Finite Group Databasebeta

← #25001359

Subgroups — #25001359

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#19135531C211yesmaximal, characteristic
2#19134597C211yesmaximal, characteristic
3#19134597C211yesmaximal, characteristic
4#19132478C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic
6#19132430C211yesmaximal, characteristic
7C43×#1834C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063248—21no—
13C2×#13063248—21no—
14#14582661—21no—
15#14582661—21no—
16#14582653—21no—
17#14582653—21no—
18C2×C4×C8×C43C2211yescharacteristic
19C43×#384C2211yescharacteristic
20C43×#384C2211yescharacteristic
21C43×#340—21no—
22C43×#340—21no—
23C22×Dic86D411yescharacteristic
24C22×C43⋊C8—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C4×Dic86—21no—
28C4×Dic86—21no—
29C4×Dic86—21no—
30C4×Dic86—21no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×C4×Dic43—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40#13063248—42no—
41#13063248—42no—
42C22×C8×C43D411yescharacteristic
43C22×C8×C43D411yescharacteristic
44C2×C4⋊C4×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×C43—21no—
50C2×C42×C43C2311yescharacteristic
51C4×C8×C43—21no—
52C4×C8×C43—21no—
53C22×C4×C43—41no—
54C22×C4×C43—41no—
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43#4111yescharacteristic
58C22×Dic43—21no—
59C22×Dic43—21no—
60C2×Dic86—21no—
61C2×Dic86—21no—
62C2×Dic86—21no—
63C2×Dic86—21no—
64C2×Dic86—21no—
65C2×Dic86SD1612yes—
66C2×C8×C43—21no—
67C2×C8×C43—21no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C4⋊C4×C43—41no—
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—41no—
80C4⋊C4×C43—81no—
81C4⋊C4×C43—81no—
82C42×C43#4111yescharacteristic
83C42×C43#4111yescharacteristic
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90C4×Dic43—41no—
91C4×Dic43—41no—
92C2×C43⋊C8—41no—
93C2×C43⋊C8—41no—
94C2×C43⋊C8—41no—
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
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—81no—
105C2×C4×C43—81no—
106C2×C4×C43—81no—
107C2×C4×C43—81no—
108C2×C4×C43—81no—
109C2×C4×C43—81no—
110C2×C4×C43#12311yescharacteristic
111C2×C4×C43#12311yescharacteristic
112C2×C4×C43#12311yescharacteristic
113C2×C4×C43#12411yescharacteristic
114C2×C4×C43#12611yescharacteristic
115C2×C4×C43#12611yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43#13511yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—22no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130Dic86—22no—
131Dic86—22no—
132Dic86—41no—
133Dic86—41no—
134C8×C43—41no—
135C8×C43—41no—
136C43⋊C8—81no—
137C43⋊C8—81no—
138C43⋊C8—81no—
139#10626—431nomaximal, Sylow
140C22×C43#39711yescharacteristic
141C22×C43#46411yescharacteristic
142C22×C43#46411yescharacteristic
143C22×C43#46511yescharacteristic
144C22×C43#46811yescharacteristic
145C22×C43#47211yescharacteristic
146C22×C43#47311yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—161no—
150C4×C43—161no—
151C4×C43#48111yescharacteristic
152C4×C43#48211yescharacteristic
153C4×C43#48311yescharacteristic
154C4×C43#48511yescharacteristic
155C4×C43#48511yescharacteristic
156C4×C43#48511yescharacteristic
157C4×C43#48811yescharacteristic
158C4×C43#49111yescharacteristic
159Dic43—42no—
160Dic43—81no—
161#1984—431no—
162#1834D4311yescharacteristic
163#1803—431no—
164#1803—431no—
165#1296—431no—
166#1296—431no—
167#1277—431no—
168C2×C43#167811yescharacteristic
169C2×C43#168011yescharacteristic
170C2×C43#169811yescharacteristic
171C2×C43#170011yescharacteristic
172C2×C43#207411yescharacteristic
