Finite Group Databasebeta

← #24989503

Subgroups — #24989503

Order 11008.

486 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic
2#19134631C212yesmaximal, complemented
3#19132931C212yesmaximal
4#19132472C211yesmaximal, characteristic, complemented
5C43×#1293C211yesmaximal, characteristic, complemented
6C23×C43⋊C8C2211yescharacteristic
7C22×C8×D43C411yescharacteristic
8C2×C4×C22⋊D43C2211yescharacteristic
9(C22⋊D43)⋊C8—22no—
10(C22⋊D43)⋊C8—22no—
11C2×#13063260—22no—
12C2×Dic43⋊C8C411yescharacteristic
13#14582863C2212yes—
14C2×(C2×D43)⋊C8C411yescharacteristic
15C2×C8×Dic43C411yescharacteristic
16#14582663—22no—
17#14582624—22no—
18#14582622—22no—
19C43×#407C2212yes—
20C2×C22⋊C8×C43C2211yescharacteristic
21C22×C22⋊D43Q811yescharacteristic
22C22×C4×D43C2×C411yescharacteristic
23C2×#10621877—22no—
24C22×C43⋊C8—42no—
25C22×C43⋊C8C2×C411yescharacteristic
26C22×C43⋊C8C2×C411yescharacteristic
27C22×C43⋊C8D412yes—
28C22×C43⋊C8D412yes—
29C2×C8×D43—21no—
30C2×C8×D43—21no—
31C2×C8×D43—42no—
32C4×C22⋊D43—22no—
33C4×C22⋊D43—22no—
34C2×Dic43⋊C4D411yescharacteristic
35C2×C22⋊Dic43Q811yescharacteristic
36C2×(C2×D43)⋊C4D411yescharacteristic
37C2×C4×Dic43C2×C411yescharacteristic
38#13063260—44no—
39Dic43⋊C8—22no—
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)—22no—
42(C2×D43)⋊C8—22no—
43C8×Dic43—21no—
44C8×Dic43—21no—
45C23×C4×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C22×C8×C43C2×C411yescharacteristic
48C22×C8×C43C2×C411yescharacteristic
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C22⋊C8×C43—22no—
52C24×C43C2×Q811yescharacteristic
53C23×D43C4⋊C411yescharacteristic
54C22×C4×C43—41no—
55C22×C4×C43—41no—
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D412yes—
59C22×C4×C43#4112yes—
60C2×C22⋊D43—22no—
61C2×C22⋊D43—22no—
62C2×C22⋊D43—22no—
63C22×Dic43C4⋊C411yescharacteristic
64C22×Dic43C4⋊C411yescharacteristic
65C22×Dic43C4⋊C411yescharacteristic
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×C4×D43—41no—
69C2×C4×D43—41no—
70M16×C43—42no—
71M16×C43—42no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—42no—
77C22⋊Dic43—22no—
78(C2×D43)⋊C4—22no—
79Dic43⋊C4—22no—
80C4×Dic43—21no—
81C4×Dic43—21no—
82#10621877—42no—
83#10621877—42no—
84C2×C43⋊C8—24no—
85C2×C43⋊C8—22no—
86C2×C43⋊C8—41no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8C22⋊C411yescharacteristic
90C2×C43⋊C8C22⋊C412yes—
91C2×C43⋊C8C22⋊C411yescharacteristic
92C8×D43—42no—
93C8×D43—42no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—41no—
97C23×C43—41no—
98C23×C43C2×C4⋊C411yescharacteristic
99C23×C43C22⋊Q812yes—
100C22×D43—21no—
101C22×D43—21no—
102C22×D43—41no—
103C22×D43—41no—
104C22×D43#10812yescomplemented
105C2×C4×C43—22no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—42no—
111C2×C4×C43C2×C22⋊C411yescharacteristic
112C2×C4×C43#11711yescharacteristic
113C2×C4×C43#12112yes—
114C22⋊D43—28no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43#10812yescomplemented
122C4×D43—42no—
123C4×D43—41no—
124C4×D43—41no—
125C8×C43—41no—
126C8×C43—41no—
127C8×C43—82no—
128C43⋊C8—21no—
129C43⋊C8—22no—
130C43⋊C8—82no—
131C43⋊C8#9912yes—
132#8611—431nomaximal, Sylow
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—22no—
136C22×C43—22no—
137C22×C43—22no—
138C22×C43—42no—
139C22×C43—42no—
140C22×C43#38011yescharacteristic
141C22×C43C2×#10811yescharacteristic
142C22×C43C2×#10811yescharacteristic
143C2×D43—22no—
144C2×D43—42no—
145C2×D43—41no—
146C2×D43—41no—
147C2×D43—42no—
148C4×C43—22no—
149C4×C43—21no—
150C4×C43C2×#9911yescharacteristic
151C4×C43#41011yescharacteristic
152Dic43—22no—
153Dic43—41no—
