Finite Group Databasebeta

← C43×#10848 #24930865

Subgroups — C43×#10848 #24930865

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#423C211yesmaximal, characteristic
2C2×C4×M16×C43C211yesmaximal, characteristic
3C43×#2285C211yesmaximal, characteristic
4C2×C43×#344C214yesmaximal
5C22×M16×C43C2212yes—
6C22×M16×C43C2212yes—
7C2×#117×C43C2212yes—
8C22×C42×C43C2211yescharacteristic
9C43×#423—21no—
10C43×#423—21no—
11C43×#423C414yescomplemented
12C2×C4⋊C8×C43—22no—
13C4×M16×C43—22no—
14C4×M16×C43—22no—
15C2×#97×C43C412yescomplemented
16C2×C4×C8×C43C412yescomplemented
17C43×#384—21no—
18C43×#382—21no—
19C43×#380C414yes—
20C4×C4⋊C4×C43—22no—
21C43×#344—28no—
22C23×C4×C43C2×C412yes—
23C23×C4×C43C2311yescharacteristic
24C2×M16×C43—22no—
25C2×M16×C43—22no—
26C2×M16×C43—22no—
27C2×M16×C43—22no—
28C2×M16×C43—22no—
29C2×M16×C43—24no—
30C2×M16×C43—24no—
31C2×M16×C43C2×C414yes—
32C2×M16×C43D414yes—
33C2×M16×C43Q814yes—
34C22×C8×C43—22no—
35C22×C8×C43C2×C414yes—
36#117×C43—24no—
37#117×C43—24no—
38C2×C4⋊C4×C43—24no—
39C2×C4⋊C4×C43—22no—
40C2×C22⋊C4×C43C2×C414yes—
41C2×C42×C43—22no—
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43C2×C412yes—
45C2×C42×C43D412yes—
46C2×C42×C43D412yes—
47C2×C42×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43Q811yescharacteristic
50C2×C42×C43Q811yescharacteristic
51C4⋊C8×C43—24no—
52C4⋊C8×C43—24no—
53#97×C43—24no—
54C4×C8×C43—24no—
55#95×C43—24no—
56C24×C43C22×C411yescharacteristic
57C22×C4×C43—24no—
58C22×C4×C43—44no—
59C22×C4×C43C4212yes—
60C22×C4×C43C4212yes—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C4⋊C412yes—
64C22×C4×C43C4⋊C412yes—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D412yes—
71C22×C4×C43C2×Q811yescharacteristic
72C22×C4×C43C2×Q812yes—
73C22×C4×C43#4112yes—
74C22×C4×C43#4112yes—
75M16×C43—24no—
76M16×C43—24no—
77M16×C43—24no—
78M16×C43—24no—
79M16×C43—28no—
80M16×C43—42no—
81M16×C43—42no—
82C2×C8×C43—24no—
83C2×C8×C43—24no—
84C2×C8×C43—24no—
85C2×C8×C43—44no—
86C2×C8×C43C4⋊C418yescomplemented
87C4⋊C4×C43—48no—
88C4⋊C4×C43—42no—
89C4⋊C4×C43—42no—
90C22⋊C4×C43—28no—
91C42×C43—44no—
92C42×C43C22⋊C412yes—
93C42×C43C22⋊C412yes—
94C42×C43C22⋊C412yes—
95C42×C43C22⋊C412yes—
96C42×C43C4⋊C411yescharacteristic
97C42×C43C4⋊C411yescharacteristic
98C42×C43C4⋊C411yescharacteristic
99C42×C43C4⋊C412yes—
100C42×C43C4⋊C412yes—
101C42×C43C4⋊C411yescharacteristic
102C23×C43—42no—
103C23×C43C2×C4211yescharacteristic
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43C2×C4⋊C411yescharacteristic
106C23×C43C4×D412yes—
107C23×C43C4×Q812yes—
108C2×C4×C43—24no—
109C2×C4×C43—24no—
110C2×C4×C43—24no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—48no—
115C2×C4×C43—44no—
116C2×C4×C43#9512yes—
117C2×C4×C43#9512yes—
118C2×C4×C43#9512yes—
119C2×C4×C43#9512yes—
120C2×C4×C43C2×C22⋊C411yescharacteristic
121C2×C4×C43C2×C22⋊C411yescharacteristic
