Finite Group Databasebeta

← #24999676

Subgroups — #24999676

Order 11008.

476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 89 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#19142870C211yesmaximal, characteristic, complemented
2#19135419C212yesmaximal
3#19135418C211yesmaximal, characteristic
4#19132477C212yesmaximal, complemented
5C43×#1295C211yesmaximal, characteristic, complemented
6C2×#13063322C2211yescharacteristic
7C2×#13063247—22no—
8C2×#13063247—22no—
9C2×#13063245—22no—
10C2×#13063236C2211yescharacteristic
11#14582833—22no—
12#14582832—22no—
13#14582831—22no—
14#14582765C2212yes—
15C2×#97×C43C2212yes—
16C43×#382C2211yescharacteristic
17C22×D172—21no—
18C22×D172—22no—
19C22×C43⋊C8—21no—
20#13063322—22no—
21#13063322—21no—
22#13063322Q812yes—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—22no—
28#13063247—44no—
29#13063247—44no—
30#13063245—44no—
31#13063236—22no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C22×C8×C43—22no—
36C2×C4⋊C4×C43D412yes—
37C2×C42×C43C2311yescharacteristic
38#97×C43—22no—
39#97×C43—22no—
40#95×C43—22no—
41C23×D43—41no—
42C22×C4×C43—22no—
43C22×C4×C43C2×D411yescharacteristic
44C22×C4×C43C2×D412yes—
45C22×Dic43—22no—
46C22×Dic43—22no—
47C2×D172—24no—
48C2×D172—22no—
49C2×D172—42no—
50C2×D172—41no—
51C2×D172—42no—
52C2×D172—42no—
53C2×D172—42no—
54C2×D172—42no—
55C2×D172—42no—
56C2×D172—42no—
57C2×C8×C43—24no—
58C2×C8×C43—42no—
59C2×C8×C43—42no—
60C4⋊C4×C43—42no—
61C42×C43C2×Q811yescharacteristic
62C42×C43#4112yes—
63C42×C43#4111yescharacteristic
64C4⋊Dic43—42no—
65C4⋊Dic43—42no—
66C4⋊Dic43—82no—
67Dic43⋊C4—82no—
68Dic43⋊C4—82no—
69C2×C43⋊C8—22no—
70C2×C43⋊C8—41no—
71C2×C43⋊C8—41no—
72C23×C43#12011yescharacteristic
73C22×D43—42no—
74C22×D43—82no—
75C22×D43—81no—
76C22×D43—82no—
77C22×D43—81no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—42no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43C22⋊Q812yes—
86C2×C4×C43C22⋊Q811yescharacteristic
87C2×C4×C43#12412yes—
88C2×C4×C43#12411yescharacteristic
89C2×Dic43—42no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95D172—44no—
96D172—44no—
97D172—44no—
98D172—82no—
99D172—82no—
100D172—82no—
101C8×C43—44no—
102C43⋊C8—42no—
103#10360—431nomaximal, Sylow
104C22×C43#39311yescharacteristic
105C22×C43#45312yes—
106C22×C43#45311yescharacteristic
107C22×C43#45412yes—
108C22×C43#45411yescharacteristic
109C2×D43—84no—
110C2×D43—82no—
111C2×D43—162no—
112C2×D43—161no—
113C2×D43—161no—
114C4×C43—21no—
115C4×C43—22no—
116C4×C43—22no—
117C4×C43—21no—
118C4×C43—82no—
119Dic43—82no—
120Dic43—82no—
121#2845—431no—
122#1961—432no—
123#1961—431no—
124#1295—432no—
125#1295D4311yescharacteristic, complemented
126C2×C43#165612yes—
127C2×C43#165611yescharacteristic
128C2×C43#165811yescharacteristic
129C2×C43#202712yes—
130C2×C43#202711yescharacteristic
131D43—162no—
132C2×#127—431no—
133C2×#102—862no—
134C2×#102—862no—
135C2×#102—862no—
136C2×#97—431no—
137C2×#97C2×D4312yes—
138#398—862no—
139#398—862no—
140#398—862no—
141#382—432no—
142#382C2×D4311yescharacteristic
143C43#1036011yescharacteristic, complemented, Sylow
144C22×D4—861no—
145C22×D4—862no—
146C22×C8—22no—
147C22×C8—861no—
148#127—432no—
149#127—862no—
150#127—861no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—862no—
154C2×C4⋊C4—862no—
155C2×C4⋊C4—862no—
156C2×C4⋊C4D17212yes—
157C2×C42C22×D4311yescharacteristic
158#102—1724no—
159#102—1724no—
160#102—1724no—
161#97—22no—
162#97—22no—
163#97—862no—
164#95—22no—
165#95—862no—
166#95—862no—
167#95—862no—
168C24—1721no—
169C2×D4—864no—
170C2×D4—862no—
171C2×D4—1722no—
172C2×D4—1722no—
173C2×D4—1722no—
174C2×D4—1722no—
175C2×D4—1722no—
176C2×D4—1722no—
177C2×D4—1722no—
178C2×D4—1721no—
179C22×C4—22no—
180C22×C4—862no—
181C22×C4—862no—
182C22×C4C2×D17211yescharacteristic
183C22×C4D4×D4312yes—
184C2×C8—24no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—862no—
188C2×C8—1721no—
189C2×C8—1721no—
190C4⋊C4—42no—
191C4⋊C4—3442no—
192C4⋊C4—3442no—
193C4⋊C4—3442no—
194C4⋊C4—1722no—
195C4⋊C4—1722no—
196C42#1062189812yes—
197C42#1062190011yescharacteristic
198C42Q8×D4311yescharacteristic
199C23—3442no—
200C23—3441no—
201C23—3442no—
202C23—3441no—
203C23—1722no—
204C23#1306329511yescharacteristic
205D4—3442no—
206D4—3442no—
207D4—3442no—
208D4—1724no—
209D4—1724no—
210D4—1724no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—1722no—
219C2×C4—1722no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4#1306330312yes—
225C2×C4#1306330511yescharacteristic
226C2×C4#1306331112yes—
227C2×C4#1306331311yescharacteristic
228C8—44no—
229C8—1722no—
230C22—3444no—
231C22—3442no—
232C22—6882no—
233C22—6881no—
234C22—6881no—
235C22#1458281211yescharacteristic
236C22#1458306812yes—
237C22#1458306911yescharacteristic
238C22#1458307312yes—
239C22#1458307411yescharacteristic
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—3442no—
246C4—3442no—
247C2—6882no—
248C2#1913388912yes—
249C2#1913389011yescharacteristic
250C2#1913389811yescharacteristic
251C2#1913575012yes—
252C2#1913575211yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43#120
prime radicalC2×#13063322C22
hypercenter#1295D43
hypocenterC43#10360
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. #19142870C2semidirect
4. #19132477C2semidirect
5. C43×#1295C2semidirect
125. #1295D43semidirect
143. C43#10360semidirect

Maximal subgroups

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

subgroupindex
#191428702
#191354192
#191354182
#191324772
C43×#12952
#1036043