Finite Group Databasebeta

← #25069457

Subgroups — #25069457

Order 11008.

902 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 167 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#19148405C211yesmaximal, characteristic
2#19144725C212yesmaximal
3#19133602C214yesmaximal
4#19133568C214yesmaximal
5#19133106C212yesmaximal
6#19132939C211yesmaximal, characteristic
7C43×#2399C211yesmaximal, characteristic
8Q8×Dic86—22no—
9#14583628—22no—
10#14583625—24no—
11#14583530—21no—
12#14583530C2214yes—
13#14583456—22no—
14#14583456C2212yes—
15#14583377—21no—
16#14583229C2214yes—
17#14583184—22no—
18#14583109—22no—
19#14583055C2214yes—
20#14583004—24no—
21#14582956C2212yes—
22#14582635C2218yes—
23#14582625C2214yes—
24C2×C4×Q8×C43C2211yescharacteristic
25C2×C4×Q8×C43C2211yescharacteristic
26C43×#398—21no—
27C43×#398C2212yes—
28C43×#395—21no—
29C43×#395C2212yes—
30C4×C4⋊C4×C43—22no—
31C43×#376C2211yescharacteristic
32C2×#10621885—24no—
33#13063325—22no—
34#13063325—22no—
35#13063325D412yes—
36#13063325D412yes—
37#13063324—24no—
38#13063324—28no—
39#13063317—24no—
40#13063317—22no—
41#13063316—24no—
42#13063316—28no—
43#13063304—22no—
44#13063304—24no—
45#13063304C2314yes—
46Q8×Dic43—24no—
47Q8×Dic43—24no—
48C4×Dic86—24no—
49C4×Dic86—24no—
50C4×Dic86—22no—
51C4×Dic86D414yes—
52#13063284—24no—
53#13063284—22no—
54#13063256—24no—
55C4⋊(C43⋊C8)—22no—
56#13063249—24no—
57#13063248—24no—
58C22⋊(C43⋊C8)C2314yes—
59#13063236—22no—
60C22×Q8×C43D411yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C4×Q8×C43—22no—
63C4×Q8×C43—22no—
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C4⋊C4×C43C2311yescharacteristic
71C2×C4⋊C4×C43C2312yes—
72C2×C42×C43—21no—
73C2×C42×C43—21no—
74C2×C42×C43D412yes—
75C2×C42×C43C2311yescharacteristic
76#95×C43—21no—
77#95×C43—22no—
78#95×C43—22no—
79#95×C43C2312yes—
80C2×Q8×C43—22no—
81C2×Q8×C43—24no—
82C2×Q8×C43—22no—
83C2×Q8×C43—42no—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2411yescharacteristic
92C2×Dic86—22no—
93C2×Dic86—24no—
94C2×Dic86C2×D414yes—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—44no—
99C4⋊C4×C43—42no—
100C4⋊C4×C43—44no—
101C42×C43—24no—
102C42×C43—22no—
103C42×C43—22no—
104C42×C43—41no—
105C42×C43—41no—
106C42×C43C2×D412yes—
107C42×C43C2×D412yes—
108C22⋊Dic43—24no—
109#10621885—48no—
110C4⋊Dic43—24no—
111C4⋊Dic43—24no—
112C4⋊Dic43—24no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43C2×D414yes—
117Dic43⋊C4—28no—
118Dic43⋊C4—24no—
119Dic43⋊C4—24no—
120C4×Dic43—28no—
121C4×Dic43—24no—
122C2×C43⋊C8—24no—
123C23×C43C22×D411yescharacteristic
124Q8×C43—28no—
125Q8×C43—24no—
126Q8×C43—42no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—24no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43#12012yes—
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#13714yes—
146C2×C4×C43C22×D412yes—
147C2×Dic43—24no—
148C2×Dic43—24no—
149Dic86—44no—
150Dic86—44no—
151Dic86—84no—
152C43⋊C8—44no—
153#18189—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43C2×#12011yescharacteristic
157C22×C43C2×#13712yes—
158C4×C43—22no—
159C4×C43—24no—
160C4×C43—21no—
161C4×C43—22no—
162C4×C43—44no—
163C4×C43—42no—
164C4×C43—42no—
165C4×C43—81no—
166C4×C43#45612yes—
167Dic43—44no—
168Dic43—44no—
169#3502—431no—
170#3113—432no—
171#2399D4311yescharacteristic
172#1611—434no—
