Finite Group Databasebeta

← #49094237

Subgroups — #49094237

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#31823597C212yesmaximal, complemented
3#31823196C212yesmaximal, complemented
4#31823189C211yesmaximal, characteristic, complemented
5#394×C281C211yesmaximal, characteristic, complemented
6C2×#17985138—21no—
7C2×#17985123—22no—
8#22582859—22no—
9#22582854—22no—
10#22582853—21no—
11#22582853C2212yes—
12#22582800—22no—
13C22⋊#14555886C2212yes—
14C22×D4×C281C2211yescharacteristic
15C2×C4⋊C4×C281C2211yescharacteristic
16C2×C22⋊C4×C281—21no—
17C2×C22⋊C4×C281—21no—
18#95×C281C2211yescharacteristic
19#17985138—42no—
20#17985138—42no—
21C2×Dic562—21no—
22C2×D1124—21no—
23C2×D1124—21no—
24C2×D1124D412yes—
25C2×C22⋊D281—22no—
26C2×C4×D281—22no—
27#17985123—44no—
28C2×#14555886—22no—
29C4⋊Dic281—21no—
30C4⋊Dic281D412yes—
31#17985115—22no—
32#17985115—22no—
33C24×C281—21no—
34C2×D4×C281—22no—
35C2×D4×C281—42no—
36C22×C4×C281—21no—
37C22×C4×C281D411yescharacteristic
38C22×C4×C281D411yescharacteristic
39C22×C4×C281C2311yescharacteristic
40C4⋊C4×C281—22no—
41C22⋊C4×C281—42no—
42C22⋊C4×C281—42no—
43C22×D281—22no—
44Dic562—42no—
45D1124—42no—
46D1124—42no—
47D1124—81no—
48C22⋊D281—42no—
49C22⋊D281—42no—
50C2×Dic281—22no—
51C4×D281—44no—
52#14555886—42no—
53C23×C281—22no—
54C23×C281—41no—
55C23×C281—41no—
56C23×C281—41no—
57C23×C281—41no—
58C23×C281—41no—
59C23×C281—41no—
60C23×C281C2×D411yescharacteristic
61D4×C281—24no—
62D4×C281—42no—
63C2×C4×C281—21no—
64C2×C4×C281—21no—
65C2×C4×C281—21no—
66C2×C4×C281—41no—
67C2×C4×C281—41no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
70C2×C4×C281—41no—
71C2×C4×C281D812yescomplemented
72C2×C4×C281C2×D412yes—
73C22×C281—21no—
74C22×C281—21no—
75C22×C281—42no—
76C22×C281—42no—
77C22×C281—42no—
78C22×C281—81no—
79C22×C281—81no—
80C22×C281—81no—
81C22×C281—81no—
82C22×C281#12011yescharacteristic
83C22×C281C2×D811yescharacteristic
84C22×C281AGL(1,ℤ/8)11yescharacteristic
85C2×D281—42no—
86C2×D281—42no—
87C2×D281—42no—
88C4×C281—22no—
89C4×C281—22no—
90C4×C281—41no—
91C4×C281—81no—
92Dic281—42no—
93C2×C281—21no—
94C2×C281—21no—
95C2×C281—82no—
96C2×C281#44711yescharacteristic
97C2×C281#45411yescharacteristic
98C2×C281B(4,𝔽2)11yescharacteristic
99D281—82no—
100C281#159811yescharacteristic, complemented, Sylow
101#1598—2811nomaximal, Sylow
102#537—2811no—
103#447—2812no—
104#394D28111yescharacteristic, complemented
105#327—2812no—
106#324—2811no—
107C2×#41—5621no—
108C22×D4C2×D28111yescharacteristic
109C2×D8—5622no—
110C22⋊Q8—5622no—
111#121—2812no—
112#121—5622no—
113#121—5621no—
114C2×C4⋊C4C2×D28111yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—5622no—
118C22⋊C8—2812no—
119#95C2×D28111yescharacteristic
120C24—21no—
121#41—11242no—
122#41—11242no—
123C2×Q8—5621no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—2812no—
127C2×D4—5621no—
128C2×D4—5621no—
129C2×D4—5622no—
130C22×C4—21no—
131C22×C4—5622no—
132C22×C4C22⋊D28111yescharacteristic
133C22×C4C22⋊D28111yescharacteristic
134C22×C4C22×D28111yescharacteristic
135D8—11244no—
136C2×C8—5622no—
137C4⋊C4—22no—
138C4⋊C4—2812no—
139C4⋊C4—5621no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—5622no—
143C22⋊C4—5622no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—5622no—
152C23C2×C22⋊D28111yescharacteristic
153Q8—11242no—
154D4—24no—
155D4—42no—
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—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5622no—
170C2×C4—11244no—
171C2×C4#1798512312yescomplemented
172C2×C4D4×D28112yes—
173C8—11242no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—11242no—
184C22—11242no—
185C22—11242no—
186C22#2258284711yescharacteristic
187C22C2×#1798512311yescharacteristic
188C22#2258290411yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—11242no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—22482no—
198C2#3182359611yescharacteristic
199C2#3182363511yescharacteristic
200C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#394×C281C2
socleC22×C281#120
hypercenter#394D281
hypocenterC281#1598
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #31824044C2semidirect
2. #31823597C2semidirect
3. #31823196C2semidirect
4. #31823189C2semidirect
5. #394×C281C2semidirect
71. C2×C4×C281D8semidirect
100. C281#1598semidirect
104. #394D281semidirect
171. C2×C4#17985123semidirect

Maximal subgroups

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

subgroupindex
#318240442
#318235972
#318231962
#318231892
#394×C2812
#1598281