C3⋊C8C2semidirect
4. C23×#208C3semidirect
12. A4×C3⋊C8C22semidirect
20. C22×#208C2×C3semidirect
21. C23×C3⋊C8C2×C3semidirect
65. C2×#208A4direct (N × H)
69. C22×C3⋊C8C22×C3semidirect
73. C2×C3×A4M16semidirect
142. #208C2×A4direct (N × H)
148. C2×C3⋊C8C2×A4semidirect
152. C3×A4C2×M16semidirect
199. C23×C3C3×M16semidirect
206. C2×A4#208direct (N × H)
243. C3⋊C8C22×A4semidirect
315. C22×C3C2×C3×M16semidirect
319. A4C2×#208direct (N × H)
349. C23C3×#208semidirect
390. C2×C3A4×M16semidirect
408. C22C2×C3×#208semidirect
419. C3C2×A4×M16semidirect
425. C2A4×#208direct (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
A4×#2082
C2×A4×C3⋊C82
C23×#2083
C2×A4×M163
C2×C3×#2084