Finite Group Databasebeta

← C2×#19135928 #25124624

Subgroups — C2×#19135928 #25124624

Order 11008.

1454 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063325C211yesmaximal, characteristic
2C22×#13063256C212yesmaximal
3#19135928C218yesmaximal, direct product factor
4C2×#14582661C212yesmaximal
5C2×#14582654C211yesmaximal, characteristic
6C2×C43×#389C211yesmaximal, characteristic
7C23×Dic86—21no—
8C23×C43⋊C8C2212yes—
9C2×#13063325—28no—
10C2×#13063325—22no—
11C2×#13063325C2214yes—
12C22×C4⋊Dic43—21no—
13C22×C4⋊Dic43C2212yes—
14C2×#13063256—28no—
15C2×#13063256C2218yes—
16#14582661C2218yes—
17#14582654C2214yes—
18C22×C4⋊C4×C43—21no—
19C22×C4⋊C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2211yescharacteristic
21C22×C42×C43C2211yescharacteristic
22C43×#389—22no—
23C43×#389C2214yes—
24C2×#95×C43—21no—
25C22×Dic86—28no—
26C22×Dic86—24no—
27C22×Dic86—44no—
28C22×Dic86—44no—
29C23×Dic43—22no—
30C22×C43⋊C8—24no—
31C22×C43⋊C8—24no—
32C22×C43⋊C8Q818yescomplemented
33C22×C43⋊C8C2314yes—
34#13063325—216no—
35#13063325—216no—
36C2×C4⋊Dic43—28no—
37C2×C4⋊Dic43—24no—
38C2×C4⋊Dic43—24no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43D418yes—
41C2×C4⋊Dic43C2314yes—
42#13063256—216no—
43C23×C4×C43—21no—
44C23×C4×C43—21no—
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C23×C4×C43C2311yescharacteristic
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—22no—
50C2×C4⋊C4×C43—24no—
51C2×C4⋊C4×C43—24no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—44no—
54C2×C4⋊C4×C43Q814yescomplemented
55C2×C4⋊C4×C43C2312yes—
56C2×C4⋊C4×C43C2312yes—
57C2×C42×C43—24no—
58C2×C42×C43D412yes—
59C2×C42×C43C2312yes—
60#95×C43—24no—
61C24×C43C2×D411yescharacteristic
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—24no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—42no—
70C22×C4×C43—42no—
71C22×C4×C43—42no—
72C22×C4×C43—42no—
73C22×C4×C43—42no—
74C22×C4×C43SD1614yes—
75C22×C4×C43SD1614yes—
76C22×C4×C43C2×D414yes—
77C22×C4×C43C2×D412yes—
78C22×C4×C43C2×D412yes—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×Q812yes—
81C22×C4×C43C2×Q814yes—
82C22×C4×C43#4112yes—
83C22×C4×C43C2411yescharacteristic
84C22×Dic43—28no—
85C22×Dic43—24no—
86C22×Dic43—44no—
87C22×Dic43—44no—
88C2×Dic86—216no—
89C2×Dic86—48no—
90C2×Dic86—432no—
91C2×Dic86—48no—
92C4⋊C4×C43—24no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—24no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—48no—
97C4⋊C4×C43C2×Q814yescomplemented
98C42×C43—24no—
99C42×C43—24no—
100C4⋊Dic43—216no—
101C4⋊Dic43—28no—
102C4⋊Dic43—24no—
103C4⋊Dic43C2×D418yes—
104C2×C43⋊C8—216no—
105C2×C43⋊C8—24no—
106C2×C43⋊C8—24no—
107C2×C43⋊C8C2×Q818yescomplemented
108C23×C43#12012yes—
109C23×C43C22⋊Q812yes—
110C23×C43C4⋊Q812yes—
111C23×C43C2×SD1612yes—
112C23×C43C2×SD1612yes—
113C23×C43AGL(1,ℤ/8)12yes—
114C23×C43#13712yes—
115C23×C43C22×D411yescharacteristic
