Finite Group Databasebeta

← C43×#10948 #24930965

Subgroups — C43×#10948 #24930965

Order 11008.

1074 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#418C212yesmaximal
2C43×#2873C211yesmaximal, characteristic, complemented
3C43×#2309C211yesmaximal, characteristic
4C43×#1740C211yesmaximal, characteristic, complemented
5C2×C43×H(3,ℤ/4)C212yesmaximal, complemented
6C23×D4×C43C2211yescharacteristic
7C22×M16×C43C2212yes—
8C2×#117×C43C2212yes—
9C2×#117×C43C2211yescharacteristic
10C2×#117×C43C2211yescharacteristic
11C43×#418—24no—
12C43×#418C418yescomplemented
13C2×#102×C43—24no—
14C43×#405—24no—
15C4×M16×C43—22no—
16C43×#390—22no—
17C43×#390C414yescomplemented
18C43×#379—22no—
19C43×#342—22no—
20C43×H(3,ℤ/4)—24no—
21C25×C43—21no—
22C22×D4×C43—22no—
23C22×D4×C43—22no—
24C22×D4×C43—21no—
25C22×D4×C43—22no—
26C22×D4×C43—22no—
27C22×D4×C43—22no—
28C22×D4×C43C2×C412yes—
29C22×D4×C43C2×C414yes—
30C23×C4×C43C2311yescharacteristic
31C2×M16×C43—22no—
32C2×M16×C43—22no—
33C2×M16×C43—22no—
34C2×M16×C43—22no—
35C2×M16×C43C2×C414yes—
36C2×M16×C43D414yes—
37C22×C8×C43D414yes—
38#117×C43—22no—
39#117×C43—22no—
40#117×C43—22no—
41#117×C43—22no—
42#117×C43—22no—
43#117×C43—22no—
44#117×C43—22no—
45#117×C43C2×C414yes—
46C2×C4⋊C4×C43—22no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43C2×C412yes—
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—28no—
52C2×C22⋊C4×C43D412yes—
53C2×C42×C43—22no—
54C2×C42×C43C2×C412yes—
55C2×C42×C43D412yes—
56#102×C43—216no—
57#97×C43—24no—
58C4×C8×C43—24no—
59C24×C43—22no—
60C24×C43—24no—
61C24×C43—42no—
62C24×C43—41no—
63C24×C43—41no—
64C24×C43—84no—
65C24×C43C2×D411yescharacteristic
66C2×D4×C43—22no—
67C2×D4×C43—24no—
68C2×D4×C43—24no—
69C2×D4×C43—24no—
70C2×D4×C43—24no—
71C2×D4×C43—24no—
72C2×D4×C43—24no—
73C2×D4×C43—24no—
74C2×D4×C43—41no—
75C2×D4×C43—42no—
76C2×D4×C43—42no—
77C2×D4×C43—41no—
78C2×D4×C43—42no—
79C2×D4×C43—42no—
80C2×D4×C43—42no—
81C2×D4×C43C4214yes—
82C22×C4×C43—22no—
83C22×C4×C43—42no—
84C22×C4×C43C22⋊C414yes—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C22×C412yes—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43#4112yes—
91C22×C4×C43#4112yes—
92C22×C4×C43#4112yes—
93M16×C43—24no—
94M16×C43—24no—
95M16×C43—24no—
96M16×C43—24no—
97C2×C8×C43—24no—
98C2×C8×C43—24no—
99C2×C8×C43C22⋊C418yescomplemented
100C4⋊C4×C43—24no—
101C4⋊C4×C43—24no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—42no—
104C22⋊C4×C43—24no—
105C22⋊C4×C43—24no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—42no—
109C22⋊C4×C43—88no—
110C42×C43—22no—
111C42×C43—22no—
112C42×C43—24no—
113C42×C43—24no—
114C42×C43—42no—
115C23×C43—24no—
116C23×C43—42no—
117C23×C43—48no—
118C23×C43—42no—
119C23×C43—44no—
120C23×C43—42no—
121C23×C43—44no—
122C23×C43—88no—
123C23×C43—88no—
124C23×C43—84no—
125C23×C43—84no—
126C23×C43C2×C22⋊C411yescharacteristic
127C23×C43C4×D412yes—
128C23×C43#12112yes—
