Finite Group Databasebeta

← C2×#19136305 #25249493

Subgroups — C2×#19136305 #25249493

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063347C211yesmaximal, characteristic
2C22×#13063265C211yesmaximal, characteristic, complemented
3#19136305C218yesmaximal, direct product factor
4C2×#14582702C212yesmaximal, complemented
5C2×#14582699C212yesmaximal, complemented
6C22×#107×C43C211yesmaximal, characteristic, complemented
7C22×#10621898—21no—
8C2×#13063347—24no—
9C2×#13063347—22no—
10C2×#13063347C418yescomplemented
11C2×#13063347C2214yes—
12C22×Dic172C2211yescharacteristic
13C22×#10621873—21no—
14C22×D344C2211yescharacteristic
15C2×#13063265—24no—
16C2×#13063265C2214yescomplemented
17C22×C43⋊C16C2212yes—
18#14582702C2218yescomplemented
19#14582699C2218yescomplemented
20C23×C8×C43C2211yescharacteristic
21C22×C4⋊C4×C43—21no—
22C2×#107×C43—22no—
23C2×#107×C43—21no—
24C2×#107×C43C2212yes—
25C2×#107×C43C2214yescomplemented
26C2×#10621898—28no—
27C2×#10621898—24no—
28C2×#10621898—42no—
29C2×#10621898—44no—
30C22×Dic86—21no—
31C22×D172—21no—
32C22×C22⋊D43—41no—
33C22×C4×D43—41no—
34#13063347—216no—
35#13063347—28no—
36#13063347C2×C4116yescomplemented
37C2×Dic172—22no—
38C2×Dic172—21no—
39C2×Dic172C2×C414yescomplemented
40C2×Dic172C2312yes—
41C2×#10621873—28no—
42C2×#10621873—24no—
43C2×D344—22no—
44C2×D344—21no—
45C2×D344C2×C414yescomplemented
46C2×D344C2312yes—
47#13063265—28no—
48C2×C43⋊C16—24no—
49C2×C43⋊C16C2314yes—
50C23×C4×C43—41no—
51C23×C4×C43D411yescharacteristic
52C22×C8×C43C2×C414yes—
53C22×C8×C43D414yes—
54C22×C8×C43D411yescharacteristic
55C22×C8×C43D412yes—
56C22×C8×C43C2311yescharacteristic
57C22×C8×C43C2312yes—
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43—24no—
60C2×C4⋊C4×C43—41no—
61C2×C4⋊C4×C43—42no—
62#107×C43—22no—
63#107×C43—24no—
64#107×C43C2314yes—
65C24×C43D811yescharacteristic
66C23×D43—41no—
67C22×C4×C43—44no—
68C22×C4×C43—42no—
69C22×C4×C43—84no—
70C22×C4×C43C22⋊C414yes—
71C22×C4×C43D811yescharacteristic
72C22×C4×C43D812yes—
73C22×C4×C43SD1614yes—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D412yes—
76C2×C22⋊D43—48no—
77C2×C22⋊D43—44no—
78C22×Dic43—41no—
79#10621898—216no—
80#10621898—416no—
81#10621898—48no—
82C2×D172—24no—
83C2×D172—22no—
84C2×D172—41no—
85C2×D172—42no—
86C2×C4×D43—48no—
87C2×C4×D43—44no—
88C2×Dic86—24no—
89C2×Dic86—22no—
90C2×Dic86—41no—
91C2×Dic86—42no—
92C2×C8×C43C22⋊C414yes—
93C2×C8×C43C22⋊C418yes—
94C2×C8×C43C22×C412yes—
95C2×C8×C43C22×C414yes—
96C2×C8×C43C2×D412yes—
97C2×C8×C43C2×D414yes—
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D412yes—
100C2×C8×C43C2411yescharacteristic
101C4⋊C4×C43—24no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—44no—
104Dic172—24no—
105Dic172—22no—
106Dic172C22×C414yescomplemented
107D344—24no—
108D344—22no—
109D344C22×C414yescomplemented
110#10621873—216no—
111C43⋊C16—24no—
112C23×C43—22no—
113C23×C43—22no—
114C23×C43#10214yes—
