Finite Group Databasebeta

← C2×#21444923 #29655727

Subgroups — C2×#21444923 #29655727

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840427C211yesmaximal, characteristic, complemented
2C2×#16840110C211yesmaximal, characteristic, complemented
3C2×#16839963C211yesmaximal, characteristic, complemented
4C2×#16839958C211yesmaximal, characteristic
5#21444923C218yesmaximal, direct product factor
6C2×#16839492C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#332C211yesmaximal, characteristic, complemented
9C22×Q8×D61—21no—
10C22×#11758190—21no—
11C22×D488—21no—
12#16840427—22no—
13#16840427—22no—
14#16840427—22no—
15#16840427C2214yescomplemented
16C2×#14519776—21no—
17C2×#14519774C2211yescharacteristic
18C2×#14519755—22no—
19C2×#14519753—21no—
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×#14519739—21no—
23#16840110—22no—
24#16840110C2214yescomplemented
25#16839963—22no—
26#16839963C2214yescomplemented
27#16839958—22no—
28#16839958C2214yes—
29C2×#14519699—21no—
30C2×#14519699—21no—
31C2×#14519697—22no—
32C2×C4×#92418C2211yescharacteristic
33#16839492C2214yescomplemented
34#16839489C2214yescomplemented
35C2×C4⋊Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#332C2214yescomplemented
39C22×Dic122—22no—
40C22×Dic122D411yescharacteristic
41C2×Q8×D61—24no—
42C2×Q8×D61—24no—
43C2×Q8×D61—44no—
44C2×Q8×D61—44no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244D411yescharacteristic
49C22×C4×D61—22no—
50C22×C4×D61—21no—
51C2×#11758190—24no—
52C2×#11758190—44no—
53C2×D488—24no—
54C2×D488—44no—
55C22×#92418—21no—
56#14519776—24no—
57#14519776—24no—
58#14519774—21no—
59#14519774—21no—
60#14519774—21no—
61#14519774C2312yes—
62#14519755—28no—
63#14519755—28no—
64#14519753—24no—
65#14519753—24no—
66C4×Dic122—21no—
67C4×Dic122—21no—
68C4×Dic122D412yes—
69C4×Dic122C2312yes—
70C4×D244—21no—
71C4×D244—21no—
72C4×D244D412yes—
73C4×D244C2312yes—
74#14519739—24no—
75#14519739—24no—
76C2×C4⋊Dic61D411yescharacteristic
77C2×C4⋊Dic61D411yescharacteristic
78C2×#11758196—22no—
79C2×#11758196—21no—
80C2×#11758198—22no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83#14519699—24no—
84#14519699—24no—
85#14519697—28no—
86C4×#92418—21no—
87C4×#92418C2312yes—
88C22×Q8×C61—21no—
89C22×C8×C61—21no—
90C22×C8×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61—21no—
93C4⋊Q8×C61D412yes—
94C4⋊Q8×C61C2312yes—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61D412yes—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61—21no—
100C4⋊C8×C61C2312yes—
101C4⋊C8×C61C2312yes—
102C23×D61—21no—
103C23×D61—41no—
104C2×Q8×C61—22no—
105C2×Q8×C61—22no—
106C2×Q8×C61—42no—
107C2×Q8×C61—42no—
108C22×C4×C61—22no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115Q8×D61—48no—
116Q8×D61—416no—
117Q8×D61—48no—
118C2×D244—21no—
119C2×D244—22no—
120C2×D244—22no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—44no—
124C2×D244—42no—
125C2×D244—42no—
126C2×D244—42no—
127C2×D244—42no—
128C2×D244—41no—
129C2×D244—41no—
130C2×D244—41no—
131C2×D244SD1614yescomplemented
132C2×D244C2×D412yes—
133C2×C4×D61—28no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—48no—
137C2×C4×D61—42no—
138C2×C4×D61—42no—
139C2×Dic122—21no—
140C2×Dic122—22no—
141C2×Dic122—28no—
142C2×Dic122—48no—
143C2×Dic122D814yescomplemented
144C2×Dic122C2×D412yes—
145C2×C8×C61—22no—
146C2×C8×C61—22no—
147C2×C8×C61—42no—
148C2×C8×C61—42no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61C2×D414yes—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2411yescharacteristic
157#11758198—28no—
158#11758198—22no—
159#11758198—22no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162C4⋊Dic61C2×D412yes—
163C4⋊Dic61C2×D412yes—
164#11758196—28no—
165#11758196—22no—
166#11758196—22no—
167C4×Dic61—22no—
168C4×Dic61—22no—
169C2×#92418—22no—
170C2×#92418—42no—
171D488—48no—
172#11758190—48no—