129C23×C43#12411yescharacteristic
130C23×C43#12711yescharacteristic
131D4×C43—28no—
132D4×C43—44no—
133D4×C43—44no—
134D4×C43—44no—
135C2×C4×C43—24no—
136C2×C4×C43—44no—
137C2×C4×C43—44no—
138C2×C4×C43—42no—
139C2×C4×C43—44no—
140C2×C4×C43—84no—
141C2×C4×C43C2×C4211yescharacteristic
142C2×C4×C43C2×C22⋊C412yes—
143C2×C4×C43#11712yes—
144C2×C4×C43#11711yescharacteristic
145C2×C4×C43C4×D412yes—
146C2×C4×C43C4×D412yes—
147C2×C4×C43C4×D412yes—
148C2×C4×C43C4×D412yes—
149C2×C4×C43C4×D412yes—
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12112yes—
152C2×C4×C43#12112yes—
153C2×C4×C43#12312yes—
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43#12412yes—
156C2×C4×C43#12612yes—
157C8×C43—28no—
158#10948C4311yesmaximal, characteristic, direct product factor, Sylow
159C22×C43—22no—
160C22×C43—24no—
161C22×C43—42no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—48no—
165C22×C43—44no—
166C22×C43—84no—
167C22×C43—88no—
168C22×C43—88no—
169C22×C43—84no—
170C22×C43C4×C22⋊C411yescharacteristic
171C22×C43#38611yescharacteristic
172C22×C43#38812yes—
173C22×C43#39011yescharacteristic
174C22×C43#39012yes—
175C4×C43—44no—
176C4×C43—82no—
177C4×C43—84no—
178C4×C43C4×C22⋊C412yes—
179C4×C43#38612yes—
180C4×C43#38812yes—
181C4×C43#38812yes—
182C2×#418C2×C4312yes—
183#2873C2×C4311yescharacteristic, complemented
184#2309C2×C4311yescharacteristic
185#1740C2×C4311yescharacteristic, complemented
186C2×H(3,ℤ/4)C2×C4312yescomplemented
187C2×C43—21no—
188C2×C43—22no—
189C2×C43—21no—
190C2×C43—22no—
191C2×C43—84no—
192C2×C43#143711yescharacteristic
193C2×C43#191012yes—
194C23×D4C22×C4311yescharacteristic
195C22×M16C22×C4312yes—
196C2×#117C22×C4312yes—
197C2×#117C22×C4311yescharacteristic
198C2×#117C22×C4311yescharacteristic
199#418—24no—
200#418C4×C4318yescomplemented
201C2×#102—24no—
202#405—24no—
203C4×M16—22no—
204#390—22no—
205#390C4×C4314yescomplemented
206#379—22no—
207#342—22no—
208H(3,ℤ/4)—24no—
209C43#1094811yescharacteristic, direct product factor, Sylow
210C25—21no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—21no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4C2×C4×C4312yes—
218C22×D4C2×C4×C4314yes—
219C23×C4C23×C4311yescharacteristic
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—22no—
224C2×M16C2×C4×C4314yes—
225C2×M16D4×C4314yes—
226C22×C8D4×C4314yes—
227#117—22no—
228#117—22no—
229#117—22no—
230#117—22no—
231#117—22no—
232#117—22no—
233#117—22no—
234#117C2×C4×C4314yes—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×C4×C4312yes—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—28no—
241C2×C22⋊C4D4×C4312yes—
242C2×C42—22no—
243C2×C42C2×C4×C4312yes—
244C2×C42D4×C4312yes—
245#102—216no—
246#97—24no—
247C4×C8—24no—
248C24—22no—
249C24—24no—
250C24—42no—
251C24—41no—
252C24—41no—
253C24—84no—
254C24C2×D4×C4311yescharacteristic
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—22no—
