Finite Group Databasebeta

← #25071452

Subgroups — #25071452

Order 11008.

910 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 207 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#19145540C212yesmaximal
2#19139800C211yesmaximal, characteristic
3#19133569C218yesmaximal
4#19133094C212yesmaximal
5#19132919C211yesmaximal, characteristic
6C43×#3502C211yesmaximal, characteristic
7C2×#13063325C2211yescharacteristic
8#14583278—22no—
9#14583251—22no—
10#14583109—24no—
11#14583054C2218yes—
12#14582952C2212yes—
13#14582819C2214yes—
14#14582806—21no—
15#14582797—22no—
16#14582768—21no—
17C4×C4⋊Dic43C2211yescharacteristic
18#14582636C2218yes—
19#14582625C2214yes—
20Q82×C43—22no—
21C43×#557—22no—
22C43×#557—24no—
23C43×#544—21no—
24C43×#544C2214yes—
25C43×#533—22no—
26C43×#533C2212yes—
27C43×#519—21no—
28C2×C4×Q8×C43C2211yescharacteristic
29C22×Dic86C2312yes—
30C2×#10621885—28no—
31#13063325—22no—
32#13063325—22no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×Dic43⋊C4—24no—
37C2×C4×Dic43—21no—
38C4⋊(C43⋊C8)—22no—
39#13063248—28no—
40C22⋊(C43⋊C8)C2314yes—
41C4×C43⋊C8—22no—
42C43⋊#95—24no—
43C43⋊#95C2312yes—
44C22×Q8×C43D411yescharacteristic
45C4⋊Q8×C43—22no—
46C4⋊Q8×C43—22no—
47C4⋊Q8×C43—24no—
48C4⋊Q8×C43—28no—
49C4⋊Q8×C43D412yes—
50C4⋊Q8×C43D412yes—
51#125×C43—24no—
52#125×C43—24no—
53#125×C43—28no—
54#125×C43—22no—
55C22⋊Q8×C43—22no—
56C22⋊Q8×C43—24no—
57C22⋊Q8×C43C2314yes—
58C4×Q8×C43—24no—
59C4×Q8×C43—24no—
60C4×Q8×C43—24no—
61C4×Q8×C43—24no—
62C4×Q8×C43—22no—
63C4×Q8×C43—22no—
64C4×Q8×C43—22no—
65C4×Q8×C43D414yes—
66#117×C43—24no—
67#117×C43—22no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C4⋊C4×C43C2312yes—
70C2×C42×C43D412yes—
71C2×C42×C43C2311yescharacteristic
72C2×Q8×C43—24no—
73C2×Q8×C43—22no—
74C2×Q8×C43—22no—
75C2×Q8×C43—22no—
76C2×Q8×C43Q1614yescomplemented
77C2×Q8×C43C2×D414yes—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D412yes—
80C22×C4×C43C2×D412yes—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2411yescharacteristic
83C22×Dic43—22no—
84C22×Dic43—22no—
85C2×Dic86—24no—
86C2×Dic86—82no—
87C4⋊C4×C43—24no—
88C4⋊C4×C43—24no—
89C4⋊C4×C43—24no—
90C4⋊C4×C43—28no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43—24no—
98C4⋊C4×C43C2×D414yes—
99C22⋊C4×C43—24no—
100C42×C43—28no—
101C42×C43—22no—
102C42×C43—22no—
103C42×C43—24no—
104C42×C43C2×D412yes—
105C42×C43C2×D412yes—
106#10621885—88no—
107C4⋊Dic43—24no—
108C4⋊Dic43—41no—
109C4⋊Dic43—42no—
110C4⋊Dic43—41no—
111Dic43⋊C4—84no—
112C4×Dic43—42no—
113C2×C43⋊C8—24no—
114C23×C43C22×D411yescharacteristic
115Q8×C43—28no—
116Q8×C43—44no—
117Q8×C43—44no—
118Q8×C43—84no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—24no—
123C2×C4×C43—24no—
124C2×C4×C43—22no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43#12012yes—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43C2×Q1614yes—
131C2×C4×C43C2×Q1612yes—
132C2×C4×C43#13712yes—
133C2×C4×C43C22×D412yes—
134C2×Dic43—24no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—44no—
138C2×Dic43—42no—
139Dic86—48no—
140C43⋊C8—44no—
141#18404—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43C2×#12011yescharacteristic
145C22×C43C22×Q1611yescharacteristic
146C22×C43C2×#13711yescharacteristic
147C4×C43—24no—
148C4×C43—21no—
149C4×C43—22no—
150C4×C43—44no—
151C4×C43—42no—
152C4×C43—44no—
153C4×C43#45114yes—
154C4×C43#45612yes—
155Dic43—44no—
156Dic43—82no—
157#3502D4311yescharacteristic
158#3209—432no—
159#2567—431no—
160#1605—438no—
