Finite Group Databasebeta

← #24989772

Subgroups — #24989772

Order 11008.

432 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143561C211yesmaximal, characteristic
2#19134616C212yesmaximal
3#19133351C211yesmaximal, characteristic, complemented
4#19132498C212yesmaximal, complemented
5C4×#107×C43C211yesmaximal, characteristic, complemented
6C4×#10621898C2211yescharacteristic
7#14583029C411yescharacteristic, complemented
8#14583029C411yescharacteristic, complemented
9#14582978C411yescharacteristic, complemented
10#14582978C411yescharacteristic, complemented
11#14582970—21no—
12#14582970—21no—
13#14582952C2211yescharacteristic
14#14582950—21no—
15#14582923C2212yes—
16C2×#13063253—22no—
17C4×#10621872—21no—
18#14582659—22no—
19#14582650—21no—
20#14582650—21no—
21C2×#107×C43—21no—
22C2×C4×C8×C43C2211yescharacteristic
23C4×C4⋊C4×C43C2212yes—
24C43×#340—21no—
25C2×#10621898D411yescharacteristic
26C2×#10621877—22no—
27C2×#10621872—21no—
28C2×#10621872—21no—
29C4×Dic86C2×C411yescharacteristic
30C4×Dic86Q811yescharacteristic
31C4×D172C2×C411yescharacteristic
32C4×D172Q811yescharacteristic
33C4×C22⋊D43—21no—
34C4×C22⋊D43—21no—
35#13063284D411yescharacteristic
36#13063282—21no—
37C42×D43—21no—
38C4⋊(C43⋊C8)—22no—
39C4⋊(C43⋊C8)—22no—
40C4⋊(C43⋊C8)C2×C411yescharacteristic
41C4⋊(C43⋊C8)C2×C411yescharacteristic
42Dic43⋊C8—21no—
43Dic43⋊C8—21no—
44#13063253—44no—
45C22⋊(C43⋊C8)—21no—
46(C2×D43)⋊C8—21no—
47(C2×D43)⋊C8—21no—
48#13063235—21no—
49#13063235—21no—
50C4×C43⋊C8—21no—
51C22×C8×C43D411yescharacteristic
52C22×C8×C43D411yescharacteristic
53C2×C4⋊C4×C43—22no—
54C2×C42×C43—22no—
55C2×C42×C43C2311yescharacteristic
56#107×C43—24no—
57C4×C8×C43C2×C411yescharacteristic
58C4×C8×C43C2×C411yescharacteristic
59C4×C8×C43D411yescharacteristic
60C4×C8×C43D411yescharacteristic
61#95×C43—22no—
62C22×C4×C43—42no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43#4111yescharacteristic
66C2×C22⋊D43—21no—
67#10621898—22no—
68#10621898—22no—
69C2×D172C4⋊C411yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×Dic86C4⋊C411yescharacteristic
74C2×C8×C43—22no—
75C2×C8×C43—41no—
76C2×C8×C43C22⋊C411yescharacteristic
77C2×C8×C43C22⋊C411yescharacteristic
78C2×C8×C43C22⋊C411yescharacteristic
79C2×C8×C43C22⋊C411yescharacteristic
80C4⋊C4×C43—24no—
81C4⋊C4×C43—42no—
82C42×C43—42no—
83C42×C43—42no—
84C42×C43C22×C411yescharacteristic
85C42×C43C2×D411yescharacteristic
86C42×C43C2×Q811yescharacteristic
87C42×C43#4111yescharacteristic
88C22⋊Dic43—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43C4⋊C411yescharacteristic
92C4⋊Dic43C4⋊C411yescharacteristic
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98#10621877—42no—
99#10621877—42no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—42no—
103#10621872—42no—
104#10621872—42no—
105C23×C43#12111yescharacteristic
106C22×D43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—44no—
111C2×C4×C43—82no—
112C2×C4×C43—82no—
113C2×C4×C43C2×C22⋊C411yescharacteristic
114C2×C4×C43C2×C4⋊C411yescharacteristic
115C2×C4×C43#11711yescharacteristic
116C2×C4×C43#12111yescharacteristic
117C2×C4×C43C22⋊Q811yescharacteristic
118C2×C4×C43C22⋊Q811yescharacteristic
119C2×C4×C43AGL(1,ℤ/8)12yes—
120C2×C4×C43#13712yes—
121C22⋊D43—41no—
122C22⋊D43—41no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126D172—22no—
127C4×D43—42no—
128C4×D43—41no—
129C4×D43—41no—
130C4×D43—42no—
131Dic86—22no—
132C8×C43—21no—
133C8×C43—21no—
134C8×C43—21no—
135C8×C43#10412yescomplemented
136C43⋊C8—41no—
137C43⋊C8—41no—
138C43⋊C8—82no—
139#8668—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#38011yescharacteristic
143C22×C43#46911yescharacteristic
144C22×C43#47011yescharacteristic
145C2×D43—41no—
146C2×D43—41no—
147C2×D43—41no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—84no—
152C4×C43C2×#10411yescharacteristic
153C4×C43#42111yescharacteristic
154C4×C43#42812yes—
155C4×C43#46812yes—
156Dic43—41no—
157Dic43—41no—
158Dic43—41no—
159#2965—431no—
160#1806—432no—
161C4×#107D4311yescharacteristic, complemented
162#1566—431no—
