Finite Group Databasebeta

← C43×#9537 #24929554

Subgroups — C43×#9537 #24929554

Order 11008.

356 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#1939C211yesmaximal, characteristic
2C4×#107×C43C211yesmaximal, characteristic
3C43×#1770C211yesmaximal, characteristic
4C43×#1279C211yesmaximal, characteristic
5C43×#1279C211yesmaximal, characteristic
6C43×#1277C211yesmaximal, characteristic
7C43×#1273C211yesmaximal, characteristic
8C2×#107×C43C411yescharacteristic
9C2×#107×C43C411yescharacteristic
10C2×C4⋊C8×C43—21no—
11C2×C4⋊C8×C43C2211yescharacteristic
12C2×C4⋊C8×C43C2211yescharacteristic
13C2×#97×C43—21no—
14C2×C4×C8×C43C2211yescharacteristic
15C2×C4×C8×C43C2211yescharacteristic
16C2×C4×C8×C43C2211yescharacteristic
17C4×C4⋊C4×C43C2211yescharacteristic
18C4×C4⋊C4×C43C2211yescharacteristic
19C43×#340C411yescharacteristic
20C43×#340C411yescharacteristic
21C43×#336—21no—
22C43×#336—21no—
23C22×C8×C43—21no—
24C22×C8×C43—21no—
25C22×C8×C43—21no—
26C22×C8×C43C2×C411yescharacteristic
27C22×C8×C43C2×C411yescharacteristic
28C22×C8×C43D411yescharacteristic
29C22×C8×C43D411yescharacteristic
30C2×C4⋊C4×C43C2×C411yescharacteristic
31C2×C4⋊C4×C43C2×C411yescharacteristic
32C2×C4⋊C4×C43C2×C411yescharacteristic
33C2×C4⋊C4×C43C2×C411yescharacteristic
34C2×C42×C43—21no—
35C2×C42×C43—21no—
36C2×C42×C43C2311yescharacteristic
37#107×C43—22no—
38#107×C43—22no—
39C4⋊C8×C43—21no—
40C4⋊C8×C43—21no—
41C4⋊C8×C43—21no—
42C4⋊C8×C43—42no—
43C4⋊C8×C43Q812yes—
44#97×C43—42no—
45C4×C8×C43—21no—
46C4×C8×C43—21no—
47C4×C8×C43—21no—
48C4×C8×C43—21no—
49C4×C8×C43—21no—
50C4×C8×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43#4111yescharacteristic
60C2×C8×C43—21no—
61C2×C8×C43—21no—
62C2×C8×C43—21no—
63C2×C8×C43—21no—
64C2×C8×C43—22no—
65C2×C8×C43—21no—
66C2×C8×C43—22no—
67C2×C8×C43—21no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43M1612yes—
80C2×C8×C43D812yes—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43M1612yes—
89C42×C43—41no—
90C42×C43—41no—
91C42×C43—41no—
92C42×C43—41no—
93C42×C43C2×Q811yescharacteristic
94C42×C43#4111yescharacteristic
95C42×C43#4111yescharacteristic
96C42×C43#4111yescharacteristic
97C23×C43C4×D411yescharacteristic
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43#11711yescharacteristic
113C2×C4×C43C4×Q811yescharacteristic
114C2×C4×C43C22⋊Q811yescharacteristic
115C2×C4×C43#12311yescharacteristic
116C2×C4×C43#12511yescharacteristic
117C2×C4×C43#12611yescharacteristic
118C2×C4×C43C2×M1611yescharacteristic
119C2×C4×C43C2×M1611yescharacteristic
120C2×C4×C43#13111yescharacteristic
121C2×C4×C43#13111yescharacteristic
122C2×C4×C43C2×D811yescharacteristic
123C2×C4×C43#13511yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×C4×C43#13711yescharacteristic
126C8×C43—22no—
127C8×C43—22no—
128C8×C43—42no—
129C8×C43—41no—
130C8×C43—42no—
131C8×C43—41no—
132C8×C43—81no—
133#9537C4311yesmaximal, characteristic, direct product factor, Sylow
134C22×C43#38711yescharacteristic
135C22×C43#43511yescharacteristic
136C22×C43#43611yescharacteristic
137C22×C43C4×D811yescharacteristic
138C22×C43#44111yescharacteristic
139C22×C43#44311yescharacteristic
140C22×C43#44411yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—42no—
144C4×C43—81no—
145C4×C43—81no—
146C4×C43—81no—
147C4×C43#43211yescharacteristic
148C4×C43#43311yescharacteristic
149C4×C43#44611yescharacteristic
150C4×C43#44611yescharacteristic
151C4×C43#47411yescharacteristic
152C4×C43#47911yescharacteristic
153C4×C43#48011yescharacteristic
154C4×C43#48511yescharacteristic
155#1939C2×C4311yescharacteristic
156C4×#107C2×C4311yescharacteristic
157#1770C2×C4311yescharacteristic
158#1279C2×C4311yescharacteristic
159#1279C2×C4311yescharacteristic
160#1277C2×C4311yescharacteristic
161#1273C2×C4311yescharacteristic
162C2×C43#158111yescharacteristic
