Finite Group Databasebeta

← C2×#23765714 #34446403

Subgroups — C2×#23765714 #34446403

Order 20224.

502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098996C211yesmaximal, characteristic, complemented
2C2×D16×D79C211yesmaximal, characteristic, complemented
3#23765714C218yesmaximal, direct product factor
4C2×#19098400C211yesmaximal, characteristic, complemented
5C2×D2528C211yesmaximal, characteristic, complemented
6C2×#19098398C211yesmaximal, characteristic, complemented
7C2×#19098396C211yesmaximal, characteristic, complemented
8C2×SD64×C79C211yesmaximal, characteristic, complemented
9C2×#14579184—21no—
10C2×D8×D79—21no—
11#19098996—22no—
12#19098996C2214yescomplemented
13C2×#14579104—21no—
14C2×D1264C2211yescharacteristic
15C2×D1264C2211yescharacteristic, complemented
16C2×#14579102—21no—
17D16×D79—22no—
18D16×D79C2214yescomplemented
19C2×C16×D79C2211yescharacteristic
20#19098400C2214yescomplemented
21D2528C2214yescomplemented
22#19098398C2214yescomplemented
23#19098396C2214yescomplemented
24C2×C79⋊C32C2211yescharacteristic, complemented
25C2×Q32×C79C2211yescharacteristic, complemented
26C2×D16×C79C2211yescharacteristic
27SD64×C79C2214yescomplemented
28C2×C32×C79C2211yescharacteristic, complemented
29C2×#11929625—41no—
30C2×D4×D79—41no—
31#14579184—24no—
32#14579184—42no—
33C2×#11929611—41no—
34C2×D632—21no—
35C2×D632—21no—
36C2×#11929609—41no—
37D8×D79—24no—
38D8×D79—42no—
39C2×C8×D79D411yescharacteristic
40#14579104—24no—
41D1264—21no—
42D1264—21no—
43D1264C2312yes—
44D1264C2312yescomplemented
45#14579102—24no—
46C2×C79⋊C16D411yescharacteristic
47C16×D79D412yes—
48C16×D79C2312yes—
49C79⋊C32C2312yescomplemented
50C2×Q16×C79—21no—
51C2×D8×C79—21no—
52Q32×C79—21no—
53Q32×C79C2312yescomplemented
54D16×C79—21no—
55D16×C79C2312yes—
56C2×C16×C79C2311yescharacteristic
57C32×C79C2312yescomplemented
58C23×D79—81no—
59#11929625—44no—
60#11929625—82no—
61C2×D316—41no—
62C2×D316—41no—
63C2×D316—81no—
64C2×C22⋊D79—81no—
65D4×D79—44no—
66D4×D79—82no—
67C2×C4×D79—81no—
68C2×C4×D79D811yescharacteristic
69#11929611—44no—
70D632—22no—
71D632—22no—
72D632—41no—
73D632—41no—
74#11929609—44no—
75C2×C79⋊C8D811yescharacteristic
76C8×D79D812yes—
77C8×D79C2×D412yes—
78C79⋊C16C2×D412yes—
79C2×Q8×C79—41no—
80C2×D4×C79—41no—
81Q16×C79—22no—
82Q16×C79—41no—
83D8×C79—22no—
84D8×C79—41no—
85C2×C8×C79C2×D411yescharacteristic
86C16×C79C2×D411yescharacteristic
87C16×C79C2411yescharacteristic
88C23×C79—81no—
89C22×D79—81no—
90C22×D79—81no—
91C22×D79—84no—
92C22×D79—164no—
93C22×D79D1611yescharacteristic
94Q8×C79—42no—
95Q8×C79—81no—
96D4×C79—42no—
97D4×C79—81no—
98C2×C4×C79—81no—
99C2×C4×C79C2×D811yescharacteristic
100C22⋊D79—84no—
101C2×Dic79D1611yescharacteristic
102D316—42no—
103D316—42no—
104D316—84no—
105D316—81no—
106D316—81no—
107C4×D79—84no—
108C4×D79D1612yes—
109C4×D79C2×D812yes—
110C8×C79C2×D811yescharacteristic
111C8×C79C22×D411yescharacteristic
112C79⋊C8C2×D812yes—
113C22×C79—82no—
114C22×C79—162no—
115C22×C79C2×D1611yescharacteristic
116C2×D79—22no—
117C2×D79—82no—
118C2×D79—82no—
119C2×D79—168no—
120C2×D79—162no—
121C2×D79—162no—
122C2×D79C2×D1612yes—
123C4×C79—82no—
124C4×C79C2×D1611yescharacteristic
125C4×C79C22×D811yescharacteristic
126Dic79C2×D1612yes—
127C2×#2263—791nomaximal, Sylow
128C2×C79—162no—
129C2×C79#226312yescomplemented
130C2×C79C22×D1611yescharacteristic
131D79—22no—
132D79—162no—
133D79—162no—
134C2×#508—791no—
135C22×D16—791no—
136#2263—798no—
137C2×SD64—791no—
138C2×SD64D7911yescharacteristic, complemented
139C2×D32—791no—
140C2×D32—791no—
141C2×M64—791no—
