Finite Group Databasebeta

← C43×#9266 #24929283

Subgroups — C43×#9266 #24929283

Order 11008.

400 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3232C211yesmaximal, characteristic
2C43×#2968C211yesmaximal, characteristic
3C43×#1532C211yesmaximal, characteristic
4C2×C43×#330C211yesmaximal, characteristic, complemented
5C43×#1470C211yesmaximal, characteristic, complemented
6C43×#1302C211yesmaximal, characteristic, complemented
7C43×#1281C211yesmaximal, characteristic, complemented
8C43×#529C2211yescharacteristic
9C2×#125×C43C2211yescharacteristic
10C43×#499—21no—
11C43×#488—21no—
12C43×#484C411yescharacteristic
13C43×#483C411yescharacteristic
14C43×#481C411yescharacteristic
15C43×#480C411yescharacteristic
16C43×#479—21no—
17C43×#478—21no—
18C43×#446—21no—
19C43×#435—21no—
20C43×#435—21no—
21C8×D4×C43—21no—
22C43×#433—21no—
23C43×#432C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C43×#431C2211yescharacteristic
26C43×#405—21no—
27C2×#97×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C43×#330—21no—
30C43×#330—21no—
31C43×#330—21no—
32C43×#329—21no—
33C43×#324—21no—
34C43×#324—21no—
35C2×M16×C43—21no—
36C22×C8×C43—21no—
37C22×C8×C43—21no—
38C22×C8×C43—21no—
39#126×C43—21no—
40#125×C43—21no—
41#125×C43—21no—
42#125×C43—21no—
43#125×C43—21no—
44#125×C43D411yescharacteristic
45#124×C43D411yescharacteristic
46#123×C43—21no—
47C22⋊Q8×C43C2×C411yescharacteristic
48#121×C43C2×C411yescharacteristic
49C4×Q8×C43D411yescharacteristic
50C4×D4×C43—21no—
51C4×D4×C43D411yescharacteristic
52#117×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#107×C43—21no—
59#107×C43—21no—
60#106×C43—21no—
61#106×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67#103×C43—21no—
68#103×C43—21no—
69#102×C43—21no—
70#102×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43C2×C411yescharacteristic
75C22⋊C8×C43C2×C411yescharacteristic
76C22⋊C8×C43D411yescharacteristic
77C22⋊C8×C43D411yescharacteristic
78#97×C43—21no—
79#97×C43—21no—
80#97×C43—21no—
81#97×C43—21no—
82#97×C43—21no—
83#97×C43D411yescharacteristic
84#97×C43D411yescharacteristic
85C4×C8×C43—21no—
86C4×C8×C43—21no—
87C4×C8×C43—21no—
88C2×Q8×C43C22⋊C411yescharacteristic
89C2×D4×C43—21no—
90C2×D4×C43C22⋊C411yescharacteristic
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97M16×C43—42no—
98C2×C8×C43—21no—
99C2×C8×C43—22no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43—42no—
106C2×C8×C43—42no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C2×C8×C43—41no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43C22⋊C411yescharacteristic
123C4⋊C4×C43C22⋊C411yescharacteristic
124C22⋊C4×C43—21no—
125C22⋊C4×C43—21no—
126C22⋊C4×C43—21no—
127C22⋊C4×C43—21no—
128C22⋊C4×C43—21no—
129C42×C43—21no—
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43C2×D411yescharacteristic
133C42×C43#4111yescharacteristic
134C23×C43—21no—
135C23×C43C4×D411yescharacteristic
136Q8×C43—41no—
137D4×C43—41no—
138D4×C43—41no—
139D4×C43—41no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C8×C43—22no—
161C8×C43—41no—
162C8×C43—41no—
163C8×C43—42no—
164C8×C43—41no—
165C8×C43—41no—
166C8×C43—41no—
167C8×C43—81no—
168#9266C4311yesmaximal, characteristic, direct product factor, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43#38611yescharacteristic
175C22×C43#44311yescharacteristic
176C22×C43#44411yescharacteristic
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—81no—
187C4×C43—81no—
188#3232C2×C4311yescharacteristic
189#2968C2×C4311yescharacteristic
190#1532C2×C4311yescharacteristic
191C2×#330C2×C4311yescharacteristic, complemented
192#1470C2×C4311yescharacteristic, complemented
193#1302C2×C4311yescharacteristic, complemented
194#1281C2×C4311yescharacteristic, complemented
