Finite Group Databasebeta

← #49096956

Subgroups — #49096956

Order 35968.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#31824034C211yesmaximal, characteristic
2#31823447C211yesmaximal, characteristic
3#31823252C214yesmaximal, complemented
4#410×C281C211yesmaximal, characteristic
5C22×Dic562C411yescharacteristic, complemented
6C2×#17985122—21no—
7#22582877—21no—
8#22582866—21no—
9#22582860C412yescomplemented
10#22582860C2212yes—
11#22582858—21no—
12#22582858—21no—
13#22582838C411yescharacteristic, complemented
14#22582798—21no—
15#22582796C2212yes—
16C2×#41×C281C2211yescharacteristic
17#117×C281—21no—
18#99×C281—21no—
19#99×C281C2212yes—
20C2×Dic562—21no—
21C2×Dic562—21no—
22C2×Dic562—41no—
23C2×Dic562—41no—
24C22×Dic281C2×C412yes—
25#17985122—22no—
26#17985122—41no—
27C2×#14555886—41no—
28C4⋊Dic281—21no—
29#17985117—22no—
30#17985117—22no—
31C22⋊Dic281—22no—
32C22⋊Dic281—22no—
33C22⋊Dic281C2×C412yes—
34C4×Dic281—21no—
35#41×C281—41no—
36#41×C281—41no—
37C2×Q8×C281D411yescharacteristic
38C2×D4×C281C2×C411yescharacteristic
39C2×D4×C281D411yescharacteristic
40C2×D4×C281C2311yescharacteristic
41C22×C4×C281C2×C411yescharacteristic
42C22×C4×C281D411yescharacteristic
43C22×C4×C281D411yescharacteristic
44C4⋊C4×C281—41no—
45C22⋊C4×C281—22no—
46C42×C281—41no—
47Dic562—42no—
48Dic562—41no—
49Dic562—41no—
50C2×Dic281—22no—
51C2×Dic281—22no—
52C2×Dic281—42no—
53#14555886—42no—
54C23×C281C22⋊C411yescharacteristic
55C23×C281C22×C411yescharacteristic
56C23×C281C2×D411yescharacteristic
57Q8×C281—41no—
58D4×C281—41no—
59D4×C281—41no—
60D4×C281—41no—
61C2×C4×C281—21no—
62C2×C4×C281—21no—
63C2×C4×C281—21no—
64C2×C4×C281—21no—
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281—42no—
68C2×C4×C281C22⋊C411yescharacteristic
69C2×C4×C281C22⋊C411yescharacteristic
70C2×C4×C281C22⋊C411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C22×C281—21no—
73C22×C281—21no—
74C22×C281—21no—
75C22×C281—41no—
76C22×C281—41no—
77C22×C281—41no—
78C22×C281C2×C22⋊C411yescharacteristic
79C4×C281—21no—
80C4×C281—21no—
81C4×C281—21no—
82C4×C281—82no—
83C4×C281#9911yescharacteristic
84C4×C281#9911yescharacteristic
85Dic281—42no—
86Dic281—42no—
87C2×C281—21no—
88C2×C281—41no—
89C2×C281—41no—
90C2×C281—41no—
91C2×C281C2×#9911yescharacteristic
92C281#212311yescharacteristic, complemented, Sylow
93#2123—2811nomaximal, Sylow
94#536—2811no—
95#413—2811no—
96#410D28111yescharacteristic
97#352—2814no—
98C2×#41C2×D28111yescharacteristic
99C22×Q8—2811no—
100C2×M16—5621no—
101C4⋊Q8—5621no—
102#124—5621no—
103#123—2812no—
104#123—2812no—
105C22⋊Q8—5621no—
106C22⋊Q8—5621no—
107#117—21no—
108#117—2811no—
109#101—5621no—
110#100—2812no—
111#99—21no—
112#99C2×D28112yes—
113#41—41no—
114#41—41no—
115C2×Q8—5621no—
116C2×Q8—5621no—
117C2×Q8—11241no—
118C2×Q8—11241no—
119C2×Q8D112411yescharacteristic
120C2×D4C4×D28111yescharacteristic
121C2×D4C22⋊D28111yescharacteristic
122C2×D4C22×D28111yescharacteristic
123C22×C4—2812no—
124C22×C4C4×D28111yescharacteristic
125C22×C4C22⋊D28111yescharacteristic
126C22×C4D112411yescharacteristic
127M16—5622no—
128M16—11241no—
129C2×C8—11241no—
130C4⋊C4—41no—
131C4⋊C4—5622no—
132C4⋊C4—5621no—
133C4⋊C4—5622no—
134C22⋊C4—22no—
135C22⋊C4—2812no—
136C22⋊C4—5622no—
137C22⋊C4—5622no—
138C42—41no—
139C42—5621no—
140C23#1798511511yescharacteristic
141C23C2×C4×D28111yescharacteristic
142C23C2×C22⋊D28111yescharacteristic
143Q8—41no—
144Q8—11242no—
145Q8—11241no—
146Q8—11241no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—5622no—
158C2×C4—5622no—
159C2×C4—11242no—
160C2×C4#1798511511yescharacteristic
161C2×C4#1798511511yescharacteristic
162C2×C4#1798511511yescharacteristic
163C2×C4C2×D112411yescharacteristic
164C8—11242no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×#1798511511yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—82no—
176C4—11242no—
177C4—11242no—
178C4#2258279311yescharacteristic
179C4#2258279311yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#2258279311yescharacteristic
subgroupG/H
centerC2C2×#22582793
commutatorC23×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#410×C281C2
socleC2×C281C2×#99
prime radicalC2×#41×C281C22
cosocleC2×D4×C281C23
hypercenter#410D281
hypocenterC281#2123
LCSG ▷ C23×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #31823252C2semidirect
5. C22×Dic562C4semidirect
9. #22582860C4semidirect
13. #22582838C4semidirect
92. C281#2123semidirect

Maximal subgroups

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

subgroupindex
#318240342
#318234472
#318232522
#410×C2812
#2123281