Finite Group Databasebeta

← C2×#21445053 #29655788

Subgroups — C2×#21445053 #29655788

Order 15616.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840417C211yesmaximal, characteristic
2C2×#16840165C211yesmaximal, characteristic, complemented
3C2×#16839964C211yesmaximal, characteristic, complemented
4#21445053C218yesmaximal, direct product factor
5C2×#16839507C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#474C211yesmaximal, characteristic, complemented
9C22×#11758222—21no—
10C22×#11758201—21no—
11#16840417—22no—
12#16840417—22no—
13#16840417—22no—
14#16840417C2214yes—
15C2×#14519777C2211yescharacteristic
16C2×#14519759—22no—
17C2×#14519756—21no—
18C2×#14519748—21no—
19C2×C4×D244C2211yescharacteristic
20C2×C4⋊C4×D61—21no—
21#16840165—22no—
22#16840165C2214yescomplemented
23#16839964—22no—
24#16839964C2214yescomplemented
25C2×#14519710—22no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519701—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839507C2214yescomplemented
30D4⋊#92418C2214yescomplemented
31#16839489C2214yescomplemented
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C61×#474—22no—
35C61×#474C2214yescomplemented
36C2×#107×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#102×C61—21no—
39C2×#11758222—24no—
40C2×#11758222—24no—
41C2×#11758222—44no—
42C2×#11758222—44no—
43C22×Dic122—21no—
44C22×D244D411yescharacteristic
45C22×C22⋊D61—22no—
46C22×C4×D61—22no—
47C22×C4×D61—21no—
48C2×#11758201—24no—
49C2×#11758201—44no—
50C22×#92418—21no—
51C22×#92418—21no—
52#14519777—21no—
53#14519777—21no—
54#14519777D412yes—
55#14519777C2312yes—
56#14519759—28no—
57#14519759—28no—
58#14519756—24no—
59#14519756—24no—
60#14519748—24no—
61#14519748—24no—
62C4×D244—21no—
63C4×D244—21no—
64C4×D244D412yes—
65C4×D244C2312yes—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61D411yescharacteristic
68C2×C4⋊Dic61D412yes—
69C2×#11758196—22no—
70C4⋊C4×D61—24no—
71C4⋊C4×D61—24no—
72C2×C22⋊Dic61—22no—
73C2×#11758198—21no—
74#14519710—28no—
75C4⋊#92418—21no—
76C4⋊#92418C2312yes—
77#14519701—24no—
78C4×#92418—21no—
79C4×#92418C2312yes—
80C22×Q8×C61—21no—
81C22×D4×C61D411yescharacteristic
82C23×C4×C61—21no—
83C22×C8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61C2312yes—
88C4×D4×C61—21no—
89C4×D4×C61—21no—
90C4×D4×C61D412yes—
91C4×D4×C61C2312yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C22⋊C4×C61—21no—
96C2×C42×C61C2311yescharacteristic
97#107×C61—24no—
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2312yes—
100#102×C61—24no—
101C24×C61—21no—
102C23×D61—21no—
103C2×Q8×C61—22no—
104C2×Q8×C61—41no—
105C2×Q8×C61—42no—
106C2×Q8×C61—42no—
107C2×D4×C61—21no—
108C2×D4×C61—22no—
109C2×D4×C61—22no—
110C2×D4×C61C2×D412yes—
111C22×C4×C61—21no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—42no—
115C22×C4×C61—42no—
116C22×C4×C61—41no—
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C2×C22⋊D61—28no—
121C2×C22⋊D61—48no—
122C22×Dic61—22no—
123C22×Dic61—21no—
124#11758222—48no—
125#11758222—416no—
126#11758222—48no—
127C2×D244—21no—
128C2×D244—22no—
129C2×D244D814yes—
130C2×D244C2×D412yes—
131C2×C4×D61—28no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—48no—
135C2×C4×D61—42no—
136C2×C4×D61—42no—
137C2×Dic122—22no—
138C2×Dic122—22no—
139C2×Dic122—42no—
140C2×Dic122—42no—
141C2×C8×C61—22no—
142C2×C8×C61—42no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61—41no—
148C4⋊C4×C61C2×D412yes—
149C22⋊C4×C61—22no—
150C22⋊C4×C61—22no—
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153C42×C61C2×D411yescharacteristic
154C42×C61C2411yescharacteristic
155C22⋊Dic61—28no—
156#11758201—48no—
157#11758198—22no—
158#11758198—22no—
159C4⋊Dic61—22no—
160C4⋊Dic61—21no—
