Finite Group Databasebeta

← #25249942

Subgroups — #25249942

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583334C211yesmaximal, characteristic
2#19143471C211yesmaximal, characteristic, complemented
3#19143446C211yesmaximal, characteristic, complemented
4#19136468C212yesmaximal, complemented
5#19136462C212yesmaximal, complemented
6#19136444C212yesmaximal, complemented
7#19136439C212yesmaximal, complemented
8#19136384C211yesmaximal, characteristic, complemented
9C2×#14582701C211yesmaximal, characteristic, complemented
10#19136191C211yesmaximal, characteristic, complemented
11C43×#2138C211yesmaximal, characteristic, complemented
12C22×D344C2211yescharacteristic
13#14583382—21no—
14#14583373—21no—
15#14583334C418yescomplemented
16C2×#13063268C2212yes—
17C2×#13063266C2212yes—
18C2×#13063265C2211yescharacteristic
19#14583010—22no—
20#14583000—22no—
21Q16×Dic43C2212yescomplemented
22D8×Dic43C2212yescomplemented
23#14582981C2212yes—
24#14582981C2212yes—
25C2×#13063259C2211yescharacteristic
26#14582903—21no—
27#14582900—21no—
28#14582854C2211yescharacteristic
29#14582726C2212yescomplemented
30#14582724C2212yescomplemented
31#14582701C2212yes—
32#14582701C2212yes—
33#14582674C2212yescomplemented
34C16×Dic43C2212yescomplemented
35C2×#135×C43C2211yescharacteristic
36C22×C16×C43C2211yescharacteristic
37C43×#427C2211yescharacteristic
38C43×#358C2211yescharacteristic, complemented
39C43×#358C2211yescharacteristic, complemented
40C43×#357C2211yescharacteristic, complemented
41C43×#357C2211yescharacteristic, complemented
42C22×D172—21no—
43C2×D344—21no—
44C2×D344—22no—
45C2×D344C2×C414yescomplemented
46C2×D344C2312yes—
47C2×#10621877D411yescharacteristic
48Q8×Dic43—22no—
49C4×D172—41no—
50C4×D172—41no—
51D4×Dic43—22no—
52D4×Dic43—42no—
53#13063287—22no—
54#13063287—22no—
55#13063284—41no—
56#13063284D411yescharacteristic
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—41no—
59C22⋊C4×D43—42no—
60#13063268C2×C418yescomplemented
61#13063266C2×C418yescomplemented
62#13063265C2×C414yescomplemented
63C2×C43⋊C16C2312yes—
64#13063259—21no—
65#13063259C2312yes—
66#13063249—22no—
67#13063246—22no—
68#13063245—22no—
69#13063245—22no—
70#13063235D412yes—
71C8×Dic43C2312yes—
72C2×#41×C43—21no—
73#135×C43—22no—
74#135×C43C2×C414yescomplemented
75C2×Q16×C43C2311yescharacteristic
76C2×SD16×C43—21no—
77C2×D8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79#117×C43—21no—
80C2×C16×C43—22no—
81C2×C16×C43C2311yescharacteristic
82C2×C16×C43C2311yescharacteristic
83#107×C43C2311yescharacteristic
84#107×C43C2311yescharacteristic
85#106×C43—21no—
86C23×D43—41no—
87#41×C43—24no—
88#41×C43—42no—
89C2×Q8×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43C2×D411yescharacteristic
94C22×Dic43—42no—
95C22×Dic43—41no—
96C2×D172—24no—
97C2×D172—22no—
98C2×D172—41no—
99C2×D172—42no—
100C2×C4×D43—42no—
101C2×C4×D43—42no—
102Q16×C43—21no—
103Q16×C43C22×C412yes—
104SD16×C43—24no—
105D8×C43—21no—
106D8×C43C22×C412yes—
107C2×C8×C43C22×C412yes—
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43#4112yes—
110C2×C8×C43C2411yescharacteristic
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C22⋊C4×C43—41no—
114C42×C43—41no—
115C22⋊Dic43—42no—
116C22⋊Dic43D812yes—
117(C2×D43)⋊C4—42no—
118(C2×D43)⋊C4—42no—
119C4⋊Dic43—22no—
120C4⋊Dic43—41no—
