Finite Group Databasebeta

← #34181944

Subgroups — #34181944

Order 20224.

342 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23763551C211yesmaximal, characteristic
2#23763516C211yesmaximal, characteristic
3#23763145C211yesmaximal, characteristic
4#23761235C211yesmaximal, characteristic
5#23761234C211yesmaximal, characteristic
6#23761234C211yesmaximal, characteristic
7C79×#1277C211yesmaximal, characteristic
8C2×C4⋊(C79⋊C8)C2211yescharacteristic
9C2×C4⋊(C79⋊C8)C2211yescharacteristic
10C2×Dic79⋊C8—21no—
11C2×Dic79⋊C8—21no—
12C2×C4×C79⋊C8C2211yescharacteristic
13C42×Dic79C2211yescharacteristic
14#19098317—21no—
15#19098317—21no—
16#19098317C411yescharacteristic
17#19098317C411yescharacteristic
18#19098317C411yescharacteristic
19#19098317C411yescharacteristic
20C2×C4⋊C8×C79C2211yescharacteristic
21C2×C4⋊C8×C79C2211yescharacteristic
22C2×C4×C8×C79C2211yescharacteristic
23C22×C79⋊C8—21no—
24C22×C79⋊C8—21no—
25C22×C79⋊C8C2×C411yescharacteristic
26C22×C79⋊C8C2×C411yescharacteristic
27C2×C4×Dic79C2×C411yescharacteristic
28C2×C4×Dic79C2×C411yescharacteristic
29C2×C4×Dic79D411yescharacteristic
30C2×C4×Dic79D411yescharacteristic
31C2×C4×Dic79Q811yescharacteristic
32C2×C4×Dic79Q811yescharacteristic
33C4⋊(C79⋊C8)—21no—
34C4⋊(C79⋊C8)—21no—
35C4⋊(C79⋊C8)—21no—
36C4⋊(C79⋊C8)—21no—
37Dic79⋊C8—42no—
38Dic79⋊C8—42no—
39C4×C79⋊C8—21no—
40C4×C79⋊C8—21no—
41C22×C8×C79—21no—
42C22×C8×C79—21no—
43C22×C8×C79C2×C411yescharacteristic
44C22×C8×C79C2×C411yescharacteristic
45C2×C42×C79C2311yescharacteristic
46C4⋊C8×C79—21no—
47C4⋊C8×C79—21no—
48C4⋊C8×C79—21no—
49C4⋊C8×C79—21no—
50C4×C8×C79—21no—
51C4×C8×C79—21no—
52C22×Dic79C4⋊C411yescharacteristic
53C22×Dic79C4⋊C411yescharacteristic
54C22×Dic79C4⋊C411yescharacteristic
55C22×Dic79C4⋊C411yescharacteristic
56C2×C79⋊C8—21no—
57C2×C79⋊C8—21no—
58C2×C79⋊C8—21no—
59C2×C79⋊C8—21no—
60C2×C79⋊C8—21no—
61C2×C79⋊C8—21no—
62C2×C79⋊C8—41no—
63C2×C79⋊C8—41no—
64C2×C79⋊C8—41no—
65C2×C79⋊C8—41no—
66C2×C79⋊C8—41no—
67C2×C79⋊C8—41no—
68C4×Dic79—22no—
69C4×Dic79—22no—
70C4×Dic79—21no—
71C4×Dic79—21no—
72C4×Dic79—21no—
73C4×Dic79—21no—
74C4×Dic79—21no—
75C4×Dic79—21no—
76C4×Dic79—21no—
77C4×Dic79—21no—
78C22×C4×C79C22×C411yescharacteristic
79C22×C4×C79C2×D411yescharacteristic
80C22×C4×C79C2×Q811yescharacteristic
81C2×C8×C79—21no—
82C2×C8×C79—21no—
83C2×C8×C79—21no—
84C2×C8×C79—21no—
85C2×C8×C79—21no—
86C2×C8×C79—21no—
87C2×C8×C79—41no—
88C2×C8×C79—41no—
89C2×C8×C79—41no—
90C2×C8×C79—41no—
91C2×C8×C79—41no—
92C2×C8×C79—41no—
93C42×C79#4111yescharacteristic
94C42×C79#4111yescharacteristic
95C42×C79#4111yescharacteristic
96C42×C79#4111yescharacteristic
97C23×C79C2×C4⋊C411yescharacteristic
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79#11711yescharacteristic
