Finite Group Databasebeta

← #25251832

Subgroups — #25251832

Order 11008.

520 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#19145335C211yesmaximal, characteristic, complemented
2#19143505C211yesmaximal, characteristic
3#19136815C211yesmaximal, characteristic, complemented
4#19136812C211yesmaximal, characteristic, complemented
5#19136764C212yesmaximal, complemented
6#19136674C212yesmaximal, complemented
7#19136546C211yesmaximal, characteristic
8#19136487C212yesmaximal, complemented
9#19136483C212yesmaximal, complemented
10#19136404C211yesmaximal, characteristic, complemented
11C43×#2191C211yesmaximal, characteristic
12#14583666—21no—
13#14583451—21no—
14#14583339C2212yes—
15#14583296C2211yescharacteristic, complemented
16#14583277C2211yescharacteristic, complemented
17#14583248—21no—
18#14583157C2211yescharacteristic
19#14583155—21no—
20#14583021—21no—
21#14583021C2212yes—
22#14583016—21no—
23#14583016C2212yes—
24#14583006C2211yescharacteristic, complemented
25#14583005C2211yescharacteristic, complemented
26#14583003—21no—
27#14582948C2211yescharacteristic
28C2×#13063252—21no—
29M16×Dic43C2211yescharacteristic
30#14582722C2212yescomplemented
31#14582721C2212yescomplemented
32#14582719C2212yescomplemented
33#14582716C2212yescomplemented
34#14582715C2212yescomplemented
35#14582709C2212yes—
36#14582681C2211yescharacteristic
37#14582676C2212yescomplemented
38C43×#575C2211yescharacteristic
39C43×#510C2212yes—
40C43×#470C2211yescharacteristic
41C43×#360C2212yes—
42C43×#349C2211yescharacteristic
43C2×Dic172C2311yescharacteristic
44C2×#10621885—21no—
45#13063332—22no—
46#13063332—22no—
47#13063332—42no—
48C2×#10621877—21no—
49C2×#10621877—42no—
50C2×#10621877D411yescharacteristic
51#13063324—21no—
52#13063323—21no—
53#13063315—41no—
54#13063304—21no—
55#13063302—41no—
56Q8×Dic43—21no—
57#13063290—21no—
58#13063290—41no—
59#13063281—41no—
60C2×C4×Dic43D411yescharacteristic
61#13063271—22no—
62#13063269—22no—
63#13063265C2312yes—
64#13063261—21no—
65#13063261C2312yes—
66#13063257C2311yescharacteristic
67#13063256—21no—
68#13063252—22no—
69#13063252—22no—
70#13063250—21no—
71#13063249—21no—
72#13063248—21no—
73#13063235D411yescharacteristic
74#13063235C2311yescharacteristic
75C8×Dic43D411yescharacteristic
76C8×Dic43C2311yescharacteristic
77C2×#41×C43—21no—
78#137×C43—22no—
79AGL(1,ℤ/8)×C43—22no—
80#135×C43—21no—
81#135×C43C2312yes—
82C2×Q16×C43C2311yescharacteristic
83C2×M16×C43C2311yescharacteristic
84C22⋊Q8×C43—21no—
85Q32×C43—22no—
86SD32×C43—22no—
87M32×C43C2312yes—
88#106×C43C2311yescharacteristic
89#103×C43—21no—
90#41×C43—22no—
91#41×C43—22no—
92#41×C43—41no—
93#41×C43—41no—
94C2×Q8×C43—21no—
95C2×Q8×C43—21no—
96C2×D4×C43—21no—
97C2×D4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43C2×D411yescharacteristic
100C22×Dic43—21no—
101C2×Dic86—21no—
102C2×Dic86—41no—
103Q16×C43—21no—
104Q16×C43—22no—
105Q16×C43#4112yes—
106SD16×C43—22no—
107SD16×C43—22no—
108D8×C43—21no—
109D8×C43#4112yes—
110M16×C43—22no—
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2411yescharacteristic
113C4⋊C4×C43—21no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊Dic43—41no—
117#10621885—42no—
118C4⋊Dic43—21no—
119C4⋊Dic43—41no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125C4×Dic43—21no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128C4×Dic43C2×D411yescharacteristic
129C4×Dic43C2×D411yescharacteristic
130#10621877—22no—
131#10621877—22no—
132#10621877—42no—
133#10621877—41no—
134#10621877—42no—
135C2×C43⋊C8—42no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—42no—
138C2×C43⋊C8C2×D411yescharacteristic
139C2×C43⋊C8C2×D411yescharacteristic
140Dic172—22no—
141C16×C43—22no—
142C43⋊C16—22no—
143C23×C43—41no—
144C23×C43AGL(1,ℤ/8)11yescharacteristic
145Q8×C43—22no—
146Q8×C43—41no—
147Q8×C43—41no—
148Q8×C43—41no—
149D4×C43—22no—
150D4×C43—41no—
151D4×C43—42no—
152D4×C43—42no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—42no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167Dic86—41no—
168Dic86—41no—
169Dic86—82no—
170C8×C43—21no—
171C8×C43C2×#4112yes—
172C43⋊C8—21no—
173C43⋊C8—42no—
174C43⋊C8AGL(1,ℤ/8)12yes—
175#33689—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—41no—
178C22×C43—42no—
179C22×C43—161no—
180C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
181C4×C43—21no—
182C4×C43—42no—
183C4×C43—81no—
184C4×C43—81no—
185C4×C43#52511yescharacteristic
186C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
