Finite Group Databasebeta

← C2×#21444847 #29652158

Subgroups — C2×#21444847 #29652158

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840357C211yesmaximal, characteristic
2C2×#16840097C211yesmaximal, characteristic, complemented
3C2×#16839700C211yesmaximal, characteristic, complemented
4#21444847C218yesmaximal, direct product factor
5C2×#16839500C211yesmaximal, characteristic, complemented
6C2×#16839496C211yesmaximal, characteristic
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#481C211yesmaximal, characteristic
9#16840357—22no—
10#16840357—22no—
11#16840357—22no—
12#16840357C2214yes—
13C2×#14519770—21no—
14C2×#14519767—21no—
15C2×#14519758—21no—
16C2×#14519758—21no—
17C2×#14519756C2211yescharacteristic
18C2×#14519754—21no—
19C2×D4×Dic61—21no—
20C22×#11758196C2211yescharacteristic
21#16840097—22no—
22#16840097C2214yescomplemented
23C2×#14519710—21no—
24C2×#14519700—21no—
25C2×C22⋊#92418C2211yescharacteristic
26#16839700—22no—
27#16839700C2214yescomplemented
28C2×#14519684—21no—
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839500C2214yescomplemented
32#16839496C2214yes—
33#16839487C2214yescomplemented
34C2×#121×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#481—22no—
37C61×#481C2214yes—
38C2×#106×C61—21no—
39C2×#102×C61—21no—
40C2×C22⋊C8×C61C2211yescharacteristic
41C22×Dic122D411yescharacteristic
42C23×Dic61—21no—
43C23×Dic61—21no—
44C23×Dic61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×#92418—21no—
47#14519770—24no—
48#14519770—24no—
49#14519767—24no—
50#14519767—24no—
51#14519758—24no—
52#14519758—24no—
53#14519758—24no—
54#14519758—24no—
55#14519756—21no—
56#14519756—21no—
57#14519756D412yes—
58#14519756C2312yes—
59#14519754—24no—
60#14519754—24no—
61D4×Dic61—24no—
62D4×Dic61—24no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61D411yescharacteristic
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196D412yes—
73C2×#11758196C2312yes—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C4×Dic61—21no—
79#14519710—24no—
80#14519700—24no—
81C22⋊#92418—21no—
82C22⋊#92418C2312yes—
83#14519684—21no—
84#14519684—24no—
85#14519684—24no—
86#14519684C2312yes—
87C22×D4×C61—21no—
88C22×D4×C61D411yescharacteristic
89C23×C4×C61—21no—
90C23×C4×C61C2311yescharacteristic
91C22×C8×C61—21no—
92#121×C61—21no—
93#121×C61—21no—
94#121×C61D412yes—
95#121×C61C2312yes—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61D411yescharacteristic
102C2×C4⋊C4×C61C2312yes—
103C2×C22⋊C4×C61—21no—
104#106×C61—24no—
105#102×C61—24no—
106C22⋊C8×C61—21no—
107C22⋊C8×C61C2312yes—
108C24×C61—21no—
109C24×C61C2×D411yescharacteristic
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61—21no—
113C2×D4×C61—42no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61C2×D412yes—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—42no—
120C22×C4×C61—44no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2411yescharacteristic
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—24no—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—42no—
142C22×Dic61—42no—
143C22×Dic61—82no—
144C22×Dic61C2×D412yes—
145C22×Dic61C2×D412yes—
146C2×Dic122—21no—
147C2×Dic122—42no—
148C2×Dic122C2×D412yes—
149C2×C8×C61—22no—
150C2×C8×C61—42no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61C2×D412yes—
157C22⋊C4×C61—22no—
158C22⋊C4×C61—22no—
159C22⋊Dic61—24no—
160C22⋊Dic61—24no—
161C22⋊Dic61—24no—
