Finite Group Databasebeta

← #34191270

Subgroups — #34191270

Order 20224.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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#23769370C211yesmaximal, characteristic
2#23763487C212yesmaximal
3#23761667C211yesmaximal, characteristic
4#23761280C212yesmaximal
5C79×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic79C2211yescharacteristic
7#19098505—22no—
8#19098497—22no—
9#19098436—22no—
10#19098423C2212yes—
11C2×C79⋊#95—22no—
12C2×C79⋊#95C2211yescharacteristic
13#19098326—22no—
14#19098326—22no—
15C2×C22⋊C8×C79C2212yes—
16C2×#95×C79C2211yescharacteristic
17C23×Dic79—21no—
18C23×Dic79—21no—
19C2×C4⋊Dic79—22no—
20C2×C4⋊Dic79—22no—
21C2×C4⋊Dic79—21no—
22C2×C4⋊Dic79D412yes—
23C2×C4⋊Dic79D412yes—
24C2×C4⋊Dic79Q812yes—
25C2×Dic79⋊C4—22no—
26C2×Dic79⋊C4—22no—
27C2×C22⋊Dic79—22no—
28C79⋊#95—22no—
29C79⋊#95—22no—
30C79⋊#95—22no—
31C79⋊#95—22no—
32C79⋊#95—44no—
33C23×C4×C79D412yes—
34C23×C4×C79C2311yescharacteristic
35C22×C8×C79—22no—
36C22⋊C8×C79—22no—
37C22⋊C8×C79—22no—
38#95×C79—22no—
39C22×Dic79—22no—
40C22×Dic79—22no—
41C22×Dic79—22no—
42C22×Dic79—22no—
43C22×Dic79—41no—
44C22×Dic79—42no—
45C22×Dic79—41no—
46C22×Dic79—41no—
47C22×Dic79—41no—
48C22×Dic79—42no—
49C22×Dic79—42no—
50C22×Dic79—42no—
51C4⋊Dic79—24no—
52C4⋊Dic79—42no—
53C4⋊Dic79—42no—
54C4⋊Dic79—42no—
55Dic79⋊C4—82no—
56Dic79⋊C4—82no—
57C22⋊Dic79—42no—
58C22⋊Dic79—42no—
59C24×C79C2×D411yescharacteristic
60C22×C4×C79—22no—
61C22×C4×C79—22no—
62C22×C4×C79—22no—
63C22×C4×C79—42no—
64C22×C4×C79—42no—
65C22×C4×C79—42no—
66C22×C4×C79C2×D412yes—
67C22×C4×C79C2×Q811yescharacteristic
68C22×C4×C79#4112yes—
69C22×C4×C79#4111yescharacteristic
70C2×C8×C79—42no—
71C2×C8×C79—42no—
72C2×C8×C79—42no—
73C23×C79—21no—
74C23×C79—21no—
75C23×C79—22no—
76C23×C79#12011yescharacteristic
77C23×C79C22⋊Q811yescharacteristic
78C23×C79#12411yescharacteristic
79C23×C79#13512yes—
80C23×C79AGL(1,ℤ/8)12yes—
81C2×C4×C79—22no—
82C2×C4×C79—22no—
83C2×C4×C79—41no—
84C2×C4×C79—41no—
85C2×C4×C79—42no—
86C2×C4×C79—44no—
87C2×C4×C79—42no—
88C2×C4×C79—42no—
89C2×C4×C79—42no—
90C2×C4×C79—82no—
91C2×C4×C79C22⋊Q812yes—
92C2×C4×C79#12412yes—
93C2×Dic79—44no—
94C2×Dic79—42no—
95C2×Dic79—42no—
96C2×Dic79—42no—
97C2×Dic79—42no—
98C2×Dic79—42no—
99C2×Dic79—42no—
100C2×Dic79—42no—
101C2×Dic79—42no—
102C2×Dic79—44no—
103C2×Dic79—82no—
104C2×Dic79—81no—
105C2×Dic79—82no—
106C2×Dic79—81no—
107C2×Dic79—81no—
108C2×Dic79—81no—
109C8×C79—82no—
110C22×C79—22no—
111C22×C79—22no—
112C22×C79—22no—
113C22×C79—22no—
114C22×C79—21no—
115C22×C79—21no—
116C22×C79—21no—
117C22×C79—21no—
118C22×C79#39311yescharacteristic
119C22×C79#44912yes—
120C22×C79#45511yescharacteristic
121C22×C79#45611yescharacteristic
122C22×C79#45812yes—
123C22×C79#47812yes—
124C22×C79#48811yescharacteristic
125C22×C79#49011yescharacteristic
126C4×C79—22no—
127C4×C79—22no—
128C4×C79—82no—
129Dic79—82no—
130Dic79—82no—
131Dic79—82no—
132Dic79—82no—
133#10346—791nomaximal, Sylow
134C2×C79—21no—
135C2×C79—22no—
136C2×C79—21no—
137C2×C79#160912yes—
138C2×C79#161212yes—
