Finite Group Databasebeta

← C43×#8591 #24928608

Subgroups — C43×#8591 #24928608

Order 11008.

496 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊Q8×C43C211yesmaximal, characteristic
2C43×#1842C211yesmaximal, characteristic
3C43×#1831C211yesmaximal, characteristic
4C2×C43×#332C212yesmaximal
5C43×#1296C212yesmaximal
6C2×C4⋊Q8×C43C2211yescharacteristic
7C2×C4×Q8×C43—21no—
8C2×C4⋊C8×C43—21no—
9C2×C4⋊C8×C43—21no—
10C2×C4⋊C8×C43C2212yes—
11C2×C4⋊C8×C43C2212yes—
12C43×#391—21no—
13C43×#389—21no—
14C43×#389C412yes—
15C43×#384C2211yescharacteristic
16C4×C4⋊C4×C43—21no—
17C4×C4⋊C4×C43C412yes—
18C43×C43C2211yescharacteristic
19C43×#336—21no—
20C43×#336—21no—
21C43×#332—24no—
22C22×Q8×C43—21no—
23C22×C8×C43—22no—
24C22×C8×C43—22no—
25C4⋊Q8×C43—21no—
26C4⋊Q8×C43—21no—
27C4⋊Q8×C43D412yes—
28C4⋊Q8×C43Q812yes—
29C4×Q8×C43—44no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43C2×C412yes—
35C2×C4⋊C4×C43C2×C412yes—
36C2×C42×C43—22no—
37C2×C42×C43C2×C411yescharacteristic
38C2×C42×C43C2×C411yescharacteristic
39C2×C42×C43D411yescharacteristic
40C2×C42×C43D411yescharacteristic
41C2×C42×C43D411yescharacteristic
42C2×C42×C43D411yescharacteristic
43C2×C42×C43C2311yescharacteristic
44C4⋊C8×C43—22no—
45C4⋊C8×C43—22no—
46C4⋊C8×C43—22no—
47C4⋊C8×C43—22no—
48C4⋊C8×C43—42no—
49C4⋊C8×C43—42no—
50#95×C43—22no—
51#95×C43—22no—
52C2×Q8×C43—22no—
53C2×Q8×C43—22no—
54C2×Q8×C43—42no—
55C2×Q8×C43—42no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C2×C8×C43—42no—
66C2×C8×C43—42no—
67C2×C8×C43—42no—
68C2×C8×C43—42no—
69C2×C8×C43—42no—
70C2×C8×C43—42no—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—44no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43C4⋊C414yes—
80C42×C43—22no—
81C42×C43—22no—
82C42×C43—21no—
83C42×C43—22no—
84C42×C43—21no—
85C42×C43—41no—
86C42×C43—44no—
87C42×C43SD1612yes—
88C42×C43Q1612yes—
89C42×C43C2×D411yescharacteristic
90C42×C43C2×Q811yescharacteristic
91C42×C43#4111yescharacteristic
92C42×C43#4111yescharacteristic
93C23×C43C2×C22⋊C411yescharacteristic
94Q8×C43—44no—
95Q8×C43—44no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—24no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43#10112yes—
114C2×C4×C43#10312yes—
115C2×C4×C43#10312yes—
116C2×C4×C43C2×C4⋊C411yescharacteristic
117C2×C4×C43#11711yescharacteristic
118C2×C4×C43#12111yescharacteristic
119C2×C4×C43#12111yescharacteristic
120C2×C4×C43C22⋊Q811yescharacteristic
121C2×C4×C43C22⋊Q811yescharacteristic
122C2×C4×C43C2×SD1611yescharacteristic
123C2×C4×C43C2×Q1611yescharacteristic
124C2×C4×C43#13512yes—
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C43AGL(1,ℤ/8)12yes—
127C2×C4×C43#13711yescharacteristic
128C8×C43—82no—
129C8×C43—82no—
130#8591C4311yesmaximal, characteristic, direct product factor, Sylow
131C22×C43#38011yescharacteristic
132C22×C43C2×#10111yescharacteristic
133C22×C43#41311yescharacteristic
134C22×C43C2×#10311yescharacteristic
135C22×C43#41611yescharacteristic
136C22×C43#41711yescharacteristic
137C22×C43#41811yescharacteristic
138C4×C43—22no—
139C4×C43—21no—
140C4×C43—21no—
141C4×C43—22no—
142C4×C43—22no—
143C4×C43—44no—
144C4×C43—41no—
145C4×C43—82no—
146C4×C43#46011yescharacteristic
147C4×C43#46211yescharacteristic
148C4×C43#46312yes—
149C4×C43#47511yescharacteristic
150C4×C43#47711yescharacteristic
151C4×C43#47812yes—
152C4×C4⋊Q8C2×C4311yescharacteristic
153#1842C2×C4311yescharacteristic
154#1831C2×C4311yescharacteristic
155C2×#332C2×C4312yes—
156#1296C2×C4312yes—
157C2×C43#154211yescharacteristic
158C2×C43#154911yescharacteristic
159C2×C43#155211yescharacteristic
