Finite Group Databasebeta

← #34197697

Subgroups — #34197697

Order 20224.

418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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#23766020C211yesmaximal, characteristic
2#23761734C211yesmaximal, characteristic
3#23761349C214yesmaximal
4C79×#1464C211yesmaximal, characteristic
5C2×#14579120C411yescharacteristic
6C22×C4⋊Dic79C411yescharacteristic
7#19098620—21no—
8#19098461—21no—
9#19098461—21no—
10#19098435C412yes—
11#19098435C2212yes—
12#19098432—21no—
13#19098428—21no—
14#19098289—21no—
15#19098287C2212yes—
16C2×#117×C79C2211yescharacteristic
17#432×C79—21no—
18#324×C79—21no—
19#323×C79C2212yes—
20C23×Dic79C2×C412yes—
21#14579120—24no—
22C2×C4⋊Dic79—21no—
23C2×C4⋊Dic79—21no—
24C2×C4⋊Dic79—21no—
25C2×C4⋊Dic79—41no—
26C2×C4⋊Dic79—41no—
27C2×Dic79⋊C4—22no—
28C2×Dic79⋊C4—22no—
29C2×C22⋊Dic79C2×C412yes—
30C2×C4×Dic79—21no—
31C4⋊(C79⋊C8)—41no—
32C22⋊(C79⋊C8)—22no—
33#14579072—41no—
34C79⋊#95—22no—
35C79⋊#95—22no—
36C23×C4×C79C2×C411yescharacteristic
37#117×C79—41no—
38#117×C79—41no—
39C2×C4⋊C4×C79D411yescharacteristic
40C2×C4⋊C4×C79D411yescharacteristic
41C2×C22⋊C4×C79C2×C411yescharacteristic
42C2×C22⋊C4×C79C2311yescharacteristic
43C2×C42×C79D411yescharacteristic
44C2×C42×C79D411yescharacteristic
45C4⋊C8×C79—41no—
46C22⋊C8×C79—22no—
47#97×C79—41no—
48C22×Dic79—22no—
49C22×Dic79—22no—
50C22×Dic79—42no—
51C22×Dic79—82no—
52C2×C79⋊C8—42no—
53C4⋊Dic79—24no—
54C4⋊Dic79—42no—
55C4⋊Dic79—41no—
56C4⋊Dic79—41no—
57Dic79⋊C4—82no—
58Dic79⋊C4—82no—
59C22⋊Dic79—22no—
60C22⋊Dic79M1614yes—
61C4×Dic79—24no—
62C24×C79C22×C411yescharacteristic
63C22×C4×C79—22no—
64C22×C4×C79—21no—
65C22×C4×C79—21no—
66C22×C4×C79—22no—
67C22×C4×C79C22⋊C411yescharacteristic
68C22×C4×C79C22⋊C411yescharacteristic
69C22×C4×C79C22⋊C411yescharacteristic
70C22×C4×C79C22⋊C411yescharacteristic
71C22×C4×C79C2×D411yescharacteristic
72C22×C4×C79C2×D411yescharacteristic
73C2×C8×C79—42no—
74C4⋊C4×C79—41no—
75C4⋊C4×C79—41no—
76C22⋊C4×C79—41no—
77C22⋊C4×C79—41no—
78C42×C79—21no—
79C42×C79—21no—
80C42×C79—21no—
81C42×C79—21no—
82C23×C79—21no—
83C23×C79—21no—
84C23×C79—41no—
85C23×C79—41no—
86C23×C79C2×C22⋊C411yescharacteristic
87C23×C79C2×M1612yes—
88C2×C4×C79—24no—
89C2×C4×C79—24no—
90C2×C4×C79—21no—
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—21no—
95C2×C4×C79—21no—
96C2×C4×C79—21no—
97C2×C4×C79—21no—
98C2×C4×C79—41no—
99C2×C4×C79—41no—
100C2×C4×C79—41no—
101C2×C4×C79—41no—
102C2×C4×C79#9911yescharacteristic
103C2×C4×C79#9911yescharacteristic
104C2×C4×C79#10112yes—
105C2×Dic79—24no—
106C2×Dic79—42no—
107C2×Dic79—42no—
108C2×Dic79—42no—
109C2×Dic79—42no—
110C2×Dic79—42no—
111C2×Dic79—84no—
112C8×C79—82no—
113C79⋊C8—82no—
114C22×C79—21no—
115C22×C79—21no—
116C22×C79—22no—
117C22×C79—42no—
118C22×C79—42no—
119C22×C79—41no—
120C22×C79—41no—
121C22×C79#40711yescharacteristic
122C22×C79C2×#9911yescharacteristic
123C22×C79C2×#10111yescharacteristic
124C4×C79—21no—
125C4×C79—21no—
126C4×C79—22no—
127C4×C79—41no—
128C4×C79—41no—
129C4×C79—41no—
130C4×C79—41no—
131Dic79—44no—
132Dic79—82no—
133#11520—791nomaximal, Sylow
