Finite Group Databasebeta

← #34185941

Subgroups — #34185941

Order 20224.

424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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#23772485C211yesmaximal, characteristic
2#23768587C211yesmaximal, characteristic
3#23762026C212yesmaximal
4#23761257C212yesmaximal
5C79×#1467C211yesmaximal, characteristic
6C2×#14579153C2211yescharacteristic
7#19098694—24no—
8#19098620—21no—
9#19098620C2212yes—
10#19098616—21no—
11#19098496—21no—
12#19098496—21no—
13#19098470C411yescharacteristic
14#19098470C411yescharacteristic
15#19098447—21no—
16#19098447—21no—
17#19098432C411yescharacteristic
18#19098428C411yescharacteristic
19C4×C4⋊Dic79C2211yescharacteristic
20#19098304—24no—
21C2×C4×Q8×C79C2211yescharacteristic
22#432×C79C2212yes—
23#324×C79—21no—
24#324×C79—21no—
25#14579153—22no—
26#14579153—22no—
27C2×C4⋊Dic79—21no—
28C2×C4⋊Dic79C2×C411yescharacteristic
29C2×C4⋊Dic79C2×C411yescharacteristic
30C2×Dic79⋊C4—21no—
31C2×Dic79⋊C4—21no—
32C2×Dic79⋊C4—21no—
33C2×Dic79⋊C4—21no—
34C2×C4×Dic79C2×C411yescharacteristic
35C2×C4×Dic79C2×C411yescharacteristic
36C4⋊(C79⋊C8)—22no—
37C4⋊(C79⋊C8)—22no—
38C4⋊(C79⋊C8)—22no—
39C22⋊(C79⋊C8)—22no—
40#14579072—22no—
41#14579072D414yes—
42C4×C79⋊C8—22no—
43C79⋊#95—21no—
44C79⋊#95—21no—
45C79⋊#95—21no—
46C79⋊#95—21no—
47C79⋊#95—21no—
48C79⋊#95—21no—
49C79⋊#95—21no—
50C22×Q8×C79C2×C411yescharacteristic
51C4×Q8×C79—22no—
52C4×Q8×C79—22no—
53C2×C4⋊C4×C79C2×C411yescharacteristic
54C2×C4⋊C4×C79D411yescharacteristic
55C2×C4⋊C4×C79D411yescharacteristic
56C2×C42×C79D411yescharacteristic
57C2×C42×C79D411yescharacteristic
58C2×C42×C79C2311yescharacteristic
59C4⋊C8×C79—22no—
60C22⋊C8×C79—22no—
61#97×C79—22no—
62C22×Dic79—21no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C2×C79⋊C8—24no—
67C4⋊Dic79—22no—
68C4⋊Dic79—22no—
69C4⋊Dic79—42no—
70Dic79⋊C4—42no—
71Dic79⋊C4—42no—
72Dic79⋊C4—41no—
73Dic79⋊C4—42no—
74Dic79⋊C4—41no—
75C4×Dic79—41no—
76C4×Dic79—41no—
77C2×Q8×C79—22no—
78C2×Q8×C79—22no—
79C2×Q8×C79—41no—
80C22×C4×C79C22⋊C411yescharacteristic
81C22×C4×C79C22⋊C411yescharacteristic
82C22×C4×C79C22⋊C411yescharacteristic
83C22×C4×C79C22⋊C411yescharacteristic
84C22×C4×C79C22×C411yescharacteristic
85C22×C4×C79C2×D411yescharacteristic
86C22×C4×C79C2×D411yescharacteristic
87C2×C8×C79—42no—
88C4⋊C4×C79—22no—
89C4⋊C4×C79—22no—
90C4⋊C4×C79—22no—
91C42×C79—21no—
92C42×C79—21no—
93C42×C79—21no—
94C42×C79—21no—
95C42×C79C2×D412yes—
96C42×C79#4112yes—
97C23×C79C2×C22⋊C411yescharacteristic
98Q8×C79—44no—
99C2×C4×C79—21no—
100C2×C4×C79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—41no—
109C2×C4×C79—41no—
110C2×C4×C79—41no—
111C2×C4×C79—41no—
112C2×C4×C79#10112yes—
113C2×C4×C79C4×D412yes—
114C2×C4×C79#12011yescharacteristic
115C2×C4×C79#12112yes—
116C2×C4×C79#12311yescharacteristic
117C2×Dic79—22no—
118C2×Dic79—41no—
119C2×Dic79—41no—
120C2×Dic79—41no—
121C2×Dic79—41no—
122C2×Dic79—41no—
123C2×Dic79—41no—
124C2×Dic79—42no—
125C2×Dic79—41no—
126C2×Dic79—41no—
127C2×Dic79—41no—
128C8×C79—82no—
129C79⋊C8—44no—
130C22×C79—21no—
131C22×C79—21no—
132C22×C79#38611yescharacteristic
133C22×C79C2×#10111yescharacteristic
134C22×C79#41311yescharacteristic
135C4×C79—22no—
136C4×C79—22no—
137C4×C79—22no—
138C4×C79—21no—
139C4×C79—21no—
140C4×C79—41no—
141C4×C79—41no—
142C4×C79—41no—
143Dic79—42no—
144Dic79—81no—
145Dic79—81no—
