Finite Group Databasebeta

← C2×#19145131 #25966227

Subgroups — C2×#19145131 #25966227

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×#14583530C212yesmaximal
2#19145131C2116yesmaximal, direct product factor
3C2×#14583307C214yesmaximal, complemented
4C2×#14583303C212yesmaximal, complemented
5C2×#14583300C212yesmaximal, complemented
6C2×#14582939C212yesmaximal
7C2×#14582937C211yesmaximal, characteristic
8C2×#14582854C211yesmaximal, characteristic
9C22×#107×C43C211yesmaximal, characteristic
10C22×#10621877C2211yescharacteristic
11#14583530—28no—
12#14583530C22116yes—
13C2×#13063324—22no—
14C2×#13063324C2214yes—
15C2×#13063316—22no—
16C2×#13063316C2214yes—
17C2×#13063304—24no—
18C2×#13063284C2212yes—
19C2×#13063284C2211yescharacteristic
20#14583307C22132yescomplemented
21#14583303C22116yescomplemented
22#14583300C22116yescomplemented
23#14582939C22116yes—
24#14582937C2218yes—
25C2×#13063259C2211yescharacteristic
26C2×#13063259C2211yescharacteristic
27C2×#13063258C2214yes—
28C2×#13063257C2212yes—
29C2×#13063256C2214yes—
30#14582854C2218yes—
31C2×#13063235C2212yes—
32C2×C8×Dic43C2212yes—
33C23×C8×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2212yes—
35C2×#107×C43C2212yes—
36C2×#107×C43C2212yes—
37C2×#107×C43C2218yes—
38C22×Dic86—24no—
39C2×#10621877Q818yescomplemented
40C2×#10621877C2314yes—
41C22×C43⋊C8C2312yes—
42#13063324—216no—
43#13063324—28no—
44#13063324C23116yes—
45#13063316—216no—
46#13063316—28no—
47#13063316C23116yes—
48#13063304—232no—
49#13063284—24no—
50#13063284D414yes—
51#13063284C2318yes—
52#13063284C2314yes—
53C2×C4⋊Dic43—24no—
54C2×C4⋊Dic43D411yescharacteristic
55C2×C4⋊Dic43D411yescharacteristic
56C2×C4⋊Dic43C2312yes—
57C2×C4⋊Dic43C2312yes—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43D412yes—
62C2×C4×Dic43—22no—
63C2×C4×Dic43C2312yes—
64#13063259C2314yes—
65#13063259C2314yes—
66#13063258C23116yes—
67#13063257C2318yes—
68#13063256C23116yes—
69#13063235C2318yes—
70C8×Dic43C2318yes—
71C23×C4×C43—22no—
72C23×C4×C43C2311yescharacteristic
73C22×C8×C43Q818yescomplemented
74C22×C8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2314yes—
77C2×C4⋊C4×C43—22no—
78C2×C4⋊C4×C43—24no—
79C2×C4⋊C4×C43C2314yes—
80C2×C4⋊C4×C43C2318yes—
81#107×C43C2318yes—
82#107×C43C2318yes—
83C24×C43C2×D411yescharacteristic
84C22×C4×C43—24no—
85C22×C4×C43—28no—
86C22×C4×C43—84no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×Q814yes—
90C22×C4×C43C2×Q814yes—
91C22×C4×C43C2411yescharacteristic
92C22×C4×C43C2412yes—
93C22×Dic43—22no—
94C22×Dic43—22no—
95C22×Dic43C2×D412yes—
96C22×Dic43C2×D412yes—
97C2×Dic86—216no—
98C2×Dic86—88no—
99C2×C8×C43C2×Q814yes—
100C2×C8×C43C2×Q814yes—
101C2×C8×C43C2×Q8116yescomplemented
102C2×C8×C43C2412yes—
103C2×C8×C43C2412yes—
104C4⋊C4×C43—28no—
105C4⋊C4×C43—24no—
106C4⋊C4×C43C2418yes—
