Finite Group Databasebeta

← C43×#29117 #24949134

Subgroups — C43×#29117 #24949134

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2629C211yesmaximal, characteristic
2C43×#2310C211yesmaximal, characteristic
3C43×#2072C212yesmaximal, complemented
4C43×#2026C212yesmaximal, complemented
5C43×#1935C212yesmaximal, complemented
6C43×#1933C212yesmaximal, complemented
7C43×#1825C212yesmaximal
8C43×#1787C212yesmaximal
9C43×#1750C211yesmaximal, characteristic
10C23×Q8×C43C2211yescharacteristic
11C2×#125×C43C2211yescharacteristic
12C2×#117×C43C2211yescharacteristic
13C2×#117×C43C2211yescharacteristic
14C2×#103×C43C2212yes—
15C2×#103×C43C2212yes—
16C2×#103×C43C2212yes—
17C2×#103×C43C2212yes—
18C2×C22⋊C8×C43C2212yes—
19C2×#97×C43C2211yescharacteristic
20C2×C4×C8×C43C2211yescharacteristic
21C43×#398—22no—
22C43×#396—22no—
23C43×#391—22no—
24C43×#391C2212yes—
25C43×#391C2212yes—
26C43×#389C2212yes—
27C43×#384C2211yescharacteristic
28C43×#381—22no—
29C43×#380C2212yes—
30C43×#340C2212yes—
31C43×#340C2212yes—
32C43×#340C2212yes—
33C43×#340C2212yes—
34C43×#336C2212yes—
35C22×Q8×C43—24no—
36C22×Q8×C43—21no—
37C22×Q8×C43—24no—
38C22×Q8×C43—41no—
39C22×Q8×C43—41no—
40C22×Q8×C43C2312yes—
41C23×C4×C43—21no—
42C23×C4×C43C2311yescharacteristic
43C22×C8×C43C2312yes—
44C22×C8×C43C2312yes—
45#125×C43—41no—
46#125×C43—41no—
47#117×C43—24no—
48#117×C43—41no—
49#117×C43—41no—
50C2×C4⋊C4×C43—22no—
51C2×C4⋊C4×C43—22no—
52C2×C4⋊C4×C43—22no—
53C2×C4⋊C4×C43D412yes—
54C2×C4⋊C4×C43C2312yes—
55C2×C4⋊C4×C43C2312yes—
56C2×C4⋊C4×C43C2312yes—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—22no—
59C2×C22⋊C4×C43D412yes—
60C2×C42×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C2×C42×C43C2311yescharacteristic
63#103×C43—24no—
64#103×C43—24no—
65#103×C43—42no—
66#103×C43—42no—
67C22⋊C8×C43—24no—
68#97×C43—41no—
69C4×C8×C43—41no—
70#95×C43—22no—
71#95×C43—24no—
72#95×C43—24no—
73#95×C43—22no—
74C24×C43C2×D411yescharacteristic
75C2×Q8×C43—24no—
76C2×Q8×C43—22no—
77C2×Q8×C43—22no—
78C2×Q8×C43—22no—
79C2×Q8×C43—22no—
80C2×Q8×C43—22no—
81C2×Q8×C43—48no—
82C2×Q8×C43—48no—
83C2×Q8×C43—42no—
84C2×Q8×C43—42no—
85C2×Q8×C43#4114yes—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—24no—
90C22×C4×C43—22no—
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—22no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4114yes—
100C22×C4×C43C2411yescharacteristic
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—24no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—42no—
113C4⋊C4×C43—44no—
114C4⋊C4×C43—82no—
115C4⋊C4×C43—82no—
116C22⋊C4×C43—42no—
117C22⋊C4×C43—42no—
118C22⋊C4×C43—82no—
119C42×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—21no—
123C42×C43—42no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43#12412yes—
129C23×C43C22×D411yescharacteristic
130Q8×C43—24no—
131Q8×C43—24no—
132Q8×C43—48no—
133Q8×C43—42no—
134Q8×C43—42no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—24no—
138C2×C4×C43—24no—
139C2×C4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—48no—
147C2×C4×C43—42no—
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×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43#12412yes—
159C2×C4×C43C2×#4112yes—
160C2×C4×C43C2×#4112yes—
161C2×C4×C43H(5,𝔽2)11yescharacteristic
162C2×C4×C43H(5,𝔽2)11yescharacteristic
163C8×C43—42no—
164C8×C43—42no—
165#29117C4311yesmaximal, characteristic, direct product factor, Sylow
166C22×C43—22no—
167C22×C43—24no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—42no—
171C22×C43#52511yescharacteristic
172C22×C43C2×#12411yescharacteristic
173C22×C43#53411yescharacteristic
174C22×C43#57712yes—
175C22×C43#57812yes—
176C4×C43—22no—
177C4×C43—44no—
178C4×C43—42no—
179C4×C43—42no—
180C4×C43—82no—
181C4×C43—82no—
182C4×C43—82no—
183C4×C43#55112yes—
184C4×C43#55112yes—
185#2629C2×C4311yescharacteristic
186#2310C2×C4311yescharacteristic