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—28no—
121C2×C4×C43—28no—
122C2×C4×C43—24no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—48no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—84no—
130C2×C4×C43#12012yes—
131C2×C4×C43C22⋊Q818yes—
132C2×C4×C43C22⋊Q812yes—
133C2×C4×C43C4⋊Q812yes—
134C2×C4×C43C4⋊Q818yes—
135C2×C4×C43C2×SD1614yes—
136C2×C4×C43C2×SD1614yes—
137C2×C4×C43C22×D412yes—
138C2×C4×C43C22×Q812yes—
139C2×C4×C43C22×Q811yescharacteristic
140C2×C4×C43C2×#4111yescharacteristic
141C2×Dic43—28no—
142C2×Dic43—44no—
143C2×Dic43—44no—
144C2×Dic43—416no—
145Dic86—432no—
146C43⋊C8—28no—
147C2×#2058—431nomaximal, Sylow
148C22×C43#39514yes—
149C22×C43#44814yes—
150C22×C43#45014yes—
151C22×C43#47514yes—
152C22×C43#47614yes—
153C22×C43#49814yes—
154C22×C43#50114yes—
155C22×C43C2×#12011yescharacteristic
156C22×C43C2×C22⋊Q811yescharacteristic
157C22×C43C2×C4⋊Q811yescharacteristic
158C22×C43C22×SD1611yescharacteristic
159C22×C43C22×SD1611yescharacteristic
160C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
161C22×C43C2×#13711yescharacteristic
162C4×C43—24no—
163C4×C43—24no—
164C4×C43—44no—
165C4×C43—82no—
166C4×C43#39514yes—
167C4×C43C2×C22⋊Q812yes—
168C4×C43C2×C4⋊Q812yes—
169Dic43—48no—
170C22×C4⋊Q8—431no—
171C22×#106—432no—
172C2×#389D4311yescharacteristic
173#2058—438no—
174C2×#340—432no—
175C2×#336—431no—
176C2×C43#205818yescomplemented
177C2×C43C2×#39511yescharacteristic
178C2×C43C2×#45011yescharacteristic
179C2×C43C2×#44811yescharacteristic
180C2×C43C2×#47611yescharacteristic
181C2×C43C2×#47511yescharacteristic
182C2×C43C2×#49811yescharacteristic
183C2×C43C2×#50111yescharacteristic
184C23×Q8—861no—
185C23×C8—432no—
186C2×C4⋊Q8—434no—
187C2×C4⋊Q8—868no—
188C2×C4⋊Q8—862no—
189C22×C4⋊C4—21no—
190C22×C4⋊C4—432no—
191C22×C4⋊C4—861no—
192C22×C4⋊C4C2×D4311yescharacteristic
193C22×C4⋊C4C2×D4311yescharacteristic
194C22×C42C2×D4311yescharacteristic
195C2×#106—438no—
196C2×#106—868no—
197#389—22no—
198#389C2×D4314yes—
199C2×#95—21no—
200#340—438no—
201#336—434no—
202C43C2×#205811yescharacteristic, complemented, Sylow
203C22×Q8—868no—
204C22×Q8—864no—
205C22×Q8—1724no—
206C22×Q8—1724no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—862no—
210C23×C4C22⋊D4311yescharacteristic
211C23×C4C22⋊D4311yescharacteristic
212C23×C4C22×D4311yescharacteristic
213C22×C8—438no—
214C22×C8—434no—
215C22×C8—864no—
216C22×C8—864no—
217C4⋊Q8—8616no—
218C4⋊Q8—8616no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—44no—
225C2×C4⋊C4—438no—
226C2×C4⋊C4—434no—
227C2×C4⋊C4—868no—
228C2×C4⋊C4—864no—
229C2×C4⋊C4—862no—
230C2×C4⋊C4—864no—
231C2×C4⋊C4Dic8614yescomplemented
232C2×C4⋊C4C22×D4312yes—
233C2×C4⋊C4C22×D4312yes—
234C2×C42—24no—
235C2×C42C22⋊D4312yes—
236C2×C42C22×D4312yes—
237#106—8616no—
238#95—24no—
239C24C2×C22⋊D4311yescharacteristic
240C2×Q8—8616no—
241C2×Q8—17232no—
242C2×Q8—1728no—
243C2×Q8—1728no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—868no—
