Finite Group Databasebeta

← #25000542

Subgroups — #25000542

Order 11008.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145739C211yesmaximal, characteristic
2#19135585C211yesmaximal, characteristic
3#19133384C211yesmaximal, characteristic
4#19133332C211yesmaximal, characteristic
5#19133015C211yesmaximal, characteristic
6#19132484C211yesmaximal, characteristic
7C43×#1549C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583295—21no—
10#14583251—21no—
11#14583229—22no—
12#14583181—21no—
13#14583181—21no—
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C4×#10621877C2211yescharacteristic
17#14582668—22no—
18#14582652—21no—
19#14582650—21no—
20#14582646—21no—
21#14582644—21no—
22#14582629—22no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×#332—22no—
27C2×#10621877—21no—
28C2×#10621877—21no—
29#13063325D411yescharacteristic
30#13063325D411yescharacteristic
31#13063317—21no—
32#13063304—21no—
33#13063304—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36#13063284—21no—
37#13063256—22no—
38#13063256—22no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)D411yescharacteristic
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063248—22no—
44#13063248—22no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8—21no—
49C22×Q8×C43—21no—
50C2×M16×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D412yes—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43D412yes—
61C22⋊C8×C43—21no—
62C4×C8×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—82no—
66C22×C4×C43—22no—
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×C4×C43#4111yescharacteristic
70C2×Dic86—21no—
71C2×Dic86—21no—
72M16×C43—81no—
73C2×C8×C43—22no—
74C2×C8×C43—41no—
75C4⋊C4×C43—22no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C42×C43C2×D411yescharacteristic
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D411yescharacteristic
82C42×C43#4111yescharacteristic
83C22⋊Dic43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90C4×Dic43—41no—
91#10621877—22no—
92#10621877—41no—
93#10621877—42no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C23×C43#12311yescharacteristic
99Q8×C43—82no—
100Q8×C43—82no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—42no—
107C2×C4×C43—82no—
108C2×C4×C43#12011yescharacteristic
109C2×C4×C43#12111yescharacteristic
110C2×C4×C43#12111yescharacteristic
111C2×C4×C43#12111yescharacteristic
112C2×C4×C43#12311yescharacteristic
113C2×C4×C43#12411yescharacteristic
114C2×Dic43—41no—
115C2×Dic43—41no—
116Dic86—41no—
117Dic86—41no—
118Dic86—41no—
119Dic86—41no—
120C8×C43—42no—
121C8×C43—81no—
122C43⋊C8—42no—
123C43⋊C8—41no—
124C43⋊C8—41no—
125C43⋊C8—81no—
126#10494—431nomaximal, Sylow
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—21no—
130C22×C43#39411yescharacteristic
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—21no—
134C4×C43—82no—
135C4×C43#45411yescharacteristic
136C4×C43#45611yescharacteristic
137C4×C43#47111yescharacteristic
138C4×C43#47112yes—
139C4×C43#47311yescharacteristic
140Dic43—81no—
141Dic43—81no—
142#3229—431no—
143#1997—431no—
144#1574—431no—
145#1561—431no—
146#1549D4311yescharacteristic
147#1485—431no—
148#1299—431no—
149C2×C43—41no—
150C2×C43#203811yescharacteristic
151C2×C43#204611yescharacteristic
152C2×C43#205211yescharacteristic
153#533—431no—
154C2×C4⋊Q8C2×D4311yescharacteristic
155#498—861no—
156#487—861no—
157#483—862no—
158#475—861no—
159#475—861no—
160#431—431no—
161#431C2×D4311yescharacteristic
162#423—431no—
163#423C2×D4311yescharacteristic
164C4×M16—431no—
165#343—862no—
166#335—861no—
167#334—861no—
168#332—22no—
169#332—861no—
170#332—861no—
171Q8⋊C8—862no—
172C43#1049411yescharacteristic, complemented, Sylow
173C22×Q8—21no—
174C2×M16—21no—
175C2×M16—861no—
176C2×M16—861no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8—431no—
182C4⋊Q8—431no—
183#125—861no—
184C22⋊Q8—861no—
185C22⋊Q8—861no—
186C4×Q8—861no—
187C4×Q8—861no—
188#117—861no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4D17212yes—
191C2×C42C22×D4311yescharacteristic
192#106—862no—
193#106—862no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—431no—
197C4⋊C8—431no—
198C4⋊C8—861no—
199C4⋊C8—861no—
200C4⋊C8C22⋊D4312yes—
201#103—862no—
202#103—862no—
203C22⋊C8—21no—
204C22⋊C8—861no—
205#97—861no—
206C4×C8—21no—
207C4×C8—861no—
208C4×C8—861no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—82no—
212C2×Q8—861no—
213C2×Q8—861no—
214C22×C4—22no—
215C22×C4C2×D17211yescharacteristic
216C22×C4#1062190011yescharacteristic
217C22×C4#1062190011yescharacteristic
218M16—81no—
219M16—862no—
220M16—1722no—
221M16—1721no—
222C2×C8—22no—
223C2×C8—41no—
224C2×C8—861no—
225C2×C8—861no—
226C2×C8—1721no—
227C2×C8—1721no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4—861no—
236C4⋊C4—1721no—
237C4⋊C4—1721no—
238C22⋊C4—1721no—
239C42—1721no—
240C42#1062189811yescharacteristic
241C42D4×D4311yescharacteristic
242C42D4×D4311yescharacteristic
243C42C2×C22⋊D4311yescharacteristic
244C23#1306330911yescharacteristic
245Q8—82no—
246Q8—82no—
247Q8—1721no—
248Q8—1721no—
249Q8—1721no—
250Q8—1721no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—82no—
258C2×C4—1721no—
259C2×C4—1721no—
260C2×C4#1306329511yescharacteristic
261C2×C4#1306329611yescharacteristic
262C2×C4#1306329711yescharacteristic
263C2×C4#1306329911yescharacteristic
264C2×C4#1306330711yescharacteristic
265C2×C4#1306331111yescharacteristic
266C8—42no—
267C8—81no—
268C8—3441no—
269C8—1722no—
270C8—1721no—
271C8—1721no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#1458281511yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—82no—
280C4—3441no—
281C4—3441no—
282C4#1458307411yescharacteristic
283C4#1458308411yescharacteristic
284C4#1458315911yescharacteristic
285C4#1458316012yes—
286C4#1458317111yescharacteristic
287C2—41no—
288C2#1913581311yescharacteristic
289C2#1913585711yescharacteristic
290C2#1913589511yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1549C2
socleC22×C43#394
prime radicalC23×C43#123
hypercenter#1549D43
hypocenterC43#10494
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
172. C43#10494semidirect

Maximal subgroups

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

subgroupindex
#191457392
#191355852
#191333842
#191333322
#191330152
#191324842
C43×#15492
#1049443