Finite Group Databasebeta

← C43×#10597 #24930614

Subgroups — C43×#10597 #24930614

Order 11008.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#1990C211yesmaximal, characteristic
2C43×#1987C211yesmaximal, characteristic
3C43×#1948C211yesmaximal, characteristic
4C43×#1939C211yesmaximal, characteristic
5C2×C43×#334C211yesmaximal, characteristic
6C2×C43×#333C211yesmaximal, characteristic
7C43×#1296C211yesmaximal, characteristic
8C2×C4⋊Q8×C43C2211yescharacteristic
9C2×#106×C43—21no—
10C2×C4⋊C8×C43—21no—
11C2×C4⋊C8×C43C2211yescharacteristic
12C2×C4⋊C8×C43C2211yescharacteristic
13C2×C4⋊C8×C43C2211yescharacteristic
14C2×C4×C8×C43C2211yescharacteristic
15C43×#384C2211yescharacteristic
16C4×C4⋊C4×C43C2211yescharacteristic
17C43×#340—21no—
18C43×#340—21no—
19C43×#340—21no—
20C43×#340—21no—
21C43×#340—21no—
22C43×#336—21no—
23C43×#334—22no—
24C43×#333—22no—
25C22×Q8×C43—21no—
26C22×C8×C43—21no—
27C22×C8×C43—21no—
28C22×C8×C43—21no—
29C22×C8×C43D411yescharacteristic
30C22×C8×C43D411yescharacteristic
31C4⋊Q8×C43—21no—
32C4⋊Q8×C43—21no—
33C4⋊Q8×C43—21no—
34C4⋊Q8×C43Q812yes—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C42×C43—21no—
43C2×C42×C43C2311yescharacteristic
44#106×C43—42no—
45C4⋊C8×C43—21no—
46C4⋊C8×C43—21no—
47C4⋊C8×C43—21no—
48C4⋊C8×C43—21no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43—42no—
51C4⋊C8×C43D412yes—
52C4×C8×C43—21no—
53C4×C8×C43—21no—
54#95×C43—21no—
55C2×Q8×C43—22no—
56C2×Q8×C43—41no—
57C2×Q8×C43—81no—
58C2×Q8×C43—81no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43#4111yescharacteristic
66C2×C8×C43—21no—
67C2×C8×C43—21no—
68C2×C8×C43—21no—
69C2×C8×C43—22no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43SD1612yes—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—22no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—81no—
93C4⋊C4×C43SD1612yes—
94C42×C43—41no—
95C42×C43—41no—
96C42×C43C2×D411yescharacteristic
97C42×C43C2×Q811yescharacteristic
98C42×C43#4111yescharacteristic
99C42×C43#4111yescharacteristic
100C23×C43#12111yescharacteristic
101Q8×C43—82no—
102Q8×C43—82no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43—81no—
116C2×C4×C43—81no—
117C2×C4×C43#12111yescharacteristic
118C2×C4×C43#12111yescharacteristic
119C2×C4×C43C22⋊Q811yescharacteristic
120C2×C4×C43C22⋊Q811yescharacteristic
121C2×C4×C43C22⋊Q811yescharacteristic
122C2×C4×C43#12611yescharacteristic
123C2×C4×C43C2×SD1611yescharacteristic
124C2×C4×C43C2×SD1611yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C8×C43—22no—
132C8×C43—42no—
133C8×C43—41no—
134C8×C43—81no—
135C8×C43—81no—
136#10597C4311yesmaximal, characteristic, direct product factor, Sylow
137C22×C43#39611yescharacteristic
138C22×C43#46111yescharacteristic
139C22×C43#46411yescharacteristic
140C22×C43#46511yescharacteristic
141C22×C43#47011yescharacteristic
142C22×C43#47111yescharacteristic
143C22×C43#47211yescharacteristic
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—42no—
147C4×C43—82no—
148C4×C43—81no—
149C4×C43—161no—
150C4×C43#46111yescharacteristic
151C4×C43#46411yescharacteristic
152C4×C43#46511yescharacteristic
153C4×C43#47011yescharacteristic
154C4×C43#47511yescharacteristic
155C4×C43#47511yescharacteristic
156C4×C43#47911yescharacteristic
157C4×C43#47911yescharacteristic
158#1990C2×C4311yescharacteristic
159#1987C2×C4311yescharacteristic
160#1948C2×C4311yescharacteristic
161#1939C2×C4311yescharacteristic
162C2×#334C2×C4311yescharacteristic
163C2×#333C2×C4311yescharacteristic
164#1296C2×C4311yescharacteristic
