Finite Group Databasebeta

← #31816648

Subgroups — #31816648

Order 17792.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#22581558C211yesmaximal, characteristic, complemented
2#22581427C211yesmaximal, characteristic, complemented
3#22581278C212yesmaximal, complemented
4#22581254C212yesmaximal, complemented
5#22581149C212yesmaximal, complemented
6#22581089C212yesmaximal, complemented
7#22581066C212yesmaximal, complemented
8C4×D1112C212yesmaximal, complemented
9#433×C139C211yesmaximal, characteristic, complemented
10C22×D556C2211yescharacteristic
11C2×D1112C2212yes—
12C2×D1112C2212yes—
13#17984839C2211yescharacteristic, complemented
14#17984834C2211yescharacteristic, complemented
15#17984827—22no—
16#17984816C2212yes—
17#17984815—22no—
18C4×D556C2212yes—
19C4×D556C2212yes—
20C4×D556C2212yescomplemented
21#17984804—22no—
22#17984801C2211yescharacteristic
23C22⋊C4×D139—22no—
24#17984776C2212yescomplemented
25#17984774C2212yescomplemented
26#17984764C2212yes—
27#17984764C2212yes—
28#17984764C2212yescomplemented
29#17984764C2212yescomplemented
30#117×C139C2211yescharacteristic
31C4⋊C8×C139C2212yescomplemented
32C22⋊C8×C139C2212yes—
33#97×C139C2211yescharacteristic, complemented
34C4×C8×C139C2211yescharacteristic, complemented
35C23×D139—21no—
36C2×D556—24no—
37C2×D556—21no—
38C2×D556—22no—
39C2×D556C2312yes—
40C2×D556C2312yes—
41C2×C22⋊D139—22no—
42C2×C4×D139—22no—
43C2×C4×D139—22no—
44C2×C4×D139—22no—
45D1112—24no—
46D1112—24no—
47C4⋊Dic139C2312yes—
48C4⋊Dic139C2312yes—
49Dic139⋊C4—22no—
50C22⋊Dic139—21no—
51(C2×D139)⋊C4—22no—
52(C2×D139)⋊C4—22no—
53(C2×D139)⋊C4—22no—
54(C2×D139)⋊C4—22no—
55C4×Dic139—21no—
56C22×C4×C139C2311yescharacteristic
57C2×C8×C139C2312yes—
58C2×C8×C139C2312yes—
59C4⋊C4×C139D412yes—
60C22⋊C4×C139D412yes—
61C42×C139C2311yescharacteristic
62C42×C139C2311yescharacteristic
63C22×D139—22no—
64C22×D139—24no—
65C22×D139—22no—
66C22×D139—82no—
67D556—24no—
68D556—22no—
69D556—22no—
70D556—22no—
71D556—82no—
72D556#4114yes—
73C22⋊D139—82no—
74C2×Dic139—22no—
75C2×Dic139—22no—
76C4×D139—82no—
77C4×D139—82no—
78C4×D139—82no—
79C23×C139C2×D411yescharacteristic
80C2×C4×C139—22no—
81C2×C4×C139C2×D412yes—
82C2×C4×C139C2×D412yes—
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2411yescharacteristic
85C8×C139—22no—
86C8×C139—22no—
87C22×C139—21no—
88C22×C139—22no—
89C22×C139C22×D411yescharacteristic
90C2×D139—24no—
91C2×D139—42no—
92C2×D139—42no—
93C2×D139—42no—
94C2×D139—42no—
95C2×D139—42no—
96C2×D139—84no—
97C4×C139—21no—
98C4×C139—22no—
99C4×C139—22no—
100C4×C139C2×#4112yes—
101Dic139—42no—
102Dic139—42no—
103C2×C139—41no—
104C2×C139#52511yescharacteristic
105C2×C139#57612yes—
106D139—44no—
107D139—82no—
108C139#312211yescharacteristic, complemented, Sylow
109#3122—1391nomaximal, Sylow
110#540—1391no—
111#518—1391no—
112#482—1392no—
113#478—1392no—
114#459—1392no—
115#447—1392no—
