Finite Group Databasebeta

← C43×#13332 #24933349

Subgroups — C43×#13332 #24933349

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#510C211yesmaximal, characteristic, complemented
2C2×C43×#509C211yesmaximal, characteristic
3C2×C43×#495C211yesmaximal, characteristic, complemented
4C2×C43×#362C211yesmaximal, characteristic, complemented
5C2×C43×#361C211yesmaximal, characteristic, complemented
6C43×#1974C211yesmaximal, characteristic, complemented
7C43×#1376C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C22×Q16×C43C2211yescharacteristic
10C22×SD16×C43—21no—
11C22×D8×C43C2211yescharacteristic
12C2×#124×C43—21no—
13C43×#510—22no—
14C43×#510—22no—
15C43×#509—22no—
16C43×#509—22no—
17C2×Q32×C43—21no—
18C2×SD32×C43—21no—
19C2×SD32×C43—21no—
20C2×D16×C43—21no—
21C2×M32×C43C2211yescharacteristic
22C2×M32×C43C2211yescharacteristic
23C43×#495—22no—
24C43×#495—22no—
25C2×#108×C43C2211yescharacteristic
26C2×#104×C43—21no—
27C43×#408—21no—
28C2×C4×C8×C43C2211yescharacteristic
29C43×#362—22no—
30C43×#361—22no—
31C2×#41×C43—21no—
32C22×Q8×C43—21no—
33C22×D4×C43—21no—
34#135×C43—21no—
35#135×C43—21no—
36#135×C43—21no—
37#135×C43—21no—
38C2×Q16×C43—21no—
39C2×Q16×C43—21no—
40C2×Q16×C43—21no—
41C2×Q16×C43—21no—
42C2×Q16×C43—21no—
43C2×Q16×C43D411yescharacteristic
44C2×Q16×C43D412yes—
45C2×SD16×C43—24no—
46C2×SD16×C43—21no—
47C2×SD16×C43—42no—
48C2×SD16×C43—42no—
49C2×D8×C43—21no—
50C2×D8×C43—21no—
51C2×D8×C43—21no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43D411yescharacteristic
55C2×D8×C43D412yes—
56C2×M16×C43—21no—
57C22×C8×C43D411yescharacteristic
58C22×C8×C43C2311yescharacteristic
59#124×C43—24no—
60#124×C43—42no—
61C2×C22⋊C4×C43—42no—
62C2×C42×C43D411yescharacteristic
63Q32×C43—24no—
64SD32×C43—24no—
65SD32×C43—24no—
66D16×C43—24no—
67M32×C43—21no—
68M32×C43—21no—
69M32×C43D412yes—
70M32×C43D412yes—
71C2×C16×C43—21no—
72C2×C16×C43—21no—
73#108×C43—21no—
74#108×C43—21no—
75#104×C43—42no—
76C22⋊C8×C43—42no—
77C4×C8×C43—21no—
78C4×C8×C43—21no—
79C24×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82#41×C43—41no—
83#41×C43—41no—
84C2×Q8×C43—22no—
85C2×Q8×C43—21no—
86C2×Q8×C43—41no—
87C2×Q8×C43—41no—
88C2×Q8×C43—41no—
89C2×Q8×C43—41no—
90C2×Q8×C43—41no—
91C2×D4×C43—22no—
92C2×D4×C43—21no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C22×C4×C43—21no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43C2×D411yescharacteristic
103Q16×C43—21no—
104Q16×C43—22no—
105Q16×C43—21no—
106Q16×C43—22no—
107Q16×C43—41no—
108Q16×C43—41no—
109SD16×C43—48no—
110SD16×C43—41no—
111SD16×C43—41no—
112D8×C43—21no—
113D8×C43—22no—
114D8×C43—21no—
115D8×C43—22no—
116D8×C43—41no—
117D8×C43—41no—
118M16×C43—41no—
119M16×C43—41no—
120C2×C8×C43—21no—
121C2×C8×C43—21no—
122C2×C8×C43—41no—
123C2×C8×C43D812yes—
124C2×C8×C43C2×D411yescharacteristic
125C2×C8×C43C2×D411yescharacteristic
126C2×C8×C43C2×D411yescharacteristic
127C2×C8×C43C2×D411yescharacteristic
