Finite Group Databasebeta

← #1705×D79 #34275904

Subgroups — #1705×D79 #34275904

Order 20224.

994 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 239 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#498×D79C213yesmaximal, complemented
2#492×D79C213yesmaximal
3#23762988C213yesmaximal, complemented
4#23762987C211yesmaximal, characteristic, complemented
5#23762986C213yesmaximal, complemented
6C82×D79C211yesmaximal, characteristic, complemented
7C79×#1705C211yesmaximal, characteristic, complemented
8C2×SD16×D79—26no—
9C4⋊Q8×D79C2213yes—
10#127×D79C2211yescharacteristic
11#19098961C2213yescomplemented
12#19098960—26no—
13#19098959C2216yescomplemented
14#19098937C2213yes—
15#19098936C2213yes—
16#19098935C2213yes—
17#19098934—26no—
18#106×D79—26no—
19C4×C8×D79C2213yes—
20C8×C79⋊C8C2213yescomplemented
21#498×C79C2213yescomplemented
22#492×C79C2213yes—
23C82×C79C2211yescharacteristic, complemented
24C2×Q8×D79—23no—
25C2×D4×D79—23no—
26C2×#11929613—26no—
27C2×#11929612—26no—
28C2×#11929611—26no—
29SD16×D79—424no—
30C2×C8×D79D416yes—
31#14579161C2313yes—
32#14579160—26no—
33#14579159—23no—
34#14579158C2311yescharacteristic
35#14579157—23no—
36C4⋊C4×D79—26no—
37C42×D79C2311yescharacteristic
38#14579093—26no—
39#14579092—212no—
40C4×C79⋊C8C2313yes—
41C8×Dic79D416yes—
42C2×SD16×C79—26no—
43C4⋊Q8×C79C2313yes—
44#127×C79C2311yescharacteristic
45#106×C79—26no—
46C4×C8×C79C2313yes—
47C23×D79—41no—
48C2×Dic158—23no—
49C2×Dic158—43no—
50Q8×D79—412no—
51C2×D316—23no—
52C2×C22⋊D79—43no—
53D4×D79—412no—
54C2×C4×D79—43no—
55C2×C4×D79C2×D413yes—
56#11929613—412no—
57#11929612—412no—
58#11929611—412no—
59C2×C79⋊C8C2×D416yes—
60C8×D79SD16124yescomplemented
61C4⋊Dic79—26no—
62Dic79⋊C4—46no—
63C4×Dic79C2×D413yes—
64C2×Q8×C79—23no—
65C2×D4×C79—23no—
66SD16×C79—412no—
67C2×C8×C79C2×D416yes—
68C4⋊C4×C79—26no—
69C42×C79C2411yescharacteristic
70C23×C79—41no—
71C22×D79—41no—
72C22×D79—86no—
73C22×D79#12711yescharacteristic
74Q8×C79—46no—
75D4×C79—46no—
76C2×C4×C79—43no—
77C2×C4×C79C22×D413yes—
78C22⋊D79—86no—
79C2×Dic79—43no—
80C2×Dic79#12713yes—
81D316—46no—
82C4×D79—86no—
83C4×D79C2×SD16112yes—
84Dic158—46no—
85Dic158—86no—
86C8×C79C2×SD16112yescomplemented
87C79⋊C8C2×SD16112yescomplemented
88C22×C79—83no—
89C22×C79C2×#12711yescharacteristic
90C2×D79—83no—
91C2×D79—164no—
92C2×D79#49216yes—
93C4×C79—83no—
94C4×C79C22×SD1616yes—
95Dic79—83no—
96Dic79#49216yes—
97C2×#1705—791nomaximal, Sylow
98C2×C79—161no—
99C2×C79C2×#49213yes—
100D79—161no—
101D79#170514yesdirect product factor
102C2×#498—793no—
103C2×#492—793no—
104#1705—793no—
105#1705—793no—
106#1705—791no—
107#1705D7911yescharacteristic, direct product factor
108C2×C82—791no—
