Finite Group Databasebeta

← C22×#16840074 #30547736

Subgroups — C22×#16840074 #30547736

Order 15616.

3006 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519748C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#16840074C2124yesmaximal, direct product factor
4C22×#14519711C211yesmaximal, characteristic, complemented
5C22×#14519710C211yesmaximal, characteristic, complemented
6C22×#14519698C211yesmaximal, characteristic, complemented
7C22×#14519689C211yesmaximal, characteristic, complemented
8C22×#102×C61C211yesmaximal, characteristic, complemented
9C23×C22⋊D61—21no—
10C23×C4×D61—21no—
11C23×C4×D61C2211yescharacteristic
12C23×#92418C2211yescharacteristic
13C2×#14519748—26no—
14C2×#14519748C22112yes—
15C22×C4⋊Dic61C2211yescharacteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196—21no—
18C2×C4⋊C4×D61—26no—
19C2×C4⋊C4×D61C22112yescomplemented
20C22×C22⋊Dic61—21no—
21#16840074C22164yesdirect product factor
22C2×#14519711C22112yescomplemented
23C2×#14519710C22112yescomplemented
24C2×#14519698C22112yescomplemented
25C2×#14519689C22112yescomplemented
26C23×D4×C61C2211yescharacteristic
27C23×C8×C61C2211yescharacteristic
28C22×C4⋊C4×C61C2211yescharacteristic
29C2×#102×C61C22112yescomplemented
30C24×D61D411yescharacteristic
31C22×C22⋊D61—212no—
32C22×C22⋊D61—48no—
33C23×Dic61—21no—
34C23×Dic61—21no—
35C23×Dic61D411yescharacteristic
36C22×C4×D61—24no—
37C22×C4×D61—24no—
38C22×C4×D61—212no—
39C22×C4×D61—48no—
40C22×C4×D61D416yes—
41C22×C4×D61C2316yes—
42C22×#92418—24no—
43C22×#92418C2316yes—
44#14519748—224no—
45#14519748C23116yes—
46C2×C4⋊Dic61—23no—
47C2×C4⋊Dic61—23no—
48C2×C4⋊Dic61C2316yes—
49C2×C4⋊Dic61C2316yes—
50C2×#11758196—212no—
51C4⋊C4×D61—224no—
52C4⋊C4×D61C23116yescomplemented
53C2×C22⋊Dic61—212no—
54#14519711C23116yescomplemented
55#14519710C23116yescomplemented
56#14519698C23116yescomplemented
57#14519689C23116yescomplemented
58C25×C61—21no—
59C22×D4×C61—23no—
60C22×D4×C61—24no—
61C22×D4×C61—24no—
62C22×D4×C61C2316yes—
63C23×C4×C61—21no—
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—24no—
66C22×C8×C61C2316yes—
67C2×C4⋊C4×C61—23no—
68C2×C4⋊C4×C61C2316yes—
69#102×C61C23116yescomplemented
70C24×C61—26no—
71C24×C61—44no—
72C24×C61—44no—
73C24×C61—44no—
74C24×C61C2×D411yescharacteristic
75C23×D61—24no—
76C23×D61—24no—
77C23×D61D818yes—
78C23×D61C2×D416yes—
79C2×D4×C61—26no—
80C2×D4×C61—212no—
81C2×D4×C61—212no—
82C2×D4×C61—412no—
83C2×D4×C61C2414yes—
84C22×C4×C61—26no—
85C22×C4×C61—44no—
86C22×C4×C61C2×D413yes—
87C22×C4×C61#4114yes—
88C22×C4×C61#4114yes—
89C22×C4×C61C2413yes—
90C2×C22⋊D61—216no—
91C2×C22⋊D61—448no—
92C22×Dic61—24no—
93C22×Dic61—26no—
94C22×Dic61—26no—
95C22×Dic61—44no—
96C22×Dic61—44no—
97C22×Dic61C2×D416yes—
98C2×C4×D61—224no—
99C2×C4×D61—212no—
100C2×C4×D61—212no—
101C2×C4×D61—216no—
102C2×C4×D61—448no—
103C2×C4×D61C2×D4112yes—
104C2×C4×D61C2414yes—
105C2×C8×C61—212no—
106C2×C8×C61C2414yes—
107C4⋊C4×C61—26no—
108C4⋊C4×C61C2414yes—
109C22⋊Dic61—216no—
110C4⋊Dic61—26no—
111C4⋊Dic61—26no—
112C4⋊Dic61C2414yes—
113C4⋊Dic61C2414yes—
114#11758196—216no—
115C2×#92418—212no—
