Finite Group Databasebeta

← C2×#21447503 #29832842

Subgroups — C2×#21447503 #29832842

Order 15616.

1306 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840313C211yesmaximal, characteristic
2C2×#16839745C212yesmaximal, complemented
3#21447503C218yesmaximal, direct product factor
4C2×#16839561C211yesmaximal, characteristic, complemented
5C2×#16839558C212yesmaximal, complemented
6C2×C61×#356C211yesmaximal, characteristic, complemented
7C22×#11758226C411yescharacteristic
8C22×#11758226C2211yescharacteristic
9C2×M16×D61—22no—
10#16840313—24no—
11#16840313C414yes—
12#16840313C2214yes—
13C2×#14519774C411yescharacteristic
14C2×#14519766C411yescharacteristic
15C2×#14519766C2211yescharacteristic
16C2×#14519752—22no—
17C2×#14519739—22no—
18C2×C42×D61C411yescharacteristic
19#16839745—24no—
20#16839745C2218yescomplemented
21C2×#14519696C2212yes—
22C2×#14519693—22no—
23#16839561C2214yescomplemented
24#16839558C2218yescomplemented
25C2×C4⋊Q8×C61C2211yescharacteristic
26C2×#101×C61C2212yes—
27C61×#356C2214yescomplemented
28C2×#11758226—22no—
29C2×#11758226—41no—
30C2×#11758226—42no—
31C2×#11758226—41no—
32C2×#11758226—42no—
33C2×#11758226—41no—
34C2×#11758226—41no—
35C2×#11758226C2×C414yes—
36C2×#11758226C2×C412yes—
37C2×#11758226D414yes—
38C2×#11758226C2312yes—
39C22×D244—22no—
40C22×D244—21no—
41C22×D244C2×C411yescharacteristic
42C22×D244C2×C411yescharacteristic
43C22×D244D412yes—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61D412yes—
48C2×#11758194—22no—
49C2×#11758189—42no—
50M16×D61—28no—
51M16×D61—44no—
52C2×C8×D61—42no—
53#14519774—22no—
54#14519774C2×C414yes—
55#14519766—22no—
56#14519766—22no—
57#14519766C2×C414yes—
58#14519766C2×C412yes—
59#14519766C2312yes—
60#14519752—28no—
61#14519752—28no—
62#14519739—28no—
63#14519739—28no—
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61C2×C411yescharacteristic
68C42×D61—22no—
69C42×D61C2×C414yes—
70#14519696—22no—
71#14519696C2314yes—
72#14519693—28no—
73C22×Q8×C61C2×C411yescharacteristic
74C22×Q8×C61C2311yescharacteristic
75C2×M16×C61—22no—
76C4⋊Q8×C61—22no—
77C4⋊Q8×C61C2×C412yes—
78C4⋊Q8×C61C2312yes—
79C2×C4⋊C4×C61—22no—
80C2×C42×C61C2×C411yescharacteristic
81#101×C61—22no—
82#101×C61C2314yes—
83C23×D61—21no—
84C23×D61C22⋊C411yescharacteristic
85C23×D61C22⋊C412yes—
86C2×Q8×C61—21no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×Q8×C61—41no—
90C2×Q8×C61—41no—
91C2×Q8×C61C22×C412yes—
92C2×Q8×C61C22×C411yescharacteristic
93C2×Q8×C61C2×D412yes—
94C2×Q8×C61C2411yescharacteristic
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C2×D412yes—
99C22×Dic61—21no—
100C22×Dic61C22⋊C411yescharacteristic
101#11758226—42no—
102#11758226—42no—
103#11758226—44no—
104#11758226—44no—
105#11758226—42no—
106#11758226—42no—
107#11758226—44no—
108#11758226—44no—
109#11758226—44no—
110#11758226—44no—
111C2×D244—24no—
112C2×D244—28no—
113C2×D244—21no—
114C2×D244—41no—
115C2×D244—41no—
116C2×D244—42no—
117C2×D244—42no—
118C2×D244—48no—
119C2×D244—41no—
120C2×D244—41no—
121C2×D244—42no—
122C2×D244—42no—
123C2×D244C22⋊C412yes—
124C2×D244C22⋊C414yes—
125C2×D244C22×C412yes—
126C2×D244C22×C412yes—
127C2×D244C2×D414yes—
128C2×C4×D61—22no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—22no—
132C2×C4×D61—24no—
133C2×C4×D61—22no—
134C2×C4×D61—24no—
135C2×C4×D61—24no—
136C2×C4×D61—44no—
137C2×C4×D61—42no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61C22⋊C412yes—
141C2×C4×D61C22⋊C414yes—
142C2×C4×D61C22×C412yes—
143C2×C4×D61C2×D414yes—
144M16×C61—24no—
145M16×C61—42no—
146C2×C8×C61—42no—
