Finite Group Databasebeta

← #25069458

Subgroups — #25069458

Order 11008.

902 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 183 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#19144721C212yesmaximal
2#19137886C211yesmaximal, characteristic
3#19133603C214yesmaximal
4#19133569C214yesmaximal
5#19133107C212yesmaximal
6#19132939C211yesmaximal, characteristic
7C43×#3502C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583227C2214yes—
10#14583181—22no—
11#14583106—22no—
12#14583054C2214yes—
13#14583004—24no—
14#14582956C2212yes—
15#14582830—21no—
16#14582829C2212yes—
17#14582819C2212yes—
18#14582818—21no—
19C4×Dic43⋊C4—22no—
20#14582745C2211yescharacteristic
21#14582636C2218yes—
22#14582625C2214yes—
23Q82×C43—22no—
24C43×#557—22no—
25C43×#557—24no—
26C43×#544—21no—
27C43×#544C2214yes—
28C43×#533—22no—
29C43×#533C2212yes—
30C43×#519—21no—
31C2×C4×Q8×C43C2211yescharacteristic
32C22×Dic86C2311yescharacteristic
33C2×#10621885—24no—
34C4×Dic86—22no—
35C4×Dic86—22no—
36C2×C4⋊Dic43C2311yescharacteristic
37C2×Dic43⋊C4—22no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—22no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43—21no—
42#13063256—24no—
43C4⋊(C43⋊C8)—22no—
44#13063249—24no—
45#13063248—24no—
46C22⋊(C43⋊C8)C2314yes—
47#13063236—22no—
48C43⋊#95—22no—
49C43⋊#95—21no—
50C43⋊#95—22no—
51C43⋊#95C2312yes—
52C22×Q8×C43D411yescharacteristic
53C4⋊Q8×C43—22no—
54C4⋊Q8×C43—22no—
55C4⋊Q8×C43—24no—
56C4⋊Q8×C43—28no—
57C4⋊Q8×C43D412yes—
58C4⋊Q8×C43D412yes—
59#125×C43—24no—
60#125×C43—24no—
61#125×C43—28no—
62#125×C43—22no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43—24no—
65C22⋊Q8×C43C2314yes—
66C4×Q8×C43—24no—
67C4×Q8×C43—24no—
68C4×Q8×C43—24no—
69C4×Q8×C43—24no—
70C4×Q8×C43—22no—
71C4×Q8×C43—22no—
72C4×Q8×C43—22no—
73C4×Q8×C43D414yes—
74#117×C43—24no—
75#117×C43—22no—
76C2×C4⋊C4×C43D411yescharacteristic
77C2×C4⋊C4×C43C2312yes—
78C2×C42×C43D412yes—
79C2×C42×C43C2311yescharacteristic
80C2×Q8×C43—24no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×Q8×C43—24no—
84C2×Q8×C43C2×D414yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2411yescharacteristic
90C22×Dic43—22no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C2×Dic86—22no—
94C2×Dic86—42no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43—24no—
98C4⋊C4×C43—28no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—24no—
104C4⋊C4×C43—24no—
105C4⋊C4×C43—24no—
106C4⋊C4×C43C2×D414yes—
107C22⋊C4×C43—24no—
108C42×C43—28no—
109C42×C43—22no—
110C42×C43—22no—
111C42×C43—24no—
112C42×C43C2×D412yes—
113C42×C43C2×D412yes—
114#10621885—48no—
115C4⋊Dic43—22no—
116Dic43⋊C4—44no—
117Dic43⋊C4—42no—
118Dic43⋊C4—44no—
119C4×Dic43—24no—
120C4×Dic43—41no—
121C4×Dic43—41no—
122C2×C43⋊C8—24no—
123C23×C43C22×D411yescharacteristic
124Q8×C43—28no—
125Q8×C43—44no—
126Q8×C43—44no—
127Q8×C43—84no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—24no—
133C2×C4×C43—24no—
134C2×C4×C43—22no—
135C2×C4×C43—41no—
136C2×C4×C43—42no—
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12012yes—
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#13714yes—
141C2×C4×C43C22×D412yes—
142C2×Dic43—24no—
143C2×Dic43—22no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—42no—
148C2×Dic43—41no—
149C2×Dic43—42no—
150Dic86—24no—
