Finite Group Databasebeta

← #24994469

Subgroups — #24994469

Order 11008.

522 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 111 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#19143680C211yesmaximal, characteristic, complemented
2#19139500C211yesmaximal, characteristic
3#19133019C212yesmaximal
4#19132455C212yesmaximal, complemented
5C43×#1801C211yesmaximal, characteristic, complemented
6C2×#13063301—21no—
7C2×C4×D172C2211yescharacteristic
8#14583030—24no—
9#14582956—22no—
10#14582952C2212yes—
11#14582829C412yes—
12#14582816C412yes—
13#14582790—22no—
14#14582765C2211yescharacteristic
15#14582756—21no—
16#14582626—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C43×#423C2212yes—
19C2×#101×C43—21no—
20C43×#343—21no—
21C22×D172C2×C411yescharacteristic
22C22×C4×D43—21no—
23#13063301—44no—
24C4×D172—22no—
25C4×D172—22no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—22no—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—21no—
32C4⋊(C43⋊C8)—24no—
33C4⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35#13063236—24no—
36C4×C43⋊C8D414yes—
37C43⋊#95—22no—
38C43⋊#95—21no—
39C43⋊#95C2×C412yes—
40C22×Q8×C43D411yescharacteristic
41C2×M16×C43—22no—
42C4×Q8×C43—22no—
43C4×Q8×C43—22no—
44C2×C4⋊C4×C43C2×C412yes—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C42×C43D412yes—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49C4⋊C8×C43—22no—
50#101×C43—42no—
51C23×D43—21no—
52C2×Q8×C43—22no—
53C2×Q8×C43—21no—
54C2×Q8×C43—22no—
55C2×Q8×C43—21no—
56C22×C4×C43C22⋊C412yes—
57C22×C4×C43C22⋊C412yes—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—22no—
62C22×Dic43—21no—
63C2×D172—22no—
64C2×D172—42no—
65C2×C4×D43—42no—
66C2×C4×D43—42no—
67C2×C4×D43—41no—
68C2×C4×D43—41no—
69M16×C43—42no—
70M16×C43—42no—
71C2×C8×C43—42no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—22no—
74C42×C43—22no—
75C42×C43—22no—
76C42×C43C2×D412yes—
77C42×C43#4112yes—
78(C2×D43)⋊C4—44no—
79(C2×D43)⋊C4—44no—
80(C2×D43)⋊C4—41no—
81(C2×D43)⋊C4—41no—
82C4⋊Dic43—22no—
83C4⋊Dic43—42no—
84Dic43⋊C4—44no—
85C2×C43⋊C8—24no—
86C23×C43C2×C22⋊C411yescharacteristic
87C22×D43—22no—
88C22×D43—41no—
89C22×D43—41no—
90C22×D43—41no—
91C22×D43—41no—
92C22×D43—41no—
93C22×D43—41no—
94Q8×C43—42no—
95Q8×C43—42no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43C4×D412yes—
104C2×C4×C43#12011yescharacteristic
105C2×C4×C43#12112yes—
106C2×C4×C43#12311yescharacteristic
107C2×C4×C43AGL(1,ℤ/8)12yes—
108C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
109C2×C4×C43#13711yescharacteristic
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—41no—
113C2×Dic43—41no—
114C2×Dic43—41no—
115C2×Dic43—42no—
116D172—24no—
117D172—42no—
118C4×D43—82no—
119C4×D43—82no—
120C8×C43—82no—
121C43⋊C8—44no—
122#9490—431nomaximal, Sylow
123C22×C43—21no—
124C22×C43—21no—
125C22×C43#38611yescharacteristic
126C22×C43#41711yescharacteristic
127C22×C43#41811yescharacteristic
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—81no—
132C2×D43—81no—
133C2×D43—81no—
134C2×D43—81no—
135C4×C43—22no—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—42no—
139C4×C43—42no—
140C4×C43#46812yes—
141C4×C43#46912yes—
142Dic43—82no—
143Dic43—81no—
144#2983—431no—
145#2536—431no—
146#1801D4311yescharacteristic, complemented
147#1486—432no—
