Finite Group Databasebeta

← C2×C4⋊(C3⋊SL(2,ℤ/4)) #11923030

Subgroups — C2×C4⋊(C3⋊SL(2,ℤ/4)) #11923030

Order 1152.

1182 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 227 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×C3⋊SL(2,ℤ/4)C212yesmaximal
3C4⋊(C3⋊SL(2,ℤ/4))C214yesmaximal, direct product factor
4C2×C4⋊SL(2,ℤ/4)—33nomaximal
5C2×#5212—31nomaximal
6C23×C3×A4C2211yescharacteristic
7C2×C3×C4×A4C414yescomplemented
8C2×C3×C4×A4C2212yes—
9C2×C3⋊SL(2,ℤ/4)—24no—
10C2×C3⋊SL(2,ℤ/4)C2214yes—
11C2×C4⋊(C3⋊Dic3)—41nomaximal
12C24×C3×C4D311yescharacteristic
13C22×C4×A4D313yes—
14C22×SL(2,ℤ/4)—36no—
15C22×#217—32no—
16C22×C4⋊Dic3—31no—
17C22×C4⋊Dic3—31no—
18C4⋊SL(2,ℤ/4)—312no—
19#5212—34no—
20#5212—34no—
21C2×C3⋊#95—32no—
22C22×C3×A4C2×C412yes—
23C22×C3×A4D412yes—
24C22×C3×A4Q812yes—
25C22×C3×A4C2311yescharacteristic
26C22×C32×C4—41no—
27C22×C3⋊Dic3—42no—
28C3×C4×A4C2×C414yescomplemented
29C3⋊SL(2,ℤ/4)—24no—
30C4⋊(C3⋊Dic3)—44no—
31C2×#380—91noSylow
32C25×C3C2×D311yescharacteristic
33C23×A4C2×D313yes—
34C23×C3×C4—31no—
35C23×C3×C4—34no—
36C23×C3×C4—31no—
37C23×C3×C4—32no—
38C23×C3×C4Dic314yescomplemented
39C23×C3×C4C2×D312yes—
40C23×Dic3—32no—
41C23×Dic3—32no—
42C2×C4×A4Dic3112yescomplemented
43C2×C4×A4C2×D316yes—
44C2×SL(2,ℤ/4)—312no—
45C2×SL(2,ℤ/4)—612no—
46C2×#217—34no—
47C2×#217—34no—
48C2×#217—64no—
49C2×#217—64no—
50C2×C4⋊Dic3—34no—
51C2×C4⋊Dic3—34no—
52C2×C4⋊Dic3—64no—
53C2×C4⋊Dic3—61no—
54C2×C4⋊Dic3—62no—
55C2×C4⋊Dic3—61no—
56C2×C4⋊Dic3—123no—
57C3⋊#95—38no—
58C23×C32—41no—
59C2×C3×A4C4⋊C414yescomplemented
60C2×C3×A4C22×C411yescharacteristic
61C2×C3×A4C2×D411yescharacteristic
62C2×C3×A4C2×Q811yescharacteristic
63C2×C32×C4—44no—
64C2×C32×C4—42no—
65C2×C3⋊Dic3—44no—
66C2×C3⋊Dic3—84no—
67C24×C4C3⋊D311yescharacteristic
68C22×C4⋊C4—91no—
69C22×C4⋊C4—91no—
70C22×C22⋊C4—92no—
71#380—94no—
72#380—94no—
73C2×#95—92no—
74C24×C3—31no—
75C24×C3—32no—
76C24×C3—31no—
77C24×C3—32no—
78C24×C3—32no—
79C24×C3Dic612yes—
80C24×C3D1212yes—
81C24×C3C2×Dic312yes—
82C24×C3C22×D311yescharacteristic
83C22×A4Dic616yes—
84C22×A4D1216yes—
85C22×A4C2×Dic316yes—
86C22×A4C22×D313yes—
87C22×C3×C4—31no—
88C22×C3×C4—34no—
89C22×C3×C4—34no—
90C22×C3×C4—32no—
91C22×C3×C4—32no—
92C22×C3×C4—32no—
93C22×C3×C4—34no—
94C22×C3×C4—38no—
95C22×C3×C4—34no—
96C22×C3×C4—43no—
97C22×C3×C4—64no—
98C22×C3×C4—62no—
99C22×C3×C4—61no—
100C22×C3×C4C2×Dic314yescomplemented
101C22×C3×C4S411yescharacteristic
102C22×Dic3—34no—
103C22×Dic3—34no—
104C22×Dic3—64no—
105C22×Dic3—62no—
106C22×Dic3—64no—
107C22×Dic3—64no—
108C22×Dic3—64no—
109C22×Dic3—64no—
110C22×Dic3—62no—
111C22×Dic3—126no—
112C4×A4C2×Dic3112yescomplemented
113SL(2,ℤ/4)—612no—
114#217—68no—
115#217—64no—
116#217—64no—
117C4⋊Dic3—68no—
118C4⋊Dic3—64no—
119C4⋊Dic3—64no—
120C4⋊Dic3—1212no—
121C22×C32—42no—
122C22×C32—42no—
123C22×C32—42no—
124C22×C32—41no—
125C3×A4C2×C4⋊C411yescharacteristic, complemented
126C32×C4—44no—
127C3⋊Dic3—84no—
