Finite Group Databasebeta

← C2×#19145134 #25966230

Subgroups — C2×#19145134 #25966230

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583527C212yesmaximal
2#19145134C2116yesmaximal, direct product factor
3C2×#14583308C214yesmaximal, complemented
4C2×#14583304C212yesmaximal, complemented
5C2×#14583301C212yesmaximal, complemented
6C2×#14582941C212yesmaximal
7C2×#14582937C211yesmaximal, characteristic
8C22×#13063259C211yesmaximal, 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#14583304C22116yescomplemented
21#14583301C22116yescomplemented
22#14582941C22116yes—
23#14582937C2218yes—
24C2×#13063259C2212yes—
25C2×#13063259C2212yes—
26C2×#13063259C2218yes—
27C2×#13063259C2211yescharacteristic
28C2×#13063259C2211yescharacteristic
29C2×#13063259C2214yes—
30C2×#13063257C2212yes—
31C2×#13063257C2214yes—
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#13063259C2314yes—
61#13063259C2318yes—
62#13063259C2314yes—
63#13063259C23116yes—
64#13063259C2318yes—
65#13063257C23116yes—
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×C43D411yescharacteristic
78C2×C4⋊C4×C43D411yescharacteristic
79C2×C22⋊C4×C43D412yes—
80C2×C42×C43C2312yes—
81#97×C43C2318yes—
82C4×C8×C43C2318yes—
83C24×C43C2×D411yescharacteristic
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×Q814yes—
89C22×C4×C43C2×Q814yes—
90C22×C4×C43C2411yescharacteristic
91C22×C4×C43C2412yes—
92C22×Dic43—22no—
93C22×Dic43—22no—
94C22×Dic43—24no—
95C22×Dic43—28no—
96C22×Dic43—84no—
97C2×Dic86—216no—
98C2×Dic86—88no—
99M16×C43C2×Q8116yescomplemented
100C2×C8×C43C2×Q814yes—
101C2×C8×C43C2×Q814yes—
102C2×C8×C43C2×Q818yes—
103C2×C8×C43C2×Q8116yescomplemented
104C2×C8×C43C2412yes—
105C2×C8×C43C2414yes—
106C2×C8×C43C2412yes—
107C4⋊C4×C43C2×D414yes—
108C4⋊C4×C43C2×D414yes—
109C22⋊C4×C43C2×D418yes—
110C42×C43C2×D414yes—
111C42×C43C2414yes—
112C22⋊Dic43—28no—
113C4⋊Dic43—28no—
114C4⋊Dic43—24no—
115C4⋊Dic43—216no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43C2414yes—
119C4⋊Dic43C2418yes—
120C4⋊Dic43C2414yes—
121Dic43⋊C4—216no—
122Dic43⋊C4—216no—
123C4×Dic43—28no—
124C23×C43—22no—
125C23×C43—22no—
126C23×C43C4⋊Q814yes—
127C23×C43C22×D412yes—
128C23×C43C22×D411yescharacteristic
129C2×C4×C43—24no—
130C2×C4×C43—24no—
131C2×C4×C43C4⋊Q818yes—
132C2×C4×C43C4⋊Q814yes—
133C2×C4×C43C22×D414yes—
134C2×C4×C43C22×D414yes—
135C2×C4×C43C22×D412yes—
136C2×C4×C43C22×D411yescharacteristic
137C2×C4×C43C22×Q812yes—
138C2×C4×C43C22×Q812yes—
139C2×C4×C43C22×Q814yes—
140C2×C4×C43C22×Q814yes—
141C2×C4×C43C2511yescharacteristic
142C2×Dic43—24no—
143C2×Dic43—24no—
144C2×Dic43—28no—
145C2×Dic43—44no—
146C2×Dic43—48no—
147C2×Dic43—44no—
