Finite Group Databasebeta

← C43×#9866 #24929883

Subgroups — C43×#9866 #24929883

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#125×C43C211yesmaximal, characteristic
2C4×C4⋊C8×C43C211yesmaximal, characteristic
3C4×C4⋊C8×C43C211yesmaximal, characteristic
4C43×#1279C212yesmaximal
5C43×#1279C212yesmaximal
6C2×#125×C43C411yescharacteristic
7C2×C4⋊C8×C43—21no—
8C2×C4⋊C8×C43C2212yes—
9C2×C4×C8×C43—21no—
10C2×C4×C8×C43C2212yes—
11C43×#389C411yescharacteristic
12C43×#389C411yescharacteristic
13C43×#387—21no—
14C43×#387—21no—
15C43×#382C411yescharacteristic
16C4×C4⋊C4×C43—21no—
17C4×C4⋊C4×C43—21no—
18C4×C4⋊C4×C43C2211yescharacteristic
19C4×C4⋊C4×C43C2211yescharacteristic
20C43×C43C2211yescharacteristic
21C43×#336—21no—
22C43×#336—21no—
23C22×C8×C43—22no—
24C22×C8×C43—22no—
25#125×C43—22no—
26#125×C43C814yescomplemented
27C2×C4⋊C4×C43—21no—
28C2×C4⋊C4×C43—21no—
29C2×C4⋊C4×C43—21no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43C2×C411yescharacteristic
32C2×C4⋊C4×C43C2×C411yescharacteristic
33C2×C4⋊C4×C43C2×C411yescharacteristic
34C2×C4⋊C4×C43C2×C411yescharacteristic
35C2×C42×C43—21no—
36C2×C42×C43—21no—
37C2×C42×C43C2×C411yescharacteristic
38C2×C42×C43C2×C411yescharacteristic
39C2×C42×C43D411yescharacteristic
40C2×C42×C43D411yescharacteristic
41C2×C42×C43D411yescharacteristic
42C2×C42×C43D411yescharacteristic
43C2×C42×C43C2311yescharacteristic
44C4⋊C8×C43—24no—
45C4⋊C8×C43—22no—
46C4⋊C8×C43Q814yes—
47C4×C8×C43—24no—
48C4×C8×C43—42no—
49#95×C43—21no—
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C2×C8×C43—24no—
67C2×C8×C43—24no—
68C2×C8×C43—42no—
69C2×C8×C43—42no—
70C2×C8×C43—42no—
71C2×C8×C43—42no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—24no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—22no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43C2×C812yes—
81C4⋊C4×C43C2×C812yes—
82C42×C43—22no—
83C42×C43—22no—
84C42×C43—22no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—41no—
88C42×C43—42no—
89C42×C43—41no—
90C42×C43—41no—
91C42×C43C2×C812yes—
92C42×C43M1612yes—
93C42×C43C2×Q812yes—
94C42×C43#4112yes—
95C23×C43C2×C22⋊C411yescharacteristic
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43C22⋊C812yes—
120C2×C4×C43C22⋊C812yes—
121C2×C4×C43#10412yes—
122C2×C4×C43C4×Q812yes—
123C2×C4×C43C22⋊Q812yes—
124C2×C4×C43#12411yescharacteristic
125C2×C4×C43C4⋊Q811yescharacteristic
126C2×C4×C43C22×C811yescharacteristic
127C2×C4×C43C2×M1611yescharacteristic
128C2×C4×C43#13112yes—
129C2×C4×C43#13512yes—
130C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C43#13711yescharacteristic
132C8×C43—44no—
133C8×C43—44no—
134#9866C4311yesmaximal, characteristic, direct product factor, Sylow
135C22×C43#39111yescharacteristic
136C22×C43C2×C22⋊C811yescharacteristic
137C22×C43#40811yescharacteristic
138C22×C43#41611yescharacteristic
139C22×C43#41711yescharacteristic
140C22×C43C2×#10411yescharacteristic
141C22×C43#42111yescharacteristic
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—22no—
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—42no—
148C4×C43—42no—
149C4×C43—41no—
150C4×C43—81no—
151C4×C43—81no—
152C4×C43C8×Q812yes—
153C4×C43#44612yes—
154C4×C43#47812yes—
155C4×C43#47912yes—
156C4×#125C2×C4311yescharacteristic
157C4×C4⋊C8C2×C4311yescharacteristic
158C4×C4⋊C8C2×C4311yescharacteristic
159#1279C2×C4312yes—
160#1279C2×C4312yes—
161C2×C43#147611yescharacteristic
162C2×C43#147711yescharacteristic
163C2×C43#148211yescharacteristic
164C2×C43#148311yescharacteristic
