Finite Group Databasebeta

← C2×#19145126 #25966221

Subgroups — C2×#19145126 #25966221

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583527C212yesmaximal
2#19145126C2116yesmaximal, direct product factor
3C2×#14583308C214yesmaximal, complemented
4C2×#14583301C212yesmaximal, complemented
5C2×#14583297C212yesmaximal, complemented
6C2×#14582941C212yesmaximal
7C2×#14582937C211yesmaximal, characteristic
8C22×#13063257C211yesmaximal, characteristic
9C2×C43×#405C211yesmaximal, characteristic
10#14583527—28no—
11#14583527C22116yes—
12C2×#13063325C2214yes—
13C2×#13063324—22no—
14C2×#13063317C2214yes—
15C2×#13063316—22no—
16C2×#13063302—24no—
17C2×#13063284C2212yes—
18C22×C4⋊Dic43C2212yes—
19#14583308C22132yescomplemented
20#14583301C22116yescomplemented
21#14583297C22116yescomplemented
22#14582941C22116yes—
23#14582937C2218yes—
24C2×#13063259C2212yes—
25C2×#13063259C2214yes—
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2214yes—
29C2×#13063257C2212yes—
30C2×#13063257C2212yes—
31C2×#13063257C2218yes—
32C22×M16×C43C2211yescharacteristic
33C23×C8×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C43×#405C2218yes—
36C2×#97×C43C2212yes—
37C2×C4×C8×C43C2212yes—
38C22×Dic86—24no—
39C23×Dic43—22no—
40#13063325—28no—
41#13063325C23116yes—
42#13063324—216no—
43#13063317—28no—
44#13063317C23116yes—
45#13063316—216no—
46#13063302—232no—
47#13063284—24no—
48#13063284C2318yes—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—24no—
52C2×C4⋊Dic43C2314yes—
53C2×C4⋊Dic43C2318yes—
54C2×C4⋊Dic43C2312yes—
55C2×C4⋊Dic43C2312yes—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×C22⋊Dic43—22no—
59C2×C4×Dic43—22no—
60#13063259C23116yes—
61#13063259C2318yes—
62#13063257C2314yes—
63#13063257C2318yes—
64#13063257C23116yes—
65#13063257C2314yes—
66#13063257C2318yes—
67C23×C4×C43C2311yescharacteristic
68C2×M16×C43Q818yescomplemented
69C2×M16×C43C2314yes—
70C22×C8×C43Q818yescomplemented
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C22×C8×C43C2312yes—
74C22×C8×C43C2314yes—
75#117×C43D414yes—
76#117×C43C2314yes—
77C2×C4⋊C4×C43D412yes—
78C2×C22⋊C4×C43D412yes—
79C2×C42×C43C2312yes—
80#97×C43C2318yes—
81C4×C8×C43C2318yes—
82C24×C43C2×D411yescharacteristic
83C22×C4×C43C2×D414yes—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×Q814yes—
87C22×C4×C43C2×Q814yes—
88C22×C4×C43C2411yescharacteristic
89C22×C4×C43C2412yes—
90C22×Dic43—22no—
91C22×Dic43—22no—
92C22×Dic43—24no—
93C22×Dic43—28no—
94C22×Dic43—84no—
95C2×Dic86—216no—
96C2×Dic86—88no—
97M16×C43C2×Q8116yescomplemented
98C2×C8×C43C2×Q814yes—
99C2×C8×C43C2×Q814yes—
100C2×C8×C43C2×Q818yes—
101C2×C8×C43C2×Q8116yescomplemented
102C2×C8×C43C2412yes—
103C2×C8×C43C2414yes—
104C2×C8×C43C2412yes—
105C4⋊C4×C43C2×D418yes—
106C22⋊C4×C43C2×D418yes—
107C42×C43C2×D414yes—
108C42×C43C2414yes—
109C22⋊Dic43—28no—
110C4⋊Dic43—28no—
