Finite Group Databasebeta

← #25066003

Subgroups — #25066003

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143551C212yesmaximal, complemented
2C4×#13063347C211yesmaximal, characteristic
3#19133418C212yesmaximal, complemented
4#19133413C212yesmaximal, complemented
5#19133406C214yesmaximal, complemented
6#19132975C212yesmaximal, complemented
7C2×#14582620C211yesmaximal, characteristic, complemented
8C43×#1564C211yesmaximal, characteristic, complemented
9C2×#13063347C411yescharacteristic
10C4×#10621898C2212yes—
11#14583023C2214yes—
12C4×Dic172C411yescharacteristic
13C4×Dic172C2211yescharacteristic
14C4×#10621873C412yes—
15C4×#10621873C2212yes—
16C4×D344C411yescharacteristic
17C4×D344C2211yescharacteristic
18#14582964C2214yes—
19(C22⋊D43)⋊C8—24no—
20#14582950—22no—
21#14582937C411yescharacteristic
22#14582896C412yes—
23C2×C4×C43⋊C8C2211yescharacteristic
24C2×C4×C43⋊C8C2211yescharacteristic
25C4×C8×D43—22no—
26#14582629C2214yes—
27#14582626C2214yes—
28#14582620C2212yes—
29#14582620C2212yes—
30C43×#431C2212yes—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#335C2212yes—
33C43×#334C2212yes—
34C2×#10621898C2×C412yes—
35#13063347C818yescomplemented
36C2×Dic172C2×C411yescharacteristic
37C2×#10621873C2×C412yes—
38C2×D344C2×C411yescharacteristic
39C22×C43⋊C8—21no—
40C22×C43⋊C8D412yes—
41C2×C8×D43—24no—
42C4×Dic86C2×C412yes—
43C4×Dic86C2312yes—
44C4×D172C2×C412yes—
45C4×D172C2312yes—
46C4×C22⋊D43—22no—
47C4×C22⋊D43—22no—
48#13063284C2×C412yes—
49#13063282—22no—
50C42×D43—22no—
51#13063259C2×C411yescharacteristic
52#13063259C2×C411yescharacteristic
53#13063257C2×C412yes—
54Dic43⋊C8—24no—
55#13063250C2×C412yes—
56#13063250C2×C412yes—
57#13063247C2×C412yes—
58#13063247C2×C412yes—
59(C2×D43)⋊C8—24no—
60C4×C43⋊C8—21no—
61C4×C43⋊C8D412yes—
62C4×C43⋊C8C2312yes—
63C4×C43⋊C8C2312yes—
64C8×Dic43—24no—
65C22×C8×C43C2×C411yescharacteristic
66C22×C8×C43C2×C411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43C2314yes—
69C22⋊C8×C43—22no—
70C4×C8×C43—22no—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C4×C8×C43C2311yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—22no—
79#10621898—24no—
80#10621898C2×C818yescomplemented
81C2×D172C22×C412yes—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×C4×D43—22no—
85C2×Dic86C22×C412yes—
86C2×C8×C43—22no—
87C2×C8×C43—24no—
88C2×C8×C43C2×C814yescomplemented
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C22×C411yescharacteristic
93C42×C43C22×C411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43#4111yescharacteristic
96C42×C43C2411yescharacteristic
97C22⋊Dic43—22no—
98(C2×D43)⋊C4—22no—
99(C2×D43)⋊C4—22no—
100C4⋊Dic43C22×C412yes—
101C4⋊Dic43C22×C412yes—
102Dic43⋊C4—22no—
103Dic43⋊C4—22no—
104C4×Dic43—22no—
105C4×Dic43—22no—
106C4×Dic43—22no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—42no—
109C2×C43⋊C8—42no—
110C2×C43⋊C8C2×D414yes—
111Dic172C2×C814yescomplemented
112D344C2×C814yescomplemented
113#10621873C2×C818yescomplemented
114C8×D43—48no—
115C23×C43C4×D411yescharacteristic
116C22×D43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43C4×D411yescharacteristic
120C2×C4×C43C4×D411yescharacteristic
121C2×C4×C43C4×D411yescharacteristic
122C2×C4×C43C22×C812yes—
123C2×C4×C43#13112yes—
124C2×C4×C43C23×C411yescharacteristic
125C2×C4×C43C22×D411yescharacteristic
126C2×C4×C43C2×#4111yescharacteristic
127C22⋊D43—28no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131D172—22no—
132D172C22×C814yes—
133C4×D43—28no—
134C4×D43—44no—
135C4×D43—44no—
136Dic86—22no—
137Dic86C22×C814yes—
138C8×C43—21no—
139C8×C43—21no—
140C8×C43—44no—
141C8×C43C22×C812yes—
142C8×C43C22×C812yes—
143C43⋊C8—24no—
144C43⋊C8—42no—
145#17849—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43C8×D412yes—
149C22×C43C2×C4×D411yescharacteristic
150C2×D43—24no—
151C2×D43—42no—
152C2×D43—42no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43C8×D412yes—
156C4×C43#44412yes—
157C4×C43C23×C811yescharacteristic
158C4×C43C2×#13111yescharacteristic
159C4×C43#57512yes—
160Dic43—24no—
161Dic43—42no—
162Dic43—42no—
163C8×#41—432no—
164C4×#135—431no—
165#1580—432no—
166#1579—432no—
167SD16⋊C8—434no—
168#1564D4311yescharacteristic, complemented
169#1476—432no—
170C2×#322—431no—
