Finite Group Databasebeta

← #25009762

Subgroups — #25009762

Order 11008.

364 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 55 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#19140006C211yesmaximal, characteristic
2#19133603C211yesmaximal, characteristic
3#19133569C211yesmaximal, characteristic
4#19132624C211yesmaximal, characteristic
5#19132600C211yesmaximal, characteristic
6#19132529C211yesmaximal, characteristic
7C43×#2028C211yesmaximal, characteristic
8#14583227—21no—
9#14583054—21no—
10#14582829C2211yescharacteristic
11#14582819C2211yescharacteristic
12#14582818—21no—
13#14582803—21no—
14#14582796—21no—
15#14582781—21no—
16#14582781—21no—
17C4×Dic43⋊C4—21no—
18#14582636—21no—
19#14582636—21no—
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#419—21no—
24C43×#391C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#339—21no—
27C22×Dic86D411yescharacteristic
28C2×#10621885—41no—
29C2×C4⋊Dic43D411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43—21no—
37#13063256—41no—
38#13063249—41no—
39#13063248—41no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C22×Q8×C43D411yescharacteristic
50C2×M16×C43—21no—
51C4⋊Q8×C43—41no—
52#125×C43—41no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#117×C43—21no—
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C42×C43D411yescharacteristic
58#103×C43—41no—
59#103×C43—41no—
60#95×C43—21no—
61#95×C43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—21no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×Dic86—41no—
78C2×Dic86—42no—
79M16×C43—41no—
80M16×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C42×C43—41no—
91C42×C43—41no—
92#10621885—82no—
93C4⋊Dic43—41no—
94Dic43⋊C4—24no—
95Dic43⋊C4—42no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99Dic43⋊C4—81no—
100C4×Dic43—42no—
101C4×Dic43—81no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43#12011yescharacteristic
105Q8×C43—42no—
106Q8×C43—81no—
107Q8×C43—81no—
108Q8×C43—81no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43#13511yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137Dic86—42no—
138Dic86—81no—
139C8×C43—81no—
140C43⋊C8—81no—
141C43⋊C8—81no—
142#12273—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43#45211yescharacteristic
146C22×C43#45511yescharacteristic
147C22×C43B(4,𝔽2)11yescharacteristic
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—42no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—81no—
154C4×C43—81no—
155C4×C43—81no—
156Dic43—42no—
157Dic43—42no—
158Dic43—42no—
159Dic43—81no—
160#2586—431no—
161#2028D4311yescharacteristic
162#1611—431no—
163#1605—431no—
164#1354—431no—
165#1346—431no—
166#1319—431no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43#160611yescharacteristic
170C2×C43#219711yescharacteristic
171C2×C43#220511yescharacteristic
172#544C2×D4311yescharacteristic
173#483—861no—
174#451—861no—
175#419—21no—
176#398—431no—
177#395—431no—
178#395—861no—
179#391—861no—
180#391C2×D4311yescharacteristic
181#389—861no—
182#387—861no—
183#387—861no—
184C4×C4⋊C4—861no—
185#343C2×D4311yescharacteristic
186#339—21no—
187#328—861no—
188#328—861no—
189#324—431no—
190#324—431no—
191C43#1227311yescharacteristic, complemented, Sylow
192C22×Q8—431no—
193C22×Q8C22⋊D4311yescharacteristic
194C2×Q16—1721no—
195C2×M16—21no—
196C4⋊Q8—41no—
197#125—41no—
198C22⋊Q8—21no—
199C22⋊Q8—21no—
200#117—21no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4C22×D4311yescharacteristic
208C2×C42—861no—
209C2×C42—861no—
210C2×C42C22⋊D4311yescharacteristic
211#106—1721no—
212#103—41no—
213#103—41no—
214#103—1721no—
215#103—1721no—
216C22⋊C8—861no—
217C22⋊C8—861no—
218#95—21no—
219#95—21no—
220#95—431no—
221#95—431no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—1721no—
234C2×Q8—1722no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4D4×D4311yescharacteristic
242C22×C4D4×D4311yescharacteristic
243C22×C4C2×C22⋊D4311yescharacteristic
244Q16—3442no—
245M16—41no—
246M16—41no—
247C2×C8—41no—
248C2×C8—1721no—
249C2×C8—1721no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—864no—
258C4⋊C4—3441no—
259C4⋊C4—3441no—
260C4⋊C4—1721no—
261C4⋊C4—1722no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C22⋊C4—41no—
265C42—41no—
266C42—41no—
267C42—3441no—
268C42—1722no—
269C23#1306329311yescharacteristic
270Q8—42no—
271Q8—81no—
272Q8—81no—
273Q8—81no—
274Q8—3441no—
275Q8—1722no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—862no—
291C2×C4—862no—
292C2×C4—862no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4#1306334511yescharacteristic
303C2×C4#1306335611yescharacteristic
304C8—81no—
305C8—3441no—
306C8—3441no—
307C22—21no—
308C22—21no—
309C22#1458305911yescharacteristic
310C22#1458307611yescharacteristic
311C22#1458308511yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—41no—
316C4—41no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—3441no—
321C4—1722no—
322C4—1722no—
323C4—1722no—
324C2—21no—
325C2—21no—
326C2#1913357311yescharacteristic
327C2#1913658411yescharacteristic
328C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2028C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2028D43
hypocenterC43#12273
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
191. C43#12273semidirect

Maximal subgroups

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

subgroupindex
#191400062
#191336032
#191335692
#191326242
#191326002
#191325292
C43×#20282
#1227343