Finite Group Databasebeta

← #31804943

Subgroups — #31804943

Order 17792.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#22581487C211yesmaximal, characteristic
2#22580819C211yesmaximal, characteristic, complemented
3#22580691C212yesmaximal, complemented
4#22580688C212yesmaximal
5#432×C139C211yesmaximal, characteristic, complemented
6#17984836—21no—
7#17984834C411yescharacteristic, complemented
8#17984830C411yescharacteristic, complemented
9#17984825—21no—
10#17984821C2211yescharacteristic
11#17984816C2211yescharacteristic
12C4×Dic278C411yescharacteristic, complemented
13C4×D556C411yescharacteristic, complemented
14C4×C22⋊D139—21no—
15#17984799—21no—
16C2×C4⋊Dic139—21no—
17C139⋊#95—21no—
18C139⋊#95C2212yes—
19C2×C42×C139C2211yescharacteristic
20C4⋊C8×C139—21no—
21C22⋊C8×C139C2212yes—
22#97×C139—21no—
23C2×Dic278C2×C411yescharacteristic
24C2×D556C2×C411yescharacteristic
25C2×C22⋊D139—21no—
26C22×Dic139—22no—
27C2×C4×D139—21no—
28C4⋊Dic139—42no—
29C4⋊Dic139C2×C411yescharacteristic
30C4⋊Dic139C2×C411yescharacteristic
31Dic139⋊C4—21no—
32Dic139⋊C4—21no—
33Dic139⋊C4—21no—
34Dic139⋊C4—21no—
35C22⋊Dic139—21no—
36(C2×D139)⋊C4—21no—
37(C2×D139)⋊C4—21no—
38(C2×D139)⋊C4—21no—
39(C2×D139)⋊C4—21no—
40C4×Dic139—21no—
41C22×C4×C139D411yescharacteristic
42C22×C4×C139D411yescharacteristic
43C22×C4×C139C2311yescharacteristic
44C2×C8×C139—22no—
45C42×C139C2×C411yescharacteristic
46C42×C139C2×C411yescharacteristic
47C42×C139D411yescharacteristic
48C42×C139D411yescharacteristic
49C22×D139—21no—
50Dic278—41no—
51D556—41no—
52C22⋊D139—41no—
53C22⋊D139—41no—
54C2×Dic139—21no—
55C2×Dic139—21no—
56C2×Dic139—21no—
57C2×Dic139—42no—
58C2×Dic139—42no—
59C2×Dic139—42no—
60C4×D139—42no—
61C23×C139C2×D411yescharacteristic
62C2×C4×C139—21no—
63C2×C4×C139—21no—
64C2×C4×C139—41no—
65C2×C4×C139—41no—
66C2×C4×C139C22⋊C411yescharacteristic
67C2×C4×C139C22⋊C411yescharacteristic
68C2×C4×C139C22⋊C411yescharacteristic
69C2×C4×C139C22⋊C411yescharacteristic
70C2×C4×C139C22×C411yescharacteristic
71C2×C4×C139C2×D411yescharacteristic
72C8×C139—42no—
73C22×C139—21no—
74C22×C139—21no—
75C22×C139C2×C22⋊C411yescharacteristic
76C22×C139AGL(1,ℤ/8)11yescharacteristic
77C22×C139#13711yescharacteristic
78C2×D139—41no—
79C2×D139—41no—
80C2×D139—41no—
81C4×C139—21no—
82C4×C139—21no—
83C4×C139—21no—
84C4×C139—21no—
85C4×C139—21no—
86C4×C139—21no—
87Dic139—41no—
88Dic139—41no—
89Dic139—41no—
90Dic139—82no—
91C2×C139—21no—
92C2×C139—21no—
93C2×C139#41011yescharacteristic
94C2×C139#41711yescharacteristic
95C2×C139#42111yescharacteristic
96D139—81no—
97C139#151211yescharacteristic, complemented, Sylow
98#1512—1391nomaximal, Sylow
99#529—1391no—
100#432D13911yescharacteristic, complemented
101#382—1391no—
102#328—1392no—
103#327—1392no—
104#126—2781no—
105#125—1391no—
106#124—1391no—
107#123—2781no—
108C22⋊Q8—1391no—
109#121—1391no—
110C4×Q8—1391no—
111C4×D4—2781no—
112C4×D4—1391no—
113#117—2781no—
114C2×C4⋊C4—2781no—
115C2×C42C2×D13911yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C2×D13912yes—
118#97—21no—
119#95—2781no—
120#95—1392no—
121C2×Q8—1391no—
122C2×D4—2781no—
123C2×D4—1391no—
124C22×C4—2781no—
125C22×C4—2782no—
126C22×C4D55611yescharacteristic
127C22×C4D55611yescharacteristic
128C22×C4C22×D13911yescharacteristic
129C2×C8—22no—
130C4⋊C4—2781no—
131C4⋊C4—2781no—
132C4⋊C4—2781no—
133C4⋊C4—2781no—
134C4⋊C4—5562no—
135C4⋊C4—1391no—
136C4⋊C4—1391no—
137C22⋊C4—2781no—
138C22⋊C4—2781no—
139C22⋊C4—2781no—
140C22⋊C4—2781no—
141C22⋊C4—2781no—
142C42—2781no—
143C42C4×D13911yescharacteristic
144C42C4×D13911yescharacteristic
145C42C22⋊D13911yescharacteristic
146C42C22⋊D13911yescharacteristic
147C23—2781no—
148C23C2×D55611yescharacteristic
149Q8—5561no—
150D4—5561no—
151D4—5561no—
152D4—5561no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—2781no—
158C2×C4—2781no—
159C2×C4—2781no—
160C2×C4—5562no—
161C2×C4—5562no—
162C2×C4—5562no—
163C2×C4—5562no—
164C2×C4(C2×D139)⋊C411yescharacteristic
165C2×C4(C2×D139)⋊C411yescharacteristic
166C2×C4(C2×D139)⋊C411yescharacteristic
167C2×C4(C2×D139)⋊C411yescharacteristic
168C2×C4C2×C4×D13911yescharacteristic
169C2×C4C2×C22⋊D13911yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—5561no—
174C22—5561no—
175C22—5561no—
176C22C2×(C2×D139)⋊C411yescharacteristic
177C22#1798487011yescharacteristic
178C22#1798487511yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—5561no—
186C4—5561no—
187C4—5561no—
188C4—11122no—
189C2—21no—
190C2—21no—
191C2—11121no—
192C2#2258092611yescharacteristic
193C2#2258095511yescharacteristic
194C2#2258096911yescharacteristic
subgroupG/H
centerC22C2×(C2×D139)⋊C4
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#432×C139C2
socleC22×C139C2×C22⋊C4
prime radical#17984816C22
cosocleC22×C4×C139C23
hypercenter#432D139
hypocenterC139#1512
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #22580819C2semidirect
3. #22580691C2semidirect
5. #432×C139C2semidirect
7. #17984834C4semidirect
8. #17984830C4semidirect
12. C4×Dic278C4semidirect
13. C4×D556C4semidirect
97. C139#1512semidirect
100. #432D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
#225808192
#225806912
#225806882
#432×C1392
#1512139