Finite Group Databasebeta

← C2×#21444877 #29655644

Subgroups — C2×#21444877 #29655644

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic, complemented
2C2×#16840138C211yesmaximal, characteristic
3C2×#16839959C211yesmaximal, characteristic, complemented
4#21444877C218yesmaximal, direct product factor
5C2×#16839505C211yesmaximal, characteristic, complemented
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839492C211yesmaximal, characteristic, complemented
8C2×C61×#460C211yesmaximal, characteristic, complemented
9C22×#11758200—21no—
10C22×#11758199—22no—
11#16840497—22no—
12#16840497—22no—
13#16840497—22no—
14#16840497C2214yescomplemented
15C2×#14519774C2211yescharacteristic
16C2×#14519766—21no—
17C2×#14519765—21no—
18C2×#14519762—22no—
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×D244—21no—
21C2×#14519739—21no—
22#16840138—22no—
23#16840138C2214yes—
24#16839959—22no—
25#16839959C2214yescomplemented
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519698—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839505C2214yescomplemented
30Q8⋊#92418C2214yescomplemented
31#16839492C2214yescomplemented
32C22×SD16×C61—21no—
33C2×#127×C61C2211yescharacteristic
34C2×C4×Q8×C61C2211yescharacteristic
35C61×#460—22no—
36C61×#460C2214yescomplemented
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#102×C61—21no—
39C22×Dic122D411yescharacteristic
40C22×D244—21no—
41C22×D244—21no—
42C22×D244D412yes—
43C22×C4×D61—22no—
44C2×#11758200—24no—
45C2×#11758200—44no—
46C2×#11758199—28no—
47C2×#11758199—48no—
48C22×#92418—21no—
49C22×#92418—21no—
50#14519774—21no—
51#14519774—21no—
52#14519774D412yes—
53#14519774C2312yes—
54#14519766—24no—
55#14519766—24no—
56#14519765—24no—
57#14519765—24no—
58#14519762—28no—
59#14519762—28no—
60C4×Dic122—21no—
61C4×Dic122—21no—
62C4×Dic122D412yes—
63C4×Dic122C2312yes—
64C4×D244—24no—
65C4×D244—24no—
66#14519739—24no—
67#14519739—24no—
68C2×C4⋊Dic61D411yescharacteristic
69C2×#11758196—21no—
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×#11758198—22no—
73C2×C4×Dic61—21no—
74C4⋊#92418—21no—
75C4⋊#92418C2312yes—
76#14519698—24no—
77C4×#92418—21no—
78C4×#92418C2312yes—
79C22×Q8×C61D411yescharacteristic
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C2×SD16×C61—24no—
84C2×SD16×C61—44no—
85C22×C8×C61—21no—
86#127×C61—21no—
87#127×C61—21no—
88#127×C61—21no—
89#127×C61C2312yes—
90C4×Q8×C61—21no—
91C4×Q8×C61—21no—
92C4×Q8×C61D412yes—
93C4×Q8×C61C2312yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61D411yescharacteristic
96C2×C42×C61—21no—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2312yes—
100#102×C61—24no—
101C24×C61—41no—
102C23×D61—22no—
103C2×Q8×C61—21no—
104C2×Q8×C61—22no—
105C2×Q8×C61—22no—
106C2×Q8×C61C2×D412yes—
107C2×D4×C61—22no—
108C2×D4×C61—22no—
109C2×D4×C61—22no—
110C2×D4×C61—44no—
111C2×D4×C61—41no—
112C2×D4×C61—41no—
113C2×D4×C61—41no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×Dic61—21no—
124C22×Dic61—21no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—42no—
131C2×D244—42no—
132C2×D244—42no—
133C2×D244—42no—
134C2×D244—44no—
135C2×D244C2×D414yes—
136C2×C4×D61—28no—
137C2×C4×D61—84no—
138C2×Dic122—22no—
139C2×Dic122—22no—
140C2×Dic122—21no—
141C2×Dic122C2×D412yes—
142SD16×C61—48no—
143C2×C8×C61—22no—
144C2×C8×C61—42no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61C2×D412yes—
149C42×C61—22no—
150C42×C61—22no—
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153C42×C61C2×D411yescharacteristic
154C42×C61C2411yescharacteristic
155#11758200—48no—
156#11758199—416no—
157#11758198—28no—
158#11758198—28no—
159#11758198—28no—
160C4⋊Dic61—21no—
161C4⋊Dic61C2×D412yes—
162#11758196—22no—
