Finite Group Databasebeta

← #24994937

Subgroups — #24994937

Order 11008.

398 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#19135555C211yesmaximal, characteristic
2#19135518C211yesmaximal, characteristic
3C4⋊C4×C43⋊C8C211yesmaximal, characteristic
4C2×#14582646C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C43×#1948C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063248—21no—
12C2×#13063248—21no—
13C2×C4×C43⋊C8—21no—
14C2×C4×C43⋊C8C2211yescharacteristic
15#14582661—21no—
16#14582661—21no—
17#14582654—21no—
18#14582646C414yescomplemented
19C2×#106×C43—21no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C43×#384C2211yescharacteristic
22C4×C4⋊C4×C43C2211yescharacteristic
23C43×#340—21no—
24C22×Dic86—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C22×C43⋊C8D411yescharacteristic
28C22×C43⋊C8D411yescharacteristic
29#13063325—21no—
30#13063325—21no—
31#13063325—21no—
32#13063325C2×C412yes—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)C2×C412yes—
39#13063248—42no—
40#13063248—42no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8—21no—
43C4×C43⋊C8—42no—
44C22×C8×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C42×C43—21no—
51C2×C42×C43C2311yescharacteristic
52#106×C43—42no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43C2×C412yes—
55#95×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43#4111yescharacteristic
62C22×Dic43—41no—
63C2×Dic86—22no—
64C2×Dic86—41no—
65C2×Dic86—41no—
66C2×Dic86—41no—
67C2×Dic86—41no—
68C2×Dic86—41no—
69C2×C8×C43—22no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—81no—
79C4⋊C4×C43D812yes—
80C4⋊C4×C43SD1612yes—
81C42×C43—41no—
82C42×C43—41no—
83C42×C43C22×C411yescharacteristic
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C42×C43#4111yescharacteristic
87C4⋊Dic43—22no—
88C4⋊Dic43—22no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—22no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8SD1612yes—
103C23×C43#12111yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43#11711yescharacteristic
116C2×C4×C43C4×D411yescharacteristic
117C2×C4×C43C4×D411yescharacteristic
118C2×C4×C43#12311yescharacteristic
119C2×C4×C43#12411yescharacteristic
120C2×C4×C43#12611yescharacteristic
121C2×C4×C43C2×D811yescharacteristic
122C2×C4×C43C2×SD1611yescharacteristic
123C2×C4×C43C2×SD1611yescharacteristic
124C2×C4×C43#13511yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×Dic43—42no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132Dic86—42no—
133Dic86—42no—
134Dic86—81no—
135Dic86—81no—
136C8×C43—42no—
137C43⋊C8—22no—
138C43⋊C8—42no—
139C43⋊C8—41no—
140C43⋊C8—81no—
141#9565—431nomaximal, Sylow
142C22×C43#38811yescharacteristic
143C22×C43#46111yescharacteristic
144C22×C43#46411yescharacteristic
145C22×C43#46511yescharacteristic
146C22×C43#46611yescharacteristic
147C22×C43#47111yescharacteristic
148C22×C43#47311yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—42no—
152C4×C43—42no—
153C4×C43—161no—
154C4×C43C4×D811yescharacteristic
155C4×C43C4×SD1611yescharacteristic
156C4×C43C4×SD1611yescharacteristic
157C4×C43#44111yescharacteristic
158C4×C43#48311yescharacteristic
159C4×C43#48511yescharacteristic
160C4×C43#48611yescharacteristic
161C4×C43#48811yescharacteristic
162Dic43—82no—
163#1990—431no—
164#1981—431no—
165#1948D4311yescharacteristic
166C8×C4⋊C4—431no—
167C2×#332—431no—
168#1296—431no—
169#1277—431no—
170C2×C43#167111yescharacteristic
171C2×C43#167311yescharacteristic
172C2×C43#168011yescharacteristic
173C2×C43#168211yescharacteristic
174C2×C43#192711yescharacteristic
175C2×C43#193011yescharacteristic
176C2×C43#193411yescharacteristic
177C2×C4⋊Q8—431no—
178C2×#106—21no—
179C2×C4⋊C8—431no—
180C2×C4⋊C8—431no—
181C2×C4⋊C8C2×D4311yescharacteristic