122C2×C4×C43C2×C4⋊C412yes—
123C2×C4×C43C2×C4⋊C411yescharacteristic
124C2×C4×C43C2×C4⋊C411yescharacteristic
125C2×C4×C43#11712yes—
126C2×C4×C43C4×D412yes—
127C2×C4×C43C4×Q812yes—
128C2×C4×C43#12112yes—
129C2×C4×C43#12112yes—
130C2×C4×C43C22⋊Q812yes—
131C2×C4×C43C22⋊Q812yes—
132C2×C4×C43#12411yescharacteristic
133C2×C4×C43#12411yescharacteristic
134C2×C4×C43#12512yes—
135C2×C4×C43#12711yescharacteristic
136C2×C4×C43C4⋊Q812yes—
137C2×C4×C43C4⋊Q811yescharacteristic
138C8×C43—28no—
139C8×C43—44no—
140#10848C4311yesmaximal, characteristic, direct product factor, Sylow
141C22×C43—22no—
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—42no—
145C22×C43—42no—
146C22×C43C2×#9511yescharacteristic
147C22×C43C4×C4⋊C412yes—
148C22×C43#38912yes—
149C22×C43#39011yescharacteristic
150C22×C43#39111yescharacteristic
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—84no—
155C4×C43#34414yescomplemented
156C4×C43#38012yes—
157C4×C43#38211yescharacteristic
158C4×C43#38411yescharacteristic
159C4×C43#38912yes—
160C4×C43#39011yescharacteristic
161C4×C43#39111yescharacteristic
162C2×#423C2×C4311yescharacteristic
163C2×C4×M16C2×C4311yescharacteristic
164#2285C2×C4311yescharacteristic
165C2×#344C2×C4314yes—
166C2×C43—21no—
167C2×C43—22no—
168C2×C43—22no—
169C2×C43—21no—
170C2×C43C4⋊#9511yescharacteristic
171C2×C43C2×#34412yes—
172C22×M16C22×C4312yes—
173C22×M16C22×C4312yes—
174C2×#117C22×C4312yes—
175C22×C42C22×C4311yescharacteristic
176#423—21no—
177#423—21no—
178#423C4×C4314yescomplemented
179C2×C4⋊C8—22no—
180C4×M16—22no—
181C4×M16—22no—
182C2×#97C4×C4312yescomplemented
183C2×C4×C8C4×C4312yescomplemented
184#384—21no—
185#382—21no—
186#380C4×C4314yes—
187C4×C4⋊C4—22no—
188#344—28no—
189C43#1084811yescharacteristic, direct product factor, Sylow
190C23×C4C2×C4×C4312yes—
191C23×C4C23×C4311yescharacteristic
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16—24no—
198C2×M16—24no—
199C2×M16C2×C4×C4314yes—
200C2×M16D4×C4314yes—
201C2×M16Q8×C4314yes—
202C22×C8—22no—
203C22×C8C2×C4×C4314yes—
204#117—24no—
205#117—24no—
206C2×C4⋊C4—24no—
207C2×C4⋊C4—22no—
208C2×C22⋊C4C2×C4×C4314yes—
209C2×C42—22no—
210C2×C42C2×C4×C4311yescharacteristic
211C2×C42C2×C4×C4311yescharacteristic
212C2×C42C2×C4×C4312yes—
213C2×C42D4×C4312yes—
214C2×C42D4×C4312yes—
215C2×C42D4×C4311yescharacteristic
216C2×C42D4×C4311yescharacteristic
217C2×C42Q8×C4311yescharacteristic
218C2×C42Q8×C4311yescharacteristic
219C4⋊C8—24no—
220C4⋊C8—24no—
221#97—24no—
222C4×C8—24no—
223#95—24no—
224C24C22×C4×C4311yescharacteristic
225C22×C4—24no—
226C22×C4—44no—
227C22×C4C42×C4312yes—
228C22×C4C42×C4312yes—
229C22×C4C22⋊C4×C4312yes—
230C22×C4C22⋊C4×C4312yes—
231C22×C4C4⋊C4×C4312yes—
232C22×C4C4⋊C4×C4312yes—
233C22×C4C22×C4×C4311yescharacteristic
234C22×C4C22×C4×C4311yescharacteristic
235C22×C4C2×D4×C4311yescharacteristic
236C22×C4C2×D4×C4311yescharacteristic