111C4⋊Dic43—24no—
112C4⋊Dic43—216no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43C2418yes—
116C4⋊Dic43C2414yes—
117C4⋊Dic43C2414yes—
118Dic43⋊C4—216no—
119Dic43⋊C4—216no—
120C4×Dic43—28no—
121C23×C43—24no—
122C23×C43C4⋊Q814yes—
123C23×C43C22×D412yes—
124C23×C43C22×D411yescharacteristic
125C2×C4×C43—28no—
126C2×C4×C43C4⋊Q818yes—
127C2×C4×C43C4⋊Q814yes—
128C2×C4×C43C22×D418yes—
129C2×C4×C43C22×D412yes—
130C2×C4×C43C22×D411yescharacteristic
131C2×C4×C43C22×Q812yes—
132C2×C4×C43C22×Q812yes—
133C2×C4×C43C22×Q814yes—
134C2×C4×C43C22×Q814yes—
135C2×C4×C43C2511yescharacteristic
136C2×Dic43—24no—
137C2×Dic43—24no—
138C2×Dic43—28no—
139C2×Dic43—44no—
140C2×Dic43—48no—
141C2×Dic43—44no—
142C2×Dic43—88no—
143Dic86—816no—
144C8×C43C22×Q814yes—
145C8×C43C22×Q814yes—
146C8×C43C22×Q818yes—
147C2×#3163—431nomaximal, Sylow
148C22×C43—28no—
149C22×C43—24no—
150C22×C43C2×C4⋊Q814yes—
151C22×C43C2×C4⋊Q812yes—
152C22×C43#57714yes—
153C22×C43C23×D411yescharacteristic
154C4×C43—28no—
155C4×C43C2×C4⋊Q814yes—
156C4×C43C2×C4⋊Q812yes—
157C4×C43C23×Q811yescharacteristic
158C4×C43C23×Q811yescharacteristic
159Dic43—44no—
160Dic43—48no—
161Dic43—44no—
162C2×#544—432no—
163#3163—4316no—
164C2×#501—434no—
165C2×#499—432no—
166C2×#498—432no—
167C2×#428—432no—
168C2×#427—431no—
169C22×#106—431no—
170C2×#405D4311yescharacteristic
171C2×C43—24no—
172C2×C43#316314yescomplemented
173C2×C43C22×C4⋊Q811yescharacteristic
174C2×C43C2×#57712yes—
175C22×M16C2×D4311yescharacteristic
176C23×C8C2×D4311yescharacteristic
177#544—4316no—
178#544—868no—
179C2×C4⋊Q8—434no—
180C2×C4⋊Q8—862no—
181C2×#125—434no—
182C2×#125—862no—
183C2×C22⋊Q8—864no—
184C2×#117—432no—
185C2×#117C2×D4311yescharacteristic
186C22×C4⋊C4—432no—
187#501—4332no—
188#499—4316no—
189#498—4316no—
190#428—4316no—
191#427—438no—
192C2×#107—434no—
193C2×#107—432no—
194C2×#106—431no—
195C2×#106—432no—
196C2×#106—434no—
197C2×#106—431no—
198C2×#106—432no—
199C2×#106—438no—
200#405C2×D4318yes—
201C2×#97C2×D4312yes—
202C2×C4×C8C2×D4312yes—
203C43C2×#316311yescharacteristic, complemented, Sylow
204C22×Q8—864no—
205C23×C4—862no—
206C23×C4C22×D4311yescharacteristic
207C2×M16Dic8618yescomplemented
208C2×M16C22×D4314yes—
209C22×C8Dic8618yescomplemented
210C22×C8C22×D4311yescharacteristic
211C22×C8C22×D4311yescharacteristic
212C22×C8C22×D4312yes—
213C22×C8C22×D4314yes—
214C4⋊Q8—4316no—
215C4⋊Q8—8616no—
216C4⋊Q8—868no—
217#125—4316no—
218#125—8616no—
219#125—868no—
220C22⋊Q8—8632no—
221#117—438no—
222#117—864no—
223#117D17214yes—
224#117C22×D4314yes—
225C2×C4⋊C4—434no—
226C2×C4⋊C4—438no—
227C2×C4⋊C4—432no—
228C2×C4⋊C4—432no—
229C2×C4⋊C4—862no—
230C2×C4⋊C4—864no—
231C2×C4⋊C4—864no—
232C2×C4⋊C4—864no—
233C2×C4⋊C4—864no—
234C2×C4⋊C4D17212yes—
235C2×C22⋊C4—862no—
236C2×C22⋊C4D17212yes—
237C2×C42—862no—
238C2×C42C22×D4312yes—
239#107—438no—
