Finite Group Databasebeta

← #34197550

Subgroups — #34197550

Order 20224.

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

normal subgroups only

This group has 428 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#23765967C211yesmaximal, characteristic
2#23761722C212yesmaximal
3#23761346C211yesmaximal, characteristic
4#23761333C212yesmaximal
5C79×#1325C211yesmaximal, characteristic
6C2×#14579161C411yescharacteristic
7C2×#14579126C411yescharacteristic
8C2×#14579126C2211yescharacteristic
9#19098613—22no—
10#19098468C411yescharacteristic
11#19098468C2211yescharacteristic
12#19098459—22no—
13C4⋊C4×Dic79—22no—
14C42×Dic79C411yescharacteristic
15#19098289C2212yes—
16#19098288—22no—
17#384×C79C2211yescharacteristic
18#324×C79C2212yes—
19C22×Dic158C2×C411yescharacteristic
20C22×Dic158C2×C411yescharacteristic
21#14579161—22no—
22#14579161C814yescomplemented
23#14579126—41no—
24#14579126—41no—
25#14579126—41no—
26#14579126—41no—
27C2×C4⋊Dic79—22no—
28C2×Dic79⋊C4—21no—
29C2×Dic79⋊C4D412yes—
30C2×C4×Dic79—21no—
31C2×C4×Dic79—21no—
32C2×C4×Dic79—21no—
33C2×C4×Dic79C2×C411yescharacteristic
34C2×C4×Dic79C2×C411yescharacteristic
35C2×C4×Dic79D412yes—
36Dic79⋊C8—42no—
37C22⋊(C79⋊C8)—22no—
38C8×Dic79—42no—
39C79⋊#95—22no—
40C79⋊#95—22no—
41C2×C4⋊C4×C79—22no—
42C2×C4⋊C4×C79C2×C411yescharacteristic
43C2×C4⋊C4×C79C2311yescharacteristic
44C2×C42×C79C2×C411yescharacteristic
45C22⋊C8×C79—22no—
46C2×Dic158—21no—
47C2×Dic158—41no—
48C2×Dic158—41no—
49C2×Dic158—41no—
50C2×Dic158—41no—
51C2×Dic158C2×C812yes—
52C2×Dic158C2×C812yes—
53C2×Dic158M1612yes—
54C22×Dic79—21no—
55C22×Dic79—21no—
56C22×Dic79C22⋊C412yes—
57C22×Dic79C22⋊C411yescharacteristic
58C22×Dic79C22⋊C411yescharacteristic
59C2×C79⋊C8—42no—
60C4⋊Dic79—28no—
61Dic79⋊C4—42no—
62Dic79⋊C4—42no—
63C4×Dic79—24no—
64C4×Dic79—22no—
65C4×Dic79—22no—
66C4×Dic79—21no—
67C4×Dic79—21no—
68C4×Dic79—41no—
69C4×Dic79—42no—
70C4×Dic79—41no—
71C4×Dic79—41no—
72C22×C4×C79—21no—
73C22×C4×C79—21no—
74C22×C4×C79C22×C411yescharacteristic
75C22×C4×C79C2×D412yes—
76C2×C8×C79—42no—
77C4⋊C4×C79—41no—
78C4⋊C4×C79—44no—
79C4⋊C4×C79—41no—
80C42×C79—21no—
81C42×C79C2×C812yes—
82C23×C79C2×C22⋊C411yescharacteristic
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—21no—
87C2×C4×C79—21no—
88C2×C4×C79—22no—
89C2×C4×C79—42no—
90C2×C4×C79—42no—
91C2×C4×C79—41no—
92C2×C4×C79C22×C811yescharacteristic
93C2×C4×C79C2×M1611yescharacteristic
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—21no—
100C2×Dic79—41no—
101C2×Dic79—41no—
102C2×Dic79—41no—
103C2×Dic79—41no—
104C2×Dic79—41no—
105C2×Dic79C22⋊C814yes—
106C2×Dic79#9911yescharacteristic
107C2×Dic79#9911yescharacteristic
108Dic158—42no—
109Dic158—42no—
110Dic158—42no—
111Dic158—42no—
112C8×C79—82no—
113C79⋊C8—82no—
114C22×C79—21no—
115C22×C79—21no—
116C22×C79C2×C22⋊C811yescharacteristic
117C22×C79C2×#9911yescharacteristic
118C22×C79#41311yescharacteristic
119C4×C79—24no—
120C4×C79—21no—
121C4×C79—21no—
122C4×C79—42no—
123C4×C79—81no—
124Dic79—21no—
125Dic79—24no—
126Dic79—42no—
127Dic79—41no—
128Dic79—42no—
129Dic79#35612yes—
