Finite Group Databasebeta

← #24994908

Subgroups — #24994908

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#19135546C211yesmaximal, characteristic
2#19135396C211yesmaximal, characteristic
3#19135351C211yesmaximal, characteristic
4#19134460C211yesmaximal, characteristic
5C2×#14582646C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C43×#1296C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063258—21no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063248—21no—
12C2×#13063248—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14C2×C8×Dic43—21no—
15C4×C4⋊Dic43C2211yescharacteristic
16#14582662—21no—
17#14582662—21no—
18#14582661—21no—
19#14582653—21no—
20#14582646C414yescomplemented
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C43×#384C2211yescharacteristic
24C22×Dic86—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8D411yescharacteristic
27C22×C43⋊C8D411yescharacteristic
28#13063325—21no—
29#13063325—21no—
30#13063325—21no—
31#13063325C2×C412yes—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4×Dic43—21no—
37#13063258—42no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)C2×C412yes—
40#13063248—42no—
41#13063248—42no—
42C4×C43⋊C8—21no—
43C4×C43⋊C8—21no—
44C8×Dic43—42no—
45C43⋊#95—21no—
46C22×C8×C43—21no—
47C22×C8×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43C2×C412yes—
56C22×C4×C43—41no—
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43#4111yescharacteristic
60C22×Dic43—21no—
61C22×Dic43—21no—
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—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—81no—
80C42×C43C22×C411yescharacteristic
81C42×C43#4111yescharacteristic
82C42×C43#4111yescharacteristic
83C42×C43#4111yescharacteristic
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—22no—
87C4⋊Dic43—22no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43SD1612yes—
91C4⋊Dic43Q1612yes—
92C4×Dic43—41no—
93C4×Dic43—41no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—22no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8D812yes—
103C23×C43#12111yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—81no—
107C2×C4×C43—81no—
108C2×C4×C43—81no—
109C2×C4×C43#11711yescharacteristic
110C2×C4×C43C4×D411yescharacteristic
111C2×C4×C43C4×D411yescharacteristic
112C2×C4×C43#12311yescharacteristic
113C2×C4×C43#12411yescharacteristic
114C2×C4×C43#12611yescharacteristic
115C2×C4×C43C2×D811yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43C2×Q1611yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—42no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132Dic86—42no—
133Dic86—42no—
134Dic86—81no—
135Dic86—81no—
136C8×C43—42no—
137C8×C43—81no—
138C43⋊C8—22no—
139C43⋊C8—42no—
140C43⋊C8—41no—
141#9561—431nomaximal, Sylow
142C22×C43#38811yescharacteristic
143C22×C43#45911yescharacteristic
144C22×C43#46411yescharacteristic
145C22×C43#46511yescharacteristic
146C22×C43#46711yescharacteristic
147C22×C43#47111yescharacteristic
148C22×C43#47311yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—161no—
152C4×C43C4×D811yescharacteristic
153C4×C43C4×SD1611yescharacteristic
154C4×C43C4×Q1611yescharacteristic
155C4×C43#44011yescharacteristic
156C4×C43#48011yescharacteristic
157C4×C43#48211yescharacteristic
158C4×C43#48711yescharacteristic
159C4×C43#48811yescharacteristic
160Dic43—42no—
161Dic43—42no—
162Dic43—82no—
163#1988—431no—
164#1956—431no—
165#1947—431no—
166C8×C4⋊C4—431no—
167C2×#332—431no—
168#1296D4311yescharacteristic
169#1277—431no—
170C2×C43#166511yescharacteristic
171C2×C43#166911yescharacteristic
172C2×C43#168011yescharacteristic
173C2×C43#168411yescharacteristic
174C2×C43#192511yescharacteristic
175C2×C43#193011yescharacteristic
176C2×C43#193311yescharacteristic
177C2×C4⋊Q8—431no—
178C2×#107—861no—