116C2×#92418C2414yes—
117C23×C61—24no—
118C23×C61—412no—
119C23×C61—412no—
120C23×C61—412no—
121C23×C61—816no—
122C23×C61#12314yes—
123C23×C61C2×D814yes—
124C23×C61#13714yes—
125C23×C61C22×D413yes—
126C22×D61—212no—
127C22×D61—212no—
128C22×D61—232no—
129C22×D61C2×D8124yes—
130C22×D61C22×D414yes—
131D4×C61—24no—
132D4×C61—24no—
133D4×C61—412no—
134C2×C4×C61—24no—
135C2×C4×C61—412no—
136C2×C4×C61#123112yes—
137C2×C4×C61C22×D413yes—
138C2×C4×C61C2×#4116yes—
139C2×C4×C61C2×#4116yes—
140C2×C4×C61C2511yescharacteristic
141C22⋊D61—432no—
142C2×Dic61—212no—
143C2×Dic61—24no—
144C2×Dic61—24no—
145C2×Dic61—412no—
146C2×Dic61—412no—
147C2×Dic61C22×D414yes—
148C4×D61—224no—
149C4×D61—24no—
150C4×D61—24no—
151C4×D61—432no—
152C8×C61—24no—
153#92418—24no—
154C22×#480—611nomaximal, Sylow
155C22×C61—44no—
156C22×C61—44no—
157C22×C61—44no—
158C22×C61—824no—
159C22×C61#480116yescomplemented
160C22×C61C2×#12316yes—
161C22×C61C22×D816yes—
162C22×C61C2×#13716yes—
163C22×C61C23×D411yescharacteristic
164C2×D61—248no—
165C2×D61—24no—
166C2×D61—24no—
167C2×D61C22×D818yes—
168C4×C61—44no—
169C4×C61C2×#12316yes—
170C4×C61C22×#4111yescharacteristic
171C4×C61C22×#4111yescharacteristic
172Dic61—24no—
173Dic61—44no—
174Dic61—44no—
175C22×#121—611no—
176C23×C4⋊C4—611no—
177C2×#480—6124no—
178C22×#107—611no—
179C22×#107—611no—
180C22×#102—611no—
181C22×#102D6111yescharacteristic, complemented
182C22×C22⋊C8—611no—
183C2×C61—84no—
184C2×C61C2×#480112yescomplemented
185C2×C61C22×#12311yescharacteristic
186C2×C61C23×D811yescharacteristic
187C2×C61C22×#13711yescharacteristic
188D61—28no—
189C23×D4—1221no—
190C23×D4C2×D6111yescharacteristic
191C24×C4—611no—
192C24×C4—1221no—
193C23×C8—611no—
194C23×C8C2×D6111yescharacteristic
195C2×#121—6112no—
196C2×#121—1226no—
197C22×C4⋊C4—611no—
198C22×C4⋊C4—611no—
199C22×C4⋊C4—6112no—
200C22×C4⋊C4—1226no—
201C22×C4⋊C4—1221no—
202C22×C4⋊C4C2×D6111yescharacteristic
203C22×C22⋊C4—1221no—
204#480—6164no—
205C2×#107—6112no—
206C2×#107—6112no—
207C2×#102—6112no—
208C2×#102C2×D61112yescomplemented
209C2×C22⋊C8—6112no—
210C61C22×#48011yescharacteristic, complemented, Sylow
211C25—21no—
212C25—611no—
213C22×D4—24no—
214C22×D4—23no—
215C22×D4—24no—
216C22×D4—12212no—
217C22×D4—2448no—
218C22×D4C22×D6116yes—
219C23×C4—21no—
220C23×C4—611no—
221C23×C4—616no—
222C23×C4—616no—
223C23×C4—12212no—
224C23×C4—1224no—
225C23×C4—1224no—
226C23×C4—1221no—
227C23×C4—1221no—
228C23×C4—2448no—
229C23×C4C22×D6111yescharacteristic
230C22×C8—24no—
231C22×C8—616no—
232C22×C8—1224no—
233C22×C8C22×D6116yes—
234#121—6116no—
235#121—12224no—
236C2×C4⋊C4—23no—
237C2×C4⋊C4—616no—
238C2×C4⋊C4—616no—
239C2×C4⋊C4—6116no—
240C2×C4⋊C4—12224no—
241C2×C4⋊C4—12212no—
242C2×C4⋊C4—1223no—
243C2×C4⋊C4—1223no—
244C2×C4⋊C4C22×D6116yes—
245C2×C22⋊C4—12212no—
246#107—6116no—
247#107—6116no—
248#102—6116no—
249#102C22×D61116yescomplemented
250C22⋊C8—6116no—
251C24—26no—
252C24—44no—
253C24—44no—
254C24—44no—
255C24—616no—
256C24—618no—
257C24—1224no—
258C24—1224no—
259C24D4×D6111yescharacteristic
260C2×D4—26no—
261C2×D4—212no—
262C2×D4—212no—
263C2×D4—412no—
