Finite Group Databasebeta

← C2×#21444888 #29655627

Subgroups — C2×#21444888 #29655627

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840473C211yesmaximal, characteristic, complemented
2C2×#16839959C211yesmaximal, characteristic, complemented
3C2×#16839954C211yesmaximal, characteristic
4#21444888C218yesmaximal, direct product factor
5C2×#16839511C211yesmaximal, characteristic, complemented
6C2×#16839494C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic, complemented
8C2×C61×#492C211yesmaximal, characteristic, complemented
9C22×#11758200—21no—
10C22×#11758199—21no—
11#16840473—22no—
12#16840473—22no—
13#16840473—22no—
14#16840473C2214yescomplemented
15C2×#14519768—21no—
16C2×#14519757—21no—
17C2×#14519753—22no—
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×#14519739—21no—
21C2×C4⋊C4×D61—21no—
22#16839959—22no—
23#16839959C2214yescomplemented
24#16839954—22no—
25#16839954C2214yes—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519698—21no—
29C2×#14519698—21no—
30#16839511C2214yescomplemented
31#16839494C2214yescomplemented
32#16839491C2214yescomplemented
33C22×SD16×C61—22no—
34C2×C4⋊Q8×C61C2211yescharacteristic
35C2×#127×C61C2211yescharacteristic
36C61×#492—22no—
37C61×#492C2214yescomplemented
38C2×C4×C8×C61C2211yescharacteristic
39C22×Dic122D411yescharacteristic
40C22×D244D411yescharacteristic
41C22×C4×D61—21no—
42C22×C4×D61—22no—
43C2×#11758200—24no—
44C2×#11758200—44no—
45C2×#11758199—24no—
46C2×#11758199—44no—
47C22×#92418—21no—
48C22×#92418—21no—
49#14519768—24no—
50#14519768—24no—
51#14519757—24no—
52#14519757—24no—
53#14519753—28no—
54#14519753—28no—
55C4×Dic122—21no—
56C4×Dic122—21no—
57C4×Dic122D412yes—
58C4×Dic122C2312yes—
59C4×D244—21no—
60C4×D244—21no—
61C4×D244D412yes—
62C4×D244C2312yes—
63#14519739—24no—
64#14519739—24no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×C4⋊Dic61D411yescharacteristic
68C2×#11758196—22no—
69C2×#11758196—21no—
70C4⋊C4×D61—24no—
71C4⋊C4×D61—24no—
72C2×#11758198—22no—
73C2×#11758198—21no—
74C2×C4×Dic61—21no—
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418C2312yes—
78C4⋊#92418C2312yes—
79#14519698—24no—
80#14519698—24no—
81C22×Q8×C61D412yes—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C2×SD16×C61—28no—
86C2×SD16×C61—48no—
87C22×C8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61D412yes—
91C4⋊Q8×C61C2312yes—
92#127×C61—21no—
93#127×C61—21no—
94#127×C61—21no—
95#127×C61C2312yes—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C42×C61C2311yescharacteristic
99C4×C8×C61—21no—
100C4×C8×C61C2312yes—
101C24×C61—41no—
102C23×D61—21no—
103C2×Q8×C61—22no—
104C2×Q8×C61—44no—
105C2×Q8×C61C2×D414yes—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61—22no—
109C2×D4×C61—44no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C2×D4×C61—41no—
113C2×D4×C61—42no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C22×C4×C61—22no—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C2×D244—21no—
125C2×D244—22no—
126C2×D244SD1614yescomplemented
127C2×D244C2×D412yes—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—28no—
131C2×C4×D61—42no—
132C2×C4×D61—42no—
133C2×C4×D61—84no—
134C2×Dic122—22no—
135C2×Dic122—22no—
136C2×Dic122—21no—
137C2×Dic122C2×D412yes—
138SD16×C61—416no—
139C2×C8×C61—24no—
140C2×C8×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2411yescharacteristic
149#11758200—48no—
150#11758199—48no—
151#11758198—28no—
152#11758198—22no—
153#11758198—22no—
154C4⋊Dic61—28no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61C2×D412yes—
158C4⋊Dic61C2×D412yes—
159#11758196—28no—
160#11758196—22no—
161#11758196—22no—
162C4×Dic61—22no—
163C4×Dic61—22no—
164C2×#92418—22no—