165C2×C43#198411yescharacteristic
166C2×C43#198611yescharacteristic
167C2×C43#198911yescharacteristic
168C2×#125C4×C4311yescharacteristic
169C2×C4⋊C8—21no—
170C2×C4⋊C8C22×C4312yes—
171C2×C4×C8—21no—
172C2×C4×C8C22×C4312yes—
173#389C4×C4311yescharacteristic
174#389C4×C4311yescharacteristic
175#387—21no—
176#387—21no—
177#382C4×C4311yescharacteristic
178C4×C4⋊C4—21no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4C22×C4311yescharacteristic
181C4×C4⋊C4C22×C4311yescharacteristic
182C43C22×C4311yescharacteristic
183#336—21no—
184#336—21no—
185C43#986611yescharacteristic, direct product factor, Sylow
186C22×C8—22no—
187C22×C8—22no—
188#125—22no—
189#125C8×C4314yescomplemented
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×C4×C4311yescharacteristic
195C2×C4⋊C4C2×C4×C4311yescharacteristic
196C2×C4⋊C4C2×C4×C4311yescharacteristic
197C2×C4⋊C4C2×C4×C4311yescharacteristic
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C2×C4×C4311yescharacteristic
201C2×C42C2×C4×C4311yescharacteristic
202C2×C42D4×C4311yescharacteristic
203C2×C42D4×C4311yescharacteristic
204C2×C42D4×C4311yescharacteristic
205C2×C42D4×C4311yescharacteristic
206C2×C42C23×C4311yescharacteristic
207C4⋊C8—24no—
208C4⋊C8—22no—
209C4⋊C8Q8×C4314yes—
210C4×C8—24no—
211C4×C8—42no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C4311yescharacteristic
223C22×C4C22⋊C4×C4311yescharacteristic
224C22×C4C22⋊C4×C4311yescharacteristic
225C22×C4C22⋊C4×C4311yescharacteristic
226C22×C4C22×C4×C4311yescharacteristic
227C22×C4C2×D4×C4311yescharacteristic
228C22×C4C2×D4×C4311yescharacteristic
229C2×C8—24no—
230C2×C8—24no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4C2×C8×C4312yes—
244C4⋊C4C2×C8×C4312yes—
245C42—22no—
246C42—22no—
247C42—22no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—42no—
252C42—41no—
253C42—41no—
254C42C2×C8×C4312yes—
255C42M16×C4312yes—
256C42C2×Q8×C4312yes—
257C42#41×C4312yes—
258C23C2×C22⋊C4×C4311yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4C22⋊C8×C4312yes—
283C2×C4C22⋊C8×C4312yes—
284C2×C4#104×C4312yes—
285C2×C4C4×Q8×C4312yes—
286C2×C4C22⋊Q8×C4312yes—
287C2×C4#124×C4311yescharacteristic
288C2×C4C4⋊Q8×C4311yescharacteristic
289C2×C4C22×C8×C4311yescharacteristic
290C2×C4C2×M16×C4311yescharacteristic
291C2×C4#131×C4312yes—
292C2×C4#135×C4312yes—
293C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
294C2×C4#137×C4311yescharacteristic
295C8—44no—
296C8—44no—
297C22C43×#39111yescharacteristic
298C22C2×C22⋊C8×C4311yescharacteristic
299C22C43×#40811yescharacteristic
300C22C43×#41611yescharacteristic
301C22C43×#41711yescharacteristic
302C22C2×#104×C4311yescharacteristic
303C22C43×#42111yescharacteristic
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—42no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4C8×Q8×C4312yes—
315C4C43×#44612yes—
316C4C43×#47812yes—
317C4C43×#47912yes—
318C2C43×#147611yescharacteristic
319C2C43×#147711yescharacteristic
320C2C43×#148211yescharacteristic
321C2C43×#148311yescharacteristic
322C2C43×#198411yescharacteristic
323C2C43×#198611yescharacteristic
324C2C43×#198911yescharacteristic
subgroupG/H
centerC22×C4×C43C2×D4
commutatorC2×C4C22×C8×C43
Frattini, cosocleC2×C42C23×C43
socle, prime radicalC23×C43C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
26. #125×C43C8semidirect
134. #9866C43direct (N × H)
185. C43#9866direct (N × H)
189. #125C8×C43semidirect

Maximal subgroups

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

subgroupindex
C4×#125×C432
C4×C4⋊C8×C432
C43×#12792
#986643