160C2×C43#155711yescharacteristic
161C2×C43#180111yescharacteristic
162C2×C43#180311yescharacteristic
163C2×C43#180411yescharacteristic
164C2×C4⋊Q8C22×C4311yescharacteristic
165C2×C4×Q8—21no—
166C2×C4⋊C8—21no—
167C2×C4⋊C8—21no—
168C2×C4⋊C8C22×C4312yes—
169C2×C4⋊C8C22×C4312yes—
170#391—21no—
171#389—21no—
172#389C4×C4312yes—
173#384C22×C4311yescharacteristic
174C4×C4⋊C4—21no—
175C4×C4⋊C4C4×C4312yes—
176C43C22×C4311yescharacteristic
177#336—21no—
178#336—21no—
179#332—24no—
180C43#859111yescharacteristic, direct product factor, Sylow
181C22×Q8—21no—
182C22×C8—22no—
183C22×C8—22no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8D4×C4312yes—
187C4⋊Q8Q8×C4312yes—
188C4×Q8—44no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×C4×C4312yes—
194C2×C4⋊C4C2×C4×C4312yes—
195C2×C42—22no—
196C2×C42C2×C4×C4311yescharacteristic
197C2×C42C2×C4×C4311yescharacteristic
198C2×C42D4×C4311yescharacteristic
199C2×C42D4×C4311yescharacteristic
200C2×C42D4×C4311yescharacteristic
201C2×C42D4×C4311yescharacteristic
202C2×C42C23×C4311yescharacteristic
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8—42no—
208C4⋊C8—42no—
209#95—22no—
210#95—22no—
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—42no—
214C2×Q8—42no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4C22⋊C4×C4311yescharacteristic
218C22×C4C22⋊C4×C4311yescharacteristic
219C22×C4C22⋊C4×C4311yescharacteristic
220C22×C4C22⋊C4×C4311yescharacteristic
221C22×C4C22×C4×C4311yescharacteristic
222C22×C4C2×D4×C4311yescharacteristic
223C22×C4C2×D4×C4311yescharacteristic
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—42no—
234C4⋊C4—44no—
235C4⋊C4—42no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4C4⋊C4×C4314yes—
239C42—22no—
240C42—22no—
241C42—21no—
242C42—22no—
243C42—21no—
244C42—41no—
245C42—44no—
246C42SD16×C4312yes—
247C42Q16×C4312yes—
248C42C2×D4×C4311yescharacteristic
249C42C2×Q8×C4311yescharacteristic
250C42#41×C4311yescharacteristic
251C42#41×C4311yescharacteristic
252C23C2×C22⋊C4×C4311yescharacteristic
253Q8—44no—
254Q8—44no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4#101×C4312yes—
273C2×C4#103×C4312yes—
274C2×C4#103×C4312yes—
275C2×C4C2×C4⋊C4×C4311yescharacteristic
276C2×C4#117×C4311yescharacteristic
277C2×C4#121×C4311yescharacteristic
278C2×C4#121×C4311yescharacteristic
279C2×C4C22⋊Q8×C4311yescharacteristic
280C2×C4C22⋊Q8×C4311yescharacteristic
281C2×C4C2×SD16×C4311yescharacteristic
282C2×C4C2×Q16×C4311yescharacteristic
283C2×C4#135×C4312yes—
284C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
285C2×C4AGL(1,ℤ/8)×C4312yes—
286C2×C4#137×C4311yescharacteristic
287C8—82no—
288C8—82no—
289C22C43×#38011yescharacteristic
290C22C2×#101×C4311yescharacteristic
291C22C43×#41311yescharacteristic
292C22C2×#103×C4311yescharacteristic
293C22C43×#41611yescharacteristic
294C22C43×#41711yescharacteristic
295C22C43×#41811yescharacteristic
296C4—22no—
297C4—22no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—44no—
303C4—82no—
304C4C43×#46011yescharacteristic
305C4C43×#46211yescharacteristic
306C4C43×#46312yes—
307C4C43×#47511yescharacteristic
308C4C43×#47711yescharacteristic
309C4C43×#47812yes—
310C2C43×#154211yescharacteristic
311C2C43×#154911yescharacteristic
312C2C43×#155211yescharacteristic
313C2C43×#155711yescharacteristic
314C2C43×#180111yescharacteristic
315C2C43×#180311yescharacteristic
316C2C43×#180411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
130. #8591C43direct (N × H)
180. C43#8591direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C4⋊Q8×C432
C43×#18422
C43×#18312
C2×C43×#3322
C43×#12962
#859143