148#1286—432no—
149C2×C43—21no—
150C2×C43—21no—
151C2×C43#189111yescharacteristic
152C2×C43#189511yescharacteristic
153C2×C43#191211yescharacteristic
154D43—82no—
155C2×C22⋊Q8—861no—
156C2×C4×Q8C2×D4311yescharacteristic
157C2×C4×D4—431no—
158#446—864no—
159#432—862no—
160#431—432no—
161#423C2×D4312yes—
162C2×#101—21no—
163#398—432no—
164#394—432no—
165#388—862no—
166#382—431no—
167#380—861no—
168#343—21no—
169D4⋊C8—864no—
170C43#949011yescharacteristic, complemented, Sylow
171C22×Q8C22⋊D4311yescharacteristic
172C22×D4—431no—
173C23×C4—861no—
174C2×M16—22no—
175C22⋊Q8—1724no—
176C4×Q8—22no—
177C4×Q8—22no—
178C4×D4—862no—
179C4×D4—862no—
180C2×C4⋊C4—431no—
181C2×C4⋊C4—862no—
182C2×C4⋊C4—861no—
183C2×C4⋊C4C4×D4312yes—
184C2×C4⋊C4C22⋊D4311yescharacteristic
185C2×C22⋊C4—862no—
186C2×C22⋊C4—862no—
187C2×C22⋊C4—861no—
188C2×C42D17212yes—
189C2×C42C22×D4311yescharacteristic
190C4⋊C8—22no—
191C4⋊C8—22no—
192C4⋊C8—864no—
193C4⋊C8—862no—
194#101—42no—
195C22⋊C8—862no—
196#97—864no—
197C4×C8—434no—
198#95—432no—
199#95—862no—
200#95—861no—
201C24—861no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—21no—
205C2×Q8—21no—
206C2×D4—862no—
207C2×D4—1722no—
208C22×C4—862no—
209C22×C4—861no—
210C22×C4—1722no—
211C22×C4—1722no—
212C22×C4—1721no—
213C22×C4—1721no—
214C22×C4(C2×D43)⋊C412yes—
215C22×C4(C2×D43)⋊C412yes—
216C22×C4C2×C4×D4311yescharacteristic
217C22×C4C2×D17211yescharacteristic
218C22×C4C2×C22⋊D4311yescharacteristic
219M16—42no—
220M16—42no—
221C2×C8—42no—
222C2×C8—864no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—862no—
226C4⋊C4—1724no—
227C4⋊C4—1722no—
228C22⋊C4—1724no—
229C22⋊C4—1724no—
230C22⋊C4—1721no—
231C22⋊C4—1721no—
232C42—22no—
233C42—22no—
234C42D4×D4312yes—
235C42#1062190012yes—
236C23—862no—
237C23—1721no—
238C23—1721no—
239C23—1721no—
240C23—1721no—
241C23—1721no—
242C23—1721no—
243C23C2×(C2×D43)⋊C411yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—864no—
247D4—1722no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—3442no—
256C2×C4—3442no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4—1721no—
260C2×C4—1722no—
261C2×C4—1721no—
262C2×C4—1721no—
263C2×C4(C22⋊D43)⋊C412yes—
264C2×C4#1306329511yescharacteristic
265C2×C4#1306329712yes—
266C2×C4#1306330911yescharacteristic
267C2×C4#1306335012yes—
268C2×C4#1306335111yescharacteristic
269C2×C4#1306335611yescharacteristic
270C8—82no—
271C8—1724no—
272C22—21no—
273C22—21no—
274C22—3441no—
275C22—3441no—
276C22—3441no—
277C22—3441no—
278C22—1722no—
279C22—1722no—
280C22—1722no—
281C22#1458277611yescharacteristic
282C22#1458289811yescharacteristic
283C22#1458290311yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—3442no—
290C4—3441no—
291C4#1458314712yes—
292C4#1458315012yes—
293C2—21no—
294C2—21no—
295C2—3442no—
296C2#1913501111yescharacteristic
297C2#1913503111yescharacteristic
298C2#1913513011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1801C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1801D43
hypocenterC43#9490
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
1. #19143680C2semidirect
4. #19132455C2semidirect
5. C43×#1801C2semidirect
146. #1801D43semidirect
170. C43#9490semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191395002
#191330192
#191324552
C43×#18012
#949043