Finite Group Databasebeta

← #31805717

Subgroups — #31805717

Order 17792.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#22581707C211yesmaximal, characteristic
2#22581363C211yesmaximal, characteristic, complemented
3#22581362C211yesmaximal, characteristic, complemented
4#22581347C211yesmaximal, characteristic
5#22580694C211yesmaximal, characteristic, complemented
6#22580692C211yesmaximal, characteristic
7#330×C139C211yesmaximal, characteristic, complemented
8C2×Dic556—21no—
9C2×#14555774—21no—
10#17984842C2211yescharacteristic
11#17984841—21no—
12#17984837—21no—
13#17984837—21no—
14#17984834C2211yescharacteristic
15#17984830C2211yescharacteristic
16#17984827—21no—
17#17984822—21no—
18#17984820—21no—
19#17984776—21no—
20#17984775—21no—
21#17984774—21no—
22#17984773—21no—
23#17984753C2211yescharacteristic
24#125×C139C2211yescharacteristic
25#97×C139C2211yescharacteristic
26#97×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278—21no—
29C2×Dic278D411yescharacteristic
30C2×D556D411yescharacteristic
31C2×C4×D139—21no—
32Dic556—42no—
33#14555774—42no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139D411yescharacteristic
39C4⋊Dic139D411yescharacteristic
40Dic139⋊C4—21no—
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—21no—
47(C2×D139)⋊C4—21no—
48C4×Dic139—21no—
49C2×C8×C139—21no—
50C2×C8×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139—21no—
53C4⋊C4×C139D411yescharacteristic
54C4⋊C4×C139D411yescharacteristic
55C42×C139C2311yescharacteristic
56C22×D139—21no—
57Dic278—41no—
58Dic278—41no—
59Dic278—41no—
60Dic278—81no—
61D556—41no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—21no—
65C2×Dic139—41no—
66C4×D139—81no—
67C139⋊C8—22no—
68C2×C4×C139—21no—
69C2×C4×C139—21no—
70C2×C4×C139C2×D411yescharacteristic
71C2×C4×C139C2×D411yescharacteristic
72C2×C4×C139C2×D411yescharacteristic
73C8×C139—22no—
74C8×C139—22no—
75C22×C139#12011yescharacteristic
76C2×D139—41no—
77C2×D139—41no—
78C2×D139—41no—
79C4×C139—21no—
80C4×C139—21no—
81C4×C139—21no—
82C4×C139—41no—
83C4×C139—41no—
84Dic139—41no—
85Dic139—41no—
86Dic139—41no—
87Dic139—81no—
88C2×C139#45311yescharacteristic
89C2×C139#45611yescharacteristic
90C2×C139#45611yescharacteristic
91D139—81no—
92C139#166011yescharacteristic, complemented, Sylow
93#1660—1391nomaximal, Sylow
94#563—1391no—
95#501—1391no—
96#501—1391no—
97#497—1391no—
98#330—1391no—
99#330D13911yescharacteristic, complemented
100#329—1391no—
101C2×Q16—2781no—
102C2×SD16—2781no—
103C4⋊Q8—2781no—
104C4⋊Q8—1391no—
105#126—2781no—
106#126—2781no—
107#125—1391no—
108#125C2×D13911yescharacteristic
109#124—1391no—
110#123—2781no—
111C22⋊Q8—2781no—
112C22⋊Q8—2781no—
113#107—2781no—
114#107—2781no—
115#106—2781no—
116#106—2781no—
117#97—1391no—
118#97C2×D13911yescharacteristic
119#97C2×D13911yescharacteristic
120C2×Q8—2781no—
121C2×Q8—2781no—
122C2×Q8—1391no—
123C2×D4—1391no—
124C22×C4—2781no—
125Q16—5562no—
126SD16—5562no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—2781no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2781no—
133C4⋊C4—2781no—
134C4⋊C4—2781no—
135C4⋊C4—2781no—
136C4⋊C4—2781no—
137C4⋊C4—2781no—
138C4⋊C4—1391no—
139C4⋊C4—1391no—
140C4⋊C4D55611yescharacteristic
141C4⋊C4D55611yescharacteristic
142C22⋊C4—2781no—
143C22⋊C4—2781no—
144C22⋊C4—2781no—
145C22⋊C4—2781no—
146C22⋊C4—2781no—
147C42—2781no—
148C42C22×D13911yescharacteristic
149C23—2781no—
150Q8—5561no—
151Q8—5561no—
152Q8—5561no—
153Q8—11121no—
154D4—5561no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—2781no—
158C2×C4—2781no—
159C2×C4—2781no—
160C2×C4—5561no—
161C2×C4—11121no—
162C2×C4D4×D13911yescharacteristic
163C2×C4D4×D13911yescharacteristic
164C2×C4C2×D55611yescharacteristic
165C8—22no—
166C8—22no—
167C8—2782no—
168C22—5561no—
169C22—5561no—
170C22—5561no—
171C22#1798481211yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—5561no—
178C4—5561no—
179C4—5561no—
180C4—11121no—
181C2—11121no—
182C2#2258112211yescharacteristic
183C2#2258113711yescharacteristic
184C2#2258113811yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#330×C139C2
socleC22×C139#120
prime radicalC2×D556D4
hypercenter#330D139
hypocenterC139#1660
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #22581363C2semidirect
3. #22581362C2semidirect
5. #22580694C2semidirect
7. #330×C139C2semidirect
92. C139#1660semidirect
99. #330D139semidirect

Maximal subgroups

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

subgroupindex
#225817072
#225813632
#225813622
#225813472
#225806942
#225806922
#330×C1392
#1660139