Finite Group Databasebeta

← C2×#19146987 #25975058

Subgroups — C2×#19146987 #25975058

Order 11008.

1942 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583610C212yesmaximal
2#19146987C2116yesmaximal, direct product factor
3C2×#14583236C214yesmaximal, complemented
4C2×#14583191C212yesmaximal, complemented
5C2×#14583141C212yesmaximal, complemented
6C2×C4×Dic172C211yesmaximal, characteristic, complemented
7C2×C8×D172C211yesmaximal, characteristic
8C2×#107×D43C212yesmaximal, complemented
9C2×C43×#500C211yesmaximal, characteristic, complemented
10C22×Dic172C2211yescharacteristic
11C22×C8×D43C2212yes—
12#14583610—28no—
13#14583610C22116yes—
14C2×#13063316—22no—
15C2×#13063305C2214yes—
16C2×#13063301—24no—
17C2×C4×Dic86C2212yes—
18C2×C4×D172C2211yescharacteristic
19C2×#13063287—22no—
20C2×C4⋊C4×D43C2214yes—
21#14583236C22132yescomplemented
22#14583191C22116yescomplemented
23#14583141C22116yescomplemented
24C4×Dic172C2218yescomplemented
25C8×D172C2218yes—
26C2×#13063259C2211yescharacteristic
27C2×#13063258C2214yes—
28#107×D43C22116yescomplemented
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063250C2212yes—
31C2×#13063248C2214yes—
32C2×(C2×D43)⋊C8C2212yes—
33C2×C4⋊Q8×C43C2212yes—
34C43×#500C2218yescomplemented
35C2×#107×C43C2212yes—
36C2×#107×C43C2212yes—
37C2×C4×C8×C43C2211yescharacteristic
38C22×Dic86C2312yes—
39C22×D172D411yescharacteristic
40C22×C4×D43—24no—
41C22×C4×D43C2312yes—
42C2×Dic172—24no—
43C2×Dic172C2314yes—
44C22×C43⋊C8C2312yes—
45C2×C8×D43—28no—
46C2×C8×D43C2318yes—
47#13063316—216no—
48#13063305—28no—
49#13063305C23116yes—
50#13063301—232no—
51C4×Dic86—24no—
52C4×Dic86C2318yes—
53C4×D172D414yes—
54C4×D172C2314yes—
55#13063287—216no—
56C2×C4⋊Dic43—24no—
57C2×C4⋊Dic43D411yescharacteristic
58C2×C4⋊Dic43C2312yes—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—24no—
61C4⋊C4×D43—28no—
62C4⋊C4×D43C23116yes—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4D412yes—
65C2×C4×Dic43—22no—
66#13063259C2314yes—
67#13063258C23116yes—
68C4⋊(C43⋊C8)C2314yes—
69#13063250C2318yes—
70#13063248C23116yes—
71(C2×D43)⋊C8C2318yes—
72C22×Q8×C43—22no—
73C22×C8×C43C2311yescharacteristic
74C22×C8×C43C2311yescharacteristic
75C4⋊Q8×C43—24no—
76C4⋊Q8×C43C2318yes—
77C2×C4⋊C4×C43—22no—
78C2×C4⋊C4×C43C2314yes—
79C2×C42×C43C2311yescharacteristic
80#107×C43C2318yes—
81#107×C43C2318yes—
82C4×C8×C43C2314yes—
83C23×D43C2×D412yes—
84C2×Q8×C43—28no—
85C2×Q8×C43—84no—
86C22×C4×C43—24no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2411yescharacteristic
90C22×Dic43—22no—
91C22×Dic43—22no—
92C22×Dic43C2×D412yes—
93C2×D172Q1618yescomplemented
94C2×D172C2×D414yes—
95C2×C4×D43—24no—
96C2×C4×D43—24no—
97C2×C4×D43—216no—
98C2×C4×D43—88no—
99C2×C4×D43C2×D414yes—
100C2×C4×D43C2414yes—
101C2×Dic86—24no—
102C2×Dic86—24no—
103C2×Dic86—22no—
104C2×Dic86C2414yes—
105C2×C8×C43—22no—
106C2×C8×C43#4114yes—
107C2×C8×C43C2412yes—
108C2×C8×C43C2412yes—
109C4⋊C4×C43—28no—
110C4⋊C4×C43—24no—
111C4⋊C4×C43C2418yes—
112C42×C43C2×D412yes—
113C42×C43C2412yes—
