Finite Group Databasebeta

← #31805492

Subgroups — #31805492

Order 17792.

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

normal subgroups only

This group has 256 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#22581608C211yesmaximal, characteristic, complemented
2#22581299C211yesmaximal, characteristic, complemented
3#22581145C211yesmaximal, characteristic, complemented
4#22580698C211yesmaximal, characteristic, complemented
5D4⋊(C139⋊C8)C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#459×C139C211yesmaximal, characteristic, complemented
8C2×#14555785—21no—
9C2×#14555770—21no—
10#17984842C2211yescharacteristic
11#17984824—22no—
12#17984821—21no—
13#17984813—21no—
14C4×D556C2211yescharacteristic
15C4⋊C4×D139—21no—
16C4⋊(C139⋊C8)C2211yescharacteristic
17#17984763—22no—
18#17984763—21no—
19C4×C139⋊C8C2211yescharacteristic
20C2×D8×C139—21no—
21#127×C139C2211yescharacteristic
22C4×D4×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24#102×C139—21no—
25#14555785—42no—
26#14555785—42no—
27C2×Dic278—21no—
28C2×D556D411yescharacteristic
29C2×C22⋊D139—22no—
30C2×C4×D139—22no—
31C2×C4×D139—21no—
32#14555770—42no—
33C2×C139⋊C8—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139D411yescharacteristic
37C4⋊Dic139D412yes—
38Dic139⋊C4—22no—
39C22⋊Dic139—22no—
40(C2×D139)⋊C4—21no—
41C2×D4×C139—21no—
42C2×D4×C139—21no—
43C2×D4×C139—21no—
44C2×D4×C139D411yescharacteristic
45C22×C4×C139—21no—
46D8×C139—42no—
47C2×C8×C139—21no—
48C4⋊C4×C139D411yescharacteristic
49C22⋊C4×C139—21no—
50C42×C139C2311yescharacteristic
51C22×D139—21no—
52Dic278—41no—
53Dic278—41no—
54D556—21no—
55D556D812yescomplemented
56C22⋊D139—44no—
57C2×Dic139—21no—
58C2×Dic139—22no—
59C4×D139—44no—
60C4×D139—41no—
61C4×D139—41no—
62C139⋊C8—41no—
63C139⋊C8—41no—
64C23×C139—21no—
65C23×C139—41no—
66D4×C139—21no—
67D4×C139—21no—
68D4×C139—42no—
69D4×C139—41no—
70D4×C139—41no—
71D4×C139—41no—
72D4×C139—41no—
73C2×C4×C139—21no—
74C2×C4×C139—41no—
75C2×C4×C139—41no—
76C2×C4×C139C2×D411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C2×C4×C139C2×D411yescharacteristic
79C8×C139—41no—
80C22×C139—41no—
81C22×C139—41no—
82C22×C139—41no—
83C22×C139—81no—
84C22×C139—81no—
85C22×C139—81no—
86C22×C139#12011yescharacteristic
87C2×D139—22no—
88C2×D139—41no—
89C2×D139—41no—
90C4×C139—21no—
91C4×C139—41no—
92C4×C139C2×D811yescharacteristic
93C4×C139#13511yescharacteristic
94C4×C139AGL(1,ℤ/8)11yescharacteristic
95C4×C139AGL(1,ℤ/8)11yescharacteristic
96Dic139—42no—
97Dic139—41no—
98C2×C139—81no—
99C2×C139—161no—
100C2×C139#44711yescharacteristic
101C2×C139#44911yescharacteristic
102C2×C139#45411yescharacteristic
103D139—42no—
104C139#162511yescharacteristic, complemented, Sylow
105#1625—1391nomaximal, Sylow
106#547—1391no—
107#486—1391no—
108#459—1391no—
109#459D13911yescharacteristic, complemented
110#332—1391no—
111D4⋊C8—1391no—
112D4⋊C8—1391no—
113C2×#41—2781no—
114C2×D8—21no—
115C2×D8—2781no—
116C4⋊Q8—1391no—
117#127C2×D13911yescharacteristic
118#123—2782no—
119C22⋊Q8—2781no—
120#121—2781no—
121C4×D4—1391no—
122C4×D4C2×D13911yescharacteristic
123C2×C4⋊C4—2781no—
124C4⋊C8—1391no—
125C4⋊C8C2×D13911yescharacteristic
126#102—21no—
127#102—2781no—
128#102—2782no—
129C4×C8—1391no—
130#41—5562no—
131#41—5562no—
132C2×Q8—2781no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2782no—
137C2×D4—1391no—
138C2×D4C22⋊D13911yescharacteristic
139C22×C4—21no—
140C22×C4—2782no—
141C22×C4—2781no—
142D8—42no—
143D8—5562no—
144C2×C8—21no—
145C2×C8—2781no—
146C2×C8—2781no—
147C4⋊C4—2782no—
148C4⋊C4—2781no—
149C4⋊C4—1391no—
150C4⋊C4—1392no—
151C4⋊C4C22⋊D13911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2782no—
154C22⋊C4—2781no—
155C42C22×D13911yescharacteristic
156C23—21no—
157C23—41no—
158C23—2781no—
159Q8—5561no—
160Q8—5561no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—2781no—
169D4—5564no—
170D4—1392no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2781no—
175C2×C4—2782no—
176C2×C4—5564no—
177C2×C4—5561no—
178C2×C4—5561no—
179C2×C4D4×D13911yescharacteristic
180C2×C4D4×D13911yescharacteristic
181C2×C4C2×C22⋊D13911yescharacteristic
182C8—41no—
183C8—5561no—
184C8—5561no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—2782no—
192C22—5561no—
193C22—5561no—
194C22#1798481011yescharacteristic
195C4—21no—
196C4—41no—
197C4—5562no—
198C4—5561no—
199C4D8×D13911yescharacteristic
200C4#1798486211yescharacteristic
201C4#1798486611yescharacteristic
202C4#1798486811yescharacteristic
203C2—81no—
204C2—161no—
205C2—5562no—
206C2#2258108511yescharacteristic
207C2#2258109611yescharacteristic
208C2#2258112411yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#459×C139C2
socleC22×C139#120
hypercenter#459D139
hypocenterC139#1625
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #22581608C2semidirect
2. #22581299C2semidirect
3. #22581145C2semidirect
4. #22580698C2semidirect
5. D4⋊(C139⋊C8)C2semidirect
6. #22580680C2semidirect
7. #459×C139C2semidirect
55. D556D8semidirect
104. C139#1625semidirect
109. #459D139semidirect

Maximal subgroups

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

subgroupindex
#225816082
#225812992
#225811452
#225806982
D4⋊(C139⋊C8)2
#225806802
#459×C1392
#1625139