101C2×C4×C79#11711yescharacteristic
102C2×C4×C79#12411yescharacteristic
103C2×C4×C79#12411yescharacteristic
104C2×C4×C79#12511yescharacteristic
105C2×C4×C79#12511yescharacteristic
106C2×C4×C79#13111yescharacteristic
107C2×C4×C79#13111yescharacteristic
108C2×C4×C79#13111yescharacteristic
109C2×C4×C79#13111yescharacteristic
110C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C79#13711yescharacteristic
113C2×C4×C79#13711yescharacteristic
114C2×Dic79—21no—
115C2×Dic79—21no—
116C2×Dic79—21no—
117C2×Dic79—21no—
118C2×Dic79—21no—
119C2×Dic79—21no—
120C2×Dic79—21no—
121C2×Dic79—21no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79#10812yes—
125C2×Dic79#10812yes—
126C8×C79—41no—
127C8×C79—41no—
128C8×C79—81no—
129C8×C79—81no—
130C79⋊C8—41no—
131C79⋊C8—41no—
132C79⋊C8—81no—
133C79⋊C8—81no—
134C22×C79#38211yescharacteristic
135C22×C79#42411yescharacteristic
136C22×C79#42411yescharacteristic
137C22×C79#42811yescharacteristic
138C22×C79#42811yescharacteristic
139C22×C79C2×#10811yescharacteristic
140C22×C79C2×#10811yescharacteristic
141C4×C79—21no—
142C4×C79—21no—
143C4×C79#43311yescharacteristic
144C4×C79#43311yescharacteristic
145C4×C79#43311yescharacteristic
146C4×C79#43311yescharacteristic
147C4×C79#48911yescharacteristic
148C4×C79#48911yescharacteristic
149C4×C79#49011yescharacteristic
150C4×C79#49111yescharacteristic
151Dic79—22no—
152Dic79—22no—
153Dic79—41no—
154Dic79—41no—
155#8789—791nomaximal, Sylow
156C2×C79#157311yescharacteristic
157C2×C79#157311yescharacteristic
158C2×C79#157411yescharacteristic
159C2×C79#157411yescharacteristic
160C2×C79#183211yescharacteristic
161C2×C79#183611yescharacteristic
162C2×C79#183711yescharacteristic
163#1842—791no—
164#1831—791no—
165#1744—791no—
166#1277—791no—
167#1277—791no—
168#1277—791no—
169#1277D7911yescharacteristic
170C79#878911yescharacteristic, complemented, Sylow
171C2×C4⋊C8—791no—
172C2×C4⋊C8—791no—
173C2×C4⋊C8—1581no—
174C2×C4⋊C8—1581no—
175C2×C4⋊C8C2×D7911yescharacteristic
176C2×C4⋊C8C2×D7911yescharacteristic
177C2×C4×C8—791no—
178C2×C4×C8C2×D7911yescharacteristic
179C43—791no—
180#336—791no—
181#336—791no—
182#336—791no—
183#336—791no—
184#336—1581no—
185#336—1581no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—791no—
189C22×C8—791no—
190C22×C8—1581no—
191C22×C8—1581no—
192C22×C8C4×D7911yescharacteristic
193C22×C8C4×D7911yescharacteristic
194C2×C42—791no—
195C2×C42—791no—
196C2×C42—791no—
197C2×C42—791no—
198C2×C42—791no—
199C2×C42—791no—
200C2×C42C22×D7911yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—3162no—
206C4⋊C8—3162no—
207C4⋊C8—1581no—
208C4⋊C8—1581no—
209C4⋊C8—1581no—
210C4⋊C8—1581no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—1581no—
214C4×C8—1581no—
215C22×C4—791no—
216C22×C4—791no—
217C22×C4—791no—
218C22×C4—791no—
