Finite Group Databasebeta

← #31816792

Subgroups — #31816792

Order 17792.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#22581506C211yesmaximal, characteristic, complemented
2C2×#17984831C211yesmaximal, characteristic
3#22581314C214yesmaximal, complemented
4#22581309C214yesmaximal, complemented
5#22580962C211yesmaximal, characteristic, complemented
6#22580959C211yesmaximal, characteristic
7#22580957C211yesmaximal, characteristic
8M16×Dic139C211yesmaximal, characteristic, complemented
9#419×C139C211yesmaximal, characteristic, complemented
10C22×D556C2211yescharacteristic
11C2×#14555769C2211yescharacteristic
12#17984841C2212yescomplemented
13#17984833C2212yescomplemented
14#17984831—22no—
15#17984831C2212yes—
16#17984831C2212yes—
17#17984819—22no—
18C4×Dic278—22no—
19#17984801C2211yescharacteristic
20C2×(C2×D139)⋊C4—22no—
21C2×C4×Dic139C2211yescharacteristic
22#17984766C2214yescomplemented
23#17984764C2214yes—
24#17984762C2214yes—
25#17984752C2212yescomplemented
26C8×Dic139C2212yescomplemented
27C22×Q8×C139C2211yescharacteristic
28C2×M16×C139C2211yescharacteristic
29#117×C139C2211yescharacteristic
30#103×C139C2214yescomplemented
31C23×D139—21no—
32C2×Dic278—22no—
33C2×D556—21no—
34C2×D556—22no—
35C2×D556—22no—
36C2×D556C2312yes—
37C22×Dic139D412yes—
38#14555769—22no—
39C2×C139⋊C8C2312yes—
40C4⋊Dic139—22no—
41C4⋊Dic139C2312yes—
42Dic139⋊C4—22no—
43Dic139⋊C4—22no—
44C22⋊Dic139—21no—
45(C2×D139)⋊C4—24no—
46(C2×D139)⋊C4—24no—
47C4×Dic139—21no—
48C4×Dic139D412yes—
49C4×Dic139C2311yescharacteristic
50C4×Dic139C2311yescharacteristic
51C2×Q8×C139—21no—
52C2×Q8×C139—22no—
53C2×Q8×C139—22no—
54C2×Q8×C139C2312yes—
55C22×C4×C139—21no—
56C22×C4×C139C2311yescharacteristic
57M16×C139—22no—
58C2×C8×C139C2312yes—
59C4⋊C4×C139C2312yes—
60C22⋊C4×C139—21no—
61C42×C139—21no—
62C22×D139—22no—
63C22×D139—44no—
64C22×D139—42no—
65Dic278—44no—
66D556—22no—
67D556—22no—
68D556—42no—
69C2×Dic139—22no—
70C2×Dic139—42no—
71C2×Dic139C2×D412yes—
72C2×Dic139C2×D412yes—
73C139⋊C8—22no—
74C23×C139C2×D411yescharacteristic
75Q8×C139—22no—
76Q8×C139—22no—
77Q8×C139—42no—
78C2×C4×C139—22no—
79C2×C4×C139—22no—
80C2×C4×C139—42no—
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139#4112yes—
83C2×C4×C139#4112yes—
84C2×C4×C139C2411yescharacteristic
85C8×C139—22no—
86C22×C139—22no—
87C22×C139#12412yes—
88C22×C139C22×D411yescharacteristic
89C2×D139—42no—
90C2×D139—44no—
91C2×D139—84no—
92C4×C139—42no—
93C4×C139—42no—
94C4×C139#12412yes—
95C4×C139C2×#4111yescharacteristic
96C4×C139C2×#4111yescharacteristic
97Dic139—22no—
98Dic139—22no—
99Dic139—42no—
100C2×C139—22no—
101C2×C139C2×#12411yescharacteristic
102C2×C139#57512yes—
103D139—82no—
104C139#314011yescharacteristic, complemented, Sylow
105#3140—1391nomaximal, Sylow
106#533—1391no—
107C2×#124—1391no—
108#489—1394no—
109#488—1394no—
110#419—1391no—
111#419D13911yescharacteristic, complemented
112#418—1391no—
113#418—1391no—
114C4×M16—1391no—
115C22×Q8C2×D13911yescharacteristic
116C22×D4—1391no—
117C2×M16—1391no—
118C2×M16C2×D13911yescharacteristic
119C4⋊Q8—1392no—
120#125—1392no—
121#124—2782no—
122#124—1392no—
123#124—1392no—
124C22⋊Q8—2782no—
125C4×Q8—2782no—
126#117—1391no—
127#117C2×D13911yescharacteristic
128C2×C22⋊C4—2782no—
129C2×C42—1391no—
130#103—1394no—
131#103C2×D13914yescomplemented
132#102—1394no—
133#102—1394no—
134#97—1392no—
135C4×C8—1392no—
136C24—2781no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—2782no—
141C2×Q8C22×D13912yes—
142C2×D4—2781no—
143C2×D4—2782no—
144C2×D4—2782no—
145C2×D4—1392no—
146C22×C4—21no—
147C22×C4—1392no—
148C22×C4C22×D13911yescharacteristic
149M16—22no—
150M16—2782no—
151C2×C8—1392no—
152C2×C8C22×D13912yes—
153C4⋊C4—2782no—
154C4⋊C4—2782no—
155C4⋊C4—2782no—
156C4⋊C4—1392no—
157C4⋊C4C22×D13912yes—
158C22⋊C4—21no—
159C22⋊C4—2784no—
160C22⋊C4—2784no—
161C22⋊C4—2781no—
162C42—21no—
163C42—2781no—
164C42—1392no—
165C42—1391no—
166C42—1391no—
167C23—2782no—
168C23—5564no—
169C23—5562no—
170C23D4×D13911yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—42no—
174Q8—5564no—
175D4—2782no—
176D4—2782no—
177D4—5562no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—2782no—
182C2×C4—5562no—
183C2×C4—1392no—
184C2×C4—1392no—
185C2×C4D4×D13911yescharacteristic
186C2×C4#1455578412yes—
187C2×C4#1455578512yes—
188C2×C4C23×D13911yescharacteristic
189C8—22no—
190C8—2782no—
191C22—22no—
192C22—5562no—
193C22—5564no—
194C22—11124no—
195C22#1798482812yes—
196C22C2×D4×D13911yescharacteristic
197C4—42no—
198C4—42no—
199C4—2782no—
200C4—2782no—
201C4—5562no—
202C4#1798482812yes—
203C4C2×#1455578411yescharacteristic
204C4C2×#1455578511yescharacteristic
205C2—22no—
206C2—11122no—
207C2C2×#1798482811yescharacteristic
208C2#2258175212yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#419×C139C2
socleC22×C139C22×D4
prime radicalC22×D556C22
hypercenter#419D139
hypocenterC139#3140
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #22581506C2semidirect
3. #22581314C2semidirect
4. #22581309C2semidirect
5. #22580962C2semidirect
8. M16×Dic139C2semidirect
9. #419×C139C2semidirect
12. #17984841C22semidirect
13. #17984833C22semidirect
22. #17984766C22semidirect
25. #17984752C22semidirect
26. C8×Dic139C22semidirect
30. #103×C139C22semidirect
104. C139#3140semidirect
111. #419D139semidirect
131. #103C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815062
C2×#179848312
#225813142
#225813092
#225809622
#225809592
#225809572
M16×Dic1392
#419×C1392
#3140139