Finite Group Databasebeta

← #34209746

Subgroups — #34209746

Order 20224.

2154 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D79)⋊C4C213yesmaximal
2C2×#95×D79C211yesmaximal, characteristic
3#23761627C213yesmaximal, complemented
4#23761626C213yesmaximal, complemented
5(C2×D79)⋊#95C213yesmaximal
6#95×Dic79C211yesmaximal, characteristic, complemented
7C2×#376×C79C211yesmaximal, characteristic, complemented
8C23×C4×D79C2213yes—
9C22×(C2×D79)⋊C4C2213yes—
10C22×(C2×D79)⋊C4C2211yescharacteristic
11C22×C4×Dic79C2213yes—
12C4×(C2×D79)⋊C4C4124yescomplemented
13C2×C79⋊#95C2213yes—
14C2×C79⋊#95C2213yes—
15C2×C79⋊#95C2216yes—
16C2×C79⋊#95C2213yes—
17C2×C79⋊#95C2213yes—
18#95×D79—24no—
19C22×C42×C79C2213yes—
20#376×C79—24no—
21C2×#95×C79C2213yes—
22C2×#95×C79C2211yescharacteristic
23C24×D79C2311yescharacteristic
24C23×Dic79C2313yes—
25C23×Dic79C2313yes—
26C23×Dic79C2311yescharacteristic
27C22×C4×D79—26no—
28C22×C4×D79—26no—
29C22×C4×D79—212no—
30C22×C4×D79—46no—
31C22×C4×D79C2×C4112yes—
32C2×(C2×D79)⋊C4—26no—
33C2×(C2×D79)⋊C4—26no—
34C2×(C2×D79)⋊C4C2×C4112yes—
35C2×(C2×D79)⋊C4C2×C4112yes—
36C2×C4×Dic79—46no—
37C2×C4×Dic79C2×C4112yescomplemented
38C79⋊#95—26no—
39C79⋊#95—26no—
40C79⋊#95—46no—
41C79⋊#95C2×C4112yescomplemented
42C79⋊#95C2×C4112yescomplemented
43C23×C4×C79C2313yes—
44C23×C4×C79C2311yescharacteristic
45C23×C4×C79C2313yes—
46C2×C42×C79—26no—
47C2×C42×C79—26no—
48C2×C42×C79C2×C4112yescomplemented
49#95×C79—26no—
50#95×C79D414yes—
51C23×D79—21no—
52C23×D79—23no—
53C23×D79—23no—
54C23×D79—21no—
55C23×D79C22×C416yes—
56C23×D79#4112yes—
57C23×D79#4116yes—
58C22×Dic79—23no—
59C22×Dic79—26no—
60C22×Dic79—23no—
61C22×Dic79—23no—
62C22×Dic79—26no—
63C22×Dic79—23no—
64C22×Dic79—23no—
65C22×Dic79—26no—
66C22×Dic79—26no—
67C22×Dic79—21no—
68C22×Dic79C22×C416yes—
69C22×Dic79C22×C416yes—
70C22×Dic79C22×C416yes—
71C2×C4×D79—224no—
72C2×C4×D79—224no—
73C2×C4×D79—412no—
74C2×C4×D79—424no—
75C2×C4×D79—424no—
76(C2×D79)⋊C4—224no—
77(C2×D79)⋊C4C42116yes—
78C4×Dic79—412no—
79C24×C79C2411yescharacteristic
80C22×C4×C79—21no—
81C22×C4×C79—23no—
82C22×C4×C79—26no—
83C22×C4×C79—26no—
84C22×C4×C79—23no—
85C22×C4×C79—23no—
86C22×C4×C79—23no—
87C22×C4×C79—23no—
88C22×C4×C79—23no—
89C22×C4×C79—23no—
90C22×C4×C79C22×C416yes—
91C22×C4×C79C22×C416yes—
92C22×C4×C79C22×C416yes—
93C22×C4×C79C2×D416yes—
94C22×C4×C79#4116yes—
95C42×C79—224no—
96C23×C79C23×C413yes—
97C23×C79C22×D411yescharacteristic
98C23×C79C2×#4113yes—
99C23×C79C2×#4111yescharacteristic
100C23×C79C2×#4113yes—
101C23×C79H(5,𝔽2)13yes—
102C23×C792−1+411yescharacteristic
103C22×D79—26no—
104C22×D79—26no—
105C22×D79—26no—
106C22×D79—26no—
107C22×D79—26no—
108C22×D79—22no—
109C22×D79—212no—
110C22×D79—26no—
111C22×D79—26no—
