Finite Group Databasebeta

← C2×#21447528 #29832908

Subgroups — C2×#21447528 #29832908

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519796C211yesmaximal, characteristic
2C22×#14519716C211yesmaximal, characteristic, complemented
3C2×#107×D61C211yesmaximal, characteristic, complemented
4#21447528C218yesmaximal, direct product factor
5C2×#16839567C211yesmaximal, characteristic, complemented
6C2×#16839565C211yesmaximal, characteristic, complemented
7C2×#16839563C211yesmaximal, characteristic, complemented
8C2×C61×#357C211yesmaximal, characteristic, complemented
9C22×#11758224—21no—
10C2×#14519796—24no—
11C2×#14519796—22no—
12C2×#14519796C418yescomplemented
13C2×#14519796C2214yes—
14C22×Dic244C2211yescharacteristic
15C22×#11758200—21no—
16C22×C8×D61C2211yescharacteristic
17C2×C4⋊C4×D61—21no—
18C2×#14519716—24no—
19C2×#14519716C2214yescomplemented
20C22×#11758185C2211yescharacteristic
21C2×#14519711C2211yescharacteristic
22C2×#14519710—21no—
23#107×D61—22no—
24#107×D61C2214yescomplemented
25#16839567C2214yescomplemented
26#16839565C2214yescomplemented
27#16839563C2214yescomplemented
28C22×D8×C61C2211yescharacteristic
29C22×C16×C61C2211yescharacteristic
30C2×#107×C61C2211yescharacteristic
31C61×#357C2214yescomplemented
32C2×#11758224—28no—
33C2×#11758224—24no—
34C2×#11758224—42no—
35C2×#11758224—44no—
36C22×Dic122—21no—
37C22×C22⋊D61—41no—
38C23×Dic61—41no—
39C22×C4×D61—41no—
40C22×C4×D61D411yescharacteristic
41#14519796—216no—
42#14519796—28no—
43#14519796C2×C4116yescomplemented
44C2×Dic244—21no—
45C2×Dic244—22no—
46C2×Dic244C2×C414yescomplemented
47C2×Dic244C2312yes—
48C2×#11758200—28no—
49C2×#11758200—24no—
50C22×#92418D411yescharacteristic
51C2×C8×D61C2×C414yes—
52C2×C8×D61D412yes—
53C2×C8×D61D414yes—
54C2×C8×D61C2312yes—
55C2×C4⋊Dic61—21no—
56C2×#11758196—41no—
57C4⋊C4×D61—24no—
58C4⋊C4×D61—42no—
59#14519716—28no—
60C2×#11758185—22no—
61C2×#11758185C2312yes—
62#14519711—21no—
63#14519711C2312yes—
64#14519710—24no—
65C22×D4×C61—21no—
66C2×D8×C61—21no—
67C2×D8×C61—22no—
68C2×D8×C61C2×C414yescomplemented
69C2×D8×C61C2312yes—
70C22×C8×C61C2311yescharacteristic
71C2×C4⋊C4×C61—21no—
72C2×C16×C61—22no—
73C2×C16×C61C2312yes—
74#107×C61—21no—
75#107×C61C2312yes—
76C24×C61—41no—
77C23×D61D811yescharacteristic
78C2×D4×C61—24no—
79C2×D4×C61—22no—
80C2×D4×C61—41no—
81C2×D4×C61—42no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C2×C22⋊D61—48no—
85C2×C22⋊D61—44no—
86C22×Dic61—41no—
87C22×Dic61—48no—
88C22×Dic61—44no—
89C22×Dic61—41no—
90C22×Dic61D811yescharacteristic
91#11758224—216no—
92#11758224—416no—
93#11758224—48no—
94C2×C4×D61—44no—
95C2×C4×D61—84no—
96C2×C4×D61C22⋊C414yes—
97C2×C4×D61D812yes—
98C2×C4×D61SD1614yes—
99C2×C4×D61C2×D412yes—
100C2×Dic122—24no—
101C2×Dic122—22no—
102C2×Dic122—41no—
103C2×Dic122—42no—
104D8×C61—24no—
105D8×C61—22no—
106D8×C61C22×C414yescomplemented
107C2×C8×C61C22×C412yes—
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D412yes—
110C2×C8×C61C2411yescharacteristic
111C4⋊C4×C61—22no—
112C4⋊C4×C61—41no—
113#11758200—216no—
114C4⋊Dic61—22no—
115C4⋊Dic61—41no—
116#11758196—44no—
117C2×#92418C22⋊C414yes—
118C2×#92418C2×D412yes—
119Dic244—24no—
120Dic244—22no—