240#107—4316no—
241#106—438no—
242#106—438no—
243#106—434no—
244#106—434no—
245#106—4316no—
246#97C22×D4318yes—
247C4×C8C22×D4318yes—
248C24C2×D17211yescharacteristic
249C2×Q8—8616no—
250C2×Q8—3448no—
251C22×C4—868no—
252C22×C4—862no—
253C22×C4—862no—
254C22×C4—864no—
255C22×C4—3444no—
256C22×C4C2×Dic8614yes—
257C22×C4C2×Dic8614yes—
258C22×C4C2×D17214yes—
259C22×C4C2×D17212yes—
260C22×C4C2×D17211yescharacteristic
261C22×C4C23×D4312yes—
262C22×C4C23×D4311yescharacteristic
263M16C2×Dic86116yescomplemented
264C2×C8C2×Dic8614yes—
265C2×C8C2×Dic8614yes—
266C2×C8C2×Dic8618yes—
267C2×C8C2×Dic86116yescomplemented
268C2×C8C23×D4312yes—
269C2×C8C23×D4314yes—
270C2×C8C23×D4312yes—
271C4⋊C4—438no—
272C4⋊C4—434no—
273C4⋊C4—434no—
274C4⋊C4—868no—
275C4⋊C4—864no—
276C4⋊C4—862no—
277C4⋊C4—862no—
278C4⋊C4—8616no—
279C4⋊C4—8616no—
280C4⋊C4—8616no—
281C4⋊C4C2×D17218yes—
282C22⋊C4—868no—
283C22⋊C4C2×D17218yes—
284C42—868no—
285C42C2×D17214yes—
286C42C23×D4314yes—
287C23—24no—
288C23#1306332514yes—
289C23C22×D17212yes—
290C23C22×D17211yescharacteristic
291Q8—34416no—
292C2×C4—28no—
293C2×C4—864no—
294C2×C4—864no—
295C2×C4—868no—
296C2×C4—3448no—
297C2×C4—1728no—
298C2×C4—1724no—
299C2×C4—1724no—
300C2×C4#1306332518yes—
301C2×C4#1306332514yes—
302C2×C4C22×D17218yes—
303C2×C4C22×D17212yes—
304C2×C4C22×D17211yescharacteristic
305C2×C4C22×Dic8612yes—
306C2×C4C22×Dic8612yes—
307C2×C4C22×Dic8614yes—
308C2×C4C22×Dic8614yes—
309C2×C4C24×D4311yescharacteristic
310C8C22×Dic8614yes—
311C8C22×Dic8614yes—
312C8C22×Dic8618yes—
313C22—24no—
314C22—28no—
315C22C2×#1306332514yes—
316C22C2×#1306332512yes—
317C22#1458371114yes—
318C22C23×D17211yescharacteristic
319C4—28no—
320C4—1728no—
321C4—1724no—
322C4—1724no—
323C4C2×#1306332514yes—
324C4C2×#1306332512yes—
325C4C23×Dic8611yescharacteristic
326C4C23×Dic8611yescharacteristic
327C2—24no—
328C2#1914512614yesdirect product factor
329C2C22×#1306332511yescharacteristic
330C2C2×#1458371112yes—
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#405C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC2×#405D43
hypocenterC43C2×#3163
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #19145126C2direct (N × H)
3. C2×#14583308C2semidirect
4. C2×#14583301C2semidirect
5. C2×#14583297C2semidirect
19. #14583308C22semidirect
20. #14583301C22semidirect
21. #14583297C22semidirect
68. C2×M16×C43Q8semidirect
70. C22×C8×C43Q8semidirect
97. M16×C43C2×Q8semidirect
101. C2×C8×C43C2×Q8semidirect
172. C2×C43#3163semidirect
203. C43C2×#3163semidirect
207. C2×M16Dic86semidirect
209. C22×C8Dic86semidirect
263. M16C2×Dic86semidirect
267. C2×C8C2×Dic86semidirect
328. C2#19145126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835272
#191451262
C2×#145833082
C2×#145833012
C2×#145832972
C2×#145829412
C2×#145829372
C22×#130632572
C2×C43×#4052
C2×#316343