Finite Group Databasebeta

← C22×#19098908 #35157452

Subgroups — C22×#19098908 #35157452

Order 20224.

3086 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579160C211yesmaximal, characteristic, complemented
2C22×#14579157C211yesmaximal, characteristic
3C2×#19098908C2124yesmaximal, direct product factor
4C22×#14579083C211yesmaximal, characteristic, complemented
5C22×#14579082C211yesmaximal, characteristic, complemented
6C22×#14579081C211yesmaximal, characteristic, complemented
7C22×C8×Dic79C211yesmaximal, characteristic, complemented
8C22×#102×C79C211yesmaximal, characteristic, complemented
9C23×Dic158—21no—
10C23×D316C2211yescharacteristic
11C23×C22⋊D79—21no—
12C23×C22⋊D79—21no—
13C23×C79⋊C8C2211yescharacteristic
14C2×#14579160—26no—
15C2×#14579160C22112yescomplemented
16C2×#14579157—26no—
17C2×#14579157C22112yes—
18C22×C4⋊Dic79C2211yescharacteristic
19C22×Dic79⋊C4—21no—
20C22×C4×Dic79C2211yescharacteristic
21#19098908C22164yesdirect product factor
22C2×#14579083C22112yescomplemented
23C2×#14579082C22112yescomplemented
24C2×#14579081C22112yescomplemented
25C2×C8×Dic79C22112yescomplemented
26C23×D4×C79C2211yescharacteristic
27C23×C8×C79C2211yescharacteristic
28C22×C4⋊C4×C79C2211yescharacteristic
29C2×#102×C79C22112yescomplemented
30C24×D79—21no—
31C22×Dic158—212no—
32C22×Dic158—48no—
33C22×D316—24no—
34C22×D316—24no—
35C22×D316—23no—
36C22×D316C2316yes—
37C22×C22⋊D79—212no—
38C22×C22⋊D79—212no—
39C22×C22⋊D79—48no—
40C22×C22⋊D79—48no—
41C23×Dic79—21no—
42C23×Dic79D411yescharacteristic
43C23×Dic79D411yescharacteristic
44C22×C79⋊C8—24no—
45C22×C79⋊C8C2316yes—
46#14579160—224no—
47#14579160C23116yescomplemented
48#14579157—224no—
49#14579157C23116yes—
50C2×C4⋊Dic79—23no—
51C2×C4⋊Dic79C2316yes—
52C2×Dic79⋊C4—212no—
53C2×C4×Dic79D416yes—
54C2×C4×Dic79C2316yes—
55#14579083C23116yescomplemented
56#14579082C23116yescomplemented
57#14579081C23116yescomplemented
58C8×Dic79C23116yescomplemented
59C25×C79—21no—
60C22×D4×C79—23no—
61C22×D4×C79—24no—
62C22×D4×C79—24no—
63C22×D4×C79C2316yes—
64C23×C4×C79—21no—
65C23×C4×C79C2311yescharacteristic
66C22×C8×C79—24no—
67C22×C8×C79C2316yes—
68C2×C4⋊C4×C79—23no—
69C2×C4⋊C4×C79C2316yes—
70#102×C79C23116yescomplemented
71C23×D79—26no—
72C23×D79—44no—
73C23×D79—44no—
74C23×D79—44no—
75C2×Dic158—216no—
76C2×Dic158—448no—
77C2×D316—26no—
78C2×D316—212no—
79C2×D316—212no—
80C2×D316—412no—
81C2×D316C2414yes—
82C2×C22⋊D79—216no—
83C2×C22⋊D79—216no—
84C2×C22⋊D79—448no—
85C2×C22⋊D79—448no—
86C22×Dic79—26no—
87C22×Dic79—44no—
88C22×Dic79D818yes—
89C22×Dic79SD1618yes—
90C22×Dic79C2×D416yes—
91C22×Dic79C2×D416yes—
92C2×C79⋊C8—212no—
93C2×C79⋊C8C2414yes—
94C4⋊Dic79—26no—
95C4⋊Dic79C2414yes—
96Dic79⋊C4—216no—
97C4×Dic79C2×D4112yes—
98C4×Dic79C2414yes—
99C24×C79—26no—
100C24×C79—44no—
101C24×C79—44no—
102C24×C79—44no—
103C24×C79C2×D411yescharacteristic
104C2×D4×C79—26no—
105C2×D4×C79—212no—
106C2×D4×C79—212no—
107C2×D4×C79—412no—
108C2×D4×C79C2414yes—
109C22×C4×C79—26no—
110C22×C4×C79—44no—
111C22×C4×C79C2×D413yes—
112C22×C4×C79#4114yes—
113C22×C4×C79#4114yes—
114C22×C4×C79C2413yes—
115C2×C8×C79—212no—
116C2×C8×C79C2414yes—
