Finite Group Databasebeta

← #49094530

Subgroups — #49094530

Order 35968.

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

normal subgroups only

This group has 212 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#31823815C211yesmaximal, characteristic, complemented
3#31823665C211yesmaximal, characteristic, complemented
4#31823211C211yesmaximal, characteristic, complemented
5D4⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#474×C281C211yesmaximal, characteristic, complemented
8C2×#17985125—21no—
9#22582879C2211yescharacteristic
10#22582865—22no—
11#22582853—21no—
12#22582850—21no—
13C4×D1124C2211yescharacteristic
14#22582838—21no—
15#22582837—21no—
16C4⋊#14555886C2211yescharacteristic
17#22582803—21no—
18#22582802—22no—
19C4×#14555886C2211yescharacteristic
20C4⋊Q8×C281C2211yescharacteristic
21C4×D4×C281C2211yescharacteristic
22#107×C281—21no—
23C4⋊C8×C281C2211yescharacteristic
24#102×C281—21no—
25C2×Dic562D412yes—
26C2×D1124D411yescharacteristic
27C2×C22⋊D281—22no—
28C2×C4×D281—21no—
29#17985125—42no—
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—41no—
58#14555886—41no—
59C23×C281—21no—
60Q8×C281—41no—
61Q8×C281—41no—
62D4×C281—21no—
63D4×C281—21no—
64C2×C4×C281—21no—
65C2×C4×C281—41no—
66C2×C4×C281—41no—
67C2×C4×C281—41no—
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C8×C281—41no—
72C22×C281—41no—
73C22×C281—41no—
74C22×C281—41no—
75C22×C281#12011yescharacteristic
76C2×D281—41no—
77C2×D281—41no—
78C2×D281—41no—
79C4×C281—21no—
80C4×C281—41no—
81C4×C281—81no—
82C4×C281#13511yescharacteristic
83C4×C281#13511yescharacteristic
84C4×C281AGL(1,ℤ/8)11yescharacteristic
85C4×C281#13711yescharacteristic
86Dic281—41no—
87Dic281—42no—
88C2×C281—81no—
89C2×C281#44911yescharacteristic
90C2×C281#45211yescharacteristic
91C2×C281#45511yescharacteristic
92D281—81no—
93C281#164611yescharacteristic, complemented, Sylow
94#1646—2811nomaximal, Sylow
95#555—2811no—
96#487—2811no—
97#474D28111yescharacteristic, complemented
98#461—2811no—
99#333—2811no—
100D4⋊C8—2811no—
101D4⋊C8—2811no—
102C2×SD16—5621no—
103C4⋊Q8—2811no—
104C4⋊Q8C2×D28111yescharacteristic
105#124—5622no—
106#121—5621no—
107#121—5621no—
108C4×D4—2811no—
109C4×D4C2×D28111yescharacteristic
110#117—5621no—
111#117—5621no—
112#107—21no—
113C4⋊C8—2811no—
114C4⋊C8C2×D28111yescharacteristic
115#103—5622no—
116#103—5621no—
117#102—21no—
118C4×C8—2811no—
119C2×Q8—21no—
120C2×Q8—2812no—
121C2×D4—2811no—
122C2×D4—5622no—
123C2×D4C22⋊D28111yescharacteristic
124C22×C4—21no—
125C22×C4—5621no—
126SD16—11242no—
127C2×C8—21no—
128C2×C8—5621no—
129C2×C8—5621no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2811no—
133C4⋊C4—5621no—
134C4⋊C4—5621no—
135C4⋊C4C22⋊D28111yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5622no—
138C22⋊C4—5622no—
139C22⋊C4—5621no—
140C42—5622no—
141C42C22×D28111yescharacteristic
142C23—21no—
143C23—5621no—
144Q8—41no—
145Q8—41no—
146Q8—11242no—
147D4—21no—
148D4—21no—
149D4—5621no—
150D4—5621no—
151D4—22482no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5621no—
157C2×C4—5622no—
158C2×C4—11241no—
159C2×C4—11241no—
160C2×C4D4×D28111yescharacteristic
161C2×C4D4×D28111yescharacteristic
162C2×C4C2×C22⋊D28111yescharacteristic
163C8—41no—
164C8—11241no—
165C8—11241no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—11241no—
170C22—11241no—
171C22—11241no—
172C22#2258284711yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—11241no—
177C4—11242no—
178C4#2258289811yescharacteristic
179C4#2258289911yescharacteristic
180C4#2258290311yescharacteristic
181C4#2258291011yescharacteristic
182C2—81no—
183C2—22481no—
184C2#3182360511yescharacteristic
185C2#3182362311yescharacteristic
186C2#3182363911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#474×C281C2
socleC22×C281#120
prime radical#31824178C2
hypercenter#474D281
hypocenterC281#1646
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #31823815C2semidirect
3. #31823665C2semidirect
4. #31823211C2semidirect
5. D4⋊#14555886C2semidirect
6. #31823190C2semidirect
7. #474×C281C2semidirect
93. C281#1646semidirect
97. #474D281semidirect

Maximal subgroups

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

subgroupindex
#318241782
#318238152
#318236652
#318232112
D4⋊#145558862
#318231902
#474×C2812
#1646281