Finite Group Databasebeta

← #24989907

Subgroups — #24989907

Order 11008.

384 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143570C211yesmaximal, characteristic
2#19133358C211yesmaximal, characteristic, complemented
3#19133118C212yesmaximal
4#19132451C212yesmaximal, complemented
5C4×#107×C43C211yesmaximal, characteristic, complemented
6#14583433C2211yescharacteristic
7#14583029C411yescharacteristic, complemented
8C8×Dic86C411yescharacteristic, complemented
9#14582978C411yescharacteristic, complemented
10#14582970—21no—
11C8×D172C411yescharacteristic, complemented
12C8×C22⋊D43—21no—
13#14582958—21no—
14#14582956C2212yes—
15#14582956C2211yescharacteristic
16#14582853—21no—
17#14582652—21no—
18#14582650—21no—
19#14582635—22no—
20#14582632—22no—
21C2×#107×C43—21no—
22C2×C4×C8×C43C2211yescharacteristic
23C4×C4⋊C4×C43C2212yes—
24C43×#340—21no—
25C2×#10621872—21no—
26C2×C8×D43—21no—
27#13063319—21no—
28#13063317Q811yescharacteristic
29#13063313Q811yescharacteristic
30#13063308—21no—
31#13063304D411yescharacteristic
32#13063299D411yescharacteristic
33C4×Dic86C2×C411yescharacteristic
34C4×D172C2×C411yescharacteristic
35C4×C22⋊D43—21no—
36#13063282—21no—
37C4⋊(C43⋊C8)—22no—
38C4⋊(C43⋊C8)C2×C411yescharacteristic
39C4⋊(C43⋊C8)C2×C411yescharacteristic
40Dic43⋊C8—21no—
41Dic43⋊C8—21no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—22no—
44(C2×D43)⋊C8—21no—
45(C2×D43)⋊C8—21no—
46#13063236—21no—
47#13063236—22no—
48#13063235—21no—
49C8×Dic43—21no—
50C22×C8×C43D411yescharacteristic
51C22×C8×C43D411yescharacteristic
52C2×C4⋊C4×C43—22no—
53C2×C42×C43—22no—
54C2×C42×C43C2311yescharacteristic
55#107×C43—24no—
56C4×C8×C43C2×C411yescharacteristic
57C4×C8×C43C2×C411yescharacteristic
58C4×C8×C43D411yescharacteristic
59C4×C8×C43D411yescharacteristic
60#95×C43—22no—
61C22×C4×C43—42no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43#4111yescharacteristic
65C2×C22⋊D43—21no—
66C2×D172C4⋊C411yescharacteristic
67C2×C4×D43—21no—
68C2×Dic86C4⋊C411yescharacteristic
69C2×C8×C43—22no—
70C2×C8×C43—41no—
71C2×C8×C43C22⋊C411yescharacteristic
72C2×C8×C43C22⋊C411yescharacteristic
73C2×C8×C43C22⋊C411yescharacteristic
74C2×C8×C43C22⋊C411yescharacteristic
75C4⋊C4×C43—24no—
76C4⋊C4×C43—42no—
77C42×C43—82no—
78C42×C43C22×C411yescharacteristic
79C42×C43C2×D411yescharacteristic
80C42×C43C2×Q811yescharacteristic
81C42×C43#4111yescharacteristic
82C22⋊Dic43—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87C4⋊Dic43C4⋊C411yescharacteristic
88C4⋊Dic43C4⋊C411yescharacteristic
89Dic43⋊C4—21no—
90Dic43⋊C4—21no—
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93C4×Dic43—21no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—42no—
97#10621872—42no—
98C8×D43—42no—
99C23×C43#12111yescharacteristic
100C22×D43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—41no—
106C2×C4×C43—44no—
107C2×C4×C43—82no—
108C2×C4×C43—82no—
109C2×C4×C43C2×C22⋊C411yescharacteristic
110C2×C4×C43C2×C4⋊C411yescharacteristic
111C2×C4×C43#11711yescharacteristic
112C2×C4×C43#12111yescharacteristic
113C2×C4×C43C22⋊Q811yescharacteristic
114C2×C4×C43C22⋊Q811yescharacteristic
115C22⋊D43—41no—
116C22⋊D43—41no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120D172—41no—
121C4×D43—41no—
122C4×D43—41no—
123Dic86—41no—
124C8×C43—21no—
125C8×C43—21no—
126C8×C43—21no—
127C8×C43#10412yes—
128C43⋊C8—41no—
129C43⋊C8—41no—
130C43⋊C8—82no—
131#8695—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43#38011yescharacteristic
135C22×C43#47211yescharacteristic
136C22×C43#47311yescharacteristic
137C2×D43—41no—
138C2×D43—41no—
139C2×D43—41no—
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—84no—
146C4×C43C2×#10411yescharacteristic
147C4×C43#42111yescharacteristic
148Dic43—41no—
149Dic43—41no—
150Dic43—41no—
151#2966—431no—
152C4×#107D4311yescharacteristic, complemented
153#1568—431no—
154#1509—432no—
