Finite Group Databasebeta

← C43×#32829 #24952846

Subgroups — C43×#32829 #24952846

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2647C211yesmaximal, characteristic, complemented
2C43×#2640C211yesmaximal, characteristic
3C43×#2095C211yesmaximal, characteristic, complemented
4C43×#2093C211yesmaximal, characteristic
5C43×#2074C211yesmaximal, characteristic, complemented
6C43×#2073C211yesmaximal, characteristic
7C43×#2068C212yesmaximal, complemented
8C43×#2067C212yesmaximal
9C43×#2057C212yesmaximal, complemented
10C43×#2042C212yesmaximal
11C43×#1832C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C43C2211yescharacteristic
13C2×#124×C43C2211yescharacteristic
14C2×#107×C43C2212yes—
15C2×#107×C43C2212yes—
16C2×C4⋊C8×C43C2212yes—
17C2×#103×C43C2212yes—
18C2×#103×C43C2212yes—
19C2×#102×C43C2212yes—
20C2×#102×C43C2212yes—
21C43×#400—22no—
22C43×#398—22no—
23C43×#397—22no—
24C43×#393—22no—
25C43×#391C2211yescharacteristic
26C43×#391C2211yescharacteristic
27C43×#390C2211yescharacteristic
28C43×#390C2211yescharacteristic
29C43×#389C2212yes—
30C43×#389C2212yes—
31C43×#384C2211yescharacteristic
32C43×#382C2211yescharacteristic
33C43×#376C2211yescharacteristic
34C43×#340C2212yes—
35C43×#340C2212yes—
36C43×#336C2211yescharacteristic
37C43×#336C2211yescharacteristic
38C43×#336C2212yes—
39C22×Q8×C43—21no—
40C22×Q8×C43C2311yescharacteristic
41C22×D4×C43C2311yescharacteristic
42C22×C8×C43C2312yes—
43C22×C8×C43C2312yes—
44C4⋊Q8×C43—42no—
45#124×C43—42no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43—22no—
49C2×C4⋊C4×C43—22no—
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C4⋊C4×C43C2311yescharacteristic
52C2×C4⋊C4×C43C2312yes—
53C2×C4⋊C4×C43C2312yes—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—22no—
57C2×C22⋊C4×C43—22no—
58C2×C42×C43C2311yescharacteristic
59C2×C42×C43C2311yescharacteristic
60C2×C42×C43C2311yescharacteristic
61#107×C43—42no—
62#107×C43—42no—
63C4⋊C8×C43—42no—
64#103×C43—42no—
65#103×C43—42no—
66#102×C43—42no—
67#102×C43—42no—
68#95×C43—22no—
69#95×C43—22no—
70#95×C43—22no—
71#95×C43—22no—
72#95×C43—22no—
73#95×C43D412yes—
74#95×C43D412yes—
75C24×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—22no—
78C2×Q8×C43—22no—
79C2×Q8×C43—21no—
80C2×Q8×C43—42no—
81C2×Q8×C43—82no—
82C2×D4×C43—21no—
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—22no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—22no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2411yescharacteristic
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—82no—
110C4⋊C4×C43—82no—
111C4⋊C4×C43—82no—
112C22⋊C4×C43—42no—
113C22⋊C4×C43—42no—
114C22⋊C4×C43—82no—
115C22⋊C4×C43—82no—
116C42×C43—21no—
117C42×C43—22no—
118C42×C43—22no—
119C42×C43—21no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—42no—
124C23×C43—42no—
125C23×C43C22×D411yescharacteristic
126Q8×C43—42no—
127Q8×C43—42no—
128Q8×C43—84no—
129D4×C43—42no—
130D4×C43—42no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43H(5,𝔽2)11yescharacteristic
155C2×C4×C43H(5,𝔽2)12yes—
156C2×C4×C432−1+412yes—
157C2×C4×C432−1+411yescharacteristic
158C8×C43—42no—
159C8×C43—42no—
160#32829C4311yesmaximal, characteristic, direct product factor, Sylow
161C22×C43—81no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43—82no—
165C22×C43—82no—
166C22×C43#53511yescharacteristic
167C22×C43#53611yescharacteristic
168C22×C43#53711yescharacteristic
169C22×C43#57612yes—
170C22×C43#57812yes—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—42no—
174C4×C43—42no—
175C4×C43—81no—
176C4×C43—82no—
177C4×C43—81no—
178C4×C43—81no—
179C4×C43—82no—
180C4×C43#56212yes—
181C4×C43#56312yes—
182#2647C2×C4311yescharacteristic, complemented
183#2640C2×C4311yescharacteristic
184#2095C2×C4311yescharacteristic, complemented
