Finite Group Databasebeta

← #31805397

Subgroups — #31805397

Order 17792.

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

normal subgroups only

This group has 228 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#22581579C211yesmaximal, characteristic
2#22581284C212yesmaximal, complemented
3#22580878C211yesmaximal, characteristic
4#22580691C212yesmaximal, complemented
5#323×C139C211yesmaximal, characteristic
6#17984821—21no—
7#17984821C2212yes—
8#17984819—22no—
9#17984819—22no—
10C2×C4⋊Dic139C2211yescharacteristic
11C2×C22⋊Dic139—21no—
12C2×C22⋊Dic139—21no—
13#17984774—22no—
14#17984767—22no—
15C139⋊#95—21no—
16C139⋊#95C2211yescharacteristic
17C2×C22⋊C4×C139C2211yescharacteristic
18C22⋊C8×C139C2212yes—
19C2×Dic278—21no—
20C2×Dic278D412yes—
21C22×Dic139—21no—
22C22×Dic139—21no—
23C22×Dic139—21no—
24C22×Dic139—21no—
25C4⋊Dic139—21no—
26C4⋊Dic139—22no—
27C4⋊Dic139D412yes—
28Dic139⋊C4—22no—
29Dic139⋊C4—22no—
30C22⋊Dic139—22no—
31C22⋊Dic139—22no—
32C22⋊Dic139—42no—
33C24×C139D411yescharacteristic
34C22×C4×C139D411yescharacteristic
35C22×C4×C139C2311yescharacteristic
36C2×C8×C139—22no—
37C22⋊C4×C139—22no—
38Dic278—42no—
39Dic278—81no—
40C2×Dic139—22no—
41C2×Dic139—22no—
42C2×Dic139—41no—
43C2×Dic139—41no—
44C2×Dic139—41no—
45C2×Dic139—41no—
46C2×Dic139—41no—
47C2×Dic139—41no—
48C2×Dic139—81no—
49C2×Dic139—81no—
50C23×C139—21no—
51C23×C139—21no—
52C23×C139—41no—
53C23×C139—41no—
54C23×C139SD1612yes—
55C23×C139C2×D411yescharacteristic
56C2×C4×C139—21no—
57C2×C4×C139—41no—
58C2×C4×C139—41no—
59C2×C4×C139C2×D412yes—
60C8×C139—42no—
61C22×C139—21no—
62C22×C139—21no—
63C22×C139—22no—
64C22×C139—42no—
65C22×C139—41no—
66C22×C139—41no—
67C22×C139—81no—
68C22×C139#12011yescharacteristic
69C22×C139C2×SD1611yescharacteristic
70C22×C139#13711yescharacteristic
71C4×C139—22no—
72C4×C139—41no—
73Dic139—42no—
74Dic139—42no—
75Dic139—81no—
76Dic139—81no—
77C2×C139—21no—
78C2×C139—21no—
79C2×C139—42no—
80C2×C139#44811yescharacteristic
81C2×C139#45511yescharacteristic
82C2×C139#45811yescharacteristic
83C139#160811yescharacteristic, complemented, Sylow
84#1608—1391nomaximal, Sylow
85#543—1391no—
86#483—1392no—
87#397—1391no—
88#328—1392no—
89#323D13911yescharacteristic
90C22⋊Q8—2782no—
91C22⋊Q8—2782no—
92C22⋊Q8—2781no—
93C22⋊Q8—1392no—
94C2×C4⋊C4—1391no—
95C2×C22⋊C4—2781no—
96C2×C22⋊C4—2781no—
97C2×C22⋊C4C2×D13911yescharacteristic
98#106—2782no—
99#103—2782no—
100C22⋊C8C2×D13912yes—
101#95—2781no—
102#95—1391no—
103C24D55611yescharacteristic
104C2×Q8—2781no—
105C2×Q8—1392no—
106C22×C4—2781no—
107C22×C4—2781no—
108C22×C4—2781no—
109C22×C4—2781no—
110C22×C4D55611yescharacteristic
111C22×C4C22×D13911yescharacteristic
112C2×C8—22no—
113C4⋊C4—2782no—
114C4⋊C4—2781no—
115C4⋊C4—2782no—
116C4⋊C4—2782no—
117C4⋊C4—1392no—
118C22⋊C4—22no—
119C22⋊C4—2782no—
120C22⋊C4—2782no—
121C22⋊C4—5562no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1455577412yes—
127C23C2×D55611yescharacteristic
128Q8—5562no—
129Q8—11121no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—2782no—
134C2×C4—2782no—
135C2×C4—5561no—
136C2×C4—5561no—
137C2×C4—5561no—
138C2×C4—5561no—
139C2×C4—5561no—
140C2×C4—5561no—
141C2×C4—11121no—
142C2×C4—11121no—
143C2×C4D4×D13912yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1798481211yescharacteristic
153C22C2×#1455577411yescharacteristic
154C22#1798487511yescharacteristic
155C4—22no—
156C4—41no—
157C4—5562no—
158C4—5562no—
159C4—11121no—
160C4—11121no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#2258109411yescharacteristic
165C2#2258113311yescharacteristic
166C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#323×C139C2
socleC22×C139#120
prime radicalC24×C139D4
hypercenter#323D139
hypocenterC139#1608
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #22581284C2semidirect
4. #22580691C2semidirect
83. C139#1608semidirect

Maximal subgroups

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

subgroupindex
#225815792
#225812842
#225808782
#225806912
#323×C1392
#1608139