Finite Group Databasebeta

← #25013406

Subgroups — #25013406

Order 11008.

516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#14582694C211yesmaximal, characteristic
2#19134984C211yesmaximal, characteristic
3#19134875C212yesmaximal
4#19132713C212yesmaximal
5C43×#2379C211yesmaximal, characteristic
6#14583374C2211yescharacteristic
7#14582908—21no—
8C2×#13063242C2211yescharacteristic
9C2×#13063240C2212yes—
10#14582772—22no—
11#14582694C414yescomplemented
12#14582665—22no—
13#14582659—21no—
14C2×#124×C43C2211yescharacteristic
15C43×#391—21no—
16C43×#388—22no—
17C43×#386C2212yes—
18C43×#385—22no—
19C43×#382—21no—
20C2×#10621877—21no—
21D4×Dic43—41no—
22D4×Dic43—41no—
23#13063284—21no—
24C2×Dic43⋊C4—42no—
25C2×C22⋊Dic43—22no—
26C2×C22⋊Dic43—22no—
27#13063249—41no—
28#13063249—41no—
29#13063242—22no—
30#13063240—22no—
31#13063240C2×C414yes—
32C43⋊#95—42no—
33C22×Q8×C43D411yescharacteristic
34C22×D4×C43C2311yescharacteristic
35C23×C4×C43D412yes—
36#124×C43—22no—
37#124×C43C2×C412yes—
38#124×C43Q812yes—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43—22no—
44C2×C22⋊C4×C43D412yes—
45C2×C42×C43—21no—
46C2×C42×C43D411yescharacteristic
47#95×C43—22no—
48#95×C43—22no—
49#95×C43—22no—
50C24×C43C2×D412yes—
51C2×Q8×C43—21no—
52C2×Q8×C43—41no—
53C2×Q8×C43—41no—
54C2×Q8×C43C4⋊C412yescomplemented
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43C22×C411yescharacteristic
58C2×D4×C43C2×Q811yescharacteristic
59C2×D4×C43#4112yes—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—42no—
65C22×C4×C43—82no—
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—22no—
68C22×Dic43—22no—
69C22×Dic43—42no—
70C4⋊C4×C43—81no—
71C4⋊C4×C43—81no—
72C4⋊C4×C43—81no—
73C22⋊C4×C43—24no—
74C22⋊C4×C43—24no—
75C22⋊C4×C43—42no—
76C22⋊C4×C43—82no—
77C42×C43—21no—
78C42×C43—81no—
79C42×C43C4⋊C412yescomplemented
80C22⋊Dic43—24no—
81C22⋊Dic43—42no—
82C22⋊Dic43—42no—
83C22⋊Dic43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86Dic43⋊C4—84no—
87C4×Dic43—41no—
88#10621877—41no—
89#10621877—41no—
90C2×C43⋊C8—41no—
91C23×C43—22no—
92C23×C43—22no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43C4×D412yes—
96C23×C43#12011yescharacteristic
97C23×C43C22⋊Q812yes—
98Q8×C43—42no—
99Q8×C43—81no—
100D4×C43—41no—
101D4×C43—41no—
102D4×C43—42no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—44no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—82no—
119C2×C4×C43C2×C4⋊C411yescharacteristic
120C2×C4×C43#12311yescharacteristic
121C2×Dic43—44no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—82no—
125C2×Dic43—82no—
126C2×Dic43—82no—
127C2×Dic43—82no—
128C43⋊C8—81no—
129#12967—431nomaximal, Sylow
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—22no—
133C22×C43—22no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43—42no—
137C22×C43—42no—
138C22×C43—82no—
139C22×C43#38511yescharacteristic
140C22×C43B(4,𝔽2)11yescharacteristic
141C22×C43#45811yescharacteristic
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—42no—
145C4×C43—42no—
146C4×C43—82no—
147C4×C43—82no—
148Dic43—84no—
149Dic43—81no—
150Dic43—81no—
151#2379D4311yescharacteristic
152C2×#354—431no—
153#1885—431no—
154#1867—432no—
155#1390—432no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43—42no—