112C22×D79C2×C4214yes—
113C22×D79#117112yes—
114C22×D79#117112yes—
115C2×C4×C79—26no—
116C2×C4×C79—26no—
117C2×C4×C79—26no—
118C2×C4×C79—26no—
119C2×C4×C79—212no—
120C2×C4×C79—212no—
121C2×C4×C79—26no—
122C2×C4×C79—26no—
123C2×C4×C79—26no—
124C2×C4×C79—43no—
125C2×C4×C79—43no—
126C2×C4×C79—43no—
127C2×C4×C79—43no—
128C2×C4×C79C2×C4214yes—
129C2×C4×C79C4×D4112yes—
130C2×Dic79—26no—
131C2×Dic79—26no—
132C2×Dic79—26no—
133C2×Dic79—26no—
134C2×Dic79—26no—
135C2×Dic79—26no—
136C2×Dic79—26no—
137C2×Dic79—26no—
138C2×Dic79—46no—
139C2×Dic79—46no—
140C2×Dic79—46no—
141C2×Dic79—46no—
142C2×Dic79C2×C4214yes—
143C4×D79—448no—
144C22×C79C22×C4211yescharacteristic
145C22×C79C2×#11713yes—
146C22×C79C2×#11713yes—
147C22×C79C2×C4×D413yes—
148C22×C79C4×#4113yes—
149C22×C79#51813yes—
150C22×C79#52013yes—
151C22×C79#54613yes—
152C22×C79#54811yescharacteristic
153C22×C79#55116yes—
154C22×C79#55213yes—
155C22×C79#55313yes—
156C2×D79—212no—
157C2×D79—212no—
158C2×D79—212no—
159C2×D79—212no—
160C2×D79—24no—
161C2×D79—24no—
162C2×D79#37618yescomplemented
163C4×C79—212no—
164C4×C79—24no—
165C4×C79—46no—
166Dic79—24no—
167Dic79—46no—
168Dic79—46no—
169#13809—791nomaximal, Sylow
170C2×C79C2×#37611yescharacteristic
171C2×C79C42×D411yescharacteristic
172C2×C79#227511yescharacteristic
173C2×C79#234213yes—
174C2×C79#234313yes—
175C2×C79#235213yes—
176C2×C79#235313yes—
177D79—28no—
178C2×C4×C22⋊C4—793no—
179C2×#376D7911yescharacteristic, complemented
180C22×#95—791no—
181#1434—793no—
182#1434—793no—
183C22⋊#95—793no—
184C4×#95—791no—
185C79#1380911yescharacteristic, complemented, Sylow
186C24×C4—793no—
187C22×C22⋊C4—791no—
188C22×C22⋊C4—793no—
189C22×C42—793no—
190C22×C42C2×D7913yes—
191C4×C22⋊C4—7924no—
192#376—24no—
193C2×#95—796no—
194C2×#95—793no—
195C2×#95—793no—
196C2×#95—793no—
197C2×#95—793no—
198C2×#95—1584no—
199C2×#95C2×D7913yes—
200C2×#95C2×D7911yescharacteristic
201C25—791no—
202C23×C4—3166no—
203C23×C4—7912no—
204C23×C4—791no—
205C23×C4—793no—
206C23×C4—793no—
207C23×C4—15812no—
208C23×C4—1586no—
209C23×C4—1586no—
210C23×C4C22×D7913yes—
211C23×C4C22×D7911yescharacteristic
212C23×C4C22×D7913yes—
213C2×C22⋊C4—7912no—
214C2×C22⋊C4—7912no—
215C2×C22⋊C4—1586no—
216C2×C22⋊C4—1586no—
217C2×C42—26no—
218C2×C42—26no—
219C2×C42—3166no—
220C2×C42—7912no—
221C2×C42C4×D79112yescomplemented
222#95—26no—
223#95—3166no—
224#95—7912no—
225#95—7912no—
226#95—1586no—
227#95—1586no—
228#95C22⋊D7914yes—
229C24—792no—
230C24—796no—
231C24—796no—
232C24—1583no—
233C24—1583no—
234C24—1581no—
235C24—1581no—
236C24C23×D7911yescharacteristic
237C22×C4—26no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—21no—
241C22×C4—23no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—23no—
247C22×C4—31624no—
