Finite Group Databasebeta

← #34209742

Subgroups — #34209742

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×C22⋊Dic79C213yesmaximal
2C2×#19098408C211yesmaximal, characteristic, complemented
3#23761626C213yesmaximal, complemented
4#23761624C213yesmaximal, complemented
5#23761623C213yesmaximal
6#95×Dic79C211yesmaximal, characteristic, complemented
7C22×#95×C79C211yesmaximal, characteristic
8C22×C22⋊Dic79C2213yes—
9C22×C22⋊Dic79C2211yescharacteristic
10C22×C4×Dic79C2213yes—
11C22×C4×Dic79C2213yes—
12C4×C22⋊Dic79C4124yescomplemented
13#19098408—24no—
14C2×C79⋊#95C2213yes—
15C2×C79⋊#95C2213yes—
16C2×C79⋊#95C2216yes—
17C2×C79⋊#95C2213yes—
18C2×C79⋊#95C2213yes—
19C24×C4×C79C2213yes—
20C2×#95×C79—24no—
21C2×#95×C79C2213yes—
22C2×#95×C79C2211yescharacteristic
23C23×Dic79C2313yes—
24C23×Dic79C2313yes—
25C23×Dic79C2311yescharacteristic
26C23×Dic79C2311yescharacteristic
27C2×C22⋊Dic79—26no—
28C2×C22⋊Dic79—26no—
29C2×C22⋊Dic79C2×C4112yes—
30C2×C22⋊Dic79C2×C4112yes—
31C2×C4×Dic79—26no—
32C2×C4×Dic79—26no—
33C2×C4×Dic79—46no—
34C2×C4×Dic79C2×C4112yescomplemented
35C2×C4×Dic79C2×C4112yescomplemented
36C79⋊#95—26no—
37C79⋊#95—26no—
38C79⋊#95—46no—
39C79⋊#95C2×C4112yescomplemented
40C79⋊#95C2×C4112yescomplemented
41C25×C79C2311yescharacteristic
42C23×C4×C79—212no—
43C23×C4×C79—26no—
44C23×C4×C79—26no—
45C23×C4×C79—46no—
46C23×C4×C79C2×C4112yes—
47C23×C4×C79C2313yes—
48C23×C4×C79C2313yes—
49#95×C79—26no—
50#95×C79D414yes—
51C22×Dic79—21no—
52C22×Dic79—23no—
53C22×Dic79—23no—
54C22×Dic79—26no—
55C22×Dic79—23no—
56C22×Dic79—23no—
57C22×Dic79—23no—
58C22×Dic79—23no—
59C22×Dic79—23no—
60C22×Dic79—23no—
61C22×Dic79—23no—
62C22×Dic79—26no—
63C22×Dic79—21no—
64C22×Dic79—23no—
65C22×Dic79C22×C416yes—
66C22×Dic79C22×C416yes—
67C22×Dic79C22×C416yes—
68C22×Dic79C22×C416yes—
69C22⋊Dic79—224no—
70C22⋊Dic79C42116yes—
71C4×Dic79—224no—
72C4×Dic79—412no—
73C24×C79—21no—
74C24×C79—23no—
75C24×C79—23no—
76C24×C79—21no—
77C24×C79C22×C416yes—
78C24×C79#4116yes—
79C24×C79#4112yes—
80C24×C79C2411yescharacteristic
81C22×C4×C79—26no—
82C22×C4×C79—26no—
83C22×C4×C79—224no—
84C22×C4×C79—23no—
85C22×C4×C79—26no—
86C22×C4×C79—23no—
87C22×C4×C79—26no—
88C22×C4×C79—224no—
89C22×C4×C79—412no—
90C22×C4×C79—424no—
91C22×C4×C79—424no—
92C22×C4×C79C22×C416yes—
93C22×C4×C79C22×C416yes—
94C22×C4×C79C2×D416yes—
95C22×C4×C79#4116yes—
96C23×C79—26no—
97C23×C79—26no—
98C23×C79—26no—
99C23×C79—26no—
100C23×C79—26no—
101C23×C79—22no—
102C23×C79—212no—
103C23×C79—26no—
104C23×C79—26no—
105C23×C79C2×C4214yes—
106C23×C79#117112yes—
107C23×C79#117112yes—
108C23×C79C23×C413yes—
109C23×C79C22×D411yescharacteristic
110C23×C79C2×#4113yes—
111C23×C79C2×#4113yes—
112C23×C79C2×#4111yescharacteristic
