Finite Group Databasebeta

← #31805608

Subgroups — #31805608

Order 17792.

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

normal subgroups only

This group has 208 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#22581664C211yesmaximal, characteristic
2#22581235C211yesmaximal, characteristic, complemented
3#22581155C211yesmaximal, characteristic
4#22580702C211yesmaximal, characteristic, complemented
5#22580685C211yesmaximal, characteristic, complemented
6#22580682C211yesmaximal, characteristic
7#487×C139C211yesmaximal, characteristic, complemented
8C2×#14555772—21no—
9#17984833—21no—
10#17984822—21no—
11#17984818—22no—
12C4×Dic278C2211yescharacteristic
13C4×D556C2211yescharacteristic
14#17984804—21no—
15C4⋊C4×D139—21no—
16#17984773—21no—
17C4⋊(C139⋊C8)C2211yescharacteristic
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984766—21no—
20#17984765—21no—
21C4⋊Q8×C139C2211yescharacteristic
22C4⋊Q8×C139C2211yescharacteristic
23#103×C139—22no—
24C4×C8×C139C2211yescharacteristic
25C2×Dic278D411yescharacteristic
26C2×D556D411yescharacteristic
27C2×C4×D139—22no—
28C2×C4×D139—21no—
29#14555772—42no—
30C2×C139⋊C8—21no—
31C2×C139⋊C8—21no—
32C4⋊Dic139—22no—
33C4⋊Dic139D411yescharacteristic
34C4⋊Dic139D411yescharacteristic
35Dic139⋊C4—22no—
36Dic139⋊C4—21no—
37(C2×D139)⋊C4—22no—
38(C2×D139)⋊C4—21no—
39C4×Dic139—21no—
40C2×Q8×C139—21no—
41C2×Q8×C139D412yes—
42C2×C8×C139—21no—
43C4⋊C4×C139—21no—
44C4⋊C4×C139—21no—
45C4⋊C4×C139—21no—
46C4⋊C4×C139—21no—
47C42×C139C2311yescharacteristic
48C22×D139—21no—
49Dic278—21no—
50Dic278—21no—
51D556—21no—
52D556SD1612yes—
53C2×Dic139—21no—
54C2×Dic139—21no—
55C2×Dic139—21no—
56C4×D139—41no—
57C4×D139—41no—
58C4×D139—82no—
59C139⋊C8—41no—
60C139⋊C8—41no—
61Q8×C139—42no—
62Q8×C139—41no—
63Q8×C139—41no—
64C2×C4×C139—22no—
65C2×C4×C139—41no—
66C2×C4×C139C2×D411yescharacteristic
67C2×C4×C139C2×D411yescharacteristic
68C2×C4×C139C2×D411yescharacteristic
69C8×C139—41no—
70C22×C139#12011yescharacteristic
71C2×D139—22no—
72C2×D139—41no—
73C2×D139—41no—
74C4×C139—21no—
75C4×C139—42no—
76C4×C139—81no—
77C4×C139C2×SD1611yescharacteristic
78C4×C139#13511yescharacteristic
79C4×C139#13711yescharacteristic
80C4×C139#13711yescharacteristic
81Dic139—41no—
82Dic139—41no—
83Dic139—41no—
84C2×C139#44811yescharacteristic
85C2×C139#45211yescharacteristic
86C2×C139#45511yescharacteristic
87D139—42no—
88C139#164311yescharacteristic, complemented, Sylow
89#1643—1391nomaximal, Sylow
90#554—1391no—
91#487D13911yescharacteristic, complemented
92#475—1391no—
93#461—1391no—
94#333—1391no—
95Q8⋊C8—1391no—
96D4⋊C8—1391no—
97C2×SD16—2781no—
98C4⋊Q8C2×D13911yescharacteristic
99C4⋊Q8C2×D13911yescharacteristic
100#125—2781no—
101C22⋊Q8—2781no—
102C22⋊Q8—2782no—
103C4×Q8—1391no—
104C4×D4—2781no—
105C4×D4—1391no—
106C2×C4⋊C4—2781no—
107#106—2781no—
108C4⋊C8—1391no—
109C4⋊C8—1391no—
110#103—22no—
111#103—2781no—
112#103—2781no—
113C4×C8C2×D13911yescharacteristic
114C2×Q8—21no—
115C2×Q8—1391no—
116C2×Q8C22⋊D13912yes—
117C2×D4—1391no—
118C22×C4—2782no—
119C22×C4—2781no—
120SD16—5562no—
121C2×C8—21no—
122C2×C8—2781no—
123C2×C8—2781no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—2782no—
129C4⋊C4—2782no—
130C4⋊C4—2781no—
131C4⋊C4—1391no—
132C4⋊C4—1391no—
133C22⋊C4—2782no—
134C22⋊C4—2781no—
135C42—2781no—
136C42C22×D13911yescharacteristic
137C23—2781no—
138Q8—42no—
139Q8—41no—
140Q8—41no—
141Q8—2781no—
142Q8—2781no—
143D4—2781no—
144D4—1392no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—2781no—
148C2×C4—2781no—
149C2×C4—2781no—
150C2×C4—5561no—
151C2×C4—5561no—
152C2×C4—11122no—
153C2×C4D4×D13911yescharacteristic
154C2×C4D4×D13911yescharacteristic
155C2×C4C2×C22⋊D13911yescharacteristic
156C8—41no—
157C8—5561no—
158C8—5561no—
159C22—2782no—
160C22—5561no—
161C22—5561no—
162C22#1798481011yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—5561no—
167C4—5561no—
168C4—5561no—
169C4SD16×D13911yescharacteristic
170C4#1798486511yescharacteristic
171C4#1798487111yescharacteristic
172C4#1798487411yescharacteristic
173C2—5562no—
174C2#2258109011yescharacteristic
175C2#2258111411yescharacteristic
176C2#2258113011yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#487×C139C2
socleC22×C139#120
prime radicalC2×D556D4
hypercenter#487D139
hypocenterC139#1643
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #22581235C2semidirect
4. #22580702C2semidirect
5. #22580685C2semidirect
7. #487×C139C2semidirect
88. C139#1643semidirect
91. #487D139semidirect

Maximal subgroups

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

subgroupindex
#225816642
#225812352
#225811552
#225807022
#225806852
#225806822
#487×C1392
#1643139