Finite Group Databasebeta

← #31819011

Subgroups — #31819011

Order 17792.

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

normal subgroups only

This group has 360 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#22581653C212yesmaximal, complemented
2#22581355C211yesmaximal, characteristic, complemented
3#22581275C212yesmaximal, complemented
4#22581265C212yesmaximal, complemented
5#22581253C212yesmaximal, complemented
6#22581203C212yesmaximal, complemented
7#22581032C211yesmaximal, characteristic, complemented
8#22580994C212yesmaximal, complemented
9C4×D8×C139C211yesmaximal, characteristic, complemented
10C2×#14555768C2212yes—
11#17984835—22no—
12#17984834C2212yes—
13#17984825—22no—
14#17984815—22no—
15#17984813C2212yes—
16#17984813C2212yes—
17C4×D556C2211yescharacteristic
18C4×C22⋊D139—22no—
19#17984800C2212yes—
20C4⋊C4×D139C2212yes—
21#17984776C2211yescharacteristic
22#17984776C2211yescharacteristic
23#17984775C2212yes—
24#17984774C2212yes—
25#17984773C2212yes—
26C4⋊(C139⋊C8)C2211yescharacteristic
27#17984763C2212yes—
28#17984763C2212yes—
29(C2×D139)⋊C8C2212yes—
30C2×D8×C139C2211yescharacteristic
31C4×D4×C139C2212yes—
32#107×C139C2211yescharacteristic
33#102×C139C2212yes—
34C4×C8×C139C2211yescharacteristic
35C2×D556D411yescharacteristic
36C2×C22⋊D139—22no—
37C2×C22⋊D139—22no—
38C2×C4×D139—22no—
39C2×C4×D139C2312yes—
40#14555768—24no—
41C2×C139⋊C8C2312yes—
42C4⋊Dic139D411yescharacteristic
43C4⋊Dic139C2312yes—
44C4⋊Dic139C2312yes—
45Dic139⋊C4—22no—
46Dic139⋊C4—22no—
47Dic139⋊C4—22no—
48C22⋊Dic139—22no—
49C22⋊Dic139—22no—
50(C2×D139)⋊C4—22no—
51(C2×D139)⋊C4D412yes—
52C4×Dic139—22no—
53C2×D4×C139C2312yes—
54C22×C4×C139—22no—
55D8×C139—22no—
56C2×C8×C139C2311yescharacteristic
57C2×C8×C139C2311yescharacteristic
58C4⋊C4×C139C2312yes—
59C22⋊C4×C139—22no—
60C42×C139C2311yescharacteristic
61C22×D139C2×D412yes—
62D556—41no—
63C22⋊D139—44no—
64C22⋊D139—82no—
65C2×Dic139—22no—
66C2×Dic139—22no—
67C2×Dic139C2×D412yes—
68C4×D139—22no—
69C4×D139—22no—
70C4×D139—82no—
71C139⋊C8—22no—
72C23×C139—22no—
73D4×C139—22no—
74D4×C139—22no—
75C2×C4×C139—22no—
76C2×C4×C139—82no—
77C2×C4×C139C2×D411yescharacteristic
78C2×C4×C139C2×D411yescharacteristic
79C2×C4×C139C2411yescharacteristic
80C8×C139—21no—
81C8×C139#4112yes—
82C22×C139—42no—
83C22×C139—42no—
84C22×C139—42no—
85C22×C139C22×D411yescharacteristic
86C2×D139—22no—
87C2×D139—22no—
88C2×D139—22no—
89C4×C139—21no—
90C4×C139—21no—
91C4×C139—42no—
92C4×C139C2×#4111yescharacteristic
93C4×C1392−1+411yescharacteristic
94Dic139—22no—
95Dic139—42no—
96Dic139—42no—
97C2×C139—82no—
98C2×C139#54711yescharacteristic
99C2×C139#57511yescharacteristic
100C2×C139#57611yescharacteristic
101D139—42no—
102C139#335511yescharacteristic, complemented, Sylow
103#3355—1391nomaximal, Sylow
104#553—1392no—
105#499—1391no—
106#482—1392no—
107#480—1392no—
108#478—1392no—
109#469—1392no—
110C4×D8D13911yescharacteristic, complemented
111#436—1391no—
112#428—1392no—
113C2×D8C2×D13911yescharacteristic
114C2×M16—1392no—
115#126—2782no—
116#125—1392no—
117#123—2782no—
118#121—2782no—
119#121—1392no—
120#121—1392no—
121C4×D4—2782no—
122C4×D4—1391no—
123C4×D4C2×D13912yes—
124#117—1392no—
125C2×C4⋊C4—1392no—
126#107—1391no—
127#107—1391no—
128#107—1392no—
129#107C2×D13911yescharacteristic
130#106—1392no—
131#106—1392no—
132C4⋊C8—1391no—
133#102—1392no—
134#102—1392no—
135#102C2×D13912yes—
136C22⋊C8—1392no—
137C4×C8C2×D13911yescharacteristic
138C2×D4—2782no—
139C2×D4—2782no—
140C2×D4—1391no—
141C2×D4C22×D13912yes—
142C22×C4—22no—
143C22×C4—2782no—
144C22×C4—1392no—
145D8—22no—
146M16—2784no—
147C2×C8—1392no—
148C2×C8C22×D13911yescharacteristic
149C2×C8C22×D13911yescharacteristic
150C4⋊C4—2782no—
151C4⋊C4—2782no—
152C4⋊C4—2782no—
153C4⋊C4—1392no—
154C4⋊C4—1392no—
155C4⋊C4—1391no—
156C4⋊C4C22×D13912yes—
157C22⋊C4—22no—
158C22⋊C4—2782no—
159C22⋊C4—2782no—
160C22⋊C4—2782no—
161C22⋊C4—1392no—
162C42—2782no—
163C42C22×D13911yescharacteristic
164C23—22no—
165C23—1392no—
166D4—22no—
167D4—22no—
168D4—5561no—
169D4—5564no—
170D4—11122no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—2782no—
174C2×C4—2782no—
175C2×C4—2782no—
176C2×C4—2782no—
177C2×C4—11122no—
178C2×C4—1392no—
179C2×C4D4×D13911yescharacteristic
180C2×C4D4×D13911yescharacteristic
181C2×C4C23×D13911yescharacteristic
182C8—21no—
183C8—2782no—
184C8#1455578512yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—2782no—
189C22—2782no—
190C22—2782no—
191C22C2×D4×D13911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—2782no—
196C4—5562no—
197C4—5562no—
198C4C2×#1455578511yescharacteristic
199C4#1798488911yescharacteristic
200C2—82no—
201C2—5562no—
202C2#2258160811yescharacteristic
203C2#2258175011yescharacteristic
204C2#2258175411yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC4×D8×C139C2
socleC22×C139C22×D4
hypercenterC4×D8D139
hypocenterC139#3355
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #22581653C2semidirect
2. #22581355C2semidirect
3. #22581275C2semidirect
4. #22581265C2semidirect
5. #22581253C2semidirect
6. #22581203C2semidirect
7. #22581032C2semidirect
8. #22580994C2semidirect
9. C4×D8×C139C2semidirect
102. C139#3355semidirect
110. C4×D8D139semidirect

Maximal subgroups

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

subgroupindex
#225816532
#225813552
#225812752
#225812652
#225812532
#225812032
#225810322
#225809942
C4×D8×C1392
#3355139