117C4⋊C4×C79—26no—
118C4⋊C4×C79C2414yes—
119C23×C79—24no—
120C23×C79—412no—
121C23×C79—412no—
122C23×C79—412no—
123C23×C79—816no—
124C23×C79#12414yes—
125C23×C79C2×D814yes—
126C23×C79C2×SD1614yes—
127C23×C79C22×D413yes—
128C22×D79—24no—
129C22×D79—412no—
130C22×D79—412no—
131C22×D79—412no—
132C22×D79—816no—
133D4×C79—24no—
134D4×C79—24no—
135D4×C79—412no—
136C2×C4×C79—24no—
137C2×C4×C79—412no—
138C2×C4×C79#124112yes—
139C2×C4×C79C22×D413yes—
140C2×C4×C79C2×#4116yes—
141C2×C4×C79C2×#4116yes—
142C2×C4×C79C2511yescharacteristic
143C22⋊D79—432no—
144C22⋊D79—432no—
145C2×Dic79—24no—
146C2×Dic79—412no—
147C2×Dic79C2×D8124yes—
148C2×Dic79C2×SD16124yes—
149C2×Dic79C22×D414yes—
150C2×Dic79C22×D414yes—
151D316—24no—
152D316—24no—
153D316—412no—
154Dic158—432no—
155C8×C79—24no—
156C79⋊C8—24no—
157C22×C79—44no—
158C22×C79—44no—
159C22×C79—44no—
160C22×C79—824no—
161C22×C79#486116yescomplemented
162C22×C79C2×#12416yes—
163C22×C79C22×D816yes—
164C22×C79C22×SD1616yes—
165C22×C79C23×D411yescharacteristic
166C2×D79—44no—
167C2×D79—44no—
168C2×D79—44no—
169C2×D79—824no—
170C4×C79—44no—
171C4×C79C2×#12416yes—
172C4×C79C22×#4111yescharacteristic
173C4×C79C22×#4111yescharacteristic
174Dic79—44no—
175Dic79C22×D818yes—
176Dic79C22×SD1618yes—
177C22×#486—791nomaximal, Sylow
178C2×C79—84no—
179C2×C79C2×#486112yescomplemented
180C2×C79C22×#12411yescharacteristic
181C2×C79C23×D811yescharacteristic
182C2×C79C23×SD1611yescharacteristic
183D79—84no—
184C22×C4⋊Q8—791no—
185C22×#127—791no—
186C2×#486—7924no—
187C22×#102—791no—
188C22×#102—791no—
189C22×#102—791no—
190C22×#102D7911yescharacteristic, complemented
191C22×C4×C8—791no—
192C79C22×#48611yescharacteristic, complemented, Sylow
193C23×Q8—1581no—
194C23×D4—791no—
195C23×D4—1581no—
196C23×D4—1581no—
197C23×D4C2×D7911yescharacteristic
198C23×C8—791no—
199C23×C8C2×D7911yescharacteristic
200C2×C4⋊Q8—7912no—
201C2×C4⋊Q8—1586no—
202C2×#127—7912no—
203C2×#127—1586no—
204C22×C4⋊C4—791no—
205C22×C4⋊C4—1581no—
206C22×C4⋊C4C2×D7911yescharacteristic
207C22×C42—791no—
208#486—7964no—
209C2×#102—7912no—
210C2×#102—7912no—
211C2×#102—7912no—
212C2×#102C2×D79112yescomplemented
213C2×C4×C8—7912no—
214C25—21no—
215C25—1581no—
216C22×Q8—3168no—
217C22×Q8—15812no—
218C22×D4—23no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—3168no—
222C22×D4—3168no—
223C22×D4—796no—
224C22×D4—15812no—
225C22×D4—15812no—
226C22×D4—1583no—
227C22×D4—1584no—
228C22×D4—1584no—
229C22×D4C22×D7916yes—
230C23×C4—21no—
231C23×C4—791no—
232C23×C4—791no—
233C23×C4—1581no—
234C23×C4C22×D7911yescharacteristic
235C22×C8—24no—
236C22×C8—796no—
237C22×C8—1584no—
238C22×C8C22×D7916yes—
239C4⋊Q8—7916no—
240C4⋊Q8—15824no—
241#127—7916no—
242#127—15824no—
243C2×C4⋊C4—23no—
244C2×C4⋊C4—796no—
245C2×C4⋊C4—15812no—
246C2×C4⋊C4—1583no—
247C2×C4⋊C4C22×D7916yes—
248C2×C42—796no—
249C2×C42—796no—
250#102—7916no—
251#102—7916no—
252#102—7916no—
253#102C22×D79116yescomplemented
254C4×C8—7916no—
255C24—26no—
256C24—44no—
257C24—44no—
258C24—44no—
259C24—3164no—
260C24—3164no—
261C24—3164no—
262C24—1586no—
263C24D4×D7911yescharacteristic
264C2×Q8—31648no—
265C2×Q8—15816no—
266C2×D4—212no—
