Finite Group Databasebeta

← C2×#19140425 #25263664

Subgroups — C2×#19140425 #25263664

Order 11008.

2614 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063317C211yesmaximal, characteristic, complemented
2#19140425C2116yesmaximal, direct product factor
3C2×#14582832C214yesmaximal, complemented
4C2×#14582822C214yesmaximal
5C2×#14582797C212yesmaximal, complemented
6C2×#14582769C211yesmaximal, characteristic, complemented
7C2×#14582759C212yesmaximal
8C22×#117×C43C211yesmaximal, characteristic
9C2×#13063317—28no—
10C2×#13063317C2218yescomplemented
11C22×C4⋊Dic43C2212yes—
12C22×C4⋊Dic43C2212yes—
13C22×C4⋊Dic43C2214yes—
14C22×Dic43⋊C4C2214yes—
15C22×Dic43⋊C4C2214yes—
16C22×C22⋊Dic43C2214yes—
17#14582832C22132yescomplemented
18#14582822C22132yes—
19#14582797C22116yescomplemented
20#14582769C2218yescomplemented
21#14582759C22116yes—
22C2×C43⋊#95C2214yes—
23C2×C43⋊#95C2214yes—
24C24×C4×C43C2211yescharacteristic
25C2×#117×C43—28no—
26C2×#117×C43C2218yes—
27C22×C4⋊C4×C43C2212yes—
28C22×C22⋊C4×C43C2212yes—
29C22×C42×C43C2211yescharacteristic
30C22×C42×C43C2211yescharacteristic
31C23×Dic43C2314yes—
32C23×Dic43C2314yes—
33#13063317—232no—
34C2×C4⋊Dic43—28no—
35C2×C4⋊Dic43—28no—
36C2×C4⋊Dic43—48no—
37C2×C4⋊Dic43C2318yes—
38C2×C4⋊Dic43C2318yes—
39C2×C4⋊Dic43C23116yes—
40C2×Dic43⋊C4—216no—
41C2×Dic43⋊C4—48no—
42C2×Dic43⋊C4C23116yes—
43C2×Dic43⋊C4C23116yes—
44C2×C22⋊Dic43—48no—
45C2×C22⋊Dic43C23116yes—
46C43⋊#95C23116yes—
47C43⋊#95C23116yes—
48C25×C43C2311yescharacteristic
49C23×C4×C43—24no—
50C23×C4×C43—24no—
51C23×C4×C43Q818yes—
52C23×C4×C43C2312yes—
53C23×C4×C43C2312yes—
54C23×C4×C43C2311yescharacteristic
55C23×C4×C43C2314yes—
56C23×C4×C43C2311yescharacteristic
57#117×C43—232no—
58C2×C4⋊C4×C43—28no—
59C2×C4⋊C4×C43C2318yes—
60C2×C22⋊C4×C43—28no—
61C2×C22⋊C4×C43C2318yes—
62C2×C42×C43—24no—
63C2×C42×C43D418yes—
64C2×C42×C43C2314yes—
65C2×C42×C43C2314yes—
66C24×C43—22no—
67C24×C43—22no—
68C24×C43—24no—
69C24×C43—24no—
70C24×C43C2×Q814yes—
71C24×C43C2412yes—
72C24×C43C2411yescharacteristic
73C22×C4×C43—232no—
74C22×C4×C43—28no—
75C22×C4×C43—28no—
76C22×C4×C43—22no—
77C22×C4×C43—24no—
78C22×C4×C43—22no—
79C22×C4×C43—24no—
80C22×C4×C43—24no—
81C22×C4×C43—24no—
82C22×C4×C43—24no—
83C22×C4×C43C2×D418yes—
84C22×C4×C43C2×D414yes—
85C22×C4×C43C2×Q8116yes—
86C22×C4×C43C2×Q814yes—
87C22×C4×C43C2×Q814yes—
88C22×C4×C43#4114yes—
89C22×C4×C43C2414yes—
90C22×C4×C43C2414yes—
91C22×C4×C43C2412yes—
92C22×C4×C43C2412yes—
93C22×Dic43—28no—
94C22×Dic43—28no—
95C22×Dic43—28no—
96C22×Dic43—28no—
97C22×Dic43—28no—
98C22×Dic43—28no—
99C22×Dic43C2418yes—
100C22×Dic43C2418yes—
101C4⋊C4×C43—216no—
102C22⋊C4×C43—216no—
103C42×C43—28no—
104C42×C43C2×D4116yes—
105C22⋊Dic43—416no—
106C4⋊Dic43—216no—
107C4⋊Dic43—216no—
108C4⋊Dic43—416no—
109Dic43⋊C4—232no—
110Dic43⋊C4—416no—
111C23×C43—28no—
112C23×C43—216no—
113C23×C43—22no—
114C23×C43—22no—
115C23×C43—24no—
116C23×C43—24no—
