Finite Group Databasebeta

← C2×#21447788 #29833942

Subgroups — C2×#21447788 #29833942

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840567C211yesmaximal, characteristic
2C2×#16840203C211yesmaximal, characteristic, complemented
3C22×#14519720C211yesmaximal, characteristic, complemented
4#21447788C218yesmaximal, direct product factor
5C2×#16839574C211yesmaximal, characteristic, complemented
6C2×#16839568C211yesmaximal, characteristic, complemented
7C2×#16839546C211yesmaximal, characteristic, complemented
8C2×C61×#473C211yesmaximal, characteristic, complemented
9C2×#14519823—21no—
10#16840567—22no—
11#16840567—22no—
12#16840567—22no—
13#16840567C2214yes—
14C2×#14519805—22no—
15C2×#14519805—21no—
16C2×#14519799—21no—
17C2×#14519799C2211yescharacteristic
18C22×D488—21no—
19C22×D488C2211yescharacteristic
20#16840203—22no—
21#16840203C2214yescomplemented
22C2×#14519723—21no—
23C2×#14519720—21no—
24C2×#14519720—22no—
25C2×#14519720—22no—
26C2×#14519720C2214yescomplemented
27C2×#14519717C2211yescharacteristic, complemented
28C22×#11758185C2211yescharacteristic, complemented
29#16839574C2214yescomplemented
30#16839568C2214yescomplemented
31#16839546C2214yescomplemented
32C2×#137×C61—21no—
33C22×Q16×C61C2211yescharacteristic, complemented
34C2×#131×C61C2211yescharacteristic
35C61×#473—22no—
36C61×#473C2214yescomplemented
37C2×#108×C61C2211yescharacteristic, complemented
38C2×#101×C61—21no—
39#14519823—24no—
40#14519823—24no—
41#14519823—42no—
42#14519823—42no—
43C2×#11758226—41no—
44C2×#11758222—22no—
45C2×#11758222—21no—
46C22×D244—22no—
47C22×D244—21no—
48C2×D4×D61—42no—
49C2×D4×D61—41no—
50#14519805—24no—
51#14519805—28no—
52#14519805—24no—
53#14519805—28no—
54#14519799—24no—
55#14519799—21no—
56#14519799—21no—
57#14519799—24no—
58#14519799D412yes—
59#14519799C2312yes—
60C2×Dic244D411yescharacteristic
61C2×#11758190—22no—
62C2×#11758190—21no—
63C2×D488—22no—
64C2×D488—24no—
65C2×D488—21no—
66C2×D488—21no—
67C2×D488—21no—
68C2×D488—24no—
69C2×D488D411yescharacteristic
70C2×D488D412yes—
71C2×D488D412yes—
72C2×D488C2312yes—
73#14519723—24no—
74#14519720—24no—
75#14519720—28no—
76#14519717—21no—
77#14519717C2312yescomplemented
78C2×#11758185—21no—
79C2×#11758185—21no—
80C2×#11758185—21no—
81C2×#11758185C2312yescomplemented
82C2×#41×C61D411yescharacteristic
83C22×Q8×C61—21no—
84#137×C61—24no—
85#137×C61—42no—
86C2×Q16×C61—21no—
87C2×Q16×C61—21no—
88C2×Q16×C61—21no—
89C2×Q16×C61—21no—
90C2×Q16×C61—21no—
91C2×Q16×C61—41no—
92C2×Q16×C61C2312yescomplemented
93C2×SD16×C61—41no—
94#131×C61—21no—
95#131×C61—21no—
96#131×C61D412yes—
97#131×C61C2312yes—
98C2×M16×C61—21no—
99C2×M16×C61—21no—
100C2×M16×C61D411yescharacteristic
101C22×C8×C61—21no—
102C22×C8×C61C2311yescharacteristic
103#108×C61—21no—
104#108×C61C2312yescomplemented
105#101×C61—24no—
106C23×D61—42no—
107C23×D61—41no—
108#41×C61—21no—
109#41×C61—21no—
110#41×C61D812yes—
111#41×C61C2×D412yes—
112C2×Q8×C61—22no—
113C2×Q8×C61—41no—
114C2×Q8×C61—41no—
115C2×Q8×C61—41no—
116C2×Q8×C61—41no—
117C2×Q8×C61—41no—
