Finite Group Databasebeta

← #24995017

Subgroups — #24995017

Order 11008.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135557C211yesmaximal, characteristic
2#19135544C211yesmaximal, characteristic
3#19135354C211yesmaximal, characteristic
4#19134465C211yesmaximal, characteristic
5#19132479C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C2×C43×#333C211yesmaximal, characteristic
8C2×#13063259—21no—
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×#13063235—21no—
11C2×C4×C43⋊C8C2211yescharacteristic
12#14582769C2211yescharacteristic
13C4×C4⋊Dic43C2211yescharacteristic
14#14582662—21no—
15#14582661—21no—
16#14582661—21no—
17#14582661—21no—
18#14582661—21no—
19#14582653—21no—
20C2×C4⋊Q8×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C43×#333C414yescomplemented
24C22×C43⋊C8—21no—
25C22×C43⋊C8D411yescharacteristic
26C22×C43⋊C8D411yescharacteristic
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4×Dic43—21no—
33#13063259—42no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36#13063235—42no—
37C4×C43⋊C8—21no—
38C4×C43⋊C8—21no—
39C43⋊#95—21no—
40C22×Q8×C43—21no—
41C22×C8×C43—21no—
42C22×C8×C43—21no—
43C4⋊Q8×C43—21no—
44C4⋊Q8×C43—21no—
45C4⋊Q8×C43—21no—
46C4⋊Q8×C43C2×C412yes—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43C2×C412yes—
53C4⋊C8×C43C2×C412yes—
54C2×Q8×C43—22no—
55C2×Q8×C43—41no—
56C2×Q8×C43—81no—
57C2×Q8×C43—81no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43#4111yescharacteristic
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—41no—
65C2×C8×C43—22no—
66C2×C8×C43—22no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C42×C43C22×C411yescharacteristic
76C42×C43#4111yescharacteristic
77C42×C43#4111yescharacteristic
78C42×C43#4111yescharacteristic
79C4⋊Dic43—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—41no—
84C4⋊Dic43—41no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—81no—
88C4×Dic43—41no—
89C4×Dic43—41no—
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⋊C8Q1612yes—
99C23×C43#12111yescharacteristic
100Q8×C43—82no—
101Q8×C43—82no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—42no—
105C2×C4×C43—81no—
106C2×C4×C43—81no—
107C2×C4×C43#11711yescharacteristic
108C2×C4×C43C4×D411yescharacteristic
109C2×C4×C43C4×D411yescharacteristic
110C2×C4×C43#12311yescharacteristic
111C2×C4×C43#12411yescharacteristic
112C2×C4×C43#12611yescharacteristic
113C2×C4×C43C2×Q1611yescharacteristic
114C2×C4×C43#13511yescharacteristic
115C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C43#13711yescharacteristic
118C2×C4×C43#13711yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—81no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C8×C43—42no—
131C8×C43—42no—
132C43⋊C8—22no—
133C43⋊C8—41no—
134C43⋊C8—81no—
135#9576—431nomaximal, Sylow
136C22×C43#38811yescharacteristic
137C22×C43#46211yescharacteristic
138C22×C43#46311yescharacteristic
139C22×C43#46811yescharacteristic
140C22×C43#47011yescharacteristic
141C22×C43#47111yescharacteristic
142C22×C43#47211yescharacteristic
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—82no—
146C4×C43C4×Q1611yescharacteristic
147C4×C43#44011yescharacteristic
148C4×C43#44011yescharacteristic
149C4×C43#44111yescharacteristic
150C4×C43#48411yescharacteristic
151C4×C43#48511yescharacteristic
152C4×C43#48911yescharacteristic
153C4×C43#49111yescharacteristic
154Dic43—81no—
155Dic43—81no—
156Dic43—161no—
157#1990—431no—
158#1987—431no—
159#1947—431no—
160#1770—431no—
161C2×#333D4311yescharacteristic
162#1296—431no—
163#1277—431no—
164C2×C43#169211yescharacteristic
165C2×C43#169611yescharacteristic
166C2×C43#169711yescharacteristic
167C2×C43#170311yescharacteristic
168C2×C43#192811yescharacteristic
