Finite Group Databasebeta

← C2×(C3⋊S4)⋊C8 #11921861

Subgroups — C2×(C3⋊S4)⋊C8 #11921861

Order 1152.

724 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×C3⋊S4C211yesmaximal, characteristic
2C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×A4⋊C8C211yesmaximal, characteristic, complemented
4(C3⋊S4)⋊C8C214yesmaximal, direct product factor
5C2×C8×S4—31nomaximal
6C2×#67⋊C8—31nomaximal
7C22×C3⋊S4C411yescharacteristic
8C2×C3×C4×A4C2211yescharacteristic
9C2×C3⋊SL(2,ℤ/4)C411yescharacteristic
10C4×C3⋊S4C412yes—
11C4×C3⋊S4C2212yes—
12C2×#3710—41nomaximal
13A4×C3⋊C8C2212yescomplemented
14C3×A4⋊C8C2212yescomplemented
15C2×C4×S4—31no—
16C2×C4×S4—61no—
17C2×C4×#67—31no—
18C23×C3⋊C8D311yescharacteristic, complemented
19C22×D3×C8—31no—
20C2×C8×A4—31no—
21C2×A4⋊C8D311yescharacteristic, complemented
22C8×S4—34no—
23C2×C3×C22⋊C8—31no—
24C2×(C2×D3)⋊C8—31no—
25C2×Dic3⋊C8—31no—
26C2×C8×Dic3—31no—
27#67⋊C8—34no—
28#67⋊C8—34no—
29C22×C3×A4C2×C411yescharacteristic
30C2×C3⋊S4C814yescomplemented
31C2×C3⋊S4C2×C412yes—
32C2×C4×C3⋊D3—41no—
33C3×C4×A4C2×C411yescharacteristic
34C3×C4×A4C2311yescharacteristic
35C3⋊SL(2,ℤ/4)C2×C412yes—
36C2×C3×C3⋊C8—41no—
37C2×C3×C3⋊C8—41no—
38#3710—44no—
39C2×C8×D4—91noSylow
40C22×S4—31no—
41C22×S4—61no—
42C23×C3×C4C2×D311yescharacteristic
43C22×#67—31no—
44C22×C4×D3—31no—
45C2×C4×A4—21no—
46C2×C4×A4C2×D311yescharacteristic
47C2×SL(2,ℤ/4)—31no—
48C2×SL(2,ℤ/4)—61no—
49C4×S4—32no—
50C4×S4—32no—
51C4×S4—62no—
52C4×S4—62no—
53C22×C3×C8—31no—
54C22×C3×C8—31no—
55C2×#217—31no—
56C4×#67—32no—
57C4×#67—32no—
58C4×#67—32no—
59C4×#67—32no—
60C2×(C2×D3)⋊C4—31no—
61C2×Dic3⋊C4—31no—
62C2×C4×Dic3—31no—
63C22×C3⋊C8—31no—
64C22×C3⋊C8—32no—
65C22×C3⋊C8—31no—
66C22×C3⋊C8C2×D312yescomplemented
67C2×D3×C8—34no—
68C2×D3×C8—61no—
69C2×D3×C8—62no—
70C2×D3×C8—61no—
71C2×D3×C8—121no—
72C8×A4—32no—
73A4⋊C8C2×D312yescomplemented
74C3×C22⋊C8—32no—
75C3×C22⋊C8—32no—
76(C2×D3)⋊C8—34no—
77Dic3⋊C8—34no—
78C8×Dic3—34no—
79C22×C3⋊D3—41no—
80C2×C3×A4C2×C812yescomplemented
81C2×C3×A4C22×C411yescharacteristic
82C3⋊S4C2×C814yescomplemented
83C2×C32×C4—41no—
84C2×C3⋊Dic3—41no—
85C4×C3⋊D3—42no—
86C4×C3⋊D3—42no—
87C3×C3⋊C8—42no—
88C3×C3⋊C8—42no—
89C23×C8—31no—
90C23×C8—91no—
91C2×C4×D4—91no—
92C8×D4—94no—
93C8×D4—94no—
94C2×C4⋊C8—91no—
95C2×C22⋊C8—31no—
96C2×C22⋊C8—91no—
97C2×C4×C8—91no—
98C24×C3C4×D311yescharacteristic
99C23×D3—31no—
100C22×A4—21no—
101C22×A4C4×D311yescharacteristic
102C2×S4—34no—
103C2×S4—32no—
104C2×S4—64no—
105C2×S4—62no—
106C22×C3×C4—31no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—31no—
110C22×C3×C4C4×D311yescharacteristic
111C22×C3×C4C22×D311yescharacteristic
112C2×#67—32no—
113C2×#67—34no—
114C2×#67—34no—
115C2×#67—32no—
116C22×Dic3—31no—
117C22×Dic3—31no—
118C22×Dic3—31no—
119C2×C4×D3—32no—
120C2×C4×D3—32no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—121no—
126C2×C4×D3—241no—
127C4×A4—21no—
128C4×A4—21no—