113C23×C79H(5,𝔽2)13yes—
114C23×C792−1+411yescharacteristic
115C2×C4×C79—26no—
116C2×C4×C79—26no—
117C2×C4×C79—212no—
118C2×C4×C79—212no—
119C2×C4×C79—26no—
120C2×C4×C79—26no—
121C2×C4×C79—26no—
122C2×C4×C79—448no—
123C2×C4×C79—46no—
124C2×C4×C79—46no—
125C2×C4×C79C4×D4112yes—
126C2×Dic79—26no—
127C2×Dic79—26no—
128C2×Dic79—26no—
129C2×Dic79—26no—
130C2×Dic79—26no—
131C2×Dic79—26no—
132C2×Dic79—26no—
133C2×Dic79—26no—
134C2×Dic79—26no—
135C2×Dic79—26no—
136C2×Dic79—43no—
137C2×Dic79—43no—
138C2×Dic79—46no—
139C2×Dic79—43no—
140C2×Dic79—43no—
141C2×Dic79—46no—
142C2×Dic79C2×C4214yes—
143C2×Dic79C2×C4214yes—
144C22×C79—212no—
145C22×C79—212no—
146C22×C79—212no—
147C22×C79—212no—
148C22×C79—24no—
149C22×C79—24no—
150C22×C79#37618yescomplemented
151C22×C79C22×C4211yescharacteristic
152C22×C79C2×#11713yes—
153C22×C79C2×#11713yes—
154C22×C79C2×C4×D413yes—
155C22×C79C4×#4113yes—
156C22×C79#51813yes—
157C22×C79#52013yes—
158C22×C79#54613yes—
159C22×C79#54811yescharacteristic
160C22×C79#55116yes—
161C22×C79#55213yes—
162C22×C79#55313yes—
163C4×C79—212no—
164C4×C79—46no—
165Dic79—24no—
166Dic79—24no—
167Dic79—46no—
168Dic79—46no—
169#13809—791nomaximal, Sylow
170C2×C79—28no—
171C2×C79C2×#37611yescharacteristic
172C2×C79C42×D411yescharacteristic
173C2×C79#227511yescharacteristic
174C2×C79#234213yes—
175C2×C79#234313yes—
176C2×C79#235213yes—
177C2×C79#235313yes—
178C2×C4×C22⋊C4—793no—
179C2×#376—791no—
180C22×#95D7911yescharacteristic
181#1434—793no—
182#1434—793no—
183C22⋊#95—793no—
184C4×#95—791no—
185C79#1380911yescharacteristic, complemented, Sylow
186C24×C4C2×D7913yes—
187C22×C22⋊C4—791no—
188C22×C22⋊C4—793no—
189C22×C42—793no—
190C22×C42—793no—
191C4×C22⋊C4—7924no—
192#376—1584no—
193C2×#95—24no—
194C2×#95—796no—
195C2×#95—793no—
196C2×#95—793no—
197C2×#95—793no—
198C2×#95—793no—
199C2×#95C2×D7913yes—
200C2×#95C2×D7911yescharacteristic
201C25C22×D7911yescharacteristic
202C23×C4—212no—
203C23×C4—26no—
204C23×C4—26no—
205C23×C4—46no—
206C23×C4—791no—
207C23×C4—791no—
208C23×C4—793no—
209C23×C4—793no—
210C23×C4C4×D79112yes—
211C23×C4C22×D7913yes—
212C23×C4C22×D7913yes—
213C2×C22⋊C4—7912no—
214C2×C22⋊C4—7912no—
215C2×C22⋊C4—1586no—
216C2×C22⋊C4—1586no—
217C2×C42—3166no—
218C2×C42—7912no—
219C2×C42—7912no—
220C2×C42—1586no—
221C2×C42—1586no—
222#95—26no—
223#95—3166no—
224#95—7912no—
225#95—7912no—
226#95—1586no—
227#95—1586no—
228#95C22⋊D7914yes—
229C24—23no—
230C24—23no—
231C24—21no—
232C24—21no—
233C24C2×C4×D7916yes—
234C24#1192962316yes—
235C24#1192962512yes—
236C24C23×D7911yescharacteristic
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—26no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—224no—
243C22×C4—23no—
244C22×C4—224no—
