Finite Group Databasebeta

← C2×#21444949 #29655879

Subgroups — C2×#21444949 #29655879

Order 15616.

1322 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×#16840433C211yesmaximal, characteristic
2C2×#16840135C211yesmaximal, characteristic, complemented
3C2×#16840058C211yesmaximal, characteristic, complemented
4C2×#16840052C211yesmaximal, characteristic, complemented
5#21444949C218yesmaximal, direct product factor
6C2×#16839505C211yesmaximal, characteristic, complemented
7C2×#16839494C211yesmaximal, characteristic, complemented
8C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#11758222—21no—
10C22×#11758190—22no—
11#16840433—22no—
12#16840433—22no—
13#16840433—22no—
14#16840433C2214yes—
15C2×#14519777C2211yescharacteristic
16C2×#14519774C2211yescharacteristic
17C2×#14519773—21no—
18C2×#14519751—21no—
19C2×#14519750—22no—
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519739—21no—
22#16840135—22no—
23#16840135C2214yescomplemented
24#16840058—22no—
25#16840058C2214yescomplemented
26#16840052—22no—
27#16840052C2214yescomplemented
28C2×#14519711—21no—
29C2×#14519708—21no—
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519702—21no—
32C2×#14519698—21no—
33#16839505C2214yescomplemented
34#16839494C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×D4⋊C8C2214yescomplemented
39C2×#11758222—24no—
40C2×#11758222—24no—
41C2×#11758222—44no—
42C2×#11758222—44no—
43C22×Dic122—21no—
44C22×Dic122D411yescharacteristic
45C22×D244—21no—
46C22×D244—21no—
47C22×D244D412yes—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C4×D61—22no—
51C2×#11758190—28no—
52C2×#11758190—48no—
53C22×#92418—21no—
54#14519777—21no—
55#14519777—21no—
56#14519777—21no—
57#14519777C2312yes—
58#14519774—21no—
59#14519774—21no—
60#14519774D412yes—
61#14519774C2312yes—
62#14519773—24no—
63#14519773—24no—
64#14519751—24no—
65#14519751—24no—
66#14519750—28no—
67#14519750—28no—
68C4×Dic122—21no—
69C4×Dic122—21no—
70C4×Dic122D412yes—
71C4×Dic122C2312yes—
72#14519739—24no—
73#14519739—24no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61D411yescharacteristic
77C2×#11758196—21no—
78C2×#11758198—22no—
79C2×C4×Dic61—21no—
80#14519711—24no—
81#14519708—24no—
82C4⋊#92418—21no—
83C4⋊#92418C2312yes—
84#14519702—24no—
85#14519698—24no—
86C22×D4×C61D411yescharacteristic
87C23×C4×C61—21no—
88C22×C8×C61—21no—
89C22×C8×C61—21no—
90C4×D4×C61—21no—
91C4×D4×C61—21no—
92C4×D4×C61D412yes—
93C4×D4×C61C2312yes—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C22⋊C4×C61—21no—
96C2×C42×C61C2311yescharacteristic
97C4⋊C8×C61—21no—
98C4⋊C8×C61C2312yes—
99C4×C8×C61—21no—
100C4×C8×C61C2312yes—
101C24×C61—21no—
102C23×D61—22no—
103C2×D4×C61—21no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61C2×D412yes—
107C22×C4×C61—21no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—42no—
111C22×C4×C61—42no—
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C2×C22⋊D61—28no—
116C2×C22⋊D61—28no—
117C2×C22⋊D61—48no—
118C2×C22⋊D61—84no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—41no—
122#11758222—48no—
123#11758222—416no—
124#11758222—48no—
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—48no—
138C2×Dic122—21no—
139C2×Dic122—22no—
140C2×Dic122—22no—
141C2×Dic122—44no—
142C2×Dic122—41no—
143C2×Dic122SD1614yescomplemented
144C2×Dic122C2×D412yes—
145C2×C8×C61—24no—
146C2×C8×C61—22no—
147C2×C8×C61—22no—
148C2×C8×C61—42no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61C2×D412yes—
151C22⋊C4×C61—22no—
152C22⋊C4×C61—22no—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2411yescharacteristic
157#11758198—28no—
158C4⋊Dic61—21no—
159C4⋊Dic61—22no—
160C4⋊Dic61—22no—
161C4⋊Dic61—41no—
162C4⋊Dic61—41no—
163C4⋊Dic61C2×D412yes—
164#11758196—22no—
165#11758196—22no—
166C4×Dic61—22no—