173C23×C61#12011yescharacteristic
174C22×D61—22no—
175C22×D61—24no—
176C22×D61—42no—
177C22×D61—42no—
178C22×D61—42no—
179C22×D61—82no—
180C22×D61—82no—
181C22×D61—82no—
182Q8×C61—42no—
183Q8×C61—42no—
184Q8×C61—44no—
185C2×C4×C61—22no—
186C2×C4×C61—24no—
187C2×C4×C61—44no—
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61#12011yescharacteristic
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61C2×D812yes—
192C2×C4×C61C2×SD1612yes—
193C2×C4×C61AGL(1,ℤ/8)12yes—
194C2×C4×C61#13712yes—
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C2×Dic61—22no—
199C2×Dic61—24no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204D244—22no—
205D244—24no—
206D244—44no—
207D244—42no—
208D244—42no—
209D244—42no—
210D244—42no—
211D244—82no—
212D244—82no—
213D244—82no—
214D244C2×SD1614yescomplemented
215C4×D61—416no—
216C4×D61—42no—
217C4×D61—42no—
218C4×D61—44no—
219Dic122—22no—
220Dic122—24no—
221Dic122—416no—
222Dic122C2×D814yescomplemented
223C8×C61—42no—
224C8×C61—42no—
225#92418—42no—
226C2×#1627—611nomaximal, Sylow
227C22×C61#44712yes—
228C22×C61#44812yes—
229C22×C61#45412yes—
230C22×C61C2×#12011yescharacteristic
231C2×D61—24no—
232C2×D61—48no—
233C2×D61—42no—
234C2×D61—42no—
235C2×D61—82no—
236C2×D61—82no—
237C2×D61—82no—
238C2×D61—164no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—44no—
242C4×C61#44712yes—
243C4×C61#44812yes—
244C4×C61C22×D811yescharacteristic
245C4×C61C22×SD1611yescharacteristic
246C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C61C2×#13711yescharacteristic
248Dic61—24no—
249Dic61—42no—
250Dic61—42no—
251C2×D4×Q8—611no—
252C2×#486—611no—
253C2×#460—611no—
254C2×#459—611no—
255#1627—618no—
256C2×#332D6111yescharacteristic, complemented
257C2×Q8⋊C8—611no—
258C2×D4⋊C8—611no—
259C2×C61#162714yescomplemented
260C2×C61C2×#44711yescharacteristic
261C2×C61C2×#44811yescharacteristic
262C2×C61C2×#45411yescharacteristic
263D61—44no—
264D61—162no—
265C23×Q8—1221no—
266C22×SD16—1221no—
267C22×D8—1221no—
268D4×Q8—614no—
269D4×Q8—1222no—
270D4×Q8—1222no—
271D4×Q8—1222no—
272C2×C4⋊Q8—1221no—
273C2×C4⋊Q8C2×D6111yescharacteristic
274C2×#127—611no—
275C2×C22⋊Q8—1221no—
276C2×C22⋊Q8—1222no—
277C2×C4×Q8—611no—
278C2×C4×D4—611no—
279C2×C4×D4—1221no—
280#486—614no—
281#486—1222no—
282#460—614no—
283#460—1222no—
284#459—614no—
285#459—1222no—
286C2×C4⋊C8C2×D6111yescharacteristic
287C2×C4⋊C8C2×D6111yescharacteristic
288C2×#102—1221no—
289C2×#102—1221no—
290C2×#102—1222no—
291C2×C4×C8—611no—
292#332C2×D6114yescomplemented
293Q8⋊C8—614no—
294D4⋊C8—614no—
295C61C2×#162711yescharacteristic, complemented, Sylow
296C22×Q8—21no—
297C22×Q8—611no—
298C22×Q8—1222no—
299C22×Q8—1224no—
300C22×Q8—1224no—
301C22×Q8—2444no—
302C22×Q8—2444no—
303C22×D4—611no—
304C22×D4—1221no—
305C22×D4—1221no—
306C22×D4—1221no—
307C23×C4—1222no—
308C23×C4—1221no—
309C2×SD16—1224no—
310C2×SD16—2444no—
311C2×D8—1224no—
312C2×D8—2444no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—1221no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—1224no—
319C4⋊Q8—1224no—
320C4⋊Q8D24412yes—
321C4⋊Q8C22×D6112yes—
322#127—612no—
323#127—1221no—
324#127—1221no—
325#127—1221no—
326C22⋊Q8—1228no—
327C22⋊Q8—1224no—
328C22⋊Q8—1224no—
329C22⋊Q8—1228no—
330C4×Q8—612no—
331C4×Q8—612no—
332C4×Q8—1221no—
333C4×Q8—1221no—
334C4×D4—612no—
335C4×D4—612no—
336C4×D4—1224no—
337C4×D4—1224no—
338C4×D4—1221no—
339C4×D4—1221no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—611no—
342C2×C4⋊C4—611no—
343C2×C4⋊C4—1222no—
344C2×C4⋊C4—1221no—
345C2×C4⋊C4D24412yes—
346C2×C22⋊C4—1222no—
347C2×C22⋊C4—1221no—
348C2×C42—1221no—
349C2×C42C22×D6111yescharacteristic
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8C22×D6112yes—
353C4⋊C8C22×D6112yes—
354#102—1224no—
355#102—1224no—
356#102—1228no—
357C4×C8—612no—
358C4×C8—1221no—
359C24—1221no—
