Finite Group Databasebeta

← #31817866

Subgroups — #31817866

Order 17792.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#22581576C212yesmaximal, complemented
2#22581246C212yesmaximal, complemented
3#22581232C212yesmaximal, complemented
4#22581201C212yesmaximal, complemented
5#22581189C211yesmaximal, characteristic
6#22581177C212yesmaximal, complemented
7#22581171C212yesmaximal, complemented
8#22580979C211yesmaximal, characteristic, complemented
9#467×C139C211yesmaximal, characteristic, complemented
10C2×#14555772C2212yes—
11C2×D1112C2211yescharacteristic
12C2×#14555769C2211yescharacteristic
13#17984841C2212yes—
14#17984837—22no—
15#17984831C2212yes—
16#17984828—22no—
17#17984824—22no—
18#17984822—22no—
19#17984816C2212yes—
20Q8×Dic139C2212yes—
21#17984804C2212yes—
22#17984801C2211yescharacteristic
23#17984776C2211yescharacteristic
24#17984775C2212yes—
25Dic139⋊C8C2212yes—
26Dic139⋊C8C2212yes—
27#17984766C2212yes—
28#17984764C2212yes—
29#17984762C2212yes—
30C2×Q16×C139C2211yescharacteristic
31C22×C8×C139C2211yescharacteristic
32C22⋊Q8×C139C2212yes—
33#107×C139C2211yescharacteristic
34#103×C139C2212yes—
35C2×Dic278—22no—
36C2×D556C2312yes—
37C2×C22⋊D139—22no—
38C2×C4×D139—22no—
39#14555772—42no—
40D1112—41no—
41#14555769—41no—
42C2×C139⋊C8C2312yes—
43C4⋊Dic139—22no—
44C4⋊Dic139D411yescharacteristic
45C4⋊Dic139D411yescharacteristic
46C4⋊Dic139C2312yes—
47Dic139⋊C4—22no—
48C22⋊Dic139D412yes—
49(C2×D139)⋊C4—22no—
50(C2×D139)⋊C4—22no—
51(C2×D139)⋊C4—22no—
52(C2×D139)⋊C4—22no—
53C4×Dic139—22no—
54C4×Dic139C2312yes—
55C2×Q8×C139C2312yes—
56C22×C4×C139C2311yescharacteristic
57Q16×C139—41no—
58C2×C8×C139—41no—
59C2×C8×C139C2311yescharacteristic
60C2×C8×C139C2311yescharacteristic
61C4⋊C4×C139—22no—
62C4⋊C4×C139C2312yes—
63C22⋊C4×C139—22no—
64C22×D139—22no—
65Dic278—82no—
66D556—22no—
67D556—22no—
68C22⋊D139—82no—
69C2×Dic139—22no—
70C2×Dic139C2×D412yes—
71C2×Dic139C2×D412yes—
72C4×D139—82no—
73C139⋊C8—22no—
74C23×C139C2×D411yescharacteristic
75Q8×C139—22no—
76Q8×C139—22no—
77C2×C4×C139—21no—
78C2×C4×C139—21no—
79C2×C4×C139—22no—
80C2×C4×C139—22no—
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139C2411yescharacteristic
83C8×C139—21no—
84C8×C139—21no—
85C22×C139—21no—
86C22×C139—21no—
87C22×C139—21no—
88C22×C139C22×D411yescharacteristic
89C2×D139—42no—
90C2×D139—42no—
91C2×D139—42no—
92C4×C139—21no—
93C4×C139—42no—
94C4×C139—42no—
95C4×C139H(5,𝔽2)11yescharacteristic
96C4×C1392−1+411yescharacteristic
97Dic139—22no—
98Dic139—22no—
99Dic139—42no—
100C2×C139—41no—
101C2×C139#53711yescharacteristic
102C2×C139#57611yescharacteristic
103C2×C139#57811yescharacteristic
104D139—82no—
105C139#326211yescharacteristic, complemented, Sylow
106#3262—1391nomaximal, Sylow
107#542—1392no—
108#477—1392no—
109#474—1392no—
110#468—1392no—
111#467D13911yescharacteristic, complemented
112#466—1391no—
113#464—1392no—
114#463—1392no—
115#424—1391no—
116C2×Q16C2×D13911yescharacteristic
117C2×SD16—1392no—
118C2×D8—1391no—
119C2×M16—1391no—
120C22×C8C2×D13911yescharacteristic
121C4⋊Q8—1392no—
122#126—2782no—
123#124—2782no—
124#124—1392no—
125#123—2782no—
126C22⋊Q8—2782no—
127C22⋊Q8C2×D13912yes—
128#121—1392no—
129C4×Q8—1392no—
130C4×D4—1392no—
131#117—1391no—
132#107—1391no—
133#107—1392no—
134#107C2×D13911yescharacteristic
135C4⋊C8—1392no—
136C4⋊C8—1392no—
137#103—1392no—
138#103C2×D13912yes—
139#102—1392no—
140#102—1392no—
141C2×Q8—2782no—
142C2×Q8C22×D13912yes—
143C2×D4—2782no—
144C2×D4—1392no—
145C22×C4—2782no—
146C22×C4C22×D13911yescharacteristic
147Q16—41no—
148SD16—5562no—
149D8—5561no—
150M16—5561no—
151C2×C8—41no—
152C2×C8—1392no—
153C2×C8C22×D13911yescharacteristic
154C2×C8C22×D13911yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—2782no—
157C4⋊C4—2782no—
158C4⋊C4—1392no—
159C4⋊C4—1391no—
160C4⋊C4—1391no—
161C4⋊C4C22×D13912yes—
162C22⋊C4—22no—
163C22⋊C4—2782no—
164C22⋊C4—2782no—
165C22⋊C4—2782no—
166C22⋊C4—2782no—
167C22⋊C4—1392no—
168C42—2782no—
169C42—1392no—
170C23—2782no—
171C23D4×D13911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—11122no—
175D4—2782no—
176D4—2782no—
177D4—11122no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—2782no—
183C2×C4—11122no—
184C2×C4—1392no—
185C2×C4—1392no—
186C2×C4D4×D13911yescharacteristic
187C2×C4C23×D13911yescharacteristic
188C8—21no—
189C8—21no—
190C8—2782no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—5562no—
195C22—5562no—
196C22—5562no—
197C22C2×D4×D13911yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—2782no—
202C4—2782no—
203C4—5562no—
204C4#1798488711yescharacteristic
205C4#1798488911yescharacteristic
206C2—41no—
207C2—11122no—
208C2#2258153011yescharacteristic
209C2#2258175511yescharacteristic
210C2#2258176611yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#467×C139C2
socleC22×C139C22×D4
prime radical#22581189C2
hypercenter#467D139
hypocenterC139#3262
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #22581576C2semidirect
2. #22581246C2semidirect
3. #22581232C2semidirect
4. #22581201C2semidirect
6. #22581177C2semidirect
7. #22581171C2semidirect
8. #22580979C2semidirect
9. #467×C139C2semidirect
105. C139#3262semidirect
111. #467D139semidirect

Maximal subgroups

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

subgroupindex
#225815762
#225812462
#225812322
#225812012
#225811892
#225811772
#225811712
#225809792
#467×C1392
#3262139