Finite Group Databasebeta

← #49096527

Subgroups — #49096527

Order 35968.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C2×#22582807C212yesmaximal, complemented
3#31823462C212yesmaximal, complemented
4#31823232C211yesmaximal, characteristic, complemented
5#384×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2212yes—
7C2×#17985122C2212yes—
8#22582859—22no—
9#22582854—22no—
10#22582853—22no—
11#22582807—24no—
12#22582802—22no—
13#22582799—22no—
14C2×C4⋊C4×C281—22no—
15C2×C4⋊C4×C281C2211yescharacteristic
16C2×C4⋊C4×C281C2211yescharacteristic
17C2×C42×C281C2211yescharacteristic
18#17985138—22no—
19#17985138—22no—
20#17985138—22no—
21#17985138—22no—
22C2×Dic562D412yes—
23C2×D1124—22no—
24C2×D1124D412yes—
25C2×C22⋊D281—22no—
26C2×C4×D281—22no—
27#17985122—22no—
28#17985122—22no—
29C2×#14555886—22no—
30C4⋊Dic281—22no—
31#17985115—24no—
32C22×C4×C281—21no—
33C22×C4×C281—21no—
34C22×C4×C281D412yes—
35C22×C4×C281C2311yescharacteristic
36C4⋊C4×C281—22no—
37C4⋊C4×C281—22no—
38C4⋊C4×C281—44no—
39C42×C281—21no—
40C42×C281D412yescomplemented
41C22×D281—22no—
42Dic562—22no—
43Dic562—22no—
44D1124—22no—
45D1124—22no—
46D1124—82no—
47C22⋊D281—42no—
48C22⋊D281—42no—
49C2×Dic281—22no—
50C4×D281—42no—
51C4×D281—42no—
52#14555886—42no—
53C23×C281C2×D411yescharacteristic
54C2×C4×C281—22no—
55C2×C4×C281—22no—
56C2×C4×C281—22no—
57C2×C4×C281—22no—
58C2×C4×C281—42no—
59C2×C4×C281—42no—
60C2×C4×C281—41no—
61C2×C4×C281C2×D412yes—
62C2×C4×C281C2×D411yescharacteristic
63C2×C4×C281#4111yescharacteristic
64C2×C4×C281#4112yes—
65C22×C281—21no—
66C22×C281—21no—
67C22×C281#12011yescharacteristic
68C22×C281#12111yescharacteristic
69C22×C281#12411yescharacteristic
70C2×D281—42no—
71C2×D281—42no—
72C2×D281—42no—
73C4×C281—24no—
74C4×C281—42no—
75C4×C281—81no—
76C4×C281#12112yes—
77C4×C281#12312yes—
78Dic281—42no—
79C2×C281—21no—
80C2×C281—21no—
81C2×C281#39411yescharacteristic
82C2×C281#45311yescharacteristic
83C2×C281#45611yescharacteristic
84D281—82no—
85C281#203911yescharacteristic, complemented, Sylow
86#2039—2811nomaximal, Sylow
87#537—2811no—
88C2×#104—2812no—
89#417—2812no—
90#384D28111yescharacteristic, complemented
91#343—2811no—
92C2×#41—2812no—
93C2×M16—2812no—
94C22⋊Q8—5622no—
95#121—5622no—
96#121—5622no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4C2×D28111yescharacteristic
99C2×C4⋊C4C2×D28111yescharacteristic
100C2×C42C2×D28111yescharacteristic
101#104—5624no—
102#103—5622no—
103#102—5622no—
104#41—5622no—
105#41—5622no—
106#41—5622no—
107#41—5622no—
108C2×Q8—2812no—
109C2×D4—2812no—
110C2×D4—5622no—
111C2×D4—5622no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—5622no—
115C22×C4C22⋊D28112yes—
116C22×C4C22×D28111yescharacteristic
117M16—5622no—
118M16—5622no—
119C2×C8—5622no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—44no—
123C4⋊C4—5622no—
124C22⋊C4—5624no—
125C42—21no—
126C42D112412yescomplemented
127C23—5622no—
128C23C2×C22⋊D28111yescharacteristic
129Q8—5622no—
130Q8—5622no—
131D4—5622no—
132D4—5622no—
133D4—11242no—
134D4—11242no—
135D4—22482no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—5622no—
144C2×C4—11242no—
145C2×C4—11242no—
146C2×C4D4×D28112yes—
147C2×C4C2×D112411yescharacteristic
148C2×C4#1798513811yescharacteristic
149C2×C4#1798513912yes—
150C8—11242no—
151C22—21no—
152C22—21no—
153C22—11242no—
154C22—11242no—
155C22—11242no—
156C22#2258284711yescharacteristic
157C22#2258285311yescharacteristic
158C22#2258286811yescharacteristic
159C4—24no—
160C4—42no—
161C4—81no—
162C4—11242no—
163C4#2258285412yes—
164C4#2258286412yes—
165C2—21no—
166C2—21no—
167C2—22482no—
168C2#3182338011yescharacteristic
169C2#3182363011yescharacteristic
170C2#3182364511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#384×C281C2
socleC22×C281#120
prime radical#31824044C2
hypercenter#384D281
hypocenterC281#2039
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#22582807C2semidirect
3. #31823462C2semidirect
4. #31823232C2semidirect
5. #384×C281C2semidirect
40. C42×C281D4semidirect
85. C281#2039semidirect
90. #384D281semidirect
126. C42D1124semidirect

Maximal subgroups

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

subgroupindex
#318240442
C2×#225828072
#318234622
#318232322
#384×C2812
#2039281