162C22⋊Dic61—22no—
163C22⋊Dic61—22no—
164C4⋊Dic61—24no—
165C4⋊Dic61—21no—
166C4⋊Dic61C2×D412yes—
167#11758196—24no—
168#11758196—24no—
169#11758196—22no—
170#11758196—22no—
171#11758196—22no—
172#11758196—22no—
173#11758196—22no—
174#11758196—22no—
175C4×Dic61—24no—
176C2×#92418—22no—
177C2×#92418—42no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61#12011yescharacteristic
185C23×C61#12011yescharacteristic
186C23×C61#13512yes—
187C23×C61#13712yes—
188C23×C61C22×D411yescharacteristic
189D4×C61—42no—
190D4×C61—42no—
191D4×C61—42no—
192D4×C61—44no—
193D4×C61—81no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—42no—
202C2×C4×C61—44no—
203C2×C4×C61—42no—
204C2×C4×C61—82no—
205C2×C4×C61—82no—
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61C22×D411yescharacteristic
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—81no—
226C2×Dic61—84no—
227C2×Dic61—84no—
228Dic122—42no—
229Dic122—81no—
230C8×C61—42no—
231#92418—42no—
232C2×#1615—611nomaximal, Sylow
233C22×C61—24no—
234C22×C61—24no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—84no—
243C22×C61#45212yes—
244C22×C61#45212yes—
245C22×C61#45412yes—
246C22×C61#45812yes—
247C22×C61C2×#12011yescharacteristic
248C22×C61C2×#13511yescharacteristic
249C22×C61C2×#13711yescharacteristic
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—42no—
255C4×C61—82no—
256Dic61—42no—
257Dic61—42no—
258Dic61—42no—
259Dic61—42no—
260Dic61—82no—
261C2×#539—611no—
262C2×#484—611no—
263C2×#481D6111yescharacteristic
264C2×#400—611no—
265#1615—618no—
266C2×#328—611no—
267C2×#327—611no—
268C2×#324—611no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—22no—
272C2×C61—82no—
273C2×C61#161514yescomplemented
274C2×C61C2×#45211yescharacteristic
275C2×C61C2×#45411yescharacteristic
276C2×C61C2×#45811yescharacteristic
277#539—614no—
278#539—1222no—
279#539—1222no—
280#539—1222no—
281C2×#126—1221no—
282C2×#125—1221no—
283C2×#123—1221no—
284C2×#123—1221no—
285C2×C22⋊Q8—611no—
286C2×C22⋊Q8—1221no—
287C2×#121C2×D6111yescharacteristic
288C2×C4×D4—1221no—
289C22×C4⋊C4—611no—
290C22×C4⋊C4C2×D6111yescharacteristic
291#484—614no—
292#484—1222no—
293#481—22no—
294#481C2×D6114yes—
295C2×#107—1221no—
296C2×#106—21no—
297C2×#103—1221no—
298C2×#102—21no—
299C2×C22⋊C8—611no—
300C2×C22⋊C8C2×D6111yescharacteristic
301#400—614no—
302#400—1222no—
303C2×#95—611no—
304C2×#95—1221no—
305C2×#95—1221no—
306#328—614no—
307#327—614no—
308#324—614no—
309C61C2×#161511yescharacteristic, complemented, Sylow
310C22×Q8—611no—
311C22×D4—21no—
312C22×D4C22⋊D6111yescharacteristic
313C23×C4—21no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—1221no—
317C23×C4—1221no—
318C23×C4C22×D6111yescharacteristic
319C22×C8—21no—
320C22×C8—1221no—
321#126—1224no—
322#126—1224no—
323#125—1224no—
324#125—1224no—
325#123—1224no—
326#123—1224no—
327#123—1224no—
328#123—1224no—
329C22⋊Q8—612no—
330C22⋊Q8—612no—
331C22⋊Q8—1224no—
332C22⋊Q8—1224no—
333C22⋊Q8—1221no—
334C22⋊Q8—1221no—
335#121—21no—
336#121—21no—
337#121C22⋊D6112yes—
338#121C22×D6112yes—
339C4×D4—1224no—
340C4×D4—1224no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—611no—
347C2×C4⋊C4—612no—
348C2×C4⋊C4—612no—
349C2×C4⋊C4—1221no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4C22⋊D6111yescharacteristic
358C2×C4⋊C4C22×D6112yes—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—1221no—
361C2×C22⋊C4—1221no—
362C2×C22⋊C4—1221no—
363C2×C22⋊C4—1221no—
