Finite Group Databasebeta

← #25013398

Subgroups — #25013398

Order 11008.

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

normal subgroups only

This group has 536 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#19137707C211yesmaximal, characteristic
2#19134984C211yesmaximal, characteristic
3#19134878C212yesmaximal
4#19132712C212yesmaximal
5C2×C43×#354C211yesmaximal, characteristic
6#14583374C2211yescharacteristic
7#14582908—21no—
8C2×#13063242C2211yescharacteristic
9#14582806—21no—
10#14582792—22no—
11#14582779C2212yes—
12#14582774—22no—
13C22⋊C4×Dic43—22no—
14#14582745—21no—
15#14582665—22no—
16#14582659—21no—
17C2×#124×C43C2211yescharacteristic
18C2×#99×C43C2212yes—
19C43×#354C414yescomplemented
20C23×Dic43D412yes—
21C2×#10621877—21no—
22D4×Dic43—42no—
23#13063284—21no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—42no—
26C2×C22⋊Dic43—22no—
27C2×C22⋊Dic43—22no—
28C2×C22⋊Dic43D412yes—
29C2×C4×Dic43—22no—
30C2×C4×Dic43—21no—
31#13063249—42no—
32#13063242—22no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—21no—
36C43⋊#95—22no—
37C43⋊#95—42no—
38C22×Q8×C43D411yescharacteristic
39C22×D4×C43C2311yescharacteristic
40#124×C43—22no—
41#124×C43C2×C412yes—
42#124×C43Q812yes—
43C2×C22⋊C4×C43—22no—
44C2×C22⋊C4×C43—22no—
45C2×C42×C43D411yescharacteristic
46#99×C43—22no—
47#99×C43C2×C414yes—
48C24×C43C2×D412yes—
49C2×Q8×C43—21no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43C4⋊C412yescomplemented
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43C22×C411yescharacteristic
56C2×D4×C43C2×Q811yescharacteristic
57C2×D4×C43#4112yes—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—42no—
61C22×C4×C43C2×D411yescharacteristic
62C22×Dic43—22no—
63C22×Dic43—22no—
64C22×Dic43—22no—
65C22×Dic43—22no—
66C22×Dic43—42no—
67C22×Dic43—44no—
68C22⋊C4×C43—24no—
69C22⋊C4×C43—24no—
70C22⋊C4×C43—24no—
71C22⋊C4×C43—42no—
72C42×C43—21no—
73C42×C43C4⋊C412yescomplemented
74C22⋊Dic43—42no—
75C22⋊Dic43—42no—
76C22⋊Dic43—44no—
77C22⋊Dic43—41no—
78C4⋊Dic43—22no—
79C4⋊Dic43—81no—
80C4⋊Dic43—84no—
81C4×Dic43—44no—
82C4×Dic43—41no—
83C4×Dic43—81no—
84#10621877—41no—
85#10621877—41no—
86C2×C43⋊C8—41no—
87C23×C43—22no—
88C23×C43—22no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43C4×D412yes—
92C23×C43#12011yescharacteristic
93C23×C43C22⋊Q812yes—
94Q8×C43—42no—
95Q8×C43—81no—
96D4×C43—41no—
97D4×C43—41no—
98D4×C43—42no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—42no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—44no—
107C2×C4×C43—82no—
108C2×C4×C43—82no—
109C2×C4×C43C2×C4⋊C411yescharacteristic
110C2×C4×C43#12311yescharacteristic
111C2×Dic43—24no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—44no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—82no—
120C2×Dic43—82no—
121C2×Dic43—82no—
122C43⋊C8—81no—
123#12965—431nomaximal, Sylow
124C22×C43—22no—
125C22×C43—22no—
126C22×C43—22no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—42no—
131C22×C43—82no—
132C22×C43#38511yescharacteristic
133C22×C43B(4,𝔽2)11yescharacteristic
134C22×C43#45811yescharacteristic
135C4×C43—21no—
136C4×C43—21no—
137C4×C43—42no—
138C4×C43—42no—
139C4×C43—84no—
140Dic43—44no—
141Dic43—82no—
142Dic43—82no—
143#2372—431no—
144C2×#354D4311yescharacteristic