161C4⋊Dic61—22no—
162C4⋊Dic61—22no—
163C4⋊Dic61C2×D412yes—
164C4⋊Dic61C2×D414yes—
165#11758196—28no—
166C2×#92418—24no—
167C2×#92418—22no—
168C2×#92418—22no—
169C2×#92418—42no—
170C23×C61—22no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61#12011yescharacteristic
175C22×D61—22no—
176C22×D61—24no—
177C22×D61—42no—
178C22×D61—42no—
179Q8×C61—42no—
180Q8×C61—42no—
181Q8×C61—82no—
182D4×C61—22no—
183D4×C61—22no—
184D4×C61—42no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—44no—
191C2×C4×C61—42no—
192C2×C4×C61—82no—
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61#12011yescharacteristic
196C2×C4×C61C2×D812yes—
197C2×C4×C61#13512yes—
198C2×C4×C61AGL(1,ℤ/8)12yes—
199C2×C4×C61#13712yes—
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C22⋊D61—416no—
204C2×Dic61—22no—
205C2×Dic61—24no—
206C2×Dic61—44no—
207C2×Dic61—42no—
208D244—22no—
209D244—24no—
210D244C2×D814yes—
211C4×D61—416no—
212C4×D61—42no—
213C4×D61—42no—
214C4×D61—44no—
215Dic122—42no—
216Dic122—42no—
217Dic122—44no—
218C8×C61—42no—
219#92418—24no—
220#92418—42no—
221C2×#1647—611nomaximal, Sylow
222C22×C61—42no—
223C22×C61—42no—
224C22×C61—42no—
225C22×C61—84no—
226C22×C61#44712yes—
227C22×C61#45212yes—
228C22×C61#45612yes—
229C22×C61C2×#12011yescharacteristic
230C2×D61—24no—
231C2×D61—48no—
232C2×D61—42no—
233C2×D61—42no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—42no—
237C4×C61—82no—
238C4×C61#44712yes—
239C4×C61#45212yes—
240C4×C61C22×D811yescharacteristic
241C4×C61C2×#13511yescharacteristic
242C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C61C2×#13711yescharacteristic
244Dic61—44no—
245Dic61—42no—
246C2×#547—611no—
247C2×#500—611no—
248C2×#474D6111yescharacteristic, complemented
249C2×#461—611no—
250#1647—618no—
251C2×#332—611no—
252C2×D4⋊C8—611no—
253C2×D4⋊C8—611no—
254C2×C61—82no—
255C2×C61#164714yescomplemented
256C2×C61C2×#44711yescharacteristic
257C2×C61C2×#45211yescharacteristic
258C2×C61C2×#45611yescharacteristic
259D61—44no—
260C22×#41—1221no—
261C22×SD16—1221no—
262#547—614no—
263#547—1222no—
264#547—1222no—
265#547—1222no—
266C2×C4⋊Q8—611no—
267C2×C4⋊Q8C2×D6111yescharacteristic
268C2×#123—1222no—
269C2×C22⋊Q8—1221no—
270C2×#121—1221no—
271C2×C4×D4—611no—
272C2×C4×D4C2×D6111yescharacteristic
273C22×C4⋊C4—1221no—
274#500—614no—
275#500—1222no—
276#474—22no—
277#474C2×D6114yescomplemented
278#461—614no—
279#461—1222no—
280C2×#107—21no—
281C2×#107—1222no—
282C2×C4⋊C8—611no—
283C2×C4⋊C8C2×D6111yescharacteristic
284C2×#103—1221no—
285C2×#102—21no—
286C2×C4×C8—611no—
287#332—614no—
288D4⋊C8—614no—
289D4⋊C8—614no—
290C61C2×#164711yescharacteristic, complemented, Sylow
291C2×#41—1224no—
292C2×#41—1224no—
293C2×#41—2444no—
294C2×#41—2444no—
295C22×Q8—21no—
296C22×Q8—1221no—
297C22×D4—611no—
298C22×D4—1222no—
299C22×D4C22⋊D6111yescharacteristic
300C23×C4—21no—
301C23×C4—1222no—
302C23×C4—1221no—
303C2×SD16—1224no—
304C2×SD16—2444no—
305C22×C8—21no—
306C22×C8—1221no—
307C22×C8—1221no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—612no—
312C4⋊Q8—612no—
313C4⋊Q8—1221no—
314C4⋊Q8—1221no—
315C4⋊Q8C22×D6112yes—
316#123—1228no—
317#123—1228no—
318C22⋊Q8—1224no—
319C22⋊Q8—1224no—
320#121—1224no—
321#121—1224no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—612no—
325C4×D4—612no—
326C4×D4—1221no—
327C4×D4—1221no—
328C4×D4C22⋊D6112yes—
329C4×D4C22×D6112yes—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—612no—
334C2×C4⋊C4—1224no—
335C2×C4⋊C4—1222no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1224no—
338C2×C4⋊C4C22⋊D6111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—1222no—
341C2×C22⋊C4—1221no—
342C2×C42C22×D6111yescharacteristic
343#107—24no—
344#107—1228no—
