Finite Group Databasebeta

← C3×SL(2,ℤ/4)⋊C8 #11920885

Subgroups — C3×SL(2,ℤ/4)⋊C8 #11920885

Order 1152.

348 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 68 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×C8×A4C211yesmaximal, characteristic
2C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic
3C2×C3×A4⋊C8C211yesmaximal, characteristic
4SL(2,ℤ/4)⋊C8C311yesmaximal, characteristic, direct product factor
5C3×#1850—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3×SL(2,ℤ/4)C411yescharacteristic
8C2×C3×SL(2,ℤ/4)C411yescharacteristic
9C3×C8×A4—21no—
10C3×A4⋊C8—21no—
11C3×Dic3⋊C8—41nomaximal
12C23×C3×C8D311yescharacteristic
13C2×C8×A4—21no—
14C2×C8×A4C2×C311yescharacteristic
15C4×SL(2,ℤ/4)C2×C311yescharacteristic
16C2×A4⋊C8C2×C311yescharacteristic
17C2×C3×C4⋊C8—31no—
18C2×C3×C4⋊C8—31no—
19C2×C3×C22⋊C8—31no—
20C3×C4×C22⋊C4—31no—
21C3×#336—31no—
22C3×#336—31no—
23C22×C3×A4C2×C411yescharacteristic
24C3×C4×A4D411yescharacteristic
25C3×C4×A4Q811yescharacteristic
26C3×SL(2,ℤ/4)—21no—
27C3×SL(2,ℤ/4)C812yescomplemented
28C2×C32×C8—41no—
29C3×C4×Dic3—41no—
30C2×C3×C3⋊C8—41no—
31#1850—31noSylow
32C23×C3×C4C2×D311yescharacteristic
33C2×C4×A4—21no—
34C2×C4×A4C22×C311yescharacteristic
35C2×SL(2,ℤ/4)C3×C411yescharacteristic
36C2×SL(2,ℤ/4)C3×C411yescharacteristic
37C22×C3×C8—21no—
38C22×C3×C8—31no—
39C22×C3×C8—31no—
40C22×C3×C8—31no—
41C22×C3×C8—31no—
42C22×C3×C8—61no—
43C2×C3×C22⋊C4—31no—
44C2×C3×C22⋊C4—31no—
45C2×C3×C42—31no—
46C2×C3×C42—31no—
47C8×A4—22no—
48C8×A4—21no—
49A4⋊C8—21no—
50C3×C4⋊C8—62no—
51C3×C4⋊C8—61no—
52C3×C4⋊C8—61no—
53C3×C22⋊C8—61no—
54C3×C22⋊C8—61no—
55C3×#95—31no—
56C3×#95—31no—
57Dic3⋊C8—41no—
58C2×C3×A4C4⋊C411yescharacteristic
59C2×C3×A4C2×C811yescharacteristic
60C2×C3×A4M1611yescharacteristic
61C2×C32×C4—41no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—41no—
64C32×C8—81no—
65C3×C3⋊C8—81no—
66C23×C8C3×D311yescharacteristic
67C2×C4⋊C8—31no—
68C2×C4⋊C8—31no—
69C2×C22⋊C8—31no—
70C4×C22⋊C4—31no—
71#336—31no—
72#336—31no—
73C24×C3C4×D311yescharacteristic
74C22×A4—21no—
75C22×A4C2×C3×C411yescharacteristic
76C22×C3×C4—31no—
77C22×C3×C4—31no—
78C22×C3×C4—31no—
79C22×C3×C4—31no—
80C22×C3×C4—31no—
81C22×C3×C4—31no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C22×C3×C4Dic611yescharacteristic
85C22×C3×C4#6711yescharacteristic
86C4×A4—21no—
87C4×A4—21no—
88C4×A4C3×D411yescharacteristic
89C4×A4C3×Q811yescharacteristic
90SL(2,ℤ/4)—21no—
91SL(2,ℤ/4)C3×C812yescomplemented
92C2×C3×C8—32no—