173#1605—434no—
174#1506—432no—
175#1467—431no—
176C2×C43—22no—
177C2×C43#300411yescharacteristic
178C2×C43C2×#45611yescharacteristic
179C2×C43#302511yescharacteristic
180Q82—862no—
181#557—864no—
182#557—862no—
183#544—434no—
184#544—861no—
185#533—432no—
186#533—862no—
187#519—861no—
188C2×C4×Q8C2×D4311yescharacteristic
189C2×C4×Q8C2×D4311yescharacteristic
190#483—434no—
191#475—862no—
192#462—862no—
193#451—434no—
194#441—864no—
195#432—432no—
196#398—21no—
197#398C2×D4312yes—
198#395—21no—
199#395C2×D4312yes—
200C4×C4⋊C4—22no—
201#376C2×D4311yescharacteristic
202#328—438no—
203#324—434no—
204C43#1818911yescharacteristic, complemented, Sylow
205C22×Q8C22⋊D4311yescharacteristic
206C22×Q8C22×D4311yescharacteristic
207C2×Q16—864no—
208C4⋊Q8—432no—
209C4⋊Q8—432no—
210C4⋊Q8—862no—
211C4⋊Q8—862no—
212C4⋊Q8—868no—
213C4⋊Q8—864no—
214#125—864no—
215#125—868no—
216#125—864no—
217#125—862no—
218C22⋊Q8—434no—
219C22⋊Q8—862no—
220C22⋊Q8—864no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8—434no—
226C4×Q8—864no—
227C4×Q8—864no—
228C4×Q8—864no—
229C4×Q8—864no—
230C4×Q8—862no—
231#117—862no—
232#117—864no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4C22⋊D4311yescharacteristic
237C2×C4⋊C4C22×D4311yescharacteristic
238C2×C4⋊C4C22×D4312yes—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42C22⋊D4312yes—
242C2×C42C22×D4311yescharacteristic
243#106—864no—
244C4⋊C8—862no—
245#103—864no—
246#103—864no—
247C22⋊C8—434no—
248#97—862no—
249#95—21no—
250#95—22no—
251#95—22no—
252#95C22×D4312yes—
253C2×Q8—22no—
254C2×Q8—24no—
255C2×Q8—22no—
256C2×Q8—42no—
257C2×Q8—434no—
258C2×Q8—864no—
259C2×Q8—862no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4C2×C22⋊D4311yescharacteristic
264C22×C4C2×C22⋊D4311yescharacteristic
265C22×C4C2×C22⋊D4312yes—
266C22×C4C2×C22⋊D4312yes—
267C22×C4C23×D4311yescharacteristic
268Q16—1728no—
269C2×C8—864no—
270C4⋊C4—22no—
271C4⋊C4—24no—
272C4⋊C4—22no—
273C4⋊C4—44no—
274C4⋊C4—42no—
275C4⋊C4—44no—
276C4⋊C4—434no—
277C4⋊C4—864no—
278C4⋊C4—864no—
279C4⋊C4—864no—
280C4⋊C4—868no—
281C4⋊C4—862no—
282C4⋊C4—862no—
283C4⋊C4—864no—
284C4⋊C4—862no—
285C4⋊C4—864no—
286C22⋊C4—864no—
287C42—24no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C42—868no—
293C42—864no—
294C42D4×D4312yes—
295C42D4×D4312yes—
296C23C22×C22⋊D4311yescharacteristic
297Q8—28no—
298Q8—24no—
299Q8—42no—
300Q8—3444no—
301Q8—1724no—
302Q8—1724no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—864no—
319C2×C4—864no—
320C2×C4#1306329311yescharacteristic
321C2×C4#1306329312yes—
322C2×C4#1306329311yescharacteristic
323C2×C4#1306335514yes—
324C2×C4C2×D4×D4312yes—
325C8—1724no—
326C22—21no—
327C22—21no—
328C22C2×#1306329311yescharacteristic
329C22C2×#1306335512yes—
330C4—21no—
331C4—22no—
332C4—22no—
333C4—24no—
334C4—44no—
335C4—42no—
336C4—42no—
337C4—81no—
338C4—1724no—
339C4—1724no—
340C4#1458308112yes—
341C2—22no—
342C2#1914382811yescharacteristic
343C2C2×#1458308111yescharacteristic
344C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2399C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#2399D43
hypocenterC43#18189
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
204. C43#18189semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191447252
#191336022
#191335682
#191331062
#191329392
C43×#23992
#1818943