360C24—2441no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×Q8—612no—
366C2×Q8—614no—
367C2×Q8—1228no—
368C2×Q8—1221no—
369C2×Q8—1222no—
370C2×Q8—2448no—
371C2×Q8—2448no—
372C2×Q8—2448no—
373C2×Q8—24416no—
374C2×D4—612no—
375C2×D4—614no—
376C2×D4—1222no—
377C2×D4—1222no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—1221no—
381C2×D4—2444no—
382C2×D4—2442no—
383C2×D4—2441no—
384C2×D4—2441no—
385C2×D4—2441no—
386C2×D4—2442no—
387C2×D4—2442no—
388C2×D4—2442no—
389C22×C4—22no—
390C22×C4—1228no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—2448no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4C2×D24411yescharacteristic
400C22×C4D4×D6111yescharacteristic
401C22×C4D4×D6111yescharacteristic
402SD16—2448no—
403D8—2448no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—42no—
407C2×C8—42no—
408C2×C8—1222no—
409C2×C8—2442no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—612no—
414C4⋊C4—612no—
415C4⋊C4—1228no—
416C4⋊C4—1222no—
417C4⋊C4—1221no—
418C4⋊C4—1221no—
419C4⋊C4—1222no—
420C4⋊C4C2×D24414yes—
421C22⋊C4—1228no—
422C22⋊C4—1222no—
423C22⋊C4—1222no—
424C42—1222no—
425C42—1222no—
426C42C2×D24411yescharacteristic
427C42D4×D6111yescharacteristic
428C42D4×D6111yescharacteristic
429C42C23×D6111yescharacteristic
430C23—1222no—
431C23—1224no—
432C23—4882no—
433C23—4882no—
434C23—4882no—
435C23—2442no—
436C23—2442no—
437C23—2442no—
438C23#1451974711yescharacteristic
439Q8—42no—
440Q8—42no—
441Q8—44no—
442Q8—614no—
443Q8—1222no—
444Q8—1224no—
445Q8—24416no—
446D4—614no—
447D4—1222no—
448D4—1224no—
449D4—4882no—
450D4—4882no—
451D4—4882no—
452D4—2444no—
453D4—2442no—
454D4—2442no—
455D4—2442no—
456D4—2442no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—44no—
460C2×C4—1222no—
461C2×C4—1224no—
462C2×C4—1222no—
463C2×C4—1222no—
464C2×C4—24416no—
465C2×C4—2442no—
466C2×C4—2442no—
467C2×C4—2442no—
468C2×C4—2442no—
469C2×C4—2444no—
470C2×C4#1451974711yescharacteristic
471C2×C4#1451974711yescharacteristic
472C2×C4#1451974711yescharacteristic
473C2×C4D8×D6112yes—
474C2×C4SD16×D6112yes—
475C2×C4#1451980412yes—
476C2×C4#1451980912yes—
477C2×C4C2×D4×D6111yescharacteristic
478C2×C4C2×D4×D6111yescharacteristic
479C2×C4C22×D24411yescharacteristic
480C8—42no—
481C8—42no—
482C8—2442no—
483C22—1224no—
484C22—9764no—
485C22—4882no—
486C22—4882no—
487C22—4882no—
488C22—2442no—
489C22—2448no—
490C22—2442no—
491C22#1683989712yes—
492C22#1683990212yes—
493C22#1683993712yes—
494C22C2×#1451974711yescharacteristic
495C4—21no—
496C4—21no—
497C4—44no—
498C4—1224no—
499C4—2442no—
500C4—2442no—
501C4#1683989712yes—
502C4#1683990212yes—
503C4C2×D8×D6111yescharacteristic
504C4C2×SD16×D6111yescharacteristic
505C4C2×#1451980411yescharacteristic
506C4C2×#1451980911yescharacteristic
507C2—9762no—
508C2—2444no—
509C2#2144492314yesdirect product factor
510C2C2×#1683989711yescharacteristic
511C2C2×#1683990211yescharacteristic
512C2C2×#1683993711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC23×C61#120
prime radicalC2×#16839958C2
hypercenterC2×#332D61
hypocenterC61C2×#1627
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#16840427C2semidirect
2. C2×#16840110C2semidirect
3. C2×#16839963C2semidirect
5. #21444923C2direct (N × H)
6. C2×#16839492C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#332C2semidirect
15. #16840427C22semidirect
24. #16840110C22semidirect
26. #16839963C22semidirect
33. #16839492C22semidirect
34. #16839489C22semidirect
38. C61×#332C22semidirect
131. C2×D244SD16semidirect
143. C2×Dic122D8semidirect
214. D244C2×SD16semidirect
222. Dic122C2×D8semidirect
256. C2×#332D61semidirect
259. C2×C61#1627semidirect
292. #332C2×D61semidirect
295. C61C2×#1627semidirect
509. C2#21444923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404272
C2×#168401102
C2×#168399632
C2×#168399582
#214449232
C2×#168394922
C2×#168394892
C2×C61×#3322
C2×#162761