Finite Group Databasebeta

← #25006676

Subgroups — #25006676

Order 11008.

360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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#19143500C211yesmaximal, characteristic
2#19136406C211yesmaximal, characteristic, complemented
3#19132899C211yesmaximal, characteristic, complemented
4#19132572C211yesmaximal, characteristic, complemented
5#19132568C211yesmaximal, characteristic, complemented
6#19132567C211yesmaximal, characteristic, complemented
7C43×#1336C211yesmaximal, characteristic, complemented
8#14583696C411yescharacteristic
9#14583664—21no—
10#14583021C411yescharacteristic
11#14583020C411yescharacteristic
12#14583019—21no—
13#14583017C2211yescharacteristic
14#14583013—21no—
15#14582946C411yescharacteristic
16#104×D43—21no—
17C4×#10621872—21no—
18C4×#10621872C2211yescharacteristic
19#14582720C2211yescharacteristic, complemented
20#14582680—21no—
21#14582676—21no—
22#14582621—21no—
23C8×C43⋊C8C2211yescharacteristic, complemented
24C43×#443C2211yescharacteristic
25C43×#364C2211yescharacteristic, complemented
26C43×#322C2211yescharacteristic, complemented
27#41×D43—21no—
28#13063357—21no—
29#13063354—21no—
30#13063352—21no—
31#13063349—21no—
32#13063347C2×C411yescharacteristic
33#13063345—21no—
34#13063333—21no—
35#13063333—41no—
36#13063332—21no—
37#13063331—21no—
38#13063331—41no—
39C2×#10621872—22no—
40C2×#10621872—41no—
41C2×#10621872C2×C411yescharacteristic
42C2×#10621872D411yescharacteristic
43M16×D43—21no—
44M16×D43—41no—
45C42×D43D411yescharacteristic
46#13063265—21no—
47#13063261C2×C411yescharacteristic
48#13063260—21no—
49#13063253—21no—
50#13063252—21no—
51#13063251—21no—
52#13063235—22no—
53#13063235C2×C411yescharacteristic
54#13063235D411yescharacteristic
55C4×C43⋊C8—21no—
56C4×C43⋊C8D411yescharacteristic
57#135×C43C2×C411yescharacteristic
58#131×C43—21no—
59M32×C43—21no—
60#108×C43C2×C411yescharacteristic
61#104×C43—21no—
62C4×C8×C43—21no—
63C4×C8×C43C2311yescharacteristic
64#41×C43—21no—
65#10621902—21no—
66Q8×D43—21no—
67#10621900—21no—
68#10621900—41no—
69D4×D43—21no—
70D4×D43—41no—
71#10621898—21no—
72#10621898—41no—
73C2×C4×D43—21no—
74C2×C4×D43—41no—
75C2×C4×D43C22⋊C411yescharacteristic
76Q16×C43M1611yescharacteristic, complemented
77SD16×C43—21no—
78D8×C43M1611yescharacteristic, complemented
79M16×C43—21no—
80M16×C43—41no—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C2×C8×C43C22×C411yescharacteristic
84C2×C8×C43C2×D411yescharacteristic
85C42×C43C2×D411yescharacteristic
86#10621885—21no—
87#10621884—21no—
88#10621883—21no—
89#10621882—21no—
90C4×Dic43—21no—
91C4×Dic43C22⋊C411yescharacteristic
92#10621877—21no—
93#10621877—41no—
94C2×C43⋊C8—22no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8C22⋊C411yescharacteristic
97C2×C43⋊C8C22⋊C411yescharacteristic
98Dic172M1611yescharacteristic, complemented
99D344M1611yescharacteristic, complemented
100#10621873—21no—
101#10621872—21no—
102#10621872—21no—
103#10621872—21no—
104#10621872—21no—
105#10621872—44no—
106#10621872—41no—
107#10621872—41no—
108#10621872—41no—
109C8×D43—41no—
110C8×D43—41no—
111C8×D43—41no—
112C16×C43—41no—
113C43⋊C16—41no—
114C22×D43—41no—
115C22×D43#10411yescharacteristic
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—41no—
119C2×C4×C43—21no—
120C2×C4×C43—41no—
121C2×C4×C43C2×C22⋊C411yescharacteristic
122C22⋊D43—41no—
123C22⋊D43—41no—
124C22⋊D43—41no—
125C2×Dic43—21no—
126C2×Dic43—41no—
127C2×Dic43#10411yescharacteristic
128D172—21no—
129D172—41no—
130C4×D43—21no—
131C4×D43—21no—
132C4×D43—41no—
133C4×D43—42no—
134C4×D43—41no—
135C4×D43—41no—
136Dic86—21no—
137Dic86—41no—
138C8×C43—42no—
139C8×C43—41no—
140C8×C43C2×M1611yescharacteristic
141C8×C43C2×M1611yescharacteristic
142C8×C43AGL(1,ℤ/8)11yescharacteristic
143C8×C43AGL(1,ℤ/8)11yescharacteristic
144C43⋊C8—24no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C43⋊C8—41no—
148#11669—431nomaximal, Sylow
149C22×C43—41no—
150C22×C43C2×#10411yescharacteristic
151C2×D43—21no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—161no—
155C4×C43—22no—
156C4×C43—41no—
157C4×C43#40711yescharacteristic
158C4×C43#41811yescharacteristic
