Finite Group Databasebeta

← C22×#19098906 #35156016

Subgroups — C22×#19098906 #35156016

Order 20224.

2358 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579141C211yesmaximal, characteristic
2C22×#14579119C211yesmaximal, characteristic
3C2×#19098906C2124yesmaximal, direct product factor
4C22×#14579092C211yesmaximal, characteristic, complemented
5C22×#14579086C211yesmaximal, characteristic, complemented
6C22×#14579084C211yesmaximal, characteristic, complemented
7C22×(C2×D79)⋊C8C211yesmaximal, characteristic
8C22×#107×C79C211yesmaximal, characteristic, complemented
9C23×Dic158C2211yescharacteristic
10C23×C4×D79C2211yescharacteristic
11C23×C79⋊C8C2211yescharacteristic
12C2×#14579141—26no—
13C2×#14579141C22112yes—
14C2×#14579119—26no—
15C2×#14579119C22112yes—
16C22×C4⋊Dic79—21no—
17C22×C4⋊Dic79C2211yescharacteristic
18C22×(C2×D79)⋊C4—21no—
19C22×(C2×D79)⋊C4—21no—
20C22×C4×Dic79—21no—
21#19098906C22164yesdirect product factor
22C2×#14579092C22112yescomplemented
23C2×#14579086C22112yescomplemented
24C2×#14579084C22112yescomplemented
25C2×(C2×D79)⋊C8C22112yes—
26C23×C8×C79C2211yescharacteristic
27C22×C4⋊C4×C79C2211yescharacteristic
28C22×C4⋊C4×C79C2211yescharacteristic
29C2×#107×C79C22112yescomplemented
30C24×D79D411yescharacteristic
31C22×Dic158—23no—
32C22×Dic158—24no—
33C22×Dic158—24no—
34C22×Dic158C2316yes—
35C23×Dic79—21no—
36C23×Dic79—21no—
37C23×Dic79D411yescharacteristic
38C22×C4×D79—24no—
39C22×C4×D79—24no—
40C22×C4×D79D416yes—
41C22×C4×D79C2316yes—
42C22×C79⋊C8—24no—
43C22×C79⋊C8C2316yes—
44#14579141—224no—
45#14579141C23116yes—
46#14579119—224no—
47#14579119C23116yes—
48C2×C4⋊Dic79—23no—
49C2×C4⋊Dic79—212no—
50C2×C4⋊Dic79C2316yes—
51C2×(C2×D79)⋊C4—212no—
52C2×(C2×D79)⋊C4—212no—
53C2×C4×Dic79—212no—
54#14579092C23116yescomplemented
55#14579086C23116yescomplemented
56#14579084C23116yescomplemented
57(C2×D79)⋊C8C23116yes—
58C23×C4×C79—21no—
59C23×C4×C79—21no—
60C23×C4×C79C2311yescharacteristic
61C22×C8×C79—24no—
62C22×C8×C79C2316yes—
63C2×C4⋊C4×C79—23no—
64C2×C4⋊C4×C79—23no—
65C2×C4⋊C4×C79C2316yes—
66C2×C4⋊C4×C79C2316yes—
67#107×C79C23116yescomplemented
68C23×D79—24no—
69C23×D79—24no—
70C23×D79—24no—
71C23×D79C2×D416yes—
72C2×Dic158—26no—
73C2×Dic158—212no—
74C2×Dic158—212no—
75C2×Dic158—412no—
76C2×Dic158C2414yes—
77C22×Dic79—24no—
78C22×Dic79—26no—
79C22×Dic79—26no—
80C22×Dic79—44no—
81C22×Dic79—44no—
82C22×Dic79C2×D416yes—
83C2×C4×D79—224no—
84C2×C4×D79—212no—
85C2×C4×D79—212no—
86C2×C4×D79C2×D4112yes—
87C2×C4×D79C2414yes—
88C2×C79⋊C8—212no—
89C2×C79⋊C8C2414yes—
90C4⋊Dic79—216no—
91C4⋊Dic79—26no—
92C4⋊Dic79C2414yes—
93(C2×D79)⋊C4—216no—
94(C2×D79)⋊C4—216no—
95C4×Dic79—216no—
96C24×C79C2×D411yescharacteristic
97C22×C4×C79—26no—
98C22×C4×C79—26no—
99C22×C4×C79—44no—
100C22×C4×C79—44no—
101C22×C4×C79C2×D413yes—
102C22×C4×C79#4114yes—
103C22×C4×C79#4114yes—
104C22×C4×C79C2413yes—
105C2×C8×C79—212no—
