Finite Group Databasebeta

← #34191351

Subgroups — #34191351

Order 20224.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#23771675C211yesmaximal, characteristic
2#23764373C212yesmaximal
3#23764219C211yesmaximal, characteristic
4#23761282C212yesmaximal
5C79×#1295C211yesmaximal, characteristic
6C2×#14579161C2211yescharacteristic
7C2×#14579084—22no—
8C2×#14579072C2211yescharacteristic
9#19098497—22no—
10#19098496—22no—
11#19098495—22no—
12#19098429C2212yes—
13#19098326—22no—
14#19098326—22no—
15C2×#97×C79C2212yes—
16#382×C79C2211yescharacteristic
17C22×Dic158—21no—
18C22×C79⋊C8—21no—
19#14579161—22no—
20#14579161—21no—
21#14579161Q812yes—
22C2×C4⋊Dic79—22no—
23C2×C4⋊Dic79—22no—
24C2×C4⋊Dic79D412yes—
25C2×C4⋊Dic79D412yes—
26C2×Dic79⋊C4—22no—
27C2×Dic79⋊C4—22no—
28#14579084—44no—
29#14579072—22no—
30C79⋊#95—22no—
31C79⋊#95—22no—
32C79⋊#95—22no—
33C22×C8×C79—22no—
34C2×C4⋊C4×C79D412yes—
35C2×C42×C79C2311yescharacteristic
36#97×C79—22no—
37#97×C79—22no—
38#95×C79—22no—
39C2×Dic158—22no—
40C2×Dic158—42no—
41C2×Dic158—42no—
42C2×Dic158—41no—
43C22×Dic79—22no—
44C22×Dic79—22no—
45C22×Dic79—41no—
46C2×C79⋊C8—22no—
47C2×C79⋊C8—41no—
48C2×C79⋊C8—41no—
49C4⋊Dic79—24no—
50C4⋊Dic79—42no—
51C4⋊Dic79—42no—
52C4⋊Dic79—42no—
53C4⋊Dic79—82no—
54Dic79⋊C4—82no—
55Dic79⋊C4—82no—
56C22×C4×C79—22no—
57C22×C4×C79C2×D412yes—
58C22×C4×C79C2×D411yescharacteristic
59C2×C8×C79—24no—
60C2×C8×C79—42no—
61C2×C8×C79—42no—
62C4⋊C4×C79—42no—
63C42×C79C2×Q811yescharacteristic
64C42×C79#4111yescharacteristic
65C42×C79#4112yes—
66C23×C79#12011yescharacteristic
67C2×C4×C79—21no—
68C2×C4×C79—21no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—42no—
72C2×C4×C79—42no—
73C2×C4×C79—42no—
74C2×C4×C79C22⋊Q812yes—
75C2×C4×C79C22⋊Q811yescharacteristic
76C2×C4×C79#12412yes—
77C2×C4×C79#12411yescharacteristic
78C2×Dic79—42no—
79C2×Dic79—42no—
80C2×Dic79—42no—
81C2×Dic79—42no—
82C2×Dic79—42no—
83C2×Dic79—42no—
84C2×Dic79—42no—
85C2×Dic79—81no—
86C2×Dic79—81no—
87Dic158—44no—
88Dic158—82no—
89C8×C79—44no—
90C79⋊C8—42no—
91C22×C79#39311yescharacteristic
92C22×C79#45311yescharacteristic
93C22×C79#45411yescharacteristic
94C22×C79#45512yes—
95C22×C79#45612yes—
96C4×C79—21no—
97C4×C79—21no—
98C4×C79—22no—
99C4×C79—22no—
100C4×C79—82no—
101Dic79—82no—
102Dic79—82no—
103Dic79—82no—
104#10361—791nomaximal, Sylow
105C2×C79#166112yes—
106C2×C79#166211yescharacteristic
107C2×C79#166311yescharacteristic
108C2×C79#202711yescharacteristic
109C2×C79#202812yes—
110#2845—791no—
111#1993—792no—
112#1960—791no—
113#1295—792no—
114#1295D7911yescharacteristic
115C79#1036111yescharacteristic, complemented, Sylow
116C2×C4⋊Q8—791no—
117C2×#103—1582no—
118C2×#97—791no—
119C2×#97C2×D7912yes—
120#398—1582no—
121#398—1582no—
122#398—1582no—
123#382—792no—
124#382C2×D7911yescharacteristic
125#340—1582no—
126#340—1582no—
127C22×Q8—1581no—
128C22×C8—22no—
129C22×C8—1581no—
130C4⋊Q8—792no—
131C4⋊Q8—1581no—
132C4⋊Q8—1582no—
133C2×C4⋊C4—792no—
134C2×C4⋊C4—792no—
135C2×C4⋊C4—1582no—
136C2×C4⋊C4—1582no—
137C2×C4⋊C4—1582no—
138C2×C4⋊C4—1582no—
139C2×C4⋊C4D31612yes—
140C2×C42C22×D7911yescharacteristic
141#103—3164no—
142#97—22no—
143#97—22no—
144#97—1582no—
145#95—22no—
146#95—1582no—
147#95—1582no—
148#95—1582no—
149C2×Q8—3162no—
150C2×Q8—3162no—
151C2×Q8—3161no—
152C2×Q8—1582no—
153C22×C4—22no—
154C22×C4—3161no—
155C22×C4—1582no—
156C22×C4—1582no—
157C22×C4D4×D7912yes—
158C22×C4C2×D31611yescharacteristic
159C2×C8—24no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—3161no—
163C2×C8—3161no—
164C2×C8—1582no—
165C4⋊C4—42no—
166C4⋊C4—3162no—
167C4⋊C4—3162no—
168C4⋊C4—3162no—
169C4⋊C4—6322no—
170C4⋊C4—6322no—
171C4⋊C4—6322no—
172C4⋊C4—1584no—
173C42Q8×D7911yescharacteristic
174C42#1192962311yescharacteristic
175C42#1192962412yes—
176C23#1457913111yescharacteristic
177Q8—3164no—
178Q8—6322no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—3162no—
187C2×C4—3162no—
188C2×C4—3162no—
189C2×C4—3162no—
190C2×C4—3162no—
191C2×C4—3162no—
192C2×C4—3162no—
193C2×C4—6321no—
194C2×C4—6321no—
195C2×C4#1457913912yes—
196C2×C4#1457914111yescharacteristic
197C2×C4#1457914712yes—
198C2×C4#1457914911yescharacteristic
199C8—44no—
200C8—3162no—
201C22#1909847611yescharacteristic
202C22#1909873311yescharacteristic
203C22#1909873811yescharacteristic
204C22#1909874212yes—
205C22#1909874712yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—6322no—
212C4—6322no—
213C4—6322no—
214C2#2376271812yes—
215C2#2376272411yescharacteristic
216C2#2376272911yescharacteristic
217C2#2376455711yescharacteristic
218C2#2376456012yes—
subgroupG/H
centerC23#14579131
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1295C2
socle, prime radicalC23×C79#120
hypercenter#1295D79
hypocenterC79#10361
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
115. C79#10361semidirect

Maximal subgroups

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

subgroupindex
#237716752
#237643732
#237642192
#237612822
C79×#12952
#1036179