Finite Group Databasebeta

← #31805718

Subgroups — #31805718

Order 17792.

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

normal subgroups only

This group has 208 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#22581697C211yesmaximal, characteristic
2#22581359C211yesmaximal, characteristic, complemented
3#22581315C211yesmaximal, characteristic, complemented
4#22580694C211yesmaximal, characteristic, complemented
5#22580693C211yesmaximal, characteristic, complemented
6#22580692C211yesmaximal, characteristic, complemented
7#497×C139C211yesmaximal, characteristic, complemented
8#17984834C2211yescharacteristic
9#17984830C2211yescharacteristic
10#17984826—21no—
11#17984824—21no—
12#17984819—21no—
13#17984818—21no—
14#17984815—21no—
15#17984814—21no—
16#17984775—21no—
17#17984773—21no—
18#17984765—21no—
19#17984762—21no—
20#17984753C2211yescharacteristic
21#17984753C2211yescharacteristic
22C2×Q16×C139—21no—
23C2×SD16×C139—21no—
24C4⋊Q8×C139C2211yescharacteristic
25#124×C139C2211yescharacteristic
26#97×C139C2211yescharacteristic
27C2×Dic278D411yescharacteristic
28C2×D556D411yescharacteristic
29C2×C22⋊D139—21no—
30C2×C22⋊D139—21no—
31C22×Dic139—21no—
32C2×C4×D139—21no—
33C2×C139⋊C8—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139D411yescharacteristic
37C4⋊Dic139D411yescharacteristic
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41C22⋊Dic139—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45C2×Q8×C139—21no—
46C2×Q8×C139D411yescharacteristic
47C2×D4×C139D411yescharacteristic
48Q16×C139—42no—
49SD16×C139—42no—
50C2×C8×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139—21no—
53C22⋊C4×C139—21no—
54C22⋊C4×C139—21no—
55C42×C139C2311yescharacteristic
56C22×D139—21no—
57Dic278—41no—
58D556—41no—
59C22⋊D139—81no—
60C22⋊D139—81no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—81no—
65C4×D139—81no—
66C139⋊C8—22no—
67C139⋊C8—41no—
68C23×C139—21no—
69Q8×C139—41no—
70Q8×C139—41no—
71Q8×C139—41no—
72D4×C139—41no—
73C2×C4×C139—21no—
74C2×C4×C139—41no—
75C2×C4×C139C2×D411yescharacteristic
76C2×C4×C139C2×D411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C8×C139—22no—
79C22×C139—41no—
80C22×C139—41no—
81C22×C139—41no—
82C22×C139#12011yescharacteristic
83C2×D139—41no—
84C2×D139—41no—
85C2×D139—41no—
86C4×C139—21no—
87C4×C139—21no—
88C4×C139—21no—
89C4×C139—41no—
90C4×C139—81no—
91Dic139—41no—
92Dic139—41no—
93Dic139—41no—
94C2×C139—81no—
95C2×C139#45311yescharacteristic
96C2×C139#45511yescharacteristic
97C2×C139#45611yescharacteristic
98D139—81no—
99C139#166111yescharacteristic, complemented, Sylow
100#1661—1391nomaximal, Sylow
101#562—1391no—
102#501—1391no—
103#497D13911yescharacteristic, complemented
104#489—1391no—
105#330—1391no—
106#329—1391no—
107#329—1391no—
108C2×Q16—21no—
109C2×SD16—21no—
110C4⋊Q8C2×D13911yescharacteristic
111#125—1391no—
112#124—1391no—
113#124C2×D13911yescharacteristic
114#123—2781no—
115#123—2781no—
116C22⋊Q8—2781no—
117C22⋊Q8—2781no—
118#121—2781no—
119#121—2781no—
120#107—2781no—
121#106—2781no—
122#103—2781no—
123#102—2781no—
124#97—1391no—
125#97—1391no—
126#97C2×D13911yescharacteristic
127C2×Q8—21no—
128C2×Q8—1391no—
129C2×Q8C22⋊D13911yescharacteristic
130C2×D4—2781no—
131C2×D4—2781no—
132C2×D4—1391no—
133C2×D4C22⋊D13911yescharacteristic
134C22×C4—2781no—
135C22×C4—2781no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—2781no—
140C2×C8—2781no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2781no—
144C4⋊C4—2781no—
145C4⋊C4—2781no—
146C4⋊C4—2781no—
147C4⋊C4—1391no—
148C4⋊C4—1391no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—2781no—
152C22⋊C4—2781no—
153C22⋊C4—2781no—
154C22⋊C4—2781no—
155C42C22×D13911yescharacteristic
156C23—21no—
157C23—2781no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—5561no—
162D4—41no—
163D4—5561no—
164D4—11121no—
165D4—11121no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—2781no—
169C2×C4—2781no—
170C2×C4—2781no—
171C2×C4—11121no—
172C2×C4—11121no—
173C2×C4D4×D13911yescharacteristic
174C2×C4D4×D13911yescharacteristic
175C2×C4C2×C22⋊D13911yescharacteristic
176C8—22no—
177C8—2782no—
178C8—5561no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—5561no—
183C22—5561no—
184C22—5561no—
185C22#1798481011yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—5561no—
192C4—5561no—
193C4—5561no—
194C2—81no—
195C2—11121no—
196C2#2258112011yescharacteristic
197C2#2258112911yescharacteristic
198C2#2258113411yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#497×C139C2
socleC22×C139#120
prime radical#22581697C2
hypercenter#497D139
hypocenterC139#1661
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #22581359C2semidirect
3. #22581315C2semidirect
4. #22580694C2semidirect
5. #22580693C2semidirect
6. #22580692C2semidirect
7. #497×C139C2semidirect
99. C139#1661semidirect
103. #497D139semidirect

Maximal subgroups

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

subgroupindex
#225816972
#225813592
#225813152
#225806942
#225806932
#225806922
#497×C1392
#1661139