Finite Group Databasebeta

← #24998044

Subgroups — #24998044

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#19145801C211yesmaximal, characteristic
2#19145137C211yesmaximal, characteristic
3#19133312C211yesmaximal, characteristic
4#19133197C211yesmaximal, characteristic
5#19133106C211yesmaximal, characteristic
6#19132488C211yesmaximal, characteristic
7C43×#2642C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583309—21no—
10#14583305—22no—
11#14583302—21no—
12#14583295—21no—
13#14583269—21no—
14#14583234—21no—
15#14583229—21no—
16#14583203—22no—
17#14582956C2211yescharacteristic
18#14582956C2211yescharacteristic
19#14582939—22no—
20C4×#10621877C2211yescharacteristic
21#14582645—22no—
22#14582641—22no—
23#14582635—22no—
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×#125×C43C2211yescharacteristic
26C43×#400—22no—
27C43×#400—22no—
28C43×#391—21no—
29C43×#391—21no—
30C43×#376C2211yescharacteristic
31C2×#10621877—21no—
32#13063325D411yescharacteristic
33#13063325D411yescharacteristic
34#13063317—21no—
35#13063304—21no—
36#13063304—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39#13063284—21no—
40#13063258—24no—
41#13063258—22no—
42#13063256—24no—
43#13063256—22no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D412yes—
46#13063248—22no—
47#13063248—22no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50#13063236—21no—
51#13063236—21no—
52#13063236D412yes—
53C4×C43⋊C8—21no—
54C22×Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59#125×C43—21no—
60#125×C43—21no—
61#125×C43—21no—
62#125×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D412yes—
69C2×C42×C43—21no—
70C2×C42×C43C2311yescharacteristic
71#95×C43—24no—
72#95×C43—24no—
73#95×C43—21no—
74#95×C43D412yes—
75C2×Q8×C43—44no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C22×C4×C43—22no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—22no—
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C2×Dic86—21no—
86C2×Dic86—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C42×C43—42no—
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43#4111yescharacteristic
104C22⋊Dic43—41no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111C4×Dic43—41no—
112#10621877—24no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—41no—
116C23×C43#12011yescharacteristic
117Q8×C43—82no—
118Q8×C43—82no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—44no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12711yescharacteristic
137C2×Dic43—41no—
138C2×Dic43—41no—
139Dic86—42no—
140Dic86—81no—
141C43⋊C8—24no—
142C43⋊C8—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—82no—
156C4×C43—81no—
157C4×C43—81no—
158C4×C43#45412yes—
159Dic43—81no—
160Dic43—81no—
161#3236—431no—
162#3165—431no—
163#2642D4311yescharacteristic
164#1556—431no—
165#1528—431no—
166#1506—431no—
167#1300—431no—
168C2×C43—22no—
169C2×C43#200311yescharacteristic
170C2×C43#200511yescharacteristic
171C2×C43#200911yescharacteristic
172#533—431no—
173C2×C4⋊Q8C2×D4311yescharacteristic
174C2×#125C2×D4311yescharacteristic
175#501—862no—
176#501—861no—
177#500—861no—
178#498—861no—
179#491—861no—
180#484—861no—
181#483—861no—
182#479—862no—
183#432—431no—
184#432—431no—
185#428—862no—
186C4×M16—431no—
187#400—22no—
188#400—22no—
189#391—21no—
190#391—21no—
191#376C2×D4311yescharacteristic
192#332—862no—
193#330—862no—
194#328—862no—
195C43#1010311yescharacteristic, complemented, Sylow
196C22×Q8—21no—
197C2×M16—861no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—431no—
203C4⋊Q8—431no—
204#125—21no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—861no—
209C22⋊Q8—861no—
210C22⋊Q8—861no—
211C4×Q8—861no—
212C4×Q8—861no—
213#117—861no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C22⋊D4311yescharacteristic
218C2×C4⋊C4C22⋊D4311yescharacteristic
219C2×C4⋊C4C22⋊D4312yes—
220C2×C42—21no—
221C2×C42C22×D4311yescharacteristic
222#107—864no—
223#107—862no—
224#106—864no—
225#106—862no—
226C4⋊C8—432no—
227C4⋊C8—861no—
228#103—862no—
229#103—862no—
230C22⋊C8—861no—
231C22⋊C8—861no—
232#97—432no—
233#97—861no—
234#97—861no—
235C4×C8—861no—
236#95—24no—
237#95—24no—
238#95—21no—
239#95C22⋊D4312yes—
240C2×Q8—44no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—861no—
244C2×Q8—861no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4C2×C22⋊D4311yescharacteristic
250C22×C4C2×C22⋊D4311yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252M16—864no—
253C2×C8—862no—
254C2×C8—862no—
255C2×C8—1721no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C22⋊C4—1721no—
275C42—42no—
276C42—1721no—
277C42D4×D4311yescharacteristic
278C42D4×D4311yescharacteristic
279C42D4×D4311yescharacteristic
280C42#1062190011yescharacteristic
281C23#1306329411yescharacteristic
282Q8—82no—
283Q8—82no—
284Q8—3441no—
285Q8—1722no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4#1306329311yescharacteristic
301C2×C4#1306329311yescharacteristic
302C2×C4#1306329611yescharacteristic
303C2×C4#1306329711yescharacteristic
304C2×C4#1306329711yescharacteristic
305C2×C4#1306332111yescharacteristic
306C8—864no—
307C8—3441no—
308C8—1722no—
309C22—21no—
310C22—21no—
311C22#1458280711yescharacteristic
312C22#1458308212yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—82no—
320C4—81no—
321C4—81no—
322C4—3441no—
323C4—3441no—
324C4#1458307112yes—
325C2—22no—
326C2#1913561711yescharacteristic
327C2#1913562911yescharacteristic
328C2#1913565511yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2642C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#2642D43
hypocenterC43#10103
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2642

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
#191458012
#191451372
#191333122
#191331972
#191331062
#191324882
C43×#26422
#1010343