Finite Group Databasebeta

← #24994949

Subgroups — #24994949

Order 11008.

382 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#19135544C211yesmaximal, characteristic
2#19135356C211yesmaximal, characteristic
3C8×C4⋊Dic43C211yesmaximal, characteristic
4C2×#14582648C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic
6#19132430C211yesmaximal, characteristic
7C43×#1990C211yesmaximal, characteristic
8C2×#13063256—21no—
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×C8×Dic43—21no—
13C4×C4⋊Dic43C2211yescharacteristic
14#14582661—21no—
15#14582661—21no—
16#14582661—21no—
17#14582653—21no—
18#14582648C414yescomplemented
19C2×C4⋊Q8×C43C2211yescharacteristic
20C2×C4×C8×C43C2211yescharacteristic
21C43×#384C2211yescharacteristic
22C43×#340—21no—
23C43×#340—21no—
24C22×C43⋊C8—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×C4⋊Dic43D411yescharacteristic
29C2×C4×Dic43—21no—
30#13063256—42no—
31C4⋊(C43⋊C8)—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)C2×C412yes—
36C4⋊(C43⋊C8)C2×C412yes—
37C8×Dic43—42no—
38C43⋊#95—21no—
39C22×Q8×C43—21no—
40C22×C8×C43D411yescharacteristic
41C22×C8×C43D411yescharacteristic
42C4⋊Q8×C43—21no—
43C4⋊Q8×C43—21no—
44C4⋊Q8×C43—21no—
45C4⋊Q8×C43C2×C412yes—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×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—
54C2×Q8×C43—22no—
55C2×Q8×C43—41no—
56C2×Q8×C43—81no—
57C2×Q8×C43—81no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43#4111yescharacteristic
63C22×Dic43—21no—
64C22×Dic43—21no—
65C2×C8×C43—21no—
66C2×C8×C43—21no—
67C2×C8×C43—21no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43SD1612yes—
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
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×C43C22×C411yescharacteristic
81C42×C43#4111yescharacteristic
82C42×C43#4111yescharacteristic
83C42×C43#4111yescharacteristic
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43SD1612yes—
87C4⋊Dic43Q1612yes—
88C4×Dic43—41no—
89C4×Dic43—41no—
90C2×C43⋊C8—22no—
91C2×C43⋊C8—22no—
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—
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—81no—
108C2×C4×C43—81no—
109C2×C4×C43—81no—
110C2×C4×C43#11711yescharacteristic
111C2×C4×C43C4×D411yescharacteristic
112C2×C4×C43C4×D411yescharacteristic
113C2×C4×C43#12311yescharacteristic
114C2×C4×C43#12411yescharacteristic
115C2×C4×C43#12611yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43C2×SD1611yescharacteristic
118C2×C4×C43C2×Q1611yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C8×C43—22no—
131C8×C43—41no—
132C43⋊C8—42no—
133C43⋊C8—42no—
134C43⋊C8—81no—
135#9567—431nomaximal, Sylow
136C22×C43#38811yescharacteristic
137C22×C43#46111yescharacteristic
138C22×C43#46411yescharacteristic
139C22×C43#46511yescharacteristic
140C22×C43#46711yescharacteristic
141C22×C43#47111yescharacteristic
142C22×C43#47211yescharacteristic
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—82no—
146C4×C43—161no—
147C4×C43C4×SD1611yescharacteristic
148C4×C43C4×SD1611yescharacteristic
149C4×C43C4×Q1611yescharacteristic
150C4×C43#44111yescharacteristic
151C4×C43#48311yescharacteristic
152C4×C43#48511yescharacteristic
153C4×C43#48711yescharacteristic
154C4×C43#48811yescharacteristic
155Dic43—42no—
156Dic43—42no—
157#1990D4311yescharacteristic
158#1987—431no—
159#1948—431no—
160C8×C4⋊C4—431no—
161C2×#333—431no—
162#1296—431no—
163#1277—431no—
164C2×C43#167111yescharacteristic
165C2×C43#167511yescharacteristic
166C2×C43#167811yescharacteristic
167C2×C43#168411yescharacteristic
168C2×C43#192711yescharacteristic
169C2×C43#193111yescharacteristic
