Finite Group Databasebeta

← C2×#21444892 #29655631

Subgroups — C2×#21444892 #29655631

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840473C211yesmaximal, characteristic, complemented
2C2×#16840136C211yesmaximal, characteristic, complemented
3C2×#16839963C211yesmaximal, characteristic, complemented
4C2×#16839958C211yesmaximal, characteristic
5#21444892C218yesmaximal, direct product factor
6C2×#16839492C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#333C211yesmaximal, characteristic, complemented
9C22×#11758190—21no—
10C22×#11758201—22no—
11C22×D488—21no—
12#16840473—22no—
13#16840473—22no—
14#16840473—22no—
15#16840473C2214yescomplemented
16C2×#14519774C2211yescharacteristic
17C2×#14519768—21no—
18C2×#14519757—21no—
19C2×#14519753—22no—
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×#14519739—21no—
23C2×C4⋊C4×D61—21no—
24#16840136—22no—
25#16840136C2214yescomplemented
26#16839963—22no—
27#16839963C2214yescomplemented
28#16839958—22no—
29#16839958C2214yes—
30C2×#14519699—21no—
31C2×#14519699—21no—
32C2×C4×#92418C2211yescharacteristic
33#16839492C2214yescomplemented
34#16839489C2214yescomplemented
35C2×C4⋊Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#333C2214yescomplemented
39C22×Dic122D411yescharacteristic
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244D411yescharacteristic
44C22×C4×D61—21no—
45C22×C4×D61—22no—
46C2×#11758190—24no—
47C2×#11758190—44no—
48C2×#11758201—28no—
49C2×#11758201—48no—
50C2×D488—24no—
51C2×D488—44no—
52C22×#92418—21no—
53#14519774—21no—
54#14519774—21no—
55#14519774—21no—
56#14519774C2312yes—
57#14519768—24no—
58#14519768—24no—
59#14519757—24no—
60#14519757—24no—
61#14519753—28no—
62#14519753—28no—
63C4×Dic122—21no—
64C4×Dic122—21no—
65C4×Dic122D412yes—
66C4×Dic122C2312yes—
67C4×D244—21no—
68C4×D244—21no—
69C4×D244D412yes—
70C4×D244C2312yes—
71#14519739—24no—
72#14519739—24no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61D411yescharacteristic
75C2×C4⋊Dic61D411yescharacteristic
76C2×#11758196—22no—
77C2×#11758196—21no—
78C4⋊C4×D61—24no—
79C4⋊C4×D61—24no—
80C2×#11758198—22no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83#14519699—24no—
84#14519699—24no—
85C4×#92418—21no—
86C4×#92418C2312yes—
87C22×Q8×C61D412yes—
88C22×C8×C61—21no—
89C22×C8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61D412yes—
93C4⋊Q8×C61C2312yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C42×C61C2311yescharacteristic
97C4⋊C8×C61—21no—
98C4⋊C8×C61—21no—
99C4⋊C8×C61C2312yes—
100C4⋊C8×C61C2312yes—
101C23×D61—21no—
102C23×D61—41no—
103C2×Q8×C61—22no—
104C2×Q8×C61—44no—
105C2×Q8×C61C2×D414yes—
106C22×C4×C61—22no—
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C2×D244—21no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—44no—
119C2×D244—42no—
120C2×D244—42no—
121C2×D244—42no—
122C2×D244—42no—
123C2×D244—41no—
124C2×D244—41no—
125C2×D244—41no—
126C2×D244SD1614yescomplemented
127C2×D244C2×D412yes—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—28no—
131C2×C4×D61—42no—
132C2×C4×D61—42no—
133C2×C4×D61—84no—
134C2×Dic122—22no—
135C2×Dic122—22no—
136C2×Dic122—21no—
137C2×Dic122C2×D412yes—
138C2×C8×C61—22no—
139C2×C8×C61—22no—
140C2×C8×C61—42no—
141C2×C8×C61—42no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—22no—
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2411yescharacteristic
150#11758201—416no—
151#11758198—28no—
152#11758198—22no—
153#11758198—22no—
154C4⋊Dic61—28no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61C2×D412yes—
158C4⋊Dic61C2×D412yes—
159#11758196—28no—
160#11758196—22no—
161#11758196—22no—
162C4×Dic61—22no—
163C4×Dic61—22no—
