Finite Group Databasebeta

← #49094240

Subgroups — #49094240

Order 35968.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824044C211yesmaximal, characteristic, complemented
2#31823599C212yesmaximal, complemented
3#31823380C211yesmaximal, characteristic, complemented
4#31823198C212yesmaximal, complemented
5#324×C281C211yesmaximal, characteristic, complemented
6C2×#17985138—21no—
7C22×D1124C2211yescharacteristic
8C2×D2248—22no—
9#22582859—22no—
10#22582854—22no—
11#22582853—21no—
12#22582853C2212yes—
13C2×#17985115—21no—
14C2×#17985115—21no—
15#22582801—22no—
16#22582786C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C23×D281—21no—
20#17985138—42no—
21#17985138—42no—
22C2×Dic562—21no—
23C2×D1124—21no—
24C2×D1124—21no—
25C2×D1124—22no—
26C2×D1124—42no—
27C2×D1124D412yes—
28C2×C22⋊D281—22no—
29C22×Dic281—21no—
30C2×C4×D281—22no—
31D2248—44no—
32C4⋊Dic281—21no—
33C4⋊Dic281D412yes—
34#17985115—22no—
35#17985115—22no—
36#17985115—42no—
37#17985115—42no—
38C22×C4×C281D411yescharacteristic
39C22×C4×C281D411yescharacteristic
40C22×C4×C281C2311yescharacteristic
41C2×C8×C281—22no—
42C4⋊C4×C281—22no—
43C22×D281—22no—
44C22×D281—22no—
45C22×D281—41no—
46C22×D281—41no—
47C22×D281—41no—
48C22×D281—41no—
49C22×D281—41no—
50C22×D281—41no—
51Dic562—42no—
52D1124—24no—
53D1124—42no—
54D1124—42no—
55D1124—42no—
56D1124—81no—
57C22⋊D281—42no—
58C22⋊D281—42no—
59C2×Dic281—22no—
60C2×Dic281—41no—
61C2×Dic281—41no—
62C2×Dic281—41no—
63C4×D281—44no—
64C23×C281C2×D411yescharacteristic
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281—21no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
70C2×C4×C281D812yescomplemented
71C2×C4×C281C2×D412yes—
72C8×C281—42no—
73C22×C281—21no—
74C22×C281—21no—
75C22×C281#12011yescharacteristic
76C22×C281C2×D811yescharacteristic
77C22×C281AGL(1,ℤ/8)11yescharacteristic
78C2×D281—42no—
79C2×D281—42no—
80C2×D281—42no—
81C2×D281—42no—
82C2×D281—42no—
83C2×D281—42no—
84C2×D281—81no—
85C2×D281—81no—
86C2×D281—81no—
87C2×D281—81no—
88C4×C281—22no—
89C4×C281—22no—
90C4×C281—41no—
91Dic281—42no—
92Dic281—81no—
93C2×C281—21no—
94C2×C281—21no—
95C2×C281#44711yescharacteristic
96C2×C281#45411yescharacteristic
97C2×C281B(4,𝔽2)11yescharacteristic
98D281—82no—
99D281—82no—
100C281#159811yescharacteristic, complemented, Sylow
101#1598—2811nomaximal, Sylow
102#537—2811no—
103#447—2812no—
104#394—2811no—
105#327—2812no—
106#324D28111yescharacteristic, complemented
107C2×#41—5621no—
108C22×D4—2811no—
109C2×D8—5622no—
110C22⋊Q8—5622no—
111#121—2812no—
112#121—5622no—
113#121—5621no—
114C2×C4⋊C4C2×D28111yescharacteristic
115C2×C22⋊C4—5621no—
116C2×C22⋊C4—5621no—
117#102—5622no—
118C22⋊C8C2×D28112yes—
119#95—2811no—
120C24—5621no—
121#41—11242no—
122#41—11242no—
123C2×Q8—5621no—
124C2×D4—2812no—
125C2×D4—5621no—
126C2×D4—5621no—
127C2×D4—5622no—
128C2×D4—5622no—
129C2×D4—11242no—
130C22×C4—5622no—
131C22×C4—5621no—
132C22×C4D112411yescharacteristic
133C22×C4D112411yescharacteristic
134C22×C4C22×D28111yescharacteristic
135D8—11244no—
136C2×C8—22no—
137C4⋊C4—22no—
138C4⋊C4—2812no—
139C4⋊C4—5621no—
140C22⋊C4—5622no—
141C22⋊C4—5622no—
142C22⋊C4—11242no—
143C22⋊C4—11242no—
144C23—5622no—
145C23—5622no—
146C23—11241no—
147C23—11241no—
148C23—11241no—
149C23—11241no—
150C23—11241no—
151C23—11241no—
152C23C2×D112411yescharacteristic
153Q8—11242no—
154D4—5624no—
155D4—11242no—
156D4—11242no—
157D4—11242no—
158D4—11242no—
159D4—11242no—
160D4—22481no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—5622no—
167C2×C4—11244no—
168C2×C4—11241no—
169C2×C4—11241no—
170C2×C4—11241no—
171C2×C4D224812yescomplemented
172C2×C4D4×D28112yes—
173C8—42no—
174C22—21no—
175C22—21no—
176C22—11242no—
177C22—11242no—
178C22—11242no—
179C22—11242no—
180C22—11242no—
181C22—11242no—
182C22—22481no—
183C22—22481no—
184C22—22481no—
185C22—22481no—
186C22#2258284911yescharacteristic
187C22C2×D224811yescharacteristic
188C22#2258290711yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—11242no—
193C4—22481no—
194C2—21no—
195C2—21no—
196C2—22482no—
197C2—22482no—
198C2#3182359911yescharacteristic
199C2#3182363811yescharacteristic
200C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
hypercenter#324D281
hypocenterC281#1598
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #31824044C2semidirect
2. #31823599C2semidirect
3. #31823380C2semidirect
4. #31823198C2semidirect
5. #324×C281C2semidirect
70. C2×C4×C281D8semidirect
100. C281#1598semidirect
106. #324D281semidirect
171. C2×C4D2248semidirect

Maximal subgroups

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

subgroupindex
#318240442
#318235992
#318233802
#318231982
#324×C2812
#1598281