121C4⋊Dic43—42no—
122C4⋊Dic43D811yescharacteristic
123C4⋊Dic43D811yescharacteristic
124C4×Dic43—42no—
125C4×Dic43C2×D412yes—
126#10621877—22no—
127C2×C43⋊C8C2×D412yes—
128D344—24no—
129D344—22no—
130D344C22×C414yes—
131C16×C43—21no—
132C16×C43—21no—
133C43⋊C16C22×C414yes—
134C23×C43—41no—
135C23×C43C2×D811yescharacteristic
136C22×D43—42no—
137C22×D43—44no—
138C22×D43—161no—
139C22×D43—161no—
140Q8×C43—22no—
141Q8×C43—41no—
142D4×C43—22no—
143D4×C43—44no—
144D4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—44no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43C4×D412yes—
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43#13512yes—
152C2×C4×C43C22×D411yescharacteristic
153C2×Dic43—42no—
154C2×Dic43—162no—
155C2×Dic43—161no—
156C2×Dic43C2×D812yes—
157C2×Dic43C2×D812yes—
158D172—24no—
159D172—42no—
160D172—44no—
161C4×D43—162no—
162C4×D43—162no—
163C8×C43C4×D412yes—
164C8×C43C23×C411yescharacteristic
165C8×C43C2×#4111yescharacteristic
166C43⋊C8—22no—
167#33454—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—42no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43C4×D812yes—
174C22×C43C22×D811yescharacteristic
175C2×D43—44no—
176C2×D43—82no—
177C2×D43—82no—
178C2×D43—164no—
179C4×C43—42no—
180C4×C43—81no—
181C4×C43—81no—
182C4×C43C4×D812yes—
183C4×C43C2×C4×D411yescharacteristic
184C4×C43C2×#13511yescharacteristic
185Dic43—22no—
186Dic43—22no—
187Dic43—82no—
188C2×#509—431no—
189#2951—431no—
190#2948—431no—
191#2177—432no—
192#2175—432no—
193C4×SD32—432no—
194C4×D16—432no—
195#2159—431no—
196#2138D4311yescharacteristic, complemented
197C2×#357—431no—
198#2108—431no—
199C2×C43—22no—
200C2×C43—82no—
201C2×C43C2×C4×D811yescharacteristic
202C2×C43#341511yescharacteristic
203C2×C43#341611yescharacteristic
204D43—84no—
205C2×#135C2×D4311yescharacteristic
206C22×D8—431no—
207#520—861no—
208#518—861no—
209#509—438no—
210C2×SD32—432no—
211C2×D16—432no—
212C2×M32—431no—
213C22×C16C2×D4311yescharacteristic
214#442—862no—
215#440—862no—
216C4×Q16—432no—
217C4×D8—432no—
218C4×D8—432no—
219C4×D8—432no—
220#427C2×D4311yescharacteristic
221C2×#107—431no—
222#418—861no—
223#417—861no—
224#405—431no—
225#367—432no—
226#366—432no—
227#358C2×D4311yescharacteristic, complemented
228#358C2×D4311yescharacteristic, complemented
229#357—432no—
230#357—432no—
231#357C2×D4311yescharacteristic, complemented
232#357C2×D4311yescharacteristic, complemented
233#346—432no—
234C4×C16—432no—
235C43#3345411yescharacteristic, complemented, Sylow
236C2×#41—21no—
237C22×D4—861no—
238#135—22no—
239#135C4×D4314yescomplemented
240C2×Q16C22×D4311yescharacteristic
241C2×SD16—21no—
242C2×D8—434no—
243C2×D8—432no—
244C2×D8—861no—
245C2×D8—862no—
246C2×D8C22×D4311yescharacteristic
247C2×M16—431no—
248C22×C8C22×D4311yescharacteristic
249C4×Q8—862no—
250C4×D4—862no—
251C4×D4—862no—
252C4×D4—862no—
253C4×D4—1721no—
254C4×D4—1721no—
255C4×D4—1722no—
256#117—21no—
257#117—431no—
258#117—1721no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—1721no—
261C2×C22⋊C4—1722no—
262SD32—438no—
263D16—438no—
264M32—434no—
265C2×C16—22no—
266C2×C16—432no—
267C2×C16C22×D4311yescharacteristic
268C2×C16C22×D4311yescharacteristic
269#107—432no—
270#107—861no—
271#107C22×D4311yescharacteristic
272#107C22×D4311yescharacteristic
273#106—21no—
274#103—862no—