170C2×C43#193311yescharacteristic
171C2×C4⋊Q8C2×D4311yescharacteristic
172C2×#106—861no—
173C2×C4⋊C8—431no—
174C2×C4⋊C8—431no—
175C2×C4⋊C8—431no—
176C2×C4×C8—861no—
177C2×C4×C8C2×D4311yescharacteristic
178#384C2×D4311yescharacteristic
179C4×C4⋊C4—431no—
180#340—21no—
181#340—21no—
182#340—861no—
183#340—861no—
184#340—861no—
185#336—861no—
186#333—434no—
187C43#956711yescharacteristic, complemented, Sylow
188C22×Q8—21no—
189C22×C8—861no—
190C22×C8—861no—
191C22×C8—861no—
192C22×C8C22⋊D4311yescharacteristic
193C22×C8C22⋊D4311yescharacteristic
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C4×D4312yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—431no—
205C2×C42—861no—
206C2×C42C22×D4311yescharacteristic
207#106—1722no—
208C4⋊C8—432no—
209C4⋊C8—432no—
210C4⋊C8—861no—
211C4⋊C8—861no—
212C4⋊C8—861no—
213C4⋊C8—861no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—1722no—
217#95—861no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—861no—
225C22×C4—861no—
226C22×C4D4×D4311yescharacteristic
227C22×C4#1062190011yescharacteristic
228C22×C4C2×C22⋊D4311yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—862no—
235C2×C8—862no—
236C2×C8—1721no—
237C2×C8—1721no—
238C2×C8—1721no—
239C2×C8—1721no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8—1721no—
243C2×C8#1062188412yes—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—432no—
254C4⋊C4—432no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C42—1721no—
258C42—1721no—
259C42C2×C4×D4311yescharacteristic
260C42#1062189811yescharacteristic
261C42#1062190011yescharacteristic
262C42#1062190011yescharacteristic
263C23#1306329611yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—862no—
275C2×C4—862no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4#1306328111yescharacteristic
281C2×C4(C22⋊D43)⋊C411yescharacteristic
282C2×C4C4×C22⋊D4311yescharacteristic
283C2×C4#1306330611yescharacteristic
284C2×C4#1306331111yescharacteristic
285C2×C4#1306331811yescharacteristic
286C2×C4SD16×D4311yescharacteristic
287C2×C4C2×#1062188411yescharacteristic
288C2×C4Q16×D4311yescharacteristic
289C2×C4#1306334511yescharacteristic
290C2×C4#1306334611yescharacteristic
291C2×C4#1306334811yescharacteristic
292C2×C4#1306335511yescharacteristic
293C2×C4#1306335611yescharacteristic
294C8—22no—
295C8—41no—
296C8—3441no—
297C8—1722no—
298C8—1722no—
299C22#1458278711yescharacteristic
300C22#1458310111yescharacteristic
301C22#1458311811yescharacteristic
302C22#1458312511yescharacteristic
303C22#1458313711yescharacteristic
304C22#1458315911yescharacteristic
305C22#1458316611yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—161no—
310C4—1722no—
311C4—1722no—
312C4#1458298411yescharacteristic
313C4C4×#1062188411yescharacteristic
314C4#1458299111yescharacteristic
315C4#1458300411yescharacteristic
316C4#1458322711yescharacteristic
317C4#1458323711yescharacteristic
318C4#1458324811yescharacteristic
319C4#1458325511yescharacteristic
320C2#1913396711yescharacteristic
321C2#1913399111yescharacteristic
322C2#1913400811yescharacteristic
323C2#1913405011yescharacteristic
324C2#1913522611yescharacteristic
325C2#1913525411yescharacteristic
326C2#1913526811yescharacteristic
subgroupG/H
centerC23#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1990C2
socle, prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1990D43
hypocenterC43#9567
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
18. #14582648C4semidirect
187. C43#9567semidirect

Maximal subgroups

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

subgroupindex
#191355442
#191353562
C8×C4⋊Dic432
C2×#145826482
#191324782
#191324302
C43×#19902
#956743