185#2093C2×C4311yescharacteristic
186#2074C2×C4311yescharacteristic, complemented
187#2073C2×C4311yescharacteristic
188#2068C2×C4312yescomplemented
189#2067C2×C4312yes—
190#2057C2×C4312yescomplemented
191#2042C2×C4312yes—
192#1832C2×C4311yescharacteristic, complemented
193C2×C43—161no—
194C2×C43#282011yescharacteristic
195C2×C43#322011yescharacteristic
196C2×C43#322311yescharacteristic
197C2×C43#324312yes—
198C2×C43#326212yes—
199C2×C4⋊Q8C22×C4311yescharacteristic
200C2×#124C22×C4311yescharacteristic
201C2×#107C22×C4312yes—
202C2×#107C22×C4312yes—
203C2×C4⋊C8C22×C4312yes—
204C2×#103C22×C4312yes—
205C2×#103C22×C4312yes—
206C2×#102C22×C4312yes—
207C2×#102C22×C4312yes—
208#400—22no—
209#398—22no—
210#397—22no—
211#393—22no—
212#391C22×C4311yescharacteristic
213#391C22×C4311yescharacteristic
214#390C22×C4311yescharacteristic
215#390C22×C4311yescharacteristic
216#389C22×C4312yes—
217#389C22×C4312yes—
218#384C22×C4311yescharacteristic
219#382C22×C4311yescharacteristic
220#376C22×C4311yescharacteristic
221#340C22×C4312yes—
222#340C22×C4312yes—
223#336C22×C4312yes—
224#336C22×C4311yescharacteristic
225#336C22×C4311yescharacteristic
226C43#3282911yescharacteristic, direct product factor, Sylow
227C22×Q8—21no—
228C22×Q8C23×C4311yescharacteristic
229C22×D4C23×C4311yescharacteristic
230C22×C8C23×C4312yes—
231C22×C8C23×C4312yes—
232C4⋊Q8—42no—
233#124—42no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4C23×C4311yescharacteristic
239C2×C4⋊C4C23×C4311yescharacteristic
240C2×C4⋊C4C23×C4312yes—
241C2×C4⋊C4C23×C4312yes—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C42C23×C4311yescharacteristic
247C2×C42C23×C4311yescharacteristic
248C2×C42C23×C4311yescharacteristic
249#107—42no—
250#107—42no—
251C4⋊C8—42no—
252#103—42no—
253#103—42no—
254#102—42no—
255#102—42no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95D4×C4312yes—
262#95D4×C4312yes—
263C24—21no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—42no—
269C2×Q8—82no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4C2×D4×C4311yescharacteristic
280C22×C4C2×D4×C4312yes—
281C22×C4C2×D4×C4312yes—
282C22×C4C2×D4×C4311yescharacteristic
283C22×C4C24×C4311yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—82no—
298C4⋊C4—82no—
299C4⋊C4—82no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—21no—
305C42—22no—
306C42—22no—
307C42—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23C22×D4×C4311yescharacteristic
314Q8—42no—
315Q8—42no—
316Q8—84no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4H(5,𝔽2)×C4311yescharacteristic
343C2×C4H(5,𝔽2)×C4312yes—
344C2×C42−1+4×C4312yes—
345C2×C42−1+4×C4311yescharacteristic
346C8—42no—
347C8—42no—
348C22—81no—
349C22—81no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22C43×#53511yescharacteristic
354C22C43×#53611yescharacteristic
355C22C43×#53711yescharacteristic
356C22C43×#57612yes—
357C22C43×#57812yes—
358C4—41no—
359C4—41no—
360C4—42no—
361C4—42no—
362C4—81no—
363C4—81no—
364C4—82no—
365C4—82no—
366C4—81no—
367C4C43×#56212yes—
368C4C43×#56312yes—
369C2—161no—
370C2C43×#282011yescharacteristic
371C2C43×#322011yescharacteristic
372C2C43×#322311yescharacteristic
373C2C43×#324312yes—
374C2C43×#326212yes—
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2647C2semidirect
3. C43×#2095C2semidirect
5. C43×#2074C2semidirect
7. C43×#2068C2semidirect
9. C43×#2057C2semidirect
11. C43×#1832C2semidirect
160. #32829C43direct (N × H)
182. #2647C2×C43semidirect
184. #2095C2×C43semidirect
186. #2074C2×C43semidirect
188. #2068C2×C43semidirect
190. #2057C2×C43semidirect
192. #1832C2×C43semidirect
226. C43#32829direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26472
C43×#26402
C43×#20952
C43×#20932
C43×#20742
C43×#20732
C43×#20682
C43×#20672
C43×#20572
C43×#20422
C43×#18322
#3282943