117C23×C43—48no—
118C23×C43—44no—
119C23×C43—44no—
120C23×C43C22×D412yes—
121C23×C43C22×Q814yes—
122C23×C43C22×Q812yes—
123C23×C43C2×#4112yes—
124C23×C43H(5,𝔽2)14yes—
125C23×C432−1+414yes—
126C23×C43C2511yescharacteristic
127C2×C4×C43—28no—
128C2×C4×C43—216no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—24no—
132C2×C4×C43—24no—
133C2×C4×C43—232no—
134C2×C4×C43—24no—
135C2×C4×C43—24no—
136C2×C4×C43—24no—
137C2×C4×C43—48no—
138C2×C4×C43C22⋊Q8116yes—
139C2×C4×C43C22×D418yes—
140C2×C4×C43C22×D414yes—
141C2×C4×C43C22×Q814yes—
142C2×C4×C43C22×Q814yes—
143C2×C4×C43C2×#4114yes—
144C2×Dic43—28no—
145C2×Dic43—28no—
146C2×Dic43—28no—
147C2×Dic43—28no—
148C2×Dic43—28no—
149C2×Dic43—28no—
150C2×Dic43—416no—
151C2×Dic43—416no—
152C2×#2629—431nomaximal, Sylow
153C22×C43—24no—
154C22×C43—28no—
155C22×C43—416no—
156C22×C43—44no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43C2×C22⋊Q814yes—
160C22×C43#53718yes—
161C22×C43#54014yes—
162C22×C43#54114yes—
163C22×C43#54418yes—
164C22×C43C23×D411yescharacteristic
165C22×C43C23×Q811yescharacteristic
166C22×C43C22×#4111yescharacteristic
167C22×C43C2×H(5,𝔽2)12yes—
168C22×C43C2×2−1+412yes—
169C4×C43—24no—
170C4×C43—28no—
171C4×C43—44no—
172C4×C43C2×C22⋊Q818yes—
173Dic43—48no—
174Dic43—48no—
175C22×#125—431no—
176C22×#117D4311yescharacteristic
177#2629—4316no—
178C2×#398—434no—
179C2×#396—434no—
180C2×#389—432no—
181C2×#384—431no—
182C2×#380—432no—
183C2×C43—44no—
184C2×C43#262918yescomplemented
185C2×C43C22×C22⋊Q811yescharacteristic
186C2×C43C2×#53712yes—
187C2×C43C2×#54011yescharacteristic
188C2×C43C2×#54111yescharacteristic
189C2×C43C2×#54412yes—
190C24×C4C2×D4311yescharacteristic
191C2×#125—438no—
192C2×#125—868no—
193C2×#117—28no—
194C2×#117C2×D4318yes—
195C22×C4⋊C4—434no—
196C22×C4⋊C4—432no—
197C22×C4⋊C4—432no—
198C22×C4⋊C4—434no—
199C22×C4⋊C4—434no—
200C22×C4⋊C4C2×D4312yes—
201C22×C22⋊C4—434no—
202C22×C22⋊C4C2×D4312yes—
203C22×C42C2×D4311yescharacteristic
204C22×C42C2×D4311yescharacteristic
205#398—4332no—
206#396—4332no—
207#389—4316no—
208#384—438no—
209#380—4316no—
210C2×#95—434no—
211C2×#95—434no—
212C43C2×#262911yescharacteristic, complemented, Sylow
213C25C22×D4311yescharacteristic
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—434no—
217C23×C4—434no—
218C23×C4Dic8618yes—
219C23×C4C22×D4312yes—
220C23×C4C22×D4314yes—
221C23×C4C22×D4311yescharacteristic
222C23×C4C22×D4312yes—
223C23×C4C22×D4311yescharacteristic
224#125—8632no—
225#117—232no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—4316no—
228C2×C4⋊C4—438no—
229C2×C4⋊C4—438no—
230C2×C4⋊C4—4316no—
231C2×C4⋊C4—4316no—
232C2×C4⋊C4—868no—
233C2×C4⋊C4—8616no—
234C2×C4⋊C4—868no—
235C2×C4⋊C4—1728no—
236C2×C4⋊C4—1728no—
237C2×C4⋊C4C22×D4318yes—
238C2×C22⋊C4—28no—
239C2×C22⋊C4—4316no—
240C2×C22⋊C4—1728no—
241C2×C22⋊C4C22×D4318yes—
242C2×C42—24no—
243C2×C42C22⋊D4318yes—
244C2×C42C22×D4314yes—
245C2×C42C22×D4314yes—