345C4⋊C8—21no—
346C4⋊C8—612no—
347C4⋊C8—1221no—
348C4⋊C8C22×D6112yes—
349#103—1224no—
350#102—24no—
351C4×C8—612no—
352C4×C8—1221no—
353C24—21no—
354C24—1221no—
355#41—2448no—
356#41—2448no—
357#41—24416no—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—1222no—
363C2×Q8—1222no—
364C2×Q8—2442no—
365C2×Q8—2442no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—612no—
370C2×D4—614no—
371C2×D4—1228no—
372C2×D4—1221no—
373C2×D4—1222no—
374C2×D4—2448no—
375C2×D4C2×C22⋊D6112yes—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—41no—
382C22×C4—1228no—
383C22×C4—1221no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—2448no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4D4×D6111yescharacteristic
391C22×C4D4×D6111yescharacteristic
392C22×C4C2×C22⋊D6111yescharacteristic
393SD16—2448no—
394C2×C8—22no—
395C2×C8—42no—
396C2×C8—1224no—
397C2×C8—1222no—
398C2×C8—1222no—
399C2×C8—2442no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—612no—
406C4⋊C4—614no—
407C4⋊C4—1228no—
408C4⋊C4—1222no—
409C4⋊C4—1221no—
410C4⋊C4—1222no—
411C4⋊C4—1222no—
412C4⋊C4C2×C22⋊D6112yes—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—1228no—
416C22⋊C4—1222no—
417C22⋊C4—1222no—
418C42D4×D6111yescharacteristic
419C42D4×D6111yescharacteristic
420C42C2×C22⋊D6111yescharacteristic
421C42C23×D6111yescharacteristic
422C23—22no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—1222no—
427C23—1224no—
428C23—2442no—
429C23—2442no—
430C23#1451974511yescharacteristic
431Q8—42no—
432Q8—42no—
433Q8—82no—
434Q8—2442no—
435Q8—2442no—
436Q8—2444no—
437D4—22no—
438D4—22no—
439D4—42no—
440D4—614no—
441D4—1222no—
442D4—1224no—
443D4—24416no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—82no—
452C2×C4—1222no—
453C2×C4—1224no—
454C2×C4—24416no—
455C2×C4—2444no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2444no—
460C2×C4#1451974511yescharacteristic
461C2×C4#1451974511yescharacteristic
462C2×C4#1451974511yescharacteristic
463C2×C4D8×D6112yes—
464C2×C4#1451979712yes—
465C2×C4#1451980112yes—
466C2×C4#1451980812yes—
467C2×C4C2×D4×D6111yescharacteristic
468C2×C4C2×D4×D6111yescharacteristic
469C2×C4C22×C22⋊D6111yescharacteristic
470C8—42no—
471C8—1224no—
472C8—2442no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—84no—
477C22—1224no—
478C22—2442no—
479C22—2442no—
480C22—2448no—
481C22#1683989412yes—
482C22#1683992212yes—
483C22#1683994312yes—
484C22C2×#1451974511yescharacteristic
485C4—21no—
486C4—21no—
487C4—42no—
488C4—82no—
489C4—2444no—
490C4—2442no—
491C4#1683989412yes—
492C4#1683992212yes—
493C4C2×D8×D6111yescharacteristic
494C4C2×#1451979711yescharacteristic
495C4C2×#1451980111yescharacteristic
496C4C2×#1451980811yescharacteristic
497C2—82no—
498C2—2444no—
499C2#2144505314yesdirect product factor
500C2C2×#1683989411yescharacteristic
501C2C2×#1683992211yescharacteristic
502C2C2×#1683994311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#474C2
socleC23×C61#120
prime radicalC2×#16840417C2
hypercenterC2×#474D61
hypocenterC61C2×#1647
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. C2×#16840165C2semidirect
3. C2×#16839964C2semidirect
4. #21445053C2direct (N × H)
5. C2×#16839507C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#474C2semidirect
22. #16840165C22semidirect
24. #16839964C22semidirect
29. #16839507C22semidirect
30. D4⋊#92418C22semidirect
31. #16839489C22semidirect
35. C61×#474C22semidirect
248. C2×#474D61semidirect
255. C2×C61#1647semidirect
277. #474C2×D61semidirect
290. C61C2×#1647semidirect
499. C2#21445053direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404172
C2×#168401652
C2×#168399642
#214450532
C2×#168395072
C2×D4⋊#924182
C2×#168394892
C2×C61×#4742
C2×#164761