151Dic86—42no—
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—44no—
165C4×C43#45612yes—
166Dic43—44no—
167Dic43—42no—
168Dic43—81no—
169#3502D4311yescharacteristic
170#3113—432no—
171#2399—431no—
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—22no—
181#557—22no—
182#557—24no—
183#544—21no—
184#544C2×D4314yes—
185#533—22no—
186#533C2×D4312yes—
187#519—21no—
188C2×C4×Q8—431no—
189C2×C4×Q8C2×D4311yescharacteristic
190#483—434no—
191#475—862no—
192#462—862no—
193#451—434no—
194#441—864no—
195#432—432no—
196#398—432no—
197#398—861no—
198#395—432no—
199#395—861no—
200C4×C4⋊C4—862no—
201#376—431no—
202#328—438no—
203#324—434no—
204C43#1818911yescharacteristic, complemented, Sylow
205C22×Q8—431no—
206C22×Q8C22⋊D4311yescharacteristic
207C2×Q16—864no—
208C4⋊Q8—22no—
209C4⋊Q8—22no—
210C4⋊Q8—24no—
211C4⋊Q8—28no—
212C4⋊Q8C22⋊D4312yes—
213C4⋊Q8C22⋊D4312yes—
214#125—24no—
215#125—24no—
216#125—28no—
217#125—22no—
218C22⋊Q8—22no—
219C22⋊Q8—24no—
220C22⋊Q8C22×D4314yes—
221C4×Q8—24no—
222C4×Q8—24no—
223C4×Q8—24no—
224C4×Q8—24no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8—862no—
229C4×Q8—862no—
230C4×Q8C22⋊D4314yes—
231#117—24no—
232#117—22no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—862no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4C22⋊D4311yescharacteristic
238C2×C4⋊C4C22×D4312yes—
239C2×C42—861no—
240C2×C42—861no—
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—432no—
250#95—861no—
251#95—862no—
252#95—862no—
253C2×Q8—24no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—24no—
257C2×Q8—862no—
258C2×Q8—1722no—
259C2×Q8C2×C22⋊D4314yes—
260C22×C4—862no—
261C22×C4—861no—
262C22×C4—861no—
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—24no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—28no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—862no—
282C4⋊C4—1724no—
283C4⋊C4—1722no—
284C4⋊C4—1724no—
285C4⋊C4C2×C22⋊D4314yes—
286C22⋊C4—24no—
287C42—28no—
288C42—22no—
289C42—22no—
290C42—24no—
291C42—864no—
292C42—1721no—
293C42—1721no—
294C42C2×C22⋊D4312yes—
295C42C2×C22⋊D4312yes—
296C23C22×C22⋊D4311yescharacteristic
297Q8—28no—
298Q8—44no—
299Q8—44no—
300Q8—84no—
301Q8—864no—
302Q8—1722no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—864no—
313C2×C4—862no—
314C2×C4—1721no—
315C2×C4—1722no—
316C2×C4—1722no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1722no—
320C2×C4#1306329411yescharacteristic
321C2×C4#1306329412yes—
322C2×C4#1306329411yescharacteristic
323C2×C4#1306335614yes—
324C2×C4C22×C22⋊D4312yes—
325C8—1724no—
326C22—21no—
327C22—21no—
328C22C2×#1306329411yescharacteristic
329C22C2×#1306335612yes—
330C4—21no—
331C4—22no—
332C4—22no—
333C4—24no—
334C4—44no—
335C4—42no—
336C4—44no—
337C4—3441no—
338C4—1724no—
339C4—1722no—
340C4#1458308212yes—
341C2—22no—
342C2#1914382911yescharacteristic
343C2C2×#1458308211yescharacteristic
344C2#1914398711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3502C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#3502D43
hypocenterC43#18189
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
204. C43#18189semidirect

Maximal subgroups

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

subgroupindex
#191447212
#191378862
#191336032
#191335692
#191331072
#191329392
C43×#35022
#1818943