246#95—4316no—
247#95—4316no—
248C24—22no—
249C24—22no—
250C24—24no—
251C24—24no—
252C24C2×Dic8614yes—
253C24C23×D4312yes—
254C24C23×D4311yescharacteristic
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—232no—
260C22×C4—28no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—438no—
266C22×C4—438no—
267C22×C4—868no—
268C22×C4—868no—
269C22×C4—868no—
270C22×C4—868no—
271C22×C4—868no—
272C22×C4—868no—
273C22×C4C2×Dic8614yes—
274C22×C4C2×Dic86116yes—
275C22×C4C2×Dic8614yes—
276C22×C4#1062189814yes—
277C22×C4C2×C22⋊D4318yes—
278C22×C4C2×C22⋊D4314yes—
279C22×C4C23×D4314yes—
280C22×C4C23×D4314yes—
281C22×C4C23×D4312yes—
282C22×C4C23×D4312yes—
283C4⋊C4—216no—
284C4⋊C4—8632no—
285C4⋊C4—8616no—
286C4⋊C4—8616no—
287C4⋊C4—17216no—
288C4⋊C4—17216no—
289C22⋊C4—216no—
290C22⋊C4—17216no—
291C42—28no—
292C42C2×C22⋊D43116yes—
293C23—28no—
294C23—22no—
295C23—22no—
296C23—24no—
297C23—24no—
298C23—216no—
299C23—48no—
300C23—44no—
301C23—44no—
302C23C22×C22⋊D4312yes—
303C23C22×Dic8614yes—
304C23C22×Dic8612yes—
305C23C2×#1062189812yes—
306C23#1306337114yes—
307C23#1306337214yes—
308C23C24×D4311yescharacteristic
309C2×C4—28no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—216no—
315C2×C4—232no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—48no—
320C2×C4—868no—
321C2×C4—868no—
322C2×C4—868no—
323C2×C4—868no—
324C2×C4—868no—
325C2×C4—868no—
326C2×C4—17216no—
327C2×C4—17216no—
328C2×C4#13063304116yes—
329C2×C4C22×C22⋊D4318yes—
330C2×C4C22×C22⋊D4314yes—
331C2×C4C22×Dic8614yes—
332C2×C4C22×Dic8614yes—
333C2×C4C2×#1062189814yes—
334C22—24no—
335C22—28no—
336C22—416no—
337C22—44no—
338C22—42no—
339C22—42no—
340C22C2×#1306330414yes—
341C22#1458347718yes—
342C22#1458350414yes—
343C22#1458351114yes—
344C22#1458352718yes—
345C22C23×C22⋊D4311yescharacteristic
346C22C23×Dic8611yescharacteristic
347C22C22×#1062189811yescharacteristic
348C22C2×#1306337112yes—
349C22C2×#1306337212yes—
350C4—24no—
351C4—28no—
352C4—44no—
353C4—1728no—
354C4—1728no—
355C4C2×#1306330418yes—
356C2—44no—
357C2#1914042518yesdirect product factor
358C2C22×#1306330411yescharacteristic
359C2C2×#1458347712yes—
360C2C2×#1458350411yescharacteristic
361C2C2×#1458351111yescharacteristic
362C2C2×#1458352712yes—
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#117×C43C2
socleC24×C43C24
prime radicalC25×C43C23
hypercenterC22×#117D43
hypocenterC43C2×#2629
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#13063317C2semidirect
2. #19140425C2direct (N × H)
3. C2×#14582832C2semidirect
5. C2×#14582797C2semidirect
6. C2×#14582769C2semidirect
10. C2×#13063317C22semidirect
17. #14582832C22semidirect
19. #14582797C22semidirect
20. #14582769C22semidirect
184. C2×C43#2629semidirect
212. C43C2×#2629semidirect
357. C2#19140425direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633172
#191404252
C2×#145828322
C2×#145828222
C2×#145827972
C2×#145827692
C2×#145827592
C22×#117×C432
C2×#262943