148C2×Dic43—88no—
149Dic86—816no—
150C8×C43C22×Q814yes—
151C8×C43C22×Q814yes—
152C8×C43C22×Q818yes—
153C2×#3164—431nomaximal, Sylow
154C22×C43—28no—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43C2×C4⋊Q814yes—
158C22×C43C2×C4⋊Q812yes—
159C22×C43#57612yes—
160C22×C43#57812yes—
161C22×C43C23×D411yescharacteristic
162C4×C43—24no—
163C4×C43—24no—
164C4×C43C2×C4⋊Q814yes—
165C4×C43C2×C4⋊Q812yes—
166C4×C43C23×Q811yescharacteristic
167C4×C43C23×Q811yescharacteristic
168Dic43—44no—
169Dic43—48no—
170Dic43—44no—
171C2×#544—432no—
172#3164—4316no—
173C2×#501—434no—
174C2×#500—432no—
175C2×#499—432no—
176C2×#428—432no—
177C2×#427—431no—
178C22×#107—431no—
179C2×#405D4311yescharacteristic
180C2×C43—24no—
181C2×C43#316414yescomplemented
182C2×C43C22×C4⋊Q811yescharacteristic
183C2×C43C2×#57611yescharacteristic
184C2×C43C2×#57811yescharacteristic
185C22×M16C2×D4311yescharacteristic
186C23×C8C2×D4311yescharacteristic
187#544—4316no—
188#544—868no—
189C2×C4⋊Q8—434no—
190C2×C4⋊Q8—862no—
191C2×#125—434no—
192C2×#125—862no—
193C2×C22⋊Q8—864no—
194C2×#117—432no—
195C2×#117C2×D4311yescharacteristic
196C22×C4⋊C4—432no—
197#501—4332no—
198#500—4316no—
199#499—4316no—
200#428—4316no—
201#427—438no—
202C2×#107—431no—
203C2×#107—432no—
204C2×#107—431no—
205C2×#107—434no—
206C2×#107—432no—
207C2×#107—438no—
208C2×#106—434no—
209C2×#106—432no—
210#405C2×D4318yes—
211C2×#97C2×D4312yes—
212C2×C4×C8C2×D4312yes—
213C43C2×#316411yescharacteristic, complemented, Sylow
214C22×Q8—864no—
215C23×C4—862no—
216C23×C4C22×D4311yescharacteristic
217C2×M16Dic8618yescomplemented
218C2×M16C22×D4314yes—
219C22×C8Dic8618yescomplemented
220C22×C8C22×D4311yescharacteristic
221C22×C8C22×D4311yescharacteristic
222C22×C8C22×D4312yes—
223C22×C8C22×D4314yes—
224C4⋊Q8—4316no—
225C4⋊Q8—8616no—
226C4⋊Q8—868no—
227#125—4316no—
228#125—8616no—
229#125—868no—
230C22⋊Q8—8632no—
231#117—438no—
232#117—864no—
233#117D17214yes—
234#117C22×D4314yes—
235C2×C4⋊C4—434no—
236C2×C4⋊C4—438no—
237C2×C4⋊C4—432no—
238C2×C4⋊C4—432no—
239C2×C4⋊C4—862no—
240C2×C4⋊C4—864no—
241C2×C4⋊C4—864no—
242C2×C4⋊C4—864no—
243C2×C4⋊C4—864no—
244C2×C4⋊C4D17211yescharacteristic
245C2×C4⋊C4D17211yescharacteristic
246C2×C22⋊C4—862no—
247C2×C22⋊C4D17212yes—
248C2×C42—862no—
249C2×C42C22×D4312yes—
250#107—438no—
251#107—438no—
252#107—434no—
253#107—434no—
254#107—4316no—
255#106—438no—
256#106—4316no—
257#97C22×D4318yes—
258C4×C8C22×D4318yes—
259C24C2×D17211yescharacteristic
260C2×Q8—8616no—
261C2×Q8—3448no—
262C22×C4—868no—
263C22×C4—862no—
264C22×C4—862no—
265C22×C4—864no—
266C22×C4—3444no—
267C22×C4C2×Dic8614yes—
268C22×C4C2×Dic8614yes—
269C22×C4C2×D17212yes—
