Finite Group Databasebeta

← C2×#21444944 #29655874

Subgroups — C2×#21444944 #29655874

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×#16840434C211yesmaximal, characteristic
2C2×#16840136C211yesmaximal, characteristic, complemented
3C2×#16840049C211yesmaximal, characteristic, complemented
4#21444944C218yesmaximal, direct product factor
5C2×#16839505C211yesmaximal, characteristic, complemented
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#477C211yesmaximal, characteristic, complemented
9C22×#11758226—21no—
10C22×#11758201—22no—
11#16840434—22no—
12#16840434—22no—
13#16840434—22no—
14#16840434C2214yes—
15C2×#14519774—21no—
16C2×#14519774C2211yescharacteristic
17C2×#14519752—21no—
18C2×#14519752—22no—
19C2×C4×D244—21no—
20C2×C4×D244C2211yescharacteristic
21#16840136—22no—
22#16840136C2214yescomplemented
23#16840049—22no—
24#16840049C2214yescomplemented
25C2×#14519708—21no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519697—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839505C2214yescomplemented
30Q8⋊#92418C2214yescomplemented
31#16839489C2214yescomplemented
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×C4×Q8×C61C2211yescharacteristic
34C61×#477—22no—
35C61×#477C2214yescomplemented
36C2×#107×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#103×C61—21no—
39C2×#11758226—24no—
40C2×#11758226—24no—
41C2×#11758226—44no—
42C2×#11758226—44no—
43C22×D244—22no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—22no—
47C22×D244D411yescharacteristic
48C22×D244D412yes—
49C22×C4×D61—22no—
50C22×C4×D61—21no—
51C2×#11758201—28no—
52C2×#11758201—48no—
53C22×#92418—21no—
54C22×#92418—21no—
55#14519774—24no—
56#14519774—24no—
57#14519774—21no—
58#14519774—21no—
59#14519774D412yes—
60#14519774C2312yes—
61#14519752—24no—
62#14519752—28no—
63#14519752—28no—
64#14519752—24no—
65C4×D244—24no—
66C4×D244—21no—
67C4×D244—21no—
68C4×D244—24no—
69C4×D244D412yes—
70C4×D244C2312yes—
71C2×C4⋊Dic61D411yescharacteristic
72C2×#11758198—22no—
73C2×#11758198—21no—
74#14519708—24no—
75C4⋊#92418—21no—
76C4⋊#92418C2312yes—
77#14519697—24no—
78C4×#92418—21no—
79C4×#92418C2312yes—
80C22×Q8×C61—21no—
81C22×Q8×C61D411yescharacteristic
82C22×C8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61C2312yes—
87C4×Q8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61D412yes—
90C4×Q8×C61C2312yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C42×C61—21no—
96C2×C42×C61C2311yescharacteristic
97#107×C61—24no—
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2312yes—
100#103×C61—24no—
101C23×D61—21no—
102C23×D61—22no—
103C2×Q8×C61—21no—
104C2×Q8×C61—22no—
105C2×Q8×C61—22no—
106C2×Q8×C61—44no—
107C2×Q8×C61—41no—
108C2×Q8×C61SD1614yescomplemented
109C2×Q8×C61C2×D412yes—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—41no—
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×Dic61—21no—
117#11758226—48no—
118#11758226—416no—
119#11758226—48no—
120C2×D244—22no—
121C2×D244—22no—
122C2×D244—28no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—21no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—28no—
129C2×D244—22no—
130C2×D244—48no—
131C2×D244—42no—
132C2×D244—42no—
133C2×D244—42no—
134C2×D244—42no—
135C2×D244—44no—
136C2×D244—84no—
137C2×D244C2×D412yes—
138C2×D244C2×D414yes—
139C2×C4×D61—28no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—48no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×C8×C61—22no—
146C2×C8×C61—42no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61C2×D412yes—
155C42×C61—22no—
156C42×C61—22no—
157C42×C61C2×D411yescharacteristic
158C42×C61C2×D411yescharacteristic
159C42×C61C2×D411yescharacteristic
160C42×C61C2411yescharacteristic
161#11758201—416no—
162#11758198—28no—
163#11758198—22no—
164#11758198—22no—
165C4⋊Dic61—21no—
