Finite Group Databasebeta

← C43×#8505 #24928522

Subgroups — C43×#8505 #24928522

Order 11008.

648 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3531C211yesmaximal, characteristic
2C43×#1995C211yesmaximal, characteristic, complemented
3C43×#1544C211yesmaximal, characteristic, complemented
4C43×#1500C212yesmaximal, complemented
5C43×#1495C212yesmaximal, complemented
6C43×#564C411yescharacteristic, complemented
7C43×#563—22no—
8C43×#563—22no—
9C43×#563C412yescomplemented
10C43×#562—22no—
11C43×#562C411yescharacteristic, complemented
12C43×#533—22no—
13C43×#533C2211yescharacteristic
14C43×#529—22no—
15C43×#529—22no—
16C43×#529C2212yes—
17C43×#431C2212yes—
18C43×#423C2211yescharacteristic
19C43×#376C2211yescharacteristic
20C43×#339—22no—
21C43×#332—22no—
22C43×#328—22no—
23C43×#327—22no—
24C43×Q8⋊C8—22no—
25C43×D4⋊C8—22no—
26C2×M16×C43—21no—
27C4⋊Q8×C43—22no—
28C4⋊Q8×C43—22no—
29C4⋊Q8×C43D412yes—
30#126×C43—22no—
31#126×C43—22no—
32#126×C43—22no—
33#126×C43—22no—
34#126×C43—22no—
35#125×C43—22no—
36#125×C43—22no—
37#125×C43—22no—
38#125×C43—22no—
39#125×C43C2×C412yes—
40#125×C43C2×C411yescharacteristic
41#125×C43C2×C411yescharacteristic
42#124×C43—22no—
43#124×C43—22no—
44#124×C43C2×C412yes—
45#123×C43—22no—
46#123×C43—22no—
47#123×C43—22no—
48#123×C43—22no—
49#123×C43—22no—
50C22⋊Q8×C43—22no—
51C22⋊Q8×C43—22no—
52C22⋊Q8×C43—22no—
53C22⋊Q8×C43—22no—
54C22⋊Q8×C43—22no—
55C22⋊Q8×C43—22no—
56C22⋊Q8×C43—22no—
57C22⋊Q8×C43D412yes—
58#121×C43—22no—
59#121×C43—22no—
60#121×C43D412yes—
61C4×Q8×C43—22no—
62C4×Q8×C43—22no—
63C4×Q8×C43D412yes—
64C4×D4×C43—22no—
65C4×D4×C43—22no—
66C4×D4×C43D412yes—
67#117×C43—22no—
68#117×C43—22no—
69#117×C43D412yes—
70C2×C42×C43—22no—
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—22no—
74C4⋊C8×C43—22no—
75C22⋊C8×C43—22no—
76C4×C8×C43—22no—
77#95×C43—22no—
78C2×Q8×C43—22no—
79C2×Q8×C43—22no—
80C2×Q8×C43C22⋊C412yes—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43C22⋊C412yes—
84C22×C4×C43—22no—
85C22×C4×C43—22no—
86C22×C4×C43—22no—
87C22×C4×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D412yes—
90M16×C43—42no—
91C2×C8×C43—42no—
92C2×C8×C43—41no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43C22⋊C412yes—
107C4⋊C4×C43C22⋊C412yes—
108C4⋊C4×C43C22⋊C412yes—
109C4⋊C4×C43C22⋊C412yes—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—22no—
112C22⋊C4×C43—22no—
113C22⋊C4×C43—22no—
114C22⋊C4×C43—22no—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—22no—
118C22⋊C4×C43—22no—
119C22⋊C4×C43—22no—
120C42×C43—22no—
121C42×C43—22no—
122C42×C43—22no—
123C42×C43—22no—
124C42×C43—22no—
125C42×C43—41no—
126C42×C43C22×C411yescharacteristic
127C42×C43C2×D411yescharacteristic
128C42×C43C2×D412yes—
129C23×C43—22no—
130C23×C43#12011yescharacteristic
131Q8×C43—42no—
132Q8×C43—82no—
133Q8×C43—82no—
134D4×C43—42no—
135D4×C43—82no—
136D4×C43—82no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—82no—
149C2×C4×C43—82no—
150C2×C4×C43—82no—
151C2×C4×C43C2×C22⋊C411yescharacteristic
152C2×C4×C43C2×C22⋊C412yes—
153C2×C4×C43#12012yes—
154C2×C4×C43#12011yescharacteristic
155C8×C43—82no—
156C8×C43—81no—
157#8505C4311yesmaximal, characteristic, direct product factor, Sylow
158C22×C43—21no—
159C22×C43—22no—
160C22×C43—42no—
161C22×C43—42no—
162C22×C43—42no—
163C22×C43#37911yescharacteristic
164C4×C43—21no—
165C4×C43—22no—
166C4×C43—22no—
167C4×C43—42no—
168C4×C43—42no—
169C4×C43—42no—
170C4×C43—42no—
171C4×C43—42no—
172C4×C43—82no—
173C4×C43#45411yescharacteristic
174C4×C43#45611yescharacteristic
175#3531C2×C4311yescharacteristic