270C22×C4C2×D17212yes—
271C22×C4C2×D17212yes—
272C22×C4C2×D17211yescharacteristic
273C22×C4C23×D4312yes—
274C22×C4C23×D4311yescharacteristic
275M16C2×Dic86116yescomplemented
276C2×C8C2×Dic8614yes—
277C2×C8C2×Dic8614yes—
278C2×C8C2×Dic8618yes—
279C2×C8C2×Dic86116yescomplemented
280C2×C8C23×D4312yes—
281C2×C8C23×D4314yes—
282C2×C8C23×D4312yes—
283C4⋊C4—434no—
284C4⋊C4—438no—
285C4⋊C4—434no—
286C4⋊C4—868no—
287C4⋊C4—864no—
288C4⋊C4—862no—
289C4⋊C4—862no—
290C4⋊C4—8616no—
291C4⋊C4—8616no—
292C4⋊C4—8616no—
293C4⋊C4C2×D17214yes—
294C4⋊C4C2×D17214yes—
295C22⋊C4—868no—
296C22⋊C4C2×D17218yes—
297C42—868no—
298C42C2×D17214yes—
299C42C23×D4314yes—
300C23—22no—
301C23—22no—
302C23#1306332514yes—
303C23C22×D17212yes—
304C23C22×D17211yescharacteristic
305Q8—34416no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—864no—
309C2×C4—864no—
310C2×C4—868no—
311C2×C4—3448no—
312C2×C4—1728no—
313C2×C4—1724no—
314C2×C4—1724no—
315C2×C4#1306332518yes—
316C2×C4#1306332514yes—
317C2×C4C22×D17214yes—
318C2×C4C22×D17214yes—
319C2×C4C22×D17212yes—
320C2×C4C22×D17211yescharacteristic
321C2×C4C22×Dic8612yes—
322C2×C4C22×Dic8612yes—
323C2×C4C22×Dic8614yes—
324C2×C4C22×Dic8614yes—
325C2×C4C24×D4311yescharacteristic
326C8C22×Dic8614yes—
327C8C22×Dic8614yes—
328C8C22×Dic8618yes—
329C22—22no—
330C22—22no—
331C22—28no—
332C22C2×#1306332514yes—
333C22C2×#1306332512yes—
334C22#1458370412yes—
335C22#1458371612yes—
336C22C23×D17211yescharacteristic
337C4—24no—
338C4—24no—
339C4—1728no—
340C4—1724no—
341C4—1724no—
342C4C2×#1306332514yes—
343C4C2×#1306332512yes—
344C4C23×Dic8611yescharacteristic
345C4C23×Dic8611yescharacteristic
346C2—24no—
347C2#1914513414yesdirect product factor
348C2C22×#1306332511yescharacteristic
349C2C2×#1458370411yescharacteristic
350C2C2×#1458371611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#405C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC2×#405D43
hypocenterC43C2×#3164
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. #19145134C2direct (N × H)
3. C2×#14583308C2semidirect
4. C2×#14583304C2semidirect
5. C2×#14583301C2semidirect
19. #14583308C22semidirect
20. #14583304C22semidirect
21. #14583301C22semidirect
68. C2×M16×C43Q8semidirect
70. C22×C8×C43Q8semidirect
99. M16×C43C2×Q8semidirect
103. C2×C8×C43C2×Q8semidirect
181. C2×C43#3164semidirect
213. C43C2×#3164semidirect
217. C2×M16Dic86semidirect
219. C22×C8Dic86semidirect
275. M16C2×Dic86semidirect
279. C2×C8C2×Dic86semidirect
347. C2#19145134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835272
#191451342
C2×#145833082
C2×#145833042
C2×#145833012
C2×#145829412
C2×#145829372
C22×#130632592
C2×C43×#4052
C2×#316443