Finite Group Databasebeta

← C43×#9387 #24929404

Subgroups — C43×#9387 #24929404

Order 11008.

582 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
1C43×#2873C211yesmaximal, characteristic, complemented
2C43×#2610C211yesmaximal, characteristic
3C43×#1527C212yesmaximal, complemented
4C43×#1464C211yesmaximal, characteristic, complemented
5C43×#1300C212yesmaximal, complemented
6C22×M16×C43—21no—
7C2×#124×C43C2211yescharacteristic
8C2×#117×C43C2211yescharacteristic
9C43×#432C2212yes—
10C43×#405—24no—
11C4×M16×C43—21no—
12C4×M16×C43C2212yes—
13C43×#395C411yescharacteristic
14C43×#394C411yescharacteristic
15C43×#393C411yescharacteristic
16C43×#392C411yescharacteristic
17C43×#390—21no—
18C43×#388—21no—
19C43×#388—21no—
20C43×#386—21no—
21C43×#376C2211yescharacteristic
22C43×#329—24no—
23C43×#324—21no—
24C43×#323—21no—
25C22×Q8×C43C2×C411yescharacteristic
26C22×D4×C43—21no—
27C22×D4×C43C2×C411yescharacteristic
28C23×C4×C43D411yescharacteristic
29C2×M16×C43—24no—
30C2×M16×C43—24no—
31C2×M16×C43—22no—
32C2×M16×C43—22no—
33C22×C8×C43—22no—
34#124×C43—22no—
35#124×C43—22no—
36#117×C43—22no—
37#117×C43—22no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43C2×C411yescharacteristic
48C2×C22⋊C4×C43D411yescharacteristic
49C2×C42×C43—21no—
50C2×C42×C43D411yescharacteristic
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—22no—
53C22⋊C8×C43—22no—
54#97×C43—22no—
55#97×C43—22no—
56#97×C43D414yescomplemented
57C4×C8×C43—22no—
58C4×C8×C43—22no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63#95×C43C2×C411yescharacteristic
64C24×C43—21no—
65C24×C43C22⋊C411yescharacteristic
66C2×Q8×C43—22no—
67C2×Q8×C43—81no—
68C2×D4×C43—22no—
69C2×D4×C43—42no—
70C2×D4×C43—42no—
71C2×D4×C43—81no—
72C2×D4×C43—81no—
73C22×C4×C43—22no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—22no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86M16×C43—28no—
87M16×C43—24no—
88M16×C43—24no—
89C2×C8×C43—28no—
90C2×C8×C43—24no—
91C2×C8×C43—42no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—81no—
95C22⋊C4×C43—22no—
96C22⋊C4×C43—22no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—81no—
103C22⋊C4×C43—81no—
104C42×C43—21no—
105C42×C43—21no—
106C42×C43—42no—
107C42×C43C2×D412yes—
108C42×C43#4112yes—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43#10412yes—
121C23×C43C2×C22⋊C411yescharacteristic
122Q8×C43—82no—
123D4×C43—82no—
124D4×C43—84no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—24no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43#10412yes—
148C2×C4×C43C4×D412yes—
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12112yes—
151C2×C4×C43#12311yescharacteristic
152C8×C43—28no—
153C8×C43—82no—
154#9387C4311yesmaximal, characteristic, direct product factor, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—22no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43—81no—
165C22×C43—81no—
166C22×C43—81no—
167C22×C43—81no—
168C22×C43—81no—
169C22×C43#38611yescharacteristic
170C22×C43C2×#10411yescharacteristic
171C22×C43C2×#10411yescharacteristic
172C4×C43—22no—
173C4×C43—21no—
174C4×C43—22no—
175C4×C43—21no—
176C4×C43—22no—
177C4×C43—42no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—81no—
181C4×C43—81no—
182#2873C2×C4311yescharacteristic, complemented
183#2610C2×C4311yescharacteristic
184#1527C2×C4312yescomplemented
185#1464C2×C4311yescharacteristic, complemented
