Finite Group Databasebeta

← #25009186

Subgroups — #25009186

Order 11008.

362 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 63 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#19133631C211yesmaximal, characteristic
3#19133563C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132622C211yesmaximal, characteristic, complemented
6#19132541C211yesmaximal, characteristic, complemented
7C43×#2843C211yesmaximal, characteristic, complemented
8#14583480C2211yescharacteristic
9#14583217—21no—
10#14583038—21no—
11C2×#13063253—21no—
12#14582898—21no—
13#14582668C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C43×#400—21no—
19C43×#400C2211yescharacteristic
20C43×#398—21no—
21C43×#398—21no—
22C43×#398—21no—
23C43×#395—21no—
24C43×#395C2211yescharacteristic
25C43×#384C2211yescharacteristic
26C43×#383—21no—
27C2×#10621898—21no—
28C2×#10621884—41no—
29C2×#10621877—21no—
30#13063305—41no—
31#13063300—41no—
32#13063299—21no—
33#13063299—21no—
34#13063256—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×C43D411yescharacteristic
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43C2311yescharacteristic
52C2×C42×C43D411yescharacteristic
53#95×C43—21no—
54#95×C43—21no—
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—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—81no—
88C4⋊C4×C43—81no—
89C4⋊C4×C43—81no—
90C4⋊C4×C43—81no—
91C4⋊C4×C43—81no—
92C4⋊C4×C43—81no—
93C42×C43—21no—
94C42×C43SD1612yescomplemented
95#10621884—82no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100#10621877—41no—
101#10621877—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C23×C43#12011yescharacteristic
106C22×D43—41no—
107Q8×C43—42no—
108Q8×C43—81no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
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—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43C2×SD1611yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C22⋊D43—81no—
135C22⋊D43—81no—
136C2×Dic43—41no—
137D172—41no—
138D172—41no—
139D172—81no—
140D172—81no—
141C4×D43—81no—
142C4×D43—81no—
143Dic86—41no—
144Dic86—41no—
145C43⋊C8—81no—
146C43⋊C8—81no—
147C43⋊C8—81no—
148#12183—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43#44811yescharacteristic
152C22×C43#45411yescharacteristic
153C22×C43B(4,𝔽2)11yescharacteristic
154C2×D43—81no—
155C2×D43—81no—
156C2×D43—81no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43—81no—
166C4×C43—81no—
167Dic43—81no—
168#2843D4311yescharacteristic, complemented
169#2039—431no—
170#1616—431no—
171#1604—431no—
172#1354—431no—
173#1353—431no—
174#1325—431no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43#159911yescharacteristic
178C2×C43#220011yescharacteristic
179C2×C43#220311yescharacteristic
180D43—161no—
181#537—431no—
182#481—861no—
183#448—861no—
184C2×#104—861no—
185#417—861no—
186#400—21no—
187#400C2×D4311yescharacteristic
188#398—21no—
189#398—21no—
190#398—21no—
191#395—21no—
192#395C2×D4311yescharacteristic
193#384C2×D4311yescharacteristic
194#383—21no—
195#343—431no—
196#327—861no—
197#327—861no—
198#324—431no—
199#324—431no—
200C43#1218311yescharacteristic, complemented, Sylow
201C2×#41—861no—
202C22×Q8C22⋊D4311yescharacteristic
203C2×SD16—1721no—
204C2×M16—861no—
205C22⋊Q8—1721no—
206#121—861no—
207#121—861no—
208#121—1721no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C22⋊D4311yescharacteristic
216C2×C4⋊C4C22⋊D4311yescharacteristic
217C2×C4⋊C4C22×D4311yescharacteristic
218C2×C42C22⋊D4311yescharacteristic
219#106—1721no—
220#104—1722no—
221#103—1721no—
222#103—1721no—
223#102—1721no—
224#102—1721no—
225C22⋊C8—861no—
226C22⋊C8—861no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95C22⋊D4311yescharacteristic
236#95C22⋊D4311yescharacteristic
237#41—1721no—
238#41—1721no—
239#41—1721no—
240#41—1721no—
241C2×Q8—41no—
242C2×Q8—81no—
243C2×Q8—861no—
244C2×D4—861no—
245C2×D4—861no—
246C2×D4—861no—
247C2×D4—1721no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—1721no—
255C22×C4C2×C22⋊D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258SD16—3442no—
259M16—1721no—
260M16—1721no—
261C2×C8—1721no—
262C2×C8—1721no—
263C2×C8—1721no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C22⋊C4—1721no—
276C22⋊C4—1721no—
277C42—21no—
278C42#1062188412yescomplemented
279C23—1721no—
280C23#1306329411yescharacteristic
281Q8—42no—
282Q8—81no—
283Q8—1721no—
284Q8—1721no—
285D4—3441no—
286D4—3441no—
287D4—3441no—
288D4—3441no—
289D4—1721no—
290D4—1721no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—3441no—
315C2×C4—3441no—
316C2×C4—1721no—
317C2×C4C2×#1062188411yescharacteristic
318C2×C4#1306335611yescharacteristic
319C8—3441no—
320C8—3441no—
321C8—3441no—
322C22—21no—
323C22—21no—
324C22—3441no—
325C22—3441no—
326C22—3441no—
327C22#1458303811yescharacteristic
328C22#1458307211yescharacteristic
329C22#1458308611yescharacteristic
330C4—21no—
331C4—21no—
332C4—42no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—3441no—
341C2—21no—
342C2—21no—
343C2—6881no—
344C2#1913353511yescharacteristic
345C2#1913660211yescharacteristic
346C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2843C2
socleC22×C43B(4,𝔽2)
prime radical#14583480C22
hypercenter#2843D43
hypocenterC43#12183
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2843

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132622C2semidirect
6. #19132541C2semidirect
7. C43×#2843C2semidirect
94. C42×C43SD16semidirect
168. #2843D43semidirect
200. C43#12183semidirect
278. C42#10621884semidirect

Maximal subgroups

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

subgroupindex
#191358192
#191336312
#191335632
#191326252
#191326222
#191325412
C43×#28432
#1218343