165C2×#92418—22no—
166C2×#92418—42no—
167C2×#92418—42no—
168C23×C61—42no—
169C23×C61—82no—
170C23×C61—82no—
171C23×C61—82no—
172C23×C61#12011yescharacteristic
173C22×D61—22no—
174C22×D61—24no—
175C22×D61—42no—
176C22×D61—42no—
177Q8×C61—44no—
178Q8×C61—82no—
179D4×C61—44no—
180D4×C61—42no—
181D4×C61—42no—
182D4×C61—42no—
183D4×C61—42no—
184D4×C61—82no—
185D4×C61—82no—
186D4×C61—82no—
187C2×C4×C61—22no—
188C2×C4×C61—24no—
189C2×C4×C61—44no—
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61#12011yescharacteristic
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61C2×SD1612yes—
194C2×C4×C61#13512yes—
195C2×C4×C61AGL(1,ℤ/8)12yes—
196C2×C4×C61#13712yes—
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C22×D411yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—22no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206D244—22no—
207D244—24no—
208D244C2×SD1614yescomplemented
209C4×D61—42no—
210C4×D61—42no—
211C4×D61—44no—
212C4×D61—88no—
213Dic122—22no—
214Dic122—22no—
215Dic122—42no—
216C8×C61—24no—
217#92418—42no—
218#92418—42no—
219C2×#1622—611nomaximal, Sylow
220C22×C61—82no—
221C22×C61—82no—
222C22×C61—82no—
223C22×C61—164no—
224C22×C61#44812yes—
225C22×C61#44912yes—
226C22×C61#45312yes—
227C22×C61C2×#12011yescharacteristic
228C2×D61—24no—
229C2×D61—48no—
230C2×D61—42no—
231C2×D61—42no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—44no—
235C4×C61#44812yes—
236C4×C61#44912yes—
237C4×C61C22×SD1611yescharacteristic
238C4×C61C2×#13511yescharacteristic
239C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C61C2×#13711yescharacteristic
241Dic61—42no—
242Dic61—42no—
243Dic61—42no—
244C2×#554—611no—
245C2×#492D6111yescharacteristic, complemented
246C2×#460—611no—
247C2×#459—611no—
248#1622—618no—
249C2×#333—611no—
250C2×Q8⋊C8—611no—
251C2×D4⋊C8—611no—
252C2×C61—162no—
253C2×C61#162214yescomplemented
254C2×C61C2×#44811yescharacteristic
255C2×C61C2×#44911yescharacteristic
256C2×C61C2×#45311yescharacteristic
257D61—44no—
258C22×SD16—22no—
259C22×SD16—1221no—
260C22×D8—1221no—
261#554—614no—
262#554—1222no—
263#554—1222no—
264#554—1222no—
265C2×C4⋊Q8C2×D6111yescharacteristic
266C2×#127C2×D6111yescharacteristic
267C2×#125—1221no—
268C2×C22⋊Q8—1221no—
269C2×C22⋊Q8—1222no—
270C2×C4×Q8—611no—
271C2×C4×D4—611no—
272C2×C4×D4—1221no—
273C22×C4⋊C4—1221no—
274#492—22no—
275#492C2×D6114yescomplemented
276#460—614no—
277#460—1222no—
278#459—614no—
279#459—1222no—
280C2×C4⋊C8—611no—
281C2×C4⋊C8—611no—
282C2×#102—1221no—
283C2×#102—1221no—
284C2×C4×C8C2×D6111yescharacteristic
285#333—614no—
286Q8⋊C8—614no—
287D4⋊C8—614no—
288C61C2×#162211yescharacteristic, complemented, Sylow
289C22×Q8—611no—
290C22×Q8C22⋊D6112yes—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—611no—
295C23×C4—1222no—
296C23×C4—1221no—
297C2×SD16—28no—
298C2×SD16—48no—
299C2×SD16—1224no—
300C2×SD16—2444no—
301C2×D8—1224no—
302C2×D8—2444no—
303C22×C8—21no—
304C22×C8—1221no—
305C22×C8—1221no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8C22⋊D6112yes—
309C4⋊Q8C22×D6112yes—
310#127—21no—
311#127—21no—
312#127—21no—
313#127C22×D6112yes—
314#125—1224no—
315#125—1224no—
316C22⋊Q8—1224no—
317C22⋊Q8—1224no—
318C22⋊Q8—1228no—
319C22⋊Q8—1228no—
320C4×Q8—612no—
321C4×Q8—612no—
322C4×Q8—1221no—
323C4×Q8—1221no—
324C4×D4—612no—
325C4×D4—612no—
326C4×D4—1224no—
327C4×D4—1224no—
328C4×D4—1221no—
329C4×D4—1221no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—1224no—
335C2×C4⋊C4—1224no—
336C2×C4⋊C4—1222no—
337C2×C4⋊C4—1222no—
338C2×C4⋊C4—1221no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1221no—
341C2×C42—1221no—
342C2×C42C22×D6111yescharacteristic
343C4⋊C8—612no—
344C4⋊C8—612no—
345C4⋊C8—1221no—
