Finite Group Databasebeta

← C43×#13234 #24933251

Subgroups — C43×#13234 #24933251

Order 11008.

464 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3058C211yesmaximal, characteristic
2C43×#2134C212yesmaximal, complemented
3C43×#2122C212yesmaximal, complemented
4C43×#1813C211yesmaximal, characteristic, complemented
5C43×#1757C211yesmaximal, characteristic, complemented
6C22×D8×C43C411yescharacteristic, complemented
7C2×#131×C43C2211yescharacteristic
8C43×#535C2212yes—
9C43×#469—21no—
10C43×#469—21no—
11C43×#466—21no—
12C43×#466—21no—
13C2×#108×C43—21no—
14C43×#427C411yescharacteristic, complemented
15C43×#418C412yescomplemented
16C43×#413C2212yes—
17C43×#413C2211yescharacteristic
18C43×#410C2211yescharacteristic
19C43×#405—21no—
20C43×#355—24no—
21C43×AΣL(1,𝔽16)—24no—
22C43×#344—21no—
23C43×#338—21no—
24C2×#41×C43C2311yescharacteristic
25C22×D4×C43C2×C412yes—
26C2×D8×C43—21no—
27C2×D8×C43—21no—
28C2×D8×C43—41no—
29C2×D8×C43—41no—
30#131×C43—41no—
31#131×C43—41no—
32C2×M16×C43—21no—
33C2×M16×C43—22no—
34C2×M16×C43C2×C411yescharacteristic
35C2×M16×C43D411yescharacteristic
36C2×M16×C43D411yescharacteristic
37C22×C8×C43C2×C411yescharacteristic
38C22×C8×C43D411yescharacteristic
39C22×C8×C43D411yescharacteristic
40#127×C43—22no—
41#124×C43—22no—
42#121×C43—22no—
43#121×C43—22no—
44#120×C43—22no—
45#120×C43—22no—
46#117×C43—21no—
47#117×C43C2×C412yes—
48#108×C43—41no—
49#108×C43—41no—
50#107×C43—21no—
51#106×C43—21no—
52#102×C43—22no—
53#102×C43—22no—
54#101×C43—22no—
55#101×C43D412yes—
56#100×C43—21no—
57#100×C43—22no—
58#99×C43—21no—
59#99×C43D412yes—
60#97×C43—41no—
61C4×C8×C43—41no—
62C24×C43—22no—
63#41×C43—41no—
64#41×C43—41no—
65C2×Q8×C43C2×D411yescharacteristic
66C2×D4×C43—22no—
67C2×D4×C43—22no—
68C2×D4×C43—42no—
69C2×D4×C43—42no—
70C2×D4×C43—42no—
71C2×D4×C43—42no—
72C2×D4×C43C2×D411yescharacteristic
73C2×D4×C43#4111yescharacteristic
74C2×D4×C43#4111yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78D8×C43—42no—
79D8×C43—41no—
80D8×C43—41no—
81M16×C43—22no—
82M16×C43—41no—
83M16×C43—41no—
84M16×C43—41no—
85M16×C43—41no—
86M16×C43—42no—
87M16×C43—42no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—41no—
95C2×C8×C43—42no—
96C2×C8×C43C22⋊C411yescharacteristic
97C2×C8×C43C22⋊C411yescharacteristic
98C2×C8×C43C22⋊C411yescharacteristic
99C2×C8×C43C22⋊C411yescharacteristic
100C4⋊C4×C43—22no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—22no—
104C22⋊C4×C43—42no—
105C22⋊C4×C43—42no—
106C42×C43—22no—
107C42×C43—41no—
108C23×C43—42no—
109C23×C43—82no—
110C23×C43—162no—
111C23×C43C4×D411yescharacteristic
112C23×C43#12111yescharacteristic
113C23×C43#12411yescharacteristic
114Q8×C43—41no—
115D4×C43—41no—
116D4×C43—41no—
117D4×C43—41no—
118D4×C43—42no—
119D4×C43—42no—
120D4×C43—82no—
121D4×C43—162no—
122D4×C43—162no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12711yescharacteristic
135C8×C43—21no—
136C8×C43—21no—
137C8×C43—21no—
138C8×C43—42no—
139C8×C43—82no—
140C8×C43#9911yescharacteristic
141C8×C43#9911yescharacteristic
142#13234C4311yesmaximal, characteristic, direct product factor, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—82no—
150C22×C43—82no—
151C22×C43—82no—
152C22×C43—164no—
153C22×C43#39011yescharacteristic
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—82no—
158C4×C43—82no—
159C4×C43C2×#9911yescharacteristic
160C4×C43#41011yescharacteristic
161#3058C2×C4311yescharacteristic
162#2134C2×C4312yescomplemented
163#2122C2×C4312yescomplemented
164#1813C2×C4311yescharacteristic, complemented
165#1757C2×C4311yescharacteristic, complemented
166C2×C43—21no—
167C2×C43—41no—
168C2×C43—41no—
169C2×C43—41no—
170C2×C43—162no—
171C2×C43#196411yescharacteristic
172C22×D8C4×C4311yescharacteristic, complemented
