Finite Group Databasebeta

← #34177407

Subgroups — #34177407

Order 20224.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#23771391C211yesmaximal, characteristic
2#23764959C211yesmaximal, characteristic
3#23764876C211yesmaximal, characteristic
4#23764873C211yesmaximal, characteristic
5#23761224C211yesmaximal, characteristic
6#23761222C211yesmaximal, characteristic
7C79×#1271C211yesmaximal, characteristic
8C2×#14579095—21no—
9C2×#14579092—21no—
10#19098503—21no—
11#19098502—21no—
12#19098501—21no—
13#19098461C2211yescharacteristic
14#19098461C2211yescharacteristic
15#19098450—21no—
16#19098449—21no—
17#19098444—21no—
18#19098433C2211yescharacteristic
19#19098326—21no—
20#19098326—21no—
21#19098326—21no—
22#19098325—21no—
23#19098318C2211yescharacteristic
24#389×C79C2211yescharacteristic
25#336×C79C2211yescharacteristic
26#336×C79C2211yescharacteristic
27C22×C79⋊C8—21no—
28C2×C4⋊Dic79—21no—
29C2×C4⋊Dic79—21no—
30C2×C4⋊Dic79—21no—
31C2×C4⋊Dic79D411yescharacteristic
32C2×C4⋊Dic79D411yescharacteristic
33C2×C4⋊Dic79D411yescharacteristic
34C2×C4⋊Dic79D411yescharacteristic
35C2×Dic79⋊C4—21no—
36C2×Dic79⋊C4—21no—
37C2×C4×Dic79—21no—
38#14579095—42no—
39#14579092—42no—
40C79⋊#95—21no—
41C79⋊#95—21no—
42C79⋊#95—21no—
43C79⋊#95—21no—
44C79⋊#95—21no—
45C79⋊#95—21no—
46C79⋊#95—21no—
47C79⋊#95—21no—
48C79⋊#95—21no—
49C22×C8×C79—21no—
50C22×C8×C79—21no—
51C2×C4⋊C4×C79—21no—
52C2×C4⋊C4×C79D411yescharacteristic
53C2×C4⋊C4×C79D411yescharacteristic
54C2×C42×C79C2311yescharacteristic
55#95×C79—21no—
56C22×Dic79—21no—
57C22×Dic79—21no—
58C22×Dic79—21no—
59C22×Dic79—21no—
60C22×Dic79—41no—
61C2×C79⋊C8—22no—
62C2×C79⋊C8—41no—
63C2×C79⋊C8—41no—
64C4⋊Dic79—21no—
65C4⋊Dic79—21no—
66C4⋊Dic79—21no—
67C4⋊Dic79—21no—
68C4⋊Dic79—41no—
69C4⋊Dic79—41no—
70C4⋊Dic79—42no—
71C4⋊Dic79—41no—
72C4⋊Dic79—41no—
73C4⋊Dic79—41no—
74C4⋊Dic79—41no—
75Dic79⋊C4—41no—
76Dic79⋊C4—41no—
77Dic79⋊C4—41no—
78Dic79⋊C4—41no—
79C4×Dic79—81no—
80C22×C4×C79—21no—
81C22×C4×C79—21no—
82C22×C4×C79C2×D411yescharacteristic
83C22×C4×C79C2×D411yescharacteristic
84C22×C4×C79C2×D411yescharacteristic
85C2×C8×C79—22no—
86C2×C8×C79—41no—
87C2×C8×C79—41no—
88C2×C8×C79—41no—
89C2×C8×C79—41no—
90C2×C8×C79—41no—
91C4⋊C4×C79—21no—
92C4⋊C4×C79—21no—
93C4⋊C4×C79—41no—
94C4⋊C4×C79—41no—
95C4⋊C4×C79—41no—
96C42×C79—41no—
97C23×C79#12011yescharacteristic
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—41no—
105C2×C4×C79—41no—
106C2×C4×C79—41no—
107C2×C4×C79—41no—
108C2×C4×C79—41no—
109C2×C4×C79—41no—
110C2×C4×C79#13511yescharacteristic
111C2×C4×C79#13511yescharacteristic
112C2×C4×C79#13511yescharacteristic
113C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C79#13711yescharacteristic
116C2×Dic79—41no—
117C2×Dic79—41no—
118C2×Dic79—41no—
119C2×Dic79—41no—
120C2×Dic79—41no—
121C2×Dic79—41no—
122C2×Dic79—41no—
123C2×Dic79—41no—
124C2×Dic79—41no—
125C2×Dic79—41no—
126C2×Dic79—41no—
127C2×Dic79—41no—
128C2×Dic79—81no—
129C2×Dic79—81no—
130C2×Dic79—81no—
131C8×C79—42no—
132C8×C79—81no—
133C79⋊C8—42no—
134C22×C79#44911yescharacteristic
135C22×C79#44911yescharacteristic
136C22×C79#45211yescharacteristic
137C22×C79#45411yescharacteristic
138C22×C79#45611yescharacteristic
139C22×C79#45611yescharacteristic
140C22×C79#45811yescharacteristic
141C4×C79—21no—
142C4×C79—21no—
143C4×C79—21no—
144C4×C79—21no—
145C4×C79—21no—
146C4×C79—21no—
147C4×C79—81no—
148C4×C79—81no—
149Dic79—81no—
150Dic79—81no—
151Dic79—81no—
152Dic79—81no—
153Dic79—161no—
154#7803—791nomaximal, Sylow
155C2×C79#160911yescharacteristic
156C2×C79#160911yescharacteristic
