Finite Group Databasebeta

← #25010197

Subgroups — #25010197

Order 11008.

306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147025C211yesmaximal, characteristic, complemented
2#19136820C211yesmaximal, characteristic, complemented
3#19136636C211yesmaximal, characteristic, complemented
4#19133951C211yesmaximal, characteristic
5#19132558C211yesmaximal, characteristic, complemented
6#19132549C211yesmaximal, characteristic, complemented
7C43×#1364C211yesmaximal, characteristic, complemented
8#14583623—21no—
9C2×#13063270—21no—
10#14583276C2211yescharacteristic
11#14583242—22no—
12#14583181—21no—
13#14583141—21no—
14#14583095—21no—
15C4×Dic172C2211yescharacteristic
16C8×D172C2211yescharacteristic
17#14582936—21no—
18#14582701—21no—
19#14582699—22no—
20C4×C43⋊C16C2211yescharacteristic
21#14582642—21no—
22C43×#500C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×D344—21no—
27C2×D344—21no—
28C2×D344—41no—
29C2×C8×D43—21no—
30#13063322—21no—
31#13063320—42no—
32#13063314—41no—
33#13063305—22no—
34Q8×Dic43—41no—
35C4×Dic86—21no—
36C4×D172D411yescharacteristic
37#13063283—22no—
38#13063270—42no—
39C2×C43⋊C16—21no—
40#13063259D411yescharacteristic
41#13063256—22no—
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063250—21no—
44#13063248—22no—
45#13063247—41no—
46(C2×D43)⋊C8—21no—
47C4⋊Q8×C43—21no—
48C2×C16×C43—21no—
49#107×C43—21no—
50#107×C43D412yes—
51C4⋊C8×C43—21no—
52C4×C8×C43C2311yescharacteristic
53C2×Q8×C43—41no—
54C2×D172—41no—
55C2×D172—41no—
56C2×D172—41no—
57C2×D172D811yescharacteristic
58C2×C4×D43—21no—
59C2×Dic86—21no—
60C2×C8×C43—41no—
61C2×C8×C43C2×D411yescharacteristic
62C2×C8×C43C2×D411yescharacteristic
63C4⋊C4×C43—22no—
64C4⋊C4×C43—41no—
65C42×C43C2×D411yescharacteristic
66(C2×D43)⋊C4—21no—
67(C2×D43)⋊C4—42no—
68(C2×D43)⋊C4—42no—
69C4⋊Dic43—21no—
70C4⋊Dic43—42no—
71C4⋊Dic43D811yescharacteristic
72Dic43⋊C4—41no—
73C4×Dic43—42no—
74C4×Dic43—41no—
75C2×C43⋊C8—21no—
76Dic172—21no—
77Dic172—21no—
78D344—42no—
79D344—41no—
80D344—41no—
81D344—82no—
82C8×D43—41no—
83C8×D43—41no—
84C16×C43—41no—
85C43⋊C16—41no—
86C22×D43—21no—
87C22×D43—81no—
88Q8×C43—81no—
89Q8×C43—81no—
90C2×C4×C43—42no—
91C2×C4×C43#12011yescharacteristic
92C2×C4×C43C2×D811yescharacteristic
93C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
94C2×Dic43—21no—
95C2×Dic43—41no—
96C2×Dic43—41no—
97D172—21no—
98D172—21no—
99D172—81no—
100D172—81no—
101D172—81no—
102D172—81no—
103D172—161no—
104C4×D43—41no—
105C4×D43—41no—
106Dic86—41no—
107Dic86—41no—
108C8×C43—21no—
109C8×C43—81no—
110C8×C43#13511yescharacteristic
111C8×C43AGL(1,ℤ/8)11yescharacteristic
112C43⋊C8—41no—
113#12341—431nomaximal, Sylow
114C22×C43#44711yescharacteristic
115C2×D43—41no—
116C2×D43—41no—
117C2×D43—41no—
118C2×D43—161no—
119C2×D43—161no—
120C2×D43—161no—
121C4×C43—21no—
122C4×C43—82no—
123C4×C43#44911yescharacteristic
124C4×C43#45411yescharacteristic
125C4×C43#50811yescharacteristic
126C4×C43#50911yescharacteristic
127Dic43—41no—
128Dic43—81no—
129Dic43—81no—
130#3342—431no—
131#2240—431no—
132#2207—431no—
133#1667—431no—
134#1364D4311yescharacteristic, complemented
