Finite Group Databasebeta

← #102×C43⋊C8 #24987362

Subgroups — #102×C43⋊C8 #24987362

Order 11008.

606 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
2C4⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
3C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic
4C2×C8×C43⋊C8C211yesmaximal, characteristic, complemented
5#19132436C211yesmaximal, characteristic, complemented
6#19132430C211yesmaximal, characteristic, complemented
7C4×#102×C43C211yesmaximal, characteristic
8C23×C43⋊C8—21no—
9D4×C43⋊C8—22no—
10D4×C43⋊C8C414yescomplemented
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×C22⋊(C43⋊C8)—21no—
14C2×C4×C43⋊C8—21no—
15C2×C4×C43⋊C8C2211yescharacteristic
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582654—21no—
18D4⋊(C43⋊C8)C414yescomplemented
19C8×C43⋊C8—22no—
20C2×C4×D4×C43C2211yescharacteristic
21C2×#102×C43C412yes—
22C2×C4×C8×C43C2211yescharacteristic
23C4×C4⋊C4×C43C2211yescharacteristic
24C43×#340C412yes—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—24no—
29C22×C43⋊C8—42no—
30C22×C43⋊C8—42no—
31C22×C43⋊C8D411yescharacteristic
32C22×C43⋊C8D411yescharacteristic
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)C2×C412yes—
36C4⋊(C43⋊C8)C2×C412yes—
37C22⋊(C43⋊C8)—24no—
38C4×C43⋊C8—21no—
39C4×C43⋊C8—42no—
40C4×C43⋊C8C2×C412yes—
41C4×C43⋊C8C2×C412yes—
42C4×C43⋊C8D412yes—
43C22×D4×C43C2×C411yescharacteristic
44C23×C4×C43—21no—
45C22×C8×C43C2×C412yes—
46C4×D4×C43—21no—
47C4×D4×C43—21no—
48C4×D4×C43C2×C412yes—
49C4×D4×C43C2×C412yes—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43C2×C412yes—
52C2×C22⋊C4×C43—21no—
53C2×C42×C43—21no—
54C2×C42×C43C2311yescharacteristic
55#102×C43C818yescomplemented
56C4×C8×C43—21no—
57C4×C8×C43—21no—
58#95×C43—21no—
59C24×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—22no—
62C2×D4×C43C4212yes—
63C2×D4×C43C2×C814yes—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—21no—
68C22×C4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43#4111yescharacteristic
75C2×C8×C43—22no—
76C2×C8×C43—22no—
77C2×C8×C43C2×C814yescomplemented
78C4⋊C4×C43—21no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43C4212yes—
81C4⋊C4×C43C2×C814yescomplemented
82C22⋊C4×C43—22no—
83C22⋊C4×C43—22no—
84C42×C43—41no—
85C42×C43—41no—
86C42×C43C22×C411yescharacteristic
87C42×C43C22×C411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43#4111yescharacteristic
90C2×C43⋊C8—24no—
91C2×C43⋊C8—22no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—22no—
95C2×C43⋊C8—22no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—48no—
101C2×C43⋊C8C22⋊C412yes—
102C2×C43⋊C8C22⋊C412yes—
103C2×C43⋊C8D812yes—
104C2×C43⋊C8SD1612yes—
105C23×C43—22no—
106C23×C43—24no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—42no—
110C23×C43C4×D411yescharacteristic
111D4×C43—22no—
112D4×C43—24no—
113D4×C43C4×C814yescomplemented
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—24no—
117C2×C4×C43—42no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43C2×C4211yescharacteristic
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43#11711yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43C22×C812yes—
132C2×C4×C43#13112yes—
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43C2×SD1611yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C8×C43—24no—
138C43⋊C8—24no—
139C43⋊C8—22no—
140C43⋊C8—42no—
141C43⋊C8—42no—
142C43⋊C8#10214yesdirect product factor
143C8×#102—431nomaximal, Sylow
144C22×C43—24no—
145C22×C43—44no—
146C22×C43—44no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43C4×C22⋊C411yescharacteristic
150C22×C43C8×D412yes—
151C22×C43C4×D811yescharacteristic
152C22×C43C4×SD1611yescharacteristic
153C22×C43#44312yes—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—44no—
157C4×C43—42no—
158C4×C43C2×C4×C811yescharacteristic
159C4×C43#40511yescharacteristic
160C4×C43C2×#10211yescharacteristic
161C4×C43#41611yescharacteristic
162C4×C43C8×D412yes—
163C4×C43C4×D811yescharacteristic
164C4×C43C4×SD1611yescharacteristic
165C2×C8×D4—431no—
166C8×C4⋊C4—431no—
167C4×#102D4311yescharacteristic
168C2×D4⋊C8—431no—
169C2×C82—431no—
170#1279—431no—
171#1277—431no—
172C2×C43—44no—
173C2×C43C8×D812yes—
174C2×C43C8×SD1612yes—
175C2×C43C8×C22⋊C411yescharacteristic
176C2×C43C4×#10211yescharacteristic
