Finite Group Databasebeta

← #49096967

Subgroups — #49096967

Order 35968.

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

normal subgroups only

This group has 258 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#31824012C211yesmaximal, characteristic
2#31823435C212yesmaximal, complemented
3#31823258C211yesmaximal, characteristic, complemented
4#31823255C212yesmaximal, complemented
5#354×C281C211yesmaximal, characteristic, complemented
6C2×#17985139C411yescharacteristic, complemented
7C2×#17985137C2211yescharacteristic
8#22582877C411yescharacteristic, complemented
9#22582875C2211yescharacteristic
10#22582867C411yescharacteristic, complemented
11#22582852—22no—
12#22582839—22no—
13#22582835—22no—
14C42×D281C411yescharacteristic, complemented
15#22582794C2212yes—
16#22582793—22no—
17#124×C281C2211yescharacteristic
18#99×C281C2212yes—
19#17985139—41no—
20#17985139—41no—
21#17985137—41no—
22#17985137—41no—
23C2×Dic562C2×C411yescharacteristic
24C2×D1124—21no—
25C2×D1124C2×C411yescharacteristic
26C2×C22⋊D281—22no—
27C2×C22⋊D281D412yes—
28C22×Dic281D412yes—
29C2×C4×D281—21no—
30C2×C4×D281—21no—
31C2×C4×D281C2×C411yescharacteristic
32#17985117—22no—
33#17985117—42no—
34C22⋊Dic281—22no—
35#17985115—22no—
36C4×Dic281—21no—
37C4×Dic281—42no—
38C4×Dic281C2×C411yescharacteristic
39C2×Q8×C281C2×C411yescharacteristic
40C2×D4×C281C2311yescharacteristic
41C22⋊C4×C281—22no—
42C22⋊C4×C281—22no—
43C42×C281C2×C411yescharacteristic
44C22×D281—21no—
45C22×D281C22⋊C411yescharacteristic
46Dic562—41no—
47D1124—41no—
48D1124—42no—
49C22⋊D281—42no—
50C22⋊D281—44no—
51C2×Dic281—21no—
52C2×Dic281—22no—
53C2×Dic281—22no—
54C2×Dic281—42no—
55C2×Dic281C22⋊C412yes—
56C2×Dic281C22⋊C411yescharacteristic
57C4×D281—21no—
58C4×D281—21no—
59C4×D281—42no—
60C4×D281—41no—
61C4×D281—41no—
62C23×C281C2×D412yes—
63Q8×C281—41no—
64D4×C281—41no—
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281—42no—
68C2×C4×C281C22×C411yescharacteristic
69C22×C281—22no—
70C22×C281—42no—
71C22×C281C2×C22⋊C411yescharacteristic
72C2×D281—21no—
73C2×D281—41no—
74C2×D281—42no—
75C2×D281—41no—
76C4×C281—21no—
77C4×C281—41no—
78C4×C281—41no—
79C4×C281—82no—
80Dic281—22no—
81Dic281—22no—
82Dic281—82no—
83Dic281#9911yescharacteristic
84Dic281#9911yescharacteristic
85C2×C281—21no—
86C2×C281—42no—
87C2×C281C2×#9911yescharacteristic
88D281—41no—
89D281—81no—
90C281#212611yescharacteristic, complemented, Sylow
91#2126—2811nomaximal, Sylow
92#532—2811no—
93#410—2812no—
94#354—2811no—
95#354D28111yescharacteristic, complemented
96#353—2812no—
97C2×#41—2811no—
98C2×#41—2811no—
99C4⋊Q8—2811no—
100#127—2811no—
101#124—2811no—
102#124C2×D28111yescharacteristic
103#121—5622no—
104C4×D4—5622no—
105#117—5622no—
106C2×C42—2811no—
107#99—2812no—
108#99—5622no—
109#99C2×D28112yes—
110#41—11241no—
111#41—11241no—
112#41—11241no—
113#41—11241no—
114C2×Q8—2811no—
115C2×Q8C4×D28111yescharacteristic
116C2×D4—2812no—
117C2×D4—2811no—
118C2×D4—5621no—
119C2×D4—5622no—
120C2×D4C22×D28111yescharacteristic
121C22×C4—2812no—
122C22×C4—2811no—
123C22×C4—5621no—
124C22×C4—5621no—
125C4⋊C4—5622no—
126C4⋊C4—11242no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—5622no—
130C22⋊C4—5622no—
131C42—2811no—
132C42—5621no—
133C42—11242no—
134C42C4×D28111yescharacteristic
135C23—2811no—
136C23—5621no—
137C23D4×D28112yes—
138Q8—41no—
139Q8—11241no—
140D4—41no—
141D4—11241no—
142D4—11242no—
143D4—11242no—
144D4—11244no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2811no—
149C2×C4—2812no—
150C2×C4—5621no—
151C2×C4—5621no—
152C2×C4—5622no—
153C2×C4—5622no—
154C2×C4—5621no—
155C2×C4—11241no—
156C2×C4—11241no—
157C2×C4—11242no—
158C2×C4—11242no—
159C2×C4C2×C4×D28111yescharacteristic
160C22—22no—
161C22—42no—
162C22—5621no—
163C22—11241no—
164C22—11242no—
165C22—11241no—
166C22C22⋊C4×D28111yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—2811no—
172C4—2811no—
173C4—5622no—
174C4—5622no—
175C4—22482no—
176C2—21no—
177C2—42no—
178C2—11241no—
179C2—22481no—
180C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#354×C281C2
socleC2×C281C2×#99
prime radical#31824012C2
cosocleC2×D4×C281C23
hypercenter#354D281
hypocenterC281#2126
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #31823435C2semidirect
3. #31823258C2semidirect
4. #31823255C2semidirect
5. #354×C281C2semidirect
6. C2×#17985139C4semidirect
8. #22582877C4semidirect
10. #22582867C4semidirect
14. C42×D281C4semidirect
90. C281#2126semidirect
95. #354D281semidirect

Maximal subgroups

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

subgroupindex
#318240122
#318234352
#318232582
#318232552
#354×C2812
#2126281