267C2×D4—212no—
268C2×D4—26no—
269C2×D4—412no—
270C2×D4—31648no—
271C2×D4—31648no—
272C2×D4—31612no—
273C2×D4—794no—
274C2×D4—15816no—
275C2×D4—15816no—
276C2×D4—15812no—
277C2×D4—15812no—
278C2×D4—1586no—
279C2×D4C23×D7914yes—
280C22×C4—26no—
281C22×C4—44no—
282C22×C4—3164no—
283C22×C4—798no—
284C22×C4—798no—
285C22×C4—796no—
286C22×C4—796no—
287C22×C4—1586no—
288C22×C4D4×D7913yes—
289C22×C4#1192962314yes—
290C22×C4#1192962414yes—
291C22×C4C23×D7913yes—
292C2×C8—212no—
293C2×C8—794no—
294C2×C8—15812no—
295C2×C8C23×D7914yes—
296C4⋊C4—26no—
297C4⋊C4—794no—
298C4⋊C4—15816no—
299C4⋊C4—1586no—
300C4⋊C4C23×D7914yes—
301C42—794no—
302C42—7912no—
303C23—24no—
304C23—412no—
305C23—412no—
306C23—412no—
307C23—816no—
308C23—31612no—
309C23—31612no—
310C23—31612no—
311C23—63216no—
312C23—1584no—
313C23#1457914714yes—
314C23D8×D7914yes—
315C23SD16×D7914yes—
316C23C2×D4×D7913yes—
317Q8—31632no—
318D4—24no—
319D4—24no—
320D4—412no—
321D4—31632no—
322D4—31632no—
323D4—31612no—
324D4—1584no—
325D4—1584no—
326C2×C4—24no—
327C2×C4—412no—
328C2×C4—31612no—
329C2×C4—7924no—
330C2×C4—7924no—
331C2×C4—794no—
332C2×C4—794no—
333C2×C4—1584no—
334C2×C4#14579147112yes—
335C2×C4C2×D4×D7913yes—
336C2×C4C2×#1192962316yes—
337C2×C4C2×#1192962416yes—
338C2×C4C24×D7911yescharacteristic
339C8—24no—
340C8—1584no—
341C22—44no—
342C22—44no—
343C22—44no—
344C22—824no—
345C22—3164no—
346C22—3164no—
347C22—3164no—
348C22—63224no—
349C22#19098908116yesdirect product factor
350C22C2×#1457914716yes—
351C22C2×D8×D7916yes—
352C22C2×SD16×D7916yes—
353C22C22×D4×D7911yescharacteristic
354C4—44no—
355C4—3164no—
356C4—798no—
357C4—798no—
358C4C2×#1457914716yes—
359C4C22×#1192962311yescharacteristic
360C4C22×#1192962411yescharacteristic
361C2—84no—
362C2—6324no—
363C2C2×#19098908112yesdirect product factor
364C2C22×#1457914711yescharacteristic
365C2C22×D8×D7911yescharacteristic
366C2C22×SD16×D7911yescharacteristic
subgroupG/H
centerC24D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC22×#102×C79C2
socleC24×C79C2×D4
prime radicalC22×#14579157C2
hypercenterC22×#102D79
hypocenterC79C22×#486
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C22×#14579160C2semidirect
3. C2×#19098908C2direct (N × H)
4. C22×#14579083C2semidirect
5. C22×#14579082C2semidirect
6. C22×#14579081C2semidirect
7. C22×C8×Dic79C2semidirect
8. C22×#102×C79C2semidirect
15. C2×#14579160C22semidirect
21. #19098908C22direct (N × H)
22. C2×#14579083C22semidirect
23. C2×#14579082C22semidirect
24. C2×#14579081C22semidirect
25. C2×C8×Dic79C22semidirect
29. C2×#102×C79C22semidirect
47. #14579160C23semidirect
55. #14579083C23semidirect
56. #14579082C23semidirect
57. #14579081C23semidirect
58. C8×Dic79C23semidirect
70. #102×C79C23semidirect
161. C22×C79#486semidirect
179. C2×C79C2×#486semidirect
190. C22×#102D79semidirect
192. C79C22×#486semidirect
212. C2×#102C2×D79semidirect
253. #102C22×D79semidirect
349. C22#19098908direct (N × H)
363. C2C2×#19098908direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791602
C22×#145791572
C2×#190989082
C22×#145790832
C22×#145790822
C22×#145790812
C22×C8×Dic792
C22×#102×C792
C22×#48679