135#1332—431no—
136D4⋊C16—431no—
137C2×C43#162511yescharacteristic
138C2×C43#218611yescharacteristic
139C2×C43#219311yescharacteristic
140D43—81no—
141D43—321no—
142#556—861no—
143C2×SD32—861no—
144#500C2×D4311yescharacteristic
145#493—431no—
146#485—862no—
147#475—861no—
148#467—861no—
149#459—861no—
150C4×Q16—431no—
151C8×D4—431no—
152#427—861no—
153C4⋊C16C2×D4311yescharacteristic
154#357—861no—
155#357—862no—
156C4×C16—431no—
157#335C2×D4311yescharacteristic
158#331—861no—
159C43#1234111yescharacteristic, complemented, Sylow
160C2×Q16—431no—
161C2×D8—861no—
162C2×D8—861no—
163C2×D8—1721no—
164C22×C8—861no—
165C4⋊Q8—21no—
166#127—861no—
167#126—1722no—
168#124—1721no—
169C22⋊Q8—862no—
170C4×Q8—861no—
171C4×Q8—1721no—
172C4×D4—431no—
173#117—862no—
174SD32—1722no—
175C2×C16—21no—
176C2×C16—861no—
177#107—21no—
178#107—431no—
179#107D17212yes—
180#106—862no—
181C4⋊C8—21no—
182C4⋊C8—431no—
183#103—862no—
184#103—861no—
185#102—1721no—
186C22⋊C8—861no—
187C4×C8C22×D4311yescharacteristic
188C2×Q8—41no—
189C2×Q8—861no—
190C2×D4—431no—
191C2×D4—1721no—
192C2×D4—1721no—
193C2×D4—1721no—
194C22×C4—861no—
195Q16—861no—
196Q16—861no—
197D8—3442no—
198D8—1722no—
199D8—1721no—
200D8—1721no—
201C2×C8—41no—
202C2×C8—861no—
203C2×C8—1721no—
204C2×C8—1721no—
205C2×C8C2×D17211yescharacteristic
206C2×C8D4×D4311yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—1722no—
212C4⋊C4—1721no—
213C22⋊C4—861no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—1722no—
217C42—1721no—
218C42D4×D4311yescharacteristic
219C16—41no—
220C16—1721no—
221C23—861no—
222C23—3441no—
223Q8—81no—
224Q8—81no—
225Q8—1721no—
226Q8—1721no—
227D4—861no—
228D4—861no—
229D4—3441no—
230D4—3441no—
231D4—3441no—
232D4—3441no—
233D4—6881no—
234C2×C4—42no—
235C2×C4—861no—
236C2×C4—1721no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4—1721no—
240C2×C4#1306329511yescharacteristic
241C2×C4D8×D4311yescharacteristic
242C2×C4#1306335211yescharacteristic
243C8—21no—
244C8—81no—
245C8—1721no—
246C8#1306334811yescharacteristic
247C8#1306335211yescharacteristic
248C22—1721no—
249C22—1721no—
250C22—1721no—
251C22—6881no—
252C22—6881no—
253C22—6881no—
254C22#1458303411yescharacteristic
255C4—21no—
256C4—82no—
257C4—3441no—
258C4—3441no—
259C4—1721no—
260C4#1458304711yescharacteristic
261C4#1458307411yescharacteristic
262C4#1458333011yescharacteristic
263C4#1458333311yescharacteristic
264C2—3441no—
265C2—13761no—
266C2#1913368511yescharacteristic
267C2#1913651911yescharacteristic
268C2#1913656211yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1364C2
socleC22×C43#447
prime radical#19133951C2
hypercenter#1364D43
hypocenterC43#12341
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #19147025C2semidirect
2. #19136820C2semidirect
3. #19136636C2semidirect
5. #19132558C2semidirect
6. #19132549C2semidirect
7. C43×#1364C2semidirect
134. #1364D43semidirect
159. C43#12341semidirect

Maximal subgroups

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

subgroupindex
#191470252
#191368202
#191366362
#191339512
#191325582
#191325492
C43×#13642
#1234143