Finite Group Databasebeta

← #34193030

Subgroups — #34193030

Order 20224.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23763528C211yesmaximal, characteristic
2#23763405C211yesmaximal, characteristic
3#23763405C211yesmaximal, characteristic
4#23761284C211yesmaximal, characteristic
5#23761284C211yesmaximal, characteristic
6#23761235C211yesmaximal, characteristic
7C79×#1984C211yesmaximal, characteristic
8C2×C4⋊(C79⋊C8)C2211yescharacteristic
9C2×C4⋊(C79⋊C8)C2211yescharacteristic
10C2×#14579085—21no—
11C2×#14579085—21no—
12#19098433C2211yescharacteristic
13#19098433C2211yescharacteristic
14#19098326—21no—
15#19098326—21no—
16#19098325—21no—
17#19098325—21no—
18C2×C4×Q8×C79C2211yescharacteristic
19C2×C4⋊C8×C79C2211yescharacteristic
20C2×C4×C8×C79C2211yescharacteristic
21#336×C79—21no—
22#336×C79—21no—
23C22×C79⋊C8—21no—
24C22×C79⋊C8—21no—
25C2×C4⋊Dic79—21no—
26C2×C4⋊Dic79—21no—
27C2×C4⋊Dic79—21no—
28C2×C4⋊Dic79—21no—
29C2×C4⋊Dic79—21no—
30C2×C4⋊Dic79—21no—
31C4⋊(C79⋊C8)—21no—
32C4⋊(C79⋊C8)—21no—
33C4⋊(C79⋊C8)—21no—
34C4⋊(C79⋊C8)—21no—
35#14579085—42no—
36#14579085—42no—
37C22×Q8×C79D411yescharacteristic
38C22×C8×C79—21no—
39C22×C8×C79D411yescharacteristic
40C22×C8×C79D411yescharacteristic
41C4×Q8×C79—21no—
42C4×Q8×C79—21no—
43C4×Q8×C79—21no—
44C4×Q8×C79—21no—
45C2×C4⋊C4×C79—21no—
46C2×C4⋊C4×C79D411yescharacteristic
47C2×C42×C79—21no—
48C2×C42×C79C2311yescharacteristic
49C4⋊C8×C79—21no—
50C4⋊C8×C79—21no—
51C4×C8×C79—21no—
52C4×C8×C79—21no—
53C22×Dic79—41no—
54C22×Dic79—41no—
55C2×C79⋊C8—41no—
56C2×C79⋊C8—41no—
57C2×C79⋊C8—41no—
58C2×C79⋊C8—41no—
59C2×C79⋊C8—41no—
60C2×C79⋊C8—41no—
61C4⋊Dic79—41no—
62C4⋊Dic79—41no—
63C4⋊Dic79—41no—
64C4⋊Dic79—41no—
65C4⋊Dic79—41no—
66C4⋊Dic79—41no—
67C4⋊Dic79—41no—
68C4⋊Dic79—41no—
69C4⋊Dic79—81no—
70C4⋊Dic79—81no—
71C2×Q8×C79—21no—
72C2×Q8×C79—21no—
73C2×Q8×C79—21no—
74C2×Q8×C79—21no—
75C2×Q8×C79—21no—
76C2×Q8×C79SD1612yes—
77C22×C4×C79—21no—
78C22×C4×C79—21no—
79C22×C4×C79C2×D411yescharacteristic
80C22×C4×C79C2×D411yescharacteristic
81C22×C4×C79#4111yescharacteristic
82C2×C8×C79—21no—
83C2×C8×C79—21no—
84C2×C8×C79—21no—
85C2×C8×C79—21no—
86C2×C8×C79—21no—
87C2×C8×C79—21no—
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—
95C42×C79—41no—
96C42×C79—41no—
97C42×C79#4111yescharacteristic
98C42×C79#4111yescharacteristic
99C42×C79#4111yescharacteristic
100C42×C79#4111yescharacteristic
101C23×C79#12111yescharacteristic
102Q8×C79—22no—
103Q8×C79—22no—
104Q8×C79—41no—
105Q8×C79—41no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—22no—
109C2×C4×C79—41no—
110C2×C4×C79—41no—
111C2×C4×C79—41no—
112C2×C4×C79—41no—
113C2×C4×C79—41no—
114C2×C4×C79#12311yescharacteristic
115C2×C4×C79#12311yescharacteristic
116C2×C4×C79#12311yescharacteristic
117C2×C4×C79#12411yescharacteristic
118C2×C4×C79#12611yescharacteristic
119C2×C4×C79#12611yescharacteristic
120C2×C4×C79C2×SD1611yescharacteristic
121C2×C4×C79#13511yescharacteristic
122C2×C4×C79#13511yescharacteristic
123C2×C4×C79#13511yescharacteristic
124C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C79#13711yescharacteristic
126C2×C4×C79#13711yescharacteristic
127C2×C4×C79#13711yescharacteristic
128C2×Dic79—81no—
129C2×Dic79—81no—
130C2×Dic79—81no—
131C2×Dic79—81no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C8×C79—41no—
135C8×C79—41no—
136C8×C79—81no—
137C79⋊C8—81no—
138C79⋊C8—81no—
139C22×C79#39711yescharacteristic
140C22×C79#46411yescharacteristic
141C22×C79#46411yescharacteristic
142C22×C79#46511yescharacteristic
143C22×C79#46811yescharacteristic
144C22×C79#47211yescharacteristic
145C22×C79#47311yescharacteristic
146C4×C79—21no—
147C4×C79—21no—
148C4×C79—42no—
149C4×C79—81no—
150C4×C79#48111yescharacteristic
151C4×C79#48211yescharacteristic
152C4×C79#48311yescharacteristic
153C4×C79#48511yescharacteristic
154C4×C79#48511yescharacteristic
155C4×C79#48511yescharacteristic
156C4×C79#48811yescharacteristic
157C4×C79#49111yescharacteristic
158Dic79—161no—
159Dic79—161no—
160#10626—791nomaximal, Sylow