145#1885—431no—
146#1867—432no—
147#1390—432no—
148C2×C43—21no—
149C2×C43—21no—
150C2×C43—42no—
151C2×C43—42no—
152C2×C43#186711yescharacteristic
153C2×C43#219712yes—
154C2×#124C2×D4311yescharacteristic
155#518—431no—
156#419—861no—
157C2×#100—431no—
158C2×#99C2×D4312yes—
159#391—861no—
160#388—862no—
161#386—432no—
162#385—862no—
163C4×C22⋊C4—862no—
164#376—861no—
165#354Dic4314yescomplemented
166#342—862no—
167#339—861no—
168C43#1296511yescharacteristic, complemented, Sylow
169C22×Q8D17211yescharacteristic
170C22×D4C22×D4311yescharacteristic
171C23×C4—432no—
172C2×M16—861no—
173#124—22no—
174#124Dic8612yes—
175#124C2×Dic4312yes—
176C4×D4—1722no—
177#117—861no—
178C2×C4⋊C4—861no—
179C2×C4⋊C4—1722no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—862no—
184C2×C22⋊C4—862no—
185C2×C42—861no—
186C2×C42—862no—
187C2×C42D17211yescharacteristic
188#103—1722no—
189#100—862no—
190#99—22no—
191#99C2×Dic4314yes—
192#95—861no—
193#95—861no—
194#95—862no—
195#95—862no—
196#95—1722no—
197C24D4×D4312yes—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8C4⋊Dic4312yescomplemented
202C2×D4—41no—
203C2×D4—41no—
204C2×D4C2×Dic8611yescharacteristic
205C2×D4#1062190012yes—
206C2×D4C22×Dic4311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—862no—
211C22×C4—862no—
212C22×C4—862no—
213C22×C4—862no—
214C22×C4—1724no—
215C22×C4—1722no—
216C22×C4C2×D17211yescharacteristic
217M16—1721no—
218M16—1721no—
219C2×C8—1721no—
220C4⋊C4—862no—
221C4⋊C4—3441no—
222C4⋊C4—3444no—
223C22⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—24no—
226C22⋊C4—42no—
227C22⋊C4—1724no—
228C22⋊C4—1722no—
229C22⋊C4—1721no—
230C22⋊C4—1722no—
231C42—21no—
232C42—3441no—
233C42—1721no—
234C42—1724no—
235C42C4⋊Dic4312yescomplemented
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23D4×Dic4312yes—
241C23#1306329511yescharacteristic
242C23#1306330212yes—
243Q8—42no—
244Q8—81no—
245D4—41no—
246D4—42no—
247D4—41no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—44no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—864no—
259C2×C4—3442no—
260C2×C4—3442no—
261C2×C4—3442no—
262C2×C4—1722no—
263C2×C4—1722no—
264C2×C4—1722no—
265C2×C4—1722no—
266C2×C4—1722no—
267C2×C4—1722no—
268C2×C4—1724no—
269C2×C4C2×C4⋊Dic4311yescharacteristic
270C2×C4#1306330911yescharacteristic
271C8—3441no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—82no—
280C22#1458277411yescharacteristic
281C22#1458308711yescharacteristic
282C22#1458309011yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—42no—
287C4—84no—
288C4—3442no—
289C4—3442no—
290C4—1724no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2—42no—
295C2#1913487811yescharacteristic
296C2#1913658812yes—
subgroupG/H
centerC22#14583087
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×#354C2
socleC22×C43B(4,𝔽2)
prime radical, cosocleC22×D4×C43C23
hypercenterC2×#354D43
hypocenterC43#12965
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
19. C43×#354C4semidirect
52. C2×Q8×C43C4⋊C4semidirect
73. C42×C43C4⋊C4semidirect
165. #354Dic43semidirect
168. C43#12965semidirect
201. C2×Q8C4⋊Dic43semidirect
235. C42C4⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
#191377072
#191349842
#191348782
#191327122
C2×C43×#3542
#1296543