163C2×C43#158711yescharacteristic
164C2×C43#158911yescharacteristic
165C2×C43#159311yescharacteristic
166C2×C43#191711yescharacteristic
167C2×C43#191811yescharacteristic
168C2×C43#192211yescharacteristic
169C2×#107C4×C4311yescharacteristic
170C2×#107C4×C4311yescharacteristic
171C2×C4⋊C8—21no—
172C2×C4⋊C8C22×C4311yescharacteristic
173C2×C4⋊C8C22×C4311yescharacteristic
174C2×#97—21no—
175C2×C4×C8C22×C4311yescharacteristic
176C2×C4×C8C22×C4311yescharacteristic
177C2×C4×C8C22×C4311yescharacteristic
178C4×C4⋊C4C22×C4311yescharacteristic
179C4×C4⋊C4C22×C4311yescharacteristic
180#340C4×C4311yescharacteristic
181#340C4×C4311yescharacteristic
182#336—21no—
183#336—21no—
184C43#953711yescharacteristic, direct product factor, Sylow
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8C2×C4×C4311yescharacteristic
189C22×C8C2×C4×C4311yescharacteristic
190C22×C8D4×C4311yescharacteristic
191C22×C8D4×C4311yescharacteristic
192C2×C4⋊C4C2×C4×C4311yescharacteristic
193C2×C4⋊C4C2×C4×C4311yescharacteristic
194C2×C4⋊C4C2×C4×C4311yescharacteristic
195C2×C4⋊C4C2×C4×C4311yescharacteristic
196C2×C42—21no—
197C2×C42—21no—
198C2×C42C23×C4311yescharacteristic
199#107—22no—
200#107—22no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—42no—
205C4⋊C8Q8×C4312yes—
206#97—42no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—21no—
210C4×C8—21no—
211C4×C8—21no—
212C4×C8—21no—
213#95—21no—
214#95—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22×C4×C4311yescharacteristic
220C22×C4C2×D4×C4311yescharacteristic
221C22×C4#41×C4311yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—22no—
227C2×C8—21no—
228C2×C8—22no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8M16×C4312yes—
242C2×C8D8×C4312yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4M16×C4312yes—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42C2×Q8×C4311yescharacteristic
256C42#41×C4311yescharacteristic
257C42#41×C4311yescharacteristic
258C42#41×C4311yescharacteristic
259C23C4×D4×C4311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4#117×C4311yescharacteristic
275C2×C4C4×Q8×C4311yescharacteristic
276C2×C4C22⋊Q8×C4311yescharacteristic
277C2×C4#123×C4311yescharacteristic
278C2×C4#125×C4311yescharacteristic
279C2×C4#126×C4311yescharacteristic
280C2×C4C2×M16×C4311yescharacteristic
281C2×C4C2×M16×C4311yescharacteristic
282C2×C4#131×C4311yescharacteristic
283C2×C4#131×C4311yescharacteristic
284C2×C4C2×D8×C4311yescharacteristic
285C2×C4#135×C4311yescharacteristic
286C2×C4#137×C4311yescharacteristic
287C2×C4#137×C4311yescharacteristic
288C8—22no—
289C8—22no—
290C8—42no—
291C8—41no—
292C8—42no—
293C8—41no—
294C8—81no—
295C22C43×#38711yescharacteristic
296C22C43×#43511yescharacteristic
297C22C43×#43611yescharacteristic
298C22C4×D8×C4311yescharacteristic
299C22C43×#44111yescharacteristic
300C22C43×#44311yescharacteristic
301C22C43×#44411yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4C43×#43211yescharacteristic
309C4C43×#43311yescharacteristic
310C4C43×#44611yescharacteristic
311C4C43×#44611yescharacteristic
312C4C43×#47411yescharacteristic
313C4C43×#47911yescharacteristic
314C4C43×#48011yescharacteristic
315C4C43×#48511yescharacteristic
316C2C43×#158111yescharacteristic
317C2C43×#158711yescharacteristic
318C2C43×#158911yescharacteristic
319C2C43×#159311yescharacteristic
320C2C43×#191711yescharacteristic
321C2C43×#191811yescharacteristic
322C2C43×#192211yescharacteristic
subgroupG/H
centerC22×C4×C43C2×D4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socle, prime radicalC23×C43C4×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ C2×C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
133. #9537C43direct (N × H)
184. C43#9537direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#19392
C4×#107×C432
C43×#17702
C43×#12792
C43×#12772
C43×#12732
#953743