115C23×C43C2×D812yes—
116C23×C43C2×D811yescharacteristic
117C22×D43—42no—
118C22×D43—44no—
119C22×D43—82no—
120C22×D43—82no—
121C2×C4×C43—44no—
122C2×C4×C43—88no—
123C2×C4×C43—84no—
124C2×C4×C43#10214yes—
125C2×C4×C43#10218yes—
126C2×C4×C43C2×C22⋊C412yes—
127C2×C4×C43C2×C22⋊C414yes—
128C2×C4×C43C2×D811yescharacteristic
129C2×C4×C43C2×D812yes—
130C2×C4×C43C2×SD1612yes—
131C2×C4×C43C2×SD1614yes—
132C2×C4×C43C22×D411yescharacteristic
133C22⋊D43—416no—
134C2×Dic43—42no—
135C2×Dic43—44no—
136D172—24no—
137D172—42no—
138D172—44no—
139C4×D43—416no—
140Dic86—24no—
141Dic86—42no—
142Dic86—44no—
143C8×C43C2×C22⋊C414yes—
144C8×C43C2×C22⋊C412yes—
145C8×C43C23×C411yescharacteristic
146C8×C43C22×D411yescharacteristic
147C2×#2139—431nomaximal, Sylow
148C22×C43—22no—
149C22×C43—22no—
150C22×C43—28no—
151C22×C43C2×#10214yes—
152C22×C43C2×#10212yes—
153C22×C43#50912yes—
154C22×C43#51012yes—
155C22×C43C22×D811yescharacteristic
156C2×D43—44no—
157C2×D43—82no—
158C2×D43—82no—
159C2×D43—88no—
160C4×C43—84no—
161C4×C43C2×#10212yes—
162C4×C43C2×#10214yes—
163C4×C43C22×C22⋊C411yescharacteristic
164C4×C43C22×SD1611yescharacteristic
165Dic43—44no—
166C22×#135—431no—
167C22×M32—431no—
168C22×#107D4311yescharacteristic, complemented
169#2139—438no—
170C2×#358—432no—
171C2×#357—432no—
172C2×C43—24no—
173C2×C43#213914yescomplemented
174C2×C43C22×#10211yescharacteristic
175C2×C43C2×#50911yescharacteristic
176C2×C43C2×#51011yescharacteristic
177D43—84no—
178C22×#41—861no—
179C2×#135—434no—
180C2×#135—438no—
181C2×#135—864no—
182C2×#135—862no—
183C22×Q16—431no—
184C22×SD16—861no—
185C22×D8—431no—
186C23×C8C2×D4311yescharacteristic
187C22×C4⋊C4—21no—
188C2×M32—434no—
189C2×M32—864no—
190C22×C16—432no—
191C2×#107—22no—
192C2×#107—21no—
193C2×#107C2×D4312yes—
194C2×#107C2×D4314yescomplemented
195#358—438no—
196#357—438no—
197C43C2×#213911yescharacteristic, complemented, Sylow
198C2×#41—868no—
199C2×#41—864no—
200C2×#41—1722no—
201C2×#41—1724no—
202C22×Q8—861no—
203C22×D4—861no—
204C22×D4—1721no—
205C23×C4—41no—
206C23×C4—1721no—
207C23×C4C22⋊D4311yescharacteristic
208#135—4316no—
209#135—8616no—
210#135—868no—
211C2×Q16—434no—
212C2×Q16—432no—
213C2×Q16—862no—
214C2×Q16—861no—
215C2×SD16—868no—
216C2×SD16—864no—
217C2×D8—434no—
218C2×D8—432no—
219C2×D8—862no—
220C2×D8—861no—
221C22×C8C4×D4314yes—
222C22×C8D17214yes—
223C22×C8C22⋊D4311yescharacteristic
224C22×C8C22⋊D4312yes—
225C22×C8C22×D4311yescharacteristic
226C22×C8C22×D4312yes—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—42no—
230C2×C4⋊C4—41no—
231M32—868no—
232C2×C16—434no—
233C2×C16—864no—
234#107—22no—
235#107—24no—
236#107C22×D4314yes—
237C24—1721no—
238C24#1062188211yescharacteristic
239#41—8616no—
240#41—17216no—
241#41—1728no—
242C2×Q8—864no—
243C2×Q8—862no—
244C2×Q8—1721no—
245C2×Q8—1722no—
246C2×D4—864no—
247C2×D4—862no—
248C2×D4—1728no—
249C2×D4—1724no—
250C2×D4—1721no—
251C2×D4—1722no—
252C22×C4—44no—
