Finite Group Databasebeta

← #31819481

Subgroups — #31819481

Order 17792.

356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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#22581675C212yesmaximal, complemented
2#22581346C212yesmaximal, complemented
3#22581337C211yesmaximal, characteristic
4#22581175C212yesmaximal, complemented
5#22581171C212yesmaximal
6#22581162C212yesmaximal, complemented
7#22581083C211yesmaximal, characteristic, complemented
8#22581052C212yesmaximal, complemented
9C4×Q16×C139C211yesmaximal, characteristic, complemented
10C2×Dic556C2211yescharacteristic
11C2×#14555775C2212yes—
12C2×#14555774C2212yes—
13C2×#14555772C2212yes—
14C2×D1112C2211yescharacteristic
15#17984840C2212yes—
16#17984837—22no—
17#17984836—22no—
18#17984831C2212yes—
19#17984830C2212yes—
20#17984820—22no—
21C4×Dic278C2211yescharacteristic
22#17984807C2212yes—
23#17984804C2212yes—
24#17984799—22no—
25C4⋊(C139⋊C8)C2211yescharacteristic
26Dic139⋊C8C2212yes—
27#17984765C2212yes—
28#17984762C2212yes—
29#17984752C2212yes—
30C2×Q16×C139C2211yescharacteristic
31C4×Q8×C139C2212yes—
32#107×C139C2211yescharacteristic
33#103×C139C2212yes—
34C4×C8×C139C2211yescharacteristic
35C2×Dic278D411yescharacteristic
36C2×Dic278C2312yes—
37C2×D556C2312yes—
38C2×C4×D139—22no—
39Dic556—41no—
40#14555775—42no—
41#14555774—24no—
42#14555772—42no—
43D1112—41no—
44C2×C139⋊C8C2312yes—
45C4⋊Dic139D411yescharacteristic
46Dic139⋊C4—22no—
47Dic139⋊C4—22no—
48Dic139⋊C4—22no—
49Dic139⋊C4D412yes—
50(C2×D139)⋊C4—22no—
51(C2×D139)⋊C4—22no—
52(C2×D139)⋊C4—22no—
53(C2×D139)⋊C4—22no—
54(C2×D139)⋊C4—22no—
55C4×Dic139—22no—
56C4×Dic139C2312yes—
57C2×Q8×C139C2312yes—
58Q16×C139—22no—
59C2×C8×C139C2311yescharacteristic
60C2×C8×C139C2311yescharacteristic
61C4⋊C4×C139—22no—
62C4⋊C4×C139C2312yes—
63C42×C139—22no—
64C42×C139C2311yescharacteristic
65C22×D139—22no—
66Dic278—22no—
67Dic278—22no—
68Dic278—41no—
69D556—22no—
70D556—22no—
71C2×Dic139—22no—
72C2×Dic139C2×D412yes—
73C2×Dic139C2×D412yes—
74C4×D139—44no—
75C139⋊C8—22no—
76Q8×C139—22no—
77Q8×C139—22no—
78C2×C4×C139—22no—
79C2×C4×C139—22no—
80C2×C4×C139C2×D411yescharacteristic
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139C2411yescharacteristic
83C8×C139—21no—
84C8×C139#4112yes—
85C22×C139C22×D411yescharacteristic
86C2×D139—42no—
87C2×D139—42no—
88C2×D139—42no—
89C4×C139—21no—
90C4×C139—21no—
91C4×C139—42no—
92C4×C139—42no—
93C4×C139C2×#4111yescharacteristic
94C4×C139H(5,𝔽2)11yescharacteristic
95Dic139—22no—
96Dic139—22no—
97Dic139—42no—
98C2×C139#55011yescharacteristic
99C2×C139#57511yescharacteristic
100C2×C139#57811yescharacteristic
101D139—82no—
102C139#340211yescharacteristic, complemented, Sylow
103#3402—1391nomaximal, Sylow
104#556—1392no—
105#497—1392no—
106#495—1391no—
107#464—1392no—
108#463—1392no—
109#462—1392no—
110#446—1391no—
111#440—1392no—
112C4×Q16D13911yescharacteristic, complemented
113C2×Q16—1392no—
114C2×Q16—1391no—
115C2×Q16C2×D13911yescharacteristic
116C2×SD16—1392no—
117C2×SD16—1392no—
118C2×D8—1391no—
119C4⋊Q8—1392no—
120#126—2782no—
121#126—2782no—
122#124—1392no—
123#124—1392no—
124C22⋊Q8—2782no—
125C4×Q8—1392no—
126C4×Q8—1391no—
127C4×Q8C2×D13912yes—
128C4×D4—1392no—
129#117—2782no—
130#107C2×D13911yescharacteristic
131C4⋊C8—1392no—
132C4⋊C8—1391no—
133#103—1392no—
134#103C2×D13912yes—
135#102—1392no—
136#97—1392no—
137C4×C8C2×D13911yescharacteristic
138C2×Q8—1392no—
139C2×Q8—1391no—
140C2×Q8C22×D13912yes—
141C2×D4—1392no—
142C22×C4—2782no—
143Q16—22no—
144Q16—5561no—
145Q16—5562no—
146SD16—2784no—
147SD16—5562no—
148D8—5561no—
149C2×C8—1392no—
150C2×C8C22×D13911yescharacteristic
151C2×C8C22×D13911yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—2782no—
154C4⋊C4—2782no—
155C4⋊C4—2782no—
156C4⋊C4—1392no—
157C4⋊C4—1391no—
158C4⋊C4C22×D13912yes—
159C22⋊C4—2782no—
160C22⋊C4—2782no—
161C22⋊C4—2782no—
162C22⋊C4—2782no—
163C22⋊C4—2782no—
164C42—22no—
165C42—2782no—
166C42—1392no—
167C42C22×D13911yescharacteristic
168C23—2782no—
169Q8—22no—
170Q8—22no—
171Q8—2782no—
172Q8—2782no—
173Q8—5561no—
174D4—2782no—
175D4—2782no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2782no—
179C2×C4—5564no—
180C2×C4—1392no—
181C2×C4—1392no—
182C2×C4D4×D13911yescharacteristic
183C2×C4D4×D13911yescharacteristic
184C2×C4C23×D13911yescharacteristic
185C8—21no—
186C8—2782no—
187C8#1455578512yes—
188C22—5562no—
189C22—5562no—
190C22—5562no—
191C22C2×D4×D13911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—2782no—
197C4—2782no—
198C4—5562no—
199C4C2×#1455578511yescharacteristic
200C4#1798488811yescharacteristic
201C2—11122no—
202C2#2258162411yescharacteristic
203C2#2258175011yescharacteristic
204C2#2258176611yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC4×Q16×C139C2
socleC22×C139C22×D4
prime radicalC2×D1112C22
hypercenterC4×Q16D139
hypocenterC139#3402
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #22581675C2semidirect
2. #22581346C2semidirect
4. #22581175C2semidirect
6. #22581162C2semidirect
7. #22581083C2semidirect
8. #22581052C2semidirect
9. C4×Q16×C139C2semidirect
102. C139#3402semidirect
112. C4×Q16D139semidirect

Maximal subgroups

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

subgroupindex
#225816752
#225813462
#225813372
#225811752
#225811712
#225811622
#225810832
#225810522
C4×Q16×C1392
#3402139