147C4⋊C4×C61—24no—
148C4⋊C4×C61—24no—
149C42×C61—21no—
150C42×C61C22×C412yes—
151#11758198—28no—
152#11758198—24no—
153#11758198—24no—
154C4×Dic61—21no—
155C4×Dic61—24no—
156C4×Dic61C22×C412yes—
157#11758194—24no—
158#11758194—42no—
159C2×#92418—42no—
160#11758189—48no—
161C8×D61—48no—
162C23×C61C2×C22⋊C411yescharacteristic
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—42no—
169C22×D61—44no—
170C22×D61—44no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61C2×C22⋊C414yes—
174C22×D61C2×C22⋊C412yes—
175Q8×C61—41no—
176Q8×C61—42no—
177Q8×C61—41no—
178Q8×C61—42no—
179Q8×C61—42no—
180C2×C4×C61—24no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—22no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C2×C22⋊C412yes—
191C2×C4×C61C23×C411yescharacteristic
192C2×C4×C61C22×D412yes—
193C2×Dic61—22no—
194C2×Dic61—42no—
195C2×Dic61#9912yes—
196C2×Dic61#9911yescharacteristic
197C2×Dic61#9911yescharacteristic
198C2×Dic61C2×C22⋊C412yes—
199D244—42no—
200D244—44no—
201D244—42no—
202D244—44no—
203D244—42no—
204D244—416no—
205D244—42no—
206D244—48no—
207C4×D61—24no—
208C4×D61—24no—
209C4×D61—24no—
210C4×D61—24no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—48no—
216C4×D61—44no—
217C4×D61—44no—
218C8×C61—44no—
219#92418—44no—
220C2×#2132—611nomaximal, Sylow
221C22×C61—22no—
222C22×C61C2×#9911yescharacteristic
223C22×C61C2×#9911yescharacteristic
224C22×C61C22×C22⋊C411yescharacteristic
225C2×D61—22no—
226C2×D61—24no—
227C2×D61—42no—
228C2×D61—42no—
229C2×D61—44no—
230C2×D61—42no—
231C2×D61—44no—
232C2×D61—44no—
233C2×D61—42no—
234C2×D61—82no—
235C2×D61—82no—
236C2×D61—82no—
237C4×C61—24no—
238C4×C61—22no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—22no—
242C4×C61—42no—
243Dic61—42no—
244Dic61C2×#9912yes—
245Dic61C2×#9912yes—
246C2×#532—611no—
247C2×#413—612no—
248#2132—618no—
249C2×#356—611no—
250C2×#356D6111yescharacteristic, complemented
251C2×#355—612no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61#213212yescomplemented
255C2×C61C22×#9911yescharacteristic
256D61—42no—
257D61—44no—
258D61—82no—
259C22×#41—611no—
260C22×#41—611no—
261C22×M16—1222no—
262#532—614no—
263#532—614no—
264#532—1224no—
265C2×C4⋊Q8C2×D6111yescharacteristic
266C2×#127—611no—
267C2×#124—611no—
268C2×#124—611no—
269C2×#121—1222no—
270C2×C4×D4—1222no—
271C22×C42—611no—
272#413—618no—
273#413—1224no—
274C2×#101—612no—
275C2×#101C2×D6112yes—
276C2×#100—1222no—
277#356—614no—
278#356C2×D6114yescomplemented
279#355—618no—
280C61C2×#213211yescharacteristic, complemented, Sylow
281C2×#41—612no—
282C2×#41—614no—
283C2×#41—612no—
284C2×#41—614no—
285C2×#41—1222no—
286C2×#41—2441no—
287C2×#41—2442no—
288C2×#41—2441no—
289C2×#41—2442no—
290C2×#41—2441no—
291C2×#41—2441no—
292C22×Q8C4×D6111yescharacteristic
293C22×Q8C22×D6111yescharacteristic
294C22×D4—611no—
295C22×D4—611no—
296C22×D4—612no—
297C22×D4—1222no—
298C22×D4—1221no—
299C23×C4—611no—
300C23×C4—612no—
301C23×C4—1221no—
302C23×C4—1221no—
303C2×M16—22no—
304C2×M16—1228no—
305C2×M16—1222no—
306C2×M16—2442no—
307C2×M16—2444no—
308C22×C8—2442no—
309C4⋊Q8—22no—
310C4⋊Q8C4×D6112yes—
311C4⋊Q8C22×D6112yes—
312#127—614no—
313#127—1222no—
314#124—614no—
315#124—612no—
316#124—612no—
317#124—1222no—
318#124—1222no—
319#121—1228no—
320#121—1228no—
321C4×D4—1228no—
322C4×D4—1228no—
323C2×C4⋊C4—22no—
324C2×C22⋊C4—1222no—
325C2×C22⋊C4—1222no—
326C2×C42—611no—
327C2×C42—614no—
328C2×C42—1222no—
329C2×C42—1221no—
330C2×C42C4×D6111yescharacteristic
331#101—22no—
332#101—614no—
333#101—1222no—
334#101C22×D6114yes—
335#100—1228no—
