Finite Group Databasebeta

← #24989648

Subgroups — #24989648

Order 11008.

542 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
1C2×C8×D172C211yesmaximal, characteristic
2#19134592C212yesmaximal
3C2×#14582652C211yesmaximal, characteristic, complemented
4#19132478C212yesmaximal, complemented
5C43×#1845C211yesmaximal, characteristic, complemented
6C22×C8×D43—21no—
7C2×C4×D172C2211yescharacteristic
8C8×D172—22no—
9C8×D172C414yescomplemented
10C2×C4⋊(C43⋊C8)C2212yes—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063245—22no—
13C2×(C2×D43)⋊C8—21no—
14#14582661—22no—
15#14582652—22no—
16C2×#107×C43—21no—
17C2×#107×C43—21no—
18C2×C4×C8×C43C2211yescharacteristic
19C43×#384C2212yes—
20C22×D172D411yescharacteristic
21C22×C4×D43—21no—
22C22×C43⋊C8—21no—
23C22×C43⋊C8—22no—
24C2×C8×D43—24no—
25C2×C8×D43—42no—
26C2×C8×D43—42no—
27C4×D172—21no—
28C4×D172—21no—
29C4×D172C2×C412yes—
30C4×D172Q812yes—
31C2×C4⋊Dic43D411yescharacteristic
32C2×(C2×D43)⋊C4—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—22no—
35C4⋊(C43⋊C8)—22no—
36C4⋊(C43⋊C8)C2×C412yes—
37#13063245—44no—
38(C2×D43)⋊C8—24no—
39C22×C8×C43D411yescharacteristic
40C22×C8×C43D411yescharacteristic
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43—22no—
43C2×C4⋊C4×C43—22no—
44C2×C42×C43C2311yescharacteristic
45#107×C43—42no—
46#107×C43—42no—
47C4×C8×C43C2×C412yes—
48C4×C8×C43D412yes—
49C23×D43—21no—
50C22×C4×C43—42no—
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43#4111yescharacteristic
54C22×Dic43—21no—
55C2×D172—21no—
56C2×D172—21no—
57C2×D172—21no—
58C2×D172C4⋊C412yes—
59C2×D172D812yes—
60C2×D172Q1612yes—
61C2×C4×D43—22no—
62C2×C4×D43—22no—
63C2×C4×D43—41no—
64C2×C4×D43—41no—
65C2×C4×D43—41no—
66C2×C4×D43—41no—
67C2×C8×C43—21no—
68C2×C8×C43—21no—
69C2×C8×C43C22⋊C412yes—
70C2×C8×C43C22⋊C412yes—
71C2×C8×C43D812yes—
72C2×C8×C43SD1612yes—
73C4⋊C4×C43—42no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—82no—
78C42×C43C22×C411yescharacteristic
79C42×C43C2×D411yescharacteristic
80C42×C43C2×Q811yescharacteristic
81C42×C43#4111yescharacteristic
82(C2×D43)⋊C4—22no—
83(C2×D43)⋊C4—22no—
84C4⋊Dic43—21no—
85C4⋊Dic43C4⋊C412yes—
86C2×C43⋊C8—22no—
87C2×C43⋊C8—41no—
88C2×C43⋊C8—41no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C8×D43—48no—
93C23×C43#12111yescharacteristic
94C22×D43—22no—
95C22×D43—22no—
96C22×D43—22no—
97C22×D43—41no—
98C22×D43—41no—
99C22×D43—41no—
100C22×D43—41no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—82no—
104C2×C4×C43—82no—
105C2×C4×C43—82no—
106C2×C4×C43C2×C22⋊C411yescharacteristic
107C2×C4×C43C2×C4⋊C411yescharacteristic
108C2×C4×C43#11711yescharacteristic
109C2×C4×C43#12111yescharacteristic
110C2×C4×C43C22⋊Q811yescharacteristic
111C2×C4×C43C22⋊Q811yescharacteristic
112C2×C4×C43C2×D811yescharacteristic
113C2×C4×C43C2×D811yescharacteristic
114C2×C4×C43C2×SD1611yescharacteristic
115C2×C4×C43C2×Q1611yescharacteristic
116C2×C4×C43#13511yescharacteristic
117C2×C4×C43#13511yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C2×Dic43—22no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123D172—22no—
124D172—22no—
125D172—22no—
126D172#10714yescomplemented
127C4×D43—42no—
128C4×D43—42no—
129C4×D43—42no—
130C4×D43—42no—
131C8×C43—22no—
132C8×C43#10214yescomplemented
133C43⋊C8—42no—
134C43⋊C8—82no—
135#8644—431nomaximal, Sylow
136C22×C43#38011yescharacteristic
137C22×C43#45911yescharacteristic
138C22×C43#46111yescharacteristic
139C22×C43#46611yescharacteristic
140C22×C43#46711yescharacteristic
141C22×C43#47211yescharacteristic
142C22×C43#47311yescharacteristic
143C2×D43—24no—
144C2×D43—42no—
145C2×D43—42no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43—42no—
149C2×D43—42no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—162no—
153C4×C43C2×#10211yescharacteristic
154C4×C43#41711yescharacteristic
155C4×C43C2×#10711yescharacteristic
156C4×C43#42711yescharacteristic
157C4×C43#46611yescharacteristic
158C4×C43#46711yescharacteristic
159C4×C43#47411yescharacteristic
160C4×C43#47611yescharacteristic
161Dic43—42no—
162C2×C8×D4—431no—
163#1845D4311yescharacteristic, complemented
164#1802—432no—
165C2×#335—431no—
166#1296—432no—
167C2×C43#166711yescharacteristic
168C2×C43#166911yescharacteristic
169C2×C43#167311yescharacteristic
170C2×C43#167511yescharacteristic
171C2×C43#180211yescharacteristic