195C2×C43—21no—
196C2×C43—21no—
197C2×C43—81no—
198C2×C43#187611yescharacteristic
199C2×C43#190611yescharacteristic
200C2×C43#191511yescharacteristic
201#529C22×C4311yescharacteristic
202C2×#125C22×C4311yescharacteristic
203#499—21no—
204#488—21no—
205#484C4×C4311yescharacteristic
206#483C4×C4311yescharacteristic
207#481C4×C4311yescharacteristic
208#480C4×C4311yescharacteristic
209#479—21no—
210#478—21no—
211#446—21no—
212#435—21no—
213#435—21no—
214C8×D4—21no—
215#433—21no—
216#432C22×C4311yescharacteristic
217#431C22×C4311yescharacteristic
218#431C22×C4311yescharacteristic
219#405—21no—
220C2×#97C22×C4311yescharacteristic
221C2×#97C22×C4311yescharacteristic
222#330—21no—
223#330—21no—
224#330—21no—
225#329—21no—
226#324—21no—
227#324—21no—
228C43#926611yescharacteristic, direct product factor, Sylow
229C2×M16—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233#126—21no—
234#125—21no—
235#125—21no—
236#125—21no—
237#125—21no—
238#125D4×C4311yescharacteristic
239#124D4×C4311yescharacteristic
240#123—21no—
241C22⋊Q8C2×C4×C4311yescharacteristic
242#121C2×C4×C4311yescharacteristic
243C4×Q8D4×C4311yescharacteristic
244C4×D4—21no—
245C4×D4D4×C4311yescharacteristic
246#117—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4C2×C4×C4311yescharacteristic
250C2×C4⋊C4C2×C4×C4311yescharacteristic
251C2×C42C23×C4311yescharacteristic
252#107—21no—
253#107—21no—
254#106—21no—
255#106—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264#102—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8C2×C4×C4311yescharacteristic
269C22⋊C8C2×C4×C4311yescharacteristic
270C22⋊C8D4×C4311yescharacteristic
271C22⋊C8D4×C4311yescharacteristic
272#97—21no—
273#97—21no—
274#97—21no—
275#97—21no—
276#97—21no—
277#97D4×C4311yescharacteristic
278#97D4×C4311yescharacteristic
279C4×C8—21no—
280C4×C8—21no—
281C4×C8—21no—
282C2×Q8C22⋊C4×C4311yescharacteristic
283C2×D4—21no—
284C2×D4C22⋊C4×C4311yescharacteristic
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×C4×C4311yescharacteristic
289C22×C4C2×D4×C4311yescharacteristic
290C22×C4#41×C4311yescharacteristic
291M16—42no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4C22⋊C4×C4311yescharacteristic
317C4⋊C4C22⋊C4×C4311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42C2×D4×C4311yescharacteristic
325C42C2×D4×C4311yescharacteristic
326C42C2×D4×C4311yescharacteristic
327C42#41×C4311yescharacteristic
328C23—21no—
329C23C4×D4×C4311yescharacteristic
330Q8—41no—
331D4—41no—
332D4—41no—
333D4—41no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4C2×C22⋊C4×C4311yescharacteristic
349C2×C4C4×D4×C4311yescharacteristic
350C2×C4#120×C4311yescharacteristic
351C2×C4#121×C4311yescharacteristic
352C2×C4#121×C4311yescharacteristic
353C2×C4#123×C4311yescharacteristic
354C8—22no—
355C8—42no—
356C8—41no—
357C8—41no—
358C8—41no—
359C8—41no—
360C8—41no—
361C8—81no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22C43×#38611yescharacteristic
368C22C43×#44311yescharacteristic
369C22C43×#44411yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C2—21no—
382C2—21no—
383C2—81no—
384C2C43×#187611yescharacteristic
385C2C43×#190611yescharacteristic
386C2C43×#191511yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radical#121×C43C2×C4
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
4. C2×C43×#330C2semidirect
5. C43×#1470C2semidirect
6. C43×#1302C2semidirect
7. C43×#1281C2semidirect
168. #9266C43direct (N × H)
191. C2×#330C2×C43semidirect
192. #1470C2×C43semidirect
193. #1302C2×C43semidirect
194. #1281C2×C43semidirect
228. C43#9266direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32322
C43×#29682
C43×#15322
C2×C43×#3302
C43×#14702
C43×#13022
C43×#12812
#926643