155#1285—432no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43#180611yescharacteristic
159C2×C43#181211yescharacteristic
160C2×C43#181611yescharacteristic
161D43—81no—
162#529—431no—
163#446—431no—
164C8×Q8—431no—
165#436—431no—
166#435—861no—
167C8×D4—431no—
168C8×D4—861no—
169#433—861no—
170#432—431no—
171#432—432no—
172C2×#107—21no—
173#405—861no—
174C2×C4×C8C2×D4311yescharacteristic
175C4×C4⋊C4C2×D4312yes—
176#340—21no—
177#335—861no—
178#334—861no—
179#328—862no—
180#327—862no—
181C43#869511yescharacteristic, complemented, Sylow
182C2×M16—861no—
183C22×C8—861no—
184C22×C8C22⋊D4311yescharacteristic
185C22×C8C22⋊D4311yescharacteristic
186#126—861no—
187#125—431no—
188#124—431no—
189#123—861no—
190C22⋊Q8—431no—
191#121—431no—
192C4×Q8—431no—
193C4×D4—431no—
194C4×D4—861no—
195#117—861no—
196C2×C4⋊C4—22no—
197C2×C42—22no—
198C2×C42C22×D4311yescharacteristic
199#107—24no—
200C4⋊C8—431no—
201C4⋊C8—431no—
202C4⋊C8—861no—
203C4⋊C8—861no—
204C4⋊C8—862no—
205C22⋊C8—861no—
206C22⋊C8—861no—
207C22⋊C8—861no—
208C22⋊C8—862no—
209#97—861no—
210#97—861no—
211#97—862no—
212C4×C8—861no—
213C4×C8C4×D4311yescharacteristic
214C4×C8C4×D4311yescharacteristic
215C4×C8D17211yescharacteristic
216C4×C8D17211yescharacteristic
217#95—22no—
218C2×Q8—431no—
219C2×D4—431no—
220C2×D4—861no—
221C22×C4—42no—
222C22×C4—861no—
223C22×C4D4×D4311yescharacteristic
224C22×C4#1062190011yescharacteristic
225C22×C4C2×C22⋊D4311yescharacteristic
226M16—1722no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—861no—
230C2×C8—861no—
231C2×C8—1722no—
232C2×C8—1722no—
233C2×C8(C2×D43)⋊C411yescharacteristic
234C2×C8(C2×D43)⋊C411yescharacteristic
235C2×C8(C2×D43)⋊C411yescharacteristic
236C2×C8(C2×D43)⋊C411yescharacteristic
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—431no—
240C4⋊C4—431no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C22⋊C4—861no—
246C22⋊C4—861no—
247C22⋊C4—861no—
248C22⋊C4—861no—
249C22⋊C4—861no—
250C42—82no—
251C42—861no—
252C42C2×C4×D4311yescharacteristic
253C42C2×D17211yescharacteristic
254C42Q8×D4311yescharacteristic
255C42#1062190211yescharacteristic
256C23—861no—
257C23#1306329611yescharacteristic
258Q8—1721no—
259D4—1721no—
260D4—1721no—
261D4—1721no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—44no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—861no—
271C2×C4—861no—
272C2×C4—861no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4C2×(C2×D43)⋊C411yescharacteristic
276C2×C4C4⋊C4×D4311yescharacteristic
277C2×C4#1306328311yescharacteristic
278C2×C4#1306330011yescharacteristic
279C2×C4#1306330111yescharacteristic
280C2×C4#1306330511yescharacteristic
281C8—21no—
282C8—21no—
283C8—21no—
284C8—3442no—
285C8—1721no—
286C8—1721no—
287C8#1306325312yes—
288C22—21no—
289C22—21no—
290C22—1721no—
291C22—1721no—
292C22—1721no—
293C22#1458275611yescharacteristic
294C22#1458316611yescharacteristic
295C22#1458317111yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—84no—
302C4—1721no—
303C4—1721no—
304C4—1721no—
305C4C2×#1306325311yescharacteristic
306C4#1458291711yescharacteristic
307C2—21no—
308C2—21no—
309C2—3441no—
310C2#1913461611yescharacteristic
311C2#1913463811yescharacteristic
312C2#1913466011yescharacteristic
subgroupG/H
centerC22#14582756
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#107×C43C2
socleC22×C43#380
prime radical#13063299D4
cosocleC2×C42×C43C23
hypercenterC4×#107D43
hypocenterC43#8695
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #19133358C2semidirect
4. #19132451C2semidirect
5. C4×#107×C43C2semidirect
7. #14583029C4semidirect
8. C8×Dic86C4semidirect
9. #14582978C4semidirect
11. C8×D172C4semidirect
152. C4×#107D43semidirect
181. C43#8695semidirect

Maximal subgroups

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

subgroupindex
#191435702
#191333582
#191331182
#191324512
C4×#107×C432
#869543