Finite Group Databasebeta

← C2×#19135471 #25100433

Subgroups — C2×#19135471 #25100433

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D344C211yesmaximal, characteristic
2C22×#13063257C211yesmaximal, characteristic, complemented
3C22×#13063247C212yesmaximal, complemented
4C2×#14582801C212yesmaximal, complemented
5#19135471C218yesmaximal, direct product factor
6C22×#97×C43C211yesmaximal, characteristic, complemented
7C23×D172C2212yes—
8C22×D344—24no—
9C22×D344—24no—
10C22×D344C418yescomplemented
11C22×D344C2214yes—
12C22×C4⋊Dic43C2212yes—
13C22×(C2×D43)⋊C4—24no—
14C2×#13063257—24no—
15C2×#13063257C2214yescomplemented
16C2×#13063247—28no—
17C2×#13063247C2218yescomplemented
18#14582801—24no—
19#14582801C2218yescomplemented
20C23×C8×C43C2211yescharacteristic
21C23×C8×C43C2211yescharacteristic
22C22×C42×C43C2211yescharacteristic
23C2×#97×C43—24no—
24C2×#97×C43C2214yescomplemented
25C24×D43—22no—
26C22×D172—24no—
27C22×D172—24no—
28C22×D172—24no—
29C22×D172—24no—
30C22×D172—22no—
31C22×D172—24no—
32C22×D172C2×C418yes—
33C22×D172C2314yes—
34C23×Dic43—22no—
35C2×D344—232no—
36C2×D344—28no—
37C2×D344—28no—
38C2×D344C2×C4116yescomplemented
39C2×C4⋊Dic43—24no—
40C2×C4⋊Dic43—24no—
41C2×C4⋊Dic43—22no—
42C2×C4⋊Dic43C2314yes—
43C2×(C2×D43)⋊C4—216no—
44C2×(C2×D43)⋊C4—416no—
45#13063257—28no—
46#13063247—216no—
47C23×C4×C43D412yes—
48C23×C4×C43C2311yescharacteristic
49C22×C8×C43—22no—
50C22×C8×C43—22no—
51C22×C8×C43C2×C414yes—
52C22×C8×C43D414yes—
53C22×C8×C43D414yes—
54C22×C8×C43D414yes—
55C22×C8×C43C2312yes—
56C22×C8×C43C2312yes—
57C2×C42×C43—22no—
58C2×C42×C43—22no—
59C2×C42×C43D412yes—
60C2×C42×C43C2312yes—
61#97×C43—28no—
62C24×C43C2×D411yescharacteristic
63C23×D43—28no—
64C23×D43—24no—
65C23×D43—44no—
66C23×D43—44no—
67C23×D43—48no—
68C23×D43—48no—
69C22×C4×C43—24no—
70C22×C4×C43—28no—
71C22×C4×C43C22×C412yes—
72C22×C4×C43C2×D412yes—
73C22×C4×C43C2×D412yes—
74C22×C4×C43C2×D412yes—
75C22×C4×C43C2×D414yes—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4112yes—
78C22×C4×C43#4112yes—
79C22×C4×C43C2411yescharacteristic
80C22×Dic43—24no—
81C22×Dic43—44no—
82C22×Dic43—48no—
83C2×D172—28no—
84C2×D172—24no—
85C2×D172—216no—
86C2×D172—216no—
87C2×D172—24no—
88C2×D172—24no—
89C2×D172—24no—
90C2×D172—24no—
91C2×D172—44no—
92C2×D172—48no—
93C2×D172—48no—
94C2×D172—44no—
95C2×D172C22×C418yes—
96C2×C8×C43—28no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43C22⋊C4116yescomplemented
100C2×C8×C43C22×C414yes—
101C2×C8×C43C2×D414yes—
102C2×C8×C43C2×D414yes—
103C2×C8×C43C2×D414yes—
104C42×C43—24no—
105C42×C43—22no—
106C42×C43—22no—
107(C2×D43)⋊C4—432no—
108C4⋊Dic43—24no—
109C4⋊Dic43—24no—
110C4⋊Dic43—44no—
111D344—232no—
112C23×C43C4×D412yes—
113C23×C43#12112yes—
114C23×C43#12712yes—
115C23×C43AGL(1,ℤ/8)18yes—
116C23×C43C22×D411yescharacteristic
117C22×D43—28no—
118C22×D43—44no—
119C22×D43—44no—
120C22×D43—48no—
121C22×D43—48no—
122C22×D43—416no—
123C22×D43—432no—
124C22×D43—816no—
125C22×D43—88no—
126C22×D43—88no—
127C2×C4×C43—24no—
128C2×C4×C43—28no—
129C2×C4×C43—48no—
