Finite Group Databasebeta

← #24989719

Subgroups — #24989719

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C43⋊C8C211yesmaximal, characteristic
2#19134766C211yesmaximal, characteristic, complemented
3#19133341C211yesmaximal, characteristic, complemented
4#19133020C211yesmaximal, characteristic
5#19132491C211yesmaximal, characteristic, complemented
6#19132490C211yesmaximal, characteristic, complemented
7C43×#1486C211yesmaximal, characteristic
8C23×C43⋊C8—21no—
9D4×C43⋊C8—21no—
10D4×C43⋊C8—21no—
11D4×C43⋊C8C412yes—
12D4×C43⋊C8C412yes—
13#14582952C2211yescharacteristic
14C2×#13063260—21no—
15C2×#13063260—21no—
16#14582923C2211yescharacteristic
17C2×C4⋊(C43⋊C8)C2211yescharacteristic
18C2×C22⋊(C43⋊C8)—21no—
19C2×C4×C43⋊C8C2211yescharacteristic
20#14582651—21no—
21#14582649—21no—
22D4⋊(C43⋊C8)—22no—
23C2×C4×D4×C43C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×D4⋊C8—22no—
27C2×#10621877—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8—22no—
30C22×C43⋊C8—22no—
31C22×C43⋊C8—42no—
32C22×C43⋊C8—42no—
33C22×C43⋊C8D411yescharacteristic
34C22×C43⋊C8D411yescharacteristic
35#13063260—42no—
36#13063260—42no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)C2×C412yes—
42C22⋊(C43⋊C8)—22no—
43C22⋊(C43⋊C8)—22no—
44C22⋊(C43⋊C8)—21no—
45C4×C43⋊C8—21no—
46C4×C43⋊C8C2×C411yescharacteristic
47C4×C43⋊C8C2×C411yescharacteristic
48C4×C43⋊C8D411yescharacteristic
49C4×C43⋊C8D411yescharacteristic
50C22×D4×C43Q811yescharacteristic
51C23×C4×C43—21no—
52C2×M16×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43—21no—
55C4×D4×C43C2×C412yes—
56C4×D4×C43D412yes—
57C2×C4⋊C4×C43Q811yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64C4×C8×C43—21no—
65C24×C43—21no—
66C2×D4×C43—24no—
67C2×D4×C43—21no—
68C2×D4×C43C4⋊C412yes—
69C22×C4×C43—22no—
70C22×C4×C43—22no—
71C22×C4×C43—21no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43—41no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×Q811yescharacteristic
78C22×C4×C43#4111yescharacteristic
79M16×C43—41no—
80M16×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43—41no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43C4⋊C412yes—
85C22⋊C4×C43—22no—
86C22⋊C4×C43—22no—
87C42×C43C22×C411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43C2×D411yescharacteristic
90C42×C43#4111yescharacteristic
91#10621877—41no—
92#10621877—41no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—22no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—44no—
99C2×C43⋊C8—44no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8C22⋊C411yescharacteristic
103C2×C43⋊C8C22⋊C411yescharacteristic
104C2×C43⋊C8C22⋊C411yescharacteristic
105C2×C43⋊C8C22⋊C411yescharacteristic
106C2×C43⋊C8D812yes—
107C2×C43⋊C8SD1612yes—
108C23×C43—24no—
109C23×C43—22no—
110C23×C43—42no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43C22⋊Q811yescharacteristic
114D4×C43—24no—
115D4×C43—22no—
116D4×C43#10814yescomplemented
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C2×C4⋊C411yescharacteristic
128C2×C4×C43#11711yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43C22⋊Q811yescharacteristic
132C2×C4×C43C2×D811yescharacteristic
133C2×C4×C43C2×SD1611yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C8×C43—81no—
137C8×C43—81no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C43⋊C8—42no—
141C43⋊C8—81no—
142C43⋊C8—81no—
143C43⋊C8#10212yes—
144C43⋊C8#10212yes—
145#8658—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—24no—
149C22×C43—44no—
150C22×C43—44no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43#38011yescharacteristic
154C22×C43#47411yescharacteristic
155C22×C43#47611yescharacteristic
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43C2×#10211yescharacteristic
161C4×C43#41711yescharacteristic
162C4×C43C2×#10812yes—
163C4×C43#45911yescharacteristic
164C4×C43#46111yescharacteristic
165C2×C8×D4—431no—
166#1848—431no—
167#1564—431no—
