Finite Group Databasebeta

← #24998030

Subgroups — #24998030

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#19145801C211yesmaximal, characteristic
2#19145137C211yesmaximal, characteristic
3#19133312C211yesmaximal, characteristic
4#19133197C211yesmaximal, characteristic
5#19133106C211yesmaximal, characteristic
6#19132488C211yesmaximal, characteristic
7C43×#2660C211yesmaximal, 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×#398—22no—
27C43×#395—22no—
28C43×#384—21no—
29C43×#382—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×C43—24no—
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C4⋊C4×C43D412yes—
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72#95×C43—24no—
73#95×C43—21no—
74#95×C43D412yes—
75C2×Q8×C43—41no—
76C2×Q8×C43—41no—
77C2×Q8×C43—82no—
78C22×C4×C43—22no—
79C22×C4×C43—21no—
80C22×C4×C43—22no—
81C22×C4×C43—21no—
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—
99C4⋊C4×C43—84no—
100C42×C43—24no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C22⋊Dic43—41no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112C4×Dic43—41no—
113#10621877—24no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—41no—
117C23×C43#12011yescharacteristic
118Q8×C43—82no—
119Q8×C43—82no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—24no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—44no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12711yescharacteristic
138C2×Dic43—41no—
139C2×Dic43—41no—
140Dic86—42no—
141Dic86—81no—
142C43⋊C8—24no—
143C43⋊C8—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—81no—
157C4×C43—81no—
158C4×C43—82no—
159C4×C43#45612yes—
160Dic43—81no—
161Dic43—81no—
162#3236—431no—
163#3165—431no—
164#2660D4311yescharacteristic
165#1556—431no—
166#1528—431no—
167#1506—431no—
168#1300—431no—
169C2×C43—22no—
170C2×C43#200511yescharacteristic
171C2×C43#200511yescharacteristic
172C2×C43#200811yescharacteristic
173#533—431no—
174C2×C4⋊Q8C2×D4311yescharacteristic
175C2×#125C2×D4311yescharacteristic
176#501—862no—
177#501—861no—
178#500—861no—
179#498—861no—
180#491—861no—
181#484—861no—
182#483—861no—
183#479—862no—
184#432—431no—
185#432—431no—
186#428—862no—
187C4×M16—431no—
188#398—22no—
189#395—22no—
190#384—21no—
191#382—21no—
192#376C2×D4311yescharacteristic
193#332—862no—
194#330—862no—
195#328—862no—
196C43#1010111yescharacteristic, complemented, Sylow
197C22×Q8—21no—
198C2×M16—861no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—431no—
204C4⋊Q8—431no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#125—861no—
210C22⋊Q8—861no—
211C22⋊Q8—861no—
212C4×Q8—861no—
213C4×Q8—861no—
214#117—861no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4C22⋊D4311yescharacteristic
220C2×C4⋊C4C22⋊D4311yescharacteristic
221C2×C4⋊C4C22⋊D4312yes—
222C2×C42—21no—
223C2×C42C22×D4311yescharacteristic
224#107—864no—
225#107—862no—
226#106—864no—
227#106—862no—
228C4⋊C8—432no—
229C4⋊C8—861no—
230#103—862no—
231#103—862no—
232C22⋊C8—861no—
233C22⋊C8—861no—
234#97—432no—
235#97—861no—
236#97—861no—
237C4×C8—861no—
238#95—24no—
239#95—21no—
240#95C22⋊D4312yes—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—82no—
244C2×Q8—861no—
245C2×Q8—861no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4C2×C22⋊D4311yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252C22×C4C2×C22⋊D4311yescharacteristic
253M16—864no—
254C2×C8—862no—
255C2×C8—862no—
256C2×C8—1721no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—84no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C22⋊C4—1721no—
277C42—24no—
278C42—1721no—
279C42D4×D4311yescharacteristic
280C42D4×D4311yescharacteristic
281C42D4×D4311yescharacteristic
282C42#1062190011yescharacteristic
283C23#1306329411yescharacteristic
284Q8—82no—
285Q8—82no—
286Q8—3441no—
287Q8—1722no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4#1306329311yescharacteristic
303C2×C4#1306329311yescharacteristic
304C2×C4#1306329611yescharacteristic
305C2×C4#1306329711yescharacteristic
306C2×C4#1306329711yescharacteristic
307C2×C4#1306332111yescharacteristic
308C8—864no—
309C8—3441no—
310C8—1722no—
311C22—21no—
312C22—21no—
313C22#1458280711yescharacteristic
314C22#1458308212yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—44no—
321C4—81no—
322C4—82no—
323C4—81no—
324C4—3441no—
325C4—3441no—
326C4#1458308112yes—
327C2—22no—
328C2#1913562911yescharacteristic
329C2#1913563111yescharacteristic
330C2#1913564811yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2660C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#2660D43
hypocenterC43#10101
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2660

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
#191458012
#191451372
#191333122
#191331972
#191331062
#191324882
C43×#26602
#1010143