Finite Group Databasebeta

← #49094553

Subgroups — #49094553

Order 35968.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#31824128C211yesmaximal, characteristic
2#31823866C211yesmaximal, characteristic, complemented
3#31823744C211yesmaximal, characteristic
4#31823674C211yesmaximal, characteristic, complemented
5#31823193C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic
7#332×C281C211yesmaximal, characteristic, complemented
8C2×Q8×D281—21no—
9C2×Dic1124—21no—
10#22582879C2211yescharacteristic
11#22582878—21no—
12#22582857—22no—
13#22582855—21no—
14C4×Dic562C2211yescharacteristic
15C4×D1124C2211yescharacteristic
16#22582841—21no—
17#22582813—21no—
18#22582812—22no—
19#22582804—21no—
20#22582801—21no—
21C4×#14555886C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25C2×Dic562—22no—
26C2×Dic562—21no—
27C2×Dic562D411yescharacteristic
28Q8×D281—42no—
29Q8×D281—42no—
30C2×D1124D411yescharacteristic
31C2×C4×D281—22no—
32C2×C4×D281—21no—
33Dic1124—42no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281D411yescharacteristic
38C4⋊Dic281D411yescharacteristic
39#17985117—22no—
40#17985117—21no—
41#17985115—22no—
42#17985115—21no—
43C4×Dic281—21no—
44C2×Q8×C281—21no—
45C2×C8×C281—21no—
46C2×C8×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281D412yes—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51Dic562—21no—
52Dic562—44no—
53Dic562—41no—
54Dic562—41no—
55Dic562D812yes—
56D1124—21no—
57D1124Q1612yescomplemented
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—41no—
62C4×D281—44no—
63C4×D281—41no—
64C4×D281—41no—
65#14555886—22no—
66Q8×C281—41no—
67Q8×C281—41no—
68C2×C4×C281—22no—
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C8×C281—41no—
73C8×C281—41no—
74C22×C281#12011yescharacteristic
75C2×D281—22no—
76C2×D281—41no—
77C2×D281—41no—
78C4×C281—21no—
79C4×C281—42no—
80C4×C281C2×D811yescharacteristic
81C4×C281C2×Q1611yescharacteristic
82C4×C281AGL(1,ℤ/8)11yescharacteristic
83C4×C281#13711yescharacteristic
84Dic281—22no—
85Dic281—41no—
86Dic281—41no—
87Dic281—81no—
88C2×C281#44711yescharacteristic
89C2×C281#45111yescharacteristic
90C2×C281#45611yescharacteristic
91D281—42no—
92C281#164911yescharacteristic, complemented, Sylow
93#1649—2811nomaximal, Sylow
94D4×Q8—2811no—
95#500—2811no—
96#474—2811no—
97#462—2811no—
98#332D28111yescharacteristic, complemented
99Q8⋊C8—2811no—
100D4⋊C8—2811no—
101C22×Q8—5621no—
102C2×Q16—5621no—
103C4⋊Q8—2811no—
104C4⋊Q8—5621no—
105C4⋊Q8C2×D28111yescharacteristic
106C22⋊Q8—5621no—
107C22⋊Q8—5622no—
108C4×Q8—2811no—
109C4×D4—2811no—
110C4×D4—5621no—
111#107—5621no—
112#107—5622no—
113C4⋊C8C2×D28111yescharacteristic
114C4⋊C8C2×D28111yescharacteristic
115#103—5621no—
116#102—5621no—
117C4×C8—2811no—
118C2×Q8—21no—
119C2×Q8—2811no—
120C2×Q8—5622no—
121C2×Q8—5621no—
122C2×Q8—11242no—
123C2×Q8—11242no—
124C2×D4—2811no—
125C22×C4—5622no—
126C22×C4—5621no—
127Q16—11242no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5621no—
131C4⋊C4—21no—
132C4⋊C4—2811no—
133C4⋊C4—2811no—
134C4⋊C4—5622no—
135C4⋊C4—5621no—
136C4⋊C4—5621no—
137C4⋊C4—5621no—
138C4⋊C4D112412yes—
139C22⋊C4—5622no—
140C22⋊C4—5621no—
141C42—5621no—
142C42C22×D28111yescharacteristic
143C23—5621no—
144Q8—41no—
145Q8—41no—
146Q8—2812no—
147Q8—5621no—
148Q8—11244no—
149Q8—11241no—
150Q8—11241no—
151D4—2812no—
152D4—5621no—
153C2×C4—22no—
154C2×C4—5621no—
155C2×C4—5621no—
156C2×C4—5621no—
157C2×C4—11244no—
158C2×C4—11241no—
159C2×C4—11241no—
160C2×C4—11241no—
161C2×C4D4×D28111yescharacteristic
162C2×C4D4×D28111yescharacteristic
163C2×C4C2×D112411yescharacteristic
164C8—41no—
165C8—41no—
166C8—5622no—
167C22—5622no—
168C22—11241no—
169C22—11241no—
170C22#2258284911yescharacteristic
171C4—21no—
172C4—42no—
173C4—5622no—
174C4—11241no—
175C4—11241no—
176C4—22481no—
177C4D8×D28111yescharacteristic
178C4Q16×D28111yescharacteristic
179C4#2258290611yescharacteristic
180C4#2258290811yescharacteristic
181C2—11242no—
182C2#3182359811yescharacteristic
183C2#3182362011yescharacteristic
184C2#3182364811yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#332×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#332D281
hypocenterC281#1649
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31823866C2semidirect
4. #31823674C2semidirect
5. #31823193C2semidirect
7. #332×C281C2semidirect
57. D1124Q16semidirect
92. C281#1649semidirect
98. #332D281semidirect

Maximal subgroups

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

subgroupindex
#318241282
#318238662
#318237442
#318236742
#318231932
#318231902
#332×C2812
#1649281