121Dic244C22×C414yescomplemented
122C8×D61C22⋊C418yes—
123C8×D61C22×C414yes—
124C8×D61C2×D414yes—
125C16×C61—22no—
126#11758185—22no—
127C23×C61—42no—
128C23×C61—44no—
129C23×C61—82no—
130C23×C61—82no—
131C23×C61C2×D811yescharacteristic
132C22×D61—22no—
133C22×D61—22no—
134C22×D61#10214yes—
135C22×D61C2×D812yes—
136D4×C61—24no—
137D4×C61—42no—
138D4×C61—44no—
139C2×C4×C61—42no—
140C2×C4×C61—82no—
141C2×C4×C61C2×C22⋊C412yes—
142C2×C4×C61C2×D811yescharacteristic
143C2×C4×C61C2×SD1612yes—
144C2×C4×C61C22×D411yescharacteristic
145C22⋊D61—416no—
146C2×Dic61—42no—
147C2×Dic61—44no—
148C2×Dic61—416no—
149C2×Dic61—42no—
150C2×Dic61—82no—
151C2×Dic61#10214yes—
152C2×Dic61C2×D812yes—
153C4×D61—88no—
154C4×D61#10218yes—
155C4×D61C2×C22⋊C414yes—
156C4×D61C2×SD1614yes—
157Dic122—24no—
158Dic122—42no—
159Dic122—44no—
160C8×C61C2×C22⋊C412yes—
161C8×C61C23×C411yescharacteristic
162C8×C61C22×D411yescharacteristic
163#92418C2×C22⋊C414yes—
164C2×#2139—611nomaximal, Sylow
165C22×C61—44no—
166C22×C61—82no—
167C22×C61—82no—
168C22×C61—88no—
169C22×C61C2×#10212yes—
170C22×C61#50912yes—
171C22×C61#51012yes—
172C22×C61C22×D811yescharacteristic
173C2×D61—22no—
174C2×D61—22no—
175C2×D61—28no—
176C2×D61C2×#10214yes—
177C4×C61—82no—
178C4×C61C2×#10212yes—
179C4×C61C22×C22⋊C411yescharacteristic
180C4×C61C22×SD1611yescharacteristic
181Dic61—44no—
182Dic61—82no—
183Dic61C2×#10214yes—
184C22×#135—611no—
185C22×M32—611no—
186C22×#107—611no—
187#2139—618no—
188C2×#358—611no—
189C2×#358—611no—
190C2×#357—611no—
191C2×#357D6111yescharacteristic, complemented
192C2×C61—84no—
193C2×C61#213914yescomplemented
194C2×C61C22×#10211yescharacteristic
195C2×C61C2×#50911yescharacteristic
196C2×C61C2×#51011yescharacteristic
197D61—24no—
198C22×#41—1221no—
199C2×#135—618no—
200C2×#135—614no—
201C2×#135—1222no—
202C2×#135—1224no—
203C22×Q16—611no—
204C22×SD16—1221no—
205C22×D8C2×D6111yescharacteristic
206C23×C8—611no—
207C22×C4⋊C4—1221no—
208C2×M32—614no—
209C2×M32—1224no—
210C22×C16—611no—
211C22×C16C2×D6111yescharacteristic
212C2×#107—611no—
213C2×#107—614no—
214C2×#107—1222no—
215C2×#107—1221no—
216C2×#107C2×D6111yescharacteristic
217#358—614no—
218#358—614no—
219#357—614no—
220#357C2×D6114yescomplemented
221C61C2×#213911yescharacteristic, complemented, Sylow
222C2×#41—1224no—
223C2×#41—1228no—
224C2×#41—2442no—
225C2×#41—2444no—
226C22×Q8—1221no—
227C22×D4—21no—
228C22×D4—2441no—
229C23×C4—611no—
230C23×C4—2441no—
231C23×C4—2441no—
232#135—6116no—
233#135—1228no—
234#135—12216no—
235C2×Q16—614no—
236C2×Q16—612no—
237C2×Q16—1222no—
238C2×Q16—1221no—
239C2×SD16—1224no—
240C2×SD16—1228no—
241C2×D8—22no—
242C2×D8—21no—
243C2×D8C4×D6114yescomplemented
244C2×D8C22×D6112yes—
245C22×C8—611no—
246C22×C8—614no—
247C22×C8—612no—
248C22×C8—614no—
249C22×C8—612no—
250C22×C8C22×D6111yescharacteristic
251C2×C4⋊C4—21no—
252C2×C4⋊C4—1224no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—2442no—
255C2×C4⋊C4—2441no—
256M32—1228no—
257C2×C16—22no—
258C2×C16—612no—
259C2×C16—1222no—
260C2×C16C22×D6112yes—
261#107—21no—
262#107—612no—
263#107—1224no—
264#107—1221no—
265#107C22×D6112yes—
266C24—41no—
267C24—611no—
268#41—12216no—
269#41—24416no—
270#41—2448no—