142C79C2×#226311yescharacteristic, complemented, Sylow
143C2×#135—1581no—
144C22×D8—1581no—
145#508—794no—
146#508—1582no—
147C2×Q32C2×D7911yescharacteristic, complemented
148C2×SD32—1581no—
149C2×D16—794no—
150C2×D16—791no—
151C2×D16—791no—
152C2×D16—1582no—
153C2×D16—1581no—
154C2×D16C2×D7911yescharacteristic
155C22×C16—791no—
156SD64—794no—
157SD64C2×D7914yescomplemented
158D32—794no—
159D32—794no—
160M64—794no—
161C2×C32—791no—
162C2×C32C2×D7911yescharacteristic, complemented
163C2×#41—3161no—
164C22×D4—3161no—
165#135—3162no—
166#135—1584no—
167C2×Q16—21no—
168C2×SD16—3161no—
169C2×D8—21no—
170C2×D8—3162no—
171C2×D8—3161no—
172C2×D8—1584no—
173C2×D8—1581no—
174C2×D8—1581no—
175C22×C8—791no—
176Q32—21no—
177Q32C22×D7912yescomplemented
178SD32—1584no—
179D16—21no—
180D16—792no—
181D16—792no—
182D16—1584no—
183D16—1581no—
184D16—1581no—
185D16C22×D7912yes—
186C2×C16—791no—
187C2×C16—792no—
188C2×C16—792no—
189C2×C16C22×D7911yescharacteristic
190C32—792no—
191C32C22×D7912yescomplemented
192C24—6321no—
193#41—3164no—
194#41—6322no—
195C2×Q8—41no—
196C2×D4—41no—
197C2×D4—3164no—
198C2×D4—3161no—
199C2×D4—3161no—
200C2×D4—6321no—
201C2×D4—6322no—
202C2×D4—6321no—
203C22×C4—791no—
204C22×C4—6321no—
205Q16—22no—
206Q16—41no—
207SD16—3164no—
208D8—22no—
209D8—41no—
210D8—3164no—
211D8—3161no—
212D8—3161no—
213D8—1582no—
214D8—1582no—
215C2×C8—791no—
216C2×C8—792no—
217C2×C8—792no—
218C2×C8D4×D7911yescharacteristic
219C16—792no—
220C16D4×D7911yescharacteristic
221C16C23×D7911yescharacteristic
222C23—81no—
223C23—791no—
224C23—6324no—
225C23—6321no—
226C23—6321no—
227C23—12644no—
228Q8—42no—
229Q8—81no—
230D4—42no—
231D4—81no—
232D4—3162no—
233D4—3162no—
234D4—6324no—
235D4—6324no—
236D4—6321no—
237D4—6321no—
238C2×C4—81no—
239C2×C4—791no—
240C2×C4—792no—
241C2×C4—792no—
242C2×C4—6324no—
243C2×C4D8×D7911yescharacteristic
244C8—792no—
245C8D8×D7911yescharacteristic
246C8C2×D4×D7911yescharacteristic
247C22—82no—
248C22—162no—
249C22—792no—
250C22—6322no—
251C22—6322no—
252C22—1582no—
253C22—12648no—
254C22—12642no—
255C22—12642no—
256C22D16×D7911yescharacteristic
257C4—82no—
258C4—792no—
259C4D16×D7911yescharacteristic
260C4C2×D8×D7911yescharacteristic
261C2—162no—
262C2—1582no—
263C2—12642no—
264C2—12642no—
265C2#2376571412yesdirect product factor
266C2C2×D16×D7911yescharacteristic
subgroupG/H
centerC22D16×D79
commutator, cosocleC16×C79C24
FrattiniC16C23×D79
FittingC2×SD64×C79C2
socleC22×C79C2×D16
hypercenterC2×SD64D79
hypocenterC79C2×#2263
LCSG ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×#19098996C2semidirect
2. C2×D16×D79C2semidirect
3. #23765714C2direct (N × H)
4. C2×#19098400C2semidirect
5. C2×D2528C2semidirect
6. C2×#19098398C2semidirect
7. C2×#19098396C2semidirect
8. C2×SD64×C79C2semidirect
12. #19098996C22semidirect
15. C2×D1264C22semidirect
18. D16×D79C22semidirect
20. #19098400C22semidirect
21. D2528C22semidirect
22. #19098398C22semidirect
23. #19098396C22semidirect
24. C2×C79⋊C32C22semidirect
25. C2×Q32×C79C22semidirect
27. SD64×C79C22semidirect
28. C2×C32×C79C22semidirect
44. D1264C23semidirect
49. C79⋊C32C23semidirect
53. Q32×C79C23semidirect
57. C32×C79C23semidirect
129. C2×C79#2263semidirect
138. C2×SD64D79semidirect
142. C79C2×#2263semidirect
147. C2×Q32C2×D79semidirect
157. SD64C2×D79semidirect
162. C2×C32C2×D79semidirect
177. Q32C22×D79semidirect
191. C32C22×D79semidirect
265. C2#23765714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190989962
C2×D16×D792
#237657142
C2×#190984002
C2×D25282
C2×#190983982
C2×#190983962
C2×SD64×C792
C2×#226379