257C22×C4—864no—
258C22×C4—1724no—
259C22×C4—1724no—
260C22×C4#1062188314yes—
261C22×C4#1062188414yes—
262C22×C4C2×Dic8612yes—
263C22×C4#1062189812yes—
264C22×C4D4×D4314yes—
265C22×C4Q8×D4314yes—
266C22×C4C2×C22⋊D4312yes—
267C22×C4C2×C22⋊D4312yes—
268C22×C4C2×C22⋊D4311yescharacteristic
269C22×C4C23×D4311yescharacteristic
270C2×C8—438no—
271C2×C8—8616no—
272C2×C8—864no—
273C2×C8—864no—
274C4⋊C4—24no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—42no—
278C4⋊C4—48no—
279C4⋊C4—438no—
280C4⋊C4—8616no—
281C4⋊C4—868no—
282C4⋊C4—864no—
283C4⋊C4C2×Dic8614yescomplemented
284C42—24no—
285C42—24no—
286C23#1306329312yes—
287C23#1306330412yes—
288C23#1306332312yes—
289C23C2×#1062188412yes—
290C23C2×#1062188312yes—
291C23#1306335012yes—
292C23#1306335512yes—
293C23C22×C22⋊D4311yescharacteristic
294Q8—17232no—
295C2×C4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—24no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—48no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—84no—
309C2×C4—868no—
310C2×C4—17216no—
311C2×C4—1724no—
312C2×C4—1724no—
313C2×C4#1306329312yes—
314C2×C4#1306330318yes—
315C2×C4#1306330412yes—
316C2×C4#1306332312yes—
317C2×C4#1306332418yes—
318C2×C4C2×#1062188414yes—
319C2×C4C2×#1062188314yes—
320C2×C4C2×D4×D4312yes—
321C2×C4C2×Q8×D4312yes—
322C2×C4C22×Dic8611yescharacteristic
323C2×C4C2×#1062189811yescharacteristic
324C8—868no—
325C22#1458281914yes—
326C22#1458303714yes—
327C22#1458304914yes—
328C22#1458318414yes—
329C22#1458318914yes—
330C22#1458329514yes—
331C22#1458330914yes—
332C22C2×#1306329311yescharacteristic
333C22C2×#1306330411yescharacteristic
334C22C2×#1306332311yescharacteristic
335C22C22×#1062188411yescharacteristic
336C22C22×#1062188311yescharacteristic
337C22C2×#1306335011yescharacteristic
338C22C2×#1306335511yescharacteristic
339C4—24no—
340C4—24no—
341C4—44no—
342C4—82no—
343C4—1728no—
344C4#1458281914yes—
345C4C2×#1306330312yes—
346C4C2×#1306332412yes—
347C2#1913592818yesdirect product factor
348C2C2×#1458281911yescharacteristic
349C2C2×#1458304911yescharacteristic
350C2C2×#1458303711yescharacteristic
351C2C2×#1458318911yescharacteristic
352C2C2×#1458318411yescharacteristic
353C2C2×#1458329511yescharacteristic
354C2C2×#1458330911yescharacteristic
subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#389C2
socle, prime radicalC24×C43C2×D4
hypercenterC2×#389D43
hypocenterC43C2×#2058
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #19135928C2direct (N × H)
32. C22×C43⋊C8Q8semidirect
54. C2×C4⋊C4×C43Q8semidirect
97. C4⋊C4×C43C2×Q8semidirect
107. C2×C43⋊C8C2×Q8semidirect
176. C2×C43#2058semidirect
202. C43C2×#2058semidirect
231. C2×C4⋊C4Dic86semidirect
283. C4⋊C4C2×Dic86semidirect
347. C2#19135928direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633252
C22×#130632562
#191359282
C2×#145826612
C2×#145826542
C2×C43×#3892
C2×#205843