Finite Group Databasebeta

← #31805515

Subgroups — #31805515

Order 17792.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#22581677C211yesmaximal, characteristic, complemented
2#22581301C211yesmaximal, characteristic, complemented
3#22581154C211yesmaximal, characteristic, complemented
4#22581149C211yesmaximal, characteristic
5#22580683C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#332×C139C211yesmaximal, characteristic, complemented
8C2×#14555774—21no—
9C2×D1112—21no—
10#17984839C2211yescharacteristic
11#17984837—22no—
12#17984831—21no—
13#17984822—21no—
14Q8×Dic139—21no—
15C4×Dic278C2211yescharacteristic
16C4×D556C2211yescharacteristic
17#17984800—21no—
18#17984764—21no—
19#17984764—21no—
20#17984762—22no—
21C4×C139⋊C8C2211yescharacteristic
22C4⋊Q8×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4⋊C8×C139C2211yescharacteristic
25C2×Dic278D411yescharacteristic
26C2×D556—21no—
27C2×D556—21no—
28C2×D556—21no—
29C2×D556D411yescharacteristic
30C2×C4×D139—21no—
31#14555774—42no—
32D1112—42no—
33C2×C139⋊C8—21no—
34C4⋊Dic139—22no—
35C4⋊Dic139D411yescharacteristic
36C4⋊Dic139D411yescharacteristic
37Dic139⋊C4—21no—
38(C2×D139)⋊C4—22no—
39(C2×D139)⋊C4—22no—
40(C2×D139)⋊C4—21no—
41C4×Dic139—22no—
42C4×Dic139—21no—
43C2×Q8×C139—21no—
44C2×C8×C139—21no—
45C2×C8×C139—21no—
46C4⋊C4×C139—21no—
47C4⋊C4×C139D412yes—
48C42×C139C2311yescharacteristic
49C22×D139—21no—
50C22×D139—41no—
51Dic278—21no—
52Dic278—21no—
53D556—21no—
54D556—21no—
55D556—42no—
56D556—41no—
57D556—41no—
58D556—41no—
59D556—41no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C4×D139—41no—
64C4×D139—41no—
65C139⋊C8—41no—
66Q8×C139—41no—
67Q8×C139—41no—
68C2×C4×C139—22no—
69C2×C4×C139C2×D411yescharacteristic
70C2×C4×C139C2×D411yescharacteristic
71C2×C4×C139C2×D411yescharacteristic
72C8×C139—41no—
73C8×C139—41no—
74C22×C139#12011yescharacteristic
75C2×D139—41no—
76C2×D139—41no—
77C2×D139—41no—
78C2×D139—81no—
79C2×D139—81no—
80C2×D139—81no—
81C4×C139—21no—
82C4×C139—42no—
83C4×C139#13511yescharacteristic
84C4×C139#13511yescharacteristic
85C4×C139AGL(1,ℤ/8)11yescharacteristic
86C4×C139AGL(1,ℤ/8)11yescharacteristic
87Dic139—41no—
88Dic139—41no—
89Dic139—41no—
90C2×C139#44911yescharacteristic
91C2×C139#44911yescharacteristic
92C2×C139#45411yescharacteristic
93D139—81no—
94D139—161no—
95C139#162811yescharacteristic, complemented, Sylow
96#1628—1391nomaximal, Sylow
97#556—1391no—
98#486—1391no—
99#460—1391no—
100#459—1391no—
101#332D13911yescharacteristic, complemented
102Q8⋊C8—1391no—
103D4⋊C8—1391no—
104C2×SD16—2781no—
105C2×D8—2781no—
106C4⋊Q8C2×D13911yescharacteristic
107#127—1391no—
108#126—2782no—
109#124—2781no—
110C22⋊Q8—2781no—
111C4×Q8—2781no—
112C4×Q8—1391no—
113C4×D4—1391no—
114#117—2781no—
115C4⋊C8C2×D13911yescharacteristic
116C4⋊C8C2×D13911yescharacteristic
117#102—2781no—
118#102—2781no—
119#102—2782no—
120C4×C8—1391no—
121C2×Q8—21no—
122C2×Q8—1391no—
123C2×D4—2781no—
124C2×D4—2781no—
125C2×D4—2781no—
126C2×D4—1391no—
127C22×C4—2781no—
128SD16—5562no—
129D8—5562no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—2781no—
133C4⋊C4—21no—
134C4⋊C4—2782no—
135C4⋊C4—2781no—
136C4⋊C4—1391no—
137C4⋊C4—1391no—
138C4⋊C4D55612yes—
139C22⋊C4—2782no—
140C22⋊C4—2782no—
141C22⋊C4—2781no—
142C42—2782no—
143C42—2781no—
144C42C22×D13911yescharacteristic
145C23—2781no—
146C23—5561no—
147Q8—41no—
148Q8—41no—
149Q8—2781no—
150Q8—2781no—
151D4—2781no—
152D4—2781no—
153D4—5562no—
154D4—5561no—
155D4—5561no—
156D4—5561no—
157D4—5561no—
158C2×C4—22no—
159C2×C4—2781no—
160C2×C4—2781no—
161C2×C4—2781no—
162C2×C4—5561no—
163C2×C4—5561no—
164C2×C4D4×D13911yescharacteristic
165C2×C4D4×D13911yescharacteristic
166C2×C4C2×D55611yescharacteristic
167C8—41no—
168C8—41no—
169C8—5561no—
170C22—5561no—
171C22—5561no—
172C22—5561no—
173C22—11121no—
174C22—11121no—
175C22—11121no—
176C22#1798481211yescharacteristic
177C4—21no—
178C4—42no—
179C4—5561no—
180C4—5561no—
181C4—5561no—
182C4#1798486311yescharacteristic
183C4#1798486511yescharacteristic
184C4#1798486611yescharacteristic
185C4#1798486911yescharacteristic
186C2—11121no—
187C2—22241no—
188C2#2258109911yescharacteristic
189C2#2258110111yescharacteristic
190C2#2258112811yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#332×C139C2
socleC22×C139#120
prime radical#22581149C2
hypercenter#332D139
hypocenterC139#1628
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #22581677C2semidirect
2. #22581301C2semidirect
3. #22581154C2semidirect
5. #22580683C2semidirect
6. #22580680C2semidirect
7. #332×C139C2semidirect
95. C139#1628semidirect
101. #332D139semidirect

Maximal subgroups

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

subgroupindex
#225816772
#225813012
#225811542
#225811492
#225806832
#225806802
#332×C1392
#1628139