Finite Group Databasebeta

← #354×D283 #49122920

Subgroups — #354×D283 #49122920

Order 36224.

284 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#124×D283C211yesmaximal, characteristic
2#99×D283C212yesmaximal
3#31826260C211yesmaximal, characteristic, complemented
4#31826259C212yesmaximal, complemented
5#354×C283C211yesmaximal, characteristic, complemented
6C2×Q8×D283C411yescharacteristic, complemented
7C2×D4×D283C2211yescharacteristic
8#22583599C411yescharacteristic, complemented
9#22583598C411yescharacteristic, complemented
10#22583597C2211yescharacteristic
11#22583596—22no—
12C22⋊C4×D283—22no—
13C22⋊C4×D283—22no—
14C42×D283C411yescharacteristic, complemented
15#22583525C2212yes—
16#22583524—22no—
17#124×C283C2211yescharacteristic
18#99×C283C2212yes—
19C23×D283D412yes—
20C2×Dic566—21no—
21C2×Dic566C2×C411yescharacteristic, complemented
22Q8×D283—41no—
23Q8×D283—41no—
24C2×D1132C2×C411yescharacteristic
25C2×C22⋊D283D412yes—
26D4×D283—41no—
27D4×D283—41no—
28C2×C4×D283—21no—
29C2×C4×D283—21no—
30C2×C4×D283—42no—
31C2×C4×D283C2×C411yescharacteristic
32C22⋊Dic283—22no—
33C22⋊Dic283—22no—
34(C2×D283)⋊C4—22no—
35(C2×D283)⋊C4—22no—
36(C2×D283)⋊C4—42no—
37C4×Dic283—21no—
38C4×Dic283C2×C411yescharacteristic, complemented
39C2×Q8×C283C2×C411yescharacteristic, complemented
40C2×D4×C283C2311yescharacteristic
41C22⋊C4×C283—22no—
42C22⋊C4×C283—22no—
43C42×C283C2×C411yescharacteristic, complemented
44C22×D283—22no—
45C22×D283—22no—
46C22×D283—44no—
47C22×D283C22⋊C411yescharacteristic
48C22×D283C22⋊C412yes—
49Dic566—42no—
50Dic566—41no—
51D1132—41no—
52C22⋊D283—42no—
53C2×Dic283—21no—
54C2×Dic283—21no—
55C2×Dic283—42no—
56C2×Dic283C22⋊C411yescharacteristic
57C4×D283—21no—
58C4×D283—21no—
59C4×D283—42no—
60C4×D283—41no—
61C4×D283—41no—
62C4×D283—84no—
63C23×C283C2×D412yes—
64Q8×C283—41no—
65D4×C283—41no—
66C2×C4×C283—21no—
67C2×C4×C283—21no—
68C2×C4×C283—42no—
69C2×C4×C283C22×C411yescharacteristic
70C22×C283—22no—
71C22×C283—42no—
72C22×C283C2×C22⋊C411yescharacteristic
73C2×D283—22no—
74C2×D283—22no—
75C2×D283—44no—
76C2×D283—42no—
77C2×D283—82no—
78C2×D283#9911yescharacteristic
79C2×D283#9911yescharacteristic
80C4×C283—21no—
81C4×C283—41no—
82C4×C283—41no—
83C4×C283—82no—
84Dic283—21no—
85Dic283—41no—
86Dic283—41no—
87Dic283—82no—
88C2×C283—21no—
89C2×C283—42no—
90C2×C283C2×#9911yescharacteristic
91D283—21no—
92D283—42no—
93D283#35412yesdirect product factor
94C283C2×#35411yescharacteristic, complemented, Sylow
95C2×#354—2831nomaximal, Sylow
96C2×#124—2831no—
97C2×#99—2832no—
98#354—2831no—
99#354—2832no—
100#354D28311yescharacteristic, direct product factor
101C22×Q8—2831no—
102C22×D4—2831no—
103#124—2831no—
104#124—2831no—
105#124—2831no—
106#124—5662no—
107#124C2×D28311yescharacteristic
108C2×C22⋊C4—5662no—
109C2×C22⋊C4—5662no—
110C2×C42—2831no—
111#99—2832no—
112#99—5662no—
113#99C2×D28312yes—
114C24—2832no—
115C2×Q8—2831no—
116C2×Q8—5661no—
117C2×Q8—11321no—
118C2×Q8—11321no—
119C2×Q8C4×D28311yescharacteristic, complemented
120C2×D4—2832no—
121C2×D4—2831no—
122C2×D4—11321no—
123C2×D4—11321no—
124C2×D4C22×D28311yescharacteristic
125C22×C4—2831no—
126C22×C4—5661no—
127C22×C4—5661no—
128C22×C4—11322no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—5662no—
132C22⋊C4—5662no—
133C22⋊C4—5662no—
134C22⋊C4—5662no—
135C22⋊C4—11322no—
136C42—2831no—
137C42—5661no—
138C42C4×D28311yescharacteristic, complemented
139C23—2831no—
140C23—2832no—
141C23—5662no—
142C23—5662no—
143C23—11324no—
144C23D4×D28312yes—
145Q8—41no—
146Q8—11321no—
147Q8—11322no—
148D4—41no—
149D4—11321no—
150D4—11322no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—2831no—
155C2×C4—5661no—
156C2×C4—5661no—
157C2×C4—5661no—
158C2×C4—5661no—
159C2×C4—11321no—
160C2×C4—11321no—
161C2×C4—11322no—
162C2×C4—11322no—
163C2×C4—22644no—
164C2×C4C2×C4×D28311yescharacteristic
165C22—22no—
166C22—42no—
167C22—2831no—
168C22—2831no—
169C22—5662no—
170C22—5662no—
171C22—11322no—
172C22—11324no—
173C22—22642no—
174C22C22⋊C4×D28311yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—5661no—
180C4—11321no—
181C4—11321no—
182C4—22642no—
183C2—21no—
184C2—42no—
185C2—2832no—
186C2—5661no—
187C2—11322no—
188C2#99×D28311yescharacteristic
subgroupG/H
centerC2#99×D283
commutatorC2×C4×C283C22×C4
FrattiniC2×D4C22×D283
Fitting#354×C283C2
socleC2×C283C2×#99
prime radicalC2×D4×D283C22
cosocleC2×D4×C283C23
hypercenter#354D283
hypocenterC283C2×#354
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #31826260C2semidirect
4. #31826259C2semidirect
5. #354×C283C2semidirect
6. C2×Q8×D283C4semidirect
8. #22583599C4semidirect
9. #22583598C4semidirect
14. C42×D283C4semidirect
21. C2×Dic566C2×C4semidirect
38. C4×Dic283C2×C4semidirect
39. C2×Q8×C283C2×C4semidirect
43. C42×C283C2×C4semidirect
93. D283#354direct (N × H)
94. C283C2×#354semidirect
100. #354D283direct (N × H)
119. C2×Q8C4×D283semidirect
138. C42C4×D283semidirect

Maximal subgroups

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

subgroupindex
#124×D2832
#99×D2832
#318262602
#318262592
#354×C2832
C2×#354283