171C2×C43—22no—
172C2×C43C2×C8×D411yescharacteristic
173C2×C43#294311yescharacteristic
174C2×C43C2×#44411yescharacteristic
175D43—44no—
176C2×#135—431no—
177C4×#41—432no—
178C8×Q8—434no—
179C4×Q16—431no—
180C4×Q16—431no—
181C4×SD16—432no—
182C4×SD16—432no—
183C4×D8—431no—
184C4×D8—431no—
185C8×D4—434no—
186C8×D4—864no—
187#431—862no—
188#431C2×D4312yes—
189#427—431no—
190#416—432no—
191C2×C4×C8—431no—
192C2×C4×C8—431no—
193C2×C4×C8—862no—
194C2×C4×C8C2×D4311yescharacteristic
195#335C2×D4312yes—
196#334C2×D4312yes—
197Q8⋊C8—434no—
198D4⋊C8—434no—
199#322—432no—
200#322—432no—
201C43#1784911yescharacteristic, complemented, Sylow
202C2×#41—432no—
203#135—438no—
204C2×Q16—431no—
205C2×SD16—432no—
206C2×D8—431no—
207C22×C8—432no—
208C22×C8—864no—
209C22×C8—861no—
210C22×C8C4×D4311yescharacteristic
211C22×C8C4×D4311yescharacteristic
212C4×Q8—432no—
213C4×Q8—432no—
214C4×D4—432no—
215C4×D4—432no—
216C4×D4—862no—
217C4×D4—862no—
218#117—432no—
219#117—862no—
220C2×C42—862no—
221C2×C42C22×D4311yescharacteristic
222#107—431no—
223#107—431no—
224#106—432no—
225C4⋊C8—864no—
226C4⋊C8C22×D4314yes—
227#103—432no—
228#103—432no—
229#102—432no—
230#102—432no—
231C22⋊C8—22no—
232C22⋊C8—864no—
233C4×C8—22no—
234C4×C8—432no—
235C4×C8—432no—
236C4×C8—432no—
237C4×C8—864no—
238C4×C8—861no—
239C4×C8C4×D4311yescharacteristic
240C4×C8C4×D4311yescharacteristic
241C4×C8C22×D4311yescharacteristic
242C4×C8C22×D4311yescharacteristic
243#41—438no—
244#41—864no—
245C2×Q8—432no—
246C2×D4—432no—
247C2×D4—862no—
248C22×C4—862no—
249C22×C4—862no—
250C22×C4—862no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C22×C4#1062190211yescharacteristic
254Q16—434no—
255SD16—438no—
256D8—434no—
257C2×C8—22no—
258C2×C8—24no—
259C2×C8—434no—
260C2×C8—862no—
261C2×C8—1728no—
262C2×C8—1722no—
263C2×C8—1722no—
264C2×C8C8×D4314yescomplemented
265C2×C8C2×C4×D4311yescharacteristic
266C2×C8C2×C4×D4311yescharacteristic
267C2×C8C2×C4×D4311yescharacteristic
268C2×C8C2×C4×D4311yescharacteristic
269C4⋊C4—432no—
270C4⋊C4—432no—
271C4⋊C4—862no—
272C4⋊C4—862no—
273C22⋊C4—862no—
274C22⋊C4—862no—
275C22⋊C4—862no—
276C42—862no—
277C42—862no—
278C42—862no—
279C42C2×C4×D4311yescharacteristic
280C42D4×D4311yescharacteristic
281C42#1062190211yescharacteristic
282C42C23×D4311yescharacteristic
283C23—862no—
284C23#1306328711yescharacteristic
285Q8—434no—
286Q8—862no—
287D4—434no—
288D4—868no—
289D4—862no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—862no—
293C2×C4—868no—
294C2×C4—862no—
295C2×C4—862no—
296C2×C4—1724no—
297C2×C4—1724no—
298C2×C4#1306328711yescharacteristic
299C2×C4#1306328711yescharacteristic
300C2×C4#1306328711yescharacteristic
301C2×C4C2×C8×D4312yes—
302C2×C4#1306333312yes—
303C2×C4C22×C4×D4311yescharacteristic
304C2×C4C2×D4×D4311yescharacteristic
305C2×C4C2×#1062190211yescharacteristic
306C8—21no—
307C8—21no—
308C8—44no—
309C8—864no—
310C8—1722no—
311C8C2×C8×D4312yes—
312C8C2×C8×D4312yes—
313C22—21no—
314C22—21no—
315C22—864no—
316C22—1722no—
317C22—1722no—
318C22#1458296412yes—
319C22C2×#1306328711yescharacteristic
320C4—21no—
321C4—21no—
322C4—864no—
323C4—1722no—
324C4—1722no—
325C4#1458296412yes—
326C4#1458302012yes—
327C4C22×C8×D4311yescharacteristic
328C4C2×#1306333311yescharacteristic
329C4#1458369612yes—
330C2—22no—
331C2—1724no—
332C2C2×#1458296411yescharacteristic
333C2#1914339511yescharacteristic
334C2C2×#1458302011yescharacteristic
subgroupG/H
centerC42D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC43×#1564C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063347C4
cosocleC42×C43C24
hypercenter#1564D43
hypocenterC43#17849
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #19143551C2semidirect
3. #19133418C2semidirect
4. #19133413C2semidirect
5. #19133406C2semidirect
6. #19132975C2semidirect
7. C2×#14582620C2semidirect
8. C43×#1564C2semidirect
35. #13063347C8semidirect
80. #10621898C2×C8semidirect
88. C2×C8×C43C2×C8semidirect
111. Dic172C2×C8semidirect
112. D344C2×C8semidirect
113. #10621873C2×C8semidirect
168. #1564D43semidirect
201. C43#17849semidirect
264. C2×C8C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191435512
C4×#130633472
#191334182
#191334132
#191334062
#191329752
C2×#145826202
C43×#15642
#1784943