157C2×C79#161511yescharacteristic
158C2×C79#162811yescharacteristic
159C2×C79#165011yescharacteristic
160C2×C79#165211yescharacteristic
161C2×C79#166311yescharacteristic
162#2810—791no—
163#2099—791no—
164#2084—791no—
165#2083—791no—
166#1271—791no—
167#1271—791no—
168#1271D7911yescharacteristic
169C79#780311yescharacteristic, complemented, Sylow
170C2×#107—1581no—
171C2×#106—1581no—
172#400—1581no—
173#400—1581no—
174#400—1581no—
175#389—791no—
176#389—791no—
177#389C2×D7911yescharacteristic
178#387—1581no—
179#387—1581no—
180#387—1581no—
181#384—791no—
182#340—1581no—
183#340—1581no—
184#340—1581no—
185#340—1581no—
186#336—791no—
187#336C2×D7911yescharacteristic
188#336C2×D7911yescharacteristic
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—1581no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—791no—
194C2×C4⋊C4—791no—
195C2×C4⋊C4—791no—
196C2×C4⋊C4—791no—
197C2×C4⋊C4—1581no—
198C2×C4⋊C4—1581no—
199C2×C4⋊C4—1581no—
200C2×C4⋊C4—1581no—
201C2×C4⋊C4—1581no—
202C2×C4⋊C4D31611yescharacteristic
203C2×C4⋊C4D31611yescharacteristic
204C2×C42—1581no—
205C2×C42C22×D7911yescharacteristic
206#107—3162no—
207#106—3162no—
208#95—21no—
209#95—1581no—
210#95—1581no—
211#95—1581no—
212#95—1581no—
213#95—1581no—
214#95—1581no—
215#95—1581no—
216#95—1581no—
217#95—1581no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—3161no—
221C22×C4—1581no—
222C22×C4—1581no—
223C22×C4—1581no—
224C22×C4—1581no—
225C22×C4D4×D7911yescharacteristic
226C22×C4D4×D7911yescharacteristic
227C22×C4C2×D31611yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—3161no—
235C2×C8—3161no—
236C2×C8—1582no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—3161no—
243C4⋊C4—3161no—
244C4⋊C4—3162no—
245C4⋊C4—3161no—
246C4⋊C4—3161no—
247C4⋊C4—3161no—
248C4⋊C4—3161no—
249C4⋊C4—3161no—
250C4⋊C4—3161no—
251C4⋊C4—3161no—
252C4⋊C4—3161no—
253C4⋊C4—1581no—
254C4⋊C4—1581no—
255C4⋊C4—1581no—
256C4⋊C4—1581no—
257C42—41no—
258C42—6321no—
259C23#1457913111yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—3161no—
273C2×C4—3161no—
274C2×C4—3161no—
275C2×C4—3161no—
276C2×C4—3161no—
277C2×C4—3161no—
278C2×C4—3161no—
279C2×C4—3161no—
280C2×C4—3161no—
281C2×C4—3161no—
282C2×C4—3161no—
283C2×C4—3161no—
284C2×C4—6321no—
285C2×C4—6321no—
286C2×C4—6321no—
287C2×C4#1457918011yescharacteristic
288C2×C4#1457918311yescharacteristic
289C2×C4#1457918411yescharacteristic
290C2×C4#1457918811yescharacteristic
291C2×C4#1457918911yescharacteristic
292C2×C4#1457919011yescharacteristic
293C8—42no—
294C8—81no—
295C8—3162no—
296C22#1909871011yescharacteristic
297C22#1909871111yescharacteristic
298C22#1909872611yescharacteristic
299C22#1909873711yescharacteristic
300C22#1909874711yescharacteristic
301C22#1909874811yescharacteristic
302C22#1909875411yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—6321no—
312C4—6321no—
313C4—6321no—
314C4—6321no—
315C4—12641no—
316C2#2376239911yescharacteristic
317C2#2376240011yescharacteristic
318C2#2376243211yescharacteristic
319C2#2376251311yescharacteristic
320C2#2376265811yescharacteristic
321C2#2376267111yescharacteristic
322C2#2376273011yescharacteristic
subgroupG/H
centerC23#14579131
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1271C2
socle, prime radicalC23×C79#120
hypercenter#1271D79
hypocenterC79#7803
LCSG ▷ C2×C42×C79 ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
169. C79#7803semidirect

Maximal subgroups

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

subgroupindex
#237713912
#237649592
#237648762
#237648732
#237612242
#237612222
C79×#12712
#780379