129C4×A4C4×D311yescharacteristic
130C4×A4C22×D311yescharacteristic
131SL(2,ℤ/4)—32no—
132SL(2,ℤ/4)—62no—
133C2×C3×C8—32no—
134C2×C3×C8—32no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C2×C3×C8—121no—
140#217—32no—
141#217—32no—
142(C2×D3)⋊C4—32no—
143(C2×D3)⋊C4—32no—
144Dic3⋊C4—32no—
145Dic3⋊C4—32no—
146C4×Dic3—32no—
147C4×Dic3—32no—
148C2×C3⋊C8—31no—
149C2×C3⋊C8—32no—
150C2×C3⋊C8—32no—
151C2×C3⋊C8—32no—
152C2×C3⋊C8—41no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8S411yescharacteristic, complemented
155D3×C8—64no—
156D3×C8—64no—
157D3×C8—124no—
158C22×C32—41no—
159C2×C3⋊D3—44no—
160C2×C3⋊D3—42no—
161C3×A4C22×C811yescharacteristic, complemented
162C32×C4—41no—
163C32×C4—41no—
164C3⋊Dic3—42no—
165C22×D4—91no—
166C23×C4—91no—
167C23×C4D3211yescharacteristic
168C22×C8—31no—
169C22×C8—31no—
170C22×C8—32no—
171C22×C8—91no—
172C22×C8—94no—
173C22×C8—91no—
174C22×C8—92no—
175C22×C8—181no—
176C22×C8—182no—
177C22×C8—181no—
178C4×D4—92no—
179C4×D4—92no—
180C4×D4—92no—
181C4×D4—92no—
182C2×C4⋊C4—91no—
183C2×C22⋊C4—91no—
184C2×C22⋊C4—91no—
185C2×C42—91no—
186C4⋊C8—94no—
187C22⋊C8—32no—
188C22⋊C8—32no—
189C22⋊C8—94no—
190C4×C8—94no—
191C23×C3—31no—
192C23×C3—31no—
193C23×C3—32no—
194C23×C3D3×C812yescomplemented
195C23×C3C2×C4×D311yescharacteristic
196C22×D3—32no—
197C22×D3—34no—
198C22×D3—61no—
199C22×D3—62no—
200C22×D3—61no—
201C22×D3—121no—
202C22×D3—241no—
203C2×A4—22no—
204C2×A4—21no—
205C2×A4D3×C812yescomplemented
206C2×A4C2×C4×D311yescharacteristic
207S4—34no—
208S4—64no—
209C2×C3×C4—31no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—41no—
217C2×C3×C4—61no—
218C2×C3×C4—81no—
219C2×C3×C4C2×S411yescharacteristic
220#67—38no—
221#67—34no—
222#67—34no—
223C2×Dic3—32no—
224C2×Dic3—34no—
225C2×Dic3—32no—
226C2×Dic3—32no—
227C2×Dic3—61no—
228C2×Dic3—62no—
229C2×Dic3—61no—
230C2×Dic3—121no—
231C2×Dic3—241no—
232C4×D3—62no—
233C4×D3—62no—
234C4×D3—62no—
235C4×D3—62no—
236C4×D3—122no—
237C4×D3—122no—
238C4×D3—242no—
239C4×D3—242no—
240C3×C8—62no—
241C3×C8—62no—
242C3×C8—122no—
243C3⋊C8—32no—
244C3⋊C8—42no—
245C3⋊C8C2×S412yescomplemented
246C2×C32—41no—
247C2×C32—42no—
248C3⋊D3—44no—
249C24—91no—
250C24#62411yescharacteristic
251C2×D4—92no—
252C2×D4—94no—
253C2×D4—94no—
254C2×D4—92no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—92no—
260C22×C4—92no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—181no—
265C22×C4—181no—
266C22×C4—181no—
267C22×C4—181no—
268C22×C4#62411yescharacteristic
269C22×C4C2×D3211yescharacteristic
270C2×C8—31no—
271C2×C8—32no—
272C2×C8—32no—
273C2×C8—61no—
274C2×C8—61no—
275C2×C8—61no—
276C2×C8—61no—
277C2×C8—92no—
278C2×C8—92no—
279C2×C8—91no—
280C2×C8—92no—
281C2×C8—184no—
282C2×C8—184no—
283C2×C8—181no—
284C4⋊C4—92no—
285C4⋊C4—92no—
286C22⋊C4—92no—
287C22⋊C4—92no—
288C22⋊C4—92no—
289C22⋊C4—92no—
290C42—92no—
291C42—92no—
292C22×C3—32no—
293C22×C3—31no—
294C22×C3—31no—
295C22×C3—31no—
296C22×C3—32no—
