Finite Group Databasebeta

← #31808091

Subgroups — #31808091

Order 17792.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#22581527C211yesmaximal, characteristic
2C2×#17984761C211yesmaximal, characteristic, complemented
3#22580751C212yesmaximal, complemented
4#22580749C212yesmaximal, complemented
5C2×#101×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C411yescharacteristic
7C2×#14555769—21no—
8#17984840C411yescharacteristic
9#17984840C2211yescharacteristic
10#17984831C411yescharacteristic
11#17984831C2211yescharacteristic
12#17984825—21no—
13#17984825—21no—
14#17984818—21no—
15#17984818—21no—
16#17984801C411yescharacteristic
17#17984761—21no—
18#17984761C2212yes—
19C22×Q8×C139C2211yescharacteristic
20C2×M16×C139—21no—
21#101×C139—21no—
22#101×C139C2212yes—
23#14555785—41no—
24#14555785—41no—
25C2×Dic278C2×C411yescharacteristic
26C2×D556C2×C411yescharacteristic
27C2×C22⋊D139—21no—
28C2×C4×D139—21no—
29#14555769—22no—
30#14555769—41no—
31C2×C139⋊C8—41no—
32C4⋊Dic139—21no—
33Dic139⋊C4—21no—
34Dic139⋊C4—21no—
35Dic139⋊C4—21no—
36Dic139⋊C4—21no—
37C22⋊Dic139—21no—
38(C2×D139)⋊C4—21no—
39(C2×D139)⋊C4—21no—
40(C2×D139)⋊C4—21no—
41(C2×D139)⋊C4—21no—
42C4×Dic139C2×C411yescharacteristic
43C4×Dic139C2×C411yescharacteristic
44C2×Q8×C139—41no—
45C2×Q8×C139—41no—
46C2×Q8×C139C2×C411yescharacteristic
47C2×Q8×C139D411yescharacteristic
48C2×Q8×C139D411yescharacteristic
49C2×Q8×C139C2311yescharacteristic
50C22×C4×C139C2×C411yescharacteristic
51C22×C4×C139D411yescharacteristic
52C22×C4×C139D411yescharacteristic
53M16×C139—22no—
54M16×C139—41no—
55C2×C8×C139—41no—
56C22×D139—21no—
57Dic278—41no—
58D556—41no—
59C22⋊D139—41no—
60C22⋊D139—41no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C4×D139—42no—
65C139⋊C8—42no—
66C23×C139C22⋊C411yescharacteristic
67Q8×C139—41no—
68Q8×C139—41no—
69Q8×C139—41no—
70Q8×C139—41no—
71C2×C4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139—21no—
74C2×C4×C139—21no—
75C2×C4×C139—21no—
76C2×C4×C139—21no—
77C2×C4×C139C22⋊C411yescharacteristic
78C2×C4×C139C22⋊C411yescharacteristic
79C2×C4×C139C22⋊C411yescharacteristic
80C2×C4×C139C22×C411yescharacteristic
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139C2×D411yescharacteristic
83C8×C139—42no—
84C22×C139—41no—
85C22×C139#9911yescharacteristic
86C22×C139#9911yescharacteristic
87C22×C139C2×C22⋊C411yescharacteristic
88C2×D139—42no—
89C2×D139—41no—
90C4×C139—21no—
91C4×C139—21no—
92C4×C139—21no—
93C4×C139—21no—
94C4×C139—21no—
95C4×C139—21no—
96Dic139—41no—
97Dic139—41no—
98Dic139—41no—
99C2×C139—21no—
100C2×C139—21no—
101C2×C139—21no—
102C2×C139C2×#9911yescharacteristic
103D139—81no—
104C139#213311yescharacteristic, complemented, Sylow
105#2133—1391nomaximal, Sylow
106#536—1391no—
107C2×#101—1391no—
108C2×#101D13911yescharacteristic, complemented
109#356—1392no—
110#355—1392no—
111C2×#41—1391no—
112C22×Q8C2×D13911yescharacteristic
113C2×M16—21no—
114C2×M16—2781no—
115C4⋊Q8—1391no—
116C4⋊Q8—1391no—
117#124—1391no—
118#124—1391no—
119#123—2781no—
120#123—2781no—
121C22⋊Q8—2781no—
122C22⋊Q8—2781no—
123#117—1391no—
124#101—21no—
125#101—2781no—
126#101—1392no—
127#101C2×D13912yes—
128#41—5561no—
129#41—5561no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—1391no—
133C2×Q8C4×D13911yescharacteristic
134C2×Q8C22⋊D13911yescharacteristic
135C2×Q8D55611yescharacteristic
136C2×Q8C22×D13911yescharacteristic
137C2×D4—2781no—
138C2×D4—1391no—
139C22×C4—2781no—
140C22×C4C4×D13911yescharacteristic
141C22×C4C22⋊D13911yescharacteristic
142C22×C4D55611yescharacteristic
143M16—22no—
144M16—41no—
145M16—2782no—
146M16—5561no—
147C2×C8—41no—
148C2×C8—5561no—
149C4⋊C4—2781no—
150C4⋊C4—2781no—
151C4⋊C4—2781no—
152C4⋊C4—2781no—
153C4⋊C4—2781no—
154C22⋊C4—2781no—
155C22⋊C4—2781no—
156C22⋊C4—2781no—
157C22⋊C4—2781no—
158C22⋊C4—2781no—
159C42—1391no—
160C42—1391no—
161C23—2781no—
162C23(C2×D139)⋊C411yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—5561no—
168D4—5561no—
169D4—5561no—
170D4—5561no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—2781no—
178C2×C4—2781no—
179C2×C4—2781no—
180C2×C4—5562no—
181C2×C4(C2×D139)⋊C411yescharacteristic
182C2×C4(C2×D139)⋊C411yescharacteristic
183C2×C4(C2×D139)⋊C411yescharacteristic
184C2×C4C2×C4×D13911yescharacteristic
185C2×C4C2×C22⋊D13911yescharacteristic
186C2×C4C2×D55611yescharacteristic
187C8—42no—
188C8—5562no—
189C22—41no—
190C22—5562no—
191C22—5561no—
192C22#1798475611yescharacteristic
193C22#1798475611yescharacteristic
194C22C2×(C2×D139)⋊C411yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—5561no—
202C4—5561no—
203C4—5561no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—11121no—
208C2C2×#1798475611yescharacteristic
subgroupG/H
centerC2C2×#17984756
commutatorC2×C4×C139C22×C4
FrattiniC2×Q8C22×D139
FittingC2×#101×C139C2
socleC2×C139C2×#99
prime radicalC2×#14555785C4
cosocleC2×Q8×C139C23
hypercenterC2×#101D139
hypocenterC139#2133
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#17984761C2semidirect
3. #22580751C2semidirect
4. #22580749C2semidirect
5. C2×#101×C139C2semidirect
104. C139#2133semidirect
108. C2×#101D139semidirect

Maximal subgroups

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

subgroupindex
#225815272
C2×#179847612
#225807512
#225807492
C2×#101×C1392
#2133139