Finite Group Databasebeta

← C43×#9766 #24929783

Subgroups — C43×#9766 #24929783

Order 11008.

396 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3167C211yesmaximal, characteristic
2C43×#1746C211yesmaximal, characteristic, complemented
3C43×#1568C211yesmaximal, characteristic, complemented
4C43×#1531C211yesmaximal, characteristic, complemented
5C43×#1530C211yesmaximal, characteristic
6C43×#1506C211yesmaximal, characteristic, complemented
7C43×#1505C211yesmaximal, characteristic
8C43×#533C2211yescharacteristic
9C43×#532C2211yescharacteristic
10C43×#498C411yescharacteristic, complemented
11C43×#492C411yescharacteristic, complemented
12C43×#487C411yescharacteristic, complemented
13C43×#486C411yescharacteristic, complemented
14C43×#465—21no—
15C43×#465—21no—
16C4×SD16×C43—21no—
17C4×SD16×C43—21no—
18C43×#432C2211yescharacteristic
19C43×#432C2211yescharacteristic
20C2×#97×C43C2211yescharacteristic
21C2×C4×C8×C43C2211yescharacteristic
22C43×#376C2211yescharacteristic
23C43×#336—21no—
24C43×#336—21no—
25C43×#335—21no—
26C43×#334—21no—
27C43×#330—22no—
28C43×#329—22no—
29C43×#328—22no—
30C43×#327—22no—
31C2×#41×C43—21no—
32C2×SD16×C43—21no—
33C2×SD16×C43—21no—
34C22×C8×C43—21no—
35C22×C8×C43D411yescharacteristic
36C22×C8×C43D411yescharacteristic
37C4⋊Q8×C43C2×C411yescharacteristic
38C4⋊Q8×C43C2×C411yescharacteristic
39C4⋊Q8×C43C2×C411yescharacteristic
40#127×C43C2×C411yescharacteristic
41#125×C43—21no—
42#124×C43—21no—
43C22⋊Q8×C43—21no—
44C22⋊Q8×C43—21no—
45#121×C43—21no—
46#121×C43—21no—
47C4×Q8×C43—21no—
48C4×Q8×C43—21no—
49C4×D4×C43—21no—
50C4×D4×C43—21no—
51#117×C43—21no—
52C2×C42×C43—21no—
53C2×C42×C43C2311yescharacteristic
54#106×C43—21no—
55#106×C43—21no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43—21no—
58#103×C43—21no—
59#103×C43—21no—
60#102×C43—21no—
61#102×C43—21no—
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64#97×C43—21no—
65#97×C43—21no—
66#97×C43—21no—
67#97×C43D412yes—
68C4×C8×C43C2×C411yescharacteristic
69C4×C8×C43C2×C411yescharacteristic
70C4×C8×C43D411yescharacteristic
71C4×C8×C43D411yescharacteristic
72#95×C43—21no—
73#95×C43D412yes—
74#41×C43—82no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—41no—
82C22×C4×C43—22no—
83C22×C4×C43—41no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87SD16×C43—42no—
88SD16×C43—42no—
89C2×C8×C43—22no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43C22⋊C411yescharacteristic
97C2×C8×C43C22⋊C411yescharacteristic
98C2×C8×C43C22⋊C411yescharacteristic
99C2×C8×C43C22⋊C411yescharacteristic
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C42×C43—41no—
112C42×C43—41no—
113C42×C43—41no—
114C42×C43C22×C411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118C23×C43—41no—
119C23×C43#12111yescharacteristic
120Q8×C43—41no—
121Q8×C43—41no—
122Q8×C43—81no—
123Q8×C43—81no—
124D4×C43—41no—
125D4×C43—41no—
126D4×C43—81no—
127D4×C43—81no—
128D4×C43—82no—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—82no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12411yescharacteristic
145C2×C4×C43#12711yescharacteristic
146C8×C43—21no—
147C8×C43—21no—
148C8×C43—21no—
149C8×C43—21no—
150C8×C43—42no—
151C8×C43—81no—
152C8×C43—81no—
153#9766C4311yesmaximal, characteristic, direct product factor, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43—81no—
159C22×C43#39011yescharacteristic
160C22×C43#47112yes—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—82no—
167C4×C43—81no—
168C4×C43—81no—
169C4×C43—81no—
170C4×C43#42111yescharacteristic
171C4×C43#42111yescharacteristic
172#3167C2×C4311yescharacteristic
173#1746C2×C4311yescharacteristic, complemented
174#1568C2×C4311yescharacteristic, complemented
175#1531C2×C4311yescharacteristic, complemented
176#1530C2×C4311yescharacteristic
177#1506C2×C4311yescharacteristic, complemented
178#1505C2×C4311yescharacteristic
179C2×C43—22no—
180C2×C43—161no—
