Finite Group Databasebeta

← C43×#13238 #24933255

Subgroups — C43×#13238 #24933255

Order 11008.

466 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
1C22×SD32×C43C211yesmaximal, characteristic
2C2×C43×#366C211yesmaximal, characteristic, complemented
3C2×C43×#358C211yesmaximal, characteristic, complemented
4C2×C43×#357C211yesmaximal, characteristic
5C2×C43×#346C211yesmaximal, characteristic, complemented
6C43×#1970C211yesmaximal, characteristic
7C43×#1969C211yesmaximal, characteristic, complemented
8C22×Q16×C43C2211yescharacteristic
9C22×D8×C43C2211yescharacteristic
10C2×SD32×C43—22no—
11C2×SD32×C43—22no—
12C2×SD32×C43C414yescomplemented
13C22×C16×C43C2211yescharacteristic
14C22×C16×C43C2211yescharacteristic
15C2×#107×C43C2211yescharacteristic
16C2×#107×C43C2211yescharacteristic
17C2×#103×C43—21no—
18C2×#102×C43—21no—
19C2×C4×C8×C43C2211yescharacteristic
20C43×#391—21no—
21C43×#390—21no—
22C43×#366—22no—
23C43×#358—22no—
24C43×#357—22no—
25C43×#346—22no—
26C22×Q8×C43—21no—
27C22×D4×C43—21no—
28C2×Q16×C43—21no—
29C2×Q16×C43—21no—
30C2×Q16×C43—21no—
31C2×Q16×C43—21no—
32C2×Q16×C43—21no—
33C2×Q16×C43C2×C412yes—
34C2×D8×C43—21no—
35C2×D8×C43—21no—
36C2×D8×C43—21no—
37C2×D8×C43—21no—
38C2×D8×C43—21no—
39C2×D8×C43C2×C412yes—
40C22×C8×C43D411yescharacteristic
41C22×C8×C43C2311yescharacteristic
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C22⋊C4×C43—42no—
45C2×C42×C43D411yescharacteristic
46SD32×C43—28no—
47C2×C16×C43—21no—
48C2×C16×C43—21no—
49C2×C16×C43C2×C412yes—
50C2×C16×C43D412yes—
51C2×C16×C43D412yes—
52C2×C16×C43D412yes—
53#107×C43—21no—
54#107×C43—21no—
55#107×C43—21no—
56#107×C43—21no—
57#103×C43—42no—
58#102×C43—42no—
59C4×C8×C43—21no—
60C4×C8×C43—21no—
61#95×C43—42no—
62C24×C43—41no—
63C2×Q8×C43—22no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×D4×C43—22no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43D812yes—
79C22×C4×C43C2×D411yescharacteristic
80Q16×C43—22no—
81Q16×C43—22no—
82Q16×C43—41no—
83Q16×C43—41no—
84D8×C43—22no—
85D8×C43—22no—
86D8×C43—41no—
87D8×C43—41no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43D812yes—
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43#4111yescharacteristic
96C2×C8×C43#4111yescharacteristic
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C22⋊C4×C43—84no—
102C42×C43—21no—
103C42×C43—21no—
104C16×C43—22no—
105C16×C43C22⋊C414yescomplemented
106C23×C43—42no—
107C23×C43—81no—
108C23×C43—81no—
109C23×C43—82no—
110C23×C43—82no—
111C23×C43C2×D811yescharacteristic
112Q8×C43—42no—
113Q8×C43—42no—
114Q8×C43—81no—
115Q8×C43—81no—
116D4×C43—42no—
117D4×C43—42no—
118D4×C43—81no—
119D4×C43—81no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—42no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43—82no—
129C2×C4×C43—82no—
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12711yescharacteristic
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C8×C43—22no—
137C8×C43C2×C22⋊C411yescharacteristic
138C8×C43C4×D411yescharacteristic
139C8×C43#12111yescharacteristic
140C8×C43#12411yescharacteristic
141#13238C4311yesmaximal, characteristic, direct product factor, Sylow
142C22×C43—84no—
143C22×C43—82no—
144C22×C43—162no—
145C22×C43—161no—
146C22×C43—161no—
147C22×C43C4×D811yescharacteristic
148C22×C43#46611yescharacteristic
149C22×C43#49311yescharacteristic
150C22×C43#50912yes—
151C22×C43#51012yes—
152C4×C43—42no—
153C4×C43—82no—
154C4×C43—161no—
155C4×C43—161no—
156C4×C43#39011yescharacteristic
157C4×C43C4×D811yescharacteristic
158C4×C43#46611yescharacteristic
159C4×C43#49511yescharacteristic
160C22×SD32C2×C4311yescharacteristic
161C2×#366C2×C4311yescharacteristic, complemented
162C2×#358C2×C4311yescharacteristic, complemented
163C2×#357C2×C4311yescharacteristic
164C2×#346C2×C4311yescharacteristic, complemented
165#1970C2×C4311yescharacteristic
166#1969C2×C4311yescharacteristic, complemented
167C2×C43—162no—
168C2×C43#197011yescharacteristic
