Finite Group Databasebeta

← C2×#21447994 #29834748

Subgroups — C2×#21447994 #29834748

Order 15616.

526 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840162C211yesmaximal, characteristic, complemented
2C2×#16839878C211yesmaximal, characteristic
3#21447994C218yesmaximal, direct product factor
4C2×#16839586C211yesmaximal, characteristic, complemented
5C2×#16839582C211yesmaximal, characteristic, complemented
6C2×#16839573C211yesmaximal, characteristic
7C2×#16839571C211yesmaximal, characteristic
8C2×C61×#365C211yesmaximal, characteristic, complemented
9C2×#14519799C2211yescharacteristic
10C2×#14519785—21no—
11C2×#14519768—21no—
12C2×#14519717C2211yescharacteristic
13#16840162—22no—
14#16840162C2214yescomplemented
15#16839878—22no—
16#16839878C2214yes—
17C2×#14519710—21no—
18C2×#14519709C2211yescharacteristic
19C2×#14519703—21no—
20C2×C8×Dic61C2211yescharacteristic
21#16839586C2214yescomplemented
22#16839582C2214yescomplemented
23#16839573C2214yes—
24#16839571C2214yes—
25C2×M32×C61C2211yescharacteristic
26C2×#108×C61C2211yescharacteristic
27C2×#106×C61C2211yescharacteristic
28C61×#365C2214yescomplemented
29C2×#11758222—21no—
30#14519799—21no—
31#14519799—21no—
32#14519799Q812yes—
33#14519799C2312yes—
34C2×Dic244Q811yescharacteristic
35C2×#11758190—21no—
36C2×D488Q811yescharacteristic
37#14519785—24no—
38#14519785—42no—
39C2×#11758189—41no—
40C22×#92418D411yescharacteristic
41C2×C8×D61—41no—
42#14519768—24no—
43#14519768—42no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—41no—
46C2×#11758196—41no—
47C2×C4×Dic61D411yescharacteristic
48#14519717—21no—
49#14519717C2312yes—
50C2×#11758185—21no—
51#14519710—24no—
52#14519709—21no—
53#14519709C2312yes—
54#14519703—24no—
55C8×Dic61D412yes—
56C8×Dic61C2312yes—
57C2×M16×C61—21no—
58C22×C8×C61C2311yescharacteristic
59C2×C4⋊C4×C61—21no—
60M32×C61—21no—
61M32×C61C2312yes—
62C2×C16×C61—21no—
63#108×C61—21no—
64#108×C61C2312yes—
65#106×C61—21no—
66#106×C61C2312yes—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C2×C22⋊D61—41no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72#11758222—22no—
73#11758222—22no—
74#11758222—41no—
75#11758222—41no—
76C2×D244—21no—
77C2×C4×D61—41no—
78C2×Dic122—21no—
79M16×C61—22no—
80M16×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61C2×D411yescharacteristic
83C2×C8×C61C2×Q811yescharacteristic
84C2×C8×C61C2×Q811yescharacteristic
85C2×C8×C61#4111yescharacteristic
86C2×C8×C61#4111yescharacteristic
87C2×C8×C61C2411yescharacteristic
88C4⋊C4×C61—22no—
89C4⋊C4×C61—41no—
90C4⋊Dic61—22no—
91C4⋊Dic61—44no—
92C4⋊Dic61—41no—
93#11758196—44no—
94C4×Dic61—21no—
95C4×Dic61C2×D412yes—
96C2×#92418SD1611yescharacteristic
97C2×#92418SD1611yescharacteristic
98C2×#92418SD1612yes—
99C2×#92418C2×D412yes—
100Dic244—21no—
101Dic244C2×Q812yes—
102D488—21no—
103D488C2×Q812yes—
104#11758190—22no—
105#11758190—22no—
106#11758189—44no—
107C8×D61—44no—
108C16×C61—22no—
109#11758185—22no—
110C23×C61AGL(1,ℤ/8)11yescharacteristic
111C22×D61—41no—
112C2×C4×C61—42no—
113C2×C4×C61—82no—
114C2×C4×C61C22⋊Q811yescharacteristic
115C2×C4×C61C22⋊Q811yescharacteristic
116C2×C4×C61C2×SD1611yescharacteristic
117C2×C4×C61C2×SD1611yescharacteristic
118C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C61C22×D411yescharacteristic
120C22⋊D61—42no—
121C22⋊D61—42no—
122C2×Dic61—22no—
123C2×Dic61—42no—
124C2×Dic61—41no—
125C2×Dic61—42no—
126C2×Dic61—82no—
127D244—22no—
128D244—41no—
129C4×D61—42no—
130C4×D61—42no—
131Dic122—22no—
132Dic122—41no—
133C8×C61—42no—
134C8×C61C22⋊Q811yescharacteristic
135C8×C61C22⋊Q811yescharacteristic
136C8×C61C22×Q811yescharacteristic
137C8×C61C2×#4111yescharacteristic
138#92418C2×SD1612yes—
139#92418C2×SD1612yes—
140C2×#2231—611nomaximal, Sylow
141C22×C61—22no—
142C22×C61#47611yescharacteristic
143C22×C61#47611yescharacteristic
144C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
145C2×D61—42no—
146C2×D61—82no—
147C4×C61—82no—
148C4×C61#47611yescharacteristic
149C4×C61#47611yescharacteristic
150C4×C61C2×C22⋊Q811yescharacteristic
151C4×C61C22×SD1611yescharacteristic
152Dic61—42no—
153Dic61—42no—
154Dic61—82no—
155C2×#499—611no—
156C2×#443—611no—
