Finite Group Databasebeta

← #25253185

Subgroups — #25253185

Order 11008.

712 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14583333C212yesmaximal, complemented
2#19146281C212yesmaximal, complemented
3#19136856C211yesmaximal, characteristic, complemented
4#19136709C212yesmaximal, complemented
5#19136650C212yesmaximal, complemented
6#19136536C212yesmaximal, complemented
7#19136508C212yesmaximal, complemented
8#19136428C211yesmaximal, characteristic, complemented
9C4×D16×C43C211yesmaximal, characteristic, complemented
10C2×#13063344C2212yes—
11C2×D8×D43C2212yescomplemented
12#14583544—22no—
13#14583333—28no—
14C2×Dic344C2211yescharacteristic, complemented
15C2×#13063270C2212yescomplemented
16C2×#13063269C2212yescomplemented
17C2×D688C2211yescharacteristic
18C2×#13063266C2212yes—
19C2×#13063264C2212yescomplemented
20#14583283C2212yescomplemented
21#14583141C2212yescomplemented
22#14583136C2212yes—
23#14583114—22no—
24#14583051—22no—
25#14583045—22no—
26C8×D172C2211yescharacteristic
27C4⋊(C43⋊C16)C2211yescharacteristic, complemented
28#14582702C2212yescomplemented
29#14582699C2212yescomplemented
30(C2×D43)⋊C16C2212yescomplemented
31C2×D16×C43C2211yescharacteristic
32C4×D8×C43C2212yescomplemented
33C43×#366C2211yescharacteristic, complemented
34C43×#357C2212yescomplemented
35C4×C16×C43C2211yescharacteristic, complemented
36C2×#10621900—22no—
37C2×D4×D43—22no—
38#13063344—24no—
39#13063344—42no—
40C2×Dic172C2312yes—
41C2×#10621873—22no—
42C2×#10621883—22no—
43C2×D344C2312yes—
44C2×#10621882—22no—
45D8×D43—24no—
46D8×D43—42no—
47C2×C8×D43C2312yes—
48#13063313—22no—
49#13063309—42no—
50#13063305—22no—
51#13063300—22no—
52#13063299—42no—
53#13063295—42no—
54C4×D172D411yescharacteristic
55C2×(C2×D43)⋊C4—42no—
56Dic344—41no—
57#13063270—24no—
58#13063269—24no—
59D688—41no—
60#13063266—24no—
61#13063264—24no—
62C2×C43⋊C16C2312yes—
63C4⋊(C43⋊C8)D411yescharacteristic
64#13063248—22no—
65#13063245—22no—
66(C2×D43)⋊C8D412yes—
67C2×D8×C43C2312yes—
68C4×D4×C43—22no—
69D16×C43D414yescomplemented
70C2×C16×C43C2311yescharacteristic
71C2×C16×C43C2311yescharacteristic
72#107×C43C2312yes—
73#102×C43—22no—
74C4×C8×C43C2311yescharacteristic
75C23×D43—42no—
76C2×D4×C43—22no—
77C22×C4×C43—42no—
78C2×C22⋊D43—42no—
79C2×C22⋊D43—42no—
80C22×Dic43—42no—
81#10621900—44no—
82#10621900—82no—
83D4×D43—44no—
84D4×D43—82no—
85C2×D172—22no—
86C2×D172—42no—
87C2×D172D811yescharacteristic
88C2×C4×D43C2×D412yes—
89C2×Dic86—22no—
90D8×C43—22no—
91D8×C43C2×D414yes—
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43C2411yescharacteristic
94C4⋊C4×C43—22no—
95C22⋊C4×C43—42no—
96C42×C43C2×D411yescharacteristic
97#10621883—44no—
98#10621882—44no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101(C2×D43)⋊C4—42no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4D812yes—
104C4⋊Dic43—42no—
105C4⋊Dic43D811yescharacteristic