164C2×#92418—24no—
165C2×#92418—22no—
166D488—48no—
167#11758190—48no—
168C23×C61#12011yescharacteristic
169C22×D61—22no—
170C22×D61—24no—
171C22×D61—42no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61—82no—
175C22×D61—82no—
176C22×D61—82no—
177Q8×C61—44no—
178Q8×C61—82no—
179C2×C4×C61—22no—
180C2×C4×C61—24no—
181C2×C4×C61—44no—
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61C2×SD1612yes—
186C2×C4×C61#13512yes—
187C2×C4×C61AGL(1,ℤ/8)12yes—
188C2×C4×C61#13712yes—
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198D244—22no—
199D244—24no—
200D244—44no—
201D244—42no—
202D244—42no—
203D244—42no—
204D244—42no—
205D244—82no—
206D244—82no—
207D244—82no—
208D244C2×SD1614yescomplemented
209C4×D61—42no—
210C4×D61—42no—
211C4×D61—44no—
212C4×D61—88no—
213Dic122—22no—
214Dic122—22no—
215Dic122—42no—
216C8×C61—42no—
217C8×C61—42no—
218#92418—24no—
219C2×#1622—611nomaximal, Sylow
220C22×C61#44812yes—
221C22×C61#44912yes—
222C22×C61#45312yes—
223C22×C61C2×#12011yescharacteristic
224C2×D61—24no—
225C2×D61—48no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—82no—
229C2×D61—82no—
230C2×D61—82no—
231C2×D61—164no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—44no—
235C4×C61#44812yes—
236C4×C61#44912yes—
237C4×C61C22×SD1611yescharacteristic
238C4×C61C2×#13511yescharacteristic
239C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C61C2×#13711yescharacteristic
241Dic61—42no—
242Dic61—42no—
243Dic61—42no—
244C2×#554—611no—
245C2×#492—611no—
246C2×#460—611no—
247C2×#459—611no—
248#1622—618no—
249C2×#333D6111yescharacteristic, complemented
250C2×Q8⋊C8—611no—
251C2×D4⋊C8—611no—
252C2×C61#162214yescomplemented
253C2×C61C2×#44811yescharacteristic
254C2×C61C2×#44911yescharacteristic
255C2×C61C2×#45311yescharacteristic
256D61—44no—
257D61—162no—
258C22×SD16—1221no—
259C22×SD16—1222no—
260C22×D8—1221no—
261#554—614no—
262#554—1222no—
263#554—1222no—
264#554—1222no—
265C2×C4⋊Q8C2×D6111yescharacteristic
266C2×#127—611no—
267C2×#125—1221no—
268C2×C22⋊Q8—1221no—
269C2×C22⋊Q8—1222no—
270C2×C4×Q8—611no—
271C2×C4×D4—611no—
272C2×C4×D4—1221no—
273C22×C4⋊C4—1221no—
274#492—614no—
275#492—1222no—
276#460—614no—
277#460—1222no—
278#459—614no—
279#459—1222no—
280C2×C4⋊C8C2×D6111yescharacteristic
281C2×C4⋊C8C2×D6111yescharacteristic
282C2×#102—1221no—
283C2×#102—1221no—
284C2×C4×C8—611no—
285#333C2×D6114yescomplemented
286Q8⋊C8—614no—
287D4⋊C8—614no—
288C61C2×#162211yescharacteristic, complemented, Sylow
289C22×Q8—611no—
290C22×Q8D24412yes—
291C22×D4—611no—
292C22×D4—1221no—
293C22×D4—1221no—
294C22×D4—1221no—
295C23×C4—1222no—
296C23×C4—1221no—
297C2×SD16—1224no—
298C2×SD16—1228no—
299C2×SD16—2444no—
300C2×SD16—2448no—
301C2×D8—1224no—
302C2×D8—2444no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—1221no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8D24412yes—
309C4⋊Q8C22×D6112yes—
310#127—612no—
311#127—1221no—
312#127—1221no—
313#127—1221no—
314#125—1224no—
315#125—1224no—
316C22⋊Q8—1224no—
317C22⋊Q8—1224no—
318C22⋊Q8—1228no—
319C22⋊Q8—1228no—
320C4×Q8—612no—
321C4×Q8—612no—
322C4×Q8—1221no—
323C4×Q8—1221no—
324C4×D4—612no—
325C4×D4—612no—
326C4×D4—1224no—
327C4×D4—1224no—
328C4×D4—1221no—
329C4×D4—1221no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—1224no—
335C2×C4⋊C4—1224no—
336C2×C4⋊C4—1222no—
337C2×C4⋊C4—1222no—
338C2×C4⋊C4—1221no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1221no—
341C2×C42—1221no—
342C2×C42C22×D6111yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8C22×D6112yes—
346C4⋊C8C22×D6112yes—
347#102—1224no—
348#102—1224no—
349C4×C8—612no—
350C4×C8—1221no—
351C24—1221no—
352C24—2441no—
