Finite Group Databasebeta

← #31805372

Subgroups — #31805372

Order 17792.

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

normal subgroups only

This group has 282 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#22581534C211yesmaximal, characteristic
2#22581092C212yesmaximal, complemented
3#22580686C212yesmaximal, complemented
4#22580679C211yesmaximal, characteristic, complemented
5#395×C139C211yesmaximal, characteristic, complemented
6C2×#14555785—21no—
7C2×#14555772—22no—
8#17984822—22no—
9#17984817—22no—
10#17984816—21no—
11#17984816C2212yes—
12#17984766—22no—
13C22⋊(C139⋊C8)C2212yes—
14C22×Q8×C139C2211yescharacteristic
15C2×C4⋊C4×C139—21no—
16C2×C4⋊C4×C139C2211yescharacteristic
17#95×C139—21no—
18#95×C139C2211yescharacteristic
19#14555785—42no—
20#14555785—42no—
21C2×Dic278—21no—
22C2×D556—21no—
23C2×D556—21no—
24C2×D556D412yes—
25C2×C22⋊D139—22no—
26C2×C4×D139—22no—
27#14555772—44no—
28C2×C139⋊C8—22no—
29C4⋊Dic139—21no—
30C4⋊Dic139D412yes—
31(C2×D139)⋊C4—22no—
32(C2×D139)⋊C4—22no—
33C2×Q8×C139—22no—
34C2×Q8×C139—42no—
35C22×C4×C139—21no—
36C22×C4×C139—21no—
37C22×C4×C139D411yescharacteristic
38C22×C4×C139D411yescharacteristic
39C22×C4×C139C2311yescharacteristic
40C4⋊C4×C139—22no—
41C4⋊C4×C139—42no—
42C22×D139—22no—
43Dic278—42no—
44D556—42no—
45D556—42no—
46D556—81no—
47C22⋊D139—42no—
48C22⋊D139—42no—
49C2×Dic139—22no—
50C4×D139—44no—
51C139⋊C8—42no—
52C23×C139C2×D411yescharacteristic
53Q8×C139—24no—
54Q8×C139—42no—
55C2×C4×C139—21no—
56C2×C4×C139—21no—
57C2×C4×C139—22no—
58C2×C4×C139—22no—
59C2×C4×C139—21no—
60C2×C4×C139—41no—
61C2×C4×C139—41no—
62C2×C4×C139—41no—
63C2×C4×C139—41no—
64C2×C4×C139—41no—
65C2×C4×C139—41no—
66C2×C4×C139SD1612yescomplemented
67C2×C4×C139C2×D412yes—
68C22×C139—21no—
69C22×C139—21no—
70C22×C139#12011yescharacteristic
71C22×C139C2×SD1611yescharacteristic
72C22×C139AGL(1,ℤ/8)11yescharacteristic
73C2×D139—42no—
74C2×D139—42no—
75C2×D139—42no—
76C4×C139—22no—
77C4×C139—22no—
78C4×C139—42no—
79C4×C139—42no—
80C4×C139—41no—
81Dic139—42no—
82C2×C139—21no—
83C2×C139—21no—
84C2×C139#45011yescharacteristic
85C2×C139#45611yescharacteristic
86C2×C139B(4,𝔽2)11yescharacteristic
87D139—82no—
88C139#160411yescharacteristic, complemented, Sylow
89#1604—1391nomaximal, Sylow
90#537—1391no—
91#448—1392no—
92#395D13911yescharacteristic, complemented
93#327—1392no—
94#324—1391no—
95C2×#41—2781no—
96C22×Q8C2×D13911yescharacteristic
97C2×SD16—2782no—
98C22⋊Q8—2782no—
99#121—2782no—
100#121—2781no—
101#121—1392no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D13911yescharacteristic
104#103—2782no—
105C22⋊C8—1392no—
106#95—21no—
107#95C2×D13911yescharacteristic
108#41—5562no—
109#41—5562no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—2781no—
113C2×D4—2781no—
114C2×D4—2781no—
115C2×D4—2782no—
116C2×D4—1392no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—2782no—
120C22×C4C22⋊D13911yescharacteristic
121C22×C4C22⋊D13911yescharacteristic
122C22×C4C22×D13911yescharacteristic
123SD16—5564no—
124C2×C8—2782no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—2781no—
128C4⋊C4—1392no—
129C22⋊C4—2782no—
130C22⋊C4—2782no—
131C23—2782no—
132C23C2×C22⋊D13911yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—5562no—
136D4—5562no—
137D4—5562no—
138D4—5562no—
139D4—5562no—
140D4—11121no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—2782no—
153C2×C4—5564no—
154C2×C4#1455577212yescomplemented
155C2×C4D4×D13912yes—
156C8—5562no—
157C22—21no—
158C22—21no—
159C22—5562no—
160C22—5562no—
161C22—5562no—
162C22#1798481011yescharacteristic
163C22C2×#1455577211yescharacteristic
164C22#1798486711yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—5562no—
171C2—21no—
172C2—21no—
173C2—11122no—
174C2#2258110311yescharacteristic
175C2#2258113511yescharacteristic
176C2#2258113911yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#395×C139C2
socleC22×C139#120
prime radical#22581534C2
hypercenter#395D139
hypocenterC139#1604
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #22581092C2semidirect
3. #22580686C2semidirect
4. #22580679C2semidirect
5. #395×C139C2semidirect
66. C2×C4×C139SD16semidirect
88. C139#1604semidirect
92. #395D139semidirect
154. C2×C4#14555772semidirect

Maximal subgroups

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

subgroupindex
#225815342
#225810922
#225806862
#225806792
#395×C1392
#1604139