Finite Group Databasebeta

← #24998047

Subgroups — #24998047

Order 11008.

458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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#19145803C211yesmaximal, characteristic
2#19145141C211yesmaximal, characteristic
3#19140543C211yesmaximal, characteristic
4#19133313C211yesmaximal, characteristic
5#19133196C211yesmaximal, characteristic
6#19133106C211yesmaximal, characteristic
7C43×#1300C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10C2×#13063317C2211yescharacteristic
11#14583308—21no—
12#14583308—22no—
13#14583304—21no—
14#14583297—21no—
15#14583268—21no—
16#14583235—21no—
17#14583230—21no—
18#14583207—22no—
19#14582956C2211yescharacteristic
20#14582941—22no—
21#14582839—22no—
22#14582839—22no—
23#14582805—21no—
24#14582805—21no—
25#14582646—22no—
26#14582640—22no—
27#14582635—22no—
28C43×#432C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C43×#376C2211yescharacteristic
31C22×Dic86—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325D411yescharacteristic
37#13063325D411yescharacteristic
38#13063317—21no—
39#13063317—21no—
40#13063317—21no—
41#13063317—21no—
42#13063317—21no—
43#13063304—21no—
44#13063304—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47#13063284—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43D411yescharacteristic
50C2×C4⋊Dic43D411yescharacteristic
51C2×C4⋊Dic43D412yes—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54#13063259—24no—
55#13063259—22no—
56#13063257—24no—
57#13063257—22no—
58C4⋊(C43⋊C8)—21no—
59#13063250—22no—
60#13063250—22no—
61C22⋊(C43⋊C8)—21no—
62#13063236—21no—
63C43⋊#95—24no—
64C43⋊#95—24no—
65C2×M16×C43—21no—
66C2×C42×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43D412yes—
69C22⋊C8×C43—21no—
70#97×C43—21no—
71#97×C43D412yes—
72C4×C8×C43—21no—
73#95×C43—21no—
74#95×C43D412yes—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—22no—
82C2×Dic86—21no—
83C2×Dic86—21no—
84C2×Dic86—44no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87M16×C43—24no—
88C2×C8×C43—22no—
89C2×C8×C43—22no—
90C42×C43—42no—
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43#4111yescharacteristic
95C22⋊Dic43—41no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—22no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43—22no—
105C4⋊Dic43—21no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114C4×Dic43—41no—
115C2×C43⋊C8—41no—
116C23×C43#12011yescharacteristic
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12711yescharacteristic
129C2×Dic43—44no—
130C2×Dic43—42no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137Dic86—42no—
138Dic86—82no—
139Dic86—82no—
140Dic86—81no—
141C8×C43—24no—
142C8×C43—42no—
143C43⋊C8—81no—
144#10103—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43#39211yescharacteristic
148C22×C43#45612yes—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—82no—
155C4×C43#45412yes—
156Dic43—81no—
157Dic43—82no—
158Dic43—81no—
159Dic43—81no—
160Dic43—81no—
161#3236—431no—
162#3165—431no—
163#2642—431no—
164#1556—431no—
165#1528—431no—
166#1506—431no—
167#1300D4311yescharacteristic
168C2×C43—22no—
169C2×C43#200311yescharacteristic
170C2×C43#200511yescharacteristic
171C2×C43#200911yescharacteristic
172#533—431no—
173C2×C4⋊Q8—431no—
174C2×#125—431no—
175#501—861no—
176#501—862no—
177#500—861no—
178#498—861no—
179#491—861no—
180#484—861no—
181#483—861no—
182#479—862no—
183#432—431no—
184#432C2×D4311yescharacteristic
185#428—862no—
186C4×M16C2×D4311yescharacteristic
187#400—862no—
188#400—862no—
189#391—861no—
190#391—861no—
191#376C2×D4311yescharacteristic
192#332—862no—
193#330—862no—
194#328—862no—
195C43#1010311yescharacteristic, complemented, Sylow
196C22×Q8—861no—
197C2×M16—21no—
198C4⋊Q8—431no—
199C4⋊Q8—431no—
200C4⋊Q8—861no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204#125—861no—
205#125—861no—
206#125—861no—
207#125—861no—
208#125—861no—
209C22⋊Q8—861no—
210C22⋊Q8—861no—
211C4×Q8—861no—
212C4×Q8—861no—
213#117—861no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—432no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C42—21no—
221C2×C42C22×D4311yescharacteristic
222#107—864no—
223#107—862no—
224#106—864no—
225#106—862no—
226C4⋊C8—861no—
227C4⋊C8D17212yes—
228#103—862no—
229#103—862no—
230C22⋊C8—21no—
231C22⋊C8—861no—
232#97—21no—
233#97—861no—
234#97D17212yes—
235C4×C8—21no—
236#95—21no—
237#95—864no—
238#95—864no—
239#95D17212yes—
240C2×Q8—861no—
241C2×Q8—861no—
242C2×Q8—1724no—
243C2×Q8—1721no—
244C2×Q8—1721no—
245C22×C4—22no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—862no—
249C22×C4C2×D17211yescharacteristic
250C22×C4D4×D4311yescharacteristic
251C22×C4D4×D4311yescharacteristic
252M16—24no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—1721no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—862no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—862no—
265C4⋊C4—861no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C22⋊C4—1721no—
275C42—42no—
276C42—1721no—
277C42C2×D17211yescharacteristic
278C42C2×D17211yescharacteristic
279C42D4×D4311yescharacteristic
280C42#1062190211yescharacteristic
281C23#1306329511yescharacteristic
282Q8—3441no—
283Q8—3442no—
284Q8—3442no—
285Q8—1722no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—1724no—
293C2×C4—1722no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1722no—
299C2×C4—1722no—
300C2×C4#1306329511yescharacteristic
301C2×C4#1306329511yescharacteristic
302C2×C4#1306330011yescharacteristic
303C2×C4#1306330011yescharacteristic
304C2×C4#1306330011yescharacteristic
305C2×C4#1306332211yescharacteristic
306C8—24no—
307C8—42no—
308C8—3441no—
309C22—21no—
310C22—21no—
311C22#1458280911yescharacteristic
312C22#1458308312yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—3442no—
320C4—3441no—
321C4—3441no—
322C4—3441no—
323C4—3441no—
324C4#1458307312yes—
325C2—22no—
326C2#1913562011yescharacteristic
327C2#1913563411yescharacteristic
328C2#1913565811yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1300C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1300D43
hypocenterC43#10103
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
195. C43#10103semidirect

Maximal subgroups

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

subgroupindex
#191458032
#191451412
#191405432
#191333132
#191331962
#191331062
C43×#13002
#1010343