353C2×Q8—22no—
354C2×Q8—44no—
355C2×Q8—612no—
356C2×Q8—1221no—
357C2×Q8—1222no—
358C2×Q8—1222no—
359C2×Q8C2×D24414yes—
360C2×D4—612no—
361C2×D4—614no—
362C2×D4—1222no—
363C2×D4—1222no—
364C2×D4—1222no—
365C2×D4—1222no—
366C2×D4—1221no—
367C2×D4—2444no—
368C2×D4—2442no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2442no—
373C2×D4—2442no—
374C2×D4—2442no—
375C22×C4—22no—
376C22×C4—1228no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—4884no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4C2×D24411yescharacteristic
386C22×C4D4×D6111yescharacteristic
387C22×C4D4×D6111yescharacteristic
388SD16—2448no—
389SD16—24416no—
390D8—2448no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—1224no—
396C2×C8—1222no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—612no—
402C4⋊C4—612no—
403C4⋊C4—1228no—
404C4⋊C4—1228no—
405C4⋊C4—1222no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—1222no—
409C22⋊C4—1228no—
410C22⋊C4—1222no—
411C22⋊C4—1222no—
412C42—1222no—
413C42—1222no—
414C42C2×D24411yescharacteristic
415C42D4×D6111yescharacteristic
416C42D4×D6111yescharacteristic
417C42C23×D6111yescharacteristic
418C23—1222no—
419C23—1224no—
420C23—4882no—
421C23—4882no—
422C23—4882no—
423C23—2442no—
424C23—2442no—
425C23—2442no—
426C23#1451974711yescharacteristic
427Q8—44no—
428Q8—82no—
429Q8—1222no—
430Q8—1222no—
431Q8—2442no—
432D4—614no—
433D4—1222no—
434D4—1224no—
435D4—4882no—
436D4—4882no—
437D4—4882no—
438D4—2444no—
439D4—2442no—
440D4—2442no—
441D4—2442no—
442D4—2442no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—44no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—4888no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2444no—
456C2×C4#1451974711yescharacteristic
457C2×C4#1451974711yescharacteristic
458C2×C4#1451974711yescharacteristic
459C2×C4SD16×D6112yes—
460C2×C4#1451980012yes—
461C2×C4#1451980412yes—
462C2×C4#1451980912yes—
463C2×C4C2×D4×D6111yescharacteristic
464C2×C4C2×D4×D6111yescharacteristic
465C2×C4C22×D24411yescharacteristic
466C8—42no—
467C8—42no—
468C8—1224no—
469C22—1224no—
470C22—9764no—
471C22—4882no—
472C22—4882no—
473C22—4882no—
474C22—2448no—
475C22—2442no—
476C22—2442no—
477C22#1683990212yes—
478C22#1683991012yes—
479C22#1683993212yes—
480C22C2×#1451974711yescharacteristic
481C4—21no—
482C4—21no—
483C4—44no—
484C4—2442no—
485C4—2442no—
486C4—2442no—
487C4#1683990212yes—
488C4#1683991012yes—
489C4C2×SD16×D6111yescharacteristic
490C4C2×#1451980011yescharacteristic
491C4C2×#1451980411yescharacteristic
492C4C2×#1451980911yescharacteristic
493C2—9762no—
494C2—2444no—
495C2#2144489214yesdirect product factor
496C2C2×#1683990211yescharacteristic
497C2C2×#1683991011yescharacteristic
498C2C2×#1683993211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#333C2
socleC23×C61#120
prime radicalC2×#16839958C2
hypercenterC2×#333D61
hypocenterC61C2×#1622
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. C2×#16840473C2semidirect
2. C2×#16840136C2semidirect
3. C2×#16839963C2semidirect
5. #21444892C2direct (N × H)
6. C2×#16839492C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#333C2semidirect
15. #16840473C22semidirect
25. #16840136C22semidirect
27. #16839963C22semidirect
33. #16839492C22semidirect
34. #16839489C22semidirect
38. C61×#333C22semidirect
126. C2×D244SD16semidirect
208. D244C2×SD16semidirect
249. C2×#333D61semidirect
252. C2×C61#1622semidirect
285. #333C2×D61semidirect
288. C61C2×#1622semidirect
495. C2#21444892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404732
C2×#168401362
C2×#168399632
C2×#168399582
#214448922
C2×#168394922
C2×#168394892
C2×C61×#3332
C2×#162261