173C2×C43#207711yescharacteristic
174C2×C43#207811yescharacteristic
175C2×C4×Q8—431no—
176C2×C4⋊C8—431no—
177C2×C4⋊C8—431no—
178C2×C4⋊C8—431no—
179C2×#103—861no—
180C2×#103—861no—
181C2×C4×C8C2×D4311yescharacteristic
182#384C2×D4311yescharacteristic
183#384C2×D4311yescharacteristic
184#340—21no—
185#340—21no—
186#340—861no—
187#340—861no—
188#336—861no—
189#336—861no—
190C43#1062611yescharacteristic, complemented, Sylow
191C22×Q8—431no—
192C22×C8—861no—
193C22×C8—861no—
194C22×C8—861no—
195C22×C8C22⋊D4311yescharacteristic
196C22×C8C22⋊D4311yescharacteristic
197C4×Q8—861no—
198C4×Q8—861no—
199C4×Q8—861no—
200C4×Q8—861no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C42—861no—
210C2×C42C22×D4311yescharacteristic
211C4⋊C8—861no—
212C4⋊C8—861no—
213C4⋊C8—861no—
214C4⋊C8—861no—
215C4⋊C8—861no—
216C4⋊C8—861no—
217#103—1722no—
218#103—1722no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—432no—
222C2×Q8—861no—
223C2×Q8—861no—
224C2×Q8—861no—
225C2×Q8—861no—
226C2×Q8—861no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4D4×D4311yescharacteristic
232C22×C4#1062190011yescharacteristic
233C22×C4C2×C22⋊D4311yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8—1721no—
243C2×C8—1721no—
244C2×C8—1721no—
245C2×C8—1721no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C42—1721no—
264C42—1721no—
265C42#1062189811yescharacteristic
266C42#1062189811yescharacteristic
267C42#1062190211yescharacteristic
268C42#1062190211yescharacteristic
269C23#1306329611yescharacteristic
270Q8—862no—
271Q8—862no—
272Q8—1721no—
273Q8—1721no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—862no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4#1306330811yescharacteristic
289C2×C4#1306331011yescharacteristic
290C2×C4#1306331011yescharacteristic
291C2×C4#1306331411yescharacteristic
292C2×C4#1306332011yescharacteristic
293C2×C4#1306332011yescharacteristic
294C2×C4SD16×D4311yescharacteristic
295C2×C4#1306334511yescharacteristic
296C2×C4#1306334511yescharacteristic
297C2×C4#1306334611yescharacteristic
298C2×C4#1306335211yescharacteristic
299C2×C4#1306335411yescharacteristic
300C2×C4#1306335511yescharacteristic
301C2×C4#1306335511yescharacteristic
302C8—41no—
303C8—41no—
304C8—3441no—
305C8—3441no—
306C8—3441no—
307C22#1458282511yescharacteristic
308C22#1458311811yescharacteristic
309C22#1458311811yescharacteristic
310C22#1458312511yescharacteristic
311C22#1458314211yescharacteristic
312C22#1458316611yescharacteristic
313C22#1458317111yescharacteristic
314C4—21no—
315C4—21no—
316C4—161no—
317C4—161no—
318C4—3441no—
319C4—1722no—
320C4#1458321911yescharacteristic
321C4#1458322511yescharacteristic
322C4#1458323111yescharacteristic
323C4#1458324011yescharacteristic
324C4#1458324011yescharacteristic
325C4#1458324311yescharacteristic
326C4#1458325611yescharacteristic
327C4#1458326911yescharacteristic
328C2#1913400811yescharacteristic
329C2#1913402211yescharacteristic
330C2#1913413211yescharacteristic
331C2#1913414611yescharacteristic
332C2#1913601411yescharacteristic
333C2#1913602911yescharacteristic
334C2#1913603611yescharacteristic
subgroupG/H
centerC23#13063296
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1834C2
socle, prime radicalC23×C43#121
hypercenter#1834D43
hypocenterC43#10626
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
190. C43#10626semidirect

Maximal subgroups

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

subgroupindex
#191355312
#191345972
#191324782
#191324302
C43×#18342
#1062643