146Dic79—81no—
147#9450—791nomaximal, Sylow
148C2×C79—21no—
149C2×C79—21no—
150C2×C79#188411yescharacteristic
151C2×C79#190111yescharacteristic
152C2×C79#191211yescharacteristic
153#2983—791no—
154#2565—791no—
155#1534—792no—
156#1467D7911yescharacteristic
157#1285—792no—
158C79#945011yescharacteristic, complemented, Sylow
159C2×#125—791no—
160C2×C4×Q8C2×D7911yescharacteristic
161#446—1584no—
162#432—792no—
163#432—1581no—
164#432C2×D7912yes—
165#431—1581no—
166#398—1581no—
167#398—1581no—
168#391—791no—
169#391—791no—
170#387—1581no—
171#387—1581no—
172#384—791no—
173#382—791no—
174C4×C4⋊C4—791no—
175#330—1584no—
176#324—21no—
177#324—21no—
178C22×Q8C4×D7911yescharacteristic
179#125—1582no—
180#125—1582no—
181C4×Q8—22no—
182C4×Q8—22no—
183C2×C4⋊C4—791no—
184C2×C4⋊C4—791no—
185C2×C4⋊C4—1581no—
186C2×C4⋊C4—1581no—
187C2×C4⋊C4—1581no—
188C2×C4⋊C4—1581no—
189C2×C4⋊C4—1581no—
190C2×C4⋊C4C4×D7911yescharacteristic
191C2×C4⋊C4C22⋊D7911yescharacteristic
192C2×C4⋊C4C22⋊D7911yescharacteristic
193C2×C42—791no—
194C2×C42—791no—
195C2×C42D31611yescharacteristic
196C2×C42D31611yescharacteristic
197C2×C42C22×D7911yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—1582no—
200C4⋊C8—1582no—
201C4⋊C8—1582no—
202C22⋊C8—22no—
203C22⋊C8—1582no—
204#97—22no—
205#97—794no—
206#97—1582no—
207C4×C8—1582no—
208#95—1581no—
209#95—1581no—
210#95—1581no—
211#95—1581no—
212#95—1581no—
213#95—1581no—
214#95—1581no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—1581no—
219C22×C4—1581no—
220C22×C4—1581no—
221C22×C4—1581no—
222C22×C4(C2×D79)⋊C411yescharacteristic
223C22×C4(C2×D79)⋊C411yescharacteristic
224C22×C4(C2×D79)⋊C411yescharacteristic
225C22×C4(C2×D79)⋊C411yescharacteristic
226C22×C4C2×C4×D7911yescharacteristic
227C22×C4C2×C22⋊D7911yescharacteristic
228C22×C4C2×D31611yescharacteristic
229C2×C8—42no—
230C2×C8—1584no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—3162no—
235C4⋊C4—3162no—
236C4⋊C4—3162no—
237C4⋊C4—3161no—
238C4⋊C4—3162no—
239C4⋊C4—3161no—
240C4⋊C4—1582no—
241C4⋊C4—1582no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—3161no—
247C42—3161no—
248C42D4×D7912yes—
249C42#1192962312yes—
250C23C2×(C2×D79)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—3161no—
266C2×C4—3161no—
267C2×C4—3161no—
268C2×C4—3161no—
269C2×C4—3161no—
270C2×C4—3161no—
271C2×C4—3162no—
272C2×C4—3161no—
273C2×C4—3161no—
274C2×C4—3161no—
275C2×C4—1582no—
276C2×C4#1457907912yes—
277C2×C4(C22⋊D79)⋊C412yes—
278C2×C4#1457913111yescharacteristic
279C2×C4#1457913312yes—
280C2×C4#1457914511yescharacteristic
281C8—82no—
282C8—3164no—
283C22—21no—
284C22—21no—
285C22#1909844011yescharacteristic
286C22C2×#1457907911yescharacteristic
287C22#1909854511yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—3162no—
297C4—6321no—
298C4—6321no—
299C4—6321no—
300C2—21no—
301C2—21no—
302C2#2376378111yescharacteristic
303C2#2376386611yescharacteristic
304C2#2376393511yescharacteristic
subgroupG/H
centerC22#19098440
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1467C2
socleC22×C79#386
prime radicalC23×C79C2×C22⋊C4
cosocleC2×C42×C79C23
hypercenter#1467D79
hypocenterC79#9450
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
158. C79#9450semidirect

Maximal subgroups

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

subgroupindex
#237724852
#237685872
#237620262
#237612572
C79×#14672
#945079