109C79C2×#170511yescharacteristic, complemented, Sylow
110C22×SD16—1586no—
111C2×C4⋊Q8—793no—
112C2×#127—791no—
113#498—796no—
114#498—793no—
115#498—1586no—
116#498C2×D7913yescomplemented
117#492—793no—
118#492—793no—
119#492—793no—
120#492—1586no—
121#492C2×D7913yes—
122C2×#106—1586no—
123C2×C4×C8—793no—
124C82—793no—
125C82C2×D7911yescharacteristic, complemented
126C22×Q8—1583no—
127C22×D4—1583no—
128C2×SD16—26no—
129C2×SD16—31624no—
130C2×SD16—1586no—
131C2×SD16—1586no—
132C2×SD16—1586no—
133C22×C8—796no—
134C4⋊Q8—793no—
135C4⋊Q8—1586no—
136C4⋊Q8—1583no—
137C4⋊Q8C22×D7913yes—
138#127—791no—
139#127—1583no—
140#127C22×D7911yescharacteristic
141C2×C4⋊C4—1586no—
142C2×C42—791no—
143#106—26no—
144#106—15812no—
145#106—1586no—
146C4×C8—796no—
147C4×C8—793no—
148C4×C8C22×D7913yes—
149C24—3161no—
150C2×Q8—23no—
151C2×Q8—3163no—
152C2×Q8—31612no—
153C2×Q8—1583no—
154C2×D4—23no—
155C2×D4—31612no—
156C2×D4—3163no—
157C2×D4—1583no—
158C22×C4—3163no—
159C22×C4—793no—
160SD16—412no—
161SD16—31612no—
162SD16—31612no—
163SD16—31612no—
164C2×C8—796no—
165C2×C8—7924no—
166C2×C8D4×D7916yes—
167C4⋊C4—26no—
168C4⋊C4—3166no—
169C4⋊C4—1586no—
170C42—793no—
171C42C23×D7911yescharacteristic
172C23—41no—
173C23—3161no—
174C23—791no—
175C23—6326no—
176Q8—46no—
177Q8—3166no—
178Q8—6326no—
179D4—46no—
180D4—3166no—
181D4—6326no—
182C2×C4—43no—
183C2×C4—3163no—
184C2×C4—793no—
185C2×C4—7912no—
186C2×C4—6326no—
187C2×C4C2×D4×D7913yes—
188C8—7912no—
189C8SD16×D79112yescomplemented
190C22—83no—
191C22—796no—
192C22—6323no—
193C22—12644no—
194C22#127×D7911yescharacteristic
195C4—83no—
196C4—796no—
197C4—6323no—
198C4C2×SD16×D7916yes—
199C2—161no—
200C2—794no—
201C2—12641no—
202C2#492×D7913yes—
subgroupG/H
centerC22#127×D79
commutator, cosocleC42×C79C24
FrattiniC42C23×D79
FittingC79×#1705C2
socleC22×C79C2×#127
prime radical#127×D79C22
hypercenter#1705D79
hypocenterC79C2×#1705
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #1705

Complements

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

NH ≅ G/Ntype
1. #498×D79C2semidirect
3. #23762988C2semidirect
4. #23762987C2semidirect
5. #23762986C2semidirect
6. C82×D79C2semidirect
7. C79×#1705C2semidirect
11. #19098961C22semidirect
13. #19098959C22semidirect
20. C8×C79⋊C8C22semidirect
21. #498×C79C22semidirect
23. C82×C79C22semidirect
60. C8×D79SD16semidirect
86. C8×C79C2×SD16semidirect
87. C79⋊C8C2×SD16semidirect
101. D79#1705direct (N × H)
107. #1705D79direct (N × H)
109. C79C2×#1705semidirect
116. #498C2×D79semidirect
125. C82C2×D79semidirect
189. C8SD16×D79semidirect

Maximal subgroups

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

subgroupindex
#498×D792
#492×D792
#237629882
#237629872
#237629862
C82×D792
C79×#17052
C2×#170579