Finite Group Databasebeta

← C43×#8917 #24928934

Subgroups — C43×#8917 #24928934

Order 11008.

338 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2995C211yesmaximal, characteristic
2C43×#1838C211yesmaximal, characteristic, complemented
3C43×#1569C211yesmaximal, characteristic, complemented
4C43×#1524C211yesmaximal, characteristic
5C43×#1495C211yesmaximal, characteristic
6C43×#1302C211yesmaximal, characteristic, complemented
7C43×#1299C211yesmaximal, characteristic, complemented
8C43×#529C2211yescharacteristic
9C43×#446—21no—
10C43×#436—21no—
11C43×#435—21no—
12C43×#435—21no—
13C43×#433—21no—
14C43×#432C2211yescharacteristic
15C43×#431C2211yescharacteristic
16C43×#424—21no—
17C43×#423C2211yescharacteristic
18C43×#423C2211yescharacteristic
19C4×M16×C43C2211yescharacteristic
20C2×#97×C43C2211yescharacteristic
21C43×#341—21no—
22C43×#341—21no—
23C43×#335—21no—
24C43×#334—21no—
25C43×#330C411yescharacteristic
26C43×#330C411yescharacteristic
27C43×#329C411yescharacteristic
28C43×#329C411yescharacteristic
29C43×Q8⋊C8—21no—
30C43×D4⋊C8—21no—
31C2×M16×C43—21no—
32C2×M16×C43—21no—
33C2×M16×C43—21no—
34C2×M16×C43D411yescharacteristic
35C2×M16×C43D411yescharacteristic
36C22×C8×C43—21no—
37C22×C8×C43—21no—
38#126×C43—21no—
39#125×C43C2×C411yescharacteristic
40#124×C43C2×C411yescharacteristic
41#123×C43—21no—
42C22⋊Q8×C43Q811yescharacteristic
43#121×C43Q811yescharacteristic
44C4×Q8×C43D411yescharacteristic
45C4×D4×C43—21no—
46C4×D4×C43D411yescharacteristic
47#117×C43—21no—
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—21no—
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43D411yescharacteristic
57C4⋊C8×C43D411yescharacteristic
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62#97×C43—21no—
63#97×C43—21no—
64#97×C43—21no—
65#97×C43C2×C411yescharacteristic
66#97×C43C2×C411yescharacteristic
67#97×C43C2×C411yescharacteristic
68#97×C43C2×C411yescharacteristic
69C4×C8×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43—21no—
72C2×Q8×C43C4⋊C411yescharacteristic
73C2×D4×C43—21no—
74C2×D4×C43C4⋊C411yescharacteristic
75C22×C4×C43—21no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×Q811yescharacteristic
78C22×C4×C43#4111yescharacteristic
79M16×C43—42no—
80M16×C43—41no—
81M16×C43—41no—
82M16×C43—42no—
83M16×C43—81no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—81no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43C4⋊C411yescharacteristic
102C4⋊C4×C43C4⋊C411yescharacteristic
103C22⋊C4×C43—21no—
104C22⋊C4×C43—21no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—21no—
107C22⋊C4×C43—21no—
108C42×C43—21no—
109C42×C43C22×C411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C23×C43—21no—
114C23×C43C22⋊Q811yescharacteristic
115Q8×C43—41no—
116D4×C43—41no—
117D4×C43—81no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43C2×C4⋊C411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43C22⋊Q811yescharacteristic
132C2×C4×C43#12311yescharacteristic
133C8×C43—22no—
134C8×C43—41no—
135C8×C43—41no—
136C8×C43—41no—
137C8×C43—41no—
138C8×C43—41no—
139C8×C43—41no—
140C8×C43—41no—
141C8×C43—81no—
142C8×C43—81no—
143#8917C4311yesmaximal, characteristic, direct product factor, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43#38511yescharacteristic
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43#45411yescharacteristic
160C4×C43#45511yescharacteristic
161#2995C2×C4311yescharacteristic
162#1838C2×C4311yescharacteristic, complemented
163#1569C2×C4311yescharacteristic, complemented
164#1524C2×C4311yescharacteristic
165#1495C2×C4311yescharacteristic
166#1302C2×C4311yescharacteristic, complemented
