Finite Group Databasebeta

← C2×#19134577 #25095954

Subgroups — C2×#19134577 #25095954

Order 11008.

1638 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×#13063284C211yesmaximal, characteristic
2C22×Dic43⋊C8C212yesmaximal, complemented
3C22×C22⋊(C43⋊C8)C211yesmaximal, characteristic
4#19134577C218yesmaximal, direct product factor
5C2×#14582653C212yesmaximal, complemented
6C22×C22⋊C8×C43C211yesmaximal, characteristic
7C23×C43⋊C8C2212yes—
8C2×#13063284—28no—
9C2×#13063284C414yes—
10C2×#13063284C2214yes—
11C22×C4⋊Dic43C412yes—
12C22×C22⋊Dic43C412yes—
13C22×C4×Dic43C2211yescharacteristic
14C22×C4×Dic43C2211yescharacteristic
15C2×Dic43⋊C8—28no—
16C2×Dic43⋊C8C2218yescomplemented
17C2×C22⋊(C43⋊C8)—24no—
18C2×C22⋊(C43⋊C8)C2214yes—
19#14582653C2218yescomplemented
20C24×C4×C43C2211yescharacteristic
21C23×C8×C43C2212yes—
22C2×C22⋊C8×C43—24no—
23C2×C22⋊C8×C43C2214yes—
24C23×Dic43C2×C412yes—
25C23×Dic43C2×C412yes—
26C22×C43⋊C8—24no—
27C22×C43⋊C8—24no—
28C22×C43⋊C8—24no—
29C22×C43⋊C8C2314yes—
30#13063284—216no—
31#13063284—216no—
32C2×C4⋊Dic43—28no—
33C2×C4⋊Dic43C2×C418yes—
34C2×C22⋊Dic43—28no—
35C2×C22⋊Dic43C2×C418yes—
36C2×C4×Dic43—24no—
37C2×C4×Dic43C2×C412yes—
38C2×C4×Dic43C2×C412yes—
39C2×C4×Dic43D418yes—
40C2×C4×Dic43C2312yes—
41C2×C4×Dic43C2312yes—
42Dic43⋊C8—216no—
43C22⋊(C43⋊C8)—28no—
44C25×C43C2×C411yescharacteristic
45C23×C4×C43—24no—
46C23×C4×C43—24no—
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43C2×C412yes—
49C23×C4×C43D414yes—
50C23×C4×C43Q814yes—
51C23×C4×C43C2312yes—
52C23×C4×C43C2311yescharacteristic
53C22×C8×C43—24no—
54C22×C8×C43—24no—
55C22×C8×C43—24no—
56C22×C8×C43C2314yes—
57C22⋊C8×C43—28no—
58C24×C43—22no—
59C24×C43—22no—
60C24×C43—24no—
61C24×C43—24no—
62C24×C43C4⋊C414yes—
63C24×C43C22×C412yes—
64C24×C43C22×C411yescharacteristic
65C22×C4×C43—24no—
66C22×C4×C43—24no—
67C22×C4×C43—216no—
68C22×C4×C43—216no—
69C22×C4×C43—24no—
70C22×C4×C43—24no—
71C22×C4×C43—22no—
72C22×C4×C43—22no—
73C22×C4×C43C4⋊C418yes—
74C22×C4×C43C4⋊C414yes—
75C22×C4×C43C22×C412yes—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D414yes—
78C22×C4×C43C2×D414yes—
79C22×C4×C43C2×D412yes—
80C22×C4×C43C2×Q814yes—
81C22×C4×C43C2×Q812yes—
82C22×C4×C43#4114yes—
83C22×C4×C43C2411yescharacteristic
84C22×Dic43—24no—
85C22×Dic43—24no—
86C22×Dic43—24no—
87C22×Dic43—24no—
88C22×Dic43—24no—
89C22×Dic43C22⋊C418yes—
90C22×Dic43C22×C414yes—
91C22×Dic43C22×C414yes—
92C2×C8×C43—24no—
93C2×C8×C43—24no—
94C2×C8×C43—24no—
95C2×C8×C43—48no—
96C22⋊Dic43—216no—
97C4⋊Dic43—216no—
98C4×Dic43—24no—
99C4×Dic43—24no—
100C4×Dic43C22⋊C418yes—
101C4×Dic43C2×D418yes—
102C2×C43⋊C8—24no—
103C2×C43⋊C8—24no—
104C2×C43⋊C8—24no—
105C2×C43⋊C8—48no—
106C23×C43—22no—
107C23×C43—22no—
108C23×C43—24no—
109C23×C43—24no—
110C23×C43—28no—
111C23×C43—28no—
112C23×C43—28no—
113C23×C43—48no—
114C23×C43—48no—
115C23×C43C2×C22⋊C412yes—