130C2×C4×C43C2×C22⋊C414yes—
131C2×C4×C43C4×D414yes—
132C2×C4×C43C4×D412yes—
133C2×C4×C43#12114yes—
134C2×C4×C43#12112yes—
135C2×C4×C43#12414yes—
136C2×C4×C43#12712yes—
137C2×C4×C43C23×C411yescharacteristic
138C2×C4×C43C22×D411yescharacteristic
139C2×C4×C43C22×D411yescharacteristic
140C2×C4×C43C22×D411yescharacteristic
141C2×C4×C43C2×#4111yescharacteristic
142C2×C4×C43C2×#4111yescharacteristic
143C2×Dic43—44no—
144C2×Dic43—48no—
145C2×Dic43—88no—
146D172—28no—
147D172—28no—
148D172—44no—
149D172—44no—
150D172—416no—
151C8×C43—24no—
152C8×C43C2×C22⋊C418yescomplemented
153C2×#1972—431nomaximal, Sylow
154C22×C43#39014yes—
155C22×C43#44218yes—
156C22×C43#46918yes—
157C22×C43#49618yes—
158C22×C43C2×C4×D411yescharacteristic
159C22×C43C2×#12111yescharacteristic
160C22×C43C2×#12711yescharacteristic
161C22×C43C2×AGL(1,ℤ/8)14yes—
162C2×D43—416no—
163C2×D43—48no—
164C2×D43—84no—
165C2×D43—84no—
166C2×D43—832no—
167C2×D43—88no—
168C4×C43—44no—
169C4×C43#39014yes—
170C4×C43C22×C22⋊C411yescharacteristic
171C4×C43C2×C4×D411yescharacteristic
172C4×C43C2×#12111yescharacteristic
173C4×C43C2×#12411yescharacteristic
174Dic43—84no—
175C23×D8—431no—
176C22×#106—431no—
177C22×#102—432no—
178C22×#97D4311yescharacteristic, complemented
179C2×#390—432no—
180#1972—438no—
181C2×C43#197218yescomplemented
182C2×C43C2×#39011yescharacteristic
183C2×C43C2×#44212yes—
184C2×C43C2×#46912yes—
185C2×C43C2×#49612yes—
186D43—88no—
187C23×D4—432no—
188C22×D8—434no—
189C22×D8—438no—
190C22×D8—864no—
191C22×D8—864no—
192C23×C8C2×D4311yescharacteristic
193C23×C8C2×D4311yescharacteristic
194C22×C4⋊C4—432no—
195C22×C22⋊C4—864no—
196C22×C42C2×D4311yescharacteristic
197C2×#106—434no—
198C2×#106—864no—
199C2×#102—438no—
200C2×#102—868no—
201C2×#97—24no—
202C2×#97C2×D4314yescomplemented
203#390—438no—
204#390—864no—
205C43C2×#197211yescharacteristic, complemented, Sylow
206C25—862no—
207C22×D4—438no—
208C22×D4—434no—
209C22×D4—864no—
210C22×D4—864no—
211C22×D4—862no—
212C22×D4—864no—
213C22×D4—864no—
214C22×D4—864no—
215C23×C4—862no—
216C23×C4D17212yes—
217C23×C4C22×D4311yescharacteristic
218C2×D8—4316no—
219C2×D8—8632no—
220C2×D8—868no—
221C2×D8—868no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8C4×D4314yes—
225C22×C8D17214yes—
226C22×C8D17214yes—
227C22×C8C22⋊D4314yes—
228C22×C8C22×D4312yes—
229C22×C8C22×D4312yes—
230C2×C4⋊C4—434no—
231C2×C4⋊C4—864no—
232C2×C4⋊C4—864no—
233C2×C4⋊C4—862no—
234C2×C22⋊C4—8616no—
235C2×C22⋊C4—17216no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42D17212yes—
239C2×C42C22×D4312yes—
240#106—868no—
241#102—8616no—
242#97—28no—
243C24—868no—
244C24—864no—
245C24—1724no—
246C24—1724no—
247C24—1728no—
248C24—1728no—
249C24C2×D17211yescharacteristic
250C2×D4—438no—
251C2×D4—8616no—
252C2×D4—8616no—
253C2×D4—868no—
254C2×D4—864no—
255C2×D4—864no—
256C2×D4—864no—
257C2×D4—864no—
258C2×D4—864no—
259C2×D4—1724no—
260C2×D4—1728no—
261C2×D4—1728no—
262C2×D4—1724no—
263C22×C4—24no—
264C22×C4—28no—
265C22×C4—864no—
266C22×C4—1724no—
267C22×C4—1728no—
268C22×C4C2×C4×D4312yes—
269C22×C4C2×D17214yes—