169C2×C43#217512yes—
170C2×C43#222012yes—
171C2×C43#225011yescharacteristic
172C2×C43#225111yescharacteristic
173C22×Q16C22×C4311yescharacteristic
174C22×D8C22×C4311yescharacteristic
175C2×SD32—22no—
176C2×SD32—22no—
177C2×SD32C4×C4314yescomplemented
178C22×C16C22×C4311yescharacteristic
179C22×C16C22×C4311yescharacteristic
180C2×#107C22×C4311yescharacteristic
181C2×#107C22×C4311yescharacteristic
182C2×#103—21no—
183C2×#102—21no—
184C2×C4×C8C22×C4311yescharacteristic
185#391—21no—
186#390—21no—
187#366—22no—
188#358—22no—
189#357—22no—
190#346—22no—
191C43#1323811yescharacteristic, direct product factor, Sylow
192C22×Q8—21no—
193C22×D4—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16C2×C4×C4312yes—
200C2×D8—21no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8C2×C4×C4312yes—
206C22×C8D4×C4311yescharacteristic
207C22×C8C23×C4311yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C22⋊C4—42no—
211C2×C42D4×C4311yescharacteristic
212SD32—28no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16C2×C4×C4312yes—
216C2×C16D4×C4312yes—
217C2×C16D4×C4312yes—
218C2×C16D4×C4312yes—
219#107—21no—
220#107—21no—
221#107—21no—
222#107—21no—
223#103—42no—
224#102—42no—
225C4×C8—21no—
226C4×C8—21no—
227#95—42no—
228C24—41no—
229C2×Q8—22no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×D4—22no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4D8×C4312yes—
245C22×C4C2×D4×C4311yescharacteristic
246Q16—22no—
247Q16—22no—
248Q16—41no—
249Q16—41no—
250D8—22no—
251D8—22no—
252D8—41no—
253D8—41no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8D8×C4312yes—
257C2×C8C22×C4×C4311yescharacteristic
258C2×C8C2×D4×C4311yescharacteristic
259C2×C8C2×D4×C4311yescharacteristic
260C2×C8C2×D4×C4311yescharacteristic
261C2×C8#41×C4311yescharacteristic
262C2×C8#41×C4311yescharacteristic
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C22⋊C4—84no—
268C42—21no—
269C42—21no—
270C16—22no—
271C16C22⋊C4×C4314yescomplemented
272C23—42no—
273C23—82no—
274C23—82no—
275C23—81no—
276C23—81no—
277C23C2×D8×C4311yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—42no—
283D4—42no—
284D4—81no—
285D4—81no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4C4×D4×C4311yescharacteristic
297C2×C4#121×C4311yescharacteristic
298C2×C4#127×C4311yescharacteristic
299C2×C4C2×D8×C4311yescharacteristic
300C2×C4#135×C4311yescharacteristic
301C2×C4#135×C4311yescharacteristic
302C8—22no—
303C8C2×C22⋊C4×C4311yescharacteristic
304C8C4×D4×C4311yescharacteristic
305C8#121×C4311yescharacteristic
306C8#124×C4311yescharacteristic
307C22—84no—
308C22—82no—
309C22—162no—
310C22—161no—
311C22—161no—
312C22C4×D8×C4311yescharacteristic
313C22C43×#46611yescharacteristic
314C22C43×#49311yescharacteristic
315C22C43×#50912yes—
316C22C43×#51012yes—
317C4—42no—
318C4—82no—
319C4—161no—
320C4—161no—
321C4C43×#39011yescharacteristic
322C4C4×D8×C4311yescharacteristic
323C4C43×#46611yescharacteristic
324C4C43×#49511yescharacteristic
325C2—162no—
326C2C43×#197011yescharacteristic
327C2C43×#217512yes—
328C2C43×#222012yes—
329C2C43×#225011yescharacteristic
330C2C43×#225111yescharacteristic
subgroupG/H
center, socleC23×C43C2×D8
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC22×D8×C43C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ C2×C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#366C2semidirect
3. C2×C43×#358C2semidirect
5. C2×C43×#346C2semidirect
7. C43×#1969C2semidirect
12. C2×SD32×C43C4semidirect
105. C16×C43C22⋊C4semidirect
141. #13238C43direct (N × H)
161. C2×#366C2×C43semidirect
162. C2×#358C2×C43semidirect
164. C2×#346C2×C43semidirect
166. #1969C2×C43semidirect
177. C2×SD32C4×C43semidirect
191. C43#13238direct (N × H)
271. C16C22⋊C4×C43semidirect

Maximal subgroups

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

subgroupindex
C22×SD32×C432
C2×C43×#3662
C2×C43×#3582
C2×C43×#3572
C2×C43×#3462
C43×#19702
C43×#19692
#1323843