237C22×C4C2×D4×C4311yescharacteristic
238C22×C4C2×D4×C4312yes—
239C22×C4C2×Q8×C4311yescharacteristic
240C22×C4C2×Q8×C4312yes—
241C22×C4#41×C4312yes—
242C22×C4#41×C4312yes—
243M16—24no—
244M16—24no—
245M16—24no—
246M16—24no—
247M16—28no—
248M16—42no—
249M16—42no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—24no—
253C2×C8—44no—
254C2×C8C4⋊C4×C4318yescomplemented
255C4⋊C4—48no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C22⋊C4—28no—
259C42—44no—
260C42C22⋊C4×C4312yes—
261C42C22⋊C4×C4312yes—
262C42C22⋊C4×C4312yes—
263C42C22⋊C4×C4312yes—
264C42C4⋊C4×C4311yescharacteristic
265C42C4⋊C4×C4311yescharacteristic
266C42C4⋊C4×C4311yescharacteristic
267C42C4⋊C4×C4312yes—
268C42C4⋊C4×C4312yes—
269C42C4⋊C4×C4311yescharacteristic
270C23—42no—
271C23C2×C42×C4311yescharacteristic
272C23C2×C22⋊C4×C4311yescharacteristic
273C23C2×C4⋊C4×C4311yescharacteristic
274C23C4×D4×C4312yes—
275C23C4×Q8×C4312yes—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—48no—
283C2×C4—44no—
284C2×C4#95×C4312yes—
285C2×C4#95×C4312yes—
286C2×C4#95×C4312yes—
287C2×C4#95×C4312yes—
288C2×C4C2×C22⋊C4×C4311yescharacteristic
289C2×C4C2×C22⋊C4×C4311yescharacteristic
290C2×C4C2×C4⋊C4×C4312yes—
291C2×C4C2×C4⋊C4×C4311yescharacteristic
292C2×C4C2×C4⋊C4×C4311yescharacteristic
293C2×C4#117×C4312yes—
294C2×C4C4×D4×C4312yes—
295C2×C4C4×Q8×C4312yes—
296C2×C4#121×C4312yes—
297C2×C4#121×C4312yes—
298C2×C4C22⋊Q8×C4312yes—
299C2×C4C22⋊Q8×C4312yes—
300C2×C4#124×C4311yescharacteristic
301C2×C4#124×C4311yescharacteristic
302C2×C4#125×C4312yes—
303C2×C4#127×C4311yescharacteristic
304C2×C4C4⋊Q8×C4312yes—
305C2×C4C4⋊Q8×C4311yescharacteristic
306C8—28no—
307C8—44no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—42no—
312C22—42no—
313C22C2×#95×C4311yescharacteristic
314C22C4×C4⋊C4×C4312yes—
315C22C43×#38912yes—
316C22C43×#39011yescharacteristic
317C22C43×#39111yescharacteristic
318C4—22no—
319C4—22no—
320C4—22no—
321C4—84no—
322C4C43×#34414yescomplemented
323C4C43×#38012yes—
324C4C43×#38211yescharacteristic
325C4C43×#38411yescharacteristic
326C4C43×#38912yes—
327C4C43×#39011yescharacteristic
328C4C43×#39111yescharacteristic
329C2—21no—
330C2—22no—
331C2—22no—
332C2—21no—
333C2C43×C4⋊#9511yescharacteristic
334C2C2×C43×#34412yes—
subgroupG/H
centerC2×C4×C43C2×C22⋊C4
commutatorC23C2×C42×C43
Frattini, cosocleC23×C4C23×C43
socleC22×C43C2×#95
prime radicalC24×C43C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
11. C43×#423C4semidirect
15. C2×#97×C43C4semidirect
16. C2×C4×C8×C43C4semidirect
86. C2×C8×C43C4⋊C4semidirect
140. #10848C43direct (N × H)
155. C4×C43#344semidirect
178. #423C4×C43semidirect
182. C2×#97C4×C43semidirect
183. C2×C4×C8C4×C43semidirect
189. C43#10848direct (N × H)
254. C2×C8C4⋊C4×C43semidirect
322. C4C43×#344semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4232
C2×C4×M16×C432
C43×#22852
C2×C43×#3442
#1084843