Finite Group Databasebeta

← #31805558

Subgroups — #31805558

Order 17792.

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

normal subgroups only

This group has 234 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
2#22581304C211yesmaximal, characteristic, complemented
3#22581244C211yesmaximal, characteristic, complemented
4#22581243C211yesmaximal, characteristic, complemented
5#22580700C211yesmaximal, characteristic, complemented
6#22580682C211yesmaximal, characteristic, complemented
7D4⋊C8×C139C211yesmaximal, characteristic, complemented
8C2×#14555785—21no—
9#17984842C2211yescharacteristic
10#17984842C2211yescharacteristic
11#17984824—22no—
12#17984821—21no—
13#17984813—21no—
14C4×D556C2211yescharacteristic
15C4⋊C4×D139—21no—
16#17984774—21no—
17#17984773—21no—
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984767—22no—
20#17984764—21no—
21#17984763—21no—
22C4×D4×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4×C8×C139C2211yescharacteristic
25#14555785—42no—
26#14555785—42no—
27C2×Dic278—21no—
28C2×Dic278—21no—
29C2×D556D411yescharacteristic
30C2×C22⋊D139—22no—
31C2×C4×D139—22no—
32C2×C4×D139—21no—
33C2×C139⋊C8—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139D411yescharacteristic
38C4⋊Dic139D412yes—
39Dic139⋊C4—22no—
40C22⋊Dic139—22no—
41(C2×D139)⋊C4—21no—
42C2×D4×C139D411yescharacteristic
43C22×C4×C139—21no—
44C2×C8×C139—21no—
45C2×C8×C139—21no—
46C4⋊C4×C139D411yescharacteristic
47C22⋊C4×C139—21no—
48C42×C139C2311yescharacteristic
49C22×D139—21no—
50Dic278—41no—
51Dic278—41no—
52Dic278—42no—
53D556—21no—
54D556SD1612yes—
55C22⋊D139—44no—
56C2×Dic139—21no—
57C2×Dic139—22no—
58C2×Dic139—41no—
59C4×D139—44no—
60C4×D139—41no—
61C4×D139—41no—
62C139⋊C8—41no—
63C23×C139—21no—
64D4×C139—21no—
65D4×C139—21no—
66C2×C4×C139—21no—
67C2×C4×C139—41no—
68C2×C4×C139—41no—
69C2×C4×C139C2×D411yescharacteristic
70C2×C4×C139C2×D411yescharacteristic
71C2×C4×C139C2×D411yescharacteristic
72C8×C139—41no—
73C8×C139—41no—
74C22×C139—41no—
75C22×C139—41no—
76C22×C139—41no—
77C22×C139#12011yescharacteristic
78C2×D139—22no—
79C2×D139—41no—
80C2×D139—41no—
81C4×C139—21no—
82C4×C139—41no—
83C4×C139C2×SD1611yescharacteristic
84C4×C139#13511yescharacteristic
85C4×C139AGL(1,ℤ/8)11yescharacteristic
86C4×C139#13711yescharacteristic
87Dic139—42no—
88Dic139—41no—
89Dic139—81no—
90C2×C139—81no—
91C2×C139#45011yescharacteristic
92C2×C139#45211yescharacteristic
93C2×C139#45411yescharacteristic
94D139—42no—
95C139#163511yescharacteristic, complemented, Sylow
96#1635—1391nomaximal, Sylow
97#547—1391no—
98#487—1391no—
99#476—1391no—
100#476—1391no—
101#332—1391no—
102D4⋊C8—1391no—
103D4⋊C8D13911yescharacteristic, complemented
104C2×#41—2781no—
105C4⋊Q8—1391no—
106C4⋊Q8—1391no—
107#123—2782no—
108C22⋊Q8—2781no—
109#121—2781no—
110C4×D4—1391no—
111C4×D4C2×D13911yescharacteristic
112C2×C4⋊C4—2781no—
113#106—2781no—
114#106—2781no—
115C4⋊C8—1391no—
116C4⋊C8C2×D13911yescharacteristic
117#103—2782no—
118#102—2781no—
119#102—2781no—
120C4×C8C2×D13911yescharacteristic
121#41—5562no—
122#41—5562no—
123C2×Q8—2781no—
124C2×Q8—2781no—
125C2×D4—2782no—
126C2×D4—1391no—
127C2×D4D55611yescharacteristic
128C22×C4—21no—
129C22×C4—2782no—
130C22×C4—2781no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2781no—
134C4⋊C4—2782no—
135C4⋊C4—2781no—
136C4⋊C4—2781no—
137C4⋊C4—2781no—
138C4⋊C4—1392no—
139C4⋊C4—1391no—
140C4⋊C4D55611yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—2782no—
143C22⋊C4—2781no—
144C42C22×D13911yescharacteristic
145C23—21no—
146C23—2781no—
147Q8—5562no—
148Q8—5561no—
149Q8—5561no—
150D4—21no—
151D4—21no—
152D4—2781no—
153D4—5564no—
154D4—1392no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—2781no—
159C2×C4—2782no—
160C2×C4—5564no—
161C2×C4—5561no—
162C2×C4—5561no—
163C2×C4—5561no—
164C2×C4D4×D13911yescharacteristic
165C2×C4D4×D13911yescharacteristic
166C2×C4C2×D55611yescharacteristic
167C8—41no—
168C8—41no—
169C8—5561no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—2782no—
174C22—5561no—
175C22—5561no—
176C22#1798481211yescharacteristic
177C4—21no—
178C4—41no—
179C4—5562no—
180C4—5561no—
181C4—11121no—
182C4SD16×D13911yescharacteristic
183C4#1798486411yescharacteristic
184C4#1798486611yescharacteristic
185C4#1798487511yescharacteristic
186C2—81no—
187C2—5562no—
188C2#2258110511yescharacteristic
189C2#2258111711yescharacteristic
190C2#2258112711yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
FittingD4⋊C8×C139C2
socleC22×C139#120
prime radical#22581608C2
hypercenterD4⋊C8D139
hypocenterC139#1635
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #22581304C2semidirect
3. #22581244C2semidirect
4. #22581243C2semidirect
5. #22580700C2semidirect
6. #22580682C2semidirect
7. D4⋊C8×C139C2semidirect
95. C139#1635semidirect
103. D4⋊C8D139semidirect

Maximal subgroups

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

subgroupindex
#225816082
#225813042
#225812442
#225812432
#225807002
#225806822
D4⋊C8×C1392
#1635139