Finite Group Databasebeta

← #24996235

Subgroups — #24996235

Order 11008.

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

normal subgroups only

This group has 402 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
1C2×#14583251C211yesmaximal, characteristic
2#19135584C211yesmaximal, characteristic
3#19133350C211yesmaximal, characteristic
4#19133280C211yesmaximal, characteristic
5#19133277C211yesmaximal, characteristic
6#19132882C211yesmaximal, characteristic
7C43×#1997C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583251—22no—
10#14583251—22no—
11#14582952C2211yescharacteristic
12#14582923C2211yescharacteristic
13C2×#13063248C414yes—
14C2×C4×C43⋊C8C2211yescharacteristic
15#14582667—22no—
16#14582649—22no—
17#14582647—22no—
18#14582645—22no—
19#14582621—22no—
20C2×C4⋊Q8×C43C2211yescharacteristic
21C43×#423C2211yescharacteristic
22C4×M16×C43C2211yescharacteristic
23C43×#343—22no—
24C22×Dic86C2×C412yes—
25C2×#10621877—21no—
26C22×C43⋊C8C2×C412yes—
27#13063325—21no—
28#13063325—21no—
29#13063325—21no—
30#13063325—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)D412yes—
36#13063248—28no—
37C22⋊(C43⋊C8)—21no—
38C4×C43⋊C8—21no—
39C4×C43⋊C8D412yes—
40C4×C43⋊C8D412yes—
41C22×Q8×C43—21no—
42C2×M16×C43—21no—
43C2×M16×C43D412yes—
44C4⋊Q8×C43—21no—
45C4⋊Q8×C43—21no—
46C4⋊Q8×C43—21no—
47C4⋊Q8×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43C2×C412yes—
50C2×C42×C43C2311yescharacteristic
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53#97×C43—21no—
54C4×C8×C43—21no—
55C2×Q8×C43—41no—
56C2×Q8×C43—41no—
57C2×Q8×C43—82no—
58C22×C4×C43—22no—
59C22×C4×C43C22×C411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43#4111yescharacteristic
62C22×Dic43—22no—
63C2×Dic86—22no—
64C2×Dic86—22no—
65C2×Dic86—44no—
66M16×C43—22no—
67M16×C43—22no—
68M16×C43—42no—
69C2×C8×C43—22no—
70C2×C8×C43—41no—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C42×C43C2×D411yescharacteristic
76C42×C43C2×D411yescharacteristic
77C42×C43C2×D411yescharacteristic
78C42×C43#4111yescharacteristic
79C4⋊Dic43—41no—
80C4⋊Dic43—41no—
81C4⋊Dic43—41no—
82C4⋊Dic43—41no—
83#10621877—42no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—42no—
86C2×C43⋊C8—41no—
87C2×C43⋊C8C22⋊C414yes—
88C23×C43C4×D411yescharacteristic
89Q8×C43—82no—
90Q8×C43—82no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—42no—
94C2×C4×C43—82no—
95C2×C4×C43C2×C22⋊C411yescharacteristic
96C2×C4×C43C4×D411yescharacteristic
97C2×C4×C43#12111yescharacteristic
98C2×C4×C43#12111yescharacteristic
99C2×C4×C43#12411yescharacteristic
100C2×C4×C43#12711yescharacteristic
101C2×C4×C43#13712yes—
102C2×C4×C43#13712yes—
103C2×Dic43—42no—
104C2×Dic43—82no—
105Dic86—44no—
106Dic86—82no—
107C8×C43—42no—
108C8×C43—81no—
109C43⋊C8—24no—
110C43⋊C8—42no—
111C43⋊C8—81no—
112#9803—431nomaximal, Sylow
113C22×C43—21no—
114C22×C43—21no—
115C22×C43#39011yescharacteristic
116C22×C43#44112yes—
117C4×C43—21no—
118C4×C43—21no—
119C4×C43—82no—
120C4×C43#41312yes—
121C4×C43#47012yes—
122C4×C43#47112yes—
123C4×C43#49711yescharacteristic
124C4×C43#49711yescharacteristic
125Dic43—82no—
126C2×#487—431no—
127#1997—431no—