154Dic43—41no—
155C2×C8×D4—431no—
156#1810—432no—
157#1465—432no—
158#1293—431no—
159#1293D4311yescharacteristic, complemented
160C2×C43—21no—
161C2×C43—21no—
162C2×C43—42no—
163C2×C43#179911yescharacteristic
164C2×C43#181011yescharacteristic
165C2×C43#181311yescharacteristic
166D43—42no—
167C23×C8—431no—
168C23×C8—431no—
169C2×C4×D4—431no—
170C8×D4—862no—
171C8×D4—862no—
172C2×#108—862no—
173C2×C4⋊C8—431no—
174#407—432no—
175#407C2×D4312yes—
176C2×C22⋊C8—431no—
177C2×C22⋊C8C2×D4311yescharacteristic
178C2×C4×C8—431no—
179#341—862no—
180#324—862no—
181#323—862no—
182C43#861111yescharacteristic, complemented, Sylow
183C22×D4—431no—
184C23×C4—431no—
185C23×C4C22×D4311yescharacteristic
186C2×M16—22no—
187C2×M16—862no—
188C22×C8—431no—
189C22×C8—432no—
190C22×C8—431no—
191C22×C8—432no—
192C22×C8—861no—
193C22×C8—861no—
194C22×C8—1722no—
195C22×C8—1722no—
196C22×C8C4×D4311yescharacteristic
197C22×C8C4×D4311yescharacteristic
198C4×D4—862no—
199C4×D4—862no—
200C2×C4⋊C4—431no—
201C2×C22⋊C4—431no—
202C2×C22⋊C4—431no—
203C2×C42—431no—
204#108—1724no—
205C4⋊C8—862no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—862no—
210C22⋊C8—862no—
211C22⋊C8—862no—
212C4×C8—861no—
213C4×C8—861no—
214C24—431no—
215C24Q8×D4311yescharacteristic
216C2×D4—862no—
217C2×D4—862no—
218C2×D4—862no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—431no—
222C22×C4—431no—
223C22×C4—431no—
224C22×C4—861no—
225C22×C4—861no—
226C22×C4—1721no—
227C22×C4—1721no—
228C22×C4C2×C4×D4311yescharacteristic
229C22×C4#1062189812yes—
230C22×C4D4×D4312yes—
231C22×C4D4×D4311yescharacteristic
232M16—42no—
233M16—42no—
234M16—1722no—
235M16—1722no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—42no—
241C2×C8—431no—
242C2×C8—431no—
243C2×C8—432no—
244C2×C8—864no—
245C2×C8—862no—
246C2×C8—1722no—
247C2×C8—1722no—
248C2×C8—1722no—
249C2×C8—1721no—
250C2×C8—1722no—
251C4⋊C4—862no—
252C22⋊C4—862no—
253C22⋊C4—862no—
254C42—861no—
255C42—861no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—432no—
261C23—861no—
262C23—861no—
263C23—1721no—
264C23—1721no—
265C23C4⋊C4×D4311yescharacteristic
266C23#1306330312yes—
267D4—868no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—432no—
275C2×C4—861no—
276C2×C4—861no—
277C2×C4—861no—
278C2×C4—861no—
279C2×C4—1722no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4C22⋊C4×D4311yescharacteristic
285C2×C4#1306328211yescharacteristic
286C2×C4#1306329812yes—
287C8—41no—
288C8—41no—
289C8—82no—
290C8—432no—
291C8—861no—
292C8—862no—
293C8—3442no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—42no—
300C22—42no—
301C22—862no—
302C22—1722no—
303C22—1722no—
304C22—1721no—
305C22—1721no—
306C22#1458275811yescharacteristic
307C22#108×D4311yescharacteristic
308C22#108×D4311yescharacteristic
309C4—22no—
310C4—21no—
311C4—862no—
312C4—1721no—
313C4—1721no—
314C4#99×D4311yescharacteristic
315C4#1458287111yescharacteristic
316C2—21no—
317C2—21no—
318C2—42no—
319C2—1722no—
320C2#1913458211yescharacteristic
321C2#1913463211yescharacteristic
322C2#1913464411yescharacteristic
subgroupG/H
centerC22#14582758
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1293C2
socleC22×C43#380
prime radicalC22×C22⋊D43Q8
cosocleC23×C4×C43C23
hypercenter#1293D43
hypocenterC43#8611
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
2. #19134631C2semidirect
4. #19132472C2semidirect
5. C43×#1293C2semidirect
104. C22×D43#108semidirect
121. C2×Dic43#108semidirect
159. #1293D43semidirect
182. C43#8611semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D43)⋊C82
#191346312
#191329312
#191324722
C43×#12932
#861143