116C23×C43C2×C4⋊C414yes—
117C23×C43C2×C4⋊C412yes—
118C23×C43#11712yes—
119C23×C43#13114yes—
120C23×C43#13114yes—
121C23×C43C23×C411yescharacteristic
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—28no—
125C2×C4×C43—28no—
126C2×C4×C43—28no—
127C2×C4×C43—216no—
128C2×C4×C43C2×C22⋊C412yes—
129C2×C4×C43C2×C4⋊C414yes—
130C2×C4×C43C2×C4⋊C412yes—
131C2×C4×C43#11712yes—
132C2×C4×C43#12118yes—
133C2×C4×C43C22⋊Q818yes—
134C2×C4×C43C22×D412yes—
135C2×C4×C43C22×D411yescharacteristic
136C2×C4×C43C22×Q811yescharacteristic
137C2×C4×C43C2×#4112yes—
138C2×Dic43—24no—
139C2×Dic43—24no—
140C2×Dic43—216no—
141C2×Dic43—24no—
142C2×Dic43—24no—
143C2×Dic43—24no—
144C2×Dic43—48no—
145C2×Dic43C2×C22⋊C418yes—
146C8×C43—44no—
147C43⋊C8—44no—
148C2×#1798—431nomaximal, Sylow
149C22×C43—24no—
150C22×C43—24no—
151C22×C43—24no—
152C22×C43—416no—
153C22×C43—44no—
154C22×C43—44no—
155C22×C43#38014yes—
156C22×C43#40818yes—
157C22×C43#42414yes—
158C22×C43#42414yes—
159C22×C43#43318yes—
160C22×C43C22×C22⋊C411yescharacteristic
161C22×C43C22×C4⋊C411yescharacteristic
162C22×C43C2×#11711yescharacteristic
163C22×C43C2×#13112yes—
164C22×C43C2×#13112yes—
165C4×C43—24no—
166C4×C43#38014yes—
167C4×C43C2×#12112yes—
168C4×C43C2×C22⋊Q812yes—
169Dic43—28no—
170Dic43—44no—
171C22×#117—431no—
172C22×C4⋊C8—432no—
173C22×C22⋊C8—431no—
174C22×C22⋊C8D4311yescharacteristic
175#1798—438no—
176C2×#336—432no—
177C2×C43—44no—
178C2×C43#179818yescomplemented
179C2×C43C2×#38011yescharacteristic
180C2×C43C2×#40812yes—
181C2×C43C2×#42411yescharacteristic
182C2×C43C2×#42411yescharacteristic
183C2×C43C2×#43312yes—
184C24×C4C2×D4311yescharacteristic
185C23×C8—432no—
186C23×C8C2×D4312yes—
187C2×#117—434no—
188C2×#117—434no—
189C2×#117—868no—
190C22×C4⋊C4—432no—
191C22×C22⋊C4—432no—
192C22×C42—431no—
193C22×C42—431no—
194C2×C4⋊C8—438no—
195C2×C4⋊C8—868no—
196C2×C22⋊C8—24no—
197C2×C22⋊C8—434no—
198C2×C22⋊C8—864no—
199C2×C22⋊C8C2×D4314yes—
200#336—438no—
201C43C2×#179811yescharacteristic, complemented, Sylow
202C25C4×D4311yescharacteristic
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—432no—
206C23×C4—432no—
207C23×C4Dic8614yes—
208C23×C4C4×D4311yescharacteristic
209C23×C4C4×D4312yes—
210C23×C4C22⋊D4314yes—
211C23×C4C22×D4312yes—
212C23×C4C22×D4311yescharacteristic
213C22×C8—24no—
214C22×C8—24no—
215C22×C8—24no—
216C22×C8—434no—
217C22×C8—864no—
218C22×C8—864no—
219C22×C8—864no—
220C22×C8C22×D4314yes—
221#117—8616no—
222#117—8616no—
223C2×C4⋊C4—438no—
224C2×C4⋊C4—868no—
225C2×C22⋊C4—438no—
226C2×C22⋊C4—868no—
227C2×C42—432no—
228C2×C42—438no—
229C2×C42—432no—
230C2×C42—432no—
231C2×C42—432no—
232C2×C42—864no—
233C4⋊C8—8616no—
234C22⋊C8—28no—
235C22⋊C8—868no—
236C24—22no—
237C24—22no—
238C24—24no—
239C24—24no—
240C24Dic43⋊C414yes—
241C24C2×C4×D4312yes—
242C24C2×C4×D4311yescharacteristic
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—216no—