139C2×C79#202511yescharacteristic
140C2×C79#202811yescharacteristic
141C2×C79#203011yescharacteristic
142#2646—791no—
143#1823—792no—
144#1445—791no—
145#1294—792no—
146#1280D7911yescharacteristic
147C79#1034611yescharacteristic, complemented, Sylow
148C22×C4⋊C4—791no—
149C2×C22⋊C8C2×D7912yes—
150#400—1582no—
151#398—1582no—
152#385—1582no—
153#380—792no—
154C2×#95—791no—
155C2×#95—1582no—
156C2×#95C2×D7911yescharacteristic
157#340—1582no—
158#340—1582no—
159C23×C4—1581no—
160C23×C4—1581no—
161C23×C4D31612yes—
162C23×C4C22×D7911yescharacteristic
163C22×C8—22no—
164C2×C4⋊C4—792no—
165C2×C4⋊C4—792no—
166C2×C4⋊C4—792no—
167C2×C4⋊C4—1581no—
168C2×C4⋊C4—1582no—
169C2×C4⋊C4—1582no—
170C2×C4⋊C4—1582no—
171C2×C4⋊C4—1582no—
172C2×C22⋊C4—1582no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—22no—
176#95—3164no—
177#95—1582no—
178#95—1582no—
179#95—1582no—
180#95—1582no—
181C24C2×D31611yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—3161no—
189C22×C4—3162no—
190C22×C4—3161no—
191C22×C4—3161no—
192C22×C4—3161no—
193C22×C4—3162no—
194C22×C4—3162no—
195C22×C4—3162no—
196C22×C4—1582no—
197C22×C4—1582no—
198C22×C4—1582no—
199C22×C4—1582no—
200C22×C4D4×D7912yes—
201C22×C4Q8×D7911yescharacteristic
202C22×C4#1192962311yescharacteristic
203C22×C4#1192962412yes—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C4⋊C4—3162no—
208C4⋊C4—3162no—
209C4⋊C4—3162no—
210C4⋊C4—6322no—
211C4⋊C4—6322no—
212C4⋊C4—1584no—
213C22⋊C4—3162no—
214C22⋊C4—3162no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1457913111yescharacteristic
219C23#1457914111yescharacteristic
220C23#1457914911yescharacteristic
221C23#1457918312yes—
222C23#1457918912yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—3162no—
234C2×C4—3164no—
235C2×C4—3162no—
236C2×C4—3162no—
237C2×C4—3162no—
238C2×C4—3162no—
239C2×C4—3162no—
240C2×C4—3162no—
241C2×C4—3162no—
242C2×C4—3164no—
243C2×C4—6321no—
244C2×C4—6322no—
245C2×C4—6321no—
246C2×C4—6321no—
247C2×C4—6321no—
248C2×C4—6322no—
249C2×C4#1457913912yes—
250C2×C4#1457914712yes—
251C8—82no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—22no—
260C22#1909847611yescharacteristic
261C22#1909871012yes—
262C22#1909874311yescharacteristic
263C22#1909874811yescharacteristic
264C22#1909875412yes—
265C22#1909886412yes—
266C22#1909891811yescharacteristic
267C22#1909892811yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—6322no—
272C4—6322no—
273C4—6322no—
274C4—6322no—
275C2—21no—
276C2—21no—
277C2—22no—
278C2#2376239912yes—
279C2#2376241612yes—
280C2#2376454711yescharacteristic
281C2#2376456211yescharacteristic
282C2#2376456811yescharacteristic
subgroupG/H
centerC23#14579131
commutator, cosocleC23×C4×C79C23
FrattiniC23×C4C22×D79
FittingC79×#1280C2
socleC23×C79#120
prime radicalC24×C79C2×D4
hypercenter#1280D79
hypocenterC79#10346
LCSG ▷ C23×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
147. C79#10346semidirect

Maximal subgroups

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

subgroupindex
#237693702
#237634872
#237616672
#237612802
C79×#12802
#1034679