167#1299C2×C4311yescharacteristic, complemented
168C2×C43—41no—
169C2×C43—81no—
170C2×C43#185811yescharacteristic
171C2×C43#186011yescharacteristic
172C2×C43#186111yescharacteristic
173#529C22×C4311yescharacteristic
174#446—21no—
175#436—21no—
176#435—21no—
177#435—21no—
178#433—21no—
179#432C22×C4311yescharacteristic
180#431C22×C4311yescharacteristic
181#424—21no—
182#423C22×C4311yescharacteristic
183#423C22×C4311yescharacteristic
184C4×M16C22×C4311yescharacteristic
185C2×#97C22×C4311yescharacteristic
186#341—21no—
187#341—21no—
188#335—21no—
189#334—21no—
190#330C4×C4311yescharacteristic
191#330C4×C4311yescharacteristic
192#329C4×C4311yescharacteristic
193#329C4×C4311yescharacteristic
194Q8⋊C8—21no—
195D4⋊C8—21no—
196C43#891711yescharacteristic, direct product factor, Sylow
197C2×M16—21no—
198C2×M16—21no—
199C2×M16—21no—
200C2×M16D4×C4311yescharacteristic
201C2×M16D4×C4311yescharacteristic
202C22×C8—21no—
203C22×C8—21no—
204#126—21no—
205#125C2×C4×C4311yescharacteristic
206#124C2×C4×C4311yescharacteristic
207#123—21no—
208C22⋊Q8Q8×C4311yescharacteristic
209#121Q8×C4311yescharacteristic
210C4×Q8D4×C4311yescharacteristic
211C4×D4—21no—
212C4×D4D4×C4311yescharacteristic
213#117—21no—
214C2×C42C23×C4311yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8D4×C4311yescharacteristic
223C4⋊C8D4×C4311yescharacteristic
224C22⋊C8—21no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228#97—21no—
229#97—21no—
230#97—21no—
231#97C2×C4×C4311yescharacteristic
232#97C2×C4×C4311yescharacteristic
233#97C2×C4×C4311yescharacteristic
234#97C2×C4×C4311yescharacteristic
235C4×C8—21no—
236C4×C8—21no—
237C4×C8—21no—
238C2×Q8C4⋊C4×C4311yescharacteristic
239C2×D4—21no—
240C2×D4C4⋊C4×C4311yescharacteristic
241C22×C4—21no—
242C22×C4C2×D4×C4311yescharacteristic
243C22×C4C2×Q8×C4311yescharacteristic
244C22×C4#41×C4311yescharacteristic
245M16—42no—
246M16—41no—
247M16—41no—
248M16—42no—
249M16—81no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—81no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4C4⋊C4×C4311yescharacteristic
268C4⋊C4C4⋊C4×C4311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C42—21no—
275C42C22×C4×C4311yescharacteristic
276C42C2×D4×C4311yescharacteristic
277C42C2×D4×C4311yescharacteristic
278C42#41×C4311yescharacteristic
279C23—21no—
280C23C22⋊Q8×C4311yescharacteristic
281Q8—41no—
282D4—41no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4C2×C4⋊C4×C4311yescharacteristic
294C2×C4C4×D4×C4311yescharacteristic
295C2×C4C4×D4×C4311yescharacteristic
296C2×C4#120×C4311yescharacteristic
297C2×C4C22⋊Q8×C4311yescharacteristic
298C2×C4#123×C4311yescharacteristic
299C8—22no—
300C8—41no—
301C8—41no—
302C8—41no—
303C8—41no—
304C8—41no—
305C8—41no—
306C8—41no—
307C8—81no—
308C8—81no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C43×#38511yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4C43×#45411yescharacteristic
325C4C43×#45511yescharacteristic
326C2—41no—
327C2—81no—
328C2C43×#185811yescharacteristic
329C2C43×#186011yescharacteristic
330C2C43×#186111yescharacteristic
subgroupG/H
centerC2×C4×C43#120
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#385
prime radical#121×C43Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1838C2semidirect
3. C43×#1569C2semidirect
6. C43×#1302C2semidirect
7. C43×#1299C2semidirect
143. #8917C43direct (N × H)
162. #1838C2×C43semidirect
163. #1569C2×C43semidirect
166. #1302C2×C43semidirect
167. #1299C2×C43semidirect
196. C43#8917direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#29952
C43×#18382
C43×#15692
C43×#15242
C43×#14952
C43×#13022
C43×#12992
#891743