Finite Group Databasebeta

← C2×D8×#11924078 #49175532

Subgroups — C2×D8×#11924078 #49175532

Order 37504.

616 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 178 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×D4×#11924078C212yesmaximal, complemented
2D8×#11924078C218yesmaximal, direct product factor
3C2×#22627693C211yesmaximal, characteristic, complemented
4C2×#22627686C212yesmaximal, complemented
5C2×C8×#11924078C211yesmaximal, characteristic, complemented
6C2×D8×D293C211yesmaximal, characteristic
7C23×#11924078—22no—
8C2×D293⋊C8C2211yescharacteristic
9D4×#11924078—24no—
10D4×#11924078C2218yescomplemented
11C2×C4⋊#11924078C2212yes—
12C2×C22⋊#11924078—22no—
13C2×C4×#11924078C2211yescharacteristic
14#22627693C2214yescomplemented
15#22627686C2218yescomplemented
16C8×#11924078C2214yescomplemented
17C2×D4×D293C2212yes—
18C2×D2344C411yescharacteristic, complemented
19C2×#17989787C412yescomplemented
20D8×D293C414yescomplemented
21D8×D293C2214yes—
22C2×C8×D293C2211yescharacteristic
23C2×D8×C293C411yescharacteristic, complemented
24C22×#11924078—28no—
25C22×#11924078—22no—
26C22×#11924078—48no—
27C22×#11924078D411yescharacteristic
28C22×#11924078D411yescharacteristic
29D293⋊C8—21no—
30D293⋊C8C2312yes—
31C2×#14556880—21no—
32C4⋊#11924078—22no—
33C4⋊#11924078C2314yes—
34C22⋊#11924078—28no—
35C4×#11924078D412yes—
36C4×#11924078C2312yes—
37C23×D293—22no—
38C2×D1172C2×C412yescomplemented
39C2×C22⋊D293—22no—
40D4×D293—22no—
41D4×D293—22no—
42D4×D293C2×C414yescomplemented
43D4×D293C2314yes—
44C2×C4×D293C2311yescharacteristic
45D2344C2×C414yescomplemented
46#17989787C2×C418yescomplemented
47C2×#14556873C2×C411yescharacteristic, complemented
48C8×D293C2×C412yescomplemented
49C8×D293C2312yes—
50C2×D4×C293C2×C412yescomplemented
51D8×C293C2×C414yescomplemented
52C2×C8×C293C2×C411yescharacteristic, complemented
53C2×#11924078—22no—
54C2×#11924078—24no—
55C2×#11924078—44no—
56C2×#11924078—416no—
57C2×#11924078D814yesdirect product factor
58C2×#11924078C2×D412yes—
59C2×#11924078C2×D412yes—
60#14556880—22no—
61C22×D293—22no—
62C22×D293—24no—
63C22×D293—24no—
64C22×D293—44no—
65C22×D293—44no—
66C22×D293C2×D411yescharacteristic
67D1172—22no—
68D1172C22×C414yescomplemented
69C22⋊D293—24no—
70C22⋊D293—24no—
71C2×Dic293#4111yescharacteristic
72C4×D293C22×C411yescharacteristic
73C4×D293C2×D411yescharacteristic
74C4×D293#4111yescharacteristic
75C4×D293C2411yescharacteristic
76#14556873C22×C412yescomplemented
77C23×C293—22no—
78D4×C293—22no—
79D4×C293C22×C414yescomplemented
80C2×C4×C293C22×C411yescharacteristic
81C8×C293C22×C412yescomplemented
82C22×C293—24no—
83C22×C293—44no—
84C22×C293C4×D411yescharacteristic
85C2×D293—24no—
86C2×D293—44no—
87C2×D293—44no—
88C2×D293—44no—
89C2×D293—48no—
90C2×D293C4×D411yescharacteristic
91C2×D293C2×D812yes—
92C2×D293#13512yes—
93C2×D293C22×D411yescharacteristic
94#11924078—22no—
95#11924078—44no—
96#11924078C2×D814yesdirect product factor
97C4×C293C4×D411yescharacteristic
98C4×C293C23×C411yescharacteristic
99Dic293C4×D411yescharacteristic
100Dic293C2×#4111yescharacteristic
101C2×C293—44no—
102C2×C293C4×D812yescomplemented
103C2×C293C2×C4×D411yescharacteristic
104D293—44no—
105D293C4×D812yescomplemented
106D293C22×D811yescharacteristic
107D293C2×#13511yescharacteristic
108C293C2×C4×D811yescharacteristic, complemented, Sylow
109C2×C4×D8—2931nomaximal, Sylow
110C22×D8—2931no—
111C2×C4×D4—2932no—
112C4×D8—2938no—
113C2×#107—2931no—
114C2×#102—2932no—
115C2×C4×C8—2931no—
