Finite Group Databasebeta

← C43×#13394 #24933411

Subgroups — C43×#13394 #24933411

Order 11008.

392 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#473C211yesmaximal, characteristic
2C2×C43×#368C211yesmaximal, characteristic, complemented
3C2×C43×#362C211yesmaximal, characteristic, complemented
4C2×C43×#358C211yesmaximal, characteristic, complemented
5C43×#2113C211yesmaximal, characteristic
6C43×#1816C211yesmaximal, characteristic
7C43×#1387C211yesmaximal, characteristic, complemented
8C2×#137×C43—21no—
9C22×Q16×C43C2211yescharacteristic
10C2×#131×C43C2211yescharacteristic
11C2×M32×C43C2211yescharacteristic
12C22×C16×C43C2211yescharacteristic
13C43×#473—22no—
14C43×#473—22no—
15C2×#108×C43C2211yescharacteristic
16C2×#108×C43C2211yescharacteristic
17C2×#107×C43C2211yescharacteristic
18C43×#417—21no—
19C2×#101×C43—21no—
20C43×#368—22no—
21C43×#362—22no—
22C43×#358—22no—
23C43×C22⋊C16—22no—
24C43×#343—21no—
25C2×#41×C43D411yescharacteristic
26C22×Q8×C43—21no—
27#137×C43—24no—
28#137×C43—42no—
29C2×Q16×C43—21no—
30C2×Q16×C43—21no—
31C2×Q16×C43—21no—
32C2×Q16×C43—21no—
33C2×Q16×C43—21no—
34C2×Q16×C43—41no—
35C2×Q16×C43D412yes—
36C2×SD16×C43—41no—
37#131×C43—21no—
38#131×C43—21no—
39#131×C43—21no—
40#131×C43—21no—
41C2×M16×C43—21no—
42C2×M16×C43—21no—
43C2×M16×C43—21no—
44C2×M16×C43D411yescharacteristic
45C22×C8×C43—21no—
46C22×C8×C43C2311yescharacteristic
47C2×C4⋊C4×C43—21no—
48M32×C43—21no—
49M32×C43—21no—
50C2×C16×C43—21no—
51C2×C16×C43—21no—
52C2×C16×C43—21no—
53C2×C16×C43D412yes—
54#108×C43—21no—
55#108×C43—21no—
56#108×C43—21no—
57#108×C43D412yes—
58#107×C43—21no—
59#107×C43—21no—
60#103×C43—41no—
61#102×C43—41no—
62#101×C43—24no—
63#41×C43—21no—
64#41×C43—21no—
65#41×C43—21no—
66#41×C43—21no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43D811yescharacteristic
74C2×D4×C43—21no—
75C2×D4×C43D811yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80Q16×C43—22no—
81Q16×C43—22no—
82Q16×C43—44no—
83Q16×C43—41no—
84Q16×C43—41no—
85SD16×C43—44no—
86M16×C43—21no—
87M16×C43—22no—
88M16×C43—21no—
89M16×C43—41no—
90M16×C43—41no—
91M16×C43—41no—
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—21no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C2×C8×C43#4111yescharacteristic
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C16×C43—22no—
108C16×C43—41no—
109C23×C43—21no—
110C23×C43#13511yescharacteristic
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—42no—
114Q8×C43—42no—
115Q8×C43—81no—
116Q8×C43—81no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—41no—
120D4×C43—41no—
121C2×C4×C43—21no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43—161no—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12311yescharacteristic
132C2×C4×C43C2×D811yescharacteristic
133C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C8×C43—41no—
136C8×C43—42no—
137C8×C43—81no—
138C8×C43#12111yescharacteristic
139C8×C43#12111yescharacteristic
140C8×C43#12311yescharacteristic
141C8×C43#12411yescharacteristic
142#13394C4311yesmaximal, characteristic, direct product factor, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43#45211yescharacteristic
149C22×C43#46611yescharacteristic
150C22×C43#48211yescharacteristic
151C4×C43—41no—
152C4×C43—82no—
153C4×C43—161no—
154C4×C43#39411yescharacteristic
155C4×C43#44711yescharacteristic
156C4×C43#46811yescharacteristic
157C4×C43#48011yescharacteristic
158C2×#473C2×C4311yescharacteristic
159C2×#368C2×C4311yescharacteristic, complemented
160C2×#362C2×C4311yescharacteristic, complemented
161C2×#358C2×C4311yescharacteristic, complemented
162#2113C2×C4311yescharacteristic
163#1816C2×C4311yescharacteristic