93C2×C3×C8—31no—
94C2×C3×C8—41no—
95C2×C3×C8—61no—
96C2×C3×C8—61no—
97C2×C3×C8—61no—
98C2×C3×C8—61no—
99C2×C3×C8—61no—
100C2×C3×C8—61no—
101C2×C3×C8—61no—
102C2×C3×C8—61no—
103C2×C3×C8—61no—
104C2×C3×C8—81no—
105C2×C3×C8S411yescharacteristic
106C3×C22⋊C4—32no—
107C3×C22⋊C4—32no—
108C3×C22⋊C4—61no—
109C3×C22⋊C4—61no—
110C3×C42—61no—
111C3×C42—61no—
112C3×C42—61no—
113C3×C42—61no—
114C4×Dic3—41no—
115C2×C3⋊C8—41no—
116C22×C32—41no—
117C3×A4C4⋊C811yescharacteristic, complemented
118C32×C4—41no—
119C32×C4—41no—
120C3×Dic3—42no—
121C3×Dic3—81no—
122C23×C4C2×C3×D311yescharacteristic
123C22×C8—21no—
124C22×C8—31no—
125C22×C8—31no—
126C22×C8—31no—
127C22×C8—31no—
128C22×C8—61no—
129C2×C22⋊C4—31no—
130C2×C22⋊C4—31no—
131C2×C42—31no—
132C2×C42—31no—
133C4⋊C8—62no—
134C4⋊C8—61no—
135C4⋊C8—61no—
136C22⋊C8—61no—
137C22⋊C8—61no—
138#95—31no—
139#95—31no—
140C23×C3—31no—
141C23×C3—31no—
142C23×C3—31no—
143C23×C3—31no—
144C23×C3D3×C811yescharacteristic
145C23×C3ΓL(1,𝔽25)11yescharacteristic
146C23×C3Dic3⋊C411yescharacteristic
147C2×A4—21no—
148C2×A4—21no—
149C2×A4—21no—
150C2×A4C3×C4⋊C411yescharacteristic
151C2×A4C2×C3×C811yescharacteristic
152C2×A4C3×M1611yescharacteristic
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—31no—
159C2×C3×C4—31no—
160C2×C3×C4—32no—
161C2×C3×C4—32no—
162C2×C3×C4—41no—
163C2×C3×C4—61no—
164C2×C3×C4—61no—
165C2×C3×C4—61no—
166C2×C3×C4—61no—
167C2×C3×C4—61no—
168C2×C3×C4—61no—
169C2×C3×C4—61no—
170C2×C3×C4—61no—
171C2×C3×C4—61no—
172C2×C3×C4—61no—
173C2×C3×C4—61no—
174C2×C3×C4—81no—
175C2×C3×C4C2×S411yescharacteristic
176C2×Dic3—41no—
177C2×Dic3—41no—
178C3×C8—21no—
179C3×C8—61no—
180C3×C8—81no—
181C3×C8—82no—
182C3×C8—121no—
183C3×C8—121no—
184C3⋊C8—81no—
185C2×C32—41no—
186C2×C32—41no—
187C2×C32—41no—
188C24C3×C4×D311yescharacteristic
189C22×C4—31no—
190C22×C4—31no—
191C22×C4—31no—
192C22×C4—31no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—31no—
196C22×C4—31no—
197C22×C4C3×Dic611yescharacteristic
198C22×C4C3×#6711yescharacteristic
199C2×C8—32no—
200C2×C8—31no—
201C2×C8—61no—
202C2×C8—61no—
203C2×C8—61no—
204C2×C8—61no—
205C2×C8—61no—
206C2×C8—61no—
207C2×C8—61no—
208C2×C8—61no—
209C2×C8—61no—
210C2×C8C3×S411yescharacteristic
211C22⋊C4—32no—
212C22⋊C4—32no—
213C22⋊C4—61no—
214C22⋊C4—61no—
215C42—61no—
216C42—61no—
217C42—61no—
218C42—61no—
219C22×C3—31no—
220C22×C3—31no—
221C22×C3—31no—
222C22×C3—31no—
223C22×C3—31no—
224C22×C3—31no—
225C22×C3—31no—
226C22×C3—31no—
227C22×C3—31no—