219C22×C4C2×C4×D7911yescharacteristic
220C22×C4D4×D7911yescharacteristic
221C22×C4Q8×D7911yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—3161no—
235C2×C8—3161no—
236C2×C8—3161no—
237C2×C8—3161no—
238C2×C8—3161no—
239C2×C8—3161no—
240C2×C8—1581no—
241C2×C8—1581no—
242C2×C8—1581no—
243C2×C8—1581no—
244C2×C8—1581no—
245C2×C8—1581no—
246C42—1582no—
247C42—1582no—
248C42—1581no—
249C42—1581no—
250C42—1581no—
251C42—1581no—
252C42—1581no—
253C42—1581no—
254C42—1581no—
255C42—1581no—
256C42#1192962311yescharacteristic
257C42#1192962311yescharacteristic
258C42#1192962411yescharacteristic
259C42#1192962411yescharacteristic
260C23C4⋊C4×D7911yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—792no—
264C2×C4—792no—
265C2×C4—1581no—
266C2×C4—1581no—
267C2×C4—1581no—
268C2×C4—1581no—
269C2×C4—1581no—
270C2×C4—1581no—
271C2×C4—1581no—
272C2×C4—1581no—
273C2×C4—1581no—
274C2×C4—1581no—
275C2×C4#1457911711yescharacteristic
276C2×C4#1457911811yescharacteristic
277C2×C4#1457914711yescharacteristic
278C2×C4#1457914711yescharacteristic
279C2×C4#1457915111yescharacteristic
280C2×C4#1457915111yescharacteristic
281C2×C4#1457916711yescharacteristic
282C2×C4#1457916711yescharacteristic
283C2×C4#1457916911yescharacteristic
284C2×C4#1457916911yescharacteristic
285C2×C4#1457918511yescharacteristic
286C2×C4#1457918811yescharacteristic
287C2×C4#1457919011yescharacteristic
288C2×C4#1457919311yescharacteristic
289C8—41no—
290C8—41no—
291C8—81no—
292C8—81no—
293C8—3161no—
294C8—3161no—
295C8—6321no—
296C8—6321no—
297C22#1909842711yescharacteristic
298C22#1909858811yescharacteristic
299C22#1909858811yescharacteristic
300C22#1909860211yescharacteristic
301C22#1909860411yescharacteristic
302C22#108×D7911yescharacteristic
303C22#108×D7911yescharacteristic
304C4—21no—
305C4—21no—
306C4—3161no—
307C4—3161no—
308C4—1582no—
309C4—1582no—
310C4#1909862111yescharacteristic
311C4#1909862111yescharacteristic
312C4#1909862211yescharacteristic
313C4#1909862511yescharacteristic
314C4#1909892111yescharacteristic
315C4#1909892411yescharacteristic
316C4#1909892611yescharacteristic
317C4#1909893011yescharacteristic
318C2#2376218211yescharacteristic
319C2#2376218411yescharacteristic
320C2#2376218711yescharacteristic
321C2#2376219011yescharacteristic
322C2#2376351811yescharacteristic
323C2#2376353211yescharacteristic
324C2#2376353611yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1277C2
socle, prime radicalC23×C79C2×C4⋊C4
cosocleC2×C42×C79C23
hypercenter#1277D79
hypocenterC79#8789
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
170. C79#8789semidirect

Maximal subgroups

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

subgroupindex
#237635512
#237635162
#237631452
#237612352
#237612342
C79×#12772
#878979