168#1486—431no—
169#1486D4311yescharacteristic
170#1301—431no—
171#1301—431no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—44no—
175C2×C43#180211yescharacteristic
176C2×C43#181011yescharacteristic
177C2×C43#181411yescharacteristic
178C23×C8—861no—
179C2×C4×D4C2×D4311yescharacteristic
180C8×D4—432no—
181C8×D4—432no—
182C8×D4—861no—
183C8×D4—861no—
184#431—431no—
185#431C2×D4311yescharacteristic
186C2×#108—861no—
187C2×#108—861no—
188#423—431no—
189#423C2×D4311yescharacteristic
190C2×C4⋊C8—431no—
191C2×C22⋊C8—861no—
192C2×C4×C8—431no—
193#335—861no—
194#334—861no—
195D4⋊C8—22no—
196D4⋊C8—862no—
197C43#865811yescharacteristic, complemented, Sylow
198C22×D4Dic8611yescharacteristic
199C23×C4—21no—
200C2×M16—21no—
201C2×M16—861no—
202C22×C8—431no—
203C22×C8—431no—
204C22×C8—862no—
205C22×C8—862no—
206C22×C8—861no—
207C22×C8—1722no—
208C22×C8—1722no—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4C4×D4312yes—
212C4×D4C22⋊D4312yes—
213C2×C4⋊C4Dic8611yescharacteristic
214C2×C22⋊C4—21no—
215C2×C42C22×D4311yescharacteristic
216#108—1722no—
217#108—1722no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—432no—
222C4⋊C8—861no—
223C4⋊C8—861no—
224C4⋊C8—861no—
225C4⋊C8—861no—
226C22⋊C8—21no—
227C22⋊C8—862no—
228C22⋊C8—862no—
229C22⋊C8—861no—
230C4×C8—21no—
231C4×C8—431no—
232C4×C8—431no—
233C4×C8—431no—
234C4×C8—431no—
235C4×C8—861no—
236C24—21no—
237C2×D4—24no—
238C2×D4—21no—
239C2×D4Dic43⋊C412yes—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4C2×Dic8611yescharacteristic
248C22×C4D4×D4311yescharacteristic
249C22×C4#1062190011yescharacteristic
250M16—41no—
251M16—41no—
252M16—1721no—
253M16—1721no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—431no—
257C2×C8—431no—
258C2×C8—432no—
259C2×C8—432no—
260C2×C8—431no—
261C2×C8—431no—
262C2×C8—861no—
263C2×C8—861no—
264C2×C8—862no—
265C2×C8—1724no—
266C2×C8—1724no—
267C2×C8—1721no—
268C2×C8—1721no—
269C2×C8—1721no—
270C2×C8—1721no—
271C4⋊C4—21no—
272C4⋊C4Dic43⋊C412yes—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C42C2×C4×D4311yescharacteristic
276C42D4×D4311yescharacteristic
277C42#1062190011yescharacteristic
278C42C2×C22⋊D4311yescharacteristic
279C23—24no—
280C23—22no—
281C23—42no—
282C23—41no—
283C23—41no—
284C23#1306330211yescharacteristic
285D4—24no—
286D4—22no—
287D4#1306326014yescomplemented
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4C22⋊C4×D4311yescharacteristic
298C2×C4C2×Dic43⋊C411yescharacteristic
299C2×C4#1306328111yescharacteristic
300C2×C4#1306329711yescharacteristic
301C2×C4#1306329711yescharacteristic
302C2×C4#1306330211yescharacteristic
303C2×C4D8×D4311yescharacteristic
304C2×C4SD16×D4311yescharacteristic
305C2×C4#1306334911yescharacteristic
306C2×C4#1306335411yescharacteristic
307C8—81no—
308C8—81no—
309C8—432no—
310C8—432no—
311C8—861no—
312C8—861no—
313C8—3441no—
314C8—3441no—
315C8—1722no—
316C22—21no—
317C22—21no—
318C22—24no—
319C22—44no—
320C22—44no—
321C22—42no—
322C22—42no—
323C22#1458275711yescharacteristic
324C22#1458317711yescharacteristic
325C22#1458318711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4#102×D4311yescharacteristic
331C4#1458289711yescharacteristic
332C4C2×#1306326012yes—
333C4#1458309211yescharacteristic
334C4#1458310211yescharacteristic
335C2—21no—
336C2—21no—
337C2—44no—
338C2#1913459311yescharacteristic
339C2#1913463111yescharacteristic
340C2#1913464711yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1486C2
socleC22×C43#380
prime radicalC22×D4×C43Q8
cosocleC2×C42×C43C23
hypercenter#1486D43
hypocenterC43#8658
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #19134766C2semidirect
3. #19133341C2semidirect
5. #19132491C2semidirect
6. #19132490C2semidirect
116. D4×C43#108semidirect
197. C43#8658semidirect
287. D4#13063260semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C43⋊C82
#191347662
#191333412
#191330202
#191324912
#191324902
C43×#14862
#865843