228C22×C3—41no—
229C22×C3—61no—
230C22×C3—81no—
231C22×C3Dic3⋊C811yescharacteristic, complemented
232C22×C3C4×S411yescharacteristic
233A4—21no—
234A4C3×C4⋊C811yescharacteristic, complemented
235C3×C4—31no—
236C3×C4—31no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—62no—
240C3×C4—62no—
241C3×C4—81no—
242C3×C4—81no—
243C3×C4—121no—
244C3×C4—121no—
245C3×C4A4⋊Q811yescharacteristic
246C3×C4GL(2,ℤ/4)11yescharacteristic
247Dic3—42no—
248Dic3—81no—
249C32—41noSylow
250C23—31no—
251C23—31no—
252C23—31no—
253C23—31no—
254C23C3×D3×C811yescharacteristic
255C23C3×ΓL(1,𝔽25)11yescharacteristic
256C23C3×Dic3⋊C411yescharacteristic
257C2×C4—31no—
258C2×C4—31no—
259C2×C4—31no—
260C2×C4—31no—
261C2×C4—31no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—32no—
265C2×C4—32no—
266C2×C4—61no—
267C2×C4—61no—
268C2×C4—61no—
269C2×C4—61no—
270C2×C4—61no—
271C2×C4—61no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4C2×C3×S411yescharacteristic
278C8—21no—
279C8—61no—
280C8—121no—
281C8—121no—
282C2×C3—31no—
283C2×C3—31no—
284C2×C3—31no—
285C2×C3—31no—
286C2×C3—41no—
287C2×C3—41no—
288C2×C3—41no—
289C2×C3—81no—
290C2×C3—81no—
291C2×C3—81no—
292C2×C3C8×S411yescharacteristic
293C2×C3#540011yescharacteristic
294C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
295C22—31no—
296C22—31no—
297C22—31no—
298C22—31no—
299C22—31no—
300C22—31no—
301C22—31no—
302C22—31no—
303C22—31no—
304C22—61no—
305C22C3×Dic3⋊C811yescharacteristic, complemented
306C22C3×C4×S411yescharacteristic
307C4—31no—
308C4—31no—
309C4—62no—
310C4—62no—
311C4—121no—
312C4—121no—
313C4C3×A4⋊Q811yescharacteristic
314C4C3×GL(2,ℤ/4)11yescharacteristic
315C3—41no—
316C3—81no—
317C3SL(2,ℤ/4)⋊C811yescharacteristic, direct product factor
318C2—31no—
319C2—31no—
320C2—31no—
321C2—31no—
322C2C3×C8×S411yescharacteristic
323C2C3×#540011yescharacteristic
324C2C3×SL(2,ℤ/4)⋊C411yescharacteristic
subgroupG/H
centerC2×C3×C4C2×S4
commutatorC2×A4C2×C3×C8
FrattiniC2×C4C2×C3×S4
FittingC23×C3×C8D3
socleC24×C3C4×D3
prime radicalC22×C3×A4C2×C4
cosocleC2×C4×A4C22×C3
hypercenterC2×C3×C8S4
hypocenterA4C3×C4⋊C8
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
4. SL(2,ℤ/4)⋊C8C3direct (N × H)
27. C3×SL(2,ℤ/4)C8semidirect
91. SL(2,ℤ/4)C3×C8semidirect
117. C3×A4C4⋊C8semidirect
231. C22×C3Dic3⋊C8semidirect
234. A4C3×C4⋊C8semidirect
305. C22C3×Dic3⋊C8semidirect
317. C3SL(2,ℤ/4)⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C3×C4×SL(2,ℤ/4)2
C2×C3×A4⋊C82
SL(2,ℤ/4)⋊C83
C3×#18503
C3×Dic3⋊C84