177C2×C43#176411yescharacteristic
178C23×C8—861no—
179C2×C4×D4C2×D4311yescharacteristic
180C8×D4—434no—
181C8×D4—862no—
182C2×C4⋊C8—431no—
183C2×C4⋊C8—431no—
184C2×#102Dic4312yes—
185C2×C22⋊C8—861no—
186C2×C4×C8—431no—
187C2×C4×C8—431no—
188C2×C4×C8—861no—
189C2×C4×C8C2×D4311yescharacteristic
190C4×C4⋊C4C2×D4311yescharacteristic
191#340Dic4312yes—
192#336—861no—
193D4⋊C8—434no—
194C82—862no—
195C43C8×#10211yescharacteristic, complemented, Sylow
196C22×D4C2×Dic4311yescharacteristic
197C23×C4—21no—
198C22×C8—431no—
199C22×C8—431no—
200C22×C8—864no—
201C22×C8—861no—
202C22×C8—861no—
203C22×C8—861no—
204C22×C8—1722no—
205C22×C8—1722no—
206C22×C8C2×Dic4312yes—
207C4×D4—21no—
208C4×D4—21no—
209C4×D4C4×D4312yes—
210C4×D4C4×D4312yes—
211C2×C4⋊C4C2×Dic4312yes—
212C2×C4⋊C4C2×Dic4311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C42—21no—
215C2×C42C22×D4311yescharacteristic
216C4⋊C8—432no—
217C4⋊C8—432no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220#102C43⋊C818yesdirect product factor
221C22⋊C8—864no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—432no—
225C4×C8—432no—
226C4×C8—432no—
227C4×C8—861no—
228C4×C8—1722no—
229#95—21no—
230C24—21no—
231C2×D4—21no—
232C2×D4—22no—
233C2×D4C2×C43⋊C814yes—
234C2×D4C4×Dic4312yes—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4D4×D4311yescharacteristic
244C22×C4#1062190011yescharacteristic
245C22×C4C22×Dic4311yescharacteristic
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—432no—
249C2×C8—432no—
250C2×C8—432no—
251C2×C8—432no—
252C2×C8—864no—
253C2×C8—862no—
254C2×C8—861no—
255C2×C8—861no—
256C2×C8—862no—
257C2×C8—862no—
258C2×C8—1728no—
259C2×C8—1721no—
260C2×C8—1721no—
261C2×C8—1721no—
262C2×C8—1721no—
263C2×C8C2×C43⋊C814yescomplemented
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4C2×C43⋊C814yescomplemented
267C4⋊C4C4×Dic4312yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42—41no—
271C42—41no—
272C42C2×C4×D4311yescharacteristic
273C42C2×C4×D4311yescharacteristic
274C42D4×D4311yescharacteristic
275C42#1062190011yescharacteristic
276C23—24no—
277C23—22no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23D4×Dic4311yescharacteristic
282D4—22no—
283D4—24no—
284D4C4×C43⋊C814yescomplemented
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4C2×C4×Dic4311yescharacteristic
297C2×C4C22⋊C4×D4311yescharacteristic
298C2×C4#1306328111yescharacteristic
299C2×C4(C22⋊D43)⋊C411yescharacteristic
300C2×C4(C22⋊D43)⋊C411yescharacteristic
301C2×C4D4×Dic4311yescharacteristic
302C2×C4C22×C43⋊C812yes—
303C2×C4#1306333212yes—
304C2×C4D8×D4311yescharacteristic
305C2×C4SD16×D4311yescharacteristic
306C2×C4#1306334411yescharacteristic
307C2×C4#1306334611yescharacteristic
308C8—24no—
309C8—434no—
310C8—864no—
311C8—862no—
312C8—1722no—
313C8—1722no—
314C22—24no—
315C22—42no—
316C22—44no—
317C22—44no—
318C22—42no—
319C22C22⋊C4×Dic4311yescharacteristic
320C22D4×C43⋊C812yes—
321C22D8×Dic4311yescharacteristic
322C22SD16×Dic4311yescharacteristic
323C22#1458301612yes—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—44no—
328C4C2×C4×C43⋊C811yescharacteristic
329C4#1458285511yescharacteristic
330C4#102×D4311yescharacteristic
331C4#1458289211yescharacteristic
332C4D4×C43⋊C812yes—
333C4#1458297911yescharacteristic
334C4#1458299011yescharacteristic
335C2—44no—
336C2D8×C43⋊C812yes—
337C2SD16×C43⋊C812yes—
338C2C22⋊C4×C43⋊C811yescharacteristic
339C2#102×Dic4311yescharacteristic
340C2#1913443511yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC4×#102×C43C2
socleC23×C43C4×D4
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC4×#102D43
hypocenterC43C8×#102
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C43⋊C8C2semidirect
4. C2×C8×C43⋊C8C2semidirect
5. #19132436C2semidirect
6. #19132430C2semidirect
10. D4×C43⋊C8C4semidirect
18. D4⋊(C43⋊C8)C4semidirect
55. #102×C43C8semidirect
77. C2×C8×C43C2×C8semidirect
81. C4⋊C4×C43C2×C8semidirect
113. D4×C43C4×C8semidirect
142. C43⋊C8#102direct (N × H)
195. C43C8×#102semidirect
220. #102C43⋊C8direct (N × H)
263. C2×C8C2×C43⋊C8semidirect
266. C4⋊C4C2×C43⋊C8semidirect
284. D4C4×C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C43⋊C82
C4⋊C4×C43⋊C82
C2×D4⋊(C43⋊C8)2
C2×C8×C43⋊C82
#191324362
#191324302
C4×#102×C432
C8×#10243