173C2×#131C22×C4311yescharacteristic
174#535C22×C4312yes—
175#469—21no—
176#469—21no—
177#466—21no—
178#466—21no—
179C2×#108—21no—
180#427C4×C4311yescharacteristic, complemented
181#418C4×C4312yescomplemented
182#413C22×C4312yes—
183#413C22×C4311yescharacteristic
184#410C22×C4311yescharacteristic
185#405—21no—
186#355—24no—
187AΣL(1,𝔽16)—24no—
188#344—21no—
189#338—21no—
190C43#1323411yescharacteristic, direct product factor, Sylow
191C2×#41C23×C4311yescharacteristic
192C22×D4C2×C4×C4312yes—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—41no—
196C2×D8—41no—
197#131—41no—
198#131—41no—
199C2×M16—21no—
200C2×M16—22no—
201C2×M16C2×C4×C4311yescharacteristic
202C2×M16D4×C4311yescharacteristic
203C2×M16D4×C4311yescharacteristic
204C22×C8C2×C4×C4311yescharacteristic
205C22×C8D4×C4311yescharacteristic
206C22×C8D4×C4311yescharacteristic
207#127—22no—
208#124—22no—
209#121—22no—
210#121—22no—
211#120—22no—
212#120—22no—
213#117—21no—
214#117C2×C4×C4312yes—
215#108—41no—
216#108—41no—
217#107—21no—
218#106—21no—
219#102—22no—
220#102—22no—
221#101—22no—
222#101D4×C4312yes—
223#100—21no—
224#100—22no—
225#99—21no—
226#99D4×C4312yes—
227#97—41no—
228C4×C8—41no—
229C24—22no—
230#41—41no—
231#41—41no—
232C2×Q8C2×D4×C4311yescharacteristic
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4C2×D4×C4311yescharacteristic
240C2×D4#41×C4311yescharacteristic
241C2×D4#41×C4311yescharacteristic
242C22×C4C22×C4×C4311yescharacteristic
243C22×C4C2×D4×C4311yescharacteristic
244C22×C4C2×D4×C4311yescharacteristic
245D8—42no—
246D8—41no—
247D8—41no—
248M16—22no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—42no—
254M16—42no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—41no—
262C2×C8—42no—
263C2×C8C22⋊C4×C4311yescharacteristic
264C2×C8C22⋊C4×C4311yescharacteristic
265C2×C8C22⋊C4×C4311yescharacteristic
266C2×C8C22⋊C4×C4311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—41no—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—22no—
274C42—41no—
275C23—42no—
276C23—82no—
277C23—162no—
278C23C4×D4×C4311yescharacteristic
279C23#121×C4311yescharacteristic
280C23#124×C4311yescharacteristic
281Q8—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—42no—
286D4—42no—
287D4—82no—
288D4—162no—
289D4—162no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4C2×C22⋊C4×C4311yescharacteristic
299C2×C4C4×D4×C4311yescharacteristic
300C2×C4#121×C4311yescharacteristic
301C2×C4#127×C4311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—42no—
306C8—82no—
307C8#99×C4311yescharacteristic
308C8#99×C4311yescharacteristic
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—82no—
316C22—82no—
317C22—82no—
318C22—164no—
319C22C43×#39011yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—82no—
324C4—82no—
325C4C2×#99×C4311yescharacteristic
326C4C43×#41011yescharacteristic
327C2—21no—
328C2—41no—
329C2—41no—
330C2—41no—
331C2—162no—
332C2C43×#196411yescharacteristic
subgroupG/H
center, socleC2×C43#1964
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×#41C23×C43
prime radicalC43×#3058C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C2×C4×C43 ◁ C2×#131×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2134C2semidirect
3. C43×#2122C2semidirect
4. C43×#1813C2semidirect
5. C43×#1757C2semidirect
6. C22×D8×C43C4semidirect
14. C43×#427C4semidirect
15. C43×#418C4semidirect
142. #13234C43direct (N × H)
162. #2134C2×C43semidirect
163. #2122C2×C43semidirect
164. #1813C2×C43semidirect
165. #1757C2×C43semidirect
172. C22×D8C4×C43semidirect
180. #427C4×C43semidirect
181. #418C4×C43semidirect
190. C43#13234direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30582
C43×#21342
C43×#21222
C43×#18132
C43×#17572
#1323443