187#2072C2×C4312yescomplemented
188#2026C2×C4312yescomplemented
189#1935C2×C4312yescomplemented
190#1933C2×C4312yescomplemented
191#1825C2×C4312yes—
192#1787C2×C4312yes—
193#1750C2×C4311yescharacteristic
194C2×C43—42no—
195C2×C43#256111yescharacteristic
196C2×C43#312611yescharacteristic
197C2×C43#312711yescharacteristic
198C2×C43#313712yes—
199C2×C43#320112yes—
200C23×Q8C22×C4311yescharacteristic
201C2×#125C22×C4311yescharacteristic
202C2×#117C22×C4311yescharacteristic
203C2×#117C22×C4311yescharacteristic
204C2×#103C22×C4312yes—
205C2×#103C22×C4312yes—
206C2×#103C22×C4312yes—
207C2×#103C22×C4312yes—
208C2×C22⋊C8C22×C4312yes—
209C2×#97C22×C4311yescharacteristic
210C2×C4×C8C22×C4311yescharacteristic
211#398—22no—
212#396—22no—
213#391—22no—
214#391C22×C4312yes—
215#391C22×C4312yes—
216#389C22×C4312yes—
217#384C22×C4311yescharacteristic
218#381—22no—
219#380C22×C4312yes—
220#340C22×C4312yes—
221#340C22×C4312yes—
222#340C22×C4312yes—
223#340C22×C4312yes—
224#336C22×C4312yes—
225C43#2911711yescharacteristic, direct product factor, Sylow
226C22×Q8—24no—
227C22×Q8—21no—
228C22×Q8—24no—
229C22×Q8—41no—
230C22×Q8—41no—
231C22×Q8C23×C4312yes—
232C23×C4—21no—
233C23×C4C23×C4311yescharacteristic
234C22×C8C23×C4312yes—
235C22×C8C23×C4312yes—
236#125—41no—
237#125—41no—
238#117—24no—
239#117—41no—
240#117—41no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4D4×C4312yes—
245C2×C4⋊C4C23×C4312yes—
246C2×C4⋊C4C23×C4312yes—
247C2×C4⋊C4C23×C4312yes—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4D4×C4312yes—
251C2×C42—21no—
252C2×C42C23×C4311yescharacteristic
253C2×C42C23×C4311yescharacteristic
254#103—24no—
255#103—24no—
256#103—42no—
257#103—42no—
258C22⋊C8—24no—
259#97—41no—
260C4×C8—41no—
261#95—22no—
262#95—24no—
263#95—24no—
264#95—22no—
265C24C2×D4×C4311yescharacteristic
266C2×Q8—24no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—48no—
273C2×Q8—48no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8#41×C4314yes—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4C2×D4×C4312yes—
288C22×C4C2×D4×C4312yes—
289C22×C4C2×D4×C4311yescharacteristic
290C22×C4#41×C4314yes—
291C22×C4C24×C4311yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—24no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—42no—
304C4⋊C4—44no—
305C4⋊C4—82no—
306C4⋊C4—82no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—82no—
310C42—21no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—42no—
315C23—21no—
316C23—21no—
317C23—22no—
318C23—22no—
319C23#124×C4312yes—
320C23C22×D4×C4311yescharacteristic
321Q8—24no—
322Q8—24no—
323Q8—48no—
324Q8—42no—
325Q8—42no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—48no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4#124×C4312yes—
350C2×C4C2×#41×C4312yes—
351C2×C4C2×#41×C4312yes—
352C2×C4H(5,𝔽2)×C4311yescharacteristic
353C2×C4H(5,𝔽2)×C4311yescharacteristic
354C8—42no—
355C8—42no—
356C22—24no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22C43×#52511yescharacteristic
362C22C2×#124×C4311yescharacteristic
363C22C43×#53411yescharacteristic
364C22C43×#57712yes—
365C22C43×#57812yes—
366C4—22no—
367C4—42no—
368C4—42no—
369C4—44no—
370C4—82no—
371C4—82no—
372C4—82no—
373C4C43×#55112yes—
374C4C43×#55112yes—
375C2—42no—
376C2C43×#256111yescharacteristic
377C2C43×#312611yescharacteristic
378C2C43×#312711yescharacteristic
379C2C43×#313712yes—
380C2C43×#320112yes—
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2072C2semidirect
4. C43×#2026C2semidirect
5. C43×#1935C2semidirect
6. C43×#1933C2semidirect
165. #29117C43direct (N × H)
187. #2072C2×C43semidirect
188. #2026C2×C43semidirect
189. #1935C2×C43semidirect
190. #1933C2×C43semidirect
225. C43#29117direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26292
C43×#23102
C43×#20722
C43×#20262
C43×#19352
C43×#19332
C43×#18252
C43×#17872
C43×#17502
#2911743