270C22×C4C2×D17212yes—
271C22×C4C2×D17211yescharacteristic
272C22×C4C2×D17212yes—
273C22×C4#1062189812yes—
274C22×C4#1062189812yes—
275C22×C4C2×C22⋊D4312yes—
276C22×C4C23×D4311yescharacteristic
277D8—8632no—
278C2×C8—28no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8(C2×D43)⋊C4116yescomplemented
282C2×C8C2×C4×D4314yes—
283C2×C8C2×D17214yes—
284C2×C8C2×D17214yes—
285C2×C8C2×C22⋊D4314yes—
286C4⋊C4—864no—
287C4⋊C4—864no—
288C4⋊C4—1724no—
289C22⋊C4—17232no—
290C42—24no—
291C42—22no—
292C42—22no—
293C23—868no—
294C23—34416no—
295C23—3448no—
296C23—3448no—
297C23—17216no—
298C23—1724no—
299C23—1728no—
300C23—1728no—
301C23—1724no—
302C23—17232no—
303C23C4×D17212yes—
304C23#1306329912yes—
305C23#1306332212yes—
306C23#1306335318yes—
307C23C22×D17211yescharacteristic
308D4—868no—
309D4—868no—
310D4—17216no—
311D4—1724no—
312D4—1724no—
313C2×C4—24no—
314C2×C4—28no—
315C2×C4—48no—
316C2×C4—3448no—
317C2×C4—1728no—
318C2×C4—1724no—
319C2×C4C2×(C2×D43)⋊C414yes—
320C2×C4C4×D17212yes—
321C2×C4C4×D17214yes—
322C2×C4#1306329912yes—
323C2×C4#1306329914yes—
324C2×C4#1306331314yes—
325C2×C4#1306332212yes—
326C2×C4C22×C4×D4311yescharacteristic
327C2×C4C22×C22⋊D4311yescharacteristic
328C2×C4C22×D17211yescharacteristic
329C2×C4C22×D17211yescharacteristic
330C2×C4C2×#1062189811yescharacteristic
331C2×C4C2×#1062189811yescharacteristic
332C8—24no—
333C8C2×(C2×D43)⋊C418yescomplemented
334C22—3444no—
335C22—3444no—
336C22—34432no—
337C22—3448no—
338C22—1728no—
339C22—17216no—
340C22#1458280114yes—
341C22#1458301218yes—
342C22#1458315218yes—
343C22#1458328818yes—
344C22C2×C4×D17211yescharacteristic
345C22C2×#1306329911yescharacteristic
346C22C2×#1306332211yescharacteristic
347C22C2×#1306335314yes—
348C4—44no—
349C4—3444no—
350C4#1458280114yes—
351C4C22×(C2×D43)⋊C411yescharacteristic
352C4C2×C4×D17211yescharacteristic
353C4C2×#1306329911yescharacteristic
354C4C2×#1306331311yescharacteristic
355C2—3448no—
356C2#1913547118yesdirect product factor
357C2C2×#1458280111yescharacteristic
358C2C2×#1458301212yes—
359C2C2×#1458315212yes—
360C2C2×#1458328812yes—
subgroupG/H
centerC24C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#97×C43C2
socleC24×C43C2×D4
prime radicalC23×D344C2
cosocleC22×C4×C43C24
hypercenterC22×#97D43
hypocenterC43C2×#1972
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
2. C22×#13063257C2semidirect
3. C22×#13063247C2semidirect
4. C2×#14582801C2semidirect
5. #19135471C2direct (N × H)
6. C22×#97×C43C2semidirect
10. C22×D344C4semidirect
15. C2×#13063257C22semidirect
17. C2×#13063247C22semidirect
19. #14582801C22semidirect
24. C2×#97×C43C22semidirect
38. C2×D344C2×C4semidirect
99. C2×C8×C43C22⋊C4semidirect
152. C8×C43C2×C22⋊C4semidirect
178. C22×#97D43semidirect
181. C2×C43#1972semidirect
202. C2×#97C2×D43semidirect
205. C43C2×#1972semidirect
281. C2×C8(C2×D43)⋊C4semidirect
333. C8C2×(C2×D43)⋊C4semidirect
356. C2#19135471direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3442
C22×#130632572
C22×#130632472
C2×#145828012
#191354712
C22×#97×C432
C2×#197243