106C2×C43⋊C8C2×D412yes—
107Dic172—22no—
108Dic172—22no—
109D344—22no—
110D344—22no—
111#10621873—82no—
112C8×D43—22no—
113C8×D43—22no—
114C16×C43—21no—
115C16×C43C2×D412yes—
116C43⋊C16—22no—
117C23×C43—42no—
118C22×D43—42no—
119C22×D43—84no—
120C22×D43—84no—
121C22×D43—162no—
122C22×D43C2×D812yes—
123D4×C43—24no—
124D4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—162no—
127C2×C4×C43C2×D811yescharacteristic
128C2×C4×C43C2×D811yescharacteristic
129C2×C4×C43C22×D411yescharacteristic
130C22⋊D43—84no—
131C22⋊D43—84no—
132C2×Dic43—42no—
133C2×Dic43—84no—
134C2×Dic43C2×D812yes—
135D172—41no—
136D172—42no—
137D172—42no—
138D172—162no—
139C4×D43—22no—
140C4×D43—22no—
141Dic86—42no—
142Dic86—42no—
143C8×C43—21no—
144C8×C43C22×D411yescharacteristic
145C8×C43H(5,𝔽2)11yescharacteristic
146C43⋊C8—22no—
147#33839—431nomaximal, Sylow
148C22×C43—44no—
149C22×C43—82no—
150C22×C43—82no—
151C22×C43C22×D811yescharacteristic
152C2×D43—22no—
153C2×D43—22no—
154C2×D43—22no—
155C2×D43—82no—
156C2×D43—82no—
157C2×D43—82no—
158C2×D43—168no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—82no—
162C4×C43D4211yescharacteristic
163C4×C43#57611yescharacteristic
164Dic43—22no—
165Dic43—82no—
166C2×#509—432no—
167#3280—432no—
168#2249—431no—
169#2220—432no—
170#2210—432no—
171#2189—432no—
172#2184—432no—
173C4×D16D4311yescharacteristic, complemented
174#2169—431no—
175C2×C43—84no—
176C2×C43D4×D811yescharacteristic
177C2×C43#341411yescharacteristic
178C2×C43#341511yescharacteristic
179D43—42no—
180D43—162no—
181C2×#135—432no—
182C22×D8—432no—
183#546—862no—
184#509—868no—
185C2×Q32—431no—
186C2×SD32—432no—
187C2×SD32—432no—
188C2×D16—432no—
189C2×D16—431no—
190C2×D16C2×D4311yescharacteristic
191C2×M32—432no—
192#495—432no—
193#467—432no—
194#466—432no—
195#463—862no—
196#450—862no—
197#449—862no—
198C4×D8C2×D4312yescomplemented
199C8×D4—431no—
200#366C2×D4311yescharacteristic, complemented
201C4⋊C16—431no—
202#358—432no—
203#357—432no—
204#357C2×D4312yescomplemented
205C22⋊C16—432no—
206C4×C16C2×D4311yescharacteristic, complemented
207C43#3383911yescharacteristic, complemented, Sylow
208C2×#41—862no—
209C22×D4—862no—
210#135—864no—
211#135—1722no—
212C2×Q16—432no—
213C2×SD16—862no—
214C2×SD16—862no—
215C2×D8—432no—
216C2×D8—862no—
217C2×D8—864no—
218C2×D8—1722no—
219C2×D8C22×D4312yes—
220C22×C8—432no—
221#124—862no—
222#123—1722no—
223C22⋊Q8—862no—
224#121—862no—
225#121—1722no—
226#120—1722no—
227C4×D4—22no—
228C4×D4—431no—
229C2×C22⋊C4—1722no—
230Q32—1721no—
231SD32—864no—
232SD32—864no—
233D16—864no—
234D16—1721no—
235D16D17214yescomplemented
236M32—864no—
237C2×C16—432no—
238C2×C16C22×D4311yescharacteristic
239C2×C16C22×D4311yescharacteristic
240#107C22×D4312yes—
241C4⋊C8—431no—
242#103—862no—
243#102—22no—
244#102—862no—
245C22⋊C8—432no—
246C4×C8C22×D4311yescharacteristic
247C24—1722no—
248#41—3442no—