245C22×C4—412no—
246C22×C4—424no—
247C22×C4—424no—
248C22×C4—796no—
249C22×C4—796no—
250C22×C4—796no—
251C22×C4—796no—
252C22×C4—1583no—
253C22×C4—1583no—
254C22×C4—1586no—
255C22×C4—1583no—
256C22×C4—1583no—
257C22×C4—1583no—
258C22×C4—1583no—
259C22×C4—1586no—
260C22×C4—1583no—
261C22×C4—1583no—
262C22×C4—1583no—
263C22×C4—1583no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4C2×C4×D7916yes—
267C22×C4C2×C4×D7916yes—
268C22×C4C2×C22⋊D7916yes—
269C22×C4#1192962416yes—
270C22⋊C4—7916no—
271C22⋊C4—15824no—
272C42—31612no—
273C42—15824no—
274C23—26no—
275C23—22no—
276C23—212no—
277C23—26no—
278C23—26no—
279C23—26no—
280C23—26no—
281C23—26no—
282C23—26no—
283C23C42×D7914yes—
284C23#14579117112yes—
285C23#14579119112yes—
286C23C22×C4×D7913yes—
287C23C22×C22⋊D7911yescharacteristic
288C23C2×#1192962313yes—
289C23C2×#1192962413yes—
290C23C2×#1192962511yescharacteristic
291C23#1457920613yes—
292C23#1457920911yescharacteristic
293C2×C4—212no—
294C2×C4—212no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—448no—
301C2×C4—46no—
302C2×C4—46no—
303C2×C4—3163no—
304C2×C4—3163no—
305C2×C4—3166no—
306C2×C4—3163no—
307C2×C4—3163no—
308C2×C4—3166no—
309C2×C4—794no—
310C2×C4—794no—
311C2×C4—1586no—
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×C4—1586no—
321C2×C4C4×C22⋊D79112yes—
322C22—212no—
323C22—212no—
324C22—212no—
325C22—212no—
326C22—24no—
327C22—24no—
328C22#1909840818yescomplemented
329C22C2×C42×D7911yescharacteristic
330C22C2×#1457911713yes—
331C22C2×#1457911913yes—
332C22C2×C4×C22⋊D7913yes—
333C22C4×#1192962413yes—
334C22#1909903613yes—
335C22#1909904413yes—
336C22#1909920713yes—
337C22#1909922411yescharacteristic
338C22#1909923916yes—
339C22#1909924813yes—
340C22#1909926113yes—
341C4—212no—
342C4—46no—
343C4—3166no—
344C4—3166no—
345C4—1584no—
346C4—1584no—
347C2—28no—
348C2C2×#1909840811yescharacteristic
349C2C42×C22⋊D7911yescharacteristic
350C2#2376575811yescharacteristic
351C2#2376624513yes—
352C2#2376625613yes—
353C2#2376632513yes—
354C2#2376633613yes—
subgroupG/H
center, FrattiniC24C23×D79
commutatorC22×C79C22×C42
FittingC22×#95×C79C2
socle, cosocleC24×C79C24
prime radicalC25×C79C23
hypercenterC22×#95D79
hypocenterC79#13809
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C2×#19098408C2semidirect
3. #23761626C2semidirect
4. #23761624C2semidirect
6. #95×Dic79C2semidirect
12. C4×C22⋊Dic79C4semidirect
34. C2×C4×Dic79C2×C4semidirect
35. C2×C4×Dic79C2×C4semidirect
39. C79⋊#95C2×C4semidirect
40. C79⋊#95C2×C4semidirect
150. C22×C79#376semidirect
185. C79#13809semidirect
328. C22#19098408semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic792
C2×#190984082
#237616262
#237616242
#237616232
#95×Dic792
C22×#95×C792
#1380979