Finite Group Databasebeta

← #25009184

Subgroups — #25009184

Order 11008.

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

normal subgroups only

This group has 362 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#19142864C211yesmaximal, characteristic, complemented
2#19133632C211yesmaximal, characteristic
3#19133564C211yesmaximal, characteristic
4#19132624C211yesmaximal, characteristic, complemented
5#19132621C211yesmaximal, characteristic, complemented
6#19132541C211yesmaximal, characteristic, complemented
7C43×#2039C211yesmaximal, characteristic
8#14583215—21no—
9#14583037—21no—
10#14582838—21no—
11#14582838C2211yescharacteristic
12#14582832—21no—
13#14582832—21no—
14#14582832—21no—
15#14582819—21no—
16#14582819C2211yescharacteristic
17#14582767—21no—
18#14582633—21no—
19#14582633—21no—
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22C43×#537C2211yescharacteristic
23C2×#104×C43—21no—
24C43×#417—21no—
25C43×#384C2211yescharacteristic
26C43×#343C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621883—41no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34#13063256—41no—
35#13063248—41no—
36#13063246—41no—
37C22⋊(C43⋊C8)—21no—
38C22⋊(C43⋊C8)—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C2×#41×C43—21no—
50C2×M16×C43—21no—
51C22⋊Q8×C43—41no—
52#121×C43—21no—
53#121×C43—21no—
54#121×C43—41no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59C2×C42×C43D411yescharacteristic
60#104×C43—42no—
61#103×C43—41no—
62#102×C43—41no—
63#41×C43—41no—
64#41×C43—41no—
65#41×C43—41no—
66#41×C43—41no—
67C2×Q8×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C2×Dic86—41no—
83C2×Dic86—81no—
84M16×C43—41no—
85M16×C43—41no—
86C2×C8×C43—41no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—81no—
92C4⋊C4×C43—81no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C42×C43—21no—
96C42×C43SD1612yescomplemented
97#10621883—82no—
98C4⋊Dic43—41no—
99C4⋊Dic43—81no—
100Dic43⋊C4—81no—
101Dic43⋊C4—81no—
102Dic43⋊C4—81no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C23×C43—41no—
106C23×C43#12011yescharacteristic
107Q8×C43—41no—
108Q8×C43—41no—
109D4×C43—41no—
110D4×C43—41no—
111D4×C43—81no—
112D4×C43—81no—
113D4×C43—81no—
114D4×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
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—81no—
129C2×C4×C43—81no—
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43#13711yescharacteristic
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—42no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143Dic86—42no—
144Dic86—81no—
145C8×C43—81no—
146C43⋊C8—81no—
147C43⋊C8—81no—
148#12183—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43—81no—
154C22×C43#44811yescharacteristic
155C22×C43#45411yescharacteristic
156C22×C43B(4,𝔽2)11yescharacteristic
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164Dic43—81no—
165Dic43—81no—
166Dic43—81no—
167Dic43—81no—
168#2843—431no—
169#2039D4311yescharacteristic
170#1616—431no—
171#1604—431no—
172#1354—431no—
173#1353—431no—
174#1325—431no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—161no—
178C2×C43#159911yescharacteristic
179C2×C43#220011yescharacteristic
180C2×C43#220311yescharacteristic
181#537C2×D4311yescharacteristic
182#481—861no—
183#448—861no—
184C2×#104—21no—
185#417—21no—
186#400—431no—
187#400—861no—
188#398—861no—
189#398—861no—
190#398—861no—
191#395—431no—
192#395—861no—
193#384C2×D4311yescharacteristic
194#383—861no—
195#343C2×D4311yescharacteristic
196#327—861no—
197#327—861no—
198#324—431no—
199#324—431no—
200C43#1218311yescharacteristic, complemented, Sylow
201C2×#41—21no—
202C22×Q8—431no—
203C2×SD16—1721no—
204C2×M16—21no—
205C22⋊Q8—41no—
206#121—21no—
207#121—21no—
208#121—41no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4C22⋊D4311yescharacteristic
217C2×C4⋊C4C22×D4311yescharacteristic
218C2×C42C22⋊D4311yescharacteristic
219#106—1721no—
220#104—42no—
221#103—41no—
222#103—1721no—
223#102—41no—
224#102—1721no—
225C22⋊C8—861no—
226C22⋊C8—861no—
227#95—431no—
228#95—431no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237#41—41no—
238#41—41no—
239#41—41no—
240#41—41no—
241C2×Q8—21no—
242C2×Q8—3441no—
243C2×Q8—1721no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4D4×D4311yescharacteristic
256C22×C4D4×D4311yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258SD16—3442no—
259M16—41no—
260M16—41no—
261C2×C8—41no—
262C2×C8—1721no—
263C2×C8—1721no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—3441no—
271C4⋊C4—3441no—
272C4⋊C4—3441no—
273C4⋊C4—3441no—
274C4⋊C4—1721no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—21no—
278C42#1062188312yescomplemented
279C23—41no—
280C23#1306329311yescharacteristic
281Q8—41no—
282Q8—41no—
283Q8—3441no—
284Q8—1722no—
285D4—41no—
286D4—41no—
287D4—81no—
288D4—81no—
289D4—81no—
290D4—81no—
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—81no—
305C2×C4—81no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1722no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4C2×#1062188311yescharacteristic
318C2×C4#1306335511yescharacteristic
319C8—81no—
320C8—3441no—
321C8—3441no—
322C22—21no—
323C22—21no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22#1458303711yescharacteristic
328C22#1458307111yescharacteristic
329C22#1458308511yescharacteristic
330C4—21no—
331C4—21no—
332C4—42no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—81no—
337C4—3441no—
338C4—3441no—
339C4—3441no—
340C4—3441no—
341C2—21no—
342C2—21no—
343C2—161no—
344C2#1913353411yescharacteristic
345C2#1913660111yescharacteristic
346C2#1913661411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2039C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#537C22
hypercenter#2039D43
hypocenterC43#12183
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #19142864C2semidirect
4. #19132624C2semidirect
5. #19132621C2semidirect
6. #19132541C2semidirect
96. C42×C43SD16semidirect
200. C43#12183semidirect
278. C42#10621883semidirect

Maximal subgroups

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

subgroupindex
#191428642
#191336322
#191335642
#191326242
#191326212
#191325412
C43×#20392
#1218343