Finite Group Databasebeta

← C43×#29867 #24949884

Subgroups — C43×#29867 #24949884

Order 11008.

698 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#477C211yesmaximal, characteristic
2C2×C43×#475C211yesmaximal, characteristic
3C43×#2862C211yesmaximal, characteristic
4C43×#2295C211yesmaximal, characteristic
5C43×#2085C214yesmaximal
6C43×#2074C214yesmaximal
7C43×#1988C211yesmaximal, characteristic
8C43×#1987C211yesmaximal, characteristic
9C43×#1831C211yesmaximal, characteristic
10C2×C4⋊Q8×C43C2211yescharacteristic
11C2×C4⋊Q8×C43C2211yescharacteristic
12C2×C4×Q8×C43C2211yescharacteristic
13C43×#477—24no—
14C43×#475—24no—
15C2×#107×C43C2212yes—
16C2×#106×C43C2212yes—
17C2×C4⋊C8×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×#103×C43C2212yes—
20C2×#103×C43C2212yes—
21C43×#391—21no—
22C43×#391—21no—
23C43×#391—22no—
24C43×#391C2212yes—
25C43×#389C2212yes—
26C43×#387—22no—
27C43×#382C2214yes—
28C4×C4⋊C4×C43—21no—
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#376—21no—
31C43×C43C2211yescharacteristic
32C43×#340C2214yes—
33C43×#340C2214yes—
34C43×#336C2214yes—
35C22×Q8×C43—21no—
36C22×Q8×C43—21no—
37C22×Q8×C43C2311yescharacteristic
38C22×C8×C43C2312yes—
39C22×C8×C43C2312yes—
40C4⋊Q8×C43—22no—
41C4⋊Q8×C43—22no—
42C4⋊Q8×C43—22no—
43C4⋊Q8×C43—22no—
44C4×Q8×C43—22no—
45C4×Q8×C43D414yes—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—22no—
50C2×C4⋊C4×C43C2312yes—
51C2×C4⋊C4×C43C2312yes—
52C2×C4⋊C4×C43C2312yes—
53C2×C4⋊C4×C43C2311yescharacteristic
54C2×C42×C43—21no—
55C2×C42×C43—21no—
56C2×C42×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D412yes—
59C2×C42×C43C2312yes—
60C2×C42×C43C2311yescharacteristic
61#107×C43—24no—
62#106×C43—24no—
63C4⋊C8×C43—22no—
64C4⋊C8×C43—22no—
65#103×C43—24no—
66#103×C43—24no—
67#95×C43—22no—
68#95×C43—22no—
69#95×C43—22no—
70#95×C43—21no—
71#95×C43—24no—
72#95×C43—24no—
73C2×Q8×C43—21no—
74C2×Q8×C43—22no—
75C2×Q8×C43—22no—
76C2×Q8×C43—44no—
77C2×Q8×C43—42no—
78C2×Q8×C43—42no—
79C2×Q8×C43—42no—
80C2×Q8×C43—42no—
81C2×Q8×C43C2×D412yes—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—22no—
86C22×C4×C43—22no—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2411yescharacteristic
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43—24no—
95C2×C8×C43—24no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—44no—
105C4⋊C4×C43—42no—
106C4⋊C4×C43—42no—
107C4⋊C4×C43C2×D412yes—
108C42×C43—24no—
109C42×C43—22no—
110C42×C43—22no—
111C42×C43—22no—
112C42×C43—22no—
113C42×C43—42no—
114C42×C43—42no—
115C42×C43C2×D412yes—
116C42×C43#4112yes—
117C23×C43C22×D411yescharacteristic
118Q8×C43—22no—
119Q8×C43—22no—
120Q8×C43—42no—
121Q8×C43—84no—
122Q8×C43—84no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—44no—
142C2×C4×C43#12112yes—
143C2×C4×C43#12112yes—
144C2×C4×C43#13512yes—
145C2×C4×C43#13712yes—
146C2×C4×C43C22×D411yescharacteristic
147C2×C4×C43C2×#4111yescharacteristic
148C2×C4×C432−1+412yes—
149C2×C4×C432−1+412yes—
150C8×C43—42no—
151C8×C43—42no—
152#29867C4311yesmaximal, characteristic, direct product factor, Sylow
153C22×C43C2×#12111yescharacteristic
154C22×C43#53612yes—
155C22×C43C2×#13511yescharacteristic
156C22×C43C2×#13711yescharacteristic
157C22×C43#57512yes—
158C4×C43—22no—
159C4×C43—42no—
160C4×C43—42no—
161C4×C43—42no—
162C4×C43—42no—
163C4×C43—82no—
164C4×C43—82no—
165C4×C43—82no—
166C4×C43#46414yes—
167C4×C43#53611yescharacteristic
168C4×C43#53611yescharacteristic
169C4×C43#54112yes—
170C2×#477C2×C4311yescharacteristic
171C2×#475C2×C4311yescharacteristic
172#2862C2×C4311yescharacteristic
173#2295C2×C4311yescharacteristic