107C22⋊Dic43—28no—
108C22⋊Dic43C2×D418yes—
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43—216no—
112C4⋊Dic43C2×D414yes—
113C4⋊Dic43C2×D414yes—
114C4⋊Dic43C2414yes—
115C4⋊Dic43C2414yes—
116Dic43⋊C4—216no—
117Dic43⋊C4—216no—
118C4×Dic43—28no—
119C4×Dic43C2×D414yes—
120C4×Dic43C2414yes—
121#10621877C2×Q8116yescomplemented
122C2×C43⋊C8C2×Q818yes—
123C2×C43⋊C8C2414yes—
124C23×C43—22no—
125C23×C43—22no—
126C23×C43C4⋊Q814yes—
127C23×C43C22×D412yes—
128C23×C43C22×D411yescharacteristic
129C2×C4×C43—28no—
130C2×C4×C43—48no—
131C2×C4×C43—88no—
132C2×C4×C43C4⋊Q818yes—
133C2×C4×C43C4⋊Q814yes—
134C2×C4×C43C22×D412yes—
135C2×C4×C43C22×D411yescharacteristic
136C2×C4×C43C22×Q812yes—
137C2×C4×C43C22×Q814yes—
138C2×C4×C43C22×Q812yes—
139C2×C4×C43C22×Q814yes—
140C2×C4×C43C2511yescharacteristic
141C2×Dic43—24no—
142C2×Dic43—24no—
143C2×Dic43—24no—
144C2×Dic43—24no—
145C2×Dic43—44no—
146C2×Dic43—44no—
147C2×Dic43C22×D414yes—
148C2×Dic43C22×D414yes—
149Dic86—816no—
150C8×C43C22×Q814yes—
151C8×C43C22×Q814yes—
152C43⋊C8C22×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—48no—
163C4×C43C2×C4⋊Q814yes—
164C4×C43C2×C4⋊Q812yes—
165C4×C43C23×Q811yescharacteristic
166C4×C43C23×Q811yescharacteristic
167Dic43—24no—
168Dic43—24no—
169Dic43—44no—
170Dic43—44no—
171C2×#544—432no—
172#3164—4316no—
173C2×#501—434no—
174C2×#500—432no—
175C2×#499—432no—
176C2×#428—432no—
177C2×#427—431no—
178C22×#107D4311yescharacteristic
179C2×#405—431no—
180C2×C43—24no—
181C2×C43#316414yescomplemented
182C2×C43C22×C4⋊Q811yescharacteristic
183C2×C43C2×#57611yescharacteristic
184C2×C43C2×#57811yescharacteristic
185C22×M16—431no—
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—431no—
195C2×#117—432no—
196C22×C4⋊C4C2×D4312yes—
197#501—4332no—
198#500—4316no—
199#499—4316no—
200#428—4316no—
201#427—438no—
202C2×#107—431no—
203C2×#107—431no—
204C2×#107—434no—
205C2×#107C2×D4312yes—
206C2×#107C2×D4312yes—
207C2×#107C2×D4318yes—
208C2×#106—432no—
209C2×#106—434no—
210#405—438no—
211C2×#97—432no—
212C2×C4×C8—432no—
213C43C2×#316411yescharacteristic, complemented, Sylow
214C22×Q8—864no—
215C23×C4—22no—
216C23×C4C22×D4311yescharacteristic
217C2×M16—438no—
218C2×M16—434no—
219C22×C8—432no—
220C22×C8Dic8618yescomplemented
221C22×C8C22×D4311yescharacteristic
222C22×C8C22×D4311yescharacteristic
223C22×C8C22×D4314yes—
224C4⋊Q8—4316no—
225C4⋊Q8—868no—
226C4⋊Q8—8616no—
227#125—4316no—
228#125—868no—
229#125—8616no—
230C22⋊Q8—8632no—
231#117—434no—
232#117—434no—
233#117—438no—
234#117—864no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—432no—
240C2×C4⋊C4—432no—
241C2×C4⋊C4—864no—
242C2×C4⋊C4—864no—
243C2×C4⋊C4—864no—
244C2×C4⋊C4C22×D4314yes—
245C2×C4⋊C4C22×D4318yes—
246C2×C22⋊C4—432no—
247C2×C22⋊C4—862no—
248C2×C42—432no—
249C2×C42—862no—
250#107—434no—
251#107—434no—
252#107—4316no—
