Finite Group Databasebeta

← C2×#21444817 #29652154

Subgroups — C2×#21444817 #29652154

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840357C211yesmaximal, characteristic
2C2×#16840093C211yesmaximal, characteristic, complemented
3C2×#16840073C211yesmaximal, characteristic
4C2×#16839694C211yesmaximal, characteristic, complemented
5#21444817C218yesmaximal, direct product factor
6C2×#16839498C211yesmaximal, characteristic, complemented
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#327C211yesmaximal, 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×C4⋊Dic61—21no—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23#16840093—22no—
24#16840093C2214yescomplemented
25#16840073—22no—
26#16840073C2214yes—
27C2×#14519710—21no—
28C2×#14519709—21no—
29C2×#14519702—21no—
30C2×#14519698—21no—
31C2×C22⋊#92418C2211yescharacteristic
32#16839694—22no—
33#16839694C2214yescomplemented
34C2×#14519684—21no—
35#16839498C2214yescomplemented
36#16839487C2214yescomplemented
37C2×#121×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C61×#327C2214yes—
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⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—24no—
70C2×C4⋊Dic61—44no—
71C2×C4⋊Dic61D411yescharacteristic
72C2×C4⋊Dic61C2312yes—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196D412yes—
81C2×#11758196C2312yes—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C4×Dic61—21no—
87#14519710—24no—
88#14519709—24no—
89#14519702—24no—
90#14519698—24no—
91C22⋊#92418—21no—
92C22⋊#92418C2312yes—
93#14519684—24no—
94C22×D4×C61—21no—
95C22×D4×C61D411yescharacteristic
96C23×C4×C61—21no—
97C23×C4×C61C2311yescharacteristic
98C22×C8×C61—21no—
99#121×C61—21no—
100#121×C61—21no—
101#121×C61D412yes—
102#121×C61C2312yes—
103C2×C4⋊C4×C61D411yescharacteristic
104C2×C22⋊C4×C61—21no—
105C22⋊C8×C61—21no—
106C22⋊C8×C61C2312yes—
107#95×C61—21no—
108#95×C61C2312yes—
109C24×C61—21no—
110C24×C61C2×D411yescharacteristic
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—21no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C2×D4×C61C2×D412yes—
118C22×C4×C61—24no—
119C22×C4×C61—21no—
120C22×C4×C61—22no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2411yescharacteristic
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—24no—
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61—42no—
141C22×Dic61—41no—
142C22×Dic61—41no—
143C22×Dic61—42no—
144C22×Dic61—42no—
145C22×Dic61—82no—
146C22×Dic61C2×D412yes—
147C22×Dic61C2×D412yes—
148C2×Dic122—21no—
149C2×Dic122—42no—
150C2×Dic122C2×D412yes—
151C2×C8×C61—22no—
152C2×C8×C61—42no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61C2×D412yes—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—22no—
157C22⋊Dic61—24no—
158C22⋊Dic61—24no—
159C22⋊Dic61—24no—
160C22⋊Dic61—22no—
161C22⋊Dic61—22no—
162C4⋊Dic61—24no—
163C4⋊Dic61—21no—
164C4⋊Dic61—22no—
165C4⋊Dic61—22no—
166C4⋊Dic61—48no—
167C4⋊Dic61—41no—
168C4⋊Dic61—41no—
169C4⋊Dic61C2×D412yes—
170#11758196—24no—
171#11758196—24no—
172#11758196—22no—
173#11758196—22no—
174#11758196—22no—
175#11758196—22no—
176#11758196—22no—
177#11758196—22no—
178C4×Dic61—24no—
179C2×#92418—22no—
180C2×#92418—42no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—22no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61#12011yescharacteristic
188C23×C61#12011yescharacteristic
189C23×C61#13512yes—
190C23×C61AGL(1,ℤ/8)12yes—
191C23×C61C22×D411yescharacteristic
192D4×C61—42no—
193D4×C61—42no—
194D4×C61—42no—
195D4×C61—44no—
196D4×C61—81no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—24no—
200C2×C4×C61—22no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—48no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61#12011yescharacteristic
210C2×C4×C61#12011yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61—81no—
229C2×Dic61—84no—
230C2×Dic61—82no—
231C2×Dic61—82no—
232Dic122—42no—
233Dic122—81no—
234C8×C61—42no—
235#92418—42no—
236C2×#1609—611nomaximal, Sylow
237C22×C61—24no—
238C22×C61—24no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—42no—
244C22×C61—42no—
245C22×C61—42no—
246C22×C61—84no—
247C22×C61#44912yes—
248C22×C61#44912yes—
249C22×C61#45612yes—
250C22×C61#45812yes—
251C22×C61C2×#12011yescharacteristic
252C22×C61C2×#13511yescharacteristic
253C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—44no—
259C4×C61—42no—
260Dic61—42no—
261Dic61—42no—
262Dic61—42no—
263Dic61—42no—
264Dic61—82no—
265C2×#539—611no—
266C2×#483—611no—
267C2×#480—611no—
268C2×#398—611no—
269#1609—618no—
270C2×#328—611no—
271C2×#327D6111yescharacteristic
272C2×#324—611no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—22no—
276C2×C61—82no—
277C2×C61#160914yescomplemented
278C2×C61C2×#44911yescharacteristic
279C2×C61C2×#45611yescharacteristic
280C2×C61C2×#45811yescharacteristic
281#539—614no—
282#539—1222no—
283#539—1222no—
284#539—1222no—
285C2×#126—1221no—
286C2×#125—1221no—
287C2×#123—1221no—
288C2×#123—1221no—
289C2×C22⋊Q8—611no—