176#1995C2×C4311yescharacteristic, complemented
177#1544C2×C4311yescharacteristic, complemented
178#1500C2×C4312yescomplemented
179#1495C2×C4312yescomplemented
180C2×C43—41no—
181C2×C43—82no—
182C2×C43#179311yescharacteristic
183C2×C43#179412yes—
184#564C4×C4311yescharacteristic, complemented
185#563—22no—
186#563—22no—
187#563C4×C4312yescomplemented
188#562—22no—
189#562C4×C4311yescharacteristic, complemented
190#533—22no—
191#533C22×C4311yescharacteristic
192#529—22no—
193#529—22no—
194#529C22×C4312yes—
195#431C22×C4312yes—
196#423C22×C4311yescharacteristic
197#376C22×C4311yescharacteristic
198#339—22no—
199#332—22no—
200#328—22no—
201#327—22no—
202Q8⋊C8—22no—
203D4⋊C8—22no—
204C43#850511yescharacteristic, direct product factor, Sylow
205C2×M16—21no—
206C4⋊Q8—22no—
207C4⋊Q8—22no—
208C4⋊Q8D4×C4312yes—
209#126—22no—
210#126—22no—
211#126—22no—
212#126—22no—
213#126—22no—
214#125—22no—
215#125—22no—
216#125—22no—
217#125—22no—
218#125C2×C4×C4312yes—
219#125C2×C4×C4311yescharacteristic
220#125C2×C4×C4311yescharacteristic
221#124—22no—
222#124—22no—
223#124C2×C4×C4312yes—
224#123—22no—
225#123—22no—
226#123—22no—
227#123—22no—
228#123—22no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236C22⋊Q8D4×C4312yes—
237#121—22no—
238#121—22no—
239#121D4×C4312yes—
240C4×Q8—22no—
241C4×Q8—22no—
242C4×Q8D4×C4312yes—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4D4×C4312yes—
246#117—22no—
247#117—22no—
248#117D4×C4312yes—
249C2×C42—22no—
250C2×C42—21no—
251C2×C42C23×C4311yescharacteristic
252C4⋊C8—22no—
253C4⋊C8—22no—
254C22⋊C8—22no—
255C4×C8—22no—
256#95—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8C22⋊C4×C4312yes—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4C22⋊C4×C4312yes—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4C2×D4×C4311yescharacteristic
268C22×C4C2×D4×C4312yes—
269M16—42no—
270C2×C8—42no—
271C2×C8—41no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4C22⋊C4×C4312yes—
286C4⋊C4C22⋊C4×C4312yes—
287C4⋊C4C22⋊C4×C4312yes—
288C4⋊C4C22⋊C4×C4312yes—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—22no—
304C42—41no—
305C42C22×C4×C4311yescharacteristic
306C42C2×D4×C4312yes—
307C42C2×D4×C4311yescharacteristic
308C23—22no—
309C23#120×C4311yescharacteristic
310Q8—42no—
311Q8—82no—
312Q8—82no—
313D4—42no—
314D4—82no—
315D4—82no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4C2×C22⋊C4×C4311yescharacteristic
331C2×C4C2×C22⋊C4×C4312yes—
332C2×C4#120×C4312yes—
333C2×C4#120×C4311yescharacteristic
334C8—82no—
335C8—81no—
336C22—21no—
337C22—22no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22C43×#37911yescharacteristic
342C4—21no—
343C4—22no—
344C4—22no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—42no—
349C4—42no—
350C4—82no—
351C4C43×#45411yescharacteristic
352C4C43×#45611yescharacteristic
353C2—41no—
354C2—82no—
355C2C43×#179311yescharacteristic
356C2C43×#179412yes—
subgroupG/H
centerC2×C4×C43#120
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#379
prime radicalC43×#3531C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1995C2semidirect
3. C43×#1544C2semidirect
4. C43×#1500C2semidirect
5. C43×#1495C2semidirect
6. C43×#564C4semidirect
9. C43×#563C4semidirect
11. C43×#562C4semidirect
157. #8505C43direct (N × H)
176. #1995C2×C43semidirect
177. #1544C2×C43semidirect
178. #1500C2×C43semidirect
179. #1495C2×C43semidirect
184. #564C4×C43semidirect
187. #563C4×C43semidirect
189. #562C4×C43semidirect
204. C43#8505direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35312
C43×#19952
C43×#15442
C43×#15002
C43×#14952
#850543