174#2085C2×C4314yes—
175#2074C2×C4314yes—
176#1988C2×C4311yescharacteristic
177#1987C2×C4311yescharacteristic
178#1831C2×C4311yescharacteristic
179C2×C43#262111yescharacteristic
180C2×C43C2×#46411yescharacteristic
181C2×C43#304011yescharacteristic
182C2×C43#323312yes—
183C2×C43#323712yes—
184C2×C4⋊Q8C22×C4311yescharacteristic
185C2×C4⋊Q8C22×C4311yescharacteristic
186C2×C4×Q8C22×C4311yescharacteristic
187#477—24no—
188#475—24no—
189C2×#107C22×C4312yes—
190C2×#106C22×C4312yes—
191C2×C4⋊C8C22×C4311yescharacteristic
192C2×C4⋊C8C22×C4311yescharacteristic
193C2×#103C22×C4312yes—
194C2×#103C22×C4312yes—
195#391—21no—
196#391—21no—
197#391—22no—
198#391C22×C4312yes—
199#389C22×C4312yes—
200#387—22no—
201#382C22×C4314yes—
202C4×C4⋊C4—21no—
203C4×C4⋊C4C22×C4311yescharacteristic
204#376—21no—
205C43C22×C4311yescharacteristic
206#340C22×C4314yes—
207#340C22×C4314yes—
208#336C22×C4314yes—
209C43#2986711yescharacteristic, direct product factor, Sylow
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8C23×C4311yescharacteristic
213C22×C8C23×C4312yes—
214C22×C8C23×C4312yes—
215C4⋊Q8—22no—
216C4⋊Q8—22no—
217C4⋊Q8—22no—
218C4⋊Q8—22no—
219C4×Q8—22no—
220C4×Q8D4×C4314yes—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4C23×C4312yes—
226C2×C4⋊C4C23×C4312yes—
227C2×C4⋊C4C23×C4312yes—
228C2×C4⋊C4C23×C4311yescharacteristic
229C2×C42—21no—
230C2×C42—21no—
231C2×C42D4×C4311yescharacteristic
232C2×C42D4×C4311yescharacteristic
233C2×C42D4×C4312yes—
234C2×C42C23×C4312yes—
235C2×C42C23×C4311yescharacteristic
236#107—24no—
237#106—24no—
238C4⋊C8—22no—
239C4⋊C8—22no—
240#103—24no—
241#103—24no—
242#95—22no—
243#95—22no—
244#95—22no—
245#95—21no—
246#95—24no—
247#95—24no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—44no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8C2×D4×C4312yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4C2×D4×C4312yes—
263C22×C4C2×D4×C4312yes—
264C22×C4C2×D4×C4311yescharacteristic
265C22×C4C2×D4×C4311yescharacteristic
266C22×C4C24×C4311yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—24no—
270C2×C8—24no—
271C4⋊C4—24no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—44no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4C2×D4×C4312yes—
283C42—24no—
284C42—22no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—42no—
289C42—42no—
290C42C2×D4×C4312yes—
291C42#41×C4312yes—
292C23C22×D4×C4311yescharacteristic
293Q8—22no—
294Q8—22no—
295Q8—42no—
296Q8—84no—
297Q8—84no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4#121×C4312yes—
318C2×C4#121×C4312yes—
319C2×C4#135×C4312yes—
320C2×C4#137×C4312yes—
321C2×C4C22×D4×C4311yescharacteristic
322C2×C4C2×#41×C4311yescharacteristic
323C2×C42−1+4×C4312yes—
324C2×C42−1+4×C4312yes—
325C8—42no—
326C8—42no—
327C22C2×#121×C4311yescharacteristic
328C22C43×#53612yes—
329C22C2×#135×C4311yescharacteristic
330C22C2×#137×C4311yescharacteristic
331C22C43×#57512yes—
332C4—22no—
333C4—42no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—82no—
338C4—82no—
339C4—82no—
340C4C43×#46414yes—
341C4C43×#53611yescharacteristic
342C4C43×#53611yescharacteristic
343C4C43×#54112yes—
344C2C43×#262111yescharacteristic
345C2C2×C43×#46411yescharacteristic
346C2C43×#304011yescharacteristic
347C2C43×#323312yes—
348C2C43×#323712yes—
subgroupG/H
center, socle, prime radicalC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
152. #29867C43direct (N × H)
209. C43#29867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4772
C2×C43×#4752
C43×#28622
C43×#22952
C43×#20852
C43×#20742
C43×#19882
C43×#19872
C43×#18312
#2986743