Finite Group Databasebeta

← #25001344

Subgroups — #25001344

Order 11008.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135532C211yesmaximal, characteristic
2#19134722C211yesmaximal, characteristic
3#19134600C211yesmaximal, characteristic
4#19132479C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C43×#1803C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×#13063249—21no—
11C2×C4×C43⋊C8C2211yescharacteristic
12#14582769C2211yescharacteristic
13#14582661—21no—
14#14582661—21no—
15#14582661—21no—
16#14582654—21no—
17#14582654—21no—
18C2×C4×Q8×C43C2211yescharacteristic
19C2×C4⋊C8×C43C2211yescharacteristic
20C2×#103×C43—21no—
21C43×#384C2211yescharacteristic
22C43×#340—21no—
23C22×C43⋊C8—21no—
24C22×C43⋊C8—21no—
25C22×C43⋊C8D411yescharacteristic
26C22×C43⋊C8D411yescharacteristic
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C4⋊(C43⋊C8)—21no—
31C4⋊(C43⋊C8)—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34#13063249—42no—
35C4×C43⋊C8—21no—
36C4×C43⋊C8—21no—
37C22×Q8×C43D411yescharacteristic
38C22×C8×C43—21no—
39C4×Q8×C43—21no—
40C4×Q8×C43—21no—
41C4×Q8×C43—21no—
42C4×Q8×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C42×C43—21no—
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52#103×C43—42no—
53C2×Q8×C43—21no—
54C2×Q8×C43—21no—
55C2×Q8×C43—21no—
56C2×Q8×C43—21no—
57C2×Q8×C43—21no—
58C2×Q8×C43D812yes—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—41no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43#4111yescharacteristic
65C22×Dic43—41no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—81no—
78C42×C43—41no—
79C42×C43—41no—
80C42×C43#4111yescharacteristic
81C42×C43#4111yescharacteristic
82C42×C43#4111yescharacteristic
83C42×C43#4111yescharacteristic
84C4⋊Dic43—41no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—81no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—21no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C23×C43#12111yescharacteristic
102Q8×C43—22no—
103Q8×C43—22no—
104Q8×C43—41no—
105Q8×C43—41no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—81no—
115C2×C4×C43—81no—
116C2×C4×C43—81no—
117C2×C4×C43#12311yescharacteristic
118C2×C4×C43#12311yescharacteristic
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43#12411yescharacteristic
121C2×C4×C43#12611yescharacteristic
122C2×C4×C43#12611yescharacteristic
123C2×C4×C43C2×D811yescharacteristic
124C2×C4×C43#13511yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C8×C43—81no—
135C43⋊C8—41no—
136C43⋊C8—41no—
137C43⋊C8—81no—
138C43⋊C8—81no—
139#10623—431nomaximal, Sylow
140C22×C43#39711yescharacteristic
141C22×C43#46411yescharacteristic
142C22×C43#46411yescharacteristic
143C22×C43#46611yescharacteristic
144C22×C43#47011yescharacteristic
145C22×C43#47111yescharacteristic
146C22×C43#47111yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—42no—
150C4×C43—81no—
151C4×C43—161no—
152C4×C43#48011yescharacteristic
153C4×C43#48011yescharacteristic
154C4×C43#48511yescharacteristic
155C4×C43#48511yescharacteristic
156C4×C43#48511yescharacteristic
157C4×C43#48511yescharacteristic
158C4×C43#48811yescharacteristic
159C4×C43#49111yescharacteristic
160Dic43—161no—
161#1984—431no—
162#1834—431no—
163#1803—431no—
164#1803D4311yescharacteristic
165#1296—431no—
166#1296—431no—
167#1277—431no—
168C2×C43#168211yescharacteristic
169C2×C43#168211yescharacteristic
170C2×C43#170411yescharacteristic
171C2×C43#170411yescharacteristic
172C2×C43#207411yescharacteristic
173C2×C43#207511yescharacteristic
174C2×C43#207911yescharacteristic
175C2×C4×Q8C2×D4311yescharacteristic
176C2×C4⋊C8—431no—
177C2×C4⋊C8—431no—
178C2×C4⋊C8C2×D4311yescharacteristic
179C2×#103—21no—
180C2×#103—861no—
181C2×C4×C8—431no—
182#384—431no—
183#384C2×D4311yescharacteristic
184#340—21no—
185#340—861no—
186#340—861no—
187#340—861no—
188#336—861no—
189#336—861no—
190C43#1062311yescharacteristic, complemented, Sylow
191C22×Q8C22⋊D4311yescharacteristic
192C22×C8—21no—
193C22×C8—431no—
194C22×C8—431no—
195C22×C8—861no—
196C22×C8—861no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4C22⋊D4311yescharacteristic
209C2×C42—21no—
210C2×C42C22×D4311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—861no—
214C4⋊C8—861no—
215C4⋊C8—861no—
216C4⋊C8—861no—
217#103—42no—
218#103—1722no—
219C4×C8—861no—
220C4×C8—861no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8#1062188212yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—1721no—
231C22×C4D4×D4311yescharacteristic
232C22×C4#1062190011yescharacteristic
233C22×C4C2×C22⋊D4311yescharacteristic
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—861no—
238C2×C8—861no—
239C2×C8—861no—
240C2×C8—861no—
241C2×C8—861no—
242C2×C8—861no—
243C2×C8—1721no—
244C2×C8—1721no—
245C2×C8—1721no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—3441no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C42—41no—
264C42—41no—
265C42#1062189811yescharacteristic
266C42#1062189811yescharacteristic
267C42#1062190011yescharacteristic
268C42#1062190011yescharacteristic
269C23#1306329711yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4#1306330611yescharacteristic
289C2×C4#1306330711yescharacteristic
290C2×C4#1306330811yescharacteristic
291C2×C4#1306331111yescharacteristic
292C2×C4#1306331811yescharacteristic
293C2×C4#1306331811yescharacteristic
294C2×C4C2×#1062188211yescharacteristic
295C2×C4#1306334511yescharacteristic
296C2×C4#1306334611yescharacteristic
297C2×C4#1306334811yescharacteristic
298C2×C4#1306335411yescharacteristic
299C2×C4#1306335511yescharacteristic
300C2×C4#1306335611yescharacteristic
301C2×C4#1306335711yescharacteristic
302C8—81no—
303C8—3441no—
304C8—3441no—
305C8—1721no—
306C8—1721no—
307C22#1458282711yescharacteristic
308C22#1458311911yescharacteristic
309C22#1458312311yescharacteristic
310C22#1458313311yescharacteristic
311C22#1458315511yescharacteristic
312C22#1458316011yescharacteristic
313C22#1458316411yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—161no—
319C4—6881no—
320C4#1458321011yescharacteristic
321C4#1458321211yescharacteristic
322C4#1458323711yescharacteristic
323C4#1458323811yescharacteristic
324C4#1458323911yescharacteristic
325C4#1458324011yescharacteristic
326C4#1458325511yescharacteristic
327C4#1458326611yescharacteristic
328C2#1913403711yescharacteristic
329C2#1913404111yescharacteristic
330C2#1913417511yescharacteristic
331C2#1913417911yescharacteristic
332C2#1913601611yescharacteristic
333C2#1913602111yescharacteristic
334C2#1913604311yescharacteristic
subgroupG/H
centerC23#13063297
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1803C2
socle, prime radicalC23×C43#121
hypercenter#1803D43
hypocenterC43#10623
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
190. C43#10623semidirect

Maximal subgroups

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

subgroupindex
#191355322
#191347222
#191346002
#191324792
#191324782
#191324292
C43×#18032
#1062343