128C25C2×C3⋊D311yescharacteristic
129C23×C4—31no—
130C23×C4—31no—
131C23×C4—32no—
132C23×C4—34no—
133C23×C4—92no—
134C23×C4—92no—
135C23×C4C3⋊Dic314yescomplemented
136C23×C4C2×C3⋊D312yes—
137C2×C4⋊C4—94no—
138C2×C4⋊C4—94no—
139C2×C4⋊C4—181no—
140C2×C4⋊C4—184no—
141C2×C4⋊C4—182no—
142C2×C4⋊C4—181no—
143C2×C22⋊C4—94no—
144C2×C22⋊C4—94no—
145C2×C22⋊C4—184no—
146C2×C22⋊C4—184no—
147#95—98no—
148C23×C3—32no—
149C23×C3—32no—
150C23×C3—32no—
151C23×C3—32no—
152C23×C3—32no—
153C23×C3—32no—
154C23×C3—31no—
155C23×C3—31no—
156C23×C3—32no—
157C23×C3—31no—
158C23×C3—32no—
159C23×C3—31no—
160C23×C3—32no—
161C23×C3—34no—
162C23×C3—34no—
163C23×C3—34no—
164C23×C3—31no—
165C23×C3—43no—
166C23×C3—61no—
167C23×C3—61no—
168C23×C3—61no—
169C23×C3—64no—
170C23×C3C4⋊Dic314yescomplemented
171C23×C3C2×Dic611yescharacteristic
172C23×C3C2×D1211yescharacteristic
173C23×C3C22×Dic311yescharacteristic
174C23×C3C2×S411yescharacteristic
175C2×A4C4⋊Dic3112yescomplemented
176C2×A4C2×Dic613yes—
177C2×A4C2×D1213yes—
178C2×A4C22×Dic313yes—
179C2×C3×C4—34no—
180C2×C3×C4—32no—
181C2×C3×C4—34no—
182C2×C3×C4—34no—
183C2×C3×C4—38no—
184C2×C3×C4—34no—
185C2×C3×C4—46no—
186C2×C3×C4—412no—
187C2×C3×C4—62no—
188C2×C3×C4—64no—
189C2×C3×C4SL(2,ℤ/4)14yescomplemented
190C2×C3×C4C2×S412yes—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—1212no—
198C2×Dic3—128no—
199C2×Dic3—124no—
200C2×Dic3—124no—
201C2×Dic3—2412no—
202C2×C32—41no—
203C2×C32—41no—
204C2×C32—44no—
205C2×C32—41no—
206C24—31no—
207C24—31no—
208C24—32no—
209C24—32no—
210C24—32no—
211C24#63412yes—
212C24C4⋊(C3⋊D3)12yes—
213C24C2×C3⋊Dic312yes—
214C24C22×C3⋊D311yescharacteristic
215C22×C4—31no—
216C22×C4—32no—
217C22×C4—32no—
218C22×C4—34no—
219C22×C4—34no—
220C22×C4—32no—
221C22×C4—34no—
222C22×C4—38no—
223C22×C4—34no—
224C22×C4—64no—
225C22×C4—62no—
226C22×C4—61no—
227C22×C4—94no—
228C22×C4—94no—
229C22×C4—184no—
230C22×C4—184no—
231C22×C4—184no—
232C22×C4—182no—
233C22×C4—184no—
234C22×C4—184no—
235C22×C4—182no—
236C22×C4C2×C3⋊Dic314yescomplemented
237C22×C4C3⋊S411yescharacteristic
238C4⋊C4—184no—
239C4⋊C4—188no—
240C4⋊C4—184no—
241C22⋊C4—188no—
242C22⋊C4—184no—
243C22⋊C4—184no—
244C22×C3—34no—
245C22×C3—31no—
246C22×C3—31no—
247C22×C3—31no—
248C22×C3—31no—
249C22×C3—31no—
250C22×C3—32no—
251C22×C3—31no—
252C22×C3—31no—
253C22×C3—32no—
254C22×C3—34no—
255C22×C3—34no—
256C22×C3—34no—
257C22×C3—34no—
258C22×C3—31no—
259C22×C3—31no—
260C22×C3—32no—
261C22×C3—46no—
262C22×C3—46no—
263C22×C3—46no—
264C22×C3—43no—
265C22×C3—62no—
266C22×C3—61no—
267C22×C3—62no—
268C22×C3—62no—
269C22×C3C2×C4⋊Dic311yescharacteristic, complemented
270C22×C3A4⋊Q812yes—
271C22×C3C4⋊S412yes—
272C22×C3C2×SL(2,ℤ/4)12yes—
273C22×C3C22×S411yescharacteristic
274A4C2×C4⋊Dic313yescomplemented
275C3×C4—34no—
276C3×C4—412no—
277C3×C4C2×SL(2,ℤ/4)14yescomplemented
278Dic3—124no—
279Dic3—124no—
280Dic3—2412no—
281C32—41noSylow
282C23—32no—
283C23—32no—
284C23—32no—
