Finite Group Databasebeta

← #25068338

Subgroups — #25068338

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143632C212yesmaximal, complemented
2C2×C4×D344C211yesmaximal, characteristic
3#19133508C212yesmaximal, complemented
4#19133423C214yesmaximal, complemented
5#19133418C212yesmaximal, complemented
6#19133037C212yesmaximal, complemented
7#19132884C211yesmaximal, characteristic, complemented
8C43×#1568C211yesmaximal, characteristic, complemented
9C22×D344C411yescharacteristic
10C2×C4×D172C2212yes—
11C4×D344C412yes—
12C4×D344C411yescharacteristic
13C4×D344C411yescharacteristic
14C4×D344C2211yescharacteristic
15C4×D344C2211yescharacteristic
16C4×D344C2212yes—
17#14582976C2214yescomplemented
18#14582972—24no—
19#14582964C2214yescomplemented
20#14582952C2211yescharacteristic
21C2×#13063259C411yescharacteristic
22C2×#13063247C412yes—
23#14582861—22no—
24C22⋊C8×D43—22no—
25C4×#10621877C2211yescharacteristic
26#14582626C2214yescomplemented
27#14582626C2214yescomplemented
28#14582621C2212yescomplemented
29#14582620C2212yescomplemented
30C43×#432C2212yes—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#335C2212yescomplemented
33C43×#334C2212yescomplemented
34C22×D172C2×C412yes—
35C22×C4×D43—22no—
36C2×D344—24no—
37C2×D344C2×C412yes—
38C2×D344C2×C411yescharacteristic
39C2×D344C2×C411yescharacteristic
40C2×#10621877—21no—
41C2×#10621872—24no—
42C2×C8×D43—24no—
43C4×D172—22no—
44C4×D172—22no—
45C4×D172C2×C412yes—
46C4×D172C2×C412yes—
47C4×D172C2312yes—
48C4×D172C2312yes—
49C2×C4⋊Dic43C2×C412yes—
50C2×(C2×D43)⋊C4—22no—
51#13063259C2×C412yes—
52#13063259C2×C411yescharacteristic
53#13063259C2×C411yescharacteristic
54C4⋊(C43⋊C8)D412yes—
55#13063247C2×C412yes—
56#13063247C2×C412yes—
57#13063247C2×C412yes—
58#13063247C2×C412yes—
59C22⋊(C43⋊C8)D412yes—
60(C2×D43)⋊C8—24no—
61(C2×D43)⋊C8—24no—
62#13063236—21no—
63C4×C43⋊C8C2312yes—
64C4×C43⋊C8C2312yes—
65C22×C8×C43C2×C411yescharacteristic
66C22×C8×C43C2×C411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43C2314yes—
69C22⋊C8×C43—22no—
70#97×C43—22no—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C4×C8×C43C2311yescharacteristic
75C23×D43—22no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—22no—
80C2×D172—22no—
81C2×D172—24no—
82C2×D172—42no—
83C2×D172C22×C412yes—
84C2×D172C22×C412yes—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—22no—
88C2×C4×D43—22no—
89C2×C4×D43—84no—
90C2×C8×C43—22no—
91C2×C8×C43—24no—
92C2×C8×C43—41no—
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C22×C411yescharacteristic
95C2×C8×C43C22×C411yescharacteristic
96C2×C8×C43C22×C411yescharacteristic
97C42×C43C22×C411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43#4111yescharacteristic
100C42×C43C2411yescharacteristic
101(C2×D43)⋊C4—22no—
102(C2×D43)⋊C4—22no—
103(C2×D43)⋊C4—22no—
104(C2×D43)⋊C4—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43C22×C412yes—
107C4⋊Dic43C22×C412yes—
108#10621877—42no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8C2×D414yes—
111D344—24no—
112D344—22no—
113D344M1614yescomplemented
114#10621872—84no—
115C8×D43—84no—
116C23×C43C4×D411yescharacteristic
117C22×D43—22no—
118C22×D43—22no—
119C22×D43—44no—
120C22×D43—44no—
121C22×D43—82no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—22no—
126C2×C4×C43C4×D411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C23×C411yescharacteristic
130C2×C4×C43C22×D411yescharacteristic
131C2×C4×C43C2×#4111yescharacteristic
132C2×Dic43—22no—
133C2×Dic43—22no—
134C2×Dic43—82no—
135D172—22no—
136D172—22no—
137D172—22no—
138D172—44no—
139D172C2×M1614yes—
140C4×D43—44no—
141C4×D43—44no—
142C4×D43—82no—
143C4×D43—82no—
144C8×C43—21no—
145C8×C43—21no—
146C8×C43—21no—
147C8×C43—44no—
148C8×C43C2×M1612yes—
149C43⋊C8—24no—
150C43⋊C8—42no—
151#18064—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43#44412yes—
155C22×C43C2×C4×D411yescharacteristic
156C2×D43—24no—
157C2×D43—42no—
158C2×D43—42no—
159C2×D43—42no—
160C2×D43—42no—
161C2×D43—42no—
162C2×D43—88no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43C22×M1611yescharacteristic
168C4×C43#56811yescharacteristic
169C4×C43#57612yes—
170Dic43—42no—
171Dic43—42no—
172#2974—432no—
173C2×C4×D8—431no—
174#1594—432no—
175#1581—434no—
176#1580—432no—
177#1568D4311yescharacteristic, complemented
178#1490—432no—
179#1451—431no—
180C2×C43—22no—
181C2×C43D4×M1611yescharacteristic
