Finite Group Databasebeta

← #24985430

Subgroups — #24985430

Order 11008.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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#19135731C212yesmaximal, complemented
2#19135694C211yesmaximal, characteristic, complemented
3#19132421C211yesmaximal, characteristic, complemented
4#19132416C212yesmaximal, complemented
5C43×#2733C211yesmaximal, characteristic
6C22×#10621885—21no—
7C2×#13063325C2211yescharacteristic
8C2×#13063248—21no—
9C2×#13063246—22no—
10#14582661—22no—
11#14582654C2211yescharacteristic
12#14582654C2212yes—
13C2×#124×C43—21no—
14C43×#394—21no—
15C43×#392—22no—
16C43×#391C2211yescharacteristic
17C43×#390C2212yes—
18C43×#388—22no—
19C22×Dic86—21no—
20C2×#10621885—42no—
21C2×#10621885—42no—
22C2×#10621885—42no—
23C22×C43⋊C8—21no—
24C22×C43⋊C8—22no—
25#13063325—42no—
26C2×C4⋊Dic43—22no—
27#13063248—42no—
28#13063246—44no—
29C22×Q8×C43D411yescharacteristic
30C22×D4×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43D412yes—
33#124×C43—42no—
34#124×C43—42no—
35C2×C4⋊C4×C43D411yescharacteristic
36C2×C4⋊C4×C43D412yes—
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43—22no—
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43—22no—
41C2×C42×C43—21no—
42C2×C42×C43C2311yescharacteristic
43#95×C43—21no—
44#95×C43—22no—
45C24×C43—22no—
46C2×Q8×C43—21no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43D812yes—
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43—42no—
53C2×D4×C43—42no—
54C2×D4×C43—42no—
55C2×D4×C43—81no—
56C2×D4×C43—81no—
57C2×D4×C43—82no—
58C2×D4×C43—81no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—22no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D412yes—
64C22×Dic43—41no—
65C2×Dic86—22no—
66C2×Dic86—41no—
67C2×Dic86—41no—
68C2×Dic86—41no—
69C2×Dic86—41no—
70C2×Dic86—41no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—41no—
73C22⋊C4×C43—44no—
74C22⋊C4×C43—42no—
75C22⋊C4×C43—42no—
76C22⋊C4×C43—42no—
77C22⋊C4×C43—42no—
78C22⋊C4×C43—82no—
79C42×C43—41no—
80C42×C43—42no—
81#10621885—48no—
82C4⋊Dic43—24no—
83C4⋊Dic43—42no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—41no—
86C2×C43⋊C8—41no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C23×C43—42no—
91C23×C43—42no—
92C23×C43—42no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43—42no—
96C23×C43—42no—
97C23×C43#12011yescharacteristic
98Q8×C43—42no—
99Q8×C43—81no—
100D4×C43—44no—
101D4×C43—82no—
102D4×C43—84no—
103D4×C43—84no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—41no—
114C2×C4×C43—42no—
115C2×C4×C43—42no—
116C2×C4×C43C2×D811yescharacteristic
117C2×C4×C43#13512yes—
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43#13712yes—
120C2×Dic43—42no—
121C2×Dic43—81no—
122C2×Dic43—81no—
123Dic86—42no—
124Dic86—42no—
125Dic86—81no—
126Dic86—81no—
127C43⋊C8—42no—
128C43⋊C8—82no—
129#7758—431nomaximal, Sylow
130C22×C43—82no—
131C22×C43—82no—
132C22×C43—82no—
133C22×C43—82no—
134C22×C43—82no—
135C22×C43—82no—
136C22×C43—82no—
137C22×C43#44711yescharacteristic
138C22×C43#45212yes—
139C22×C43#45311yescharacteristic
140C22×C43#45512yes—
141C22×C43B(4,𝔽2)11yescharacteristic
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—22no—
145C4×C43—22no—
146C4×C43—42no—
147C4×C43—82no—
148C4×C43—81no—
149Dic43—82no—
150#2733D4311yescharacteristic
151#2023—432no—
152#2016—431no—
153#1272—431no—
154#1270—432no—
155C2×C43—162no—
156C2×C43#159511yescharacteristic
157C2×C43#160612yes—
158C2×C43#163411yescharacteristic
159C2×C43#164112yes—
160C2×C43#165911yescharacteristic
161C22×Q16—861no—
162C2×C4⋊Q8—431no—
163C2×#124—21no—
164C2×#103—861no—
165C2×#102—862no—
166#394—21no—
167#392—22no—
168#391C2×D4311yescharacteristic
169#390C2×D4312yes—
170#388—22no—
171#340—862no—
172#336—431no—
173#336—432no—
174C43#775811yescharacteristic, complemented, Sylow
175C22×Q8—861no—
176C22×Q8C22⋊D4311yescharacteristic
177C22×D4—21no—
178C22×D4—21no—
179C22×D4C22⋊D4312yes—
180C2×Q16—1722no—
181C2×Q16—1722no—
182C2×Q16—1722no—
183C22×C8—861no—
184C22×C8—862no—
185C4⋊Q8—1722no—
186#124—42no—
187#124—42no—
188C2×C4⋊C4—862no—
189C2×C4⋊C4C22⋊D4312yes—
190C2×C4⋊C4C22⋊D4311yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C42—21no—
196C2×C42C22×D4311yescharacteristic
197#103—1722no—
198#102—1724no—
199#95—21no—
200#95—22no—
201C24—22no—
202C2×Q8—21no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—862no—
206C2×Q8—1721no—
207C2×Q8—1721no—
208C2×Q8—1721no—
209C2×Q8—1721no—
210C2×Q8—1721no—
211C2×Q8#1062188212yes—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—81no—
218C2×D4—81no—
219C2×D4—81no—
220C2×D4—82no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—1721no—
225C22×C4C2×C22⋊D4311yescharacteristic
226C22×C4C2×C22⋊D4312yes—
227Q16—1728no—
228C2×C8—862no—
229C2×C8—1722no—
230C2×C8—1722no—
231C2×C8—1722no—
232C2×C8—1721no—
233C2×C8—1721no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—864no—
237C4⋊C4—1722no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—82no—
244C42—41no—
245C42—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23#1306329411yescharacteristic
254Q8—42no—
255Q8—81no—
256Q8—3441no—
257Q8—3441no—
258Q8—1722no—
259Q8—1722no—
260D4—44no—
261D4—82no—
262D4—84no—
263D4—84no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—3441no—
277C2×C4—3441no—
278C2×C4—1722no—
279C2×C4C2×#1062188211yescharacteristic
280C2×C4#1306334512yes—
281C2×C4#1306335111yescharacteristic
282C2×C4#1306335512yes—
283C8—3442no—
284C8—1722no—
285C22—82no—
286C22—82no—
287C22—82no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22#1458303311yescharacteristic
293C22#1458306112yes—
294C22#1458306711yescharacteristic
295C22#1458307712yes—
296C22#1458308611yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—22no—
301C4—42no—
302C4—82no—
303C4—81no—
304C4—3442no—
305C2—162no—
306C2#1913351311yescharacteristic
307C2#1913357512yes—
308C2#1913374011yescharacteristic
309C2#1913378812yes—
310C2#1913390111yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2733C2
socleC23×C43#120
hypercenter#2733D43
hypocenterC43#7758
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #19135731C2semidirect
2. #19135694C2semidirect
3. #19132421C2semidirect
4. #19132416C2semidirect
174. C43#7758semidirect

Maximal subgroups

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

subgroupindex
#191357312
#191356942
#191324212
#191324162
C43×#27332
#775843