285C23—32no—
286C23—32no—
287C23—32no—
288C23—31no—
289C23—31no—
290C23—32no—
291C23—31no—
292C23—32no—
293C23—31no—
294C23—32no—
295C23—34no—
296C23—34no—
297C23—34no—
298C23—31no—
299C23—61no—
300C23—64no—
301C23—61no—
302C23—61no—
303C23C4⋊(C3⋊Dic3)14yescomplemented
304C23C2×#63411yescharacteristic
305C23C2×C4⋊(C3⋊D3)11yescharacteristic
306C23C22×C3⋊Dic311yescharacteristic
307C23C2×C3⋊S411yescharacteristic
308C2×C4—34no—
309C2×C4—32no—
310C2×C4—34no—
311C2×C4—34no—
312C2×C4—38no—
313C2×C4—34no—
314C2×C4—62no—
315C2×C4—64no—
316C2×C4—184no—
317C2×C4—184no—
318C2×C4—184no—
319C2×C4—184no—
320C2×C4—184no—
321C2×C4—184no—
322C2×C4—368no—
323C2×C4—364no—
324C2×C4—364no—
325C2×C4C3⋊SL(2,ℤ/4)14yescomplemented
326C2×C4C2×C3⋊S412yes—
327C2×C3—31no—
328C2×C3—31no—
329C2×C3—34no—
330C2×C3—31no—
331C2×C3—31no—
332C2×C3—412no—
333C2×C3—43no—
334C2×C3—43no—
335C2×C3—43no—
336C2×C3C4⋊SL(2,ℤ/4)14yescomplemented
337C2×C3C2×A4⋊Q811yescharacteristic
338C2×C3C2×C4⋊S411yescharacteristic
339C2×C3C22×SL(2,ℤ/4)11yescharacteristic
340C22—34no—
341C22—31no—
342C22—31no—
343C22—31no—
344C22—34no—
345C22—34no—
346C22—34no—
347C22—34no—
348C22—31no—
349C22—31no—
350C22—32no—
351C22—31no—
352C22—31no—
353C22—32no—
354C22—31no—
355C22—31no—
356C22—32no—
357C22—62no—
358C22—61no—
359C22—62no—
360C22—62no—
361C22C2×C4⋊(C3⋊Dic3)11yescharacteristic, complemented
362C22#6425912yes—
363C22C4⋊(C3⋊S4)12yes—
364C22C2×C3⋊SL(2,ℤ/4)12yes—
365C22C22×C3⋊S411yescharacteristic
366C4—34no—
367C4—364no—
368C4—364no—
369C4C2×C3⋊SL(2,ℤ/4)14yescomplemented
370C3—43no—
371C3C2×C4⋊SL(2,ℤ/4)11yescharacteristic, complemented
372C2—31no—
373C2—31no—
374C2—34no—
375C2—31no—
376C2—31no—
377C2C4⋊(C3⋊SL(2,ℤ/4))14yesdirect product factor
378C2C2×#6425911yescharacteristic
379C2C2×C4⋊(C3⋊S4)11yescharacteristic
380C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC22C22×C3⋊S4
FittingC24×C3×C4D3
socleC25×C3C2×D3
prime radicalC23×C3×A4C22
cosocleC22×C3×A4C23
hypercenterC22×C4C3⋊S4
hypocenterC3×A4C2×C4⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C4⋊(C3⋊SL(2,ℤ/4))C2direct (N × H)
7. C2×C3×C4×A4C4semidirect
28. C3×C4×A4C2×C4semidirect
38. C23×C3×C4Dic3semidirect
42. C2×C4×A4Dic3semidirect
59. C2×C3×A4C4⋊C4semidirect
100. C22×C3×C4C2×Dic3semidirect
112. C4×A4C2×Dic3semidirect
125. C3×A4C2×C4⋊C4semidirect
135. C23×C4C3⋊Dic3semidirect
170. C23×C3C4⋊Dic3semidirect
175. C2×A4C4⋊Dic3semidirect
189. C2×C3×C4SL(2,ℤ/4)semidirect
236. C22×C4C2×C3⋊Dic3semidirect
269. C22×C3C2×C4⋊Dic3semidirect
274. A4C2×C4⋊Dic3semidirect
277. C3×C4C2×SL(2,ℤ/4)semidirect
303. C23C4⋊(C3⋊Dic3)semidirect
325. C2×C4C3⋊SL(2,ℤ/4)semidirect
336. C2×C3C4⋊SL(2,ℤ/4)semidirect
361. C22C2×C4⋊(C3⋊Dic3)semidirect
369. C4C2×C3⋊SL(2,ℤ/4)semidirect
371. C3C2×C4⋊SL(2,ℤ/4)semidirect
377. C2C4⋊(C3⋊SL(2,ℤ/4))direct (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×C3⋊SL(2,ℤ/4)2
C4⋊(C3⋊SL(2,ℤ/4))2
C2×C4⋊SL(2,ℤ/4)3
C2×#52123
C2×C4⋊(C3⋊Dic3)4