253C22×C4—42no—
254C22×C4—84no—
255C22×C4—1721no—
256C22×C4—1728no—
257C22×C4—1724no—
258C22×C4(C2×D43)⋊C414yes—
259C22×C4#1062188212yes—
260C22×C4#1062188211yescharacteristic
261C22×C4#1062188414yes—
262C22×C4C2×C22⋊D4312yes—
263C22×C4C2×C22⋊D4311yescharacteristic
264Q16—434no—
265Q16—864no—
266Q16—862no—
267SD16—8616no—
268D8—434no—
269D8—864no—
270D8—862no—
271C2×C8(C2×D43)⋊C414yes—
272C2×C8(C2×D43)⋊C418yes—
273C2×C8C2×C4×D4312yes—
274C2×C8C2×C4×D4314yes—
275C2×C8C2×D17212yes—
276C2×C8C2×D17214yes—
277C2×C8C2×C22⋊D4311yescharacteristic
278C2×C8C2×C22⋊D4312yes—
279C2×C8C23×D4311yescharacteristic
280C4⋊C4—24no—
281C4⋊C4—44no—
282C4⋊C4—42no—
283C16—864no—
284C23—22no—
285C23—22no—
286C23—3442no—
287C23—3442no—
288C23—1724no—
289C23—1722no—
290C23#1306324514yes—
291C23C2×#1062188212yes—
292C23C2×#1062188211yescharacteristic
293Q8—864no—
294Q8—1724no—
295Q8—1722no—
296D4—864no—
297D4—17216no—
298D4—1724no—
299D4—1722no—
300C2×C4—44no—
301C2×C4—88no—
302C2×C4—84no—
303C2×C4—1724no—
304C2×C4—1722no—
305C2×C4—17216no—
306C2×C4#1306324514yes—
307C2×C4#1306324518yes—
308C2×C4C2×(C2×D43)⋊C412yes—
309C2×C4C2×(C2×D43)⋊C414yes—
310C2×C4C2×#1062188212yes—
311C2×C4C2×#1062188211yescharacteristic
312C2×C4C2×#1062188412yes—
313C2×C4C2×#1062188414yes—
314C2×C4C22×C22⋊D4311yescharacteristic
315C8C2×(C2×D43)⋊C412yes—
316C8C2×(C2×D43)⋊C414yes—
317C8C22×C4×D4311yescharacteristic
318C8C22×D17211yescharacteristic
319C22—28no—
320C22—22no—
321C22—22no—
322C22—3448no—
323C22—3442no—
324C22—3442no—
325C22—1724no—
326C22C2×#1306324514yes—
327C22C2×#1306324512yes—
328C22#1458333512yes—
329C22#1458334012yes—
330C22C22×#1062188211yescharacteristic
331C4—84no—
332C4—1724no—
333C4C2×#1306324514yes—
334C4C2×#1306324512yes—
335C4C22×(C2×D43)⋊C411yescharacteristic
336C4C22×#1062188411yescharacteristic
337C2—24no—
338C2—3444no—
339C2#1913630514yesdirect product factor
340C2C22×#1306324511yescharacteristic
341C2C2×#1458333511yescharacteristic
342C2C2×#1458334011yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC22×#107×C43C2
socleC23×C43C2×D8
prime radicalC22×#13063347C2
cosocleC2×C8×C43C24
hypercenterC22×#107D43
hypocenterC43C2×#2139
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C22×#13063265C2semidirect
3. #19136305C2direct (N × H)
4. C2×#14582702C2semidirect
5. C2×#14582699C2semidirect
6. C22×#107×C43C2semidirect
10. C2×#13063347C4semidirect
16. C2×#13063265C22semidirect
18. #14582702C22semidirect
19. #14582699C22semidirect
25. C2×#107×C43C22semidirect
36. #13063347C2×C4semidirect
39. C2×Dic172C2×C4semidirect
45. C2×D344C2×C4semidirect
106. Dic172C22×C4semidirect
109. D344C22×C4semidirect
168. C22×#107D43semidirect
173. C2×C43#2139semidirect
194. C2×#107C2×D43semidirect
197. C43C2×#2139semidirect
339. C2#19136305direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633472
C22×#130632652
#191363052
C2×#145827022
C2×#145826992
C22×#107×C432
C2×#213943