182C2×C43#294811yescharacteristic
183C2×C43C2×#44411yescharacteristic
184D43—44no—
185D43—82no—
186C22×D8—431no—
187C2×C4×D4—432no—
188C4×D8—431no—
189C4×D8—432no—
190C4×D8—431no—
191C4×D8—431no—
192C4×D8—432no—
193C4×D8—431no—
194#436—434no—
195#435—864no—
196C8×D4—434no—
197#432C2×D4312yes—
198#431—431no—
199C2×#107—431no—
200C2×#102—432no—
201#407—862no—
202C2×C22⋊C8—862no—
203C4×M16—431no—
204C2×C4×C8C2×D4311yescharacteristic
205#335C2×D4312yescomplemented
206#334C2×D4312yescomplemented
207D4⋊C8—434no—
208D4⋊C8—434no—
209#322—432no—
210#322—432no—
211C43#1806411yescharacteristic, complemented, Sylow
212C22×D4—432no—
213C23×C4—862no—
214C2×D8—431no—
215C2×D8—432no—
216C2×D8—431no—
217C2×D8—864no—
218C2×M16—864no—
219C2×M16—861no—
220C22×C8—864no—
221C22×C8C4×D4311yescharacteristic
222C22×C8C4×D4311yescharacteristic
223C4×D4—432no—
224C4×D4—432no—
225C4×D4—432no—
226C4×D4—432no—
227C4×D4—862no—
228C4×D4—862no—
229C2×C4⋊C4—432no—
230C2×C22⋊C4—862no—
231C2×C42C22×D4311yescharacteristic
232#107—432no—
233#107—431no—
234#107—431no—
235C4⋊C8—432no—
236C4⋊C8C22×D4314yes—
237#102—432no—
238#102—432no—
239#102—432no—
240#102—432no—
241C22⋊C8—22no—
242C22⋊C8—432no—
243C22⋊C8—864no—
244C22⋊C8—864no—
245#97—22no—
246#97—861no—
247C4×C8—432no—
248C4×C8—432no—
249C4×C8C4×D4311yescharacteristic
250C4×C8C4×D4311yescharacteristic
251C4×C8C22×D4311yescharacteristic
252C4×C8C22×D4311yescharacteristic
253C24—862no—
254C2×D4—432no—
255C2×D4—432no—
256C2×D4—864no—
257C2×D4—862no—
258C2×D4—1722no—
259C22×C4—862no—
260C22×C4—862no—
261C22×C4—862no—
262C22×C4—862no—
263C22×C4—862no—
264C22×C4—3444no—
265C22×C4C2×C4×D4311yescharacteristic
266C22×C4D4×D4311yescharacteristic
267C22×C4#1062190211yescharacteristic
268D8—434no—
269D8—864no—
270D8—862no—
271M16—3444no—
272M16—1722no—
273C2×C8—22no—
274C2×C8—24no—
275C2×C8—41no—
276C2×C8—434no—
277C2×C8—862no—
278C2×C8—3444no—
279C2×C8C2×C4×D4311yescharacteristic
280C2×C8C2×C4×D4311yescharacteristic
281C2×C8C2×C4×D4311yescharacteristic
282C2×C8C2×C4×D4311yescharacteristic
283C4⋊C4—432no—
284C4⋊C4—432no—
285C4⋊C4—862no—
286C22⋊C4—862no—
287C22⋊C4—862no—
288C22⋊C4—862no—
289C22⋊C4—862no—
290C42C2×C4×D4311yescharacteristic
291C42D4×D4311yescharacteristic
292C42#1062190211yescharacteristic
293C42C23×D4311yescharacteristic
294C23—862no—
295C23—862no—
296C23—3442no—
297C23—1724no—
298C23—1724no—
299C23#1306328711yescharacteristic
300D4—434no—
301D4—862no—
302D4—862no—
303D4—862no—
304D4—1724no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—862no—
310C2×C4—862no—
311C2×C4—3442no—
312C2×C4—3442no—
313C2×C4—3442no—
314C2×C4—1724no—
315C2×C4—1724no—
316C2×C4#1306328711yescharacteristic
317C2×C4#1306328711yescharacteristic
318C2×C4#1306328711yescharacteristic
319C2×C4C22×C4×D4311yescharacteristic
320C2×C4C2×D4×D4311yescharacteristic
321C2×C4C2×#1062190211yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8—44no—
326C8—864no—
327C8—1722no—
328C8M16×D4312yes—
329C22—21no—
330C22—21no—
331C22—864no—
332C22—3448no—
333C22—1722no—
334C22—1722no—
335C22—1722no—
336C22—1722no—
337C22—1722no—
338C22#1458302012yes—
339C22C2×#1306328711yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—1722no—
345C4—1722no—
346C4C2×M16×D4311yescharacteristic
347C4#1458366511yescharacteristic
348C4#1458370112yes—
349C2—22no—
350C2—3442no—
351C2—1724no—
352C2#1914333011yescharacteristic
353C2#1914344611yescharacteristic
354C2C2×#1458302011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1568C2
socleC22×C43C2×C4×D4
prime radicalC22×D344C4
cosocleC42×C43C24
hypercenter#1568D43
hypocenterC43#18064
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
1. #19143632C2semidirect
3. #19133508C2semidirect
4. #19133423C2semidirect
5. #19133418C2semidirect
6. #19133037C2semidirect
7. #19132884C2semidirect
8. C43×#1568C2semidirect
17. #14582976C22semidirect
19. #14582964C22semidirect
26. #14582626C22semidirect
27. #14582626C22semidirect
28. #14582621C22semidirect
29. #14582620C22semidirect
32. C43×#335C22semidirect
33. C43×#334C22semidirect
113. D344M16semidirect
177. #1568D43semidirect
205. #335C2×D43semidirect
206. #334C2×D43semidirect
211. C43#18064semidirect

Maximal subgroups

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

subgroupindex
#191436322
C2×C4×D3442
#191335082
#191334232
#191334182
#191330372
#191328842
C43×#15682
#1806443