159Dic43—21no—
160Dic43—41no—
161Dic43—41no—
162#2956—431no—
163#2165—431no—
164#1455—431no—
165#1336—431no—
166#1336D4311yescharacteristic, complemented
167#1335—431no—
168#1335—431no—
169C2×C43—21no—
170C2×C43—81no—
171C2×C43#149011yescharacteristic
172D43—41no—
173D43—81no—
174#575—431no—
175#568—861no—
176#444—431no—
177#444—431no—
178#444—861no—
179#443—431no—
180#443—861no—
181#443C2×D4311yescharacteristic
182#430—431no—
183C2×#104—861no—
184C4×M16—431no—
185C4×M16—861no—
186#364—431no—
187#364C2×D4311yescharacteristic, complemented
188#349—861no—
189#347—861no—
190#322—861no—
191#322C2×D4311yescharacteristic, complemented
192C82—431no—
193C43#1166911yescharacteristic, complemented, Sylow
194C2×#41—861no—
195#137—861no—
196#137—861no—
197AGL(1,ℤ/8)—861no—
198AGL(1,ℤ/8)—861no—
199#135—431no—
200#135—861no—
201#135C4×D4311yescharacteristic
202#131—21no—
203#131—861no—
204#131—861no—
205#131—861no—
206#131—1721no—
207#131—1721no—
208C2×M16—431no—
209C2×M16—431no—
210C2×M16—862no—
211C2×M16—861no—
212C2×M16—1721no—
213C2×M16—1721no—
214C2×C42—431no—
215M32—21no—
216M32—861no—
217#108—431no—
218#108—861no—
219#108C4×D4311yescharacteristic
220#104—21no—
221#104—861no—
222#104—861no—
223#104—861no—
224#97—431no—
225#97—431no—
226#97—862no—
227C4×C8—21no—
228C4×C8—431no—
229C4×C8—861no—
230C4×C8C22×D4311yescharacteristic
231#41—21no—
232#41—861no—
233#41—861no—
234#41—861no—
235#41—1721no—
236#41—1721no—
237C2×Q8—861no—
238C2×D4—861no—
239C2×D4—1721no—
240C22×C4—431no—
241C22×C4—861no—
242C22×C4—1721no—
243Q16—431no—
244Q16—861no—
245Q16#1062187211yescharacteristic, complemented
246SD16—21no—
247SD16—861no—
248SD16—861no—
249SD16—861no—
250D8—431no—
251D8—861no—
252D8#1062187211yescharacteristic, complemented
253M16—21no—
254M16—41no—
255M16—861no—
256M16—861no—
257M16—861no—
258M16—861no—
259M16—861no—
260M16—1724no—
261M16—1721no—
262M16—1721no—
263M16—1721no—
264M16—1721no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—862no—
270C2×C8—1721no—
271C2×C8—1721no—
272C2×C8—1721no—
273C2×C8—1721no—
274C2×C8C2×C4×D4311yescharacteristic
275C2×C8D4×D4311yescharacteristic
276C42—431no—
277C42—861no—
278C42D4×D4311yescharacteristic
279C16—41no—
280C16—1721no—
281C23—431no—
282C23—1721no—
283Q8—21no—
284Q8—861no—
285Q8—1721no—
286D4—21no—
287D4—41no—
288D4—861no—
289D4—1721no—
290D4—1721no—
291D4—1721no—
292D4—1721no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—431no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—1722no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4C22⋊C4×D4311yescharacteristic
305C8—42no—
306C8—41no—
307C8—864no—
308C8—861no—
309C8—861no—
310C8—1721no—
311C8M16×D4311yescharacteristic
312C8C2×#1062187211yescharacteristic
313C8#1306334911yescharacteristic
314C8#1306335211yescharacteristic
315C22—41no—
316C22—861no—
317C22—1721no—
318C22—1721no—
319C22—6881no—
320C22#104×D4311yescharacteristic
321C4—22no—
322C4—41no—
323C4—861no—
324C4—1721no—
325C4—1721no—
326C4#1458286111yescharacteristic
327C4#1458290211yescharacteristic
328C2—21no—
329C2—81no—
330C2—3441no—
331C2—1721no—
332C2#1913303611yescharacteristic
subgroupG/H
centerC4#14582902
commutatorC2×C8×C43C22×C4
FrattiniC4×C8C22×D43
FittingC43×#1336C2
socleC2×C43#1490
prime radical#14583696C4
cosocleC4×C8×C43C23
hypercenter#1336D43
hypocenterC43#11669
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #1336

Complements

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

NH ≅ G/Ntype
2. #19136406C2semidirect
3. #19132899C2semidirect
4. #19132572C2semidirect
5. #19132568C2semidirect
6. #19132567C2semidirect
7. C43×#1336C2semidirect
19. #14582720C22semidirect
23. C8×C43⋊C8C22semidirect
25. C43×#364C22semidirect
26. C43×#322C22semidirect
76. Q16×C43M16semidirect
78. D8×C43M16semidirect
98. Dic172M16semidirect
99. D344M16semidirect
166. #1336D43semidirect
187. #364C2×D43semidirect
191. #322C2×D43semidirect
193. C43#11669semidirect
245. Q16#10621872semidirect
252. D8#10621872semidirect

Maximal subgroups

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

subgroupindex
#191435002
#191364062
#191328992
#191325722
#191325682
#191325672
C43×#13362
#1166943