114(C2×D43)⋊C4—216no—
115(C2×D43)⋊C4C2×D418yes—
116C4⋊Dic43—22no—
117C4⋊Dic43—216no—
118C4⋊Dic43C2×D414yes—
119C4⋊Dic43C2414yes—
120Dic43⋊C4—28no—
121Dic43⋊C4—216no—
122C4×Dic43—28no—
123C2×C43⋊C8—24no—
124C2×C43⋊C8C2414yes—
125Dic172—28no—
126C8×D43—216no—
127C23×C43C22×D411yescharacteristic
128C22×D43—24no—
129C22×D43—24no—
130C22×D43C2×Q1618yes—
131C22×D43C22×D414yes—
132Q8×C43—88no—
133C2×C4×C43—22no—
134C2×C4×C43—28no—
135C2×C4×C43—48no—
136C2×C4×C43C2×Q1614yes—
137C2×C4×C43C22×D412yes—
138C2×C4×C43C22×D411yescharacteristic
139C2×C4×C43C22×D412yes—
140C2×C4×C43C2×#4112yes—
141C2×C4×C432−1+412yes—
142C2×C4×C43C2511yescharacteristic
143C2×Dic43—24no—
144C2×Dic43—24no—
145C2×Dic43—24no—
146C2×Dic43—44no—
147C2×Dic43—44no—
148C2×Dic43C22×D414yes—
149D172C2×Q16116yescomplemented
150C4×D43—28no—
151C4×D43—24no—
152C4×D43—24no—
153C4×D43—816no—
154Dic86—24no—
155Dic86—24no—
156Dic86—44no—
157C8×C43—22no—
158C8×C43C2×#4114yes—
159C43⋊C8—24no—
160C2×#3338—431nomaximal, Sylow
161C22×C43#54712yes—
162C22×C43C22×Q1612yes—
163C22×C43#57612yes—
164C22×C43C23×D411yescharacteristic
165C2×D43—216no—
166C2×D43—24no—
167C2×D43—24no—
168C2×D43C22×Q1618yes—
169C4×C43—22no—
170C4×C43—48no—
171C4×C43#54712yes—
172C4×C43C22×Q1614yes—
173C4×C43C22×#4111yescharacteristic
174C4×C43C2×2−1+411yescharacteristic
175Dic43—24no—
176Dic43—44no—
177Dic43—44no—
178C2×#554—432no—
179#3338—4316no—
180C2×#500D4311yescharacteristic, complemented
181C2×#484—434no—
182C2×#477—432no—
183C2×#467—432no—
184C2×C4×Q16—431no—
185C2×C8×D4—431no—
186C22×#107—432no—
187C2×C43#333814yescomplemented
188C2×C43C2×#54711yescharacteristic
189C2×C43C23×Q1611yescharacteristic
190C2×C43C2×#57611yescharacteristic
191D43—28no—
192C22×Q16—431no—
193C23×C8—432no—
194#554—4316no—
195#554—868no—
196C2×C4⋊Q8C2×D4312yes—
197C2×#125—862no—
198C2×C22⋊Q8—434no—
199C2×C22⋊Q8—864no—
200C2×C4×Q8—432no—
201C2×C4×D4—431no—
202C2×C4×D4—862no—
203C22×C4⋊C4—434no—
204#500C2×D4318yescomplemented
205#484—4332no—
206#477—4316no—
207#467—4316no—
208C4×Q16—438no—
209C8×D4—438no—
210C2×#107—431no—
211C2×#107—434no—
212C2×#107—4316no—
213C2×#107C2×D4312yes—
214C2×#107C2×D4312yes—
215C2×C4⋊C8—431no—
216C2×#103—432no—
217C2×#103—434no—
218C2×C22⋊C8—432no—
219C2×C4×C8C2×D4311yescharacteristic
220C43C2×#333811yescharacteristic, complemented, Sylow
221C22×Q8—22no—
222C22×Q8—432no—
223C22×D4—431no—
224C23×C4—432no—
225C23×C4—864no—
226C2×Q16—434no—
227C2×Q16—864no—
228C22×C8—432no—
229C22×C8—438no—
230C22×C8—868no—
231C22×C8C22×D4311yescharacteristic
232C22×C8C22×D4311yescharacteristic
233C4⋊Q8—24no—
234C4⋊Q8C22×D4318yes—
235#125—8616no—
236C22⋊Q8—4316no—
237C22⋊Q8—8632no—
238C22⋊Q8—868no—
239C4×Q8—438no—
240C4×Q8—864no—
241C4×D4—434no—
242C4×D4—434no—
243C4×D4—8616no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—432no—
247C2×C4⋊C4—4316no—
248C2×C4⋊C4—868no—
249C2×C4⋊C4—864no—
250C2×C4⋊C4—864no—
251C2×C4⋊C4—862no—
252C2×C4⋊C4C22×D4314yes—
253C2×C22⋊C4—432no—
254C2×C22⋊C4—864no—
255C2×C42—862no—
