Finite Group Databasebeta

← #24998033

Subgroups — #24998033

Order 11008.

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

normal subgroups only

This group has 474 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#19140714C211yesmaximal, characteristic
4#19133311C211yesmaximal, 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#14582831—22no—
22#14582820—22no—
23#14582769—21no—
24#14582765—21no—
25#14582644—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⋊Dic43—24no—
50C2×C4⋊Dic43D412yes—
51C2×C4⋊Dic43D411yescharacteristic
52C2×C4⋊Dic43D411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55#13063259—24no—
56#13063259—22no—
57#13063257—24no—
58#13063257—22no—
59C4⋊(C43⋊C8)—21no—
60#13063250—22no—
61#13063250—22no—
62C22⋊(C43⋊C8)—21no—
63#13063236—21no—
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—22no—
81C22×Dic43—21no—
82C2×Dic86—21no—
83C2×Dic86—21no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86—82no—
87M16×C43—24no—
88C2×C8×C43—22no—
89C2×C8×C43—22no—
90C42×C43—24no—
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—
108C4⋊Dic43—84no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114Dic43⋊C4—41no—
115C4×Dic43—41no—
116C2×C43⋊C8—41no—
117C23×C43#12011yescharacteristic
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—24no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×Dic43—42no—
131C2×Dic43—44no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138Dic86—42no—
139Dic86—82no—
140Dic86—82no—
141Dic86—81no—
142C8×C43—24no—
143C8×C43—42no—
144C43⋊C8—81no—
145#10101—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43#39211yescharacteristic
149C22×C43#45612yes—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—44no—
156C4×C43#45612yes—
157Dic43—81no—
158Dic43—81no—
159Dic43—82no—
160Dic43—81no—
161Dic43—81no—
162#3236—431no—
163#3165—431no—
164#2660—431no—
165#1556—431no—
166#1528—431no—
167#1506—431no—
168#1300D4311yescharacteristic
169C2×C43—22no—
170C2×C43#200511yescharacteristic
171C2×C43#200511yescharacteristic
172C2×C43#200811yescharacteristic
173#533—431no—
174C2×C4⋊Q8—431no—
175C2×#125—431no—
176#501—861no—
177#501—862no—
178#500—861no—
179#498—861no—
180#491—861no—
181#484—861no—
182#483—861no—
183#479—862no—
184#432—431no—
185#432C2×D4311yescharacteristic
186#428—862no—
187C4×M16C2×D4311yescharacteristic
188#398—862no—
189#395—862no—
190#384—861no—
191#382—861no—
192#376C2×D4311yescharacteristic
193#332—862no—
194#330—862no—
195#328—862no—
196C43#1010111yescharacteristic, complemented, Sylow
197C22×Q8—861no—
198C2×M16—21no—
199C4⋊Q8—431no—
200C4⋊Q8—431no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205#125—861no—
206#125—861no—
207#125—861no—
208#125—861no—
209#125—861no—
210C22⋊Q8—861no—
211C22⋊Q8—861no—
212C4×Q8—861no—
213C4×Q8—861no—
214#117—861no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—432no—
218C2×C4⋊C4—864no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4—861no—
222C2×C42—21no—
223C2×C42C22×D4311yescharacteristic
224#107—864no—
225#107—862no—
226#106—864no—
227#106—862no—
228C4⋊C8—861no—
229C4⋊C8D17212yes—
230#103—862no—
231#103—862no—
232C22⋊C8—21no—
233C22⋊C8—861no—
234#97—21no—
235#97—861no—
236#97D17212yes—
237C4×C8—21no—
238#95—21no—
239#95—864no—
240#95D17212yes—
241C2×Q8—861no—
242C2×Q8—861no—
243C2×Q8—3442no—
244C2×Q8—1721no—
245C2×Q8—1721no—
246C22×C4—22no—
247C22×C4—861no—
248C22×C4—862no—
249C22×C4—861no—
250C22×C4C2×D17211yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253M16—24no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—1721no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—862no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—862no—
266C4⋊C4—861no—
267C4⋊C4—3444no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C22⋊C4—1721no—
277C42—24no—
278C42—1721no—
279C42C2×D17211yescharacteristic
280C42C2×D17211yescharacteristic
281C42D4×D4311yescharacteristic
282C42#1062190211yescharacteristic
283C23#1306329511yescharacteristic
284Q8—3441no—
285Q8—3442no—
286Q8—3442no—
287Q8—1722no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—1722no—
295C2×C4—1724no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1722no—
301C2×C4—1722no—
302C2×C4#1306329511yescharacteristic
303C2×C4#1306329511yescharacteristic
304C2×C4#1306330011yescharacteristic
305C2×C4#1306330011yescharacteristic
306C2×C4#1306330011yescharacteristic
307C2×C4#1306332211yescharacteristic
308C8—24no—
309C8—42no—
310C8—3441no—
311C22—21no—
312C22—21no—
313C22#1458280911yescharacteristic
314C22#1458308312yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—44no—
321C4—3441no—
322C4—3441no—
323C4—3442no—
324C4—3441no—
325C4—3441no—
326C4#1458308312yes—
327C2—22no—
328C2#1913563411yescharacteristic
329C2#1913563411yescharacteristic
330C2#1913565111yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1300C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1300D43
hypocenterC43#10101
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
196. C43#10101semidirect

Maximal subgroups

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

subgroupindex
#191458032
#191451412
#191407142
#191333112
#191331962
#191331062
C43×#13002
#1010143