157#2231—618no—
158C2×#365—611no—
159C2×#365D6111yescharacteristic, complemented
160C2×#364—611no—
161C2×#360—611no—
162C2×#360—611no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61#223112yescomplemented
166C2×C61C2×#47611yescharacteristic
167D61—82no—
168C2×#135—611no—
169C2×#131—1221no—
170C2×#125—1221no—
171C2×M32—611no—
172C2×M32C2×D6111yescharacteristic
173#499—614no—
174#499—1222no—
175#443—614no—
176#443—1222no—
177C2×#108C2×D6111yescharacteristic
178C2×#107—1221no—
179C2×#106—611no—
180C2×#106C2×D6111yescharacteristic
181C2×#104—1221no—
182C2×C4×C8—611no—
183#365—614no—
184#365C2×D6114yescomplemented
185#364—614no—
186#360—614no—
187#360—614no—
188C61C2×#223111yescharacteristic, complemented, Sylow
189C2×#41—1221no—
190#135—612no—
191#135—612no—
192#135—1221no—
193#135—1221no—
194C2×Q16—611no—
195C2×SD16—1221no—
196C2×D8—611no—
197#131—1224no—
198#131—2442no—
199C2×M16—21no—
200C2×M16—2441no—
201C22×C8—611no—
202C22×C8—2441no—
203C22×C8C22×D6111yescharacteristic
204#125—1224no—
205#125—2442no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—2441no—
209C2×C4⋊C4—2441no—
210C2×C42—611no—
211M32—21no—
212M32—612no—
213M32—1221no—
214M32C22×D6112yes—
215C2×C16—21no—
216C2×C16—1221no—
217#108—21no—
218#108C22×D6112yes—
219#107—1224no—
220#106—21no—
221#106—612no—
222#106—1221no—
223#106C22×D6112yes—
224#104—1224no—
225C4×C8—612no—
226C4×C8—612no—
227#41—1222no—
228#41—1222no—
229#41—2441no—
230#41—2441no—
231C2×Q8—1221no—
232C2×D4—1221no—
233C2×D4—2441no—
234C22×C4—41no—
235C22×C4—1221no—
236C22×C4—2441no—
237C22×C4—2441no—
238C22×C4D4×D6111yescharacteristic
239Q16—612no—
240Q16—1221no—
241SD16—1222no—
242SD16—1222no—
243D8—612no—
244D8—1221no—
245M16—22no—
246M16—41no—
247M16—2444no—
248C2×C8—41no—
249C2×C8—612no—
250C2×C8—611no—
251C2×C8—611no—
252C2×C8—612no—
253C2×C8—2444no—
254C2×C8#1175822211yescharacteristic
255C2×C8#1175822211yescharacteristic
256C2×C8D4×D6111yescharacteristic
257C2×C8Q8×D6111yescharacteristic
258C2×C8Q8×D6111yescharacteristic
259C2×C8C23×D6111yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—1222no—
263C4⋊C4—2444no—
264C4⋊C4—2444no—
265C4⋊C4—2441no—
266C42—612no—
267C42—1221no—
268C16—22no—
269C16—1222no—
270C23—2441no—
271C23#1451980411yescharacteristic
272Q8—1222no—
273Q8—2441no—
274D4—1222no—
275D4—2442no—
276D4—2442no—
277D4—2441no—
278C2×C4—42no—
279C2×C4—82no—
280C2×C4—1222no—
281C2×C4—4882no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4—2441no—
285C2×C4—2442no—
286C2×C4—2442no—
287C2×C4#1451975511yescharacteristic
288C2×C4#1451975511yescharacteristic
289C2×C4SD16×D6111yescharacteristic
290C2×C4SD16×D6111yescharacteristic
291C2×C4#1451980411yescharacteristic
292C2×C4C2×D4×D6111yescharacteristic
293C8—42no—
294C8—612no—
295C8—612no—
296C8#1451975511yescharacteristic
297C8#1451975511yescharacteristic
298C8C2×Q8×D6111yescharacteristic
299C8C2×#1175822211yescharacteristic
300C22—22no—
301C22—4882no—
302C22—2442no—
303C22#1684005111yescharacteristic
304C22#1684005111yescharacteristic
305C22C2×#1451980411yescharacteristic
306C4—82no—
307C4—4882no—
308C4—2442no—
309C4—2442no—
310C4#1684005111yescharacteristic
311C4#1684005111yescharacteristic
312C4C2×#1451975511yescharacteristic
313C4C2×SD16×D6111yescharacteristic
314C2—21no—
315C2—21no—
316C2—4882no—
317C2#2144799412yesdirect product factor
318C2C2×#1684005111yescharacteristic
subgroupG/H
centerC22#16840051
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#365C2
socleC22×C61#476
prime radicalC2×#14519799C22
hypercenterC2×#365D61
hypocenterC61C2×#2231
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
1. C2×#16840162C2semidirect
3. #21447994C2direct (N × H)
4. C2×#16839586C2semidirect
5. C2×#16839582C2semidirect
8. C2×C61×#365C2semidirect
14. #16840162C22semidirect
21. #16839586C22semidirect
22. #16839582C22semidirect
28. C61×#365C22semidirect
159. C2×#365D61semidirect
165. C2×C61#2231semidirect
184. #365C2×D61semidirect
188. C61C2×#2231semidirect
317. C2#21447994direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401622
C2×#168398782
#214479942
C2×#168395862
C2×#168395822
C2×#168395732
C2×#168395712
C2×C61×#3652
C2×#223161