Finite Group Databasebeta

← #49094437

Subgroups — #49094437

Order 35968.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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#31823842C211yesmaximal, characteristic, complemented
2#31823758C211yesmaximal, characteristic, complemented
3#31823753C211yesmaximal, characteristic
4#31823212C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic
7#554×C281C211yesmaximal, characteristic
8C2×#17985128—22no—
9#22582879C2211yescharacteristic
10#22582812—21no—
11#22582810—21no—
12C4⋊#14555886C2211yescharacteristic
13C4⋊#14555886C2211yescharacteristic
14#22582803—21no—
15#22582800—21no—
16C4×#14555886C2211yescharacteristic
17C4⋊Q8×C281C2211yescharacteristic
18#125×C281—21no—
19C22⋊Q8×C281—21no—
20C22⋊Q8×C281—22no—
21C4×Q8×C281C2211yescharacteristic
22C4×D4×C281—21no—
23C4×D4×C281C2211yescharacteristic
24C2×C4⋊C4×C281—21no—
25C2×Dic562—21no—
26#17985128—44no—
27C2×#14555886—21no—
28C2×#14555886—21no—
29C2×#14555886—21no—
30C4⋊Dic281—21no—
31C4⋊Dic281—21no—
32C2×Q8×C281D411yescharacteristic
33C2×Q8×C281D412yes—
34C2×D4×C281D411yescharacteristic
35C22×C4×C281—22no—
36C22×C4×C281—21no—
37C4⋊C4×C281—22no—
38C4⋊C4×C281—22no—
39C4⋊C4×C281—21no—
40C4⋊C4×C281—21no—
41C4⋊C4×C281—21no—
42C4⋊C4×C281D411yescharacteristic
43C4⋊C4×C281D411yescharacteristic
44C22⋊C4×C281—22no—
45C22⋊C4×C281—21no—
46C42×C281—21no—
47C42×C281C2311yescharacteristic
48Dic562—42no—
49C2×Dic281—41no—
50#14555886—22no—
51#14555886—41no—
52#14555886—41no—
53C23×C281—21no—
54Q8×C281—21no—
55Q8×C281—21no—
56Q8×C281—42no—
57D4×C281—21no—
58D4×C281Q1612yescomplemented
59C2×C4×C281—21no—
60C2×C4×C281—21no—
61C2×C4×C281—21no—
62C2×C4×C281—22no—
63C2×C4×C281—41no—
64C2×C4×C281—41no—
65C2×C4×C281—82no—
66C2×C4×C281C2×D411yescharacteristic
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C22×C281—22no—
70C22×C281—41no—
71C22×C281—41no—
72C22×C281#12011yescharacteristic
73C4×C281—21no—
74C4×C281—41no—
75C4×C281—41no—
76C4×C281—41no—
77C4×C281—42no—
78C4×C281C2×Q1611yescharacteristic
79C4×C281#13511yescharacteristic
80C4×C281#13711yescharacteristic
81C4×C281#13711yescharacteristic
82Dic281—81no—
83C2×C281—42no—
84C2×C281#45111yescharacteristic
85C2×C281#45211yescharacteristic
86C2×C281#45311yescharacteristic
87C281#163211yescharacteristic, complemented, Sylow
88#1632—2811nomaximal, Sylow
89#554D28111yescharacteristic
90#494—2811no—
91#477—2811no—
92#476—2811no—
93#333—2811no—
94Q8⋊C8—2811no—
95D4⋊C8—2811no—
96C2×Q16—5622no—
97C4⋊Q8—2811no—
98C4⋊Q8C2×D28111yescharacteristic
99#125—21no—
100C22⋊Q8—21no—
101C22⋊Q8—22no—
102C4×Q8C2×D28111yescharacteristic
103C4×D4—21no—
104C4×D4C2×D28111yescharacteristic
105C2×C4⋊C4—21no—
106#107—5621no—
107#106—5621no—
108C4⋊C8—2811no—
109C4⋊C8—2811no—
110#103—5621no—
111#102—5621no—
112C4×C8—2811no—
113C2×Q8—5621no—
114C2×Q8C22⋊D28111yescharacteristic
115C2×Q8C22⋊D28112yes—
116C2×D4C22⋊D28111yescharacteristic
117C22×C4—22no—
118C22×C4—21no—
119Q16—11244no—
120C2×C8—5621no—
121C2×C8—5621no—
122C2×C8—5621no—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—5621no—
129C4⋊C4—5621no—
130C4⋊C4C22⋊D28111yescharacteristic
131C4⋊C4C22⋊D28111yescharacteristic
132C22⋊C4—22no—
133C22⋊C4—21no—
134C42—21no—
135C42C22×D28111yescharacteristic
136C23—21no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—11242no—
141D4—21no—
142D4#1798512812yescomplemented
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—82no—
150C2×C4—11241no—
151C2×C4C2×C22⋊D28111yescharacteristic
152C2×C4C2×C22⋊D28111yescharacteristic
153C2×C4C2×C22⋊D28111yescharacteristic
154C8—5622no—
155C8—11241no—
156C8—11241no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#2258284811yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—41no—
165C4—42no—
166C4—22481no—
167C4C2×#1798512811yescharacteristic
168C4#2258289911yescharacteristic
169C4#2258290911yescharacteristic
170C4#2258291011yescharacteristic
171C2—42no—
172C2#3182361911yescharacteristic
173C2#3182362511yescharacteristic
174C2#3182363111yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#554×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenter#554D281
hypocenterC281#1632
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #31823842C2semidirect
2. #31823758C2semidirect
4. #31823212C2semidirect
5. Q8⋊#14555886C2semidirect
58. D4×C281Q16semidirect
87. C281#1632semidirect
142. D4#17985128semidirect

Maximal subgroups

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

subgroupindex
#318238422
#318237582
#318237532
#318232122
Q8⋊#145558862
D4⋊#145558862
#554×C2812
#1632281