169C2×C43#193111yescharacteristic
170C2×C43#193511yescharacteristic
171C2×C4⋊Q8C2×D4311yescharacteristic
172C2×#107—861no—
173C2×C4⋊C8—431no—
174C2×C4⋊C8C2×D4311yescharacteristic
175C2×C4⋊C8C2×D4311yescharacteristic
176C2×#97—861no—
177C2×C4×C8—431no—
178#384—431no—
179C4×C4⋊C4—431no—
180#340—861no—
181#340—861no—
182#340—861no—
183#340—861no—
184#340—861no—
185#336—861no—
186#333Dic4314yescomplemented
187C43#957611yescharacteristic, complemented, Sylow
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—431no—
192C22×C8—431no—
193C22×C8—861no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C2×Dic4312yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C42—861no—
206C2×C42C22×D4311yescharacteristic
207#107—1722no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—861no—
211C4⋊C8—861no—
212C4⋊C8C2×Dic4312yes—
213C4⋊C8C2×Dic4312yes—
214#97—1722no—
215C4×C8—861no—
216C4×C8—861no—
217#95—861no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—41no—
223C22×C4—861no—
224C22×C4—861no—
225C22×C4—1721no—
226C22×C4#1062189811yescharacteristic
227C22×C4D4×D4311yescharacteristic
228C22×C4D4×D4311yescharacteristic
229C2×C8—22no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—432no—
236C2×C8—861no—
237C2×C8—861no—
238C2×C8—861no—
239C2×C8—861no—
240C2×C8—861no—
241C2×C8—1721no—
242C2×C8—1721no—
243C2×C8—1721no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—3441no—
253C4⋊C4—1721no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C42—1721no—
258C42—1721no—
259C42#1062189811yescharacteristic
260C42#1062190011yescharacteristic
261C42#1062190011yescharacteristic
262C42C22×Dic4311yescharacteristic
263C23#1306329811yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—3441no—
272C2×C4—3441no—
273C2×C4—3441no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4#1306328411yescharacteristic
281C2×C4D4×Dic4311yescharacteristic
282C2×C4D4×Dic4311yescharacteristic
283C2×C4#1306330711yescharacteristic
284C2×C4#1306331111yescharacteristic
285C2×C4#1306331811yescharacteristic
286C2×C4Q16×D4311yescharacteristic
287C2×C4#1306334811yescharacteristic
288C2×C4#1306335211yescharacteristic
289C2×C4#1306335211yescharacteristic
290C2×C4#1306335411yescharacteristic
291C2×C4#1306335411yescharacteristic
292C2×C4#1306335711yescharacteristic
293C2×C4#1306335711yescharacteristic
294C8—42no—
295C8—42no—
296C8—862no—
297C8—3441no—
298C8—1721no—
299C22#1458279211yescharacteristic
300C22#1458310811yescharacteristic
301C22#1458311711yescharacteristic
302C22#1458314811yescharacteristic
303C22#1458315611yescharacteristic
304C22#1458316111yescharacteristic
305C22#1458316811yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—3441no—
310C4—3441no—
311C4—6881no—
312C4Q16×Dic4311yescharacteristic
313C4#1458300011yescharacteristic
314C4#1458300011yescharacteristic
315C4#1458300611yescharacteristic
316C4#1458323311yescharacteristic
317C4#1458323911yescharacteristic
318C4#1458326011yescharacteristic
319C4#1458326611yescharacteristic
320C2#1913410411yescharacteristic
321C2#1913412211yescharacteristic
322C2#1913413111yescharacteristic
323C2#1913417311yescharacteristic
324C2#1913523811yescharacteristic
325C2#1913525911yescharacteristic
326C2#1913528711yescharacteristic
subgroupG/H
centerC23#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#333C2
socle, prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenterC2×#333D43
hypocenterC43#9576
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
23. C43×#333C4semidirect
186. #333Dic43semidirect
187. C43#9576semidirect

Maximal subgroups

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

subgroupindex
#191355572
#191355442
#191353542
#191344652
#191324792
#191324292
C2×C43×#3332
#957643