Finite Group Databasebeta

← #49095220

Subgroups — #49095220

Order 35968.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#17985138C211yesmaximal, characteristic
2C2×#22582793C214yesmaximal, complemented
3#31823326C211yesmaximal, characteristic, complemented
4#381×C281C211yesmaximal, characteristic, complemented
5C2×#17985138—28no—
6C2×#17985138—22no—
7C2×#17985138—22no—
8C22×Dic562C411yescharacteristic, complemented
9C22×D1124C411yescharacteristic, complemented
10C22×C22⋊D281C2212yes—
11C22×C4×D281C412yescomplemented
12C2×C22⋊Dic281C2212yes—
13#22582793—28no—
14#22582786—22no—
15C23×C4×C281C2211yescharacteristic
16C2×C22⋊C4×C281C2212yes—
17#95×C281—22no—
18C23×D281C2×C412yes—
19#17985138—216no—
20#17985138—216no—
21C2×Dic562—24no—
22C2×Dic562—22no—
23C2×D1124—24no—
24C2×D1124—22no—
25C2×C22⋊D281—24no—
26C2×C22⋊D281—22no—
27C2×C22⋊D281—22no—
28C2×C22⋊D281D418yes—
29C22×Dic281—22no—
30C22×Dic281C2×C412yes—
31C2×C4×D281—24no—
32C2×C4×D281—24no—
33C2×C4×D281—24no—
34C22⋊Dic281—24no—
35C24×C281C2311yescharacteristic
36C22×C4×C281—24no—
37C22×C4×C281—22no—
38C22×C4×C281C2×C411yescharacteristic
39C22×C4×C281C2×C411yescharacteristic
40C22×C4×C281D412yes—
41C22×C4×C281D412yes—
42C22⋊C4×C281—24no—
43C22×D281—22no—
44C22×D281—22no—
45C22×D281—44no—
46C22×D281C22⋊C414yes—
47Dic562—28no—
48D1124—28no—
49C22⋊D281—28no—
50C22⋊D281—28no—
51C2×Dic281—22no—
52C2×Dic281—22no—
53C2×Dic281—44no—
54C2×Dic281—42no—
55C2×Dic281C22⋊C414yes—
56C4×D281—216no—
57C23×C281—42no—
58C23×C281C22×C411yescharacteristic
59C23×C281C2×D414yes—
60C23×C281C2×D411yescharacteristic
61C23×C281C2×D411yescharacteristic
62C2×C4×C281—22no—
63C2×C4×C281—22no—
64C2×C4×C281—24no—
65C2×C4×C281—24no—
66C2×C4×C281—44no—
67C2×C4×C281—42no—
68C2×C4×C281C22⋊C412yes—
69C2×C4×C281C22⋊C412yes—
70C22×C281—22no—
71C22×C281—22no—
72C22×C281—22no—
73C22×C281—44no—
74C22×C281C2×C22⋊C412yes—
75C22×C281C2×C22⋊C411yescharacteristic
76C22×C281#12012yes—
77C22×C281#12012yes—
78C2×D281—24no—
79C2×D281—44no—
80C2×D281—44no—
81C2×D281—44no—
82C4×C281—22no—
83C4×C281—22no—
84C4×C281—82no—
85Dic281—24no—
86Dic281—82no—
87C2×C281—22no—
88C2×C281—22no—
89C2×C281—22no—
90C2×C281#37911yescharacteristic
91C2×C281#41012yes—
92D281—44no—
93C281#178211yescharacteristic, complemented, Sylow
94#1782—2811nomaximal, Sylow
95C22×#41—2811no—
96C2×#99—2814no—
97#381—2811no—
98#381D28111yescharacteristic, complemented
99C2×#41—5628no—
100C2×#41—5622no—
101C2×#41—5622no—
102C22×Q8—2811no—
103C22×D4—2812no—
104C22×D4—2811no—
105C23×C4—2812no—
106C23×C4C2×D28111yescharacteristic
107C2×C22⋊C4—2812no—
108C2×C22⋊C4C2×D28112yes—
109#99—5628no—
110#95—22no—
111#95—5622no—
112C24—2812no—
113C24C22×D28111yescharacteristic
114#41—56216no—
115#41—56216no—
116C2×Q8—5624no—
117C2×Q8—5622no—
118C2×D4—2818no—
119C2×D4—5624no—
120C2×D4—5624no—
121C2×D4—5622no—
122C2×D4—5622no—
123C2×D4—5622no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—2812no—
127C22×C4—5624no—
128C22×C4—5624no—
129C22×C4—5624no—
130C22×C4—5622no—
131C22×C4C4×D28111yescharacteristic
132C22×C4C4×D28111yescharacteristic
133C22×C4C22⋊D28112yes—
134C22×C4D112412yes—
135C22⋊C4—24no—
136C22⋊C4—5624no—
137C23—42no—
138C23—2814no—
139C23—5622no—
140C23—5622no—
141C23—11244no—
142C23C2×C4×D28111yescharacteristic
143C23D4×D28114yes—
144C23C2×C22⋊D28111yescharacteristic
145C23C2×D112411yescharacteristic
146Q8—5628no—
147D4—5628no—
148D4—5628no—
149D4—5628no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—44no—
155C2×C4—42no—
156C2×C4—2814no—
157C2×C4—56216no—
158C2×C4—5622no—
159C2×C4—5622no—
160C2×C4—11244no—
161C2×C4—11242no—
162C2×C4#1798511512yes—
163C2×C4#1798511512yes—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—5624no—
169C22—11244no—
170C22—11244no—
171C22—11244no—
172C22C22⋊C4×D28112yes—
173C22C2×#1798511511yescharacteristic
174C22#2258284712yes—
175C22#2258284912yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—5624no—
180C4—22482no—
181C2—22no—
182C2—22no—
183C2—22no—
184C2—11244no—
185C2#3182331811yescharacteristic
186C2#3182343612yes—
subgroupG/H
centerC22C2×#17985115
commutatorC23×C281C22×C4
FrattiniC24C22×D281
Fitting#381×C281C2
socleC22×C281C2×C22⋊C4
prime radicalC22×#17985138C2
cosocleC24×C281C23
hypercenter#381D281
hypocenterC281#1782
LCSG ▷ C23×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22582793C2semidirect
3. #31823326C2semidirect
4. #381×C281C2semidirect
8. C22×Dic562C4semidirect
9. C22×D1124C4semidirect
11. C22×C4×D281C4semidirect
93. C281#1782semidirect
98. #381D281semidirect

Maximal subgroups

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

subgroupindex
C22×#179851382
C2×#225827932
#318233262
#381×C2812
#1782281