253#107C22×D4318yes—
254#107C22×D4318yes—
255#106—438no—
256#106—4316no—
257#97—438no—
258C4×C8—438no—
259C24D4×D4311yescharacteristic
260C2×Q8—8616no—
261C2×Q8—3448no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—84no—
265C22×C4—432no—
266C22×C4—432no—
267C22×C4—862no—
268C22×C4—862no—
269C22×C4C2×Dic8614yes—
270C22×C4D4×D4312yes—
271C22×C4D4×D4311yescharacteristic
272C22×C4Q8×D4314yes—
273C22×C4C23×D4312yes—
274C22×C4C23×D4311yescharacteristic
275M16—4316no—
276C2×C8—438no—
277C2×C8—434no—
278C2×C8C2×Dic8614yes—
279C2×C8C2×Dic8614yes—
280C2×C8C2×Dic86116yescomplemented
281C2×C8C23×D4312yes—
282C2×C8C23×D4312yes—
283C4⋊C4—24no—
284C4⋊C4—28no—
285C4⋊C4—434no—
286C4⋊C4—434no—
287C4⋊C4—434no—
288C4⋊C4—434no—
289C4⋊C4—8616no—
290C4⋊C4—8616no—
291C4⋊C4—8616no—
292C4⋊C4—862no—
293C4⋊C4—862no—
294C4⋊C4C23×D4318yes—
295C22⋊C4—438no—
296C22⋊C4—868no—
297C42—434no—
298C42—434no—
299C42—868no—
300C23—22no—
301C23—22no—
302C23#1306332414yes—
303C23C2×D4×D4312yes—
304C23C2×D4×D4311yescharacteristic
305Q8—34416no—
306C2×C4—28no—
307C2×C4—48no—
308C2×C4—88no—
309C2×C4—434no—
310C2×C4—434no—
311C2×C4—864no—
312C2×C4—864no—
313C2×C4—864no—
314C2×C4—864no—
315C2×C4—1724no—
316C2×C4—1724no—
317C2×C4#1306332418yes—
318C2×C4#1306332414yes—
319C2×C4C2×D4×D4311yescharacteristic
320C2×C4C2×D4×D4312yes—
321C2×C4C2×Q8×D4312yes—
322C2×C4C2×Q8×D4314yes—
323C2×C4C22×Dic8612yes—
324C2×C4C22×Dic8614yes—
325C2×C4C24×D4311yescharacteristic
326C8—438no—
327C8C22×Dic8614yes—
328C8C22×Dic8614yes—
329C22—22no—
330C22—22no—
331C22—28no—
332C22C2×#1306332414yes—
333C22C2×#1306332412yes—
334C22#1458370012yes—
335C22#1458371212yes—
336C22C22×D4×D4311yescharacteristic
337C4—48no—
338C4—864no—
339C4—864no—
340C4—1724no—
341C4—1724no—
342C4C2×#1306332412yes—
343C4C2×#1306332414yes—
344C4C22×Q8×D4311yescharacteristic
345C4C23×Dic8611yescharacteristic
346C2—24no—
347C2#1914513114yesdirect product factor
348C2C22×#1306332411yescharacteristic
349C2C2×#1458370011yescharacteristic
350C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#107×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC22×#107D43
hypocenterC43C2×#3164
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #19145131C2direct (N × H)
3. C2×#14583307C2semidirect
4. C2×#14583303C2semidirect
5. C2×#14583300C2semidirect
20. #14583307C22semidirect
21. #14583303C22semidirect
22. #14583300C22semidirect
39. C2×#10621877Q8semidirect
73. C22×C8×C43Q8semidirect
101. C2×C8×C43C2×Q8semidirect
121. #10621877C2×Q8semidirect
181. C2×C43#3164semidirect
213. C43C2×#3164semidirect
220. C22×C8Dic86semidirect
280. C2×C8C2×Dic86semidirect
347. C2#19145131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835302
#191451312
C2×#145833072
C2×#145833032
C2×#145833002
C2×#145829392
C2×#145829372
C2×#145828542
C22×#107×C432
C2×#316443