161C2×C79#167811yescharacteristic
162C2×C79#168011yescharacteristic
163C2×C79#169811yescharacteristic
164C2×C79#170011yescharacteristic
165C2×C79#207411yescharacteristic
166C2×C79#207711yescharacteristic
167C2×C79#207811yescharacteristic
168#1984D7911yescharacteristic
169#1834—791no—
170#1803—791no—
171#1803—791no—
172#1296—791no—
173#1296—791no—
174#1277—791no—
175C79#1062611yescharacteristic, complemented, Sylow
176C2×C4×Q8C2×D7911yescharacteristic
177C2×C4⋊C8—791no—
178C2×C4⋊C8—791no—
179C2×C4⋊C8C2×D7911yescharacteristic
180C2×#103—1581no—
181C2×#103—1581no—
182C2×C4×C8C2×D7911yescharacteristic
183#384—791no—
184#384—791no—
185#340—1581no—
186#340—1581no—
187#340—1581no—
188#340—1581no—
189#336—21no—
190#336—21no—
191C22×Q8D31611yescharacteristic
192C22×C8—21no—
193C22×C8—1581no—
194C22×C8—1581no—
195C22×C8C22⋊D7911yescharacteristic
196C22×C8C22⋊D7911yescharacteristic
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—1581no—
203C2×C4⋊C4—1581no—
204C2×C4⋊C4—1581no—
205C2×C4⋊C4—1581no—
206C2×C4⋊C4—1581no—
207C2×C4⋊C4—1581no—
208C2×C4⋊C4D31611yescharacteristic
209C2×C42—21no—
210C2×C42C22×D7911yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—1581no—
214C4⋊C8—1581no—
215C4⋊C8—1581no—
216C4⋊C8—1581no—
217#103—3162no—
218#103—3162no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8#1192961312yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—3161no—
230C22×C4—3161no—
231C22×C4C2×C22⋊D7911yescharacteristic
232C22×C4C2×D31611yescharacteristic
233C22×C4#1192962411yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—3161no—
244C2×C8—3161no—
245C2×C8—3161no—
246C2×C8—3161no—
247C2×C8—3161no—
248C2×C8—3161no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—3161no—
254C4⋊C4—3161no—
255C4⋊C4—3161no—
256C4⋊C4—3161no—
257C4⋊C4—3161no—
258C4⋊C4—3161no—
259C4⋊C4—3161no—
260C4⋊C4—3161no—
261C4⋊C4—6321no—
262C4⋊C4—6321no—
263C42—41no—
264C42—41no—
265C42#1192962311yescharacteristic
266C42#1192962311yescharacteristic
267C42#1192962311yescharacteristic
268C42#1192962311yescharacteristic
269C23#1457913511yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—6321no—
283C2×C4—6321no—
284C2×C4—6321no—
285C2×C4—6321no—
286C2×C4—6321no—
287C2×C4—6321no—
288C2×C4#1457914211yescharacteristic
289C2×C4#1457914511yescharacteristic
290C2×C4#1457914511yescharacteristic
291C2×C4#1457914811yescharacteristic
292C2×C4#1457915411yescharacteristic
293C2×C4#1457915411yescharacteristic
294C2×C4C2×#1192961311yescharacteristic
295C2×C4#1457918111yescharacteristic
296C2×C4#1457918111yescharacteristic
297C2×C4#1457918311yescharacteristic
298C2×C4#1457918911yescharacteristic
299C2×C4#1457919211yescharacteristic
300C2×C4#1457919211yescharacteristic
301C2×C4#1457919411yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—6321no—
306C8—6321no—
307C22#1909848811yescharacteristic
308C22#1909878511yescharacteristic
309C22#1909878511yescharacteristic
310C22#1909879211yescharacteristic
311C22#1909880911yescharacteristic
312C22#1909883311yescharacteristic
313C22#1909883811yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—12641no—
319C4—12641no—
320C4#1909888211yescharacteristic
321C4#1909888811yescharacteristic
322C4#1909889411yescharacteristic
323C4#1909890111yescharacteristic
324C4#1909890111yescharacteristic
325C4#1909890511yescharacteristic
326C4#1909891711yescharacteristic
327C4#1909893111yescharacteristic
328C2#2376281611yescharacteristic
329C2#2376283011yescharacteristic
330C2#2376294011yescharacteristic
331C2#2376295411yescharacteristic
332C2#2376481811yescharacteristic
333C2#2376483311yescharacteristic
334C2#2376484011yescharacteristic
subgroupG/H
centerC23#14579135
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1984C2
socle, prime radicalC23×C79#121
hypercenter#1984D79
hypocenterC79#10626
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
175. C79#10626semidirect

Maximal subgroups

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

subgroupindex
#237635282
#237634052
#237612842
#237612352
C79×#19842
#1062679