Finite Group Databasebeta

← #24999328

Subgroups — #24999328

Order 11008.

504 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 103 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#19145739C211yesmaximal, characteristic
3#19142972C211yesmaximal, characteristic
4#19135571C211yesmaximal, characteristic
5#19133281C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic
7C43×#1546C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10#14583304—21no—
11#14583295—21no—
12#14583251—21no—
13#14583250—21no—
14#14583235—22no—
15#14583229—22no—
16#14583195—22no—
17#14583181—22no—
18#14582952C2211yescharacteristic
19#14582806—22no—
20#14582804—22no—
21#14582764—22no—
22C42×Dic43C2211yescharacteristic
23#14582660—22no—
24#14582644—22no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#431C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C43×#332—22no—
29C22×Dic86—21no—
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325D411yescharacteristic
35#13063325D411yescharacteristic
36#13063317—21no—
37#13063304—21no—
38#13063304—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41#13063284—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43D412yes—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43D412yes—
47#13063259—24no—
48#13063256—24no—
49C4⋊(C43⋊C8)D412yes—
50#13063250—24no—
51#13063248—24no—
52C22⋊(C43⋊C8)—21no—
53C4×C43⋊C8—21no—
54C43⋊#95—28no—
55C22×Q8×C43—21no—
56C2×M16×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43D412yes—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43D412yes—
67C22⋊C8×C43—21no—
68C4×C8×C43—21no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—42no—
72C2×Q8×C43—42no—
73C22×C4×C43—22no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×Dic43—22no—
78C22×Dic43—22no—
79C2×Dic86—21no—
80C2×Dic86—21no—
81C2×Dic86—44no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84M16×C43—42no—
85C2×C8×C43—22no—
86C2×C8×C43—41no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43#4111yescharacteristic
95C22⋊Dic43—41no—
96C4⋊Dic43—22no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—22no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106C4×Dic43—24no—
107C4×Dic43—22no—
108C4×Dic43—22no—
109C4×Dic43—42no—
110C4×Dic43—41no—
111C2×C43⋊C8—22no—
112C23×C43#12011yescharacteristic
113Q8×C43—82no—
114Q8×C43—81no—
115Q8×C43—81no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—42no—
119C2×C4×C43—44no—
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×C43#13512yes—
127C2×C4×C43#13712yes—
128C2×Dic43—24no—
129C2×Dic43—42no—
130C2×Dic43—42no—
131C2×Dic43—44no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—42no—
135Dic86—42no—
136Dic86—42no—
137Dic86—82no—
138Dic86—82no—
139C8×C43—42no—
140C8×C43—81no—
141C43⋊C8—42no—
142#10296—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43#39211yescharacteristic
146C22×C43#45212yes—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—82no—
150C4×C43#45412yes—
151C4×C43#45612yes—
152C4×C43#46412yes—
153C4×C43#49511yescharacteristic
154C4×C43#49711yescharacteristic
155Dic43—44no—
156Dic43—81no—
157Dic43—82no—
158Dic43—81no—
159#3230—431no—
160#3229—431no—
161#2862—431no—
162#1994—431no—
163#1549—431no—
164#1546D4311yescharacteristic
165#1276—431no—
166C2×C43—22no—
167C2×C43#200311yescharacteristic
168C2×C43#200511yescharacteristic
169C2×C43#201511yescharacteristic
170#533—431no—
171C2×C4⋊Q8—431no—
172C2×C4⋊Q8C2×D4311yescharacteristic
173#500—861no—
174#498—861no—
175#487—861no—
176#487—861no—
177#484—862no—
178#483—862no—
179#477—862no—
180#475—862no—
181#431—431no—
182#431C2×D4311yescharacteristic
183#423C2×D4311yescharacteristic
184#391—862no—
185#391—862no—
186#382—862no—
187C43—431no—
188#339—862no—
189#332—22no—
190#332—862no—
191C43#1029611yescharacteristic, complemented, Sylow
192C22×Q8—21no—
193C22×Q8—861no—
194C2×M16—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—431no—
200C4⋊Q8—431no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205#125—861no—
206C22⋊Q8—861no—
207C22⋊Q8—861no—
208C4×Q8—861no—
209C4×Q8—861no—
210#117—861no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—432no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4D17212yes—
215C2×C42—432no—
216C2×C42—861no—
217C2×C42—861no—
218C2×C42C22×D4311yescharacteristic
219#107—864no—
220#106—864no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—432no—
224C4⋊C8C22⋊D4312yes—
225#103—864no—
226#103—864no—
227C22⋊C8—21no—
228C22⋊C8—861no—
229C4×C8—21no—
230C4×C8—861no—
231#95—868no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—861no—
237C2×Q8—861no—
238C2×Q8—1724no—
239C2×Q8—1721no—
240C2×Q8—1721no—
241C22×C4—22no—
242C22×C4—862no—
243C22×C4—862no—
244C22×C4C2×D17211yescharacteristic
245C22×C4D4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247M16—42no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—862no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—862no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—862no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C22⋊C4—1721no—
266C42—864no—
267C42—862no—
268C42—862no—
269C42—1722no—
270C42—1721no—
271C42#1062189811yescharacteristic
272C42D4×D4311yescharacteristic
273C42D4×D4311yescharacteristic
274C42C2×C22⋊D4311yescharacteristic
275C23#1306329511yescharacteristic
276Q8—82no—
277Q8—81no—
278Q8—81no—
279Q8—3442no—
280Q8—3442no—
281Q8—1722no—
282Q8—1722no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—864no—
288C2×C4—1724no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1722no—
292C2×C4—1722no—
293C2×C4—1722no—
294C2×C4#1306329311yescharacteristic
295C2×C4#1306329511yescharacteristic
296C2×C4#1306329811yescharacteristic
297C2×C4#1306329811yescharacteristic
298C2×C4#1306329911yescharacteristic
299C2×C4#1306332111yescharacteristic
300C2×C4#1306334412yes—
301C2×C4#1306335412yes—
302C8—42no—
303C8—81no—
304C8—1722no—
305C22—21no—
306C22—21no—
307C22#1458280811yescharacteristic
308C22#1458306212yes—
309C4—21no—
310C4—21no—
311C4—82no—
312C4—3442no—
313C4—3441no—
314C4—3441no—
315C4—1724no—
316C4#1458307412yes—
317C4#1458308012yes—
318C4#1458312012yes—
319C4#1458328211yescharacteristic
320C4#1458329011yescharacteristic
321C2—22no—
322C2#1913561911yescharacteristic
323C2#1913563211yescharacteristic
324C2#1913569111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1546C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1546D43
hypocenterC43#10296
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
191. C43#10296semidirect

Maximal subgroups

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

subgroupindex
#191457482
#191457392
#191429722
#191355712
#191332812
#191324272
C43×#15462
#1029643