172C2×C43#180811yescharacteristic
173C2×C43#181611yescharacteristic
174D43—44no—
175C23×C8—861no—
176C2×C4×D4—431no—
177C8×D4—434no—
178C8×D4—862no—
179C2×#107—21no—
180C2×#107—21no—
181C2×C4⋊C8—431no—
182C2×C4⋊C8—432no—
183C2×#102—862no—
184C2×C22⋊C8—861no—
185C2×C4×C8C2×D4311yescharacteristic
186#384C2×D4312yes—
187#340—862no—
188#335—862no—
189C43#864411yescharacteristic, complemented, Sylow
190C22×D4—431no—
191C23×C4—861no—
192C22×C8—861no—
193C22×C8—864no—
194C22×C8—862no—
195C22×C8—1722no—
196C22×C8—1722no—
197C22×C8C22⋊D4311yescharacteristic
198C22×C8C22⋊D4311yescharacteristic
199C4×D4—432no—
200C4×D4—432no—
201C4×D4—861no—
202C4×D4—861no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—431no—
207C2×C22⋊C4—861no—
208C2×C42C22×D4311yescharacteristic
209#107—42no—
210#107—42no—
211C4⋊C8—432no—
212C4⋊C8—861no—
213C4⋊C8—862no—
214C4⋊C8—862no—
215#102—1724no—
216C22⋊C8—864no—
217C4×C8C4×D4312yes—
218C4×C8D17212yes—
219C24—861no—
220C2×D4—432no—
221C2×D4—432no—
222C2×D4—432no—
223C2×D4—861no—
224C2×D4—861no—
225C2×D4—861no—
226C22×C4—42no—
227C22×C4—861no—
228C22×C4—862no—
229C22×C4—862no—
230C22×C4—1721no—
231C22×C4—1721no—
232C22×C4—1721no—
233C22×C4—1721no—
234C22×C4D4×D4311yescharacteristic
235C22×C4#1062190011yescharacteristic
236C22×C4C2×C22⋊D4311yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—862no—
240C2×C8—1722no—
241C2×C8—1722no—
242C2×C8—1722no—
243C2×C8—1721no—
244C2×C8—1721no—
245C2×C8—1728no—
246C2×C8(C2×D43)⋊C412yes—
247C2×C8(C2×D43)⋊C412yes—
248C2×C8#1062188212yes—
249C2×C8#1062188412yes—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—82no—
255C4⋊C4—432no—
256C4⋊C4—861no—
257C22⋊C4—862no—
258C22⋊C4—862no—
259C42C2×C4×D4311yescharacteristic
260C42C2×D17211yescharacteristic
261C42Q8×D4311yescharacteristic
262C42#1062190211yescharacteristic
263C23—862no—
264C23—862no—
265C23—862no—
266C23—1721no—
267C23—1721no—
268C23—1721no—
269C23—1721no—
270C23#1306329611yescharacteristic
271D4—434no—
272D4—862no—
273D4—862no—
274D4—862no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—862no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1722no—
284C2×C4—1722no—
285C2×C4—1722no—
286C2×C4—1722no—
287C2×C4C2×(C2×D43)⋊C411yescharacteristic
288C2×C4C4⋊C4×D4311yescharacteristic
289C2×C4#1306328311yescharacteristic
290C2×C4#1306330011yescharacteristic
291C2×C4#1306330111yescharacteristic
292C2×C4#1306330511yescharacteristic
293C2×C4D8×D4311yescharacteristic
294C2×C4C2×#1062188211yescharacteristic
295C2×C4C2×#1062188411yescharacteristic
296C2×C4Q16×D4311yescharacteristic
297C2×C4#1306334411yescharacteristic
298C2×C4#1306334811yescharacteristic
299C2×C4#1306335111yescharacteristic
300C2×C4#1306335611yescharacteristic
301C8—22no—
302C8—3442no—
303C8—1722no—
304C8#1306324514yescomplemented
305C22—864no—
306C22—1722no—
307C22—1722no—
308C22—1722no—
309C22—1722no—
310C22—1722no—
311C22—1722no—
312C22#1458275611yescharacteristic
313C22#1458309111yescharacteristic
314C22#1458310111yescharacteristic
315C22#1458313211yescharacteristic
316C22#1458313711yescharacteristic
317C22#1458316611yescharacteristic
318C22#1458317111yescharacteristic
319C4—21no—
320C4—21no—
321C4—162no—
322C4—1722no—
323C4C2×#1306324511yescharacteristic
324C4#1458289811yescharacteristic
325C4#107×D4311yescharacteristic
326C4#1458293611yescharacteristic
327C4#1458313611yescharacteristic
328C4#1458314111yescharacteristic
329C4#1458317611yescharacteristic
330C4#1458318611yescharacteristic
331C2—1724no—
332C2#1913394711yescharacteristic
333C2#1913395711yescharacteristic
334C2#1913398111yescharacteristic
335C2#1913399111yescharacteristic
336C2#1913459211yescharacteristic
337C2#1913462111yescharacteristic
338C2#1913466011yescharacteristic
subgroupG/H
centerC23#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1845C2
socleC23×C43#121
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1845D43
hypocenterC43#8644
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
3. C2×#14582652C2semidirect
4. #19132478C2semidirect
5. C43×#1845C2semidirect
9. C8×D172C4semidirect
126. D172#107semidirect
132. C8×C43#102semidirect
163. #1845D43semidirect
189. C43#8644semidirect
304. C8#13063245semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D1722
#191345922
C2×#145826522
#191324782
C43×#18452
#864443