166C4⋊Dic61C2×D412yes—
167C2×#92418—24no—
168C2×#92418—22no—
169C2×#92418—22no—
170C2×#92418—42no—
171C23×C61#12011yescharacteristic
172C22×D61—22no—
173C22×D61—24no—
174C22×D61—44no—
175C22×D61—42no—
176C22×D61—42no—
177C22×D61—44no—
178C22×D61—44no—
179C22×D61—42no—
180Q8×C61—22no—
181Q8×C61—24no—
182Q8×C61—44no—
183Q8×C61—82no—
184Q8×C61C2×SD1614yescomplemented
185C2×C4×C61—22no—
186C2×C4×C61—24no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—82no—
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61C2×SD1612yes—
196C2×C4×C61#13512yes—
197C2×C4×C61AGL(1,ℤ/8)12yes—
198C2×C4×C61#13712yes—
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C2×Dic61—22no—
203C2×Dic61—42no—
204D244—22no—
205D244—22no—
206D244—44no—
207D244—416no—
208D244—42no—
209D244—42no—
210D244—42no—
211D244—42no—
212D244—44no—
213D244—42no—
214D244—44no—
215D244—82no—
216D244—88no—
217C4×D61—416no—
218C4×D61—42no—
219C4×D61—42no—
220C4×D61—44no—
221C8×C61—42no—
222#92418—24no—
223#92418—42no—
224C2×#1631—611nomaximal, Sylow
225C22×C61#45012yes—
226C22×C61#45212yes—
227C22×C61#45312yes—
228C22×C61C2×#12011yescharacteristic
229C2×D61—44no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—44no—
233C2×D61—44no—
234C2×D61—42no—
235C2×D61—84no—
236C2×D61—88no—
237C4×C61—24no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—42no—
241C4×C61—82no—
242C4×C61#45012yes—
243C4×C61#45212yes—
244C4×C61C22×SD1611yescharacteristic
245C4×C61C2×#13511yescharacteristic
246C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C61C2×#13711yescharacteristic
248Dic61—42no—
249C2×#550—611no—
250C2×#492—611no—
251C2×#477D6111yescharacteristic, complemented
252C2×#476—611no—
253#1631—618no—
254C2×#331—611no—
255C2×Q8⋊C8—611no—
256C2×D4⋊C8—611no—
257C2×C61#163114yescomplemented
258C2×C61C2×#45011yescharacteristic
259C2×C61C2×#45211yescharacteristic
260C2×C61C2×#45311yescharacteristic
261D61—82no—
262D61—84no—
263C22×#41—1221no—
264C22×SD16—1222no—
265#550—614no—
266#550—1222no—
267#550—1222no—
268#550—1222no—
269C2×C4⋊Q8C2×D6111yescharacteristic
270C2×#127—611no—
271C2×#127—1221no—
272C2×#121—1222no—
273C2×#121—1221no—
274C2×C4×Q8C2×D6111yescharacteristic
275C2×C4×D4—611no—
276C2×C4×D4—1221no—
277#492—614no—
278#492—1222no—
279#477—22no—
280#477C2×D6114yescomplemented
281#476—614no—
282#476—1222no—
283C2×#107—21no—
284C2×#106—1221no—
285C2×C4⋊C8—611no—
286C2×C4⋊C8C2×D6111yescharacteristic
287C2×#103—21no—
288C2×#102—1221no—
289C2×C4×C8—611no—
290#331—614no—
291Q8⋊C8—614no—
292D4⋊C8—614no—
293C61C2×#163111yescharacteristic, complemented, Sylow
294C2×#41—1224no—
295C2×#41—1224no—
296C2×#41—2444no—
297C2×#41—2444no—
298C22×Q8—21no—
299C22×Q8C22⋊D6111yescharacteristic
300C22×D4—611no—
301C22×D4—612no—
302C22×D4—1222no—
303C22×D4—1222no—
304C22×D4—1221no—
305C22×D4—1221no—
306C23×C4—1222no—
307C23×C4—1221no—
308C2×SD16—1228no—
309C2×SD16—2448no—
310C22×C8—21no—
311C22×C8—1221no—
312C22×C8—1221no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8C22×D6112yes—
317#127—612no—
318#127—612no—
319#127—1224no—
320#127—1224no—
321#127—1221no—
322#127—1221no—
323#121—1228no—
324#121—1224no—
325#121—1228no—
326#121—1224no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8C22⋊D6112yes—
330C4×Q8C22×D6112yes—
331C4×D4—612no—
332C4×D4—612no—
333C4×D4—1224no—
334C4×D4—1224no—
335C4×D4—1221no—
336C4×D4—1221no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—611no—
341C2×C4⋊C4C22⋊D6111yescharacteristic
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1221no—
344C2×C42—21no—
345C2×C42C22×D6111yescharacteristic
346#107—24no—
347#106—1224no—
348C4⋊C8—21no—
349C4⋊C8—612no—
350C4⋊C8—1221no—
351C4⋊C8C22×D6112yes—
352#103—24no—
353#102—1224no—
354C4×C8—612no—
355C4×C8—1221no—
356C24—1221no—
357C24—1222no—
358#41—2448no—
359#41—24416no—