163#1303—432no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43#180611yescharacteristic
167C2×C43#180911yescharacteristic
168C2×C43#181411yescharacteristic
169D43—81no—
170C4×#41—431no—
171#446—431no—
172#446—431no—
173#436—431no—
174#436—431no—
175#435—861no—
176#435—861no—
177#431—431no—
178#431—861no—
179C2×#107—21no—
180#423—432no—
181C2×#104—862no—
182C4×M16—861no—
183C2×C4×C8C2×D4311yescharacteristic
184C4×C4⋊C4C2×D4312yes—
185#340—21no—
186#339—862no—
187#334—861no—
188#334—861no—
189C43#866811yescharacteristic, complemented, Sylow
190C2×#41—431no—
191C2×M16—861no—
192C2×M16—861no—
193C2×M16—862no—
194C22×C8C22⋊D4311yescharacteristic
195C22×C8C22⋊D4311yescharacteristic
196C4×Q8—431no—
197C4×Q8—431no—
198C4×D4—431no—
199C4×D4—431no—
200C4×D4—861no—
201C4×D4—861no—
202#117—431no—
203#117—861no—
204C2×C4⋊C4—22no—
205C2×C42—22no—
206C2×C42—861no—
207C2×C42C22×D4311yescharacteristic
208#107—24no—
209C4⋊C8—431no—
210C4⋊C8—431no—
211C4⋊C8—861no—
212C4⋊C8—861no—
213C4⋊C8—862no—
214C4⋊C8—862no—
215#104—1724no—
216C22⋊C8—861no—
217C22⋊C8—861no—
218C22⋊C8—861no—
219#97—861no—
220#97—861no—
221C4×C8—861no—
222C4×C8C4×D4311yescharacteristic
223C4×C8C4×D4311yescharacteristic
224C4×C8D17211yescharacteristic
225C4×C8D17211yescharacteristic
226#95—22no—
227#41—862no—
228#41—862no—
229C2×Q8—431no—
230C2×D4—431no—
231C2×D4—861no—
232C22×C4—42no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4D4×D4311yescharacteristic
237C22×C4#1062190011yescharacteristic
238C22×C4C2×C22⋊D4311yescharacteristic
239M16—1722no—
240M16—1722no—
241M16—1722no—
242M16—1722no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—861no—
246C2×C8—861no—
247C2×C8—1722no—
248C2×C8(C2×D43)⋊C411yescharacteristic
249C2×C8(C2×D43)⋊C411yescharacteristic
250C2×C8(C2×D43)⋊C411yescharacteristic
251C2×C8(C2×D43)⋊C411yescharacteristic
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—431no—
255C4⋊C4—431no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C22⋊C4—861no—
259C22⋊C4—861no—
260C22⋊C4—861no—
261C42—42no—
262C42—42no—
263C42—861no—
264C42—861no—
265C42—861no—
266C42C2×C4×D4311yescharacteristic
267C42C2×D17211yescharacteristic
268C42Q8×D4311yescharacteristic
269C42#1062190211yescharacteristic
270C23—861no—
271C23#1306329611yescharacteristic
272Q8—862no—
273D4—862no—
274D4—1721no—
275D4—1721no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—861no—
283C2×C4—861no—
284C2×C4—861no—
285C2×C4—1722no—
286C2×C4—1722no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4C2×(C2×D43)⋊C411yescharacteristic
290C2×C4C4⋊C4×D4311yescharacteristic
291C2×C4#1306328311yescharacteristic
292C2×C4#1306330011yescharacteristic
293C2×C4#1306330111yescharacteristic
294C2×C4#1306330511yescharacteristic
295C2×C4#1306334912yes—
296C2×C4#1306335712yes—
297C8—21no—
298C8—21no—
299C8—21no—
300C8—3442no—
301C8—1721no—
302C8—1721no—
303C8#1306325312yescomplemented
304C22—21no—
305C22—21no—
306C22—1721no—
307C22—1721no—
308C22—1721no—
309C22#1458275611yescharacteristic
310C22#1458314911yescharacteristic
311C22#1458315411yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—84no—
316C4—1721no—
317C4—1721no—
318C4—1721no—
319C4C2×#1306325311yescharacteristic
320C4#1458291711yescharacteristic
321C4#1458294012yes—
322C4#1458314612yes—
323C2—21no—
324C2—21no—
325C2—3441no—
326C2#1913461611yescharacteristic
327C2#1913462911yescharacteristic
328C2#1913464611yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#107×C43C2
socleC22×C43#380
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenterC4×#107D43
hypocenterC43#8668
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. #19133351C2semidirect
4. #19132498C2semidirect
5. C4×#107×C43C2semidirect
7. #14583029C4semidirect
8. #14583029C4semidirect
9. #14582978C4semidirect
10. #14582978C4semidirect
135. C8×C43#104semidirect
161. C4×#107D43semidirect
189. C43#8668semidirect
303. C8#13063253semidirect

Maximal subgroups

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

subgroupindex
#191435612
#191346162
#191333512
#191324982
C4×#107×C432
#866843