128C2×C8×C43C2×D411yescharacteristic
129C2×C8×C43#4111yescharacteristic
130C22⋊C4×C43—48no—
131C42×C43—21no—
132C42×C43D812yes—
133C16×C43—22no—
134C16×C43—22no—
135C23×C43—42no—
136C23×C43—41no—
137C23×C43—84no—
138C23×C43—81no—
139C23×C43—81no—
140C23×C43AGL(1,ℤ/8)11yescharacteristic
141Q8×C43—41no—
142Q8×C43—42no—
143Q8×C43—42no—
144Q8×C43—41no—
145Q8×C43—81no—
146Q8×C43—81no—
147D4×C43—42no—
148D4×C43—41no—
149D4×C43—42no—
150D4×C43—41no—
151D4×C43—81no—
152D4×C43—81no—
153D4×C43—81no—
154D4×C43—81no—
155C2×C4×C43—22no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43#12011yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12711yescharacteristic
166C2×C4×C43C2×D811yescharacteristic
167C2×C4×C43C2×D811yescharacteristic
168C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
169C8×C43—22no—
170C8×C43—81no—
171C8×C43#12011yescharacteristic
172C8×C43#12011yescharacteristic
173C8×C43#12111yescharacteristic
174C8×C43#12111yescharacteristic
175#13332C4311yesmaximal, characteristic, direct product factor, Sylow
176C22×C43—22no—
177C22×C43—84no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43—81no—
181C22×C43—162no—
182C22×C43—162no—
183C22×C43#44711yescharacteristic
184C22×C43#45911yescharacteristic
185C22×C43#49611yescharacteristic
186C4×C43—42no—
187C4×C43—81no—
188C4×C43—82no—
189C4×C43#39211yescharacteristic
190C4×C43#44711yescharacteristic
191C4×C43#45911yescharacteristic
192C4×C43#49311yescharacteristic
193C2×#510C2×C4311yescharacteristic, complemented
194C2×#509C2×C4311yescharacteristic
195C2×#495C2×C4311yescharacteristic, complemented
196C2×#362C2×C4311yescharacteristic, complemented
197C2×#361C2×C4311yescharacteristic, complemented
198#1974C2×C4311yescharacteristic, complemented
199#1376C2×C4311yescharacteristic, complemented
200C2×C43—21no—
201C2×C43—21no—
202C2×C43—161no—
203C2×C43—162no—
204C2×C43#201111yescharacteristic
205C2×C43#221212yes—
206C2×#135C22×C4311yescharacteristic
207C22×Q16C22×C4311yescharacteristic
208C22×SD16—21no—
209C22×D8C22×C4311yescharacteristic
210C2×#124—21no—
211#510—22no—
212#510—22no—
213#509—22no—
214#509—22no—
215C2×Q32—21no—
216C2×SD32—21no—
217C2×SD32—21no—
218C2×D16—21no—
219C2×M32C22×C4311yescharacteristic
220C2×M32C22×C4311yescharacteristic
221#495—22no—
222#495—22no—
223C2×#108C22×C4311yescharacteristic
224C2×#104—21no—
225#408—21no—
226C2×C4×C8C22×C4311yescharacteristic
227#362—22no—
228#361—22no—
229C43#1333211yescharacteristic, direct product factor, Sylow
230C2×#41—21no—
231C22×Q8—21no—
232C22×D4—21no—
233#135—21no—
234#135—21no—
235#135—21no—
236#135—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16—21no—
242C2×Q16D4×C4312yes—
243C2×Q16D4×C4311yescharacteristic
244C2×SD16—24no—
245C2×SD16—21no—
246C2×SD16—42no—
247C2×SD16—42no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8D4×C4312yes—
254C2×D8D4×C4311yescharacteristic
255C2×M16—21no—
256C22×C8D4×C4311yescharacteristic
