Finite Group Databasebeta

← #34176595

Subgroups — #34176595

Order 20224.

456 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 119 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#23765969C211yesmaximal, characteristic
2#23763515C212yesmaximal
3#23761226C211yesmaximal, characteristic
4#23761225C212yesmaximal
5C79×#1272C211yesmaximal, characteristic
6C2×#14579159C411yescharacteristic
7C2×Q8×Dic79C411yescharacteristic
8C2×#14579126C411yescharacteristic
9C2×Dic79⋊C8—22no—
10#19098469C2211yescharacteristic
11#19098460—22no—
12#19098432C411yescharacteristic
13#19098414—22no—
14C42×Dic79C2211yescharacteristic
15#19098318C2212yes—
16#19098317—22no—
17#391×C79C2211yescharacteristic
18#336×C79C2212yes—
19C22×Dic158C2×C411yescharacteristic
20C22×C79⋊C8—22no—
21#14579159—22no—
22#14579159—22no—
23Q8×Dic79—42no—
24#14579126—42no—
25C2×C4⋊Dic79—21no—
26C2×C4⋊Dic79C2×C411yescharacteristic
27C2×Dic79⋊C4—22no—
28C2×Dic79⋊C4—22no—
29C2×Dic79⋊C4—21no—
30C2×C4×Dic79—21no—
31C2×C4×Dic79—21no—
32C2×C4×Dic79C2×C411yescharacteristic
33C2×C4×Dic79C2×C411yescharacteristic
34C2×C4×Dic79D412yes—
35C2×C4×Dic79D412yes—
36Dic79⋊C8—44no—
37C79⋊#95—22no—
38C22×Q8×C79C2×C411yescharacteristic
39C22×C8×C79—22no—
40C2×C4⋊C4×C79C2×C411yescharacteristic
41C2×C42×C79C2311yescharacteristic
42#95×C79—22no—
43C2×Dic158—21no—
44C2×Dic158—41no—
45C2×Dic158—41no—
46C2×Dic158M1612yes—
47C22×Dic79—21no—
48C22×Dic79—21no—
49C22×Dic79C22⋊C411yescharacteristic
50C22×Dic79C22⋊C412yes—
51C22×Dic79C22⋊C411yescharacteristic
52C2×C79⋊C8—42no—
53C2×C79⋊C8—42no—
54C2×C79⋊C8—42no—
55C4⋊Dic79—41no—
56C4⋊Dic79—42no—
57Dic79⋊C4—28no—
58Dic79⋊C4—44no—
59Dic79⋊C4—42no—
60C4×Dic79—22no—
61C4×Dic79—21no—
62C4×Dic79—21no—
63C4×Dic79—42no—
64C4×Dic79—42no—
65C4×Dic79—42no—
66C4×Dic79SD1614yes—
67C4×Dic79Q1614yes—
68C2×Q8×C79—21no—
69C2×Q8×C79—41no—
70C2×Q8×C79—41no—
71C2×Q8×C79M1612yes—
72C22×C4×C79—21no—
73C22×C4×C79—21no—
74C22×C4×C79C22×C411yescharacteristic
75C22×C4×C79C2×D412yes—
76C2×C8×C79—42no—
77C2×C8×C79—42no—
78C2×C8×C79—42no—
79C4⋊C4×C79—41no—
80C42×C79—41no—
81C23×C79C2×C22⋊C411yescharacteristic
82Q8×C79—42no—
83Q8×C79—42no—
84C2×C4×C79—22no—
85C2×C4×C79—21no—
86C2×C4×C79—21no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79—41no—
90C2×C4×C79—41no—
91C2×C4×C79—41no—
92C2×C4×C79—42no—
93C2×C4×C79C2×M1611yescharacteristic
94C2×C4×C79C2×M1611yescharacteristic
95C2×C4×C79C2×SD1612yes—
96C2×C4×C79C2×Q1612yes—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—21no—
101C2×Dic79—22no—
102C2×Dic79—41no—
103C2×Dic79—41no—
104C2×Dic79—41no—
105C2×Dic79—42no—
106C2×Dic79#10012yes—
107C2×Dic79#10314yes—
108C2×Dic79#10314yes—
109Dic158—42no—
110Dic158—42no—
111C8×C79—82no—
112C79⋊C8—82no—
113C22×C79#40711yescharacteristic
114C22×C79#41011yescharacteristic
115C22×C79C2×#10011yescharacteristic
116C22×C79C2×#10312yes—
117C22×C79#42112yes—
118C4×C79—21no—
119C4×C79—21no—
120C4×C79—22no—
121C4×C79—22no—
122C4×C79—42no—
123C4×C79—81no—
124Dic79—24no—
125Dic79—41no—
126Dic79—42no—
127Dic79—81no—
128Dic79#33314yes—
