Finite Group Databasebeta

← C43×#7732 #24927749

Subgroups — C43×#7732 #24927749

Order 11008.

420 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2860C211yesmaximal, characteristic
2C43×#1831C211yesmaximal, characteristic, complemented
3C43×#1831C211yesmaximal, characteristic, complemented
4C43×#1271C212yesmaximal, complemented
5C43×#1270C212yesmaximal
6C2×#126×C43—21no—
7C2×C4⋊C8×C43—21no—
8C2×C4⋊C8×C43—21no—
9C43×#390C411yescharacteristic
10C43×#390C411yescharacteristic
11C43×#390C2211yescharacteristic
12C43×#389C411yescharacteristic
13C43×#389C411yescharacteristic
14C43×#389C2211yescharacteristic
15C43×#388—21no—
16C43×#388—21no—
17C43×#388—21no—
18C43×C43C2211yescharacteristic
19C43×#336—21no—
20C43×#336—21no—
21C43×#336C2212yes—
22C43×#336C2212yes—
23C22×D4×C43C2×C411yescharacteristic
24C22×C8×C43—22no—
25C22×C8×C43—22no—
26#126×C43—42no—
27#126×C43—42no—
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×C22⋊C4×C43—21no—
35C2×C22⋊C4×C43—21no—
36C2×C22⋊C4×C43—21no—
37C2×C22⋊C4×C43—21no—
38C2×C22⋊C4×C43—21no—
39C2×C22⋊C4×C43—21no—
40C2×C42×C43C2×C411yescharacteristic
41C2×C42×C43C2×C411yescharacteristic
42C2×C42×C43D411yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—42no—
48C4⋊C8×C43—42no—
49#95×C43—21no—
50#95×C43—21no—
51#95×C43—21no—
52C24×C43—21no—
53C2×D4×C43—22no—
54C2×D4×C43—41no—
55C2×D4×C43—41no—
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—42no—
67C2×C8×C43—42no—
68C2×C8×C43—42no—
69C2×C8×C43—42no—
70C2×C8×C43—42no—
71C2×C8×C43—42no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C22⋊C4×C43—42no—
80C22⋊C4×C43—42no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C42×C43—22no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—41no—
91C42×C43—41no—
92C42×C43—41no—
93C42×C43—41no—
94C42×C43D812yes—
95C42×C43SD1612yes—
96C23×C43—41no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43C2×C22⋊C411yescharacteristic
104D4×C43—82no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43#10212yes—
131C2×C4×C43#10212yes—
132C2×C4×C43#13112yes—
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43C2×SD1611yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43#13711yescharacteristic
137C8×C43—82no—
138C8×C43—82no—
139#7732C4311yesmaximal, characteristic, direct product factor, Sylow
140C22×C43—81no—
141C22×C43—81no—
142C22×C43—81no—
143C22×C43—81no—
144C22×C43—81no—
145C22×C43—81no—
146C22×C43—81no—
147C22×C43#40811yescharacteristic
148C22×C43#41011yescharacteristic
149C22×C43#41311yescharacteristic
150C22×C43C2×#10211yescharacteristic
151C22×C43#41711yescharacteristic
152C22×C43#42111yescharacteristic
153C22×C43#42111yescharacteristic
154C4×C43—22no—
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43—81no—
166#2860C2×C4311yescharacteristic
167#1831C2×C4311yescharacteristic, complemented
168#1831C2×C4311yescharacteristic, complemented
169#1271C2×C4312yescomplemented
170#1270C2×C4312yes—
171C2×C43—161no—
172C2×C43#147311yescharacteristic
173C2×C43#148011yescharacteristic
174C2×C43#149511yescharacteristic
175C2×C43#151211yescharacteristic
176C2×C43#151711yescharacteristic
177C2×C43#153511yescharacteristic
178C2×C43#154711yescharacteristic
179C2×#126—21no—
180C2×C4⋊C8—21no—
181C2×C4⋊C8—21no—
182#390C4×C4311yescharacteristic
183#390C4×C4311yescharacteristic
184#390C22×C4311yescharacteristic
185#389C4×C4311yescharacteristic
186#389C4×C4311yescharacteristic
187#389C22×C4311yescharacteristic
188#388—21no—
189#388—21no—
190#388—21no—
191C43C22×C4311yescharacteristic
192#336—21no—
193#336—21no—
194#336C22×C4312yes—
195#336C22×C4312yes—
196C43#773211yescharacteristic, direct product factor, Sylow
197C22×D4C2×C4×C4311yescharacteristic
198C22×C8—22no—
199C22×C8—22no—
200#126—42no—
201#126—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C4311yescharacteristic
206C2×C4⋊C4C2×C4×C4311yescharacteristic
207C2×C4⋊C4C2×C4×C4311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×C4×C4311yescharacteristic
215C2×C42C2×C4×C4311yescharacteristic
216C2×C42D4×C4311yescharacteristic
217C2×C42D4×C4311yescharacteristic
218C2×C42D4×C4311yescharacteristic
219C2×C42D4×C4311yescharacteristic
220C2×C42C23×C4311yescharacteristic
221C4⋊C8—42no—
222C4⋊C8—42no—
223#95—21no—
224#95—21no—
225#95—21no—
226C24—21no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C22⋊C4×C4311yescharacteristic
234C22×C4C22⋊C4×C4311yescharacteristic
235C22×C4C22⋊C4×C4311yescharacteristic
236C22×C4C22⋊C4×C4311yescharacteristic
237C22×C4C22×C4×C4311yescharacteristic
238C22×C4C2×D4×C4311yescharacteristic
239C22×C4C2×D4×C4311yescharacteristic
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C42—22no—
262C42—21no—
263C42—21no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42D8×C4312yes—
269C42SD16×C4312yes—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊C4×C4311yescharacteristic
278D4—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4#102×C4312yes—
305C2×C4#102×C4312yes—
306C2×C4#131×C4312yes—
307C2×C4C2×D8×C4311yescharacteristic
308C2×C4C2×SD16×C4311yescharacteristic
309C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
310C2×C4#137×C4311yescharacteristic
311C8—82no—
312C8—82no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22C43×#40811yescharacteristic
321C22C43×#41011yescharacteristic
322C22C43×#41311yescharacteristic
323C22C2×#102×C4311yescharacteristic
324C22C43×#41711yescharacteristic
325C22C43×#42111yescharacteristic
326C22C43×#42111yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—161no—
340C2C43×#147311yescharacteristic
341C2C43×#148011yescharacteristic
342C2C43×#149511yescharacteristic
343C2C43×#151211yescharacteristic
344C2C43×#151711yescharacteristic
345C2C43×#153511yescharacteristic
346C2C43×#154711yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1831C2semidirect
3. C43×#1831C2semidirect
4. C43×#1271C2semidirect
139. #7732C43direct (N × H)
167. #1831C2×C43semidirect
168. #1831C2×C43semidirect
169. #1271C2×C43semidirect
196. C43#7732direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28602
C43×#18312
C43×#12712
C43×#12702
#773243