Finite Group Databasebeta

← #31806852

Subgroups — #31806852

Order 17792.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#22581464C211yesmaximal, characteristic
2C2×#17984770C212yesmaximal, complemented
3#22580917C211yesmaximal, characteristic, complemented
4#22580713C212yesmaximal, complemented
5C2×#117×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2211yescharacteristic
7C2×#14555769C2212yes—
8#17984825—21no—
9#17984821C412yescomplemented
10#17984816C412yescomplemented
11#17984811—21no—
12C4×C22⋊D139—22no—
13#17984801C2211yescharacteristic
14#17984770—24no—
15C22⋊(C139⋊C8)—22no—
16C23×C4×C139C2211yescharacteristic
17#117×C139—24no—
18C2×C4⋊C4×C139—21no—
19C2×C22⋊C4×C139—21no—
20C2×C42×C139C2212yes—
21#14555785—22no—
22#14555785—22no—
23C2×Dic278C2×C411yescharacteristic
24C2×D556C2×C411yescharacteristic
25C2×C22⋊D139—22no—
26C2×C22⋊D139—21no—
27C2×C4×D139—21no—
28#14555769—22no—
29#14555769—22no—
30C2×C139⋊C8—22no—
31C4⋊Dic139C2×C412yes—
32Dic139⋊C4—22no—
33C22⋊Dic139—22no—
34C22⋊Dic139—21no—
35(C2×D139)⋊C4—22no—
36C4×Dic139—21no—
37C24×C139D411yescharacteristic
38C22×C4×C139—22no—
39C22×C4×C139—22no—
40C22×C4×C139—22no—
41C22×C4×C139C2×C412yes—
42C22×C4×C139D411yescharacteristic
43C22×C4×C139D412yes—
44C22×C4×C139C2311yescharacteristic
45C4⋊C4×C139—24no—
46C22⋊C4×C139—24no—
47C42×C139—22no—
48C42×C139D414yescomplemented
49C22×D139—21no—
50Dic278—22no—
51D556—22no—
52C22⋊D139—44no—
53C22⋊D139—41no—
54C22⋊D139—41no—
55C2×Dic139—22no—
56C2×Dic139—21no—
57C4×D139—42no—
58C139⋊C8—42no—
59C23×C139—21no—
60C23×C139—21no—
61C23×C139—42no—
62C23×C139C22⋊C412yes—
63C23×C139C2×D411yescharacteristic
64C2×C4×C139—21no—
65C2×C4×C139—21no—
66C2×C4×C139—24no—
67C2×C4×C139—24no—
68C2×C4×C139—24no—
69C2×C4×C139—44no—
70C2×C4×C139C22⋊C412yes—
71C2×C4×C139C22×C411yescharacteristic
72C2×C4×C139C2×D412yes—
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139#4112yes—
75C22×C139—22no—
76C22×C139—22no—
77C22×C139—22no—
78C22×C139—22no—
79C22×C139—42no—
80C22×C139—42no—
81C22×C139C2×C22⋊C411yescharacteristic
82C22×C139#12011yescharacteristic
83C22×C139#12311yescharacteristic
84C2×D139—41no—
85C2×D139—42no—
86C4×C139—22no—
87C4×C139—44no—
88C4×C139C4×D412yes—
89C4×C139#12112yes—
90Dic139—41no—
91Dic139—42no—
92C2×C139—21no—
93C2×C139—21no—
94C2×C139—42no—
95C2×C139#38611yescharacteristic
96C2×C139#42112yes—
97D139—81no—
98C139#189711yescharacteristic, complemented, Sylow
99#1897—1391nomaximal, Sylow
100#525—1391no—
101C2×#117D13911yescharacteristic, complemented
102C2×#104—1392no—
103#407—1391no—
104#339—1392no—
105C2×#41—1391no—
106C23×C4C2×D13911yescharacteristic
107C2×M16—1392no—
108#123—2781no—
109C22⋊Q8—1392no—
110#121—1392no—
111#120—2781no—
112C4×D4—2782no—
113#117—24no—
114#117—1391no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D13912yes—
118#104—2784no—
119C22⋊C8—2782no—
120C24C22⋊D13911yescharacteristic
121#41—2782no—
122#41—2782no—
123C2×Q8—1391no—
124C2×D4—2782no—
125C2×D4—2781no—
126C2×D4—1391no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—2781no—
131C22×C4C4×D13912yes—
132C22×C4C22⋊D13911yescharacteristic
133C22×C4D55612yes—
134C22×C4C22×D13911yescharacteristic
135M16—2782no—
136M16—2782no—
137C2×C8—2782no—
138C4⋊C4—24no—
139C4⋊C4—2782no—
140C4⋊C4—1392no—
141C22⋊C4—24no—
142C22⋊C4—2782no—
143C22⋊C4—2781no—
144C22⋊C4—2782no—
145C42—22no—
146C42—2781no—
147C42C22⋊D13914yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—2781no—
152C23(C2×D139)⋊C412yes—
153C23C2×C22⋊D13911yescharacteristic
154Q8—2782no—
155D4—2782no—
156D4—5564no—
157D4—5561no—
158D4—5561no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—2782no—
166C2×C4—2781no—
167C2×C4—5562no—
168C2×C4(C2×D139)⋊C412yes—
169C2×C4C2×C4×D13911yescharacteristic
170C2×C4C2×C22⋊D13912yes—
171C2×C4C2×D55611yescharacteristic
172C2×C4#1455578512yes—
173C8—5562no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—5561no—
181C22—5562no—
182C22C2×(C2×D139)⋊C411yescharacteristic
183C22#1798481111yescharacteristic
184C22#1798482511yescharacteristic
185C4—22no—
186C4—44no—
187C4—5561no—
188C4—5562no—
189C4C4×C22⋊D13912yes—
190C4#1798481612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—11121no—
195C2#2258083211yescharacteristic
196C2#2258097112yes—
subgroupG/H
centerC2×C4C2×D556
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
FittingC2×#117×C139C2
socleC22×C139C2×C22⋊C4
prime radical#22581464C2
cosocleC22×C4×C139C23
hypercenterC2×#117D139
hypocenterC139#1897
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#17984770C2semidirect
3. #22580917C2semidirect
4. #22580713C2semidirect
5. C2×#117×C139C2semidirect
9. #17984821C4semidirect
10. #17984816C4semidirect
48. C42×C139D4semidirect
98. C139#1897semidirect
101. C2×#117D139semidirect
147. C42C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225814642
C2×#179847702
#225809172
#225807132
C2×#117×C1392
#1897139