Finite Group Databasebeta

← #31805496

Subgroups — #31805496

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#22581300C211yesmaximal, characteristic, complemented
3#22581149C211yesmaximal, characteristic, complemented
4#22581148C211yesmaximal, characteristic, complemented
5#22580700C211yesmaximal, characteristic, complemented
6#22580682C211yesmaximal, characteristic, complemented
7D4⋊C8×C139C211yesmaximal, characteristic, complemented
8C2×#14555785—21no—
9C2×D1112—21no—
10C2×#14555770—21no—
11#17984842C2211yescharacteristic
12#17984839C2211yescharacteristic
13#17984824—22no—
14#17984821—21no—
15#17984813—21no—
16C4×D556C2211yescharacteristic
17C4⋊C4×D139—21no—
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984764—22no—
20#17984764—21no—
21#17984762—21no—
22C4×D4×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4×C8×C139C2211yescharacteristic
25#14555785—42no—
26#14555785—42no—
27C2×Dic278—21no—
28C2×D556—21no—
29C2×D556—21no—
30C2×D556—21no—
31C2×D556D411yescharacteristic
32C2×C22⋊D139—22no—
33C2×C4×D139—22no—
34C2×C4×D139—21no—
35D1112—42no—
36#14555770—42no—
37C2×C139⋊C8—21no—
38C4⋊Dic139—21no—
39C4⋊Dic139D411yescharacteristic
40C4⋊Dic139D412yes—
41Dic139⋊C4—22no—
42C22⋊Dic139—22no—
43(C2×D139)⋊C4—21no—
44C2×D4×C139D411yescharacteristic
45C22×C4×C139—21no—
46C2×C8×C139—21no—
47C2×C8×C139—21no—
48C4⋊C4×C139D411yescharacteristic
49C22⋊C4×C139—21no—
50C42×C139C2311yescharacteristic
51C22×D139—21no—
52C22×D139—41no—
53Dic278—41no—
54Dic278—41no—
55D556—21no—
56D556—42no—
57D556—41no—
58D556—41no—
59D556—41no—
60D556—41no—
61D556D812yescomplemented
62C22⋊D139—44no—
63C2×Dic139—21no—
64C2×Dic139—22no—
65C4×D139—44no—
66C4×D139—41no—
67C4×D139—41no—
68C139⋊C8—41no—
69C23×C139—21no—
70D4×C139—21no—
71D4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139—41no—
74C2×C4×C139—41no—
75C2×C4×C139C2×D411yescharacteristic
76C2×C4×C139C2×D411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C8×C139—41no—
79C8×C139—41no—
80C22×C139—41no—
81C22×C139—41no—
82C22×C139—41no—
83C22×C139#12011yescharacteristic
84C2×D139—22no—
85C2×D139—41no—
86C2×D139—41no—
87C2×D139—81no—
88C2×D139—81no—
89C2×D139—81no—
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#44711yescharacteristic
100C2×C139#44911yescharacteristic
101C2×C139#45411yescharacteristic
102D139—42no—
103D139—161no—
104C139#162511yescharacteristic, complemented, Sylow
105#1625—1391nomaximal, Sylow
106#547—1391no—
107#486—1391no—
108#459—1391no—
109#459—1391no—
110#332—1391no—
111D4⋊C8—1391no—
112D4⋊C8D13911yescharacteristic, complemented
113C2×#41—2781no—
114C2×D8—2781no—
115C2×D8—2781no—
116C4⋊Q8—1391no—
117#127—1391no—
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—2781no—
127#102—2782no—
128#102—2781no—
129C4×C8C2×D13911yescharacteristic
130#41—5562no—
131#41—5562no—
132C2×Q8—2781no—
133C2×D4—2782no—
134C2×D4—2781no—
135C2×D4—2781no—
136C2×D4—2781no—
137C2×D4—1391no—
138C2×D4D55611yescharacteristic
139C22×C4—21no—
140C22×C4—2782no—
141C22×C4—2781no—
142D8—5562no—
143D8—5562no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—2781no—
147C4⋊C4—2782no—
148C4⋊C4—2781no—
149C4⋊C4—1391no—
150C4⋊C4—1392no—
151C4⋊C4D55611yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2782no—
154C22⋊C4—2781no—
155C42C22×D13911yescharacteristic
156C23—21no—
157C23—2781no—
158C23—5561no—
159Q8—5561no—
160Q8—5561no—
161D4—21no—
162D4—21no—
163D4—2781no—
164D4—5562no—
165D4—5564no—
166D4—5561no—
167D4—5561no—
168D4—5561no—
169D4—5561no—
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×D55611yescharacteristic
182C8—41no—
183C8—41no—
184C8—5561no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—2782no—
189C22—5561no—
190C22—5561no—
191C22—11121no—
192C22—11121no—
193C22—11121no—
194C22#1798481211yescharacteristic
195C4—21no—
196C4—41no—
197C4—5562no—
198C4—5561no—
199C4D8×D13911yescharacteristic
200C4#1798486411yescharacteristic
201C4#1798486911yescharacteristic
202C4#1798487011yescharacteristic
203C2—81no—
204C2—5562no—
205C2—22241no—
206C2#2258108811yescharacteristic
207C2#2258110011yescharacteristic
208C2#2258112711yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
FittingD4⋊C8×C139C2
socleC22×C139#120
hypercenterD4⋊C8D139
hypocenterC139#1625
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
1. #22581608C2semidirect
2. #22581300C2semidirect
3. #22581149C2semidirect
4. #22581148C2semidirect
5. #22580700C2semidirect
6. #22580682C2semidirect
7. D4⋊C8×C139C2semidirect
61. D556D8semidirect
104. C139#1625semidirect
112. D4⋊C8D139semidirect

Maximal subgroups

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

subgroupindex
#225816082
#225813002
#225811492
#225811482
#225807002
#225806822
D4⋊C8×C1392
#1625139