181C2×C43#196311yescharacteristic
182C2×C43#197611yescharacteristic
183C2×C43#197711yescharacteristic
184#533C22×C4311yescharacteristic
185#532C22×C4311yescharacteristic
186#498C4×C4311yescharacteristic, complemented
187#492C4×C4311yescharacteristic, complemented
188#487C4×C4311yescharacteristic, complemented
189#486C4×C4311yescharacteristic, complemented
190#465—21no—
191#465—21no—
192C4×SD16—21no—
193C4×SD16—21no—
194#432C22×C4311yescharacteristic
195#432C22×C4311yescharacteristic
196C2×#97C22×C4311yescharacteristic
197C2×C4×C8C22×C4311yescharacteristic
198#376C22×C4311yescharacteristic
199#336—21no—
200#336—21no—
201#335—21no—
202#334—21no—
203#330—22no—
204#329—22no—
205#328—22no—
206#327—22no—
207C43#976611yescharacteristic, direct product factor, Sylow
208C2×#41—21no—
209C2×SD16—21no—
210C2×SD16—21no—
211C22×C8—21no—
212C22×C8D4×C4311yescharacteristic
213C22×C8D4×C4311yescharacteristic
214C4⋊Q8C2×C4×C4311yescharacteristic
215C4⋊Q8C2×C4×C4311yescharacteristic
216C4⋊Q8C2×C4×C4311yescharacteristic
217#127C2×C4×C4311yescharacteristic
218#125—21no—
219#124—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222#121—21no—
223#121—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×D4—21no—
227C4×D4—21no—
228#117—21no—
229C2×C42—21no—
230C2×C42C23×C4311yescharacteristic
231#106—21no—
232#106—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235#103—21no—
236#103—21no—
237#102—21no—
238#102—21no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241#97—21no—
242#97—21no—
243#97—21no—
244#97D4×C4312yes—
245C4×C8C2×C4×C4311yescharacteristic
246C4×C8C2×C4×C4311yescharacteristic
247C4×C8D4×C4311yescharacteristic
248C4×C8D4×C4311yescharacteristic
249#95—21no—
250#95D4×C4312yes—
251#41—82no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4C2×D4×C4311yescharacteristic
262C22×C4C2×D4×C4311yescharacteristic
263C22×C4#41×C4311yescharacteristic
264SD16—42no—
265SD16—42no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8C22⋊C4×C4311yescharacteristic
274C2×C8C22⋊C4×C4311yescharacteristic
275C2×C8C22⋊C4×C4311yescharacteristic
276C2×C8C22⋊C4×C4311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—41no—
289C42—41no—
290C42—41no—
291C42C22×C4×C4311yescharacteristic
292C42C2×D4×C4311yescharacteristic
293C42C2×D4×C4311yescharacteristic
294C42#41×C4311yescharacteristic
295C23—41no—
296C23#121×C4311yescharacteristic
297Q8—41no—
298Q8—41no—
299Q8—81no—
300Q8—81no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—82no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—82no—
317C2×C4C2×C22⋊C4×C4311yescharacteristic
318C2×C4C4×D4×C4311yescharacteristic
319C2×C4C4×D4×C4311yescharacteristic
320C2×C4#121×C4311yescharacteristic
321C2×C4#124×C4311yescharacteristic
322C2×C4#127×C4311yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—21no—
327C8—42no—
328C8—81no—
329C8—81no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C43×#39011yescharacteristic
336C22C43×#47112yes—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4C43×#42111yescharacteristic
347C4C43×#42111yescharacteristic
348C2—22no—
349C2—161no—
350C2C43×#196311yescharacteristic
351C2C43×#197611yescharacteristic
352C2C43×#197711yescharacteristic
subgroupG/H
center, socleC22×C43#390
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1746C2semidirect
3. C43×#1568C2semidirect
4. C43×#1531C2semidirect
6. C43×#1506C2semidirect
10. C43×#498C4semidirect
11. C43×#492C4semidirect
12. C43×#487C4semidirect
13. C43×#486C4semidirect
153. #9766C43direct (N × H)
173. #1746C2×C43semidirect
174. #1568C2×C43semidirect
175. #1531C2×C43semidirect
177. #1506C2×C43semidirect
186. #498C4×C43semidirect
187. #492C4×C43semidirect
188. #487C4×C43semidirect
189. #486C4×C43semidirect
207. C43#9766direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31672
C43×#17462
C43×#15682
C43×#15312
C43×#15302
C43×#15062
C43×#15052
#976643