Finite Group Databasebeta

← #25001310

Subgroups — #25001310

Order 11008.

366 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135532C211yesmaximal, characteristic
2#19134754C211yesmaximal, characteristic
3#19134600C211yesmaximal, characteristic
4#19132479C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C43×#1803C211yesmaximal, characteristic
8C2×#13063258—21no—
9C2×#13063258—21no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063249—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14#14582769C2211yescharacteristic
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—
30#13063258—42no—
31#13063258—42no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36#13063249—42no—
37C4×C43⋊C8—21no—
38C4×C43⋊C8—21no—
39C22×Q8×C43D411yescharacteristic
40C22×C8×C43—21no—
41C4×Q8×C43—21no—
42C4×Q8×C43—21no—
43C4×Q8×C43—21no—
44C4×Q8×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C42×C43—21no—
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54#103×C43—42no—
55C2×Q8×C43—21no—
56C2×Q8×C43—21no—
57C2×Q8×C43—21no—
58C2×Q8×C43—21no—
59C2×Q8×C43—21no—
60C2×Q8×C43D812yes—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43#4111yescharacteristic
67C22×Dic43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—81no—
80C42×C43—41no—
81C42×C43—41no—
82C42×C43#4111yescharacteristic
83C42×C43#4111yescharacteristic
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—81no—
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—
101C2×C43⋊C8SD1612yes—
102C2×C43⋊C8Q1612yes—
103C23×C43#12111yescharacteristic
104Q8×C43—22no—
105Q8×C43—22no—
106Q8×C43—41no—
107Q8×C43—41no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—22no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—81no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43#12311yescharacteristic
121C2×C4×C43#12311yescharacteristic
122C2×C4×C43#12411yescharacteristic
123C2×C4×C43#12611yescharacteristic
124C2×C4×C43#12611yescharacteristic
125C2×C4×C43C2×D811yescharacteristic
126C2×C4×C43C2×SD1611yescharacteristic
127C2×C4×C43C2×Q1611yescharacteristic
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×C4×C43#13711yescharacteristic
132C2×C4×C43#13711yescharacteristic
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C8×C43—81no—
137C43⋊C8—22no—
138C43⋊C8—22no—
139C43⋊C8—81no—
140C43⋊C8—81no—
141#10617—431nomaximal, Sylow
142C22×C43#39711yescharacteristic
143C22×C43#46011yescharacteristic
144C22×C43#46211yescharacteristic
145C22×C43#46611yescharacteristic
146C22×C43#47011yescharacteristic
147C22×C43#47211yescharacteristic
148C22×C43#47311yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—42no—
152C4×C43—81no—
153C4×C43—161no—
154C4×C43#48011yescharacteristic
155C4×C43#48011yescharacteristic
156C4×C43#48311yescharacteristic
157C4×C43#48411yescharacteristic
158C4×C43#48511yescharacteristic
159C4×C43#48511yescharacteristic
160C4×C43#48711yescharacteristic
161C4×C43#48911yescharacteristic
162Dic43—161no—
163#1984—431no—
164#1845—431no—
165#1803—431no—
166#1803D4311yescharacteristic
167#1296—431no—
168#1296—431no—
169#1277—431no—
170C2×C43#166811yescharacteristic
171C2×C43#167411yescharacteristic
172C2×C43#169011yescharacteristic
173C2×C43#169611yescharacteristic
174C2×C43#207211yescharacteristic
175C2×C43#207511yescharacteristic
176C2×C43#207811yescharacteristic
177C2×C4×Q8C2×D4311yescharacteristic
178C2×#107—861no—
179C2×#107—861no—
180C2×C4⋊C8—431no—
181C2×C4⋊C8—431no—
182C2×C4⋊C8C2×D4311yescharacteristic
183C2×#103—21no—
184C2×#103—861no—
185C2×C4×C8—431no—
186#384—431no—
187#384C2×D4311yescharacteristic
188#340—21no—
189#340—861no—
190#336—861no—
191#336—861no—
192C43#1061711yescharacteristic, complemented, Sylow
193C22×Q8C22⋊D4311yescharacteristic
194C22×C8—21no—
195C22×C8—431no—
196C22×C8—431no—
197C22×C8—861no—
198C22×C8—861no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4C22⋊D4311yescharacteristic
211C2×C42—21no—
212C2×C42C22×D4311yescharacteristic
213#107—1722no—
214#107—1722no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—861no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221#103—42no—
222#103—1722no—
223C4×C8—861no—
224C4×C8—861no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8#1062188212yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—1721no—
235C22×C4D4×D4311yescharacteristic
236C22×C4#1062190011yescharacteristic
237C22×C4C2×C22⋊D4311yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—432no—
242C2×C8—432no—
243C2×C8—861no—
244C2×C8—861no—
245C2×C8—861no—
246C2×C8—861no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8—1721no—
252C2×C8—1721no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—3441no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C42—41no—
268C42—41no—
269C42#1062189811yescharacteristic
270C42#1062189811yescharacteristic
271C42#1062190011yescharacteristic
272C42#1062190011yescharacteristic
273C23#1306329711yescharacteristic
274Q8—22no—
275Q8—22no—
276Q8—41no—
277Q8—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—3441no—
290C2×C4—3441no—
291C2×C4—3441no—
292C2×C4#1306330611yescharacteristic
293C2×C4#1306330711yescharacteristic
294C2×C4#1306330811yescharacteristic
295C2×C4#1306331111yescharacteristic
296C2×C4#1306331811yescharacteristic
297C2×C4#1306331811yescharacteristic
298C2×C4C2×#1062188211yescharacteristic
299C2×C4SD16×D4311yescharacteristic
300C2×C4Q16×D4311yescharacteristic
301C2×C4#1306334511yescharacteristic
302C2×C4#1306335211yescharacteristic
303C2×C4#1306335511yescharacteristic
304C2×C4#1306335611yescharacteristic
305C2×C4#1306335711yescharacteristic
306C8—81no—
307C8—862no—
308C8—862no—
309C8—3441no—
310C8—3441no—
311C22#1458282711yescharacteristic
312C22#1458309711yescharacteristic
313C22#1458310711yescharacteristic
314C22#1458313311yescharacteristic
315C22#1458315511yescharacteristic
316C22#1458316711yescharacteristic
317C22#1458317211yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—81no—
322C4—161no—
323C4—6881no—
324C4#1458321011yescharacteristic
325C4#1458321211yescharacteristic
326C4#1458322811yescharacteristic
327C4#1458323311yescharacteristic
328C4#1458323711yescharacteristic
329C4#1458324011yescharacteristic
330C4#1458324811yescharacteristic
331C4#1458326011yescharacteristic
332C2#1913395311yescharacteristic
333C2#1913398711yescharacteristic
334C2#1913408711yescharacteristic
335C2#1913412111yescharacteristic
336C2#1913600611yescharacteristic
337C2#1913602111yescharacteristic
338C2#1913603811yescharacteristic
subgroupG/H
centerC23#13063297
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1803C2
socle, prime radicalC23×C43#121
hypercenter#1803D43
hypocenterC43#10617
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
192. C43#10617semidirect

Maximal subgroups

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

subgroupindex
#191355322
#191347542
#191346002
#191324792
#191324782
#191324292
C43×#18032
#1061743