116#442—1392no—
117C4×D8—1392no—
118#433D13911yescharacteristic, complemented
119C22×D4—1391no—
120C2×D8—1392no—
121C2×D8—1392no—
122#127—1391no—
123#125—1391no—
124#123—2782no—
125#121—2782no—
126#121—1392no—
127C4×D4—2782no—
128C4×D4—1392no—
129C4×D4—1392no—
130C4×D4—1392no—
131#117—1391no—
132#117C2×D13911yescharacteristic
133C2×C22⋊C4—2782no—
134#107—1392no—
135#106—1392no—
136C4⋊C8C2×D13912yescomplemented
137#102—1392no—
138#102—1392no—
139#102—1392no—
140#102—1392no—
141C22⋊C8C2×D13912yes—
142#97C2×D13911yescharacteristic, complemented
143C4×C8C2×D13911yescharacteristic, complemented
144C24—2781no—
145C2×D4—2784no—
146C2×D4—2782no—
147C2×D4—2781no—
148C2×D4—2782no—
149C2×D4—1392no—
150C2×D4—1392no—
151C22×C4—2782no—
152C22×C4—2782no—
153C22×C4—2782no—
154C22×C4C22×D13911yescharacteristic
155D8—2784no—
156D8—2784no—
157C2×C8C22×D13912yes—
158C2×C8C22×D13912yes—
159C4⋊C4—2782no—
160C4⋊C4—1392no—
161C4⋊C4—1392no—
162C4⋊C4D55612yes—
163C22⋊C4—2781no—
164C22⋊C4—2782no—
165C22⋊C4—2782no—
166C22⋊C4—2782no—
167C22⋊C4—2782no—
168C22⋊C4D55612yes—
169C42—2781no—
170C42C22×D13911yescharacteristic
171C42C22×D13911yescharacteristic
172C23—2784no—
173C23—2782no—
174C23—2782no—
175C23—11122no—
176C23C2×D55611yescharacteristic
177D4—2784no—
178D4—2782no—
179D4—2782no—
180D4—2782no—
181D4—11122no—
182D4—11122no—
183D4—1394no—
184C2×C4—22no—
185C2×C4—2782no—
186C2×C4—2782no—
187C2×C4—11122no—
188C2×C4—11122no—
189C2×C4—11122no—
190C2×C4C2×D55611yescharacteristic
191C2×C4C2×D55612yes—
192C2×C4C2×D55612yes—
193C2×C4C23×D13911yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—2784no—
199C22—5562no—
200C22—5562no—
201C22—5562no—
202C22—5562no—
203C22—5562no—
204C22—11124no—
205C22C22×D55611yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—5562no—
210C4—5562no—
211C4#41×D13912yes—
212C2—41no—
213C2—5564no—
214C2—11122no—
215C2#2258146511yescharacteristic
216C2#2258175812yes—
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#433×C139C2
socleC22×C139C22×D4
hypercenter#433D139
hypocenterC139#3122
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #22581558C2semidirect
2. #22581427C2semidirect
3. #22581278C2semidirect
4. #22581254C2semidirect
5. #22581149C2semidirect
6. #22581089C2semidirect
7. #22581066C2semidirect
8. C4×D1112C2semidirect
9. #433×C139C2semidirect
13. #17984839C22semidirect
14. #17984834C22semidirect
20. C4×D556C22semidirect
24. #17984776C22semidirect
25. #17984774C22semidirect
28. #17984764C22semidirect
29. #17984764C22semidirect
31. C4⋊C8×C139C22semidirect
33. #97×C139C22semidirect
34. C4×C8×C139C22semidirect
108. C139#3122semidirect
118. #433D139semidirect
136. C4⋊C8C2×D139semidirect
142. #97C2×D139semidirect
143. C4×C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815582
#225814272
#225812782
#225812542
#225811492
#225810892
#225810662
C4×D11122
#433×C1392
#3122139