275#102—862no—
276#102—862no—
277#102—862no—
278#97—432no—
279C4×C8—432no—
280C24—1721no—
281#41—24no—
282#41—42no—
283C2×Q8—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—864no—
287C2×D4—862no—
288C2×D4—1721no—
289C2×D4—1722no—
290C22×C4—41no—
291C22×C4—1722no—
292C22×C4—1722no—
293C22×C4—1722no—
294C22×C4—1721no—
295C22×C4D4×D4311yescharacteristic
296Q16—21no—
297Q16C2×C4×D4312yes—
298SD16—24no—
299D8—21no—
300D8—434no—
301D8—864no—
302D8—862no—
303D8C2×C4×D4312yes—
304M16—862no—
305C2×C8—432no—
306C2×C8C2×C4×D4312yes—
307C2×C8D4×D4311yescharacteristic
308C2×C8#1062190012yes—
309C2×C8C23×D4311yescharacteristic
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—431no—
313C4⋊C4—431no—
314C4⋊C4—862no—
315C4⋊C4—1722no—
316C4⋊C4—1721no—
317C22⋊C4—41no—
318C22⋊C4—432no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1722no—
322C42—41no—
323C42—432no—
324C42—1722no—
325C16—21no—
326C16—21no—
327C16—434no—
328C23—41no—
329C23—1722no—
330C23—1724no—
331C23—6881no—
332C23—6881no—
333C23D8×D4311yescharacteristic
334Q8—22no—
335Q8—41no—
336D4—22no—
337D4—44no—
338D4—41no—
339D4—864no—
340D4—1722no—
341D4—1724no—
342C2×C4—41no—
343C2×C4—44no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—432no—
347C2×C4—432no—
348C2×C4—1722no—
349C2×C4—6882no—
350C2×C4—6882no—
351C2×C4—6882no—
352C2×C4—6881no—
353C2×C4(C22⋊D43)⋊C412yes—
354C2×C4D8×D4311yescharacteristic
355C2×C4#1306334612yes—
356C2×C4C2×D4×D4311yescharacteristic
357C8—862no—
358C8(C22⋊D43)⋊C412yes—
359C8C22×C4×D4311yescharacteristic
360C8C2×#1062190011yescharacteristic
361C22—21no—
362C22—21no—
363C22—42no—
364C22—81no—
365C22—81no—
366C22—3442no—
367C22—3442no—
368C22—1724no—
369C22—6884no—
370C22#1458297912yes—
371C22C2×D8×D4311yescharacteristic
372C4—42no—
373C4—81no—
374C4—81no—
375C4—862no—
376C4—862no—
377C4—3442no—
378C4#1458297912yes—
379C4C2×(C22⋊D43)⋊C411yescharacteristic
380C4C2×#1306334611yescharacteristic
381C2—22no—
382C2—82no—
383C2—3444no—
384C2C2×#1458297911yescharacteristic
385C2#1914773311yescharacteristic
386C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2138C2
socleC22×C43C22×D8
prime radicalC2×#14583334C2
cosocleC2×C8×C43C24
hypercenter#2138D43
hypocenterC43#33454
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
2. #19143471C2semidirect
3. #19143446C2semidirect
4. #19136468C2semidirect
5. #19136462C2semidirect
6. #19136444C2semidirect
7. #19136439C2semidirect
8. #19136384C2semidirect
9. C2×#14582701C2semidirect
10. #19136191C2semidirect
11. C43×#2138C2semidirect
15. #14583334C4semidirect
21. Q16×Dic43C22semidirect
22. D8×Dic43C22semidirect
29. #14582726C22semidirect
30. #14582724C22semidirect
33. #14582674C22semidirect
34. C16×Dic43C22semidirect
38. C43×#358C22semidirect
39. C43×#358C22semidirect
40. C43×#357C22semidirect
41. C43×#357C22semidirect
45. C2×D344C2×C4semidirect
60. #13063268C2×C4semidirect
61. #13063266C2×C4semidirect
62. #13063265C2×C4semidirect
74. #135×C43C2×C4semidirect
196. #2138D43semidirect
227. #358C2×D43semidirect
228. #358C2×D43semidirect
231. #357C2×D43semidirect
232. #357C2×D43semidirect
235. C43#33454semidirect
239. #135C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833342
#191434712
#191434462
#191364682
#191364622
#191364442
#191364392
#191363842
C2×#145827012
#191361912
C43×#21382
#3345443