248C22×C4—216no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—438no—
252C22×C4—434no—
253C22×C4—434no—
254C22×C4—864no—
255C22×C4—864no—
256C22×C4—864no—
257C22×C4—864no—
258C22×C4—864no—
259C22×C4Dic43⋊C414yes—
260C22×C4Dic43⋊C418yes—
261C22×C4C2×Dic8614yes—
262C22×C4C2×Dic8612yes—
263C22×C4C2×C4×D4312yes—
264C22×C4C2×C4×D4311yescharacteristic
265C22×C4D4×D4314yes—
266C22×C4#1062190014yes—
267C22×C4C2×C22⋊D4314yes—
268C22×C4C2×C22⋊D4312yes—
269C22×C4C23×D4311yescharacteristic
270C2×C8—24no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—48no—
274C2×C8—864no—
275C2×C8—864no—
276C2×C8—864no—
277C2×C8—1728no—
278C4⋊C4—8616no—
279C22⋊C4—8616no—
280C42—438no—
281C42—438no—
282C42—864no—
283C42—864no—
284C23—22no—
285C23—22no—
286C23—24no—
287C23—24no—
288C23—28no—
289C23—28no—
290C23—28no—
291C23—48no—
292C23—48no—
293C23C22⋊C4×D4312yes—
294C23C2×Dic43⋊C414yes—
295C23C2×Dic43⋊C412yes—
296C23#1306328112yes—
297C23#1306333114yes—
298C23#1306333314yes—
299C23C22×C4×D4311yescharacteristic
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—28no—
303C2×C4—28no—
304C2×C4—28no—
305C2×C4—216no—
306C2×C4—438no—
307C2×C4—8616no—
308C2×C4—864no—
309C2×C4—864no—
310C2×C4—864no—
311C2×C4—864no—
312C2×C4—864no—
313C2×C4—1728no—
314C2×C4C22⋊C4×D4312yes—
315C2×C4C2×Dic43⋊C414yes—
316C2×C4C2×Dic43⋊C412yes—
317C2×C4#1306328112yes—
318C2×C4#1306329718yes—
319C2×C4#1306330218yes—
320C2×C4C2×D4×D4312yes—
321C2×C4C22×C22⋊D4311yescharacteristic
322C2×C4C22×Dic8611yescharacteristic
323C2×C4C2×#1062190012yes—
324C8—44no—
325C8—1724no—
326C22—24no—
327C22—24no—
328C22—24no—
329C22—44no—
330C22—416no—
331C22—44no—
332C22#1458275714yes—
333C22#1458286418yes—
334C22#1458292514yes—
335C22#1458292714yes—
336C22#1458295718yes—
337C22C2×C22⋊C4×D4311yescharacteristic
338C22C22×Dic43⋊C411yescharacteristic
339C22C2×#1306328111yescharacteristic
340C22C2×#1306333112yes—
341C22C2×#1306333312yes—
342C4—24no—
343C4—868no—
344C4—1724no—
345C4#1458275714yes—
346C4C2×#1306329712yes—
347C4C2×#1306330212yes—
348C2—44no—
349C2#1913457718yesdirect product factor
350C2C2×#1458275711yescharacteristic
351C2C2×#1458286412yes—
352C2C2×#1458292511yescharacteristic
353C2C2×#1458292711yescharacteristic
354C2C2×#1458295712yes—
subgroupG/H
centerC23×C4C22×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C22⋊C8×C43C2
socleC24×C43C22×C4
prime radicalC25×C43C2×C4
cosocleC22×C4×C43C24
hypercenterC22×C22⋊C8D43
hypocenterC43C2×#1798
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×Dic43⋊C8C2semidirect
4. #19134577C2direct (N × H)
5. C2×#14582653C2semidirect
16. C2×Dic43⋊C8C22semidirect
19. #14582653C22semidirect
178. C2×C43#1798semidirect
201. C43C2×#1798semidirect
349. C2#19134577direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632842
C22×Dic43⋊C82
C22×C22⋊(C43⋊C8)2
#191345772
C2×#145826532
C22×C22⋊C8×C432
C2×#179843