297C22×C3—32no—
298C22×C3—41no—
299C22×C3—61no—
300C22×C3—81no—
301C22×C3C2×D3×C811yescharacteristic, complemented
302C22×C3C4×S411yescharacteristic
303C2×D3—34no—
304C2×D3—62no—
305C2×D3—64no—
306C2×D3—62no—
307C2×D3—64no—
308C2×D3—122no—
309C2×D3—124no—
310C2×D3—242no—
311C2×D3—244no—
312A4—21no—
313A4C2×D3×C811yescharacteristic, complemented
314C3×C4—31no—
315C3×C4—31no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—81no—
319C3×C4—81no—
320C3×C4C4×S411yescharacteristic
321C3×C4C22×S411yescharacteristic
322Dic3—34no—
323Dic3—62no—
324Dic3—62no—
325Dic3—122no—
326Dic3—242no—
327C32—41noSylow
328C23—31no—
329C23—31no—
330C23—32no—
331C23—92no—
332C23—94no—
333C23—181no—
334C23—182no—
335C23—181no—
336C23#371012yescomplemented
337C23C2×#62411yescharacteristic
338D4—98no—
339D4—94no—
340D4—94no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—61no—
349C2×C4—92no—
350C2×C4—94no—
351C2×C4—92no—
352C2×C4—92no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—181no—
356C2×C4—182no—
357C2×C4—181no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4D3×S411yescharacteristic
361C8—32no—
362C8—62no—
363C8—62no—
364C8—92no—
365C2×C3—31no—
366C2×C3—31no—
367C2×C3—32no—
368C2×C3—41no—
369C2×C3—42no—
370C2×C3—81no—
371C2×C3—82no—
372C2×C3C8×S412yescomplemented
373C2×C3C2×C4×S411yescharacteristic
374D3—64no—
375D3—124no—
376D3—244no—
377C22—32no—
378C22—31no—
379C22—31no—
380C22—31no—
381C22—32no—
382C22—32no—
383C22—61no—
384C22—94no—
385C22—182no—
386C22—184no—
387C22—182no—
388C22—184no—
389C22C2×#371011yescharacteristic, complemented
390C22(C3⋊S4)⋊C411yescharacteristic
391C4—31no—
392C4—31no—
393C4—94no—
394C4—182no—
395C4—182no—
396C4(C3⋊S4)⋊C411yescharacteristic
397C4C2×D3×S411yescharacteristic
398C3—41no—
399C3—81no—
400C3C2×C8×S411yescharacteristic, complemented
401C2—31no—
402C2—31no—
403C2—32no—
404C2—184no—
405C2(C3⋊S4)⋊C812yesdirect product factor
406C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×S4
commutator, hypocenterC3×A4C22×C8
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3C4×D3
prime radicalC22×C3⋊S4C4
cosocleC3×C4×A4C23
LCSG ▷ C3×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4×C3⋊C8C2semidirect
3. C2×C3×A4⋊C8C2semidirect
4. (C3⋊S4)⋊C8C2direct (N × H)
13. A4×C3⋊C8C22semidirect
14. C3×A4⋊C8C22semidirect
18. C23×C3⋊C8D3semidirect
21. C2×A4⋊C8D3semidirect
30. C2×C3⋊S4C8semidirect
66. C22×C3⋊C8C2×D3semidirect
73. A4⋊C8C2×D3semidirect
80. C2×C3×A4C2×C8semidirect
82. C3⋊S4C2×C8semidirect
154. C2×C3⋊C8S4semidirect
161. C3×A4C22×C8semidirect
194. C23×C3D3×C8semidirect
205. C2×A4D3×C8semidirect
245. C3⋊C8C2×S4semidirect
301. C22×C3C2×D3×C8semidirect
313. A4C2×D3×C8semidirect
336. C23#3710semidirect
372. C2×C3C8×S4semidirect
389. C22C2×#3710semidirect
400. C3C2×C8×S4semidirect
405. C2(C3⋊S4)⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊S42
C2×A4×C3⋊C82
C2×C3×A4⋊C82
(C3⋊S4)⋊C82
C2×C8×S43
C2×#67⋊C83
C2×#37104