164#1387C2×C4311yescharacteristic, complemented
165C2×C43—21no—
166C2×C43—21no—
167C2×C43—81no—
168C2×C43#203311yescharacteristic
169C2×C43#222211yescharacteristic
170C2×C43#222311yescharacteristic
171C2×#137—21no—
172C22×Q16C22×C4311yescharacteristic
173C2×#131C22×C4311yescharacteristic
174C2×M32C22×C4311yescharacteristic
175C22×C16C22×C4311yescharacteristic
176#473—22no—
177#473—22no—
178C2×#108C22×C4311yescharacteristic
179C2×#108C22×C4311yescharacteristic
180C2×#107C22×C4311yescharacteristic
181#417—21no—
182C2×#101—21no—
183#368—22no—
184#362—22no—
185#358—22no—
186C22⋊C16—22no—
187#343—21no—
188C43#1339411yescharacteristic, direct product factor, Sylow
189C2×#41D4×C4311yescharacteristic
190C22×Q8—21no—
191#137—24no—
192#137—42no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—41no—
199C2×Q16D4×C4312yes—
200C2×SD16—41no—
201#131—21no—
202#131—21no—
203#131—21no—
204#131—21no—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16D4×C4311yescharacteristic
209C22×C8—21no—
210C22×C8C23×C4311yescharacteristic
211C2×C4⋊C4—21no—
212M32—21no—
213M32—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16D4×C4312yes—
218#108—21no—
219#108—21no—
220#108—21no—
221#108D4×C4312yes—
222#107—21no—
223#107—21no—
224#103—41no—
225#102—41no—
226#101—24no—
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8D8×C4311yescharacteristic
238C2×D4—21no—
239C2×D4D8×C4311yescharacteristic
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C2×D4×C4311yescharacteristic
244Q16—22no—
245Q16—22no—
246Q16—44no—
247Q16—41no—
248Q16—41no—
249SD16—44no—
250M16—21no—
251M16—22no—
252M16—21no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8C2×D4×C4311yescharacteristic
264C2×C8C2×D4×C4311yescharacteristic
265C2×C8C2×D4×C4311yescharacteristic
266C2×C8#41×C4311yescharacteristic
267C2×C8#41×C4311yescharacteristic
268C2×C8#41×C4311yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C16—22no—
272C16—41no—
273C23—21no—
274C23#135×C4311yescharacteristic
275Q8—21no—
276Q8—21no—
277Q8—42no—
278Q8—42no—
279Q8—81no—
280Q8—81no—
281D4—21no—
282D4—21no—
283D4—41no—
284D4—41no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—161no—
293C2×C4#120×C4311yescharacteristic
294C2×C4#121×C4311yescharacteristic
295C2×C4#123×C4311yescharacteristic
296C2×C4C2×D8×C4311yescharacteristic
297C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
298C2×C4#137×C4311yescharacteristic
299C8—41no—
300C8—42no—
301C8—81no—
302C8#121×C4311yescharacteristic
303C8#121×C4311yescharacteristic
304C8#123×C4311yescharacteristic
305C8#124×C4311yescharacteristic
306C22—21no—
307C22—21no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C43×#45211yescharacteristic
312C22C43×#46611yescharacteristic
313C22C43×#48211yescharacteristic
314C4—41no—
315C4—82no—
316C4—161no—
317C4C43×#39411yescharacteristic
318C4C43×#44711yescharacteristic
319C4C43×#46811yescharacteristic
320C4C43×#48011yescharacteristic
321C2—21no—
322C2—21no—
323C2—81no—
324C2C43×#203311yescharacteristic
325C2C43×#222211yescharacteristic
326C2C43×#222311yescharacteristic
subgroupG/H
center, socleC22×C43#466
commutator, Frattini, cosocleC22×C8C23×C43
prime radicalC2×#41×C43D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×#131×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#368C2semidirect
3. C2×C43×#362C2semidirect
4. C2×C43×#358C2semidirect
7. C43×#1387C2semidirect
142. #13394C43direct (N × H)
159. C2×#368C2×C43semidirect
160. C2×#362C2×C43semidirect
161. C2×#358C2×C43semidirect
164. #1387C2×C43semidirect
188. C43#13394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4732
C2×C43×#3682
C2×C43×#3622
C2×C43×#3582
C43×#21132
C43×#18162
C43×#13872
#1339443