167C4×Dic61—22no—
168C2×#92418—22no—
169C2×#92418—42no—
170#11758190—416no—
171C23×C61—22no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61#12011yescharacteristic
176C22×D61—24no—
177C22×D61—44no—
178C22×D61—44no—
179C22×D61—44no—
180D4×C61—22no—
181D4×C61—22no—
182D4×C61—42no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—44no—
189C2×C4×C61#12011yescharacteristic
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61#12011yescharacteristic
192C2×C4×C61C2×SD1612yes—
193C2×C4×C61#13512yes—
194C2×C4×C61AGL(1,ℤ/8)12yes—
195C2×C4×C61#13712yes—
196C2×C4×C61C22×D411yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C22×D411yescharacteristic
199C22⋊D61—416no—
200C22⋊D61—88no—
201C2×Dic61—22no—
202C2×Dic61—24no—
203C2×Dic61—22no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—82no—
207D244—44no—
208D244—42no—
209D244—42no—
210D244—42no—
211D244—42no—
212D244—44no—
213D244—44no—
214D244—82no—
215C4×D61—416no—
216Dic122—22no—
217Dic122—24no—
218Dic122—44no—
219Dic122—82no—
220Dic122C2×SD1614yescomplemented
221C8×C61—24no—
222C8×C61—42no—
223#92418—42no—
224C2×#1631—611nomaximal, Sylow
225C22×C61—42no—
226C22×C61—42no—
227C22×C61—42no—
228C22×C61—84no—
229C22×C61#45012yes—
230C22×C61#45212yes—
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#45012yes—
241C4×C61#45212yes—
242C4×C61C22×SD1611yescharacteristic
243C4×C61C2×#13511yescharacteristic
244C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C61C2×#13711yescharacteristic
246Dic61—24no—
247Dic61—42no—
248Dic61—82no—
249C2×#550—611no—
250C2×#492—611no—
251C2×#477—611no—
252C2×#476—611no—
253#1631—618no—
254C2×#331—611no—
255C2×Q8⋊C8—611no—
256C2×D4⋊C8D6111yescharacteristic, complemented
257C2×C61—82no—
258C2×C61#163114yescomplemented
259C2×C61C2×#45011yescharacteristic
260C2×C61C2×#45211yescharacteristic
261C2×C61C2×#45311yescharacteristic
262D61—84no—
263C22×#41—1221no—
264C22×SD16—1222no—
265#550—614no—
266#550—1222no—
267#550—1222no—
268#550—1222no—
269C2×C4⋊Q8—611no—
270C2×#127—611no—
271C2×#127—1221no—
272C2×#121—1222no—
273C2×#121—1221no—
274C2×C4×Q8—611no—
275C2×C4×D4—1221no—
276C2×C4×D4C2×D6111yescharacteristic
277#492—614no—
278#492—1222no—
279#477—614no—
280#477—1222no—
281#476—614no—
282#476—1222no—
283C2×#107—1221no—
284C2×#106—1221no—
285C2×C4⋊C8—611no—
286C2×C4⋊C8C2×D6111yescharacteristic
287C2×#103—1221no—
288C2×#102—1221no—
289C2×C4×C8C2×D6111yescharacteristic
290#331—614no—
291Q8⋊C8—614no—
292D4⋊C8C2×D6114yescomplemented
293C61C2×#163111yescharacteristic, complemented, Sylow
294C2×#41—1224no—
295C2×#41—1224no—
296C2×#41—2444no—
297C2×#41—2444no—
298C22×Q8—611no—
299C22×Q8—1221no—
300C22×D4—612no—
301C22×D4—1222no—
302C22×D4—1222no—
303C22×D4—1221no—
304C22×D4—1221no—
305C22×D4D24411yescharacteristic
306C23×C4—21no—
307C23×C4—1222no—
308C2×SD16—1228no—
309C2×SD16—2448no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—1221no—
313C4⋊Q8—612no—
314C4⋊Q8—1221no—
315C4⋊Q8—1221no—
316C4⋊Q8—1221no—
317#127—612no—
318#127—612no—
319#127—1224no—
320#127—1224no—
321#127—1221no—
322#127—1221no—
323#121—1228no—
324#121—1228no—
325#121—1224no—
326#121—1224no—
327C4×Q8—612no—
328C4×Q8—612no—
329C4×Q8—1221no—
330C4×Q8—1221no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—1224no—
334C4×D4—1224no—
335C4×D4D24412yes—
336C4×D4C22×D6112yes—
337C2×C4⋊C4—611no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4—1221no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4D24411yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—1222no—
344C2×C42—1221no—
345C2×C42C22×D6111yescharacteristic
346#107—1224no—
347#106—1224no—
348C4⋊C8—21no—
349C4⋊C8—612no—
350C4⋊C8—1221no—
351C4⋊C8C22×D6112yes—
352#103—1224no—
353#102—1224no—
354C4×C8—21no—
355C4×C8C22×D6112yes—