346C4⋊C8—1221no—
347#102—1224no—
348#102—1224no—
349C4×C8—21no—
350C4×C8C22×D6112yes—
351C24—41no—
352C24—1221no—
353C2×Q8—22no—
354C2×Q8—44no—
355C2×Q8—612no—
356C2×Q8—1221no—
357C2×Q8—1222no—
358C2×Q8—1222no—
359C2×Q8C2×C22⋊D6114yes—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—44no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—612no—
372C2×D4—614no—
373C2×D4—1221no—
374C2×D4—1222no—
375C22×C4—22no—
376C22×C4—1228no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—4884no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4D4×D6111yescharacteristic
386C22×C4D4×D6111yescharacteristic
387C22×C4C2×C22⋊D6111yescharacteristic
388SD16—416no—
389SD16—2448no—
390D8—2448no—
391C2×C8—24no—
392C2×C8—22no—
393C2×C8—1222no—
394C2×C8—1222no—
395C2×C8—2442no—
396C2×C8—2442no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—612no—
402C4⋊C4—612no—
403C4⋊C4—1228no—
404C4⋊C4—1228no—
405C4⋊C4—1222no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—1222no—
409C22⋊C4—1228no—
410C22⋊C4—1222no—
411C22⋊C4—1222no—
412C42—1222no—
413C42—1222no—
414C42D4×D6111yescharacteristic
415C42D4×D6111yescharacteristic
416C42C2×C22⋊D6111yescharacteristic
417C42C23×D6111yescharacteristic
418C23—42no—
419C23—82no—
420C23—82no—
421C23—82no—
422C23—1222no—
423C23—1224no—
424C23—2442no—
425C23—2442no—
426C23#1451974511yescharacteristic
427Q8—44no—
428Q8—82no—
429Q8—1222no—
430Q8—1222no—
431Q8—2442no—
432D4—44no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—82no—
438D4—82no—
439D4—82no—
440D4—614no—
441D4—1222no—
442D4—1224no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—44no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—4888no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2444no—
456C2×C4#1451974511yescharacteristic
457C2×C4#1451974511yescharacteristic
458C2×C4#1451974511yescharacteristic
459C2×C4SD16×D6112yes—
460C2×C4#1451979812yes—
461C2×C4#1451980412yes—
462C2×C4#1451980612yes—
463C2×C4C2×D4×D6111yescharacteristic
464C2×C4C2×D4×D6111yescharacteristic
465C2×C4C22×C22⋊D6111yescharacteristic
466C8—24no—
467C8—2442no—
468C8—2442no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—164no—
473C22—1224no—
474C22—2448no—
475C22—2442no—
476C22—2442no—
477C22#1683989912yes—
478C22#1683990612yes—
479C22#1683992912yes—
480C22C2×#1451974511yescharacteristic
481C4—21no—
482C4—21no—
483C4—44no—
484C4—2442no—
485C4—2442no—
486C4—2442no—
487C4#1683989912yes—
488C4#1683990612yes—
489C4C2×SD16×D6111yescharacteristic
490C4C2×#1451979811yescharacteristic
491C4C2×#1451980411yescharacteristic
492C4C2×#1451980611yescharacteristic
493C2—162no—
494C2—2444no—
495C2#2144488814yesdirect product factor
496C2C2×#1683989911yescharacteristic
497C2C2×#1683990611yescharacteristic
498C2C2×#1683992911yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#492C2
socleC23×C61#120
prime radicalC2×#16839954C2
hypercenterC2×#492D61
hypocenterC61C2×#1622
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. C2×#16840473C2semidirect
2. C2×#16839959C2semidirect
4. #21444888C2direct (N × H)
5. C2×#16839511C2semidirect
6. C2×#16839494C2semidirect
7. C2×#16839491C2semidirect
8. C2×C61×#492C2semidirect
14. #16840473C22semidirect
23. #16839959C22semidirect
30. #16839511C22semidirect
31. #16839494C22semidirect
32. #16839491C22semidirect
37. C61×#492C22semidirect
126. C2×D244SD16semidirect
208. D244C2×SD16semidirect
245. C2×#492D61semidirect
253. C2×C61#1622semidirect
275. #492C2×D61semidirect
288. C61C2×#1622semidirect
495. C2#21444888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404732
C2×#168399592
C2×#168399542
#214448882
C2×#168395112
C2×#168394942
C2×#168394912
C2×C61×#4922
C2×#162261