249#41—1724no—
250C2×Q8—862no—
251C2×D4—22no—
252C2×D4—431no—
253C2×D4—862no—
254C2×D4—3442no—
255C2×D4—1722no—
256C2×D4—1722no—
257C2×D4—1724no—
258C2×D4—1722no—
259C22×C4—42no—
260C22×C4—432no—
261C22×C4—1722no—
262Q16—862no—
263Q16—862no—
264SD16—3442no—
265SD16—1724no—
266D8—22no—
267D8—862no—
268D8—862no—
269D8—1724no—
270D8C2×D17214yes—
271C2×C8—432no—
272C2×C8—862no—
273C2×C8—862no—
274C2×C8D4×D4311yescharacteristic
275C2×C8C23×D4311yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—431no—
278C4⋊C4—1722no—
279C22⋊C4—42no—
280C22⋊C4—432no—
281C22⋊C4—1722no—
282C22⋊C4—1722no—
283C22⋊C4—1722no—
284C22⋊C4—1722no—
285C42D4×D4311yescharacteristic
286C16—21no—
287C16—862no—
288C16C2×D17212yes—
289C23—42no—
290C23—432no—
291C23—3444no—
292C23—3444no—
293C23—1722no—
294C23—6882no—
295Q8—1722no—
296Q8—1722no—
297D4—24no—
298D4—42no—
299D4—3444no—
300D4—3444no—
301D4—1721no—
302D4—1722no—
303D4—1722no—
304D4—6882no—
305C2×C4—42no—
306C2×C4—162no—
307C2×C4—432no—
308C2×C4—862no—
309C2×C4—862no—
310C2×C4—3444no—
311C2×C4—1722no—
312C2×C4D8×D4311yescharacteristic
313C2×C4D8×D4311yescharacteristic
314C2×C4C2×D4×D4311yescharacteristic
315C8—21no—
316C8—862no—
317C8C22×D17211yescharacteristic
318C8#1306337111yescharacteristic
319C22—44no—
320C22—82no—
321C22—82no—
322C22—862no—
323C22—862no—
324C22—862no—
325C22—3442no—
326C22—3442no—
327C22—3442no—
328C22—6888no—
329C22C2×D8×D4311yescharacteristic
330C4—21no—
331C4—21no—
332C4—82no—
333C4—862no—
334C4—3442no—
335C4D4×D17211yescharacteristic
336C4#1458370111yescharacteristic
337C2—84no—
338C2—1722no—
339C2—6882no—
340C2D8×D17211yescharacteristic
341C2#1914772811yescharacteristic
342C2#1914773211yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×D16×C43C2
socleC22×C43C22×D8
hypercenterC4×D16D43
hypocenterC43#33839
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. C2×#14583333C2semidirect
2. #19146281C2semidirect
3. #19136856C2semidirect
4. #19136709C2semidirect
5. #19136650C2semidirect
6. #19136536C2semidirect
7. #19136508C2semidirect
8. #19136428C2semidirect
9. C4×D16×C43C2semidirect
11. C2×D8×D43C22semidirect
14. C2×Dic344C22semidirect
15. C2×#13063270C22semidirect
16. C2×#13063269C22semidirect
19. C2×#13063264C22semidirect
20. #14583283C22semidirect
21. #14583141C22semidirect
27. C4⋊(C43⋊C16)C22semidirect
28. #14582702C22semidirect
29. #14582699C22semidirect
30. (C2×D43)⋊C16C22semidirect
32. C4×D8×C43C22semidirect
33. C43×#366C22semidirect
34. C43×#357C22semidirect
35. C4×C16×C43C22semidirect
69. D16×C43D4semidirect
173. C4×D16D43semidirect
198. C4×D8C2×D43semidirect
200. #366C2×D43semidirect
204. #357C2×D43semidirect
206. C4×C16C2×D43semidirect
207. C43#33839semidirect
235. D16D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145833332
#191462812
#191368562
#191367092
#191366502
#191365362
#191365082
#191364282
C4×D16×C432
#3383943