Finite Group Databasebeta

← #49094447

Subgroups — #49094447

Order 35968.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 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#31824178C211yesmaximal, characteristic
2#31823842C211yesmaximal, characteristic, complemented
3#31823750C211yesmaximal, characteristic, complemented
4#31823211C211yesmaximal, characteristic, complemented
5D4⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#476×C281C211yesmaximal, characteristic, complemented
8C2×#17985128—22no—
9#22582879C2211yescharacteristic
10#22582865—22no—
11#22582853—21no—
12#22582850—21no—
13C4×D1124C2211yescharacteristic
14#22582838—21no—
15#22582837—21no—
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic
18#22582799—21no—
19C4×#14555886C2211yescharacteristic
20C4⋊Q8×C281C2211yescharacteristic
21C4×D4×C281C2211yescharacteristic
22#106×C281—21no—
23C4⋊C8×C281C2211yescharacteristic
24#102×C281—21no—
25C2×Dic562D412yes—
26C2×D1124D411yescharacteristic
27C2×C22⋊D281—22no—
28C2×C4×D281—21no—
29#17985128—44no—
30C2×#14555886—21no—
31C2×#14555886—21no—
32C4⋊Dic281—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281D411yescharacteristic
35C22⋊Dic281—22no—
36#17985115—22no—
37#17985115—21no—
38C4×Dic281—22no—
39C2×Q8×C281—21no—
40C2×D4×C281D411yescharacteristic
41C22×C4×C281—21no—
42C2×C8×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281D411yescharacteristic
46C22⋊C4×C281—21no—
47C42×C281C2311yescharacteristic
48C22×D281—21no—
49Dic562—42no—
50D1124—21no—
51D1124—21no—
52C22⋊D281—82no—
53C2×Dic281—21no—
54C2×Dic281—22no—
55C4×D281—41no—
56C4×D281—41no—
57#14555886—22no—
58#14555886—41no—
59C23×C281—21no—
60Q8×C281—42no—
61D4×C281—21no—
62D4×C281—21no—
63C2×C4×C281—21no—
64C2×C4×C281—41no—
65C2×C4×C281—41no—
66C2×C4×C281—41no—
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C8×C281—41no—
71C22×C281—41no—
72C22×C281—41no—
73C22×C281—41no—
74C22×C281#12011yescharacteristic
75C2×D281—41no—
76C2×D281—41no—
77C2×D281—41no—
78C4×C281—21no—
79C4×C281—41no—
80C4×C281—81no—
81C4×C281#13511yescharacteristic
82C4×C281#13511yescharacteristic
83C4×C281#13711yescharacteristic
84C4×C281#13711yescharacteristic
85Dic281—41no—
86Dic281—42no—
87C2×C281—81no—
88C2×C281#45211yescharacteristic
89C2×C281#45211yescharacteristic
90C2×C281#45311yescharacteristic
91D281—81no—
92C281#163411yescharacteristic, complemented, Sylow
93#1634—2811nomaximal, Sylow
94#555—2811no—
95#494—2811no—
96#476—2811no—
97#476D28111yescharacteristic, complemented
98#333—2811no—
99D4⋊C8—2811no—
100D4⋊C8—2811no—
101C2×Q16—5622no—
102C4⋊Q8—2811no—
103C4⋊Q8C2×D28111yescharacteristic
104#124—5622no—
105#121—5621no—
106#121—5621no—
107C4×D4—2811no—
108C4×D4C2×D28111yescharacteristic
109#117—5621no—
110#117—5621no—
111#106—21no—
112#106—5621no—
113C4⋊C8—2811no—
114C4⋊C8C2×D28111yescharacteristic
115#102—21no—
116#102—5621no—
117C4×C8—2811no—
118C2×Q8—21no—
119C2×Q8—2812no—
120C2×D4—2811no—
121C2×D4—5622no—
122C2×D4C22⋊D28111yescharacteristic
123C22×C4—21no—
124C22×C4—5621no—
125Q16—11244no—
126C2×C8—21no—
127C2×C8—5621no—
128C2×C8—5621no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2811no—
132C4⋊C4—5621no—
133C4⋊C4—5621no—
134C4⋊C4C22⋊D28111yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—5622no—
137C22⋊C4—5622no—
138C22⋊C4—5621no—
139C42—5622no—
140C42C22×D28111yescharacteristic
141C23—21no—
142C23—5621no—
143Q8—42no—
144Q8—11242no—
145D4—21no—
146D4—21no—
147D4—5621no—
148D4—5621no—
149D4—22482no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—5621no—
155C2×C4—5622no—
156C2×C4—11241no—
157C2×C4—11241no—
158C2×C4D4×D28111yescharacteristic
159C2×C4D4×D28111yescharacteristic
160C2×C4C2×C22⋊D28111yescharacteristic
161C8—41no—
162C8—5622no—
163C8—11241no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—11241no—
168C22—11241no—
169C22—11241no—
170C22#2258284711yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—11241no—
175C4—11242no—
176C4#2258289911yescharacteristic
177C4#2258290011yescharacteristic
178C4#2258290811yescharacteristic
179C4#2258291011yescharacteristic
180C2—81no—
181C2—22481no—
182C2#3182362211yescharacteristic
183C2#3182362311yescharacteristic
184C2#3182362911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#476×C281C2
socleC22×C281#120
prime radical#31824178C2
hypercenter#476D281
hypocenterC281#1634
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31823842C2semidirect
3. #31823750C2semidirect
4. #31823211C2semidirect
5. D4⋊#14555886C2semidirect
6. #31823190C2semidirect
7. #476×C281C2semidirect
92. C281#1634semidirect
97. #476D281semidirect

Maximal subgroups

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

subgroupindex
#318241782
#318238422
#318237502
#318232112
D4⋊#145558862
#318231902
#476×C2812
#1634281