Finite Group Databasebeta

← #31805548

Subgroups — #31805548

Order 17792.

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

normal subgroups only

This group has 218 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#22581668C211yesmaximal, characteristic
2#22581332C211yesmaximal, characteristic, complemented
3#22581240C211yesmaximal, characteristic, complemented
4#22580701C211yesmaximal, characteristic, complemented
5D4⋊(C139⋊C8)C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#476×C139C211yesmaximal, characteristic, complemented
8C2×#14555775—22no—
9#17984842C2211yescharacteristic
10#17984828—22no—
11#17984816—21no—
12#17984813—21no—
13C4×D556C2211yescharacteristic
14#17984801—21no—
15#17984800—21no—
16#17984773—21no—
17C4⋊(C139⋊C8)C2211yescharacteristic
18#17984762—21no—
19C4×C139⋊C8C2211yescharacteristic
20C4⋊Q8×C139C2211yescharacteristic
21C4×D4×C139C2211yescharacteristic
22#106×C139—21no—
23C4⋊C8×C139C2211yescharacteristic
24#102×C139—21no—
25C2×Dic278D412yes—
26C2×D556D411yescharacteristic
27C2×C22⋊D139—22no—
28C2×C4×D139—21no—
29#14555775—44no—
30C2×C139⋊C8—21no—
31C2×C139⋊C8—21no—
32C4⋊Dic139—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139D411yescharacteristic
35C22⋊Dic139—22no—
36(C2×D139)⋊C4—22no—
37(C2×D139)⋊C4—21no—
38C4×Dic139—22no—
39C2×Q8×C139—21no—
40C2×D4×C139D411yescharacteristic
41C22×C4×C139—21no—
42C2×C8×C139—21no—
43C4⋊C4×C139—21no—
44C4⋊C4×C139—21no—
45C4⋊C4×C139D411yescharacteristic
46C22⋊C4×C139—21no—
47C42×C139C2311yescharacteristic
48C22×D139—21no—
49Dic278—42no—
50D556—21no—
51D556—21no—
52C22⋊D139—82no—
53C2×Dic139—21no—
54C2×Dic139—22no—
55C4×D139—41no—
56C4×D139—41no—
57C139⋊C8—22no—
58C139⋊C8—41no—
59C23×C139—21no—
60Q8×C139—42no—
61D4×C139—21no—
62D4×C139—21no—
63C2×C4×C139—21no—
64C2×C4×C139—41no—
65C2×C4×C139—41no—
66C2×C4×C139—41no—
67C2×C4×C139C2×D411yescharacteristic
68C2×C4×C139C2×D411yescharacteristic
69C2×C4×C139C2×D411yescharacteristic
70C8×C139—41no—
71C22×C139—41no—
72C22×C139—41no—
73C22×C139—41no—
74C22×C139#12011yescharacteristic
75C2×D139—41no—
76C2×D139—41no—
77C2×D139—41no—
78C4×C139—21no—
79C4×C139—41no—
80C4×C139—81no—
81C4×C139#13511yescharacteristic
82C4×C139#13511yescharacteristic
83C4×C139#13711yescharacteristic
84C4×C139#13711yescharacteristic
85Dic139—41no—
86Dic139—42no—
87C2×C139—81no—
88C2×C139#45211yescharacteristic
89C2×C139#45211yescharacteristic
90C2×C139#45311yescharacteristic
91D139—81no—
92C139#163411yescharacteristic, complemented, Sylow
93#1634—1391nomaximal, Sylow
94#555—1391no—
95#494—1391no—
96#476—1391no—
97#476D13911yescharacteristic, complemented
98#333—1391no—
99D4⋊C8—1391no—
100D4⋊C8—1391no—
101C2×Q16—2782no—
102C4⋊Q8—1391no—
103C4⋊Q8C2×D13911yescharacteristic
104#124—2782no—
105#121—2781no—
106#121—2781no—
107C4×D4—1391no—
108C4×D4C2×D13911yescharacteristic
109#117—2781no—
110#117—2781no—
111#106—21no—
112#106—2781no—
113C4⋊C8—1391no—
114C4⋊C8C2×D13911yescharacteristic
115#102—21no—
116#102—2781no—
117C4×C8—1391no—
118C2×Q8—21no—
119C2×Q8—1392no—
120C2×D4—2782no—
121C2×D4—1391no—
122C2×D4C22⋊D13911yescharacteristic
123C22×C4—21no—
124C22×C4—2781no—
125Q16—5564no—
126C2×C8—21no—
127C2×C8—2781no—
128C2×C8—2781no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2781no—
132C4⋊C4—2781no—
133C4⋊C4—1391no—
134C4⋊C4C22⋊D13911yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2782no—
137C22⋊C4—2782no—
138C22⋊C4—2781no—
139C42—2782no—
140C42C22×D13911yescharacteristic
141C23—21no—
142C23—2781no—
143Q8—42no—
144Q8—5562no—
145D4—21no—
146D4—21no—
147D4—2781no—
148D4—2781no—
149D4—11122no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—2781no—
155C2×C4—2782no—
156C2×C4—5561no—
157C2×C4—5561no—
158C2×C4D4×D13911yescharacteristic
159C2×C4D4×D13911yescharacteristic
160C2×C4C2×C22⋊D13911yescharacteristic
161C8—41no—
162C8—2782no—
163C8—5561no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—5561no—
168C22—5561no—
169C22—5561no—
170C22#1798481011yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—5561no—
175C4—5562no—
176C4#1798486211yescharacteristic
177C4#1798486311yescharacteristic
178C4#1798487111yescharacteristic
179C4#1798487311yescharacteristic
180C2—81no—
181C2—11121no—
182C2#2258111211yescharacteristic
183C2#2258111311yescharacteristic
184C2#2258111911yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#476×C139C2
socleC22×C139#120
prime radical#22581668C2
hypercenter#476D139
hypocenterC139#1634
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #22581332C2semidirect
3. #22581240C2semidirect
4. #22580701C2semidirect
5. D4⋊(C139⋊C8)C2semidirect
6. #22580680C2semidirect
7. #476×C139C2semidirect
92. C139#1634semidirect
97. #476D139semidirect

Maximal subgroups

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

subgroupindex
#225816682
#225813322
#225812402
#225807012
D4⋊(C139⋊C8)2
#225806802
#476×C1392
#1634139