Finite Group Databasebeta

← #25008963

Subgroups — #25008963

Order 11008.

380 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 59 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#19135819C211yesmaximal, characteristic
2#19133597C211yesmaximal, characteristic
3#19133563C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132541C211yesmaximal, characteristic, complemented
7C43×#2792C211yesmaximal, characteristic, complemented
8#14583480C2211yescharacteristic
9#14583212—21no—
10#14583038—21no—
11C2×#13063253—21no—
12#14582898—21no—
13#14582668C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C43×#398—21no—
19C43×#398C2211yescharacteristic
20C43×#395—21no—
21C43×#395C2211yescharacteristic
22C43×#389—21no—
23C43×#389—21no—
24C43×#387—21no—
25C43×#387—21no—
26C43×#384C2211yescharacteristic
27C2×#10621898—21no—
28C2×#10621884—41no—
29C2×#10621877—21no—
30#13063305—41no—
31#13063300—41no—
32#13063299—21no—
33#13063299—21no—
34#13063258—41no—
35#13063253—42no—
36#13063249—41no—
37#13063248—41no—
38#13063245—41no—
39#13063245—41no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42C22×Q8×C43D411yescharacteristic
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43C2311yescharacteristic
53C2×C42×C43—21no—
54C2×C42×C43D411yescharacteristic
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62#95×C43D411yescharacteristic
63C2×Q8×C43—41no—
64C2×Q8×C43—81no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C2×C22⋊D43—41no—
75#10621898—41no—
76#10621898—41no—
77#10621898—41no—
78#10621898—41no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—21no—
82C2×C4×D43—41no—
83C2×Dic86—21no—
84C4⋊C4×C43—24no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—81no—
91C4⋊C4×C43—81no—
92C4⋊C4×C43—81no—
93C4⋊C4×C43—81no—
94C4⋊C4×C43—81no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—81no—
98#10621884—82no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103#10621877—41no—
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C23×C43#12011yescharacteristic
109C22×D43—41no—
110Q8×C43—42no—
111Q8×C43—81no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C22⋊D43—81no—
139C22⋊D43—81no—
140C2×Dic43—41no—
141D172—41no—
142D172—41no—
143D172—81no—
144D172—81no—
145C4×D43—81no—
146C4×D43—81no—
147Dic86—41no—
148Dic86—41no—
149C43⋊C8—81no—
150C43⋊C8—81no—
151C43⋊C8—81no—
152#12146—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43#44911yescharacteristic
156C22×C43#45411yescharacteristic
157C22×C43B(4,𝔽2)11yescharacteristic
158C2×D43—81no—
159C2×D43—81no—
160C2×D43—81no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—42no—
164C4×C43—42no—
165C4×C43—42no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—81no—
169C4×C43—81no—
170C4×C43—81no—
171Dic43—81no—
172#2792D4311yescharacteristic, complemented
173#2039—431no—
174#1610—431no—
175#1604—431no—
176#1354—431no—
177#1346—431no—
178#1325—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43#159711yescharacteristic
182C2×C43#220011yescharacteristic
183C2×C43#220511yescharacteristic
184D43—161no—
185#537—431no—
186#480—861no—
187#448—861no—
188C2×#104—861no—
189#417—861no—
190#398—21no—
191#398C2×D4311yescharacteristic
192#395—21no—
193#395C2×D4311yescharacteristic
194#389—21no—
195#389—21no—
196#387—21no—
197#387—21no—
198#384C2×D4311yescharacteristic
199#343—431no—
200#327—861no—
201#327—861no—
202#324—431no—
203#324—431no—
204C43#1214611yescharacteristic, complemented, Sylow
205C2×#41—861no—
206C22×Q8C22⋊D4311yescharacteristic
207C2×SD16—1721no—
208C2×M16—861no—
209C22⋊Q8—1721no—
210#121—861no—
211#121—861no—
212#121—1721no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C22⋊D4311yescharacteristic
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C4⋊C4C22×D4311yescharacteristic
223C2×C42—21no—
224C2×C42C22⋊D4311yescharacteristic
225#107—1721no—
226#104—1722no—
227#103—1721no—
228#103—1721no—
229#102—1721no—
230#102—1721no—
231C22⋊C8—861no—
232C22⋊C8—861no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95C22⋊D4311yescharacteristic
240#95C22⋊D4311yescharacteristic
241#41—1721no—
242#41—1721no—
243#41—1721no—
244#41—1721no—
245C2×Q8—41no—
246C2×Q8—81no—
247C2×Q8—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4—861no—
251C2×D4—1721no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—1721no—
259C22×C4C2×C22⋊D4311yescharacteristic
260C22×C4C2×C22⋊D4311yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262SD16—3442no—
263M16—1721no—
264M16—1721no—
265C2×C8—1721no—
266C2×C8—1721no—
267C2×C8—1721no—
268C4⋊C4—24no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—81no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C22⋊C4—1721no—
282C22⋊C4—1721no—
283C42—21no—
284C42—21no—
285C42—81no—
286C23—1721no—
287C23#1306329411yescharacteristic
288Q8—42no—
289Q8—81no—
290Q8—1721no—
291Q8—1721no—
292D4—3441no—
293D4—3441no—
294D4—3441no—
295D4—3441no—
296D4—1721no—
297D4—1721no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—1721no—
325C2×C4#1306334511yescharacteristic
326C2×C4#1306335011yescharacteristic
327C8—3441no—
328C8—3441no—
329C8—3441no—
330C22—21no—
331C22—21no—
332C22—3441no—
333C22—3441no—
334C22—3441no—
335C22#1458304411yescharacteristic
336C22#1458307211yescharacteristic
337C22#1458308611yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—3441no—
349C2—21no—
350C2—21no—
351C2—6881no—
352C2#1913352411yescharacteristic
353C2#1913660211yescharacteristic
354C2#1913662511yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2792C2
socleC22×C43B(4,𝔽2)
prime radical#14583480C22
hypercenter#2792D43
hypocenterC43#12146
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2792

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132601C2semidirect
6. #19132541C2semidirect
7. C43×#2792C2semidirect
172. #2792D43semidirect
204. C43#12146semidirect

Maximal subgroups

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

subgroupindex
#191358192
#191335972
#191335632
#191326252
#191326012
#191325412
C43×#27922
#1214643