Finite Group Databasebeta

← #25008699

Subgroups — #25008699

Order 11008.

476 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 71 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#19136523C212yesmaximal, complemented
2#19135593C211yesmaximal, characteristic
3#19132607C212yesmaximal, complemented
4#19132519C211yesmaximal, characteristic, complemented
5C43×#3189C211yesmaximal, characteristic, complemented
6C22×D344C2211yescharacteristic
7C2×#13063299—21no—
8C2×#13063268—22no—
9C2×#13063247—21no—
10#14582699—22no—
11C22⋊(C43⋊C16)C2212yes—
12#14582662C2211yescharacteristic
13C2×C22⋊Q8×C43—21no—
14C43×#484—22no—
15C43×#467—21no—
16C43×#467C2212yes—
17C43×#451—22no—
18C2×C22⋊C8×C43C2211yescharacteristic
19C22×D172—21no—
20C22×C22⋊D43—41no—
21C2×D344—22no—
22C2×D344—42no—
23#13063299—42no—
24#13063299—42no—
25C2×C4⋊Dic43—21no—
26C2×(C2×D43)⋊C4—41no—
27#13063268—44no—
28C2×C43⋊C16—22no—
29#13063247—42no—
30C22×Q8×C43—21no—
31C23×C4×C43D411yescharacteristic
32C2×Q16×C43—21no—
33C2×Q16×C43D412yescomplemented
34C22×C8×C43D411yescharacteristic
35C22×C8×C43C2311yescharacteristic
36C22⋊Q8×C43—22no—
37C22⋊Q8×C43—22no—
38C22⋊Q8×C43—41no—
39C22⋊Q8×C43—41no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—41no—
42C2×C22⋊C4×C43—41no—
43#107×C43—21no—
44#107×C43D412yescomplemented
45#103×C43—22no—
46#103×C43—22no—
47C22⋊C8×C43—22no—
48C24×C43D811yescharacteristic
49C23×D43—41no—
50C2×Q8×C43—22no—
51C2×Q8×C43—41no—
52C2×Q8×C43—81no—
53C2×Q8×C43—81no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—41no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43D811yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C2×C22⋊D43—44no—
63C2×C22⋊D43—82no—
64C2×C22⋊D43—82no—
65C22×Dic43—41no—
66C2×D172—22no—
67C2×D172—41no—
68C2×D172—41no—
69C2×D172—41no—
70C2×D172—41no—
71C2×D172—41no—
72Q16×C43—42no—
73Q16×C43—81no—
74C2×C8×C43—21no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43C2×D412yes—
78C4⋊C4×C43—22no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—42no—
81C4⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C22⋊C4×C43—42no—
84(C2×D43)⋊C4—44no—
85C4⋊Dic43—22no—
86C4⋊Dic43—41no—
87D344—24no—
88D344—42no—
89C43⋊C16—42no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43—41no—
93C23×C43—41no—
94C23×C43SD3212yescomplemented
95C23×C43C2×D811yescharacteristic
96C22×D43—42no—
97C22×D43—81no—
98C22×D43—81no—
99C22×D43—81no—
100C22×D43—81no—
101C22×D43—81no—
102C22×D43—81no—
103Q8×C43—42no—
104Q8×C43—42no—
105Q8×C43—82no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—81no—
115C2×C4×C43—82no—
116C2×C4×C43—82no—
117C2×C4×C43#12011yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C22⋊D43—88no—
120C2×Dic43—42no—
121C2×Dic43—81no—
122C2×Dic43—81no—
123D172—42no—
124D172—42no—
125D172—81no—
126D172—81no—
127C8×C43—22no—
128C8×C43—41no—
129#12103—431nomaximal, Sylow
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—22no—
133C22×C43—42no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—81no—
137C22×C43#44711yescharacteristic
138C22×C43C2×SD3211yescharacteristic
139C22×C43#51011yescharacteristic
140C2×D43—82no—
141C2×D43—82no—
142C2×D43—82no—
143C2×D43—161no—
144C2×D43—161no—
145C2×D43—161no—
146C2×D43—161no—
147C4×C43—21no—
148C4×C43—41no—
149C4×C43—82no—
150C4×C43—82no—
151C4×C43#45311yescharacteristic
152C4×C43B(4,𝔽2)11yescharacteristic
153Dic43—82no—
154#3189D4311yescharacteristic, complemented
155#2187—432no—
156#1999—431no—
157#1348—432no—
158#1314—431no—
159C2×C43—21no—
160C2×C43—21no—
161C2×C43—42no—
162C2×C43#159511yescharacteristic