248C22×C4—31624no—
249C22×C4—31612no—
250C22×C4—796no—
251C22×C4—796no—
252C22×C4—796no—
253C22×C4—15824no—
254C22×C4—1583no—
255C22×C4—1583no—
256C22×C4—1586no—
257C22×C4—1586no—
258C22×C4—1583no—
259C22×C4—1586no—
260C22×C4—1586no—
261C22×C4—1583no—
262C22×C4—15824no—
263C22×C4—1583no—
264C22×C4—1581no—
265C22×C4C2×C4×D7916yes—
266C22×C4C2×C4×D7916yes—
267C22×C4C2×C4×D7916yes—
268C22×C4C2×C22⋊D7916yes—
269C22×C4#1192962416yes—
270C22⋊C4—7916no—
271C22⋊C4—15824no—
272C42—224no—
273C42—31612no—
274C23—794no—
275C23—7912no—
276C23—7912no—
277C23—1586no—
278C23—1582no—
279C23—15812no—
280C23—1586no—
281C23—1586no—
282C23—1586no—
283C23—1586no—
284C23—1586no—
285C23—1586no—
286C23C22×C4×D7913yes—
287C23C22×C22⋊D7911yescharacteristic
288C23#41×D7913yes—
289C23#41×D7911yescharacteristic
290C23C2×#1192962413yes—
291C23#1457920713yes—
292C23#1457920811yescharacteristic
293C2×C4—212no—
294C2×C4—212no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—43no—
303C2×C4—43no—
304C2×C4—43no—
305C2×C4—43no—
306C2×C4—31648no—
307C2×C4—3166no—
308C2×C4—3166no—
309C2×C4—3166no—
310C2×C4—3166no—
311C2×C4—794no—
312C2×C4—1586no—
313C2×C4—1586no—
314C2×C4—1586no—
315C2×C4—1586no—
316C2×C4—1586no—
317C2×C4—1586no—
318C2×C4—1586no—
319C2×C4—1586no—
320C2×C4C42×D7914yes—
321C2×C4C4×C22⋊D79112yes—
322C22—798no—
323C22—1584no—
324C22—15812no—
325C22—15812no—
326C22—15812no—
327C22—1584no—
328C22—15812no—
329C22C2×C42×D7911yescharacteristic
330C22#117×D7913yes—
331C22#117×D7913yes—
332C22C2×C4×C22⋊D7913yes—
333C22C4×#1192962413yes—
334C22#1909903713yes—
335C22#1909904313yes—
336C22#1909920113yes—
337C22#1909922011yescharacteristic
338C22#1909923716yes—
339C22#1909925213yes—
340C22#1909925713yes—
341C4—212no—
342C4—24no—
343C4—46no—
344C4—3166no—
345C4—3166no—
346C4—1584no—
347C2—1588no—
348C2#376×D7911yescharacteristic
349C2C42×C22⋊D7911yescharacteristic
350C2#2376576211yescharacteristic
351C2#2376625013yes—
352C2#2376626113yes—
353C2#2376633013yes—
354C2#2376634113yes—
subgroupG/H
center, FrattiniC24C23×D79
commutatorC22×C79C22×C42
FittingC2×#376×C79C2
socle, cosocleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#376D79
hypocenterC79#13809
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
3. #23761627C2semidirect
4. #23761626C2semidirect
6. #95×Dic79C2semidirect
7. C2×#376×C79C2semidirect
12. C4×(C2×D79)⋊C4C4semidirect
37. C2×C4×Dic79C2×C4semidirect
41. C79⋊#95C2×C4semidirect
42. C79⋊#95C2×C4semidirect
48. C2×C42×C79C2×C4semidirect
162. C2×D79#376semidirect
179. C2×#376D79semidirect
185. C79#13809semidirect
221. C2×C42C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D79)⋊C42
C2×#95×D792
#237616272
#237616262
(C2×D79)⋊#952
#95×Dic792
C2×#376×C792
#1380979