130#11478—791nomaximal, Sylow
131C2×C79—21no—
132C2×C79—21no—
133C2×C79#145911yescharacteristic
134C2×C79#212611yescharacteristic
135C2×C79C2×#35611yescharacteristic
136C4×C4⋊Q8—791no—
137#1461—792no—
138#1325—791no—
139#1325D7911yescharacteristic
140#1319—792no—
141C79#1147811yescharacteristic, complemented, Sylow
142C2×C4⋊Q8—791no—
143C2×C4×Q8—791no—
144C2×C4×Q8—791no—
145#431—1582no—
146#391—791no—
147#391—791no—
148#389—1582no—
149#384C2×D7911yescharacteristic
150C4×C4⋊C4—1582no—
151C43—791no—
152#324—792no—
153#324—1582no—
154#324C2×D7912yes—
155C22×Q8—791no—
156C22×Q8—791no—
157C4⋊Q8—794no—
158C4⋊Q8—1582no—
159C4×Q8—3161no—
160C4×Q8—3161no—
161C4×Q8—3161no—
162C4×Q8—3161no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—792no—
165C2×C4⋊C4—1581no—
166C2×C4⋊C4—1582no—
167C2×C4⋊C4C4×D7911yescharacteristic
168C2×C4⋊C4C22×D7911yescharacteristic
169C2×C42—791no—
170C2×C42—791no—
171C2×C42—792no—
172C2×C42—1581no—
173C2×C42—1581no—
174C2×C42—1581no—
175C2×C42C4×D7911yescharacteristic
176C4⋊C8—3162no—
177C22⋊C8—22no—
178C22⋊C8—1582no—
179C4×C8—3162no—
180#95—1582no—
181#95—1582no—
182C2×Q8—3161no—
183C2×Q8—3161no—
184C2×Q8—3161no—
185C2×Q8—3161no—
186C2×Q8—792no—
187C2×Q8—792no—
188C2×Q8—792no—
189C2×Q8—1581no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—791no—
193C22×C4—792no—
194C22×C4—791no—
195C22×C4—1581no—
196C22×C4—1581no—
197C22×C4C2×C4×D7911yescharacteristic
198C22×C4D4×D7912yes—
199C2×C8—42no—
200C2×C8—3162no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—44no—
204C4⋊C4—3162no—
205C4⋊C4—3162no—
206C4⋊C4—1588no—
207C42—21no—
208C42—3161no—
209C42—3162no—
210C42—3161no—
211C42—3161no—
212C42—1582no—
213C42—1582no—
214C42—1581no—
215C42—1581no—
216C42—1584no—
217C42C8×D7912yes—
218C23C22⋊C4×D7911yescharacteristic
219Q8—3162no—
220Q8—3162no—
221Q8—3162no—
222Q8—3162no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—3161no—
233C2×C4—3161no—
234C2×C4—3161no—
235C2×C4—3161no—
236C2×C4—3161no—
237C2×C4—791no—
238C2×C4—794no—
239C2×C4—791no—
240C2×C4—1582no—
241C2×C4—1582no—
242C2×C4—1581no—
243C2×C4—1582no—
244C2×C4—1582no—
245C2×C4—1582no—
246C2×C4C2×C8×D7911yescharacteristic
247C2×C4M16×D7911yescharacteristic
248C8—82no—
249C8—6322no—
250C22—21no—
251C22—21no—
252C22C22⋊C8×D7911yescharacteristic
253C22#99×D7911yescharacteristic
254C22#1909854611yescharacteristic
255C4—24no—
256C4—21no—
257C4—21no—
258C4—42no—
259C4—81no—
260C4—3162no—
261C4—3162no—
262C4—3161no—
263C4—792no—
264C4—1584no—
265C4—1581no—
266C2—21no—
267C2—21no—
268C2#2376171711yescharacteristic
269C2#2376506211yescharacteristic
270C2#356×D7911yescharacteristic
subgroupG/H
centerC22#99×D79
commutatorC2×C4×C79C22×C8
FrattiniC2×C4⋊C4C22×D79
FittingC79×#1325C2
socleC22×C79C2×#99
prime radicalC23×C79C2×C22⋊C4
cosocleC2×C4⋊C4×C79C23
hypercenter#1325D79
hypocenterC79#11478
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
22. #14579161C8semidirect
141. C79#11478semidirect

Maximal subgroups

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

subgroupindex
#237659672
#237617222
#237613462
#237613332
C79×#13252
#1147879