Finite Group Databasebeta

← #25013428

Subgroups — #25013428

Order 11008.

424 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137776C211yesmaximal, characteristic
2#19134989C211yesmaximal, characteristic
3#19134812C212yesmaximal
4#19132721C212yesmaximal
5C2×C43×#356C211yesmaximal, characteristic
6#14583377C2211yescharacteristic
7#14582941—22no—
8#14582908—21no—
9C2×#13063244C2211yescharacteristic
10#14582806—21no—
11#14582806C2212yes—
12#14582785—22no—
13#14582785—22no—
14#14582767—21no—
15#14582660—22no—
16#14582659—21no—
17C2×C4⋊Q8×C43C2211yescharacteristic
18C2×#101×C43C2212yes—
19C43×#356C414yescomplemented
20C2×#10621877—21no—
21Q8×Dic43—42no—
22#13063284—21no—
23#13063284—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43D412yes—
26C2×C4×Dic43—21no—
27C2×C4×Dic43D412yes—
28#13063259—42no—
29#13063257—42no—
30#13063249—42no—
31#13063244—22no—
32C43⋊#95—22no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—21no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C22×Q8×C43D411yescharacteristic
39C22×Q8×C43C2311yescharacteristic
40C2×M16×C43—22no—
41C4⋊Q8×C43—22no—
42C4⋊Q8×C43C2×C412yes—
43C4⋊Q8×C43Q812yes—
44C2×C4⋊C4×C43—22no—
45C2×C42×C43D411yescharacteristic
46#101×C43—22no—
47#101×C43C2×C414yes—
48C2×Q8×C43—21no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43—41no—
53C2×Q8×C43C4⋊C412yes—
54C2×Q8×C43C22×C411yescharacteristic
55C2×Q8×C43C2×Q811yescharacteristic
56C2×Q8×C43#4112yes—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D412yes—
61C22×Dic43—22no—
62C22×Dic43—22no—
63M16×C43—24no—
64M16×C43—42no—
65C2×C8×C43—42no—
66C4⋊C4×C43—24no—
67C4⋊C4×C43—24no—
68C42×C43—21no—
69C42×C43C4⋊C412yes—
70C22⋊Dic43—41no—
71C4⋊Dic43—22no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74C4⋊Dic43—42no—
75C4⋊Dic43—81no—
76C4×Dic43—41no—
77C4×Dic43—42no—
78C4×Dic43—42no—
79C4×Dic43—81no—
80#10621877—41no—
81#10621877—41no—
82C2×C43⋊C8—41no—
83C23×C43#12011yescharacteristic
84Q8×C43—41no—
85Q8×C43—41no—
86Q8×C43—42no—
87Q8×C43—42no—
88Q8×C43—81no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—42no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43C2×C4⋊C411yescharacteristic
99C2×C4×C43C4×D412yes—
100C2×C4×C43C22⋊Q812yes—
101C2×C4×C43#12311yescharacteristic
102C2×Dic43—44no—
103C2×Dic43—44no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C8×C43—44no—
108C43⋊C8—81no—
109#12971—431nomaximal, Sylow
110C22×C43—22no—
111C22×C43#38511yescharacteristic
112C22×C43B(4,𝔽2)11yescharacteristic
113C22×C43#45811yescharacteristic
114C4×C43—21no—
115C4×C43—22no—
116C4×C43—21no—
117C4×C43—22no—
118C4×C43—42no—
119C4×C43—42no—
120Dic43—82no—
121Dic43—82no—
122Dic43—82no—
123#2381—431no—
124C2×#356D4311yescharacteristic
125#1886—431no—
126#1857—432no—
127#1394—432no—
128C2×C43—21no—
129C2×C43—21no—
130C2×C43#186711yescharacteristic
131C2×C43#220312yes—
132C2×C4⋊Q8C2×D4311yescharacteristic
133#519—431no—
134#428—862no—
135#419—861no—
136C2×#101—431no—
137C2×#101C2×D4312yes—
138#391—432no—
139#391—861no—
140#387—862no—
141#387—862no—
142#383—861no—
143#356Dic4314yescomplemented
144#339—862no—
145#339—861no—
146C43#1297111yescharacteristic, complemented, Sylow
147C22×Q8D17211yescharacteristic
148C22×Q8C22×D4311yescharacteristic
149C2×M16—22no—
150C2×M16—861no—
151C4⋊Q8—22no—
152C4⋊Q8Dic8612yes—
153C4⋊Q8C2×Dic4312yes—
154C4×Q8—1722no—
155#117—861no—
156#117—862no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4—861no—
160C2×C42—432no—
161C2×C42—861no—
162C2×C42D17211yescharacteristic
163#107—1722no—
164#106—1722no—
165#103—1722no—
166#101—22no—
167#101—862no—
168#101C2×Dic4314yes—
169#95—861no—
170#95—862no—
171#95—861no—
172#95—862no—
173#95—862no—
174#95—862no—
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8C4⋊Dic4312yes—
181C2×Q8C2×Dic8611yescharacteristic
182C2×Q8#1062190012yes—
183C2×Q8C22×Dic4311yescharacteristic
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—862no—
187C22×C4—862no—
188C22×C4C2×D17211yescharacteristic
189C22×C4D4×D4312yes—
190M16—24no—
191M16—42no—
192M16—1721no—
193M16—1721no—
194C2×C8—42no—
195C2×C8—1721no—
196C4⋊C4—24no—
197C4⋊C4—24no—
198C4⋊C4—862no—
199C4⋊C4—862no—
200C4⋊C4—862no—
201C4⋊C4—3441no—
202C4⋊C4—1722no—
203C22⋊C4—1721no—
204C42—21no—
205C42—3441no—
206C42—1722no—
207C42—1722no—
208C42—1721no—
209C42C4⋊Dic4312yes—
210C23#1306329511yescharacteristic
211Q8—41no—
212Q8—42no—
213Q8—41no—
214Q8—42no—
215Q8—81no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—1724no—
226C2×C4—1724no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4—1722no—
230C2×C4C2×C4⋊Dic4311yescharacteristic
231C2×C4D4×Dic4312yes—
232C2×C4#1306330212yes—
233C2×C4#1306330911yescharacteristic
234C8—44no—
235C8—3441no—
236C22—22no—
237C22#1458277411yescharacteristic
238C22#1458308711yescharacteristic
239C22#1458309011yescharacteristic
240C4—22no—
241C4—21no—
242C4—21no—
243C4—22no—
244C4—42no—
245C4—42no—
246C4—3442no—
247C4—3442no—
248C4—3442no—
249C2—21no—
250C2—21no—
251C2#1913487811yescharacteristic
252C2#1913661712yes—
subgroupG/H
centerC22#14583087
commutatorC2×Q8×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC2×C43×#356C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
cosocleC22×Q8×C43C23
hypercenterC2×#356D43
hypocenterC43#12971
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
19. C43×#356C4semidirect
143. #356Dic43semidirect
146. C43#12971semidirect

Maximal subgroups

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

subgroupindex
#191377762
#191349892
#191348122
#191327212
C2×C43×#3562
#1297143