134C2×C79—21no—
135C2×C79—21no—
136C2×C79—42no—
137C2×C79#146311yescharacteristic
138C2×C79#212211yescharacteristic
139C2×C79#212311yescharacteristic
140#2317—791no—
141#1464—791no—
142#1464D7911yescharacteristic
143#1326—794no—
144C79#1152011yescharacteristic, complemented, Sylow
145C2×#117—791no—
146C2×#117C2×D7911yescharacteristic
147C22×C4⋊C4—791no—
148#432—21no—
149#432—1581no—
150#389—1581no—
151#389—1581no—
152#385—792no—
153#385—792no—
154#384—1581no—
155#382—1581no—
156#324—21no—
157#324—1581no—
158#323—792no—
159#323C2×D7912yes—
160C23×C4—792no—
161C23×C4C4×D7911yescharacteristic
162#117—41no—
163#117—41no—
164#117—1584no—
165C2×C4⋊C4—3161no—
166C2×C4⋊C4—3161no—
167C2×C4⋊C4—1581no—
168C2×C4⋊C4—1581no—
169C2×C4⋊C4—1582no—
170C2×C4⋊C4—1582no—
171C2×C4⋊C4—1581no—
172C2×C4⋊C4D31611yescharacteristic
173C2×C4⋊C4C22⋊D7911yescharacteristic
174C2×C22⋊C4—792no—
175C2×C22⋊C4C4×D7911yescharacteristic
176C2×C22⋊C4C22×D7911yescharacteristic
177C2×C42—1581no—
178C2×C42D31611yescharacteristic
179C2×C42C22⋊D7911yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—3161no—
182C22⋊C8—22no—
183C22⋊C8—1582no—
184#97—41no—
185#97—3161no—
186#95—1582no—
187#95—1582no—
188C24C2×C4×D7911yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—3162no—
194C22×C4—6322no—
195C22×C4—1582no—
196C22×C4—1582no—
197C22×C4(C2×D79)⋊C411yescharacteristic
198C22×C4(C2×D79)⋊C411yescharacteristic
199C22×C4(C2×D79)⋊C411yescharacteristic
200C22×C4(C2×D79)⋊C411yescharacteristic
201C22×C4C2×C22⋊D7911yescharacteristic
202C22×C4C2×D31611yescharacteristic
203C2×C8—42no—
204C2×C8—3162no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—3162no—
208C4⋊C4—3161no—
209C4⋊C4—3161no—
210C4⋊C4—6322no—
211C4⋊C4—6322no—
212C4⋊C4—1584no—
213C22⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4—794no—
216C22⋊C4—1582no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—1584no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×(C2×D79)⋊C411yescharacteristic
227C23M16×D7912yes—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—3162no—
243C2×C4—3162no—
244C2×C4—3162no—
245C2×C4—3162no—
246C2×C4—3162no—
247C2×C4—6324no—
248C2×C4—1584no—
249C2×C4#1457907511yescharacteristic
250C2×C4#1457907511yescharacteristic
251C2×C4#1457907912yes—
252C8—82no—
253C8—6322no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1909852611yescharacteristic
262C22C2×#1457907511yescharacteristic
263C22C2×#1457907911yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—3164no—
272C4—6322no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#2376172911yescharacteristic
277C2#2376505111yescharacteristic
278C2#2376505311yescharacteristic
subgroupG/H
centerC22C2×#14579075
commutator, prime radicalC24×C79C22×C4
FrattiniC2×C22⋊C4C22×D79
FittingC79×#1464C2
socleC22×C79C2×#99
cosocleC2×C22⋊C4×C79C23
hypercenter#1464D79
hypocenterC79#11520
LCSG ▷ C24×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
144. C79#11520semidirect

Maximal subgroups

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

subgroupindex
#237660202
#237617342
#237613492
C79×#14642
#1152079