264C2×D4—12216no—
265C2×D4—24448no—
266C2×D4C23×D6114yes—
267C22×C4—26no—
268C22×C4—44no—
269C22×C4—616no—
270C22×C4—6112no—
271C22×C4—614no—
272C22×C4—12216no—
273C22×C4—1224no—
274C22×C4—12212no—
275C22×C4—12212no—
276C22×C4—12224no—
277C22×C4—1226no—
278C22×C4—1226no—
279C22×C4—24448no—
280C22×C4—2444no—
281C22×C4—2444no—
282C22×C4#1175822214yes—
283C22×C4D4×D6113yes—
284C22×C4#1175822414yes—
285C22×C4C23×D6113yes—
286C2×C8—212no—
287C2×C8—614no—
288C2×C8—12212no—
289C2×C8C23×D6114yes—
290C4⋊C4—26no—
291C4⋊C4—614no—
292C4⋊C4—614no—
293C4⋊C4—12216no—
294C4⋊C4—1226no—
295C4⋊C4—1226no—
296C4⋊C4C23×D6114yes—
297C22⋊C4—12216no—
298C23—24no—
299C23—412no—
300C23—412no—
301C23—412no—
302C23—816no—
303C23—6124no—
304C23—614no—
305C23—12212no—
306C23—12212no—
307C23—12232no—
308C23#1451975914yes—
309C23D8×D6114yes—
310C23#1451980614yes—
311C23C2×D4×D6113yes—
312D4—24no—
313D4—24no—
314D4—412no—
315D4—24432no—
316C2×C4—24no—
317C2×C4—412no—
318C2×C4—614no—
319C2×C4—12212no—
320C2×C4—12224no—
321C2×C4—1224no—
322C2×C4—1224no—
323C2×C4—1224no—
324C2×C4—1224no—
325C2×C4—24432no—
326C2×C4—24412no—
327C2×C4—24412no—
328C2×C4#14519759112yes—
329C2×C4C2×D4×D6113yes—
330C2×C4C2×#1175822416yes—
331C2×C4C2×#1175822216yes—
332C2×C4C24×D6111yescharacteristic
333C8—24no—
334C8—1224no—
335C22—44no—
336C22—44no—
337C22—44no—
338C22—824no—
339C22—618no—
340C22—12248no—
341C22—1224no—
342C22—1224no—
343C22#16840074116yesdirect product factor
344C22C2×#1451975916yes—
345C22C2×D8×D6116yes—
346C22C2×#1451980616yes—
347C22C22×D4×D6111yescharacteristic
348C4—44no—
349C4—1224no—
350C4—2444no—
351C4—2444no—
352C4C2×#1451975916yes—
353C4C22×#1175822411yescharacteristic
354C4C22×#1175822211yescharacteristic
355C2—84no—
356C2—1228no—
357C2C2×#16840074112yesdirect product factor
358C2C22×#1451975911yescharacteristic
359C2C22×D8×D6111yescharacteristic
360C2C22×#1451980611yescharacteristic
subgroupG/H
centerC24D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#102×C61C2
socleC24×C61C2×D4
prime radicalC22×#14519748C2
hypercenterC22×#102D61
hypocenterC61C22×#480
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
3. C2×#16840074C2direct (N × H)
4. C22×#14519711C2semidirect
5. C22×#14519710C2semidirect
6. C22×#14519698C2semidirect
7. C22×#14519689C2semidirect
8. C22×#102×C61C2semidirect
19. C2×C4⋊C4×D61C22semidirect
21. #16840074C22direct (N × H)
22. C2×#14519711C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519698C22semidirect
25. C2×#14519689C22semidirect
29. C2×#102×C61C22semidirect
52. C4⋊C4×D61C23semidirect
54. #14519711C23semidirect
55. #14519710C23semidirect
56. #14519698C23semidirect
57. #14519689C23semidirect
69. #102×C61C23semidirect
159. C22×C61#480semidirect
181. C22×#102D61semidirect
184. C2×C61C2×#480semidirect
208. C2×#102C2×D61semidirect
210. C61C22×#480semidirect
249. #102C22×D61semidirect
343. C22#16840074direct (N × H)
357. C2C2×#16840074direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197482
C22×C4⋊C4×D612
C2×#168400742
C22×#145197112
C22×#145197102
C22×#145196982
C22×#145196892
C22×#102×C612
C22×#48061