Finite Group Databasebeta

← #34197708

Subgroups — #34197708

Order 20224.

280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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#23772050C211yesmaximal, characteristic
2#23765209C212yesmaximal, complemented
3#23761353C211yesmaximal, characteristic, complemented
4#23761337C212yesmaximal
5C79×#1328C211yesmaximal, characteristic, complemented
6#19099031C411yescharacteristic
7#19098623—22no—
8#19098619—22no—
9#19098590C411yescharacteristic
10#19098531C2211yescharacteristic
11#19098529C411yescharacteristic
12M16×Dic79C2211yescharacteristic
13C2×#14579071C411yescharacteristic
14#19098383—22no—
15#19098345C2212yes—
16#19098340—22no—
17#424×C79C2211yescharacteristic
18#349×C79C2212yes—
19C2×#11929624C2×C411yescharacteristic
20C2×#11929608C2×C411yescharacteristic
21C22×C79⋊C8C2×C411yescharacteristic
22#14579126—21no—
23#14579123—21no—
24(C22⋊D79)⋊C4—22no—
25#14579118—21no—
26C2×C4×Dic79C2×C411yescharacteristic
27C42×D79—21no—
28#14579101—22no—
29C4⋊(C79⋊C8)—22no—
30(C2×D79)⋊C8—22no—
31(C2×D79)⋊C8—22no—
32#14579071—21no—
33#14579071—21no—
34#14579071D412yes—
35C8×Dic79D412yes—
36C2×M16×C79C2311yescharacteristic
37C22×C8×C79C2×C411yescharacteristic
38#117×C79C2×C411yescharacteristic
39M32×C79—22no—
40C4⋊C8×C79—22no—
41#11929624—41no—
42#11929624—41no—
43C2×Dic158M1611yescharacteristic
44C2×D316M1611yescharacteristic
45C2×C22⋊D79—21no—
46C22×Dic79—21no—
47C2×C4×D79—22no—
48C2×C4×D79—21no—
49#11929608—41no—
50C2×C79⋊C8—21no—
51C2×C79⋊C8—41no—
52C2×C79⋊C8C22⋊C412yes—
53Dic79⋊C4—22no—
54(C2×D79)⋊C4—22no—
55C4×Dic79—22no—
56C4×Dic79—21no—
57C4×Dic79C22⋊C411yescharacteristic
58C4×Dic79C22⋊C411yescharacteristic
59C79⋊C16—42no—
60C22×C4×C79C22×C411yescharacteristic
61M16×C79—41no—
62C2×C8×C79—21no—
63C2×C8×C79—41no—
64C2×C8×C79C2×D412yes—
65C4⋊C4×C79—21no—
66C22⋊C4×C79M1612yes—
67C42×C79—21no—
68C16×C79—42no—
69C23×C79C2×M1611yescharacteristic
70C22×D79—21no—
71C2×C4×C79—21no—
72C2×C4×C79—21no—
73C2×C4×C79—22no—
74C2×C4×C79C2×C22⋊C411yescharacteristic
75C2×C4×C79C2×M1611yescharacteristic
76C22⋊D79—42no—
77C2×Dic79—21no—
78C2×Dic79—21no—
79C2×Dic79—21no—
80C2×Dic79—81no—
81D316—41no—
82C4×D79—41no—
83C4×D79—41no—
84C4×D79—82no—
85Dic158—41no—
86C8×C79—22no—
87C8×C79—41no—
88C79⋊C8—22no—
89C79⋊C8—41no—
90C22×C79—21no—
91C22×C79—41no—
92C22×C79#40711yescharacteristic
93C2×D79—42no—
94C2×D79—41no—
95C4×C79—21no—
96C4×C79—42no—
97C4×C79#41011yescharacteristic
98C4×C79#41311yescharacteristic
99Dic79—41no—
100Dic79—41no—
101Dic79—41no—
102#11523—791nomaximal, Sylow
103C2×C79—21no—
104C2×C79—41no—
105C2×C79#146411yescharacteristic
106D79—81no—
107#2923—791no—
108#2165—792no—
109#1328—791no—
110#1328D7911yescharacteristic, complemented
111#1321—792no—
112C79#1152311yescharacteristic, complemented, Sylow
113C4×#41—791no—
114#433—1582no—
115#432—1582no—
116#424—791no—
117#424C2×D7911yescharacteristic
118#408—791no—
119#408—791no—
120C4×M16—791no—
121C2×#97—791no—
122#364—1582no—
123#349—792no—
124#349C2×D7912yes—
125#347—1582no—
126C2×#41—791no—
127C2×M16—791no—
128C2×M16C22×D7911yescharacteristic
129C22×C8—791no—
130C22×C8C4×D7911yescharacteristic
131C4×Q8—1581no—
132C4×D4—1581no—
133C4×D4—1582no—
134#117—1581no—
135#117C4×D7911yescharacteristic
136C2×C42—791no—
137C2×C42—1581no—
138M32—22no—
139M32—1582no—
140C4⋊C8—22no—
141C4⋊C8—1582no—
142C22⋊C8—1582no—
143C22⋊C8—1582no—
144#97—792no—
145#97—1581no—
146#97—1581no—
147C4×C8—792no—
148#41—3161no—
149#41—3161no—
150C2×Q8—791no—
151C2×D4—791no—
152C2×D4—1581no—
153C22×C4—1582no—
154C22×C4—1581no—
155C22×C4—1581no—
156C22×C4C2×C4×D7911yescharacteristic
157M16—41no—
158M16—3161no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—3161no—
162C2×C8—792no—
163C2×C8—1581no—
164C2×C8D4×D7912yes—
165C4⋊C4—21no—
166C4⋊C4—1582no—
167C22⋊C4—1582no—
168C22⋊C4#1192960712yes—
169C42—21no—
170C42—791no—
171C42—791no—
172C42—1582no—
173C42—1581no—
174C16—42no—
175C16—3162no—
176C23—1581no—
177C23C2×#1192960711yescharacteristic
178Q8—3161no—
179D4—3161no—
180D4—3162no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—3161no—
185C2×C4—3161no—
186C2×C4—6322no—
187C2×C4—6321no—
188C2×C4—1581no—
189C2×C4—1581no—
190C2×C4—1581no—
191C2×C4C22⋊C4×D7911yescharacteristic
192C2×C4M16×D7911yescharacteristic
193C8—22no—
194C8—41no—
195C8—3161no—
196C8—1582no—
197C22—21no—
198C22—41no—
199C22—3162no—
200C22—3161no—
201C22#1909852511yescharacteristic
202C4—21no—
203C4—42no—
204C4—3161no—
205C4—3161no—
206C4—3161no—
207C4#1909853511yescharacteristic
208C4#1909854611yescharacteristic
209C2—21no—
210C2—41no—
211C2—6321no—
212C2#2376173311yescharacteristic
subgroupG/H
centerC4#19098535
commutatorC22×C4×C79C22×C4
FrattiniC2×M16C22×D79
FittingC79×#1328C2
socleC2×C79#1464
prime radicalC2×#11929624C2×C4
cosocleC2×M16×C79C23
hypercenter#1328D79
hypocenterC79#11523
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
2. #23765209C2semidirect
3. #23761353C2semidirect
5. C79×#1328C2semidirect
110. #1328D79semidirect
112. C79#11523semidirect

Maximal subgroups

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

subgroupindex
#237720502
#237652092
#237613532
#237613372
C79×#13282
#1152379