Finite Group Databasebeta

← #31806880

Subgroups — #31806880

Order 17792.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#17984873C211yesmaximal, characteristic
2#22581719C211yesmaximal, characteristic
3#22580969C211yesmaximal, characteristic
4#22580962C211yesmaximal, characteristic, complemented
5#22580725C211yesmaximal, characteristic, complemented
6C139⋊#338C211yesmaximal, characteristic, complemented
7C2×#101×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9#17984873—22no—
10#17984873—22no—
11C2×#14555775C412yescomplemented
12C2×#14555772C412yescomplemented
13#17984850—22no—
14#17984848—22no—
15C2×#14555769C2211yescharacteristic
16C2×#14555769C2211yescharacteristic
17M16×D139—22no—
18#17984801C2211yescharacteristic
19#17984768—22no—
20#17984766—22no—
21C22×Q8×C139C2211yescharacteristic
22C2×M16×C139C2211yescharacteristic
23C2×M16×C139C2211yescharacteristic
24#101×C139—22no—
25#14555785—21no—
26#14555785—21no—
27#14555785D412yes—
28#14555785D412yes—
29C2×Dic278C2×C411yescharacteristic
30C2×D556C2×C411yescharacteristic
31C2×C22⋊D139—21no—
32C2×C4×D139—21no—
33#14555775—24no—
34#14555772—24no—
35#14555769—21no—
36#14555769—21no—
37#14555769—21no—
38#14555769—21no—
39#14555768—24no—
40C2×C139⋊C8C2×C412yes—
41C2×C139⋊C8D412yes—
42C8×D139—24no—
43C4⋊Dic139—21no—
44C22⋊Dic139—21no—
45C4×Dic139—21no—
46C2×Q8×C139—21no—
47C2×Q8×C139—21no—
48C2×Q8×C139—21no—
49C2×Q8×C139—21no—
50C2×Q8×C139—21no—
51C2×Q8×C139C2×C412yes—
52C22×C4×C139—21no—
53C22×C4×C139C2311yescharacteristic
54M16×C139—21no—
55M16×C139—21no—
56M16×C139—21no—
57M16×C139D412yes—
58C2×C8×C139—21no—
59C2×C8×C139—21no—
60C22×D139—21no—
61Dic278—21no—
62Dic278C22⋊C412yes—
63D556—21no—
64D556C22⋊C412yes—
65C22⋊D139—22no—
66C22⋊D139—22no—
67C2×Dic139—21no—
68C2×Dic139—41no—
69C4×D139—22no—
70C4×D139—22no—
71C139⋊C8—22no—
72C139⋊C8—22no—
73C23×C139#4111yescharacteristic
74Q8×C139—22no—
75Q8×C139—22no—
76Q8×C139—41no—
77Q8×C139—41no—
78C2×C4×C139—22no—
79C2×C4×C139—41no—
80C2×C4×C139—41no—
81C2×C4×C139C22×C411yescharacteristic
82C2×C4×C139C2×D411yescharacteristic
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2×D411yescharacteristic
85C2×C4×C139C2×D411yescharacteristic
86C2×C4×C139#4111yescharacteristic
87C8×C139—22no—
88C8×C139—41no—
89C22×C139—41no—
90C22×C139C4×D411yescharacteristic
91C22×C139#12111yescharacteristic
92C22×C139#12311yescharacteristic
93C2×D139—22no—
94C2×D139—81no—
95C4×C139—42no—
96C4×C139C2×C22⋊C411yescharacteristic
97C4×C139C4×D411yescharacteristic
98C4×C139#12011yescharacteristic
99C4×C139#12111yescharacteristic
100Dic139—22no—
101Dic139—81no—
102C2×C139—21no—
103C2×C139—21no—
104C2×C139—21no—
105C2×C139#38611yescharacteristic
106D139—42no—
107C139#190211yescharacteristic, complemented, Sylow
108#1902—1391nomaximal, Sylow
109C2×#137—1391no—
110#568—1391no—
111#421—1391no—
112#419—1391no—
113C2×#101D13911yescharacteristic, complemented
114#344—1391no—
115#338—1391no—
116C2×#41—1391no—
117C22×Q8C2×D13911yescharacteristic
118#137—2782no—
119#137—2782no—
120C2×Q16—1392no—
121C2×SD16—1392no—
122#131—2782no—
123#131—2782no—
124C2×M16—2782no—
125C2×M16—1391no—
126C2×M16—1391no—
127C2×M16C2×D13911yescharacteristic
128C2×M16C2×D13911yescharacteristic
129#117—1391no—
130#104—2782no—
131#103—2782no—
132#101—22no—
133#41—2781no—
134#41—2781no—
135#41—1392no—
136#41—1392no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—1391no—
143C2×Q8C4×D13912yes—
144C2×D4—2781no—
145C2×D4—1391no—
146C22×C4—21no—
147C22×C4—2781no—
148C22×C4C22×D13911yescharacteristic
149Q16—2784no—
150SD16—2784no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—2784no—
155M16—2781no—
156M16—2781no—
157M16—2781no—
158M16—2781no—
159M16C22⋊D13912yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—2784no—
163C2×C8—1392no—
164C2×C8—1392no—
165C4⋊C4—2781no—
166C22⋊C4—2781no—
167C42—2781no—
168C23—2781no—
169C23#1455578511yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—2781no—
175Q8—1392no—
176D4—2782no—
177D4—2782no—
178D4—2781no—
179D4—1392no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—2781no—
184C2×C4—2782no—
185C2×C4—2782no—
186C2×C4—5561no—
187C2×C4C2×C4×D13911yescharacteristic
188C2×C4D4×D13911yescharacteristic
189C2×C4D4×D13911yescharacteristic
190C2×C4D4×D13911yescharacteristic
191C2×C4C2×C22⋊D13911yescharacteristic
192C2×C4#1455578411yescharacteristic
193C8—22no—
194C8—41no—
195C8—2782no—
196C8—2782no—
197C22—41no—
198C22—2782no—
199C22—11121no—
200C22C4×C22⋊D13911yescharacteristic
201C22#1798481511yescharacteristic
202C22#1798482411yescharacteristic
203C4—42no—
204C4—2782no—
205C4—11121no—
206C4C22⋊C4×D13911yescharacteristic
207C4(C22⋊D139)⋊C411yescharacteristic
208C4#1798481011yescharacteristic
209C4#1798481311yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—5562no—
214C2#2258082911yescharacteristic
subgroupG/H
centerC2#22580829
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
FittingC2×#101×C139C2
socleC2×C139#386
prime radicalC2×#14555785C22
cosocleC22×C4×C139C23
hypercenterC2×#101D139
hypocenterC139#1902
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
4. #22580962C2semidirect
5. #22580725C2semidirect
6. C139⋊#338C2semidirect
7. C2×#101×C139C2semidirect
11. C2×#14555775C4semidirect
12. C2×#14555772C4semidirect
107. C139#1902semidirect
113. C2×#101D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848732
#225817192
#225809692
#225809622
#225807252
C139⋊#3382
C2×#101×C1392
#1902139