Finite Group Databasebeta

← C43×#10444 #24930461

Subgroups — C43×#10444 #24930461

Order 11008.

440 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#461C211yesmaximal, characteristic
2C43×#1800C211yesmaximal, characteristic
3C43×#1571C211yesmaximal, characteristic, complemented
4C43×#1546C211yesmaximal, characteristic, complemented
5C43×#1546C211yesmaximal, characteristic, complemented
6C43×#1478C211yesmaximal, characteristic
7C43×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C43—21no—
9C2×C4⋊Q8×C43C2211yescharacteristic
10C2×C4×D4×C43C2211yescharacteristic
11C43×#461—22no—
12C43×#461—22no—
13C43×#431C2211yescharacteristic
14C43×#431C2211yescharacteristic
15C43×#423C2211yescharacteristic
16C43×#423C2211yescharacteristic
17C2×C4⋊C8×C43C2211yescharacteristic
18C2×#103×C43—21no—
19C2×#100×C43—21no—
20C43×#343—21no—
21C43×#335—22no—
22C43×#332—22no—
23C43×#332—22no—
24C43×D4⋊C8—22no—
25C22×Q8×C43—21no—
26C22×D4×C43D411yescharacteristic
27C23×C4×C43—21no—
28C2×SD16×C43—24no—
29C2×SD16×C43—42no—
30C2×SD16×C43—42no—
31C2×M16×C43—21no—
32C2×M16×C43—21no—
33C22×C8×C43—21no—
34C4⋊Q8×C43—21no—
35C4⋊Q8×C43—21no—
36C4⋊Q8×C43—21no—
37C4⋊Q8×C43D412yes—
38C4×D4×C43—21no—
39C4×D4×C43—21no—
40C4×D4×C43—21no—
41C4×D4×C43—21no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C22⋊C4×C43—21no—
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—21no—
48C4⋊C8×C43—21no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43D412yes—
54C4⋊C8×C43D412yes—
55#103×C43—24no—
56#100×C43—42no—
57C22⋊C8×C43—21no—
58C22⋊C8×C43—21no—
59C4×C8×C43—21no—
60C4×C8×C43—21no—
61C24×C43—21no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43D812yes—
74C22×C4×C43—21no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43—82no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×C4×C43#4111yescharacteristic
82SD16×C43—48no—
83M16×C43—41no—
84M16×C43—41no—
85M16×C43—41no—
86M16×C43—41no—
87C2×C8×C43—22no—
88C2×C8×C43—22no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—41no—
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C23×C43—22no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—81no—
110C23×C43—81no—
111C23×C43#12311yescharacteristic
112Q8×C43—42no—
113Q8×C43—42no—
114Q8×C43—81no—
115Q8×C43—81no—
116D4×C43—22no—
117D4×C43—22no—
118D4×C43—41no—
119D4×C43—41no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—42no—
124C2×C4×C43—82no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—82no—
128C2×C4×C43—81no—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C2×C4×C43#12411yescharacteristic
135C2×C4×C43C2×D811yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C8×C43—42no—
140C8×C43—42no—
141C8×C43—81no—
142C8×C43—81no—
143C8×C43—81no—
144#10444C4311yesmaximal, characteristic, direct product factor, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—42no—
148C22×C43—82no—
149C22×C43—82no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43#39411yescharacteristic
153C22×C43#48011yescharacteristic
154C22×C43#48211yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—82no—
159C4×C43—81no—
160C4×C43#44711yescharacteristic
161C4×C43#45211yescharacteristic
162C4×C43#46611yescharacteristic
163C4×C43#46811yescharacteristic
164C4×C43#47112yes—
165C2×#461C2×C4311yescharacteristic
166#1800C2×C4311yescharacteristic
167#1571C2×C4311yescharacteristic, complemented
168#1546C2×C4311yescharacteristic, complemented
169#1546C2×C4311yescharacteristic, complemented
170#1478C2×C4311yescharacteristic
171#1301C2×C4311yescharacteristic, complemented
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—82no—
175C2×C43#203311yescharacteristic
176C2×C43#204611yescharacteristic
177C2×C43#204911yescharacteristic
178C22×SD16—21no—
179C2×C4⋊Q8C22×C4311yescharacteristic
180C2×C4×D4C22×C4311yescharacteristic
181#461—22no—
182#461—22no—
183#431C22×C4311yescharacteristic
184#431C22×C4311yescharacteristic
185#423C22×C4311yescharacteristic
186#423C22×C4311yescharacteristic
187C2×C4⋊C8C22×C4311yescharacteristic
188C2×#103—21no—
189C2×#100—21no—
190#343—21no—
191#335—22no—
192#332—22no—
193#332—22no—
194D4⋊C8—22no—
195C43#1044411yescharacteristic, direct product factor, Sylow
196C22×Q8—21no—
197C22×D4D4×C4311yescharacteristic
198C23×C4—21no—
199C2×SD16—24no—
200C2×SD16—42no—
201C2×SD16—42no—
202C2×M16—21no—
203C2×M16—21no—
204C22×C8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8D4×C4312yes—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4D4×C4311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C42C23×C4311yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8D4×C4312yes—
225C4⋊C8D4×C4312yes—
226#103—24no—
227#100—42no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232C24—21no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4D8×C4312yes—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—82no—
250C22×C4C2×D4×C4311yescharacteristic
251C22×C4#41×C4311yescharacteristic
252C22×C4#41×C4311yescharacteristic
253SD16—48no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C42C2×D4×C4311yescharacteristic
274C42C2×D4×C4311yescharacteristic
275C42C2×D4×C4311yescharacteristic
276C42#41×C4311yescharacteristic
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23#123×C4311yescharacteristic
283Q8—42no—
284Q8—42no—
285Q8—81no—
286Q8—81no—
287D4—22no—
288D4—22no—
289D4—41no—
290D4—41no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4#120×C4311yescharacteristic
301C2×C4#121×C4311yescharacteristic
302C2×C4#121×C4311yescharacteristic
303C2×C4#121×C4311yescharacteristic
304C2×C4#123×C4311yescharacteristic
305C2×C4#124×C4311yescharacteristic
306C2×C4C2×D8×C4311yescharacteristic
307C2×C4#135×C4311yescharacteristic
308C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
309C2×C4#137×C4311yescharacteristic
310C8—42no—
311C8—42no—
312C8—81no—
313C8—81no—
314C8—81no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—82no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22C43×#39411yescharacteristic
323C22C43×#48011yescharacteristic
324C22C43×#48211yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—82no—
329C4—81no—
330C4C43×#44711yescharacteristic
331C4C43×#45211yescharacteristic
332C4C43×#46611yescharacteristic
333C4C43×#46811yescharacteristic
334C4C43×#47112yes—
335C2—21no—
336C2—21no—
337C2—82no—
338C2C43×#203311yescharacteristic
339C2C43×#204611yescharacteristic
340C2C43×#204911yescharacteristic
subgroupG/H
center, socleC22×C43#394
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#1571C2semidirect
4. C43×#1546C2semidirect
5. C43×#1546C2semidirect
7. C43×#1301C2semidirect
144. #10444C43direct (N × H)
167. #1571C2×C43semidirect
168. #1546C2×C43semidirect
169. #1546C2×C43semidirect
171. #1301C2×C43semidirect
195. C43#10444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4612
C43×#18002
C43×#15712
C43×#15462
C43×#14782
C43×#13012
#1044443