Finite Group Databasebeta

← C43×#14471 #24934488

Subgroups — C43×#14471 #24934488

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#391C211yesmaximal, characteristic
2C43×#1446C212yesmaximal
3C43×#1442C214yesmaximal
4C43×#1436C212yesmaximal
5C43×#1436C214yesmaximal
6C43×C4⋊#95C212yesmaximal
7C23×Q8×C43C2211yescharacteristic
8C22×C4⋊C4×C43C2212yes—
9C22×C4⋊C4×C43C2211yescharacteristic
10C22×C4⋊C4×C43C2212yes—
11C22×C42×C43C2212yes—
12C22×C42×C43C2211yescharacteristic
13C43×#391C418yescomplemented
14C2×#95×C43C2214yes—
15C2×#95×C43C2214yes—
16C2×#95×C43C2214yes—
17C2×#95×C43C2212yes—
18C2×#95×C43C2212yes—
19C2×#95×C43C2214yes—
20C2×#95×C43C2212yes—
21C2×#95×C43C2214yes—
22C22×Q8×C43—24no—
23C22×Q8×C43—42no—
24C22×Q8×C43—41no—
25C22×Q8×C43—41no—
26C22×Q8×C43C2×C414yes—
27C23×C4×C43C2314yes—
28C23×C4×C43C2312yes—
29C23×C4×C43C2312yes—
30C23×C4×C43C2314yes—
31C23×C4×C43C2312yes—
32C23×C4×C43C2311yescharacteristic
33C2×C4⋊C4×C43—24no—
34C2×C4⋊C4×C43—41no—
35C2×C4⋊C4×C43—41no—
36C2×C4⋊C4×C43—42no—
37C2×C4⋊C4×C43—42no—
38C2×C4⋊C4×C43—42no—
39C2×C4⋊C4×C43—42no—
40C2×C4⋊C4×C43C2×C414yes—
41C2×C4⋊C4×C43Q818yescomplemented
42C2×C42×C43—42no—
43C2×C42×C43—42no—
44C2×C42×C43—44no—
45C2×C42×C43C2×C414yes—
46#95×C43—28no—
47#95×C43—28no—
48#95×C43—42no—
49#95×C43—44no—
50#95×C43—44no—
51#95×C43—42no—
52#95×C43—42no—
53#95×C43C2×C4116yes—
54C24×C43C2411yescharacteristic
55C2×Q8×C43—28no—
56C2×Q8×C43—44no—
57C2×Q8×C43—44no—
58C2×Q8×C43—48no—
59C2×Q8×C43—48no—
60C22×C4×C43—24no—
61C22×C4×C43—24no—
62C22×C4×C43—24no—
63C22×C4×C43—24no—
64C22×C4×C43—24no—
65C22×C4×C43—24no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—24no—
73C22×C4×C43—24no—
74C22×C4×C43—24no—
75C22×C4×C43—24no—
76C22×C4×C43—22no—
77C22×C4×C43—24no—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—24no—
82C22×C4×C43—24no—
83C22×C4×C43—24no—
84C22×C4×C43—24no—
85C22×C4×C43—22no—
86C22×C4×C43—24no—
87C22×C4×C43—24no—
88C22×C4×C43C22×C414yes—
89C22×C4×C43C22×C414yes—
90C22×C4×C43C22×C412yes—
91C22×C4×C43C22×C414yes—
92C22×C4×C43C2×Q818yes—
93C22×C4×C43C2×Q814yes—
94C22×C4×C43#4114yes—
95C22×C4×C43#4114yes—
96C4⋊C4×C43—44no—
97C4⋊C4×C43—48no—
98C4⋊C4×C43—48no—
99C42×C43—44no—
100C42×C43—48no—
101C23×C43C23×C411yescharacteristic
102C23×C43C22×Q812yes—
103C23×C43C2×#4112yes—
104C23×C43C2×#4112yes—
105C23×C43H(5,𝔽2)12yes—
106C23×C43H(5,𝔽2)11yescharacteristic
107C23×C43H(5,𝔽2)11yescharacteristic
108C23×C43H(5,𝔽2)12yes—
109C23×C432−1+412yes—
110Q8×C43—416no—
111C2×C4×C43—24no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—24no—
115C2×C4×C43—24no—
116C2×C4×C43—24no—
117C2×C4×C43—24no—
118C2×C4×C43—24no—
119C2×C4×C43—24no—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—24no—
123C2×C4×C43—24no—
124C2×C4×C43—24no—
125C2×C4×C43—28no—
126C2×C4×C43—28no—
127C2×C4×C43—28no—
128C2×C4×C43—28no—
129C2×C4×C43—44no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43—44no—
133C2×C4×C43—44no—
134C2×C4×C43—42no—
135C2×C4×C43—44no—
136C2×C4×C43—44no—
137C2×C4×C43—42no—
138C2×C4×C43—44no—
139C2×C4×C43—44no—
140C2×C4×C43—44no—
141C2×C4×C43—44no—
142C2×C4×C43—44no—
143C2×C4×C43—44no—
144C2×C4×C43—44no—
145C2×C4×C43#11714yes—
146C2×C4×C43C4×Q818yes—
147#14471C4311yesmaximal, characteristic, direct product factor, Sylow
148C22×C43C2×#11711yescharacteristic
149C22×C43C2×C4×Q812yes—
150C22×C43#51811yescharacteristic
151C22×C43#51811yescharacteristic
152C22×C43#52012yes—
153C22×C43#53812yes—
154C22×C43#53812yes—
155C22×C43#53812yes—
156C22×C43#53912yes—
157C22×C43#54312yes—
158C22×C43#54412yes—
159C22×C43#55412yes—
160C22×C43#55412yes—
161C22×C43#55511yescharacteristic
162C22×C43#55612yes—
163C22×C43#55712yes—
164C22×C43Q8211yescharacteristic
165C22×C43#55912yes—
