Finite Group Databasebeta

← #34177581

Subgroups — #34177581

Order 20224.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#23771388C211yesmaximal, characteristic
2#23764964C212yesmaximal
3#23764938C211yesmaximal, characteristic
4#23761224C212yesmaximal
5C79×#1272C211yesmaximal, characteristic
6C2×#14579094—21no—
7C2×#14579085—21no—
8#19098502—21no—
9#19098495—22no—
10#19098470—21no—
11#19098461C2212yes—
12#19098450—22no—
13#19098433C2211yescharacteristic
14#19098326—22no—
15#19098326—22no—
16#19098318C2211yescharacteristic
17#391×C79C2211yescharacteristic
18#336×C79C2212yes—
19C22×C79⋊C8—21no—
20C2×C4⋊Dic79—21no—
21C2×C4⋊Dic79—22no—
22C2×C4⋊Dic79—21no—
23C2×C4⋊Dic79—21no—
24C2×C4⋊Dic79D412yes—
25C2×C4⋊Dic79D412yes—
26C2×Dic79⋊C4—22no—
27C2×C4×Dic79—21no—
28#14579094—42no—
29#14579085—42no—
30C79⋊#95—21no—
31C79⋊#95—22no—
32C79⋊#95—22no—
33C79⋊#95—22no—
34C22×Q8×C79D411yescharacteristic
35C22×C8×C79—22no—
36C2×C4⋊C4×C79D411yescharacteristic
37C2×C42×C79C2311yescharacteristic
38#95×C79—22no—
39C22×Dic79—22no—
40C22×Dic79—22no—
41C22×Dic79—41no—
42C2×C79⋊C8—22no—
43C2×C79⋊C8—41no—
44C2×C79⋊C8—41no—
45C4⋊Dic79—22no—
46C4⋊Dic79—22no—
47C4⋊Dic79—42no—
48C4⋊Dic79—41no—
49C4⋊Dic79—41no—
50C4⋊Dic79—44no—
51C4⋊Dic79—81no—
52C4⋊Dic79—81no—
53Dic79⋊C4—42no—
54Dic79⋊C4—42no—
55C4×Dic79—81no—
56C2×Q8×C79—21no—
57C2×Q8×C79—41no—
58C2×Q8×C79—41no—
59C2×Q8×C79Q1612yes—
60C22×C4×C79—21no—
61C22×C4×C79—21no—
62C22×C4×C79C2×D411yescharacteristic
63C22×C4×C79C2×D412yes—
64C2×C8×C79—42no—
65C2×C8×C79—42no—
66C2×C8×C79—42no—
67C4⋊C4×C79—41no—
68C42×C79—41no—
69C23×C79#12011yescharacteristic
70Q8×C79—42no—
71Q8×C79—81no—
72C2×C4×C79—21no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—21no—
76C2×C4×C79—22no—
77C2×C4×C79—41no—
78C2×C4×C79—41no—
79C2×C4×C79—41no—
80C2×C4×C79—42no—
81C2×C4×C79C2×Q1611yescharacteristic
82C2×C4×C79#13512yes—
83C2×C4×C79#13712yes—
84C2×C4×C79#13711yescharacteristic
85C2×Dic79—42no—
86C2×Dic79—42no—
87C2×Dic79—42no—
88C2×Dic79—42no—
89C2×Dic79—42no—
90C2×Dic79—42no—
91C2×Dic79—81no—
92C2×Dic79—82no—
93C8×C79—82no—
94C79⋊C8—42no—
95C22×C79#45111yescharacteristic
96C22×C79#45212yes—
97C22×C79#45311yescharacteristic
98C22×C79#45412yes—
99C22×C79#45811yescharacteristic
100C4×C79—21no—
101C4×C79—21no—
102C4×C79—22no—
103C4×C79—22no—
104C4×C79—42no—
105C4×C79—81no—
106Dic79—82no—
107Dic79—82no—
108Dic79—161no—
109#7831—791nomaximal, Sylow
110C2×C79#161411yescharacteristic
111C2×C79#161512yes—
112C2×C79#163411yescharacteristic
113C2×C79#163612yes—
114C2×C79#165711yescharacteristic
115#2809—791no—
116#2100—792no—
117#2095—791no—
118#1272D7911yescharacteristic
119#1271—792no—
120C79#783111yescharacteristic, complemented, Sylow
121C2×#107—1581no—
122C2×#103—1581no—
123#400—1581no—
124#398—1582no—
125#391—1581no—
126#391C2×D7911yescharacteristic
127#389—792no—
128#387—1582no—
129#384—791no—
130#340—1582no—
131#340—1582no—
132#336—791no—
133#336C2×D7912yes—
134C22×Q8D31611yescharacteristic
135C22×C8—22no—
136C22×C8—1581no—
137C2×C4⋊C4—792no—
138C2×C4⋊C4—792no—
139C2×C4⋊C4—1582no—
140C2×C4⋊C4—1581no—
141C2×C4⋊C4—1582no—
142C2×C4⋊C4—1581no—
143C2×C4⋊C4—1581no—
144C2×C4⋊C4D31611yescharacteristic
145C2×C42—1581no—
146C2×C42C22×D7911yescharacteristic
147#107—3162no—
148#103—3162no—
149#95—22no—
150#95—1581no—
151#95—1582no—
152#95—1582no—
153#95—1582no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8Dic31612yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—3161no—
161C22×C4—1582no—
162C22×C4—1582no—
163C22×C4D4×D7912yes—
164C22×C4C2×D31611yescharacteristic
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—3161no—
169C2×C8—3161no—
170C2×C8—1582no—
171C4⋊C4—41no—
172C4⋊C4—3162no—
173C4⋊C4—3161no—
174C4⋊C4—3161no—
175C4⋊C4—3164no—
176C4⋊C4—3162no—
177C4⋊C4—3162no—
178C4⋊C4—6321no—
179C4⋊C4—6321no—
180C4⋊C4—1582no—
181C4⋊C4—1582no—
182C42—41no—
183C42—6321no—
184C23#1457913111yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—3162no—
197C2×C4—3162no—
198C2×C4—3162no—
199C2×C4—3162no—
200C2×C4—3162no—
201C2×C4—3162no—
202C2×C4—6321no—
203C2×C4—6322no—
204C2×C4C2×Dic31611yescharacteristic
205C2×C4#1457918212yes—
206C2×C4#1457919312yes—
207C2×C4#1457919411yescharacteristic
208C8—82no—
209C8—3162no—
210C22#1909872111yescharacteristic
211C22#1909872812yes—
212C22#1909873311yescharacteristic
213C22#1909873712yes—
214C22#1909875411yescharacteristic
215C4—22no—
216C4—22no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—81no—
221C4—6322no—
222C4—6322no—
223C4—12641no—
224C2#2376242711yescharacteristic
225C2#2376243412yes—
226C2#2376254611yescharacteristic
227C2#2376256112yes—
228C2#2376269911yescharacteristic
subgroupG/H
centerC23#14579131
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1272C2
socle, prime radicalC23×C79#120
hypercenter#1272D79
hypocenterC79#7831
LCSG ▷ C2×C42×C79 ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
120. C79#7831semidirect

Maximal subgroups

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

subgroupindex
#237713882
#237649642
#237649382
#237612242
C79×#12722
#783179