257C22×C8C23×C4311yescharacteristic
258#124—24no—
259#124—42no—
260C2×C22⋊C4—42no—
261C2×C42D4×C4311yescharacteristic
262Q32—24no—
263SD32—24no—
264SD32—24no—
265D16—24no—
266M32—21no—
267M32—21no—
268M32D4×C4312yes—
269M32D4×C4312yes—
270C2×C16—21no—
271C2×C16—21no—
272#108—21no—
273#108—21no—
274#104—42no—
275C22⋊C8—42no—
276C4×C8—21no—
277C4×C8—21no—
278C24—41no—
279#41—41no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8—22no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C4311yescharacteristic
302Q16—21no—
303Q16—22no—
304Q16—21no—
305Q16—22no—
306Q16—41no—
307Q16—41no—
308SD16—48no—
309SD16—41no—
310SD16—41no—
311D8—21no—
312D8—22no—
313D8—21no—
314D8—22no—
315D8—41no—
316D8—41no—
317M16—41no—
318M16—41no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8D8×C4312yes—
323C2×C8C2×D4×C4311yescharacteristic
324C2×C8C2×D4×C4311yescharacteristic
325C2×C8C2×D4×C4311yescharacteristic
326C2×C8C2×D4×C4311yescharacteristic
327C2×C8C2×D4×C4311yescharacteristic
328C2×C8#41×C4311yescharacteristic
329C22⋊C4—48no—
330C42—21no—
331C42D8×C4312yes—
332C16—22no—
333C16—22no—
334C23—42no—
335C23—41no—
336C23—84no—
337C23—81no—
338C23—81no—
339C23AGL(1,ℤ/8)×C4311yescharacteristic
340Q8—41no—
341Q8—42no—
342Q8—42no—
343Q8—41no—
344Q8—81no—
345Q8—81no—
346D4—42no—
347D4—41no—
348D4—42no—
349D4—41no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4#120×C4311yescharacteristic
363C2×C4#121×C4311yescharacteristic
364C2×C4#127×C4311yescharacteristic
365C2×C4C2×D8×C4311yescharacteristic
366C2×C4C2×D8×C4311yescharacteristic
367C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
368C8—22no—
369C8—81no—
370C8#120×C4311yescharacteristic
371C8#120×C4311yescharacteristic
372C8#121×C4311yescharacteristic
373C8#121×C4311yescharacteristic
374C22—22no—
375C22—84no—
376C22—82no—
377C22—81no—
378C22—82no—
379C22—162no—
380C22—162no—
381C22C43×#44711yescharacteristic
382C22C43×#45911yescharacteristic
383C22C43×#49611yescharacteristic
384C4—42no—
385C4—81no—
386C4—82no—
387C4C43×#39211yescharacteristic
388C4C43×#44711yescharacteristic
389C4C43×#45911yescharacteristic
390C4C43×#49311yescharacteristic
391C2—21no—
392C2—21no—
393C2—162no—
394C2—161no—
395C2C43×#201111yescharacteristic
396C2C43×#221212yes—
subgroupG/H
center, socleC22×C43#459
commutator, Frattini, cosocleC22×C8C23×C43
prime radicalC2×C43×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#510C2semidirect
3. C2×C43×#495C2semidirect
4. C2×C43×#362C2semidirect
5. C2×C43×#361C2semidirect
6. C43×#1974C2semidirect
7. C43×#1376C2semidirect
175. #13332C43direct (N × H)
193. C2×#510C2×C43semidirect
195. C2×#495C2×C43semidirect
196. C2×#362C2×C43semidirect
197. C2×#361C2×C43semidirect
198. #1974C2×C43semidirect
199. #1376C2×C43semidirect
229. C43#13332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5102
C2×C43×#5092
C2×C43×#4952
C2×C43×#3622
C2×C43×#3612
C43×#19742
C43×#13762
#1333243