165C2×C43#167111yescharacteristic
166C2×C43#167811yescharacteristic
167C2×C43#169511yescharacteristic
168C2×C43#170411yescharacteristic
169C2×C43#206311yescharacteristic
170C2×C43#206611yescharacteristic
171C2×C43#206611yescharacteristic
172C2×C4⋊Q8C22×C4311yescharacteristic
173C2×#106—21no—
174C2×C4⋊C8—21no—
175C2×C4⋊C8C22×C4311yescharacteristic
176C2×C4⋊C8C22×C4311yescharacteristic
177C2×C4⋊C8C22×C4311yescharacteristic
178C2×C4×C8C22×C4311yescharacteristic
179#384C22×C4311yescharacteristic
180C4×C4⋊C4C22×C4311yescharacteristic
181#340—21no—
182#340—21no—
183#340—21no—
184#340—21no—
185#340—21no—
186#336—21no—
187#334—22no—
188#333—22no—
189C43#1059711yescharacteristic, direct product factor, Sylow
190C22×Q8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8D4×C4311yescharacteristic
195C22×C8D4×C4311yescharacteristic
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8Q8×C4312yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4D4×C4311yescharacteristic
206C2×C4⋊C4D4×C4311yescharacteristic
207C2×C42—21no—
208C2×C42C23×C4311yescharacteristic
209#106—42no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—42no—
216C4⋊C8D4×C4312yes—
217C4×C8—21no—
218C4×C8—21no—
219#95—21no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4C2×D4×C4311yescharacteristic
229C22×C4C2×D4×C4311yescharacteristic
230C22×C4#41×C4311yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—22no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8SD16×C4312yes—
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4SD16×C4312yes—
259C42—41no—
260C42—41no—
261C42C2×D4×C4311yescharacteristic
262C42C2×Q8×C4311yescharacteristic
263C42#41×C4311yescharacteristic
264C42#41×C4311yescharacteristic
265C23#121×C4311yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4#121×C4311yescharacteristic
283C2×C4#121×C4311yescharacteristic
284C2×C4C22⋊Q8×C4311yescharacteristic
285C2×C4C22⋊Q8×C4311yescharacteristic
286C2×C4C22⋊Q8×C4311yescharacteristic
287C2×C4#126×C4311yescharacteristic
288C2×C4C2×SD16×C4311yescharacteristic
289C2×C4C2×SD16×C4311yescharacteristic
290C2×C4#135×C4311yescharacteristic
291C2×C4#135×C4311yescharacteristic
292C2×C4#137×C4311yescharacteristic
293C2×C4#137×C4311yescharacteristic
294C2×C4#137×C4311yescharacteristic
295C2×C4#137×C4311yescharacteristic
296C8—22no—
297C8—42no—
298C8—41no—
299C8—81no—
300C8—81no—
301C22C43×#39611yescharacteristic
302C22C43×#46111yescharacteristic
303C22C43×#46411yescharacteristic
304C22C43×#46511yescharacteristic
305C22C43×#47011yescharacteristic
306C22C43×#47111yescharacteristic
307C22C43×#47211yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—82no—
312C4—81no—
313C4—161no—
314C4C43×#46111yescharacteristic
315C4C43×#46411yescharacteristic
316C4C43×#46511yescharacteristic
317C4C43×#47011yescharacteristic
318C4C43×#47511yescharacteristic
319C4C43×#47511yescharacteristic
320C4C43×#47911yescharacteristic
321C4C43×#47911yescharacteristic
322C2C43×#167111yescharacteristic
323C2C43×#167811yescharacteristic
324C2C43×#169511yescharacteristic
325C2C43×#170411yescharacteristic
326C2C43×#206311yescharacteristic
327C2C43×#206611yescharacteristic
328C2C43×#206611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C43#121
commutator, Frattini, cosocleC2×C42C23×C43
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
136. #10597C43direct (N × H)
189. C43#10597direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#19902
C43×#19872
C43×#19482
C43×#19392
C2×C43×#3342
C2×C43×#3332
C43×#12962
#1059743