Finite Group Databasebeta

← #24999311

Subgroups — #24999311

Order 11008.

588 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 113 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#19145748C211yesmaximal, characteristic
2#19145545C211yesmaximal, characteristic
3#19142993C211yesmaximal, characteristic
4#19135572C211yesmaximal, characteristic
5#19133279C211yesmaximal, characteristic
6#19133275C211yesmaximal, characteristic
7C43×#1276C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325—22no—
10C2×#13063325C2211yescharacteristic
11C2×#13063325C2211yescharacteristic
12#14583304—21no—
13#14583279—21no—
14#14583250—21no—
15#14583250—21no—
16#14583235—22no—
17#14583195—22no—
18#14583110—22no—
19#14583057—22no—
20#14582923C2211yescharacteristic
21#14582769—22no—
22#14582769—22no—
23#14582659—22no—
24#14582647—22no—
25#14582646—22no—
26C43×#431C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C43×C43C2211yescharacteristic
29C22×Dic86—21no—
30C22×Dic86D412yes—
31C2×Dic172—24no—
32C2×#10621877—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38#13063325—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325—48no—
42#13063325D411yescharacteristic
43#13063325D411yescharacteristic
44#13063317—21no—
45#13063304—21no—
46#13063304—21no—
47C4×Dic86—21no—
48C4×Dic86—21no—
49#13063284—21no—
50C2×C4⋊Dic43—28no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43D412yes—
55#13063259—24no—
56C4⋊(C43⋊C8)—21no—
57C4⋊(C43⋊C8)—21no—
58#13063250—24no—
59#13063250—24no—
60C2×C42×C43—21no—
61C2×C42×C43—21no—
62C2×C42×C43D412yes—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43D412yes—
65C4⋊C8×C43D412yes—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C4×C8×C43—21no—
69C4×C8×C43—21no—
70C22×C4×C43—22no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—22no—
75C22×Dic43—22no—
76C2×Dic86—21no—
77C2×Dic86—22no—
78C2×Dic86—21no—
79C2×Dic86—22no—
80C2×Dic86—44no—
81C2×Dic86—44no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×C8×C43—22no—
85C2×C8×C43—22no—
86C42×C43—24no—
87C42×C43—24no—
88C42×C43—22no—
89C42×C43Q1614yescomplemented
90C42×C43C2×D411yescharacteristic
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43#4111yescharacteristic
94C22⋊Dic43—41no—
95C4⋊Dic43—21no—
96C4⋊Dic43—22no—
97C4⋊Dic43—21no—
98C4⋊Dic43—22no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—416no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110C4×Dic43—41no—
111#10621877—42no—
112C2×C43⋊C8—41no—
113Dic172—84no—
114C23×C43#12011yescharacteristic
115C2×C4×C43—24no—
116C2×C4×C43—24no—
117C2×C4×C43—24no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43#12011yescharacteristic
121C2×C4×C43#12011yescharacteristic
122C2×C4×C43#12111yescharacteristic
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12111yescharacteristic
125C2×C4×C43#12711yescharacteristic
126C2×C4×C43C2×Q1612yes—
127C2×C4×C43#13712yes—
128C2×Dic43—44no—
129C2×Dic43—44no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134Dic86—42no—
135Dic86—44no—
136Dic86—42no—
137Dic86—82no—
138Dic86—82no—
139Dic86—82no—
140C8×C43—42no—
141C8×C43—42no—
142C43⋊C8—81no—
143#10293—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43#39211yescharacteristic
147C22×C43#45112yes—
148C4×C43—28no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43#45312yes—
152C4×C43#45612yes—
153C4×C43#46212yes—
154C4×C43#49411yescharacteristic
155C4×C43#49711yescharacteristic
156Dic43—82no—
157Dic43—81no—
158Dic43—82no—
159Dic43—81no—
160#3230—431no—
161#3209—431no—