128#1997D4311yescharacteristic
129#1566—431no—
130#1549—431no—
131#1548—431no—
132#1451—431no—
133C2×C43—22no—
134C2×C43#196711yescharacteristic
135C2×C43#197111yescharacteristic
136C2×C43#197711yescharacteristic
137C2×C4⋊Q8—431no—
138C2×C4⋊Q8C2×D4311yescharacteristic
139#487—862no—
140#487—862no—
141#431—431no—
142#423—431no—
143#423C2×D4311yescharacteristic
144C2×#103—434no—
145C4×M16C2×D4311yescharacteristic
146C2×C4×C8—431no—
147#343—22no—
148#343—862no—
149#334—862no—
150#333—862no—
151#332—862no—
152#322—862no—
153C43#980311yescharacteristic, complemented, Sylow
154C22×Q8—21no—
155C22×Q8—432no—
156C2×M16—21no—
157C2×M16—861no—
158C2×M16C22⋊D4312yes—
159C22×C8—432no—
160C4⋊Q8—21no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—861no—
165C4⋊Q8—861no—
166C4⋊Q8—861no—
167C4⋊Q8—861no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—861no—
170C2×C4⋊C4—861no—
171C2×C4⋊C4C4×D4312yes—
172C2×C42C22×D4311yescharacteristic
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8—432no—
176C4⋊C8—861no—
177C4⋊C8—861no—
178#103—868no—
179C22⋊C8—861no—
180#97—21no—
181C4×C8—21no—
182C4×C8—432no—
183C4×C8—432no—
184C4×C8—861no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—82no—
188C2×Q8—862no—
189C2×Q8—862no—
190C2×Q8—1724no—
191C22×C4—22no—
192C22×C4—862no—
193C22×C4C2×C4×D4311yescharacteristic
194C22×C4#1062189811yescharacteristic
195C22×C4C2×C22⋊D4311yescharacteristic
196M16—22no—
197M16—22no—
198M16—42no—
199M16—1722no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—434no—
203C2×C8—862no—
204C2×C8—1722no—
205C2×C8—1721no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—1721no—
211C4⋊C4—1721no—
212C4⋊C4—1721no—
213C4⋊C4—1721no—
214C42D4×D4311yescharacteristic
215C42D4×D4311yescharacteristic
216C42D4×D4311yescharacteristic
217C42#1062190011yescharacteristic
218C23C4×C22⋊D4311yescharacteristic
219Q8—82no—
220Q8—82no—
221Q8—3442no—
222Q8—1724no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4—3442no—
228C2×C4—1722no—
229C2×C4C22⋊C4×D4311yescharacteristic
230C2×C4(C22⋊D43)⋊C411yescharacteristic
231C2×C4#1306329711yescharacteristic
232C2×C4#1306329811yescharacteristic
233C2×C4#1306331111yescharacteristic
234C2×C4#1306332111yescharacteristic
235C2×C4#1306335512yes—
236C2×C4#1306335612yes—
237C8—42no—
238C8—81no—
239C8—864no—
240C8—3441no—
241C8—1722no—
242C22—21no—
243C22—21no—
244C22#1458279911yescharacteristic
245C22#1458300412yes—
246C4—21no—
247C4—21no—
248C4—82no—
249C4—3442no—
250C4#1458288212yes—
251C4#1458315512yes—
252C4#1458316112yes—
253C4#1458329111yescharacteristic
254C4#1458329411yescharacteristic
255C2—22no—
256C2#1913544311yescharacteristic
257C2#1913546511yescharacteristic
258C2#1913549511yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1997C2
socleC22×C43#390
prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenter#1997D43
hypocenterC43#9803
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
153. C43#9803semidirect

Maximal subgroups

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

subgroupindex
C2×#145832512
#191355842
#191333502
#191332802
#191332772
#191328822
C43×#19972
#980343