163#11758196—22no—
164C4×Dic61—22no—
165C4×Dic61—22no—
166C2×#92418—24no—
167C2×#92418—22no—
168C2×#92418—22no—
169C2×#92418—42no—
170C23×C61—42no—
171C23×C61—82no—
172C23×C61—82no—
173C23×C61—82no—
174C23×C61#12011yescharacteristic
175C22×D61—24no—
176C22×D61—44no—
177C22×D61—44no—
178C22×D61—44no—
179Q8×C61—22no—
180Q8×C61—22no—
181Q8×C61—42no—
182D4×C61—44no—
183D4×C61—42no—
184D4×C61—42no—
185D4×C61—42no—
186D4×C61—42no—
187D4×C61—82no—
188D4×C61—82no—
189D4×C61—82no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61#12011yescharacteristic
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#12011yescharacteristic
198C2×C4×C61#13512yes—
199C2×C4×C61#13512yes—
200C2×C4×C61AGL(1,ℤ/8)12yes—
201C2×C4×C61AGL(1,ℤ/8)12yes—
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209D244—44no—
210D244—42no—
211D244—42no—
212D244—42no—
213D244—42no—
214D244—44no—
215D244—44no—
216D244—82no—
217C4×D61—88no—
218Dic122—22no—
219Dic122—22no—
220Dic122—42no—
221C8×C61—42no—
222#92418—24no—
223#92418—42no—
224C2×#1620—611nomaximal, Sylow
225C22×C61—82no—
226C22×C61—82no—
227C22×C61—82no—
228C22×C61—164no—
229C22×C61#44912yes—
230C22×C61#44912yes—
231C22×C61#45312yes—
232C22×C61C2×#12011yescharacteristic
233C2×D61—44no—
234C2×D61—44no—
235C2×D61—44no—
236C2×D61—88no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—42no—
240C4×C61—42no—
241C4×C61#44912yes—
242C4×C61#44912yes—
243C4×C61C2×#13511yescharacteristic
244C4×C61C2×#13511yescharacteristic
245C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
247Dic61—42no—
248Dic61—42no—
249C2×#559—611no—
250C2×#493—611no—
251C2×#460—611no—
252C2×#460D6111yescharacteristic, complemented
253#1620—618no—
254C2×#331—611no—
255C2×Q8⋊C8—611no—
256C2×Q8⋊C8—611no—
257C2×C61—162no—
258C2×C61#162014yescomplemented
259C2×C61C2×#44911yescharacteristic
260C2×C61C2×#44911yescharacteristic
261C2×C61C2×#45311yescharacteristic
262D61—84no—
263C22×SD16—21no—
264C22×SD16—1221no—
265C22×D8—1222no—
266#559—614no—
267#559—1222no—
268#559—1222no—
269#559—1222no—
270C2×#127—611no—
271C2×#127C2×D6111yescharacteristic
272C2×#124—1221no—
273C2×#124—1221no—
274C2×#123—1222no—
275C2×C4×Q8—611no—
276C2×C4×Q8C2×D6111yescharacteristic
277C2×C4×D4—1221no—
278C2×C4×D4—1221no—
279#493—614no—
280#493—1222no—
281#460—22no—
282#460—614no—
283#460—1222no—
284#460C2×D6114yescomplemented
285C2×C4⋊C8—611no—
286C2×C4⋊C8C2×D6111yescharacteristic
287C2×#102—21no—
288C2×#102—1221no—
289C2×C4×C8—611no—
290#331—614no—
291Q8⋊C8—614no—
292Q8⋊C8—614no—
293C61C2×#162011yescharacteristic, complemented, Sylow
294C22×Q8—611no—
295C22×Q8C22⋊D6111yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—612no—
300C22×D4—1221no—
301C22×D4—1221no—
302C23×C4—1222no—
303C2×SD16—24no—
304C2×SD16—44no—
305C2×SD16—1224no—
306C2×SD16—2444no—
307C2×D8—1228no—
308C2×D8—2448no—
309C22×C8—21no—
310C22×C8—1221no—
311C22×C8—1221no—
312#127—21no—
313#127—21no—
314#127—21no—
315#127—612no—
316#127—612no—
317#127—1221no—
318#127—1221no—
319#127C22×D6112yes—
320#124—1224no—
321#124—1224no—
322#124—1224no—
323#124—1224no—
324#123—1228no—
325#123—1228no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8—612no—
329C4×Q8—612no—
330C4×Q8—1221no—
331C4×Q8—1221no—
332C4×Q8C22⋊D6112yes—
333C4×Q8C22×D6112yes—
334C4×D4—1224no—
335C4×D4—1224no—
336C4×D4—1224no—
337C4×D4—1224no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—611no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4C22⋊D6111yescharacteristic
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1222no—
344C2×C22⋊C4—1222no—
345C2×C42—21no—
346C2×C42—1221no—
347C2×C42C22×D6111yescharacteristic
348C4⋊C8—21no—
349C4⋊C8—612no—
350C4⋊C8—1221no—
351C4⋊C8C22×D6112yes—