166C22×C43H(3,𝔽4)11yescharacteristic
167C22×C43#56212yes—
168C22×C43#56311yescharacteristic
169C4×C43—24no—
170C4×C43—28no—
171C4×C43—44no—
172C4×C43—44no—
173C4×C43—48no—
174C4×C43—84no—
175C2×#391C2×C4311yescharacteristic
176#1446C2×C4312yes—
177#1442C2×C4314yes—
178#1436C2×C4312yes—
179#1436C2×C4314yes—
180C4⋊#95C2×C4312yes—
181C2×C43#231211yescharacteristic
182C2×C43#232912yes—
183C2×C43#235512yes—
184C2×C43#236911yescharacteristic
185C2×C43#237911yescharacteristic
186C2×C43#280412yes—
187C2×C43#280512yes—
188C2×C43#280612yes—
189C2×C43#280812yes—
190C23×Q8C22×C4311yescharacteristic
191C22×C4⋊C4C22×C4312yes—
192C22×C4⋊C4C22×C4311yescharacteristic
193C22×C4⋊C4C22×C4312yes—
194C22×C42C22×C4312yes—
195C22×C42C22×C4311yescharacteristic
196#391C4×C4318yescomplemented
197C2×#95C22×C4314yes—
198C2×#95C22×C4314yes—
199C2×#95C22×C4314yes—
200C2×#95C22×C4312yes—
201C2×#95C22×C4312yes—
202C2×#95C22×C4314yes—
203C2×#95C22×C4312yes—
204C2×#95C22×C4314yes—
205C43#1447111yescharacteristic, direct product factor, Sylow
206C22×Q8—24no—
207C22×Q8—42no—
208C22×Q8—41no—
209C22×Q8—41no—
210C22×Q8C2×C4×C4314yes—
211C23×C4C23×C4314yes—
212C23×C4C23×C4312yes—
213C23×C4C23×C4312yes—
214C23×C4C23×C4314yes—
215C23×C4C23×C4312yes—
216C23×C4C23×C4311yescharacteristic
217C2×C4⋊C4—24no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—42no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4C2×C4×C4314yes—
225C2×C4⋊C4Q8×C4318yescomplemented
226C2×C42—42no—
227C2×C42—44no—
228C2×C42—42no—
229C2×C42C2×C4×C4314yes—
230#95—28no—
231#95—28no—
232#95—42no—
233#95—44no—
234#95—44no—
235#95—42no—
236#95—42no—
237#95C2×C4×C43116yes—
238C24C24×C4311yescharacteristic
239C2×Q8—28no—
240C2×Q8—44no—
241C2×Q8—44no—
242C2×Q8—48no—
243C2×Q8—48no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4C22×C4×C4314yes—
273C22×C4C22×C4×C4314yes—
274C22×C4C22×C4×C4312yes—
275C22×C4C22×C4×C4314yes—
276C22×C4C2×Q8×C4318yes—
277C22×C4C2×Q8×C4314yes—
278C22×C4#41×C4314yes—
279C22×C4#41×C4314yes—
280C4⋊C4—44no—
281C4⋊C4—48no—
282C4⋊C4—48no—
283C42—44no—
284C42—48no—
285C23C23×C4×C4311yescharacteristic
286C23C22×Q8×C4312yes—
287C23C2×#41×C4312yes—
288C23C2×#41×C4312yes—
289C23H(5,𝔽2)×C4312yes—
290C23H(5,𝔽2)×C4311yescharacteristic
291C23H(5,𝔽2)×C4311yescharacteristic
292C23H(5,𝔽2)×C4312yes—
293C232−1+4×C4312yes—
294Q8—416no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—28no—
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4#117×C4314yes—
330C2×C4C4×Q8×C4318yes—
331C22C2×#117×C4311yescharacteristic
332C22C2×C4×Q8×C4312yes—
333C22C43×#51811yescharacteristic
334C22C43×#51811yescharacteristic
335C22C43×#52012yes—
336C22C43×#53812yes—
337C22C43×#53812yes—
338C22C43×#53812yes—
339C22C43×#53912yes—
340C22C43×#54312yes—
341C22C43×#54412yes—
342C22C43×#55412yes—
343C22C43×#55412yes—
344C22C43×#55511yescharacteristic
345C22C43×#55612yes—
346C22C43×#55712yes—
347C22Q82×C4311yescharacteristic
348C22C43×#55912yes—
349C22C43×H(3,𝔽4)11yescharacteristic
350C22C43×#56212yes—
351C22C43×#56311yescharacteristic
352C4—28no—
353C4—24no—
354C4—44no—
355C4—48no—
356C4—44no—
357C4—84no—
358C2C43×#231211yescharacteristic
359C2C43×#232912yes—
360C2C43×#235512yes—
361C2C43×#236911yescharacteristic
362C2C43×#237911yescharacteristic
363C2C43×#280412yes—
364C2C43×#280512yes—
365C2C43×#280612yes—
366C2C43×#280812yes—
subgroupG/H
center, socle, prime radicalC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
13. C43×#391C4semidirect
41. C2×C4⋊C4×C43Q8semidirect
147. #14471C43direct (N × H)
196. #391C4×C43semidirect
205. C43#14471direct (N × H)
225. C2×C4⋊C4Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3912
C43×#14462
C43×#14422
C43×#14362
C43×C4⋊#952
#1447143