Finite Group Databasebeta

← #49094436

Subgroups — #49094436

Order 35968.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824173C211yesmaximal, characteristic
2#31823842C211yesmaximal, characteristic, complemented
3#31823750C211yesmaximal, characteristic
4#31823211C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic
7#477×C281C211yesmaximal, characteristic, complemented
8C2×#17985128—22no—
9#22582879C2211yescharacteristic
10#22582871—21no—
11#22582857—22no—
12#22582855—21no—
13C4×D1124—21no—
14C4×D1124C2211yescharacteristic
15C4⋊C4×D281—21no—
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic
18#22582799—21no—
19C4×#14555886C2211yescharacteristic
20C4⋊Q8×C281C2211yescharacteristic
21C4×Q8×C281C2211yescharacteristic
22#107×C281—21no—
23C4⋊C8×C281C2211yescharacteristic
24#103×C281—21no—
25C2×Dic562D412yes—
26C2×D1124D411yescharacteristic
27C2×C4×D281—22no—
28C2×C4×D281—21no—
29#17985128—44no—
30C2×#14555886—21no—
31C2×#14555886—21no—
32C4⋊Dic281—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281D411yescharacteristic
35#17985117—22no—
36#17985117—22no—
37#17985115—22no—
38#17985115—21no—
39C2×Q8×C281—21no—
40C2×Q8×C281D411yescharacteristic
41C2×C8×C281—21no—
42C4⋊C4×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281D411yescharacteristic
46C42×C281—21no—
47C42×C281C2311yescharacteristic
48C22×D281—21no—
49Dic562—42no—
50D1124—21no—
51D1124Q1612yescomplemented
52C2×Dic281—21no—
53C2×Dic281—22no—
54C4×D281—41no—
55C4×D281—41no—
56C4×D281—82no—
57#14555886—22no—
58#14555886—41no—
59Q8×C281—21no—
60Q8×C281—21no—
61Q8×C281—42no—
62C2×C4×C281—21no—
63C2×C4×C281—21no—
64C2×C4×C281—41no—
65C2×C4×C281C2×D411yescharacteristic
66C2×C4×C281C2×D411yescharacteristic
67C2×C4×C281C2×D411yescharacteristic
68C8×C281—41no—
69C22×C281#12011yescharacteristic
70C2×D281—22no—
71C2×D281—41no—
72C2×D281—41no—
73C4×C281—21no—
74C4×C281—41no—
75C4×C281—41no—
76C4×C281—81no—
77C4×C281C2×Q1611yescharacteristic
78C4×C281#13511yescharacteristic
79C4×C281#13711yescharacteristic
80C4×C281#13711yescharacteristic
81Dic281—41no—
82Dic281—42no—
83C2×C281#45111yescharacteristic
84C2×C281#45211yescharacteristic
85C2×C281#45311yescharacteristic
86D281—42no—
87C281#163211yescharacteristic, complemented, Sylow
88#1632—2811nomaximal, Sylow
89#554—2811no—
90#494—2811no—
91#477D28111yescharacteristic, complemented
92#476—2811no—
93#333—2811no—
94Q8⋊C8—2811no—
95D4⋊C8—2811no—
96C2×Q16—5622no—
97C4⋊Q8—2811no—
98C4⋊Q8C2×D28111yescharacteristic
99#125—5621no—
100C22⋊Q8—5622no—
101C22⋊Q8—5621no—
102C4×Q8C2×D28111yescharacteristic
103C4×D4—2811no—
104C4×D4—5621no—
105C2×C4⋊C4—5621no—
106#107—21no—
107#106—5621no—
108C4⋊C8—2811no—
109C4⋊C8C2×D28111yescharacteristic
110#103—21no—
111#102—5621no—
112C4×C8—2811no—
113C2×Q8—21no—
114C2×Q8—2812no—
115C2×Q8C22⋊D28111yescharacteristic
116C2×D4—2811no—
117C22×C4—5622no—
118C22×C4—5621no—
119Q16—11244no—
120C2×C8—21no—
121C2×C8—5621no—
122C2×C8—5621no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2811no—
127C4⋊C4—5622no—
128C4⋊C4—5622no—
129C4⋊C4—5621no—
130C4⋊C4—5621no—
131C4⋊C4C22⋊D28111yescharacteristic
132C22⋊C4—5622no—
133C22⋊C4—5621no—
134C42—21no—
135C42C22×D28111yescharacteristic
136C23—5621no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—11242no—
141D4—2812no—
142D4—5621no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—5621no—
147C2×C4—5622no—
148C2×C4—11241no—
149C2×C4—11241no—
150C2×C4—22482no—
151C2×C4D4×D28111yescharacteristic
152C2×C4D4×D28111yescharacteristic
153C2×C4C2×C22⋊D28111yescharacteristic
154C8—41no—
155C8—5622no—
156C8—11241no—
157C22—5622no—
158C22—11241no—
159C22—11241no—
160C22#2258284711yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—11241no—
166C4—11242no—
167C4Q16×D28111yescharacteristic
168C4#2258289911yescharacteristic
169C4#2258291011yescharacteristic
170C4#2258291111yescharacteristic
171C2—11242no—
172C2#3182361711yescharacteristic
173C2#3182362311yescharacteristic
174C2#3182362911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#477×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#477D281
hypocenterC281#1632
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #31823842C2semidirect
4. #31823211C2semidirect
5. Q8⋊#14555886C2semidirect
7. #477×C281C2semidirect
51. D1124Q16semidirect
87. C281#1632semidirect
91. #477D281semidirect

Maximal subgroups

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

subgroupindex
#318241732
#318238422
#318237502
#318232112
Q8⋊#145558862
#318231902
#477×C2812
#1632281