163C2×C43#218511yescharacteristic
164C2×C43#219011yescharacteristic
165D43—162no—
166C22×D8—431no—
167C2×C22⋊Q8—21no—
168C2×#121—861no—
169C2×SD32—862no—
170#484—22no—
171#467—21no—
172#467C2×D4312yes—
173#451—22no—
174C2×#102—861no—
175C2×C22⋊C8C2×D4311yescharacteristic
176#357—862no—
177C22⋊C16—432no—
178#340—431no—
179C43#1210311yescharacteristic, complemented, Sylow
180C22×Q8—21no—
181C22×D4—861no—
182C22×D4—1721no—
183C23×C4C22⋊D4311yescharacteristic
184C2×Q16—21no—
185C2×Q16C22⋊D4312yescomplemented
186C2×D8—862no—
187C2×D8—1722no—
188C22×C8C22⋊D4311yescharacteristic
189C22×C8C22×D4311yescharacteristic
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192C22⋊Q8—41no—
193C22⋊Q8—41no—
194#121—1722no—
195#121—1722no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—861no—
199C2×C22⋊C4—41no—
200C2×C22⋊C4—1721no—
201SD32—1724no—
202C2×C16—862no—
203#107—21no—
204#107C22⋊D4312yescomplemented
205#103—22no—
206#103—22no—
207#102—1722no—
208C22⋊C8—22no—
209C24—1721no—
210C24#1062188211yescharacteristic
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—81no—
214C2×Q8—81no—
215C2×D4—862no—
216C2×D4—3442no—
217C2×D4—3442no—
218C2×D4—1721no—
219C2×D4—1721no—
220C2×D4—1721no—
221C2×D4—1724no—
222C2×D4—1721no—
223C2×D4—1721no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—1721no—
231C22×C4#1062188211yescharacteristic
232C22×C4C2×C22⋊D4311yescharacteristic
233Q16—42no—
234Q16—81no—
235D8—864no—
236D8—1722no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8C2×C22⋊D4312yes—
241C4⋊C4—22no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—862no—
246C4⋊C4—1721no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—1724no—
250C16—1722no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—3441no—
256C23—3441no—
257C23—3441no—
258C23—3441no—
259C23—3441no—
260C23—3441no—
261C23—1722no—
262C23#1306326812yescomplemented
263C23C2×#1062188211yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—82no—
267D4—3441no—
268D4—3448no—
269D4—3441no—
270D4—1722no—
271D4—1722no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—3441no—
284C2×C4—3441no—
285C2×C4—1722no—
286C2×C4#1306329411yescharacteristic
287C2×C4#1306335111yescharacteristic
288C8—22no—
289C8—41no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—3442no—
298C22—3442no—
299C22—3442no—
300C22—6881no—
301C22—6881no—
302C22—6881no—
303C22—6881no—
304C22#1458303311yescharacteristic
305C22C2×#1306326811yescharacteristic
306C22#1458334011yescharacteristic
307C4—21no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4—3442no—
312C4#1458306711yescharacteristic
313C4#1458308611yescharacteristic
314C2—21no—
315C2—21no—
316C2—42no—
317C2—6882no—
318C2#1913351311yescharacteristic
319C2#1913651211yescharacteristic
320C2#1913654111yescharacteristic
subgroupG/H
centerC22#14583033
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#3189C2
socleC22×C43#447
prime radical#19135593C2
hypercenter#3189D43
hypocenterC43#12103
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #3189

Complements

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

NH ≅ G/Ntype
1. #19136523C2semidirect
3. #19132607C2semidirect
4. #19132519C2semidirect
5. C43×#3189C2semidirect
33. C2×Q16×C43D4semidirect
44. #107×C43D4semidirect
94. C23×C43SD32semidirect
154. #3189D43semidirect
179. C43#12103semidirect
185. C2×Q16C22⋊D43semidirect
204. #107C22⋊D43semidirect
262. C23#13063268semidirect

Maximal subgroups

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

subgroupindex
#191365232
#191355932
#191326072
#191325192
C43×#31892
#1210343