352#102—24no—
353#102—1224no—
354C4×C8—612no—
355C4×C8—1221no—
356C24—41no—
357C24—1222no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—612no—
362C2×Q8—1221no—
363C2×Q8—1222no—
364C2×Q8—1222no—
365C2×Q8C2×C22⋊D6112yes—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—44no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—614no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—1222no—
381C2×D4—1222no—
382C2×D4—1222no—
383C2×D4—2444no—
384C2×D4—2442no—
385C2×D4—2442no—
386C2×D4—2442no—
387C2×D4—2442no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—1228no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—4884no—
394C22×C4D4×D6111yescharacteristic
395C22×C4D4×D6111yescharacteristic
396C22×C4C2×C22⋊D6111yescharacteristic
397SD16—48no—
398SD16—2448no—
399D8—24416no—
400C2×C8—22no—
401C2×C8—42no—
402C2×C8—1224no—
403C2×C8—1222no—
404C2×C8—1222no—
405C2×C8—2442no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—612no—
410C4⋊C4—1222no—
411C4⋊C4—1221no—
412C4⋊C4—1222no—
413C4⋊C4C2×C22⋊D6112yes—
414C22⋊C4—1228no—
415C22⋊C4—1228no—
416C22⋊C4—1228no—
417C42—22no—
418C42—22no—
419C42—1222no—
420C42—1222no—
421C42D4×D6111yescharacteristic
422C42D4×D6111yescharacteristic
423C42C2×C22⋊D6111yescharacteristic
424C42C23×D6111yescharacteristic
425C23—42no—
426C23—82no—
427C23—82no—
428C23—82no—
429C23—1224no—
430C23—2444no—
431C23—2444no—
432C23—2444no—
433C23#1451974511yescharacteristic
434Q8—22no—
435Q8—22no—
436Q8—42no—
437Q8—1222no—
438Q8—1222no—
439Q8—2442no—
440D4—44no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—82no—
446D4—82no—
447D4—82no—
448D4—4882no—
449D4—2444no—
450D4—2442no—
451D4—2442no—
452D4—2442no—
453D4—2442no—
454D4—2444no—
455D4—2444no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—4888no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4#1451974511yescharacteristic
467C2×C4#1451974511yescharacteristic
468C2×C4#1451974511yescharacteristic
469C2×C4#1451979712yes—
470C2×C4#1451979812yes—
471C2×C4#1451980312yes—
472C2×C4#1451980412yes—
473C2×C4C2×D4×D6111yescharacteristic
474C2×C4C2×D4×D6111yescharacteristic
475C2×C4C22×C22⋊D6111yescharacteristic
476C8—42no—
477C8—1224no—
478C8—2442no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—164no—
483C22—4888no—
484C22—2444no—
485C22—2444no—
486C22—2444no—
487C22#1683990512yes—
488C22#1683990612yes—
489C22#1683992812yes—
490C22C2×#1451974511yescharacteristic
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—2442no—
496C4—2442no—
497C4#1683990512yes—
498C4#1683990612yes—
499C4C2×#1451979711yescharacteristic
500C4C2×#1451979811yescharacteristic
501C4C2×#1451980311yescharacteristic
502C4C2×#1451980411yescharacteristic
503C2—162no—
504C2—4884no—
505C2#2144487714yesdirect product factor
506C2C2×#1683990511yescharacteristic
507C2C2×#1683990611yescharacteristic
508C2C2×#1683992811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#460C2
socleC23×C61#120
prime radicalC2×#16840138C2
hypercenterC2×#460D61
hypocenterC61C2×#1620
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#16840497C2semidirect
3. C2×#16839959C2semidirect
4. #21444877C2direct (N × H)
5. C2×#16839505C2semidirect
6. C2×Q8⋊#92418C2semidirect
7. C2×#16839492C2semidirect
8. C2×C61×#460C2semidirect
14. #16840497C22semidirect
25. #16839959C22semidirect
29. #16839505C22semidirect
30. Q8⋊#92418C22semidirect
31. #16839492C22semidirect
36. C61×#460C22semidirect
252. C2×#460D61semidirect
258. C2×C61#1620semidirect
284. #460C2×D61semidirect
293. C61C2×#1620semidirect
505. C2#21444877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
C2×#168401382
C2×#168399592
#214448772
C2×#168395052
C2×Q8⋊#924182
C2×#168394922
C2×C61×#4602
C2×#162061