290C2×C22⋊Q8—1221no—
291C2×#121C2×D6111yescharacteristic
292C2×C4×D4—1221no—
293C22×C4⋊C4—611no—
294C22×C4⋊C4—611no—
295C22×C4⋊C4—1221no—
296#483—614no—
297#483—1222no—
298#480—614no—
299#480—1222no—
300C2×#107—1221no—
301C2×#106—1221no—
302C2×#103—1221no—
303C2×#102—1221no—
304C2×C22⋊C8—611no—
305C2×C22⋊C8C2×D6111yescharacteristic
306#398—614no—
307#398—1222no—
308C2×#95—1221no—
309C2×#95C2×D6111yescharacteristic
310#328—614no—
311#327C2×D6114yes—
312#324—614no—
313C61C2×#160911yescharacteristic, complemented, Sylow
314C22×Q8—611no—
315C22×D4—21no—
316C22×D4D24411yescharacteristic
317C23×C4—21no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—1221no—
321C23×C4—1221no—
322C23×C4C22×D6111yescharacteristic
323C22×C8—21no—
324C22×C8—1221no—
325#126—1224no—
326#126—1224no—
327#125—1224no—
328#125—1224no—
329#123—1224no—
330#123—1224no—
331#123—1224no—
332#123—1224no—
333C22⋊Q8—612no—
334C22⋊Q8—612no—
335C22⋊Q8—1224no—
336C22⋊Q8—1224no—
337C22⋊Q8—1221no—
338C22⋊Q8—1221no—
339#121—21no—
340#121—21no—
341#121D24412yes—
342#121C22×D6112yes—
343C4×D4—1224no—
344C4×D4—1224no—
345C2×C4⋊C4—611no—
346C2×C4⋊C4—612no—
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⋊C4—1221no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1221no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4—1224no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4—2444no—
364C2×C4⋊C4D24411yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—1221no—
367C2×C22⋊C4—1221no—
368C2×C22⋊C4—1221no—
369C2×C22⋊C4—1221no—
370C2×C42—1221no—
371#107—1224no—
372#106—1224no—
373#103—1224no—
374#102—1224no—
375C22⋊C8—21no—
376C22⋊C8—612no—
377C22⋊C8—1221no—
378C22⋊C8C22×D6112yes—
379#95—21no—
380#95—1224no—
381#95C22×D6112yes—
382C24—21no—
383C24D4×D6111yescharacteristic
384C2×Q8—612no—
385C2×Q8—1221no—
386C2×Q8—2442no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4C2×D24412yes—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—612no—
401C22×C4—612no—
402C22×C4—1224no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—4882no—
413C22×C4—2441no—
414C22×C4—2441no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4C2×D24411yescharacteristic
419C22×C4C2×D24411yescharacteristic
420C22×C4D4×D6111yescharacteristic
421C22×C4D4×D6111yescharacteristic
422C22×C4D4×D6111yescharacteristic
423C22×C4C23×D6111yescharacteristic
424C2×C8—22no—
425C2×C8—42no—
426C2×C8—1222no—
427C2×C8—2442no—
428C4⋊C4—21no—
429C4⋊C4—612no—
430C4⋊C4—1224no—
431C4⋊C4—1224no—
432C4⋊C4—1224no—
433C4⋊C4—1222no—
434C4⋊C4—1222no—
435C4⋊C4—1222no—
436C4⋊C4—1222no—
437C4⋊C4—1222no—
438C4⋊C4—1221no—
439C4⋊C4—1222no—
440C4⋊C4—1222no—
441C4⋊C4—1222no—
442C4⋊C4—2448no—
443C4⋊C4—2441no—
444C4⋊C4—2441no—
445C4⋊C4C2×D24412yes—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—1224no—
449C22⋊C4—1224no—
450C22⋊C4—1224no—
451C22⋊C4—1222no—
452C22⋊C4—1222no—
453C42—1224no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23#1451974711yescharacteristic
461C23#1451974711yescharacteristic
462C23#1451979812yes—
463C23#1451980112yes—
464C23C2×D4×D6111yescharacteristic
465Q8—4881no—
466Q8—2442no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—44no—
471D4—81no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—48no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—1222no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—4882no—
491C2×C4—4882no—
492C2×C4—4881no—
493C2×C4—4884no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4#1451974711yescharacteristic
504C2×C4#1451974711yescharacteristic
505C2×C4C2×D4×D6111yescharacteristic
506C2×C4C22×D24411yescharacteristic
507C8—42no—
508C8—2442no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—24no—
514C22—24no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—84no—
519C22#1683990812yes—
520C22#1683990812yes—
521C22#1683994612yes—
522C22#1683995312yes—
523C22C2×#1451974711yescharacteristic
524C22C2×#1451979811yescharacteristic
525C22C2×#1451980111yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—44no—
531C4—42no—
532C4—4882no—
533C4—2442no—
534C4—2442no—
535C4—2442no—
536C4—2442no—
537C2—21no—
538C2—21no—
539C2—22no—
540C2—82no—
541C2#2144481714yesdirect product factor
542C2C2×#1683990811yescharacteristic
543C2C2×#1683994611yescharacteristic
544C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#327C2
socleC23×C61#120
prime radicalC2×#121×C61C22
hypercenterC2×#327D61
hypocenterC61C2×#1609
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16840093C2semidirect
4. C2×#16839694C2semidirect
5. #21444817C2direct (N × H)
6. C2×#16839498C2semidirect
7. C2×#16839487C2semidirect
24. #16840093C22semidirect
33. #16839694C22semidirect
35. #16839498C22semidirect
36. #16839487C22semidirect
277. C2×C61#1609semidirect
313. C61C2×#1609semidirect
541. C2#21444817direct (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×#168400932
C2×#168400732
C2×#168396942
#214448172
C2×#168394982
C2×#168394872
C2×C61×#3272
C2×#160961