106C2×C8×C79C2414yes—
107C4⋊C4×C79—26no—
108C4⋊C4×C79—26no—
109C4⋊C4×C79C2414yes—
110C4⋊C4×C79C2414yes—
111C23×C79#12314yes—
112C23×C79#13514yes—
113C23×C79#13714yes—
114C23×C79C22×D413yes—
115C22×D79—212no—
116C22×D79—212no—
117C22×D79—212no—
118C22×D79—416no—
119C22×D79C22×D414yes—
120C2×C4×C79—24no—
121C2×C4×C79—24no—
122C2×C4×C79—412no—
123C2×C4×C79—412no—
124C2×C4×C79#123112yes—
125C2×C4×C79C22×D413yes—
126C2×C4×C79C2×#4116yes—
127C2×C4×C79C2×#4116yes—
128C2×C4×C79C2511yescharacteristic
129C2×Dic79—212no—
130C2×Dic79—24no—
131C2×Dic79—24no—
132C2×Dic79—412no—
133C2×Dic79—412no—
134C2×Dic79C22×D414yes—
135C4×D79—224no—
136C4×D79—24no—
137C4×D79—24no—
138Dic158—24no—
139Dic158—24no—
140Dic158—412no—
141C8×C79—24no—
142C79⋊C8—24no—
143C22×C79#485116yescomplemented
144C22×C79C2×#12316yes—
145C22×C79C2×#13516yes—
146C22×C79C2×#13716yes—
147C22×C79C23×D411yescharacteristic
148C2×D79—24no—
149C2×D79—24no—
150C2×D79—24no—
151C2×D79—424no—
152C4×C79—44no—
153C4×C79—44no—
154C4×C79C2×#12316yes—
155C4×C79C22×#4111yescharacteristic
156C4×C79C22×#4111yescharacteristic
157Dic79—24no—
158Dic79—44no—
159Dic79—44no—
160C22×#485—791nomaximal, Sylow
161C2×C79C2×#485112yescomplemented
162C2×C79C22×#12311yescharacteristic
163C2×C79C22×#13511yescharacteristic
164C2×C79C22×#13711yescharacteristic
165D79—44no—
166C22×C22⋊Q8—791no—
167C22×#117—791no—
168C2×#485—7924no—
169C22×#107D7911yescharacteristic, complemented
170C22×#106—791no—
171C22×#103—791no—
172C22×#103—791no—
173C22×C22⋊C8—791no—
174C79C22×#48511yescharacteristic, complemented, Sylow
175C23×Q8—791no—
176C24×C4—791no—
177C23×C8—791no—
178C23×C8C2×D7911yescharacteristic
179C2×C22⋊Q8—7912no—
180C2×C22⋊Q8—1586no—
181C2×#117—7912no—
182C2×#117—1586no—
183C22×C4⋊C4—791no—
184C22×C4⋊C4—1581no—
185C22×C4⋊C4C2×D7911yescharacteristic
186C22×C4⋊C4C2×D7911yescharacteristic
187C22×C22⋊C4—1581no—
188C22×C22⋊C4—1581no—
189C22×C42—1581no—
190#485—7964no—
191C2×#107C2×D79112yescomplemented
192C2×#106—7912no—
193C2×#103—7912no—
194C2×#103—7912no—
195C2×C22⋊C8—7912no—
196C25—791no—
197C22×Q8—796no—
198C22×Q8—1584no—
199C22×Q8—1584no—
200C22×Q8—1583no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—791no—
204C23×C4—796no—
205C23×C4—796no—
206C23×C4—1581no—
207C23×C4—1581no—
208C23×C4—1584no—
209C23×C4—1584no—
210C23×C4C22×D7911yescharacteristic
211C22×C8—24no—
212C22×C8—796no—
213C22×C8—1584no—
214C22×C8C22×D7916yes—
215C22⋊Q8—7916no—
216C22⋊Q8—15824no—
217#117—7916no—
218#117—15824no—
219C2×C4⋊C4—23no—
220C2×C4⋊C4—23no—
221C2×C4⋊C4—796no—
222C2×C4⋊C4—15812no—
223C2×C4⋊C4—1583no—
224C2×C4⋊C4C22×D7916yes—
225C2×C4⋊C4C22×D7916yes—
226C2×C22⋊C4—15812no—
227C2×C22⋊C4—15812no—
228C2×C42—15812no—
229#107C22×D79116yescomplemented
230#106—7916no—
231#103—7916no—
232#103—7916no—
233C22⋊C8—7916no—
234C24—796no—
235C24—1584no—
236C24—1584no—
237C24—1584no—
238C24D4×D7911yescharacteristic
239C2×Q8—31612no—