360#41—2448no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—44no—
365C2×Q8—41no—
366C2×Q8#1175820114yescomplemented
367C2×Q8C2×C22⋊D6112yes—
368C2×D4—612no—
369C2×D4—614no—
370C2×D4—1228no—
371C2×D4—1228no—
372C2×D4—1222no—
373C2×D4—1222no—
374C2×D4—1222no—
375C2×D4—1222no—
376C2×D4—1222no—
377C2×D4—1221no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—4884no—
381C2×D4—2444no—
382C2×D4—2448no—
383C2×D4—2442no—
384C2×D4—2442no—
385C2×D4—2442no—
386C2×D4—2442no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—1228no—
391C22×C4—1221no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—2448no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4D4×D6111yescharacteristic
398C22×C4D4×D6111yescharacteristic
399C22×C4C2×C22⋊D6111yescharacteristic
400SD16—24416no—
401C2×C8—22no—
402C2×C8—42no—
403C2×C8—1224no—
404C2×C8—1222no—
405C2×C8—1222no—
406C2×C8—2442no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—612no—
415C4⋊C4—1221no—
416C4⋊C4C2×C22⋊D6112yes—
417C22⋊C4—1228no—
418C22⋊C4—1222no—
419C22⋊C4—1222no—
420C42—22no—
421C42—22no—
422C42D4×D6111yescharacteristic
423C42D4×D6111yescharacteristic
424C42C2×C22⋊D6111yescharacteristic
425C42C23×D6111yescharacteristic
426C23—1222no—
427C23—1224no—
428C23—2444no—
429C23—2442no—
430C23—2442no—
431C23—2444no—
432C23—2442no—
433C23—2444no—
434C23#1451974511yescharacteristic
435Q8—22no—
436Q8—24no—
437Q8—44no—
438Q8—82no—
439Q8C2×#1175820114yescomplemented
440D4—1222no—
441D4—1222no—
442D4—4882no—
443D4—4888no—
444D4—2444no—
445D4—24416no—
446D4—2442no—
447D4—2442no—
448D4—2442no—
449D4—2442no—
450D4—2444no—
451D4—2442no—
452D4—2444no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—82no—
460C2×C4—1222no—
461C2×C4—24416no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4—2444no—
466C2×C4#1451974511yescharacteristic
467C2×C4#1451974511yescharacteristic
468C2×C4#1451974511yescharacteristic
469C2×C4C2×#1175820112yes—
470C2×C4#1451980012yes—
471C2×C4#1451980212yes—
472C2×C4#1451980912yes—
473C2×C4C2×D4×D6111yescharacteristic
474C2×C4C2×D4×D6111yescharacteristic
475C2×C4C22×C22⋊D6111yescharacteristic
476C8—42no—
477C8—1224no—
478C8—2442no—
479C22—4884no—
480C22—4888no—
481C22—2442no—
482C22—2444no—
483C22—2444no—
484C22—2442no—
485C22—2442no—
486C22—2444no—
487C22#1683991212yes—
488C22#1683992312yes—
489C22#1683992812yes—
490C22C2×#1451974511yescharacteristic
491C4—21no—
492C4—21no—
493C4—24no—
494C4—42no—
495C4—82no—
496C4—2442no—
497C4#1683991212yes—
498C4#1683992312yes—
499C4C22×#1175820111yescharacteristic
500C4C2×#1451980011yescharacteristic
501C4C2×#1451980211yescharacteristic
502C4C2×#1451980911yescharacteristic
503C2—4882no—
504C2—4884no—
505C2#2144494414yesdirect product factor
506C2C2×#1683991211yescharacteristic
507C2C2×#1683992311yescharacteristic
508C2C2×#1683992811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#477C2
socleC23×C61#120
prime radicalC2×#16840434C2
hypercenterC2×#477D61
hypocenterC61C2×#1631
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×#16840136C2semidirect
3. C2×#16840049C2semidirect
4. #21444944C2direct (N × H)
5. C2×#16839505C2semidirect
6. C2×Q8⋊#92418C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#477C2semidirect
22. #16840136C22semidirect
24. #16840049C22semidirect
29. #16839505C22semidirect
30. Q8⋊#92418C22semidirect
31. #16839489C22semidirect
35. C61×#477C22semidirect
108. C2×Q8×C61SD16semidirect
184. Q8×C61C2×SD16semidirect
251. C2×#477D61semidirect
257. C2×C61#1631semidirect
280. #477C2×D61semidirect
293. C61C2×#1631semidirect
366. C2×Q8#11758201semidirect
439. Q8C2×#11758201semidirect
505. C2#21444944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404342
C2×#168401362
C2×#168400492
#214449442
C2×#168395052
C2×Q8⋊#924182
C2×#168394892
C2×C61×#4772
C2×#163161