Finite Group Databasebeta

← #31805508

Subgroups — #31805508

Order 17792.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#22581618C211yesmaximal, 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×Q8×D139—21no—
9C2×#14555774—21no—
10C2×D1112—21no—
11#17984841—21no—
12#17984839C2211yescharacteristic
13#17984820—22no—
14#17984818—21no—
15C4×Dic278C2211yescharacteristic
16C4×D556C2211yescharacteristic
17#17984804—21no—
18#17984764—21no—
19#17984764—21no—
20#17984762—22no—
21C4×C139⋊C8C2211yescharacteristic
22C4⋊Q8×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4⋊C8×C139C2211yescharacteristic
25C2×Dic278—22no—
26C2×Dic278D411yescharacteristic
27Q8×D139—42no—
28Q8×D139—42no—
29C2×D556—21no—
30C2×D556—21no—
31C2×D556—21no—
32C2×D556D411yescharacteristic
33C2×C4×D139—22no—
34C2×C4×D139—21no—
35#14555774—42no—
36D1112—42no—
37C2×C139⋊C8—21no—
38C4⋊Dic139D411yescharacteristic
39C4⋊Dic139D411yescharacteristic
40Dic139⋊C4—22no—
41Dic139⋊C4—21no—
42(C2×D139)⋊C4—22no—
43(C2×D139)⋊C4—21no—
44C4×Dic139—21no—
45C2×Q8×C139—21no—
46C2×C8×C139—21no—
47C2×C8×C139—21no—
48C4⋊C4×C139—21no—
49C4⋊C4×C139D412yes—
50C42×C139C2311yescharacteristic
51C22×D139—21no—
52C22×D139—41no—
53Dic278—21no—
54Dic278—44no—
55Dic278D812yescomplemented
56D556—21no—
57D556—42no—
58D556—41no—
59D556—41no—
60D556—41no—
61D556—41no—
62D556SD1612yescomplemented
63C2×Dic139—21no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C4×D139—44no—
67C4×D139—41no—
68C4×D139—41no—
69C139⋊C8—41no—
70Q8×C139—41no—
71Q8×C139—41no—
72C2×C4×C139—22no—
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139C2×D411yescharacteristic
75C2×C4×C139C2×D411yescharacteristic
76C8×C139—41no—
77C8×C139—41no—
78C22×C139#12011yescharacteristic
79C2×D139—22no—
80C2×D139—41no—
81C2×D139—41no—
82C2×D139—81no—
83C2×D139—81no—
84C2×D139—81no—
85C4×C139—21no—
86C4×C139—42no—
87C4×C139C2×D811yescharacteristic
88C4×C139C2×SD1611yescharacteristic
89C4×C139AGL(1,ℤ/8)11yescharacteristic
90C4×C139#13711yescharacteristic
91Dic139—22no—
92Dic139—41no—
93Dic139—41no—
94C2×C139#44711yescharacteristic
95C2×C139#44811yescharacteristic
96C2×C139#45411yescharacteristic
97D139—42no—
98D139—161no—
99C139#162711yescharacteristic, complemented, Sylow
100#1627—1391nomaximal, Sylow
101D4×Q8—1391no—
102#486—1391no—
103#460—1391no—
104#459—1391no—
105#332D13911yescharacteristic, complemented
106Q8⋊C8—1391no—
107D4⋊C8—1391no—
108C22×Q8—2781no—
109C2×SD16—2781no—
110C2×D8—2781no—
111C4⋊Q8—2781no—
112C4⋊Q8C2×D13911yescharacteristic
113#127—1391no—
114C22⋊Q8—2781no—
115C22⋊Q8—2782no—
116C4×Q8—1391no—
117C4×D4—2781no—
118C4×D4—1391no—
119C4⋊C8C2×D13911yescharacteristic
120C4⋊C8C2×D13911yescharacteristic
121#102—2781no—
122#102—2781no—
123#102—2782no—
124C4×C8—1391no—
125C2×Q8—21no—
126C2×Q8—2782no—
127C2×Q8—5562no—
128C2×Q8—5562no—
129C2×Q8—1391no—
130C2×D4—2781no—
131C2×D4—2781no—
132C2×D4—2781no—
133C2×D4—1391no—
134C22×C4—2782no—
135C22×C4—2781no—
136SD16—5562no—
137D8—5562no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2781no—
141C4⋊C4—21no—
142C4⋊C4—2782no—
143C4⋊C4—2781no—
144C4⋊C4—1391no—
145C4⋊C4—1391no—
146C4⋊C4D55612yes—
147C22⋊C4—2782no—
148C22⋊C4—2781no—
149C42—2781no—
150C42C22×D13911yescharacteristic
151C23—2781no—
152C23—5561no—
153Q8—41no—
154Q8—41no—
155Q8—2781no—
156Q8—5564no—
157Q8—1392no—
158D4—2781no—
159D4—5562no—
160D4—5561no—
161D4—5561no—
162D4—5561no—
163D4—5561no—
164D4—1392no—
165C2×C4—22no—
166C2×C4—2781no—
167C2×C4—2781no—
168C2×C4—2781no—
169C2×C4—5564no—
170C2×C4—5561no—
171C2×C4—5561no—
172C2×C4D4×D13911yescharacteristic
173C2×C4D4×D13911yescharacteristic
174C2×C4C2×D55611yescharacteristic
175C8—41no—
176C8—41no—
177C8—5561no—
178C22—2782no—
179C22—5561no—
180C22—5561no—
181C22—11121no—
182C22—11121no—
183C22—11121no—
184C22#1798481211yescharacteristic
185C4—21no—
186C4—42no—
187C4—2782no—
188C4—5561no—
189C4—5561no—
190C4D8×D13911yescharacteristic
191C4SD16×D13911yescharacteristic
192C4#1798486911yescharacteristic
193C4#1798487411yescharacteristic
194C2—5562no—
195C2—22241no—
196C2#2258108811yescharacteristic
197C2#2258109311yescharacteristic
198C2#2258112811yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#332×C139C2
socleC22×C139#120
prime radical#22581149C2
hypercenter#332D139
hypocenterC139#1627
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. #22581618C2semidirect
2. #22581301C2semidirect
3. #22581154C2semidirect
5. #22580683C2semidirect
6. #22580680C2semidirect
7. #332×C139C2semidirect
55. Dic278D8semidirect
62. D556SD16semidirect
99. C139#1627semidirect
105. #332D139semidirect

Maximal subgroups

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

subgroupindex
#225816182
#225813012
#225811542
#225811492
#225806832
#225806802
#332×C1392
#1627139