258C2×D4—24no—
259C2×D4—24no—
260C2×D4—24no—
261C2×D4—24no—
262C2×D4—24no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4C42×C4314yes—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4C22⋊C4×C4314yes—
274C22×C4C22×C4×C4312yes—
275C22×C4C22×C4×C4311yescharacteristic
276C22×C4C2×D4×C4312yes—
277C22×C4C2×D4×C4312yes—
278C22×C4C2×D4×C4311yescharacteristic
279C22×C4#41×C4312yes—
280C22×C4#41×C4312yes—
281C22×C4#41×C4312yes—
282M16—24no—
283M16—24no—
284M16—24no—
285M16—24no—
286C2×C8—24no—
287C2×C8—24no—
288C2×C8C22⋊C4×C4318yescomplemented
289C4⋊C4—24no—
290C4⋊C4—24no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C22⋊C4—24no—
294C22⋊C4—24no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—42no—
298C22⋊C4—88no—
299C42—22no—
300C42—22no—
301C42—24no—
302C42—24no—
303C42—42no—
304C23—24no—
305C23—42no—
306C23—48no—
307C23—42no—
308C23—44no—
309C23—42no—
310C23—44no—
311C23—88no—
312C23—88no—
313C23—84no—
314C23—84no—
315C23C2×C22⋊C4×C4311yescharacteristic
316C23C4×D4×C4312yes—
317C23#121×C4312yes—
318C23#124×C4311yescharacteristic
319C23#127×C4311yescharacteristic
320D4—28no—
321D4—44no—
322D4—44no—
323D4—44no—
324C2×C4—24no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—84no—
330C2×C4C2×C42×C4311yescharacteristic
331C2×C4C2×C22⋊C4×C4312yes—
332C2×C4#117×C4312yes—
333C2×C4#117×C4311yescharacteristic
334C2×C4C4×D4×C4312yes—
335C2×C4C4×D4×C4312yes—
336C2×C4C4×D4×C4312yes—
337C2×C4C4×D4×C4312yes—
338C2×C4C4×D4×C4312yes—
339C2×C4#120×C4311yescharacteristic
340C2×C4#121×C4312yes—
341C2×C4#121×C4312yes—
342C2×C4#123×C4312yes—
343C2×C4#123×C4311yescharacteristic
344C2×C4#124×C4312yes—
345C2×C4#126×C4312yes—
346C8—28no—
347C22—22no—
348C22—24no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—48no—
353C22—44no—
354C22—84no—
355C22—88no—
356C22—88no—
357C22—84no—
358C22C4×C22⋊C4×C4311yescharacteristic
359C22C43×#38611yescharacteristic
360C22C43×#38812yes—
361C22C43×#39012yes—
362C22C43×#39011yescharacteristic
363C4—44no—
364C4—82no—
365C4—84no—
366C4C4×C22⋊C4×C4312yes—
367C4C43×#38612yes—
368C4C43×#38812yes—
369C4C43×#38812yes—
370C2—21no—
371C2—22no—
372C2—21no—
373C2—22no—
374C2—84no—
375C2C43×#143711yescharacteristic
376C2C43×#191012yes—
subgroupG/H
center, socleC22×C43#386
commutatorC2×C4C2×C42×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC23×D4×C43C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2873C2semidirect
4. C43×#1740C2semidirect
5. C2×C43×H(3,ℤ/4)C2semidirect
12. C43×#418C4semidirect
17. C43×#390C4semidirect
99. C2×C8×C43C22⋊C4semidirect
158. #10948C43direct (N × H)
183. #2873C2×C43semidirect
185. #1740C2×C43semidirect
186. C2×H(3,ℤ/4)C2×C43semidirect
200. #418C4×C43semidirect
205. #390C4×C43semidirect
209. C43#10948direct (N × H)
288. C2×C8C22⋊C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4182
C43×#28732
C43×#23092
C43×#17402
C2×C43×H(3,ℤ/4)2
#1094843