116C22×D4—2932no—
117C23×C4—5862no—
118C2×D8—2932no—
119C2×D8—2934no—
120C2×D8—2934no—
121C2×D8—2931no—
122C2×D8#1192407811yescharacteristic, direct product factor
123C22×C8—2931no—
124C22×C8—2931no—
125C4×D4—2938no—
126C4×D4—5864no—
127C2×C4⋊C4—2932no—
128C2×C22⋊C4—5862no—
129C2×C42—2931no—
130#107—2934no—
131#102—2938no—
132C4×C8—2934no—
133C24—5862no—
134C2×D4—2934no—
135C2×D4—2934no—
136C2×D4—2932no—
137C2×D4—5862no—
138C2×D4—5862no—
139C2×D4—5862no—
140C2×D4C2×#1192407812yescomplemented
141C22×C4—2931no—
142C22×C4—2931no—
143C22×C4—2931no—
144C22×C4—5868no—
145C22×C4—5862no—
146C22×C4—11728no—
147D8—2938no—
148D8—2934no—
149D8C2×#1192407814yesdirect product factor
150C2×C8—2931no—
151C2×C8—2932no—
152C2×C8—2932no—
153C2×C8—2932no—
154C2×C8—5861no—
155C2×C8—5861no—
156C2×C8C2×#1192407811yescharacteristic, complemented
157C4⋊C4—2934no—
158C4⋊C4—5862no—
159C22⋊C4—5868no—
160C42—2932no—
161C42—2932no—
162C23—22no—
163C23—2931no—
164C23—5864no—
165C23—5864no—
166C23—5862no—
167C23—11724no—
168C23—11724no—
169D4—22no—
170D4—2934no—
171D4—5864no—
172D4—5864no—
173D4—5862no—
174D4C22×#1192407814yescomplemented
175C2×C4—2932no—
176C2×C4—2934no—
177C2×C4—2931no—
178C2×C4—2931no—
179C2×C4—2931no—
180C2×C4—2931no—
181C2×C4—2931no—
182C2×C4—2932no—
183C2×C4—5862no—
184C2×C4—5864no—
185C2×C4—117216no—
186C2×C4—11724no—
187C2×C4C22×#1192407811yescharacteristic
188C8—2932no—
189C8—5862no—
190C8C22×#1192407812yescomplemented
191C22—24no—
192C22—44no—
193C22—2932no—
194C22—2932no—
195C22—2931no—
196C22—2931no—
197C22—5864no—
198C22—11724no—
199C22—11724no—
200C22—11728no—
201C22—11724no—
202C22D4×#1192407811yescharacteristic
203C4—2934no—
204C4—2931no—
205C4—2931no—
206C4—5862no—
207C4—11724no—
208C4D4×#1192407811yescharacteristic
209C4C23×#1192407811yescharacteristic
210C2—44no—
211C2—2931no—
212C2—2931no—
213C2—2932no—
214C2—11724no—
215C2D8×#1192407812yesdirect product factor
216C2C2×D4×#1192407811yescharacteristic
subgroupG/H
centerC22D4×#11924078
commutatorC4×C293C23×C4
FrattiniC4C23×#11924078
FittingC2×D8×C293C4
socleC22×C293C4×D4
prime radicalC2×D8×D293C2
cosocleC4×D293C24
hypercenterC2×D8#11924078
hypocenterC293C2×C4×D8
LCSG ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#11924078C2semidirect
2. D8×#11924078C2direct (N × H)
3. C2×#22627693C2semidirect
4. C2×#22627686C2semidirect
5. C2×C8×#11924078C2semidirect
10. D4×#11924078C22semidirect
14. #22627693C22semidirect
15. #22627686C22semidirect
16. C8×#11924078C22semidirect
18. C2×D2344C4semidirect
19. C2×#17989787C4semidirect
20. D8×D293C4semidirect
23. C2×D8×C293C4semidirect
38. C2×D1172C2×C4semidirect
42. D4×D293C2×C4semidirect
45. D2344C2×C4semidirect
46. #17989787C2×C4semidirect
47. C2×#14556873C2×C4semidirect
48. C8×D293C2×C4semidirect
50. C2×D4×C293C2×C4semidirect
51. D8×C293C2×C4semidirect
52. C2×C8×C293C2×C4semidirect
57. C2×#11924078D8direct (N × H)
68. D1172C22×C4semidirect
76. #14556873C22×C4semidirect
79. D4×C293C22×C4semidirect
81. C8×C293C22×C4semidirect
96. #11924078C2×D8direct (N × H)
102. C2×C293C4×D8semidirect
105. D293C4×D8semidirect
108. C293C2×C4×D8semidirect
122. C2×D8#11924078direct (N × H)
140. C2×D4C2×#11924078semidirect
149. D8C2×#11924078direct (N × H)
156. C2×C8C2×#11924078semidirect
174. D4C22×#11924078semidirect
190. C8C22×#11924078semidirect
215. C2D8×#11924078direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#119240782
D8×#119240782
C2×#226276932
C2×#226276862
C2×C8×#119240782
C2×D8×D2932
C2×C4×D8293