271C2×Q8—1222no—
272C2×Q8—1224no—
273C2×Q8—2441no—
274C2×Q8—2442no—
275C2×D4—22no—
276C2×D4—24no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—2448no—
280C2×D4—2444no—
281C22×C4—41no—
282C22×C4—611no—
283C22×C4—612no—
284C22×C4—614no—
285C22×C4—612no—
286C22×C4—614no—
287C22×C4—4884no—
288C22×C4—2444no—
289C22×C4—2448no—
290C22×C4—2444no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4D4×D6111yescharacteristic
294Q16—614no—
295Q16—1222no—
296Q16—1224no—
297SD16—12216no—
298D8—22no—
299D8—24no—
300D8C2×C4×D6114yescomplemented
301C2×C8—612no—
302C2×C8—614no—
303C2×C8—614no—
304C2×C8—614no—
305C2×C8—618no—
306C2×C8C2×C4×D6112yes—
307C2×C8D4×D6112yes—
308C2×C8D4×D6111yescharacteristic
309C2×C8C23×D6111yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—1222no—
313C4⋊C4—2444no—
314C4⋊C4—2441no—
315C16—22no—
316C16—1222no—
317C23—44no—
318C23—42no—
319C23—82no—
320C23—82no—
321C23—614no—
322C23—612no—
323C23—1222no—
324C23—1222no—
325C23D8×D6111yescharacteristic
326Q8—1224no—
327Q8—2444no—
328Q8—2442no—
329D4—24no—
330D4—44no—
331D4—42no—
332D4—24416no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—614no—
336C2×C4—612no—
337C2×C4—614no—
338C2×C4—618no—
339C2×C4—614no—
340C2×C4—4888no—
341C2×C4—4882no—
342C2×C4—24416no—
343C2×C4—2442no—
344C2×C4—2444no—
345C2×C4—2442no—
346C2×C4C22⋊C4×D6112yes—
347C2×C4D8×D6111yescharacteristic
348C2×C4SD16×D6112yes—
349C2×C4C2×D4×D6111yescharacteristic
350C8—614no—
351C8C22⋊C4×D6112yes—
352C8C22×C4×D6111yescharacteristic
353C8C2×D4×D6111yescharacteristic
354C22—44no—
355C22—82no—
356C22—88no—
357C22—82no—
358C22—614no—
359C22—1222no—
360C22—1228no—
361C22—1222no—
362C22#102×D6112yes—
363C22#1684019612yes—
364C22#1684020112yes—
365C22C2×D8×D6111yescharacteristic
366C4—82no—
367C4—614no—
368C4—4882no—
369C4—2444no—
370C4#102×D6112yes—
371C4C2×C22⋊C4×D6111yescharacteristic
372C4C2×SD16×D6111yescharacteristic
373C2—84no—
374C2—1224no—
375C2#2144752814yesdirect product factor
376C2C2×#102×D6111yescharacteristic
377C2C2×#1684019611yescharacteristic
378C2C2×#1684020111yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C61×#357C2
socleC23×C61C2×D8
prime radicalC22×#14519796C2
cosocleC2×C8×C61C24
hypercenterC2×#357D61
hypocenterC61C2×#2139
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C22×#14519716C2semidirect
3. C2×#107×D61C2semidirect
4. #21447528C2direct (N × H)
5. C2×#16839567C2semidirect
6. C2×#16839565C2semidirect
7. C2×#16839563C2semidirect
8. C2×C61×#357C2semidirect
12. C2×#14519796C4semidirect
19. C2×#14519716C22semidirect
24. #107×D61C22semidirect
25. #16839567C22semidirect
26. #16839565C22semidirect
27. #16839563C22semidirect
31. C61×#357C22semidirect
43. #14519796C2×C4semidirect
46. C2×Dic244C2×C4semidirect
68. C2×D8×C61C2×C4semidirect
106. D8×C61C22×C4semidirect
121. Dic244C22×C4semidirect
191. C2×#357D61semidirect
193. C2×C61#2139semidirect
220. #357C2×D61semidirect
221. C61C2×#2139semidirect
243. C2×D8C4×D61semidirect
300. D8C2×C4×D61semidirect
375. C2#21447528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197962
C22×#145197162
C2×#107×D612
#214475282
C2×#168395672
C2×#168395652
C2×#168395632
C2×C61×#3572
C2×#213961