356C24—21no—
357C24—1222no—
358#41—2448no—
359#41—2448no—
360#41—24416no—
361C2×Q8—612no—
362C2×Q8—614no—
363C2×Q8—1221no—
364C2×Q8—1222no—
365C2×Q8—1222no—
366C2×Q8—2444no—
367C2×Q8—2441no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—614no—
372C2×D4—1228no—
373C2×D4—1228no—
374C2×D4—1222no—
375C2×D4—1222no—
376C2×D4—1222no—
377C2×D4—1222no—
378C2×D4—1222no—
379C2×D4—4884no—
380C2×D4—2444no—
381C2×D4—2448no—
382C2×D4—2442no—
383C2×D4—2442no—
384C2×D4—2442no—
385C2×D4—2442no—
386C2×D4C2×D24412yes—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—1228no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—2448no—
396C22×C4—2441no—
397C22×C4C2×D24411yescharacteristic
398C22×C4D4×D6111yescharacteristic
399C22×C4D4×D6111yescharacteristic
400SD16—24416no—
401C2×C8—24no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—42no—
405C2×C8—1222no—
406C2×C8—2442no—
407C4⋊C4—21no—
408C4⋊C4—612no—
409C4⋊C4—1222no—
410C4⋊C4—1221no—
411C4⋊C4—1222no—
412C4⋊C4—1222no—
413C4⋊C4—1222no—
414C4⋊C4—2441no—
415C4⋊C4—2441no—
416C4⋊C4C2×D24412yes—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—1228no—
420C42—1222no—
421C42—1222no—
422C42C2×D24411yescharacteristic
423C42D4×D6111yescharacteristic
424C42D4×D6111yescharacteristic
425C42C23×D6111yescharacteristic
426C23—22no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—1224no—
431C23—2444no—
432C23—2444no—
433C23—2444no—
434C23#1451974711yescharacteristic
435Q8—614no—
436Q8—1222no—
437Q8—1224no—
438Q8—4882no—
439Q8—2444no—
440D4—22no—
441D4—22no—
442D4—42no—
443D4—4882no—
444D4—4888no—
445D4—2444no—
446D4—24416no—
447D4—2442no—
448D4—2442no—
449D4—2442no—
450D4—2442no—
451D4—2444no—
452D4—2444no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—1222no—
460C2×C4—1224no—
461C2×C4—1222no—
462C2×C4—4882no—
463C2×C4—24416no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4#1451974711yescharacteristic
467C2×C4#1451974711yescharacteristic
468C2×C4#1451974711yescharacteristic
469C2×C4SD16×D6112yes—
470C2×C4#1451979912yes—
471C2×C4#1451980112yes—
472C2×C4#1451981012yes—
473C2×C4C2×D4×D6111yescharacteristic
474C2×C4C2×D4×D6111yescharacteristic
475C2×C4C22×D24411yescharacteristic
476C8—24no—
477C8—42no—
478C8—2442no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—84no—
483C22—4888no—
484C22—2444no—
485C22—2444no—
486C22—2444no—
487C22#1683991412yes—
488C22#1683992612yes—
489C22#1683993112yes—
490C22C2×#1451974711yescharacteristic
491C4—21no—
492C4—21no—
493C4—42no—
494C4—1224no—
495C4—4882no—
496C4—2442no—
497C4#1683991412yes—
498C4#1683992612yes—
499C4C2×SD16×D6111yescharacteristic
500C4C2×#1451979911yescharacteristic
501C4C2×#1451980111yescharacteristic
502C4C2×#1451981011yescharacteristic
503C2—82no—
504C2—4884no—
505C2#2144494914yesdirect product factor
506C2C2×#1683991411yescharacteristic
507C2C2×#1683992611yescharacteristic
508C2C2×#1683993111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radicalC2×#16840433C2
hypercenterC2×D4⋊C8D61
hypocenterC61C2×#1631
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16840135C2semidirect
3. C2×#16840058C2semidirect
4. C2×#16840052C2semidirect
5. #21444949C2direct (N × H)
6. C2×#16839505C2semidirect
7. C2×#16839494C2semidirect
8. C2×C61×D4⋊C8C2semidirect
23. #16840135C22semidirect
25. #16840058C22semidirect
27. #16840052C22semidirect
33. #16839505C22semidirect
34. #16839494C22semidirect
38. C61×D4⋊C8C22semidirect
143. C2×Dic122SD16semidirect
220. Dic122C2×SD16semidirect
256. C2×D4⋊C8D61semidirect
258. C2×C61#1631semidirect
292. D4⋊C8C2×D61semidirect
293. C61C2×#1631semidirect
505. C2#21444949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404332
C2×#168401352
C2×#168400582
C2×#168400522
#214449492
C2×#168395052
C2×#168394942
C2×C61×D4⋊C82
C2×#163161