179C2×C4⋊C8—431no—
180C2×C4⋊C8C2×D4311yescharacteristic
181C2×C4⋊C8C2×D4311yescharacteristic
182C2×#103—861no—
183C2×#103—861no—
184C2×C4×C8—431no—
185C2×C4×C8—861no—
186#384C2×D4311yescharacteristic
187C4×C4⋊C4—431no—
188#340—861no—
189#340—861no—
190#340—861no—
191#336—861no—
192#332—434no—
193C43#956111yescharacteristic, complemented, Sylow
194C22×Q8—861no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—431no—
198C22×C8—431no—
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—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C42—861no—
212C2×C42C22×D4311yescharacteristic
213#107—1722no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—432no—
218C4⋊C8—861no—
219C4⋊C8C4×D4312yes—
220#103—1722no—
221#103—1722no—
222C4×C8—861no—
223C4×C8—861no—
224C4×C8—1722no—
225#95—861no—
226C2×Q8—862no—
227C2×Q8—1721no—
228C2×Q8—1721no—
229C2×Q8—1721no—
230C2×Q8—1721no—
231C2×Q8—1721no—
232C22×C4—41no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—1721no—
236C22×C4#1062189811yescharacteristic
237C22×C4D4×D4311yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—432no—
246C2×C8—861no—
247C2×C8—861no—
248C2×C8—862no—
249C2×C8—861no—
250C2×C8—861no—
251C2×C8—861no—
252C2×C8—1721no—
253C2×C8—1721no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—432no—
260C4⋊C4—432no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—862no—
264C4⋊C4—862no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C42—1721no—
268C42—1721no—
269C42C2×C4×D4311yescharacteristic
270C42#1062189811yescharacteristic
271C42#1062190011yescharacteristic
272C42#1062190211yescharacteristic
273C23#1306329811yescharacteristic
274Q8—3441no—
275Q8—3441no—
276Q8—1722no—
277Q8—1722no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—862no—
284C2×C4—862no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—1722no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4#1306328211yescharacteristic
293C2×C4(C22⋊D43)⋊C411yescharacteristic
294C2×C4#1306328711yescharacteristic
295C2×C4#1306331011yescharacteristic
296C2×C4#1306331111yescharacteristic
297C2×C4#1306332011yescharacteristic
298C2×C4D8×D4311yescharacteristic
299C2×C4SD16×D4311yescharacteristic
300C2×C4Q16×D4311yescharacteristic
301C2×C4#1306334411yescharacteristic
302C2×C4#1306334611yescharacteristic
303C2×C4#1306334611yescharacteristic
304C2×C4#1306335211yescharacteristic
305C2×C4#1306335711yescharacteristic
306C8—42no—
307C8—81no—
308C8—862no—
309C8—1721no—
310C8—1722no—
311C22#1458278811yescharacteristic
312C22#1458309311yescharacteristic
313C22#1458312411yescharacteristic
314C22#1458312711yescharacteristic
315C22#1458313911yescharacteristic
316C22#1458316111yescharacteristic
317C22#1458317311yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—3442no—
322C4—1722no—
323C4—1722no—
324C4#1458297911yescharacteristic
325C4#1458298611yescharacteristic
326C4#1458299311yescharacteristic
327C4#1458300211yescharacteristic
328C4#1458321411yescharacteristic
329C4#1458322511yescharacteristic
330C4#1458324811yescharacteristic
331C4#1458325211yescharacteristic
332C2#1913393511yescharacteristic
333C2#1913395911yescharacteristic
334C2#1913402811yescharacteristic
335C2#1913405611yescharacteristic
336C2#1913521311yescharacteristic
337C2#1913524811yescharacteristic
338C2#1913526911yescharacteristic
subgroupG/H
centerC23#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1296C2
socle, prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1296D43
hypocenterC43#9561
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
20. #14582646C4semidirect
193. C43#9561semidirect

Maximal subgroups

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

subgroupindex
#191355462
#191353962
#191353512
#191344602
C2×#145826462
#191324292
C43×#12962
#956143