129#7653—791nomaximal, Sylow
130C2×C79#146611yescharacteristic
131C2×C79#148712yes—
132C2×C79#151812yes—
133C2×C79#153611yescharacteristic
134C2×C79C2×#33311yescharacteristic
135C4×C4⋊Q8—791no—
136#1831—792no—
137#1272—791no—
138#1272—792no—
139#1272D7911yescharacteristic
140C79#765311yescharacteristic, complemented, Sylow
141C2×C4⋊Q8—791no—
142C2×C4×Q8—791no—
143C2×C4×Q8—791no—
144C2×C4⋊C8—1582no—
145#391—791no—
146#391C2×D7911yescharacteristic
147#389—1582no—
148#384—791no—
149C4×C4⋊C4—1582no—
150C43—791no—
151#336—792no—
152#336—1582no—
153#336C2×D7912yes—
154C22×Q8—791no—
155C22×Q8C4×D7911yescharacteristic
156C22×C8—22no—
157C22×C8—1582no—
158C4⋊Q8—1582no—
159C4⋊Q8—1582no—
160C4×Q8—3162no—
161C4×Q8—3162no—
162C2×C4⋊C4—791no—
163C2×C4⋊C4—1581no—
164C2×C4⋊C4—1581no—
165C2×C4⋊C4—1582no—
166C2×C4⋊C4—1582no—
167C2×C4⋊C4C4×D7911yescharacteristic
168C2×C42—792no—
169C2×C42—792no—
170C2×C42—791no—
171C2×C42—791no—
172C2×C42—1581no—
173C2×C42—1581no—
174C2×C42C22×D7911yescharacteristic
175C4⋊C8—3164no—
176#95—22no—
177#95—1582no—
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—3161no—
182C2×Q8—3161no—
183C2×Q8—792no—
184C2×Q8—1581no—
185C2×Q8#1192960712yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—791no—
189C22×C4—792no—
190C22×C4—791no—
191C22×C4—1581no—
192C22×C4—1581no—
193C22×C4C2×C4×D7911yescharacteristic
194C22×C4D4×D7912yes—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—3162no—
199C2×C8—3162no—
200C2×C8—3162no—
201C4⋊C4—41no—
202C4⋊C4—3161no—
203C4⋊C4—3164no—
204C4⋊C4—3162no—
205C4⋊C4—3162no—
206C4⋊C4—1588no—
207C42—41no—
208C42—3162no—
209C42—3162no—
210C42—3162no—
211C42—794no—
212C42—794no—
213C42—1582no—
214C42—1581no—
215C42—1581no—
216C23C22⋊C4×D7911yescharacteristic
217Q8—42no—
218Q8—42no—
219Q8—3162no—
220Q8—3162no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—3161no—
231C2×C4—3161no—
232C2×C4—3161no—
233C2×C4—3162no—
234C2×C4—792no—
235C2×C4—794no—
236C2×C4—794no—
237C2×C4—1582no—
238C2×C4—1581no—
239C2×C4—1582no—
240C2×C4—1582no—
241C2×C4—1582no—
242C2×C4M16×D7911yescharacteristic
243C2×C4C2×#1192960711yescharacteristic
244C2×C4SD16×D7912yes—
245C2×C4Q16×D7912yes—
246C8—82no—
247C8—6322no—
248C22#1909852511yescharacteristic
249C22#1909853511yescharacteristic
250C22#100×D7911yescharacteristic
251C22#103×D7912yes—
252C22#1909857812yes—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—81no—
259C4—3162no—
260C4—3161no—
261C4—794no—
262C4—6321no—
263C4—1584no—
264C2#2376173911yescharacteristic
265C2#2376182712yes—
266C2#2376196212yes—
267C2#2376203311yescharacteristic
268C2#333×D7911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D79
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1272C2
socle, prime radicalC23×C79C2×C22⋊C4
cosocleC2×C42×C79C23
hypercenter#1272D79
hypocenterC79#7653
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
140. C79#7653semidirect

Maximal subgroups

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

subgroupindex
#237659692
#237635152
#237612262
#237612252
C79×#12722
#765379