364C2×C42—1221no—
365#107—1224no—
366#106—24no—
367#103—1224no—
368#102—24no—
369C22⋊C8—21no—
370C22⋊C8—612no—
371C22⋊C8—1221no—
372C22⋊C8C22×D6112yes—
373#95—612no—
374#95—1224no—
375#95—1224no—
376#95—1221no—
377C24—21no—
378C24D4×D6111yescharacteristic
379C2×Q8—612no—
380C2×Q8—1221no—
381C2×Q8—2442no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4C2×C22⋊D6112yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—44no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—612no—
396C22×C4—612no—
397C22×C4—1224no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1222no—
405C22×C4—1222no—
406C22×C4—1222no—
407C22×C4—4882no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4D4×D6111yescharacteristic
413C22×C4D4×D6111yescharacteristic
414C22×C4D4×D6111yescharacteristic
415C22×C4C2×C22⋊D6111yescharacteristic
416C22×C4C2×C22⋊D6111yescharacteristic
417C22×C4C23×D6111yescharacteristic
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—1222no—
421C2×C8—2442no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—612no—
428C4⋊C4—1224no—
429C4⋊C4—1224no—
430C4⋊C4—1224no—
431C4⋊C4—1222no—
432C4⋊C4—1222no—
433C4⋊C4—1222no—
434C4⋊C4—1222no—
435C4⋊C4—1222no—
436C4⋊C4—1221no—
437C4⋊C4—1222no—
438C4⋊C4C2×C22⋊D6112yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—1224no—
442C22⋊C4—1224no—
443C22⋊C4—1224no—
444C22⋊C4—1222no—
445C22⋊C4—1222no—
446C42—1224no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23#1451974511yescharacteristic
454C23#1451974511yescharacteristic
455C23#1451979812yes—
456C23#1451980612yes—
457C23C2×D4×D6111yescharacteristic
458Q8—4881no—
459Q8—2442no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—44no—
464D4—81no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—4884no—
484C2×C4—4881no—
485C2×C4—4884no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4—2442no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4#1451974511yescharacteristic
496C2×C4#1451974511yescharacteristic
497C2×C4C2×D4×D6111yescharacteristic
498C2×C4C22×C22⋊D6111yescharacteristic
499C8—42no—
500C8—2442no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—24no—
506C22—24no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22#1683992112yes—
512C22#1683992112yes—
513C22#1683993312yes—
514C22#1683995112yes—
515C22C2×#1451974511yescharacteristic
516C22C2×#1451979811yescharacteristic
517C22C2×#1451980611yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—82no—
524C4—4882no—
525C4—2442no—
526C4—2442no—
527C4—2442no—
528C4—2442no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—82no—
533C2#2144484714yesdirect product factor
534C2C2×#1683992111yescharacteristic
535C2C2×#1683993311yescharacteristic
536C2C2×#1683995111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#481C2
socleC23×C61#120
prime radicalC2×#121×C61C22
hypercenterC2×#481D61
hypocenterC61C2×#1615
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#16840097C2semidirect
3. C2×#16839700C2semidirect
4. #21444847C2direct (N × H)
5. C2×#16839500C2semidirect
7. C2×#16839487C2semidirect
22. #16840097C22semidirect
27. #16839700C22semidirect
31. #16839500C22semidirect
33. #16839487C22semidirect
273. C2×C61#1615semidirect
309. C61C2×#1615semidirect
533. C2#21444847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403572
C2×#168400972
C2×#168397002
#214448472
C2×#168395002
C2×#168394962
C2×#168394872
C2×C61×#4812
C2×#161561