336C24—612no—
337C24—611no—
338C24—1221no—
339#41—2442no—
340#41—2444no—
341#41—2442no—
342#41—2444no—
343#41—2442no—
344#41—2442no—
345#41—2444no—
346#41—2444no—
347#41—2444no—
348#41—2444no—
349C2×Q8—21no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8C2×C4×D6112yes—
355C2×Q8C2×C4×D6111yescharacteristic
356C2×Q8D4×D6112yes—
357C2×Q8C23×D6111yescharacteristic
358C2×D4—612no—
359C2×D4—612no—
360C2×D4—614no—
361C2×D4—614no—
362C2×D4—612no—
363C2×D4—1228no—
364C2×D4—1224no—
365C2×D4—1221no—
366C2×D4—2442no—
367C2×D4—2441no—
368C2×D4—2442no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2448no—
373C2×D4—2442no—
374C2×D4—2442no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—611no—
378C22×C4—612no—
379C22×C4—614no—
380C22×C4—612no—
381C22×C4—614no—
382C22×C4—1222no—
383C22×C4—1224no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—1224no—
389C22×C4—1224no—
390C22×C4—1221no—
391C22×C4—2444no—
392C22×C4—2442no—
393C22×C4—2441no—
394C22×C4—2441no—
395C22×C4C2×C4×D6111yescharacteristic
396C22×C4D4×D6112yes—
397M16—24no—
398M16—42no—
399M16—1224no—
400M16—2448no—
401M16—2442no—
402C2×C8—42no—
403C2×C8—2448no—
404C2×C8—2442no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C22⋊C4—1228no—
408C22⋊C4—1224no—
409C22⋊C4—1224no—
410C42—21no—
411C42—612no—
412C42—1224no—
413C42—1221no—
414C42C2×C4×D6112yes—
415C23—614no—
416C23—612no—
417C23—1222no—
418C23—1221no—
419C23—1221no—
420C23—1222no—
421C23—1222no—
422C23—2444no—
423C23—2444no—
424C23—2442no—
425C23—2441no—
426C23—2441no—
427C23C22⋊C4×D6111yescharacteristic
428Q8—41no—
429Q8—42no—
430Q8—41no—
431Q8—42no—
432Q8—42no—
433D4—2444no—
434D4—2442no—
435D4—2442no—
436D4—2444no—
437D4—2442no—
438D4—24416no—
439D4—2442no—
440D4—2448no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—612no—
451C2×C4—612no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—1224no—
455C2×C4—1224no—
456C2×C4—1224no—
457C2×C4—1224no—
458C2×C4—1222no—
459C2×C4—1222no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—2448no—
464C2×C4—2444no—
465C2×C4—2444no—
466C2×C4—2442no—
467C2×C4C22⋊C4×D6111yescharacteristic
468C2×C4C22⋊C4×D6112yes—
469C2×C4C22×C4×D6111yescharacteristic
470C2×C4C2×D4×D6112yes—
471C8—44no—
472C8—2444no—
473C22—22no—
474C22—1222no—
475C22—1224no—
476C22—4882no—
477C22—4882no—
478C22—4882no—
479C22—2444no—
480C22—2442no—
481C22—2444no—
482C22—2442no—
483C22—2442no—
484C22—2444no—
485C22—2442no—
486C22#99×D6111yescharacteristic
487C22#99×D6111yescharacteristic
488C22C2×C22⋊C4×D6111yescharacteristic
489C4—24no—
490C4—22no—
491C4—21no—
492C4—21no—
493C4—22no—
494C4—42no—
495C4—612no—
496C4—612no—
497C4—2442no—
498C2—21no—
499C2—21no—
500C2—4882no—
501C2—2444no—
502C2—2442no—
503C2#2144750312yesdirect product factor
504C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C23×C4
FrattiniC2×Q8C23×D61
FittingC2×C61×#356C2
socleC22×C61C2×#99
prime radicalC2×#16840313C2
cosocleC2×Q8×C61C24
hypercenterC2×#356D61
hypocenterC61C2×#2132
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
2. C2×#16839745C2semidirect
3. #21447503C2direct (N × H)
4. C2×#16839561C2semidirect
5. C2×#16839558C2semidirect
6. C2×C61×#356C2semidirect
20. #16839745C22semidirect
23. #16839561C22semidirect
24. #16839558C22semidirect
27. C61×#356C22semidirect
250. C2×#356D61semidirect
254. C2×C61#2132semidirect
278. #356C2×D61semidirect
280. C61C2×#2132semidirect
503. C2#21447503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403132
C2×#168397452
#214475032
C2×#168395612
C2×#168395582
C2×C61×#3562
C2×#213261