Finite Group Databasebeta

← #25009670

Subgroups — #25009670

Order 11008.

332 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135940C211yesmaximal, characteristic
2#19133636C211yesmaximal, characteristic
3#19133568C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic
5#19132622C211yesmaximal, characteristic
6#19132541C211yesmaximal, characteristic
7C43×#2843C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583234—21no—
10#14583055—21no—
11#14582939—21no—
12#14582668C2211yescharacteristic
13#14582659—21no—
14#14582635—21no—
15#14582635—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C43×#400—21no—
19C43×#400C2211yescharacteristic
20C43×#398—21no—
21C43×#398—21no—
22C43×#398—21no—
23C43×#395—21no—
24C43×#395C2211yescharacteristic
25C43×#384C2211yescharacteristic
26C43×#383—21no—
27C2×#10621885—41no—
28C2×#10621877—21no—
29#13063324—41no—
30#13063316—41no—
31#13063304—21no—
32#13063304—21no—
33#13063284—21no—
34#13063258—41no—
35#13063258—41no—
36#13063256—41no—
37#13063249—41no—
38#13063248—41no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C22×Q8×C43D411yescharacteristic
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C42×C43D411yescharacteristic
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43D411yescharacteristic
61#95×C43D411yescharacteristic
62C2×Q8×C43—41no—
63C2×Q8×C43—81no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C2×Dic86—21no—
74C2×Dic86—21no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—81no—
79C4⋊C4×C43—81no—
80C4⋊C4×C43—81no—
81C4⋊C4×C43—81no—
82C4⋊C4×C43—81no—
83C4⋊C4×C43—81no—
84C42×C43—21no—
85C42×C43Q1612yescomplemented
86C22⋊Dic43—41no—
87#10621885—82no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C4×Dic43—41no—
95#10621877—22no—
96#10621877—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C23×C43#12011yescharacteristic
101Q8×C43—42no—
102Q8×C43—81no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43C2×Q1611yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×Dic43—41no—
129C2×Dic43—41no—
130Dic86—81no—
131Dic86—81no—
132C43⋊C8—42no—
133C43⋊C8—81no—
134C43⋊C8—81no—
135#12259—431nomaximal, Sylow
136C22×C43—21no—
137C22×C43—21no—
138C22×C43#45111yescharacteristic
139C22×C43#45611yescharacteristic
140C22×C43B(4,𝔽2)11yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—42no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C43—81no—
147C4×C43—81no—
148C4×C43—81no—
149C4×C43—81no—
150C4×C43—81no—
151Dic43—81no—
152Dic43—81no—
153#2843D4311yescharacteristic
154#2060—431no—
155#1617—431no—
156#1605—431no—
157#1354—431no—
158#1353—431no—
159#1325—431no—
160C2×C43—21no—
161C2×C43—21no—
162C2×C43#160511yescharacteristic
163C2×C43#220011yescharacteristic
164C2×C43#220311yescharacteristic
165#544—431no—
166#484—861no—
167#451—861no—
168#428—861no—
169#400—21no—
170#400C2×D4311yescharacteristic
171#398—21no—
172#398—21no—
173#398—21no—
174#395—21no—
175#395C2×D4311yescharacteristic
176#384C2×D4311yescharacteristic
177#383—21no—
178#343—431no—
179#339—861no—
180#328—861no—
181#328—861no—
182#324—431no—
183#324—431no—
184C43#1225911yescharacteristic, complemented, Sylow
185C22×Q8C22⋊D4311yescharacteristic
186C2×Q16—1721no—
187C2×M16—861no—
188C4⋊Q8—1721no—
189#125—1721no—
190C22⋊Q8—861no—
191C22⋊Q8—861no—
192#117—861no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C22⋊D4311yescharacteristic
200C2×C4⋊C4C22⋊D4311yescharacteristic
201C2×C4⋊C4C22×D4311yescharacteristic
202C2×C42C22⋊D4311yescharacteristic
203#107—1721no—
204#107—1721no—
205#106—1721no—
206#103—1721no—
207#103—1721no—
208C22⋊C8—861no—
209C22⋊C8—861no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95C22⋊D4311yescharacteristic
219#95C22⋊D4311yescharacteristic
220C2×Q8—41no—
221C2×Q8—81no—
222C2×Q8—861no—
223C2×Q8—861no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4C2×C22⋊D4311yescharacteristic
231C22×C4C2×C22⋊D4311yescharacteristic
232C22×C4C2×C22⋊D4311yescharacteristic
233Q16—3442no—
234M16—862no—
235M16—1721no—
236C2×C8—1721no—
237C2×C8—1721no—
238C2×C8—1721no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—1721no—
253C4⋊C4—1721no—
254C22⋊C4—1721no—
255C42—21no—
256C42—1721no—
257C42#1062188512yescomplemented
258C23#1306329411yescharacteristic
259Q8—42no—
260Q8—81no—
261Q8—3441no—
262Q8—3441no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4C2×#1062188511yescharacteristic
289C2×C4#1306335611yescharacteristic
290C8—3441no—
291C8—3441no—
292C8—1722no—
293C22—21no—
294C22—21no—
295C22#1458305511yescharacteristic
296C22#1458308211yescharacteristic
297C22#1458308611yescharacteristic
298C4—21no—
299C4—21no—
300C4—42no—
301C4—41no—
302C4—41no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—3441no—
309C4—3441no—
310C2—21no—
311C2—21no—
312C2#1913356911yescharacteristic
313C2#1913660211yescharacteristic
314C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2843C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2843D43
hypocenterC43#12259
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2843

Complements

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

NH ≅ G/Ntype
85. C42×C43Q16semidirect
184. C43#12259semidirect
257. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191359402
#191336362
#191335682
#191326252
#191326222
#191325412
C43×#28432
#1225943