182C2×#103—861no—
183C2×#103—861no—
184C2×C4×C8—431no—
185C2×C4×C8—861no—
186#384C2×D4311yescharacteristic
187C4×C4⋊C4C2×D4311yescharacteristic
188#340—21no—
189#340—861no—
190#340—861no—
191#336—861no—
192#332—434no—
193C43#956511yescharacteristic, complemented, Sylow
194C22×Q8—861no—
195C22×C8—21no—
196C22×C8—431no—
197C22×C8—431no—
198C22×C8—861no—
199C22×C8—861no—
200C4⋊Q8—432no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4C22⋊D4311yescharacteristic
210C2×C4⋊C4C22⋊D4311yescharacteristic
211C2×C42—21no—
212C2×C42C22×D4311yescharacteristic
213#106—42no—
214C4⋊C8—21no—
215C4⋊C8—432no—
216C4⋊C8—861no—
217C4⋊C8—861no—
218C4⋊C8—861no—
219C4⋊C8C4×D4312yes—
220#103—1722no—
221#103—1722no—
222C4×C8—861no—
223C4×C8—861no—
224C4×C8—1722no—
225#95—21no—
226C2×Q8—862no—
227C2×Q8—1721no—
228C2×Q8—1721no—
229C2×Q8—1721no—
230C2×Q8—1721no—
231C2×Q8—1721no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—1721no—
236C22×C4D4×D4311yescharacteristic
237C22×C4#1062190011yescharacteristic
238C22×C4C2×C22⋊D4311yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—432no—
243C2×C8—861no—
244C2×C8—861no—
245C2×C8—862no—
246C2×C8—861no—
247C2×C8—861no—
248C2×C8—861no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8—1721no—
252C2×C8—1721no—
253C2×C8—1721no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—81no—
261C4⋊C4—862no—
262C4⋊C4—862no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4#1062188212yes—
266C4⋊C4#1062188412yes—
267C42—41no—
268C42—41no—
269C42C2×C4×D4311yescharacteristic
270C42#1062189811yescharacteristic
271C42#1062190211yescharacteristic
272C42#1062190211yescharacteristic
273C23#1306329711yescharacteristic
274Q8—3441no—
275Q8—3441no—
276Q8—1722no—
277Q8—1722no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
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—1722no—
292C2×C4#1306328311yescharacteristic
293C2×C4C4×C22⋊D4311yescharacteristic
294C2×C4#1306328711yescharacteristic
295C2×C4#1306331011yescharacteristic
296C2×C4#1306331411yescharacteristic
297C2×C4#1306332011yescharacteristic
298C2×C4C2×#1062188211yescharacteristic
299C2×C4SD16×D4311yescharacteristic
300C2×C4C2×#1062188411yescharacteristic
301C2×C4#1306334511yescharacteristic
302C2×C4#1306334511yescharacteristic
303C2×C4#1306334611yescharacteristic
304C2×C4#1306335411yescharacteristic
305C2×C4#1306335411yescharacteristic
306C8—42no—
307C8—862no—
308C8—3441no—
309C8—1722no—
310C8—1721no—
311C22#1458278911yescharacteristic
312C22#1458310211yescharacteristic
313C22#1458311911yescharacteristic
314C22#1458313011yescharacteristic
315C22#1458313311yescharacteristic
316C22#1458316011yescharacteristic
317C22#1458317211yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—161no—
323C4—3442no—
324C4C4×#1062188211yescharacteristic
325C4#1458298611yescharacteristic
326C4C4×#1062188411yescharacteristic
327C4#1458300511yescharacteristic
328C4#1458323111yescharacteristic
329C4#1458324311yescharacteristic
330C4#1458324711yescharacteristic
331C4#1458325611yescharacteristic
332C2#1913397211yescharacteristic
333C2#1913398211yescharacteristic
334C2#1913402311yescharacteristic
335C2#1913403711yescharacteristic
336C2#1913522811yescharacteristic
337C2#1913524911yescharacteristic
338C2#1913527711yescharacteristic
subgroupG/H
centerC23#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1948C2
socle, prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1948D43
hypocenterC43#9565
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
18. #14582646C4semidirect
193. C43#9565semidirect

Maximal subgroups

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

subgroupindex
#191355552
#191355182
C4⋊C4×C43⋊C82
C2×#145826462
#191324782
#191324292
C43×#19482
#956543