187Dic43—22no—
188Dic43—41no—
189Dic43—81no—
190Dic43—81no—
191#3185—431no—
192#2956—431no—
193#2239—431no—
194#2239—431no—
195#2230—432no—
196#2214—432no—
197#2191—431no—
198#2191D4311yescharacteristic
199#2180—432no—
200#2180—432no—
201#2165—431no—
202C2×C43—21no—
203C2×C43—41no—
204C2×C43—82no—
205C2×C43#310911yescharacteristic
206#575C2×D4311yescharacteristic
207#568—861no—
208#533—861no—
209#510—432no—
210#510C2×D4312yes—
211#498—431no—
212#494—431no—
213#487—861no—
214#470—431no—
215#470—861no—
216#470C2×D4311yescharacteristic
217#444—432no—
218#444—861no—
219#443—432no—
220#443—861no—
221#441—431no—
222#441—431no—
223#441—861no—
224#430—431no—
225C2×#104—861no—
226C4×M16—431no—
227#365—432no—
228#365—432no—
229#364—432no—
230#362—432no—
231#362—432no—
232#360—432no—
233#360C2×D4312yes—
234#349—431no—
235#349C2×D4311yescharacteristic
236#347—432no—
237C43#3368911yescharacteristic, complemented, Sylow
238C2×#41—21no—
239#137—22no—
240AGL(1,ℤ/8)—22no—
241#135—21no—
242#135C22×D4312yes—
243C2×Q16—431no—
244C2×Q16—861no—
245C2×Q16C22×D4311yescharacteristic
246#131—862no—
247#131—862no—
248#131—1722no—
249C2×M16—431no—
250C2×M16—861no—
251C2×M16—1722no—
252C2×M16C22×D4311yescharacteristic
253C4⋊Q8—861no—
254C4⋊Q8—861no—
255#125—1721no—
256C22⋊Q8—21no—
257C22⋊Q8—861no—
258C22⋊Q8—1721no—
259C4×Q8—861no—
260C4×Q8—861no—
261C4×Q8—1721no—
262#117—1721no—
263C2×C42—431no—
264Q32—22no—
265Q32—862no—
266SD32—22no—
267SD32—862no—
268M32—432no—
269M32C22×D4312yes—
270#108—432no—
271#108—861no—
272#106—431no—
273#106—861no—
274#106C22×D4311yescharacteristic
275#104—862no—
276#104—862no—
277#103—21no—
278#103—861no—
279#103—861no—
280#103—861no—
281#97—431no—
282#97—431no—
283C4×C8—431no—
284C4×C8—431no—
285#41—22no—
286#41—22no—
287#41—41no—
288#41—41no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—861no—
292C2×Q8—1721no—
293C2×D4—21no—
294C2×D4—41no—
295C22×C4—41no—
296C22×C4—861no—
297C22×C4D4×D4311yescharacteristic
298Q16—21no—
299Q16—22no—
300Q16—862no—
301Q16—1722no—
302Q16#1062190012yes—
303SD16—22no—
304SD16—22no—
305D8—21no—
306D8#1062190012yes—
307M16—22no—
308M16—862no—
309M16—862no—
310M16—1722no—
311M16—1722no—
312M16—1721no—
313C2×C8—431no—
314C2×C8—431no—
315C2×C8—1722no—
316C2×C8—1722no—
317C2×C8—1721no—
318C2×C8D4×D4311yescharacteristic
319C2×C8C23×D4311yescharacteristic
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—861no—
323C4⋊C4—1721no—
324C4⋊C4—1721no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C22⋊C4—41no—
330C22⋊C4—1721no—
331C42—431no—
332C42—431no—
333C42—861no—
334C42—1721no—
335C42—1721no—
336C16—22no—
337C16—862no—
338C23—41no—
339C23#1306334911yescharacteristic
340Q8—22no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—3442no—
345Q8—1721no—
346Q8—1721no—
347D4—22no—
348D4—41no—
349D4—42no—
350D4—42no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—1722no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4#1306334911yescharacteristic
364C2×C4C2×D4×D4311yescharacteristic
365C8—21no—
366C8—432no—
367C8—861no—
368C8—1722no—
369C8C2×#1062190012yes—
370C22—21no—
371C22—41no—
372C22—42no—
373C22—161no—
374C22C2×#1306334911yescharacteristic
375C4—21no—
376C4—42no—
377C4—81no—
378C4—81no—
379C4—862no—
380C4—3441no—
381C4—3441no—
382C4—1721no—
383C4#1458340511yescharacteristic
384C4AGL(1,ℤ/8)×D4311yescharacteristic
385C2—21no—
386C2—41no—
387C2—82no—
388C2#1914468111yescharacteristic
subgroupG/H
centerC2#19144681
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2191C2
socleC2×C43#3109
prime radicalC43×#575C22
hypercenter#2191D43
hypocenterC43#33689
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2191

Complements

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

NH ≅ G/Ntype
1. #19145335C2semidirect
3. #19136815C2semidirect
4. #19136812C2semidirect
5. #19136764C2semidirect
6. #19136674C2semidirect
8. #19136487C2semidirect
9. #19136483C2semidirect
10. #19136404C2semidirect
15. #14583296C22semidirect
16. #14583277C22semidirect
24. #14583006C22semidirect
25. #14583005C22semidirect
30. #14582722C22semidirect
31. #14582721C22semidirect
32. #14582719C22semidirect
33. #14582716C22semidirect
34. #14582715C22semidirect
37. #14582676C22semidirect
237. C43#33689semidirect

Maximal subgroups

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

subgroupindex
#191453352
#191435052
#191368152
#191368122
#191367642
#191366742
#191365462
#191364872
#191364832
#191364042
C43×#21912
#3368943