161#1503—432no—
162#1461—431no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43C2×#45111yescharacteristic
166C2×C43C2×#45611yescharacteristic
167C2×C43#302711yescharacteristic
168Q82—22no—
169#557—22no—
170#557—24no—
171#544—21no—
172#544C2×D4314yes—
173#533—22no—
174#533C2×D4312yes—
175C2×C4⋊Q8—431no—
176#519—21no—
177C2×C4×Q8C2×D4311yescharacteristic
178#494—862no—
179#487—862no—
180#462—864no—
181#451—438no—
182#431—432no—
183#395—434no—
184#391—861no—
185#389—862no—
186#384—861no—
187C4×C4⋊C4—431no—
188#328—438no—
189#324—434no—
190C43#1840411yescharacteristic, complemented, Sylow
191C22×Q8—432no—
192C22×Q8C22⋊D4311yescharacteristic
193C2×Q16—868no—
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C4⋊Q8—24no—
197C4⋊Q8—28no—
198C4⋊Q8—862no—
199C4⋊Q8—862no—
200C4⋊Q8C22⋊D4312yes—
201C4⋊Q8C22⋊D4312yes—
202#125—24no—
203#125—24no—
204#125—28no—
205#125—22no—
206C22⋊Q8—22no—
207C22⋊Q8—24no—
208C22⋊Q8C22×D4314yes—
209C4×Q8—24no—
210C4×Q8—24no—
211C4×Q8—24no—
212C4×Q8—24no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×Q8C22⋊D4314yes—
217#117—24no—
218#117—22no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—864no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4C22⋊D4311yescharacteristic
224C2×C4⋊C4C22×D4312yes—
225C2×C42—861no—
226C2×C42C22⋊D4312yes—
227C2×C42C22×D4311yescharacteristic
228C4⋊C8—862no—
229#103—868no—
230C22⋊C8—434no—
231C4×C8—862no—
232#95—432no—
233#95—864no—
234C2×Q8—24no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—864no—
239C2×Q8—3442no—
240C2×Q8#1062188514yescomplemented
241C2×Q8C2×C22⋊D4314yes—
242C22×C4—862no—
243C22×C4—862no—
244C22×C4C2×C22⋊D4311yescharacteristic
245C22×C4C2×C22⋊D4312yes—
246C22×C4C2×C22⋊D4312yes—
247C22×C4C2×C22⋊D4311yescharacteristic
248C22×C4C23×D4311yescharacteristic
249Q16—3448no—
250C2×C8—864no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—28no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—864no—
263C4⋊C4—3444no—
264C4⋊C4—1721no—
265C4⋊C4—1722no—
266C4⋊C4—1721no—
267C4⋊C4C2×C22⋊D4314yes—
268C22⋊C4—24no—
269C42—28no—
270C42—22no—
271C42—22no—
272C42—24no—
273C42—1722no—
274C42C2×C22⋊D4312yes—
275C42C2×C22⋊D4312yes—
276C23C22×C22⋊D4311yescharacteristic
277Q8—28no—
278Q8—44no—
279Q8—44no—
280Q8—84no—
281Q8—1728no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—864no—
291C2×C4—1724no—
292C2×C4—1722no—
293C2×C4—1722no—
294C2×C4—1722no—
295C2×C4#1306329411yescharacteristic
296C2×C4#1306329412yes—
297C2×C4#1306329411yescharacteristic
298C2×C4C2×#1062188514yes—
299C2×C4C2×#1062188512yes—
300C2×C4#1306335612yes—
301C2×C4C22×C22⋊D4312yes—
302C8—1724no—
303C22—21no—
304C22—21no—
305C22C2×#1306329411yescharacteristic
306C22C22×#1062188511yescharacteristic
307C22C2×#1306335611yescharacteristic
308C4—21no—
309C4—22no—
310C4—24no—
311C4—44no—
312C4—42no—
313C4—44no—
314C4—3442no—
315C4—1724no—
316C4#1458305514yes—
317C4#1458308212yes—
318C2—21no—
319C2—21no—
320C2C2×#1458305511yescharacteristic
321C2C2×#1458308211yescharacteristic
322C2#1914399711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3502C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#3502D43
hypocenterC43#18404
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
76. C2×Q8×C43Q16semidirect
190. C43#18404semidirect
240. C2×Q8#10621885semidirect

Maximal subgroups

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

subgroupindex
#191455402
#191398002
#191335692
#191330942
#191329192
C43×#35022
#1840443