Finite Group Databasebeta

← #24999308

Subgroups — #24999308

Order 11008.

588 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 113 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#19145746C211yesmaximal, characteristic
2#19145543C211yesmaximal, characteristic
3#19135572C211yesmaximal, characteristic
4#19133280C211yesmaximal, characteristic
5#19133276C211yesmaximal, characteristic
6#19132428C211yesmaximal, characteristic
7C43×#2868C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583302—21no—
10#14583278—21no—
11#14583251—21no—
12#14583249—21no—
13#14583234—22no—
14#14583191—22no—
15#14583106—22no—
16#14583055—22no—
17#14582952C2211yescharacteristic
18#14582952C2211yescharacteristic
19#14582923C2211yescharacteristic
20#14582659—22no—
21#14582648—22no—
22#14582645—22no—
23C2×C4⋊Q8×C43—22no—
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#384—22no—
27C43×#384—22no—
28C43×C43C2211yescharacteristic
29C2×#10621885—24no—
30C2×#10621877—21no—
31#13063325D411yescharacteristic
32#13063325D411yescharacteristic
33#13063317—21no—
34#13063304—21no—
35#13063304—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38#13063284—21no—
39#13063258—24no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D412yes—
43C4⋊(C43⋊C8)D412yes—
44#13063249—24no—
45#13063248—24no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C22×Q8×C43—21no—
51C22×Q8×C43D412yes—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—48no—
61C2×C4⋊C4×C43—28no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43D412yes—
66C2×C42×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43D412yes—
69C2×C42×C43C2311yescharacteristic
70C2×Q8×C43—22no—
71C2×Q8×C43—22no—
72C2×Q8×C43—44no—
73C2×Q8×C43—44no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C22×C4×C43—22no—
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×Dic86—21no—
83C2×Dic86—21no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—416no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C42×C43—24no—
94C42×C43—24no—
95C42×C43—22no—
96C42×C43Q1614yescomplemented
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101C22⋊Dic43—41no—
102#10621885—84no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C4×Dic43—41no—
110#10621877—42no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114C23×C43#12011yescharacteristic
115Q8×C43—44no—
116Q8×C43—82no—
117Q8×C43—82no—
118Q8×C43—82no—
119C2×C4×C43—24no—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—44no—
125C2×C4×C43—44no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43#12011yescharacteristic
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12711yescharacteristic
134C2×C4×C43C2×Q1612yes—
135C2×C4×C43#13712yes—
136C2×Dic43—41no—
137C2×Dic43—41no—
138Dic86—42no—
139Dic86—42no—
140C43⋊C8—42no—
141C43⋊C8—42no—
142C43⋊C8—81no—
143#10293—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43#39211yescharacteristic
147C22×C43#45112yes—
148C4×C43—28no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—82no—
152C4×C43—82no—
153C4×C43#45312yes—
154C4×C43#45612yes—
155C4×C43#46212yes—
156C4×C43#49411yescharacteristic
157C4×C43#49711yescharacteristic
158Dic43—81no—
159Dic43—81no—
160#3230—431no—
161#3209—431no—
162#2868D4311yescharacteristic
163#1994—431no—
164#1549—431no—
165#1548—431no—
166#1276—431no—
167C2×C43—22no—
168C2×C43#200211yescharacteristic
169C2×C43#200511yescharacteristic
170C2×C43#201611yescharacteristic
171#533—431no—
172C2×C4⋊Q8—22no—
173C2×C4⋊Q8C2×D4311yescharacteristic
174C2×C4⋊Q8C2×D4311yescharacteristic
175#500—861no—
176#494—861no—
177#487—861no—
178#487—861no—
179#484—862no—
180#477—862no—
181#462—862no—
182#451—862no—
183#431—431no—
184#431—431no—
185#423—431no—
186#384—22no—
187#384—22no—
188C43C2×D4311yescharacteristic
189#339—862no—
190#333—862no—
191#332—862no—
192C43#1029311yescharacteristic, complemented, Sylow
193C22×Q8—21no—
194C22×Q8C22⋊D4312yes—
195C2×Q16—864no—
196C2×M16—861no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—48no—
206C4⋊Q8—431no—
207C4⋊Q8—431no—
208#125—861no—
209C22⋊Q8—861no—
210C22⋊Q8—861no—
211C4×Q8—861no—
212C4×Q8—861no—
213#117—861no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C22⋊D4312yes—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42C22⋊D4312yes—
222C2×C42C22×D4311yescharacteristic
223#107—864no—
224C4⋊C8—432no—
225C4⋊C8—432no—
226C4⋊C8—861no—
227C4⋊C8—861no—
228#103—864no—
229#103—864no—
230C22⋊C8—861no—
231C22⋊C8—861no—
232C4×C8—861no—
233C4×C8—861no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—44no—
237C2×Q8—44no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—861no—
241C2×Q8—861no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4C2×C22⋊D4311yescharacteristic
246C22×C4C2×C22⋊D4311yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248Q16—3444no—
249M16—1722no—
250C2×C8—862no—
251C2×C8—862no—
252C2×C8—1721no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—416no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C22⋊C4—1721no—
269C42—24no—
270C42—24no—
271C42—22no—
272C42—1721no—
273C42#1062188514yescomplemented
274C42D4×D4311yescharacteristic
275C42D4×D4311yescharacteristic
276C42D4×D4311yescharacteristic
277C42#1062190011yescharacteristic
278C23#1306329411yescharacteristic
279Q8—44no—
280Q8—82no—
281Q8—82no—
282Q8—82no—
283Q8—1722no—
284Q8—1722no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4#1306329311yescharacteristic
297C2×C4#1306329311yescharacteristic
298C2×C4#1306329611yescharacteristic
299C2×C4#1306329711yescharacteristic
300C2×C4#1306329711yescharacteristic
301C2×C4#1306332111yescharacteristic
302C2×C4C2×#1062188512yes—
303C2×C4#1306335612yes—
304C8—3441no—
305C8—1722no—
306C8—1722no—
307C22—21no—
308C22—21no—
309C22#1458280711yescharacteristic
310C22#1458305512yes—
311C4—28no—
312C4—21no—
313C4—21no—
314C4—82no—
315C4—82no—
316C4—3441no—
317C4—3441no—
318C4#1458306612yes—
319C4#1458308112yes—
320C4#1458310612yes—
321C4#1458327811yescharacteristic
322C4#1458329111yescharacteristic
323C2—22no—
324C2#1913561011yescharacteristic
325C2#1913563111yescharacteristic
326C2#1913569511yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2868C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#2868D43
hypocenterC43#10293
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2868

Complements

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

NH ≅ G/Ntype
96. C42×C43Q16semidirect
192. C43#10293semidirect
273. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191457462
#191455432
#191355722
#191332802
#191332762
#191324282
C43×#28682
#1029343