256C2×C42C22×D4311yescharacteristic
257#107—434no—
258#107—4316no—
259#107C22×D4318yes—
260#107C22×D4318yes—
261C4⋊C8—434no—
262#103—438no—
263#103—4316no—
264C22⋊C8—438no—
265C4×C8C22×D4314yes—
266C24—432no—
267C2×Q8—28no—
268C2×Q8—84no—
269C2×Q8—434no—
270C2×Q8—862no—
271C2×Q8—864no—
272C2×Q8—864no—
273C2×D4—438no—
274C2×D4—434no—
275C22×C4—24no—
276C22×C4—432no—
277C22×C4—434no—
278C22×C4—434no—
279C22×C4—8616no—
280C22×C4—864no—
281C22×C4—864no—
282C22×C4—862no—
283C22×C4—862no—
284C22×C4—3448no—
285C22×C4D4×D4311yescharacteristic
286C22×C4D4×D4311yescharacteristic
287C22×C4C23×D4311yescharacteristic
288Q16—868no—
289C2×C8—22no—
290C2×C8—434no—
291C2×C8—864no—
292C2×C8—8616no—
293C2×C8#1062190214yes—
294C2×C8C23×D4312yes—
295C2×C8C23×D4312yes—
296C4⋊C4—28no—
297C4⋊C4—24no—
298C4⋊C4—434no—
299C4⋊C4—434no—
300C4⋊C4—8616no—
301C4⋊C4—8616no—
302C4⋊C4—862no—
303C4⋊C4—868no—
304C4⋊C4C23×D4318yes—
305C22⋊C4—438no—
306C22⋊C4—8616no—
307C42—868no—
308C42D4×D4312yes—
309C42C23×D4312yes—
310C23—438no—
311C23—434no—
312C23—864no—
313C23—864no—
314C23C2×D4×D4311yescharacteristic
315Q8—88no—
316Q8—864no—
317Q8—864no—
318Q8—1724no—
319D4—4316no—
320C2×C4—22no—
321C2×C4—28no—
322C2×C4—48no—
323C2×C4—434no—
324C2×C4—864no—
325C2×C4—868no—
326C2×C4—864no—
327C2×C4—864no—
328C2×C4—864no—
329C2×C4—864no—
330C2×C4—34416no—
331C2×C4—1724no—
332C2×C4—1724no—
333C2×C4Q16×D4314yes—
334C2×C4C2×D4×D4312yes—
335C2×C4C2×D4×D4311yescharacteristic
336C2×C4C2×D4×D4312yes—
337C2×C4C2×#1062190212yes—
338C2×C4#1306337312yes—
339C2×C4C24×D4311yescharacteristic
340C8—22no—
341C8—864no—
342C8C2×#1062190214yes—
343C22—438no—
344C22—864no—
345C22—864no—
346C22—8616no—
347C22#1458355212yes—
348C22C2×Q16×D4312yes—
349C22#1458370012yes—
350C22C22×D4×D4311yescharacteristic
351C4—22no—
352C4—48no—
353C4—864no—
354C4—1724no—
355C4—1724no—
356C4#1458355212yes—
357C4C2×Q16×D4314yes—
358C4C22×#1062190211yescharacteristic
359C4C2×#1306337311yescharacteristic
360C2—868no—
361C2#1914698714yesdirect product factor
362C2C2×#1458355211yescharacteristic
363C2C22×Q16×D4311yescharacteristic
364C2C2×#1458370011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#500C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenterC2×#500D43
hypocenterC43C2×#3338
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. #19146987C2direct (N × H)
3. C2×#14583236C2semidirect
4. C2×#14583191C2semidirect
5. C2×#14583141C2semidirect
6. C2×C4×Dic172C2semidirect
8. C2×#107×D43C2semidirect
9. C2×C43×#500C2semidirect
21. #14583236C22semidirect
22. #14583191C22semidirect
23. #14583141C22semidirect
24. C4×Dic172C22semidirect
28. #107×D43C22semidirect
34. C43×#500C22semidirect
93. C2×D172Q16semidirect
149. D172C2×Q16semidirect
180. C2×#500D43semidirect
187. C2×C43#3338semidirect
204. #500C2×D43semidirect
220. C43C2×#3338semidirect
361. C2#19146987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836102
#191469872
C2×#145832362
C2×#145831912
C2×#145831412
C2×C4×Dic1722
C2×C8×D1722
C2×#107×D432
C2×C43×#5002
C2×#333843