Finite Group Databasebeta

← #49096347

Subgroups — #49096347

Order 35968.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22582907C212yesmaximal, complemented
2#31824044C211yesmaximal, characteristic, complemented
3C2×#22582805C212yesmaximal, complemented
4#31823364C211yesmaximal, characteristic, complemented
5#343×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2212yes—
7C22×D1124C2211yescharacteristic
8#22582907—24no—
9#22582907—24no—
10C2×#17985127—22no—
11C2×D2248—22no—
12#22582859—22no—
13#22582854—22no—
14#22582853—22no—
15C2×#17985115—22no—
16C2×C4×Dic281C2211yescharacteristic
17#22582805—24no—
18C2×M16×C281C2212yes—
19C2×C4⋊C4×C281C2211yescharacteristic
20C23×D281—21no—
21#17985138—22no—
22#17985138—22no—
23#17985138—22no—
24#17985138—22no—
25C2×Dic562D412yes—
26C2×D1124—22no—
27C2×D1124—22no—
28C2×D1124—22no—
29C2×D1124—21no—
30C2×D1124D412yes—
31C2×D1124D412yescomplemented
32C2×C22⋊D281—22no—
33C22×Dic281—21no—
34C2×C4×D281—22no—
35#17985127—28no—
36D2248—28no—
37C4⋊Dic281—22no—
38#17985115—24no—
39#17985115—44no—
40C4×Dic281—22no—
41C22×C4×C281D412yes—
42C22×C4×C281C2311yescharacteristic
43M16×C281—22no—
44M16×C281D414yescomplemented
45C2×C8×C281—22no—
46C4⋊C4×C281—22no—
47C22×D281—22no—
48C22×D281—22no—
49C22×D281—42no—
50C22×D281—42no—
51C22×D281—41no—
52C22×D281—41no—
53Dic562—22no—
54Dic562—22no—
55D1124—22no—
56D1124—24no—
57D1124—22no—
58D1124—42no—
59D1124—82no—
60C22⋊D281—42no—
61C22⋊D281—42no—
62C2×Dic281—22no—
63C2×Dic281—22no—
64C2×Dic281—41no—
65C2×Dic281—41no—
66C4×D281—42no—
67C4×D281—42no—
68C23×C281C2×D411yescharacteristic
69C2×C4×C281—22no—
70C2×C4×C281—42no—
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D412yes—
73C2×C4×C281C2×D412yes—
74C2×C4×C281#4111yescharacteristic
75C8×C281—24no—
76C22×C281—21no—
77C22×C281—21no—
78C22×C281#12011yescharacteristic
79C22×C281#12111yescharacteristic
80C22×C281#12711yescharacteristic
81C2×D281—44no—
82C2×D281—42no—
83C2×D281—42no—
84C2×D281—42no—
85C2×D281—42no—
86C2×D281—82no—
87C2×D281—81no—
88C2×D281—81no—
89C4×C281—42no—
90C4×C281#12012yes—
91C4×C281#12112yes—
92Dic281—42no—
93Dic281—42no—
94C2×C281—21no—
95C2×C281—21no—
96C2×C281#39211yescharacteristic
97C2×C281#45311yescharacteristic
98C2×C281#45411yescharacteristic
99D281—82no—
100D281—82no—
101C281#200611yescharacteristic, complemented, Sylow
102#2006—2811nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2812no—
104#537—2811no—
105C2×#104—2812no—
106#390—2811no—
107#343D28111yescharacteristic, complemented
108C2×#41—2812no—
109C22×D4—2811no—
110AGL(1,ℤ/8)—5624no—
111AGL(1,ℤ/8)—5624no—
112C2×SD16—5622no—
113C2×D8—5622no—
114C2×M16C2×D28112yes—
115C22⋊Q8—5622no—
116#121—5622no—
117#121—5622no—
118C2×C4⋊C4C2×D28111yescharacteristic
119C2×C22⋊C4—5622no—
120C2×C42—2811no—
121#104—5624no—
122C24—5621no—
123#41—5622no—
124#41—5622no—
125#41—5622no—
126#41—5622no—
127C2×Q8—2812no—
128C2×D4—2812no—
129C2×D4—2812no—
130C2×D4—5622no—
131C2×D4—5622no—
132C2×D4—5622no—
133C2×D4—5622no—
134C2×D4—5621no—
135C22×C4—5621no—
136C22×C4—5622no—
137C22×C4D112412yes—
138C22×C4C22×D28111yescharacteristic
139SD16—5628no—
140D8—5628no—
141M16—22no—
142M16D112414yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—5622no—
146C22⋊C4—5624no—
147C22⋊C4—11244no—
148C42—5622no—
149C23—5622no—
150C23—5622no—
151C23—11242no—
152C23—11242no—
153C23—11241no—
154C23—11241no—
155C23C2×D112411yescharacteristic
156Q8—5622no—
157Q8—5622no—
158D4—5622no—
159D4—5624no—
160D4—5622no—
161D4—11242no—
162D4—11242no—
163D4—11242no—
164D4—22482no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—5622no—
168C2×C4—5622no—
169C2×C4—11241no—
170C2×C4—11241no—
171C2×C4—11242no—
172C2×C4—11242no—
173C2×C4D4×D28111yescharacteristic
174C2×C4D4×D28112yes—
175C2×C4C2×D112412yes—
176C2×C4#1798513911yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—11244no—
181C22—11242no—
182C22—11242no—
183C22—11242no—
184C22—11242no—
185C22—22482no—
186C22—22481no—
187C22—22481no—
188C22#2258284911yescharacteristic
189C22#2258285411yescharacteristic
190C22#2258287611yescharacteristic
191C4—42no—
192C4—11242no—
193C4—11242no—
194C4#2258284912yes—
195C4#2258285412yes—
196C2—21no—
197C2—21no—
198C2—22482no—
199C2—22482no—
200C2#3182337311yescharacteristic
201C2#3182363311yescharacteristic
202C2#3182363811yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#343×C281C2
socleC22×C281#120
hypercenter#343D281
hypocenterC281#2006
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#22582907C2semidirect
2. #31824044C2semidirect
3. C2×#22582805C2semidirect
4. #31823364C2semidirect
5. #343×C281C2semidirect
31. C2×D1124D4semidirect
44. M16×C281D4semidirect
101. C281#2006semidirect
107. #343D281semidirect
142. M16D1124semidirect

Maximal subgroups

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

subgroupindex
C2×#225829072
#318240442
C2×#225828052
#318233642
#343×C2812
#2006281