159C2×C43—42no—
160C2×C43#186711yescharacteristic
161C2×C43#219911yescharacteristic
162C2×C43#220111yescharacteristic
163C2×#124C2×D4311yescharacteristic
164#518—431no—
165#419—861no—
166C2×#100—431no—
167C2×#99—432no—
168#391—21no—
169#388—22no—
170#386C2×D4312yes—
171#385—22no—
172#385—862no—
173#382—21no—
174#354—434no—
175#342—862no—
176#339—861no—
177C43#1296711yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D4311yescharacteristic
179C22×D4C22×D4311yescharacteristic
180C23×C4C22⋊D4312yes—
181C2×M16—861no—
182#124—22no—
183#124Dic8612yes—
184#124C4×D4312yes—
185C4×D4—1721no—
186C4×D4—1721no—
187#117—861no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—1722no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—862no—
195C2×C22⋊C4—862no—
196C2×C22⋊C4C22⋊D4312yes—
197C2×C42—21no—
198C2×C42C22⋊D4311yescharacteristic
199#103—1721no—
200#103—1721no—
201#100—862no—
202#99—434no—
203#99—862no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—1722no—
208C24C2×C22⋊D4312yes—
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8Dic43⋊C412yescomplemented
213C2×D4—41no—
214C2×D4—41no—
215C2×D4C2×Dic8611yescharacteristic
216C2×D4C2×C4×D4311yescharacteristic
217C2×D4#1062189812yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—82no—
224C22×C4—862no—
225C22×C4—862no—
226C22×C4—1722no—
227C22×C4C2×C22⋊D4311yescharacteristic
228M16—1721no—
229M16—1721no—
230C2×C8—1721no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—861no—
235C4⋊C4—861no—
236C4⋊C4—3444no—
237C22⋊C4—24no—
238C22⋊C4—24no—
239C22⋊C4—42no—
240C22⋊C4—82no—
241C22⋊C4—864no—
242C22⋊C4—1722no—
243C22⋊C4—1722no—
244C22⋊C4—1721no—
245C42—21no—
246C42—81no—
247C42—1721no—
248C42Dic43⋊C412yescomplemented
249C23—22no—
250C23—22no—
251C23—42no—
252C23—42no—
253C23C4×C22⋊D4312yes—
254C23#1306329411yescharacteristic
255C23#1306330412yes—
256Q8—42no—
257Q8—81no—
258D4—41no—
259D4—41no—
260D4—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—82no—
277C2×C4—3442no—
278C2×C4—3442no—
279C2×C4—3442no—
280C2×C4—3442no—
281C2×C4—1724no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4C2×Dic43⋊C411yescharacteristic
285C2×C4#1306330811yescharacteristic
286C8—3441no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—82no—
296C22#1458277211yescharacteristic
297C22#1458308611yescharacteristic
298C22#1458308911yescharacteristic
299C4—21no—
300C4—21no—
301C4—42no—
302C4—42no—
303C4—82no—
304C4—82no—
305C4—3444no—
306C4—3441no—
307C4—3441no—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2#1913487611yescharacteristic
313C2#1913659611yescharacteristic
314C2#1913660811yescharacteristic
subgroupG/H
centerC22#14583086
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#2379C2
socleC22×C43B(4,𝔽2)
prime radical, cosocleC22×D4×C43C23
hypercenter#2379D43
hypocenterC43#12967
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2379

Complements

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

NH ≅ G/Ntype
11. #14582694C4semidirect
54. C2×Q8×C43C4⋊C4semidirect
79. C42×C43C4⋊C4semidirect
177. C43#12967semidirect
212. C2×Q8Dic43⋊C4semidirect
248. C42Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145826942
#191349842
#191348752
#191327132
C43×#23792
#1296743