Finite Group Databasebeta

← #354×D139 #31808063

Subgroups — #354×D139 #31808063

Order 17792.

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

normal subgroups only

This group has 284 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#124×D139C211yesmaximal, characteristic
2#99×D139C212yesmaximal
3#22580748C211yesmaximal, characteristic, complemented
4#22580747C212yesmaximal, complemented
5#354×C139C211yesmaximal, characteristic, complemented
6C2×Q8×D139C411yescharacteristic, complemented
7C2×D4×D139C2211yescharacteristic
8#17984831C411yescharacteristic, complemented
9#17984830C411yescharacteristic, complemented
10#17984829C2211yescharacteristic
11#17984828—22no—
12C22⋊C4×D139—22no—
13C22⋊C4×D139—22no—
14C42×D139C411yescharacteristic, complemented
15#17984757C2212yes—
16#17984756—22no—
17#124×C139C2211yescharacteristic
18#99×C139C2212yes—
19C23×D139D412yes—
20C2×Dic278—21no—
21C2×Dic278C2×C411yescharacteristic, complemented
22Q8×D139—41no—
23Q8×D139—41no—
24C2×D556C2×C411yescharacteristic
25C2×C22⋊D139D412yes—
26D4×D139—41no—
27D4×D139—41no—
28C2×C4×D139—21no—
29C2×C4×D139—21no—
30C2×C4×D139—42no—
31C2×C4×D139C2×C411yescharacteristic
32C22⋊Dic139—22no—
33C22⋊Dic139—22no—
34(C2×D139)⋊C4—22no—
35(C2×D139)⋊C4—22no—
36(C2×D139)⋊C4—42no—
37C4×Dic139—21no—
38C4×Dic139C2×C411yescharacteristic, complemented
39C2×Q8×C139C2×C411yescharacteristic, complemented
40C2×D4×C139C2311yescharacteristic
41C22⋊C4×C139—22no—
42C22⋊C4×C139—22no—
43C42×C139C2×C411yescharacteristic, complemented
44C22×D139—22no—
45C22×D139—22no—
46C22×D139—44no—
47C22×D139C22⋊C411yescharacteristic
48C22×D139C22⋊C412yes—
49Dic278—42no—
50Dic278—41no—
51D556—41no—
52C22⋊D139—42no—
53C2×Dic139—21no—
54C2×Dic139—21no—
55C2×Dic139—42no—
56C2×Dic139C22⋊C411yescharacteristic
57C4×D139—21no—
58C4×D139—21no—
59C4×D139—42no—
60C4×D139—41no—
61C4×D139—41no—
62C4×D139—84no—
63C23×C139C2×D412yes—
64Q8×C139—41no—
65D4×C139—41no—
66C2×C4×C139—21no—
67C2×C4×C139—21no—
68C2×C4×C139—42no—
69C2×C4×C139C22×C411yescharacteristic
70C22×C139—22no—
71C22×C139—42no—
72C22×C139C2×C22⋊C411yescharacteristic
73C2×D139—22no—
74C2×D139—22no—
75C2×D139—44no—
76C2×D139—42no—
77C2×D139—82no—
78C2×D139#9911yescharacteristic
79C2×D139#9911yescharacteristic
80C4×C139—21no—
81C4×C139—41no—
82C4×C139—41no—
83C4×C139—82no—
84Dic139—21no—
85Dic139—41no—
86Dic139—41no—
87Dic139—82no—
88C2×C139—21no—
89C2×C139—42no—
90C2×C139C2×#9911yescharacteristic
91D139—21no—
92D139—42no—
93D139#35412yesdirect product factor
94C139C2×#35411yescharacteristic, complemented, Sylow
95C2×#354—1391nomaximal, Sylow
96C2×#124—1391no—
97C2×#99—1392no—
98#354—1391no—
99#354—1392no—
100#354D13911yescharacteristic, direct product factor
101C22×Q8—1391no—
102C22×D4—1391no—
103#124—2782no—
104#124—1391no—
105#124—1391no—
106#124—1391no—
107#124C2×D13911yescharacteristic
108C2×C22⋊C4—2782no—
109C2×C22⋊C4—2782no—
110C2×C42—1391no—
111#99—2782no—
112#99—1392no—
113#99C2×D13912yes—
114C24—1392no—
115C2×Q8—2781no—
116C2×Q8—5561no—
117C2×Q8—5561no—
118C2×Q8—1391no—
119C2×Q8C4×D13911yescharacteristic, complemented
120C2×D4—5561no—
121C2×D4—5561no—
122C2×D4—1392no—
123C2×D4—1391no—
124C2×D4C22×D13911yescharacteristic
125C22×C4—2781no—
126C22×C4—2781no—
127C22×C4—5562no—
128C22×C4—1391no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—2782no—
132C22⋊C4—2782no—
133C22⋊C4—2782no—
134C22⋊C4—2782no—
135C22⋊C4—5562no—
136C42—2781no—
137C42—1391no—
138C42C4×D13911yescharacteristic, complemented
139C23—2782no—
140C23—2782no—
141C23—5564no—
142C23—1391no—
143C23—1392no—
144C23D4×D13912yes—
145Q8—41no—
146Q8—5561no—
147Q8—5562no—
148D4—41no—
149D4—5561no—
150D4—5562no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—2781no—
155C2×C4—2781no—
156C2×C4—2781no—
157C2×C4—2781no—
158C2×C4—5562no—
159C2×C4—5561no—
160C2×C4—5561no—
161C2×C4—5562no—
162C2×C4—11124no—
163C2×C4—1391no—
164C2×C4C2×C4×D13911yescharacteristic
165C22—22no—
166C22—42no—
167C22—2782no—
168C22—2782no—
169C22—5562no—
170C22—5564no—
171C22—11122no—
172C22—1391no—
173C22—1391no—
174C22C22⋊C4×D13911yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—2781no—
180C4—5561no—
181C4—5561no—
182C4—11122no—
183C2—21no—
184C2—42no—
185C2—2781no—
186C2—5562no—
187C2—1392no—
188C2#99×D13911yescharacteristic
subgroupG/H
centerC2#99×D139
commutatorC2×C4×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#354×C139C2
socleC2×C139C2×#99
prime radicalC2×D4×D139C22
cosocleC2×D4×C139C23
hypercenter#354D139
hypocenterC139C2×#354
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #22580748C2semidirect
4. #22580747C2semidirect
5. #354×C139C2semidirect
6. C2×Q8×D139C4semidirect
8. #17984831C4semidirect
9. #17984830C4semidirect
14. C42×D139C4semidirect
21. C2×Dic278C2×C4semidirect
38. C4×Dic139C2×C4semidirect
39. C2×Q8×C139C2×C4semidirect
43. C42×C139C2×C4semidirect
93. D139#354direct (N × H)
94. C139C2×#354semidirect
100. #354D139direct (N × H)
119. C2×Q8C4×D139semidirect
138. C42C4×D139semidirect

Maximal subgroups

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

subgroupindex
#124×D1392
#99×D1392
#225807482
#225807472
#354×C1392
C2×#354139