Finite Group Databasebeta

← #25009429

Subgroups — #25009429

Order 11008.

346 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 59 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#19142479C211yesmaximal, characteristic
2#19135756C211yesmaximal, characteristic
3#19133639C211yesmaximal, characteristic
4#19133571C211yesmaximal, characteristic
5#19132626C211yesmaximal, characteristic
6#19132623C211yesmaximal, characteristic
7C43×#1319C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583235—21no—
10#14583057—21no—
11#14582908—21no—
12#14582841—21no—
13#14582838C2211yescharacteristic
14#14582833—21no—
15#14582819C2211yescharacteristic
16#14582806—21no—
17#14582803—21no—
18#14582786—21no—
19#14582783—21no—
20#14582668C2211yescharacteristic
21#14582659—21no—
22#14582637—21no—
23#14582637—21no—
24C43×#391C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×Dic172—41no—
29C2×#10621877—21no—
30#13063324—41no—
31#13063316—41no—
32#13063304—21no—
33#13063304—21no—
34#13063284—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×C4×Dic43—21no—
41#13063259—41no—
42#13063250—41no—
43#13063250—41no—
44#13063249—41no—
45#13063249—41no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95D411yescharacteristic
54C43⋊#95D411yescharacteristic
55C22×Q8×C43D411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C42×C43D411yescharacteristic
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43Q1612yescomplemented
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C2×Dic86—21no—
76C2×Dic86—21no—
77C2×Dic86—41no—
78C2×Dic86—42no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C4⋊C4×C43—41no—
82C42×C43—41no—
83C22⋊Dic43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—41no—
89C4⋊Dic43—81no—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—81no—
95C4×Dic43—41no—
96C4×Dic43—81no—
97#10621877—41no—
98#10621877—41no—
99C2×C43⋊C8—41no—
100Dic172—82no—
101C23×C43#12011yescharacteristic
102Q8×C43—42no—
103Q8×C43—81no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43C2×Q1611yescharacteristic
117C2×C4×C43#13711yescharacteristic
118C2×Dic43—22no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—42no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131Dic86—42no—
132Dic86—81no—
133Dic86—81no—
134Dic86—81no—
135C8×C43—81no—
136C8×C43—81no—
137C43⋊C8—81no—
138#12222—431nomaximal, Sylow
139C22×C43—21no—
140C22×C43—21no—
141C22×C43#45111yescharacteristic
142C22×C43#45511yescharacteristic
143C22×C43B(4,𝔽2)11yescharacteristic
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—42no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—81no—
150Dic43—42no—
151Dic43—81no—
152Dic43—81no—
153Dic43—81no—
154Dic43—81no—
155Dic43—81no—
156#2799—431no—
157#2028—431no—
158#1617—431no—
159#1605—431no—
160#1354—431no—
161#1353—431no—
162#1319D4311yescharacteristic
163C2×C43—21no—
164C2×C43—21no—
165C2×C43#160211yescharacteristic
166C2×C43#219711yescharacteristic
167C2×C43#220311yescharacteristic
168#544—431no—
169#484—861no—
170#451—861no—
171#419—861no—
172#400—431no—
173#400—861no—
174#398—861no—
175#395—431no—
176#391—861no—
177#391—861no—
178#391C2×D4311yescharacteristic
179#387—861no—
180#387—861no—
181#343—431no—
182#339—861no—
183#328—861no—
184#328—861no—
185#324C2×D4311yescharacteristic
186#324C2×D4311yescharacteristic
187C43#1222211yescharacteristic, complemented, Sylow
188C22×Q8—431no—
189C22×Q8D17211yescharacteristic
190C2×Q16—1721no—
191C2×M16—861no—
192C4⋊Q8—1721no—
193#125—1721no—
194C22⋊Q8—861no—
195C22⋊Q8—861no—
196#117—861no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4C22×D4311yescharacteristic
203C2×C42—861no—
204C2×C42D17211yescharacteristic
205#107—1721no—
206#103—1721no—
207#103—1721no—
208#103—1721no—
209#103—1721no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212#95—21no—
213#95—21no—
214#95—431no—
215#95—431no—
216#95—861no—
217#95—861no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95—861no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—861no—
227C2×Q8—861no—
228C2×Q8—1721no—
229C2×Q8—1722no—
230C2×Q8Dic17212yescomplemented
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4C2×D17211yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C22×C4D4×D4311yescharacteristic
240Q16—3442no—
241M16—1721no—
242M16—1721no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—1721no—
246C4⋊C4—41no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—3441no—
252C4⋊C4—3441no—
253C4⋊C4—1721no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C4⋊C4—1722no—
257C4⋊C4—1722no—
258C22⋊C4—1721no—
259C42—41no—
260C42—3441no—
261C42—1721no—
262C23#1306329511yescharacteristic
263Q8—42no—
264Q8—81no—
265Q8—3441no—
266Q8—3441no—
267Q8—3441no—
268Q8—1722no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—862no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1722no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4C2×Dic17211yescharacteristic
295C2×C4#1306335811yescharacteristic
296C8—81no—
297C8—81no—
298C8—3441no—
299C22—21no—
300C22—21no—
301C22#1458305711yescharacteristic
302C22#1458307911yescharacteristic
303C22#1458308711yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—81no—
310C4—3441no—
311C4—3441no—
312C4—3441no—
313C4—3441no—
314C4—3441no—
315C4—1722no—
316C2—21no—
317C2—21no—
318C2#1913355411yescharacteristic
319C2#1913658811yescharacteristic
320C2#1913661711yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1319D43
hypocenterC43#12222
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
65. C2×Q8×C43Q16semidirect
187. C43#12222semidirect
230. C2×Q8Dic172semidirect

Maximal subgroups

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

subgroupindex
#191424792
#191357562
#191336392
#191335712
#191326262
#191326232
C43×#13192
#1222243