186#1300C2×C4312yescomplemented
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—42no—
190C2×C43—161no—
191C2×C43#188411yescharacteristic
192C2×C43#189611yescharacteristic
193C2×C43#191411yescharacteristic
194C22×M16—21no—
195C2×#124C22×C4311yescharacteristic
196C2×#117C22×C4311yescharacteristic
197#432C22×C4312yes—
198#405—24no—
199C4×M16—21no—
200C4×M16C22×C4312yes—
201#395C4×C4311yescharacteristic
202#394C4×C4311yescharacteristic
203#393C4×C4311yescharacteristic
204#392C4×C4311yescharacteristic
205#390—21no—
206#388—21no—
207#388—21no—
208#386—21no—
209#376C22×C4311yescharacteristic
210#329—24no—
211#324—21no—
212#323—21no—
213C43#938711yescharacteristic, direct product factor, Sylow
214C22×Q8C2×C4×C4311yescharacteristic
215C22×D4—21no—
216C22×D4C2×C4×C4311yescharacteristic
217C23×C4D4×C4311yescharacteristic
218C2×M16—24no—
219C2×M16—24no—
220C2×M16—22no—
221C2×M16—22no—
222C22×C8—22no—
223#124—22no—
224#124—22no—
225#117—22no—
226#117—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C4311yescharacteristic
229C2×C4⋊C4D4×C4311yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4C2×C4×C4311yescharacteristic
237C2×C22⋊C4D4×C4311yescharacteristic
238C2×C42—21no—
239C2×C42D4×C4311yescharacteristic
240C2×C42C23×C4311yescharacteristic
241C4⋊C8—22no—
242C22⋊C8—22no—
243#97—22no—
244#97—22no—
245#97D4×C4314yescomplemented
246C4×C8—22no—
247C4×C8—22no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95C2×C4×C4311yescharacteristic
252#95C2×C4×C4311yescharacteristic
253C24—21no—
254C24C22⋊C4×C4311yescharacteristic
255C2×Q8—22no—
256C2×Q8—81no—
257C2×D4—22no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—81no—
261C2×D4—81no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22⋊C4×C4311yescharacteristic
270C22×C4C22⋊C4×C4311yescharacteristic
271C22×C4C22⋊C4×C4311yescharacteristic
272C22×C4C22×C4×C4311yescharacteristic
273C22×C4C2×D4×C4311yescharacteristic
274C22×C4C2×D4×C4311yescharacteristic
275M16—28no—
276M16—24no—
277M16—24no—
278C2×C8—28no—
279C2×C8—24no—
280C2×C8—42no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—81no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C42—21no—
294C42—21no—
295C42—42no—
296C42C2×D4×C4312yes—
297C42#41×C4312yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#104×C4312yes—
310C23C2×C22⋊C4×C4311yescharacteristic
311Q8—82no—
312D4—82no—
313D4—84no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4#104×C4312yes—
337C2×C4C4×D4×C4312yes—
338C2×C4#120×C4311yescharacteristic
339C2×C4#121×C4312yes—
340C2×C4#123×C4311yescharacteristic
341C8—28no—
342C8—82no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C43×#38611yescharacteristic
358C22C2×#104×C4311yescharacteristic
359C22C2×#104×C4311yescharacteristic
360C4—22no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2C43×#188411yescharacteristic
375C2C43×#189611yescharacteristic
376C2C43×#191411yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#392C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2873C2semidirect
3. C43×#1527C2semidirect
4. C43×#1464C2semidirect
5. C43×#1300C2semidirect
56. #97×C43D4semidirect
154. #9387C43direct (N × H)
182. #2873C2×C43semidirect
184. #1527C2×C43semidirect
185. #1464C2×C43semidirect
186. #1300C2×C43semidirect
213. C43#9387direct (N × H)
245. #97D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#28732
C43×#26102
C43×#15272
C43×#14642
C43×#13002
#938743