240C2×Q8—794no—
241C2×Q8—15812no—
242C2×Q8—15812no—
243C2×Q8—1586no—
244C22×C4—26no—
245C22×C4—26no—
246C22×C4—44no—
247C22×C4—44no—
248C22×C4—3164no—
249C22×C4—3164no—
250C22×C4—796no—
251C22×C4—794no—
252C22×C4—7912no—
253C22×C4—1586no—
254C22×C4—1586no—
255C22×C4—1584no—
256C22×C4—15812no—
257C22×C4—15812no—
258C22×C4—15824no—
259C22×C4D4×D7913yes—
260C22×C4#1192962414yes—
261C22×C4#1192962514yes—
262C22×C4C23×D7913yes—
263C2×C8—212no—
264C2×C8—794no—
265C2×C8—15812no—
266C2×C8C23×D7914yes—
267C4⋊C4—26no—
268C4⋊C4—26no—
269C4⋊C4—794no—
270C4⋊C4—15816no—
271C4⋊C4—1586no—
272C4⋊C4C23×D7914yes—
273C4⋊C4C23×D7914yes—
274C22⋊C4—15816no—
275C22⋊C4—15816no—
276C42—15816no—
277C23—31616no—
278C23—794no—
279C23—15812no—
280C23—15812no—
281C23—15812no—
282C23#1457914614yes—
283C23#1457918014yes—
284C23#1457919314yes—
285C23C2×D4×D7913yes—
286Q8—31612no—
287Q8—1584no—
288Q8—1584no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—412no—
292C2×C4—412no—
293C2×C4—31612no—
294C2×C4—31612no—
295C2×C4—794no—
296C2×C4—1584no—
297C2×C4—1584no—
298C2×C4—15812no—
299C2×C4—15824no—
300C2×C4—1584no—
301C2×C4—1584no—
302C2×C4#14579146112yes—
303C2×C4C2×D4×D7913yes—
304C2×C4C2×#1192962416yes—
305C2×C4C2×#1192962516yes—
306C2×C4C24×D7911yescharacteristic
307C8—24no—
308C8—1584no—
309C22—31624no—
310C22—1584no—
311C22—1584no—
312C22—1584no—
313C22#19098906116yesdirect product factor
314C22C2×#1457914616yes—
315C22C2×#1457918016yes—
316C22C2×#1457919316yes—
317C22C22×D4×D7911yescharacteristic
318C4—44no—
319C4—44no—
320C4—3164no—
321C4—3164no—
322C4—1584no—
323C4C2×#1457914616yes—
324C4C22×#1192962411yescharacteristic
325C4C22×#1192962511yescharacteristic
326C2—3164no—
327C2C2×#19098906112yesdirect product factor
328C2C22×#1457914611yescharacteristic
329C2C22×#1457918011yescharacteristic
330C2C22×#1457919311yescharacteristic
subgroupG/H
centerC24D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC22×#107×C79C2
socleC24×C79C2×D4
prime radicalC24×D79D4
hypercenterC22×#107D79
hypocenterC79C22×#485
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
3. C2×#19098906C2direct (N × H)
4. C22×#14579092C2semidirect
5. C22×#14579086C2semidirect
6. C22×#14579084C2semidirect
8. C22×#107×C79C2semidirect
21. #19098906C22direct (N × H)
22. C2×#14579092C22semidirect
23. C2×#14579086C22semidirect
24. C2×#14579084C22semidirect
29. C2×#107×C79C22semidirect
54. #14579092C23semidirect
55. #14579086C23semidirect
56. #14579084C23semidirect
67. #107×C79C23semidirect
143. C22×C79#485semidirect
161. C2×C79C2×#485semidirect
169. C22×#107D79semidirect
174. C79C22×#485semidirect
191. C2×#107C2×D79semidirect
229. #107C22×D79semidirect
313. C22#19098906direct (N × H)
327. C2C2×#19098906direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791412
C22×#145791192
C2×#190989062
C22×#145790922
C22×#145790862
C22×#145790842
C22×(C2×D79)⋊C82
C22×#107×C792
C22×#48579