162#2868—431no—
163#1994—431no—
164#1549—431no—
165#1548—431no—
166#1276D4311yescharacteristic
167C2×C43—22no—
168C2×C43#200211yescharacteristic
169C2×C43#200511yescharacteristic
170C2×C43#201611yescharacteristic
171#533—431no—
172C2×C4⋊Q8—431no—
173C2×C4⋊Q8—431no—
174C2×C4⋊Q8—862no—
175#500—861no—
176#494—861no—
177#487—861no—
178#487—861no—
179#484—862no—
180#477—862no—
181#462—862no—
182#451—862no—
183#431C2×D4311yescharacteristic
184#431C2×D4311yescharacteristic
185#423—431no—
186#384—862no—
187#384—862no—
188C43C2×D4311yescharacteristic
189#339—862no—
190#333—862no—
191#332—862no—
192C43#1029311yescharacteristic, complemented, Sylow
193C22×Q8—432no—
194C22×Q8—861no—
195C2×Q16—864no—
196C2×M16—861no—
197C4⋊Q8—431no—
198C4⋊Q8—431no—
199C4⋊Q8—861no—
200C4⋊Q8—861no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205C4⋊Q8—861no—
206C4⋊Q8—861no—
207C4⋊Q8—1728no—
208#125—861no—
209C22⋊Q8—861no—
210C22⋊Q8—861no—
211C4×Q8—861no—
212C4×Q8—861no—
213#117—861no—
214C2×C4⋊C4—432no—
215C2×C4⋊C4—868no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42D17212yes—
222C2×C42C22×D4311yescharacteristic
223#107—864no—
224C4⋊C8—861no—
225C4⋊C8—861no—
226C4⋊C8D17212yes—
227C4⋊C8D17212yes—
228#103—864no—
229#103—864no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232C4×C8—21no—
233C4×C8—21no—
234C2×Q8—861no—
235C2×Q8—862no—
236C2×Q8—861no—
237C2×Q8—862no—
238C2×Q8—1724no—
239C2×Q8—1724no—
240C2×Q8—1721no—
241C2×Q8—1721no—
242C22×C4—22no—
243C22×C4—862no—
244C22×C4—862no—
245C22×C4C2×D17211yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4D4×D4311yescharacteristic
248Q16—3444no—
249M16—1722no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—1721no—
253C4⋊C4—861no—
254C4⋊C4—862no—
255C4⋊C4—861no—
256C4⋊C4—862no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—17216no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C22⋊C4—1721no—
269C42—24no—
270C42—24no—
271C42—22no—
272C42—1721no—
273C42Dic17214yescomplemented
274C42C2×D17211yescharacteristic
275C42C2×D17211yescharacteristic
276C42D4×D4311yescharacteristic
277C42#1062190211yescharacteristic
278C23#1306329511yescharacteristic
279Q8—3442no—
280Q8—3442no—
281Q8—3442no—
282Q8—1722no—
283Q8—1724no—
284Q8—1722no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—1724no—
291C2×C4—1724no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4#1306329511yescharacteristic
297C2×C4#1306329511yescharacteristic
298C2×C4#1306330011yescharacteristic
299C2×C4#1306330011yescharacteristic
300C2×C4#1306330011yescharacteristic
301C2×C4#1306332211yescharacteristic
302C2×C4C2×Dic17212yes—
303C2×C4#1306335812yes—
304C8—42no—
305C8—42no—
306C8—3441no—
307C22—21no—
308C22—21no—
309C22#1458280911yescharacteristic
310C22#1458305712yes—
311C4—28no—
312C4—21no—
313C4—21no—
314C4—3442no—
315C4—3442no—
316C4—3441no—
317C4—3441no—
318C4#1458306812yes—
319C4#1458308312yes—
320C4#1458311012yes—
321C4#1458327911yescharacteristic
322C4#1458329311yescharacteristic
323C2—22no—
324C2#1913561311yescharacteristic
325C2#1913563411yescharacteristic
326C2#1913569711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1276C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1276D43
hypocenterC43#10293
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
89. C42×C43Q16semidirect
192. C43#10293semidirect
273. C42Dic172semidirect

Maximal subgroups

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

subgroupindex
#191457482
#191455452
#191429932
#191355722
#191332792
#191332752
C43×#12762
#1029343