118C2×Q8×C61D811yescharacteristic
119C2×D4×C61—21no—
120C2×D4×C61D811yescharacteristic
121C22×C4×C61—21no—
122C22×C4×C61—41no—
123C22×C4×C61C2×D411yescharacteristic
124C2×C22⋊D61—42no—
125C2×C22⋊D61—41no—
126#11758226—44no—
127#11758226—44no—
128D4×D61—48no—
129D4×D61—48no—
130D4×D61—44no—
131D4×D61—44no—
132#11758222—28no—
133#11758222—22no—
134#11758222—22no—
135#11758222—44no—
136#11758222—41no—
137#11758222—41no—
138C2×D244—28no—
139C2×D244—21no—
140C2×D244—22no—
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—42no—
144C2×D244—44no—
145C2×D244—41no—
146C2×D244—41no—
147C2×D244—41no—
148C2×C4×D61—42no—
149C2×C4×D61—41no—
150C2×Dic122—21no—
151Q16×C61—22no—
152Q16×C61—22no—
153Q16×C61—44no—
154Q16×C61—41no—
155Q16×C61—41no—
156SD16×C61—44no—
157M16×C61—21no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—41no—
162M16×C61C2×D412yes—
163C2×C8×C61—21no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—41no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2411yescharacteristic
173Dic244—21no—
174Dic244C2×D412yes—
175D488—28no—
176D488—21no—
177D488—22no—
178D488—22no—
179D488—22no—
180D488C2×D412yes—
181D488C2×D414yes—
182#11758190—28no—
183#11758190—22no—
184#11758190—22no—
185#11758185—22no—
186#11758185—22no—
187C23×C61—21no—
188C23×C61AGL(1,ℤ/8)11yescharacteristic
189C22×D61—42no—
190C22×D61—41no—
191C22×D61—48no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—162no—
195C22×D61—164no—
196Q8×C61—21no—
197Q8×C61—42no—
198Q8×C61—42no—
199Q8×C61—81no—
200Q8×C61—81no—
201Q8×C61C2×D812yes—
202D4×C61—22no—
203D4×C61—22no—
204D4×C61—21no—
205D4×C61C2×D812yes—
206C2×C4×C61—21no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—42no—
210C2×C4×C61—81no—
211C2×C4×C61—81no—
212C2×C4×C61#12011yescharacteristic
213C2×C4×C61#12011yescharacteristic
214C2×C4×C61C2×D811yescharacteristic
215C2×C4×C61C2×D811yescharacteristic
216C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C22⋊D61—48no—
219C22⋊D61—42no—
220C22⋊D61—42no—
221C2×Dic61—41no—
222D244—24no—
223D244—22no—
224D244—48no—
225D244—42no—
226D244—41no—
227D244—42no—
228D244—42no—
229C4×D61—48no—
230C4×D61—42no—
231C4×D61—42no—
232Dic122—22no—
233Dic122—41no—
234C8×C61—22no—
235C8×C61—42no—
236C8×C61#12011yescharacteristic
237C8×C61#12011yescharacteristic
238C8×C61C22×D411yescharacteristic
239C8×C61C22×D411yescharacteristic
240C2×#2194—611nomaximal, Sylow
241C22×C61—22no—
242C22×C61—22no—
243C22×C61—42no—
244C22×C61#44711yescharacteristic
245C22×C61#44711yescharacteristic
246C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
247C2×D61—44no—
248C2×D61—42no—
249C2×D61—84no—
250C2×D61—82no—
251C2×D61—162no—
252C2×D61—162no—
253C2×D61—168no—
254C4×C61—22no—
255C4×C61—82no—
256C4×C61#44711yescharacteristic
257C4×C61#44711yescharacteristic
258C4×C61C2×#12011yescharacteristic
259C4×C61C22×D811yescharacteristic
260Dic61—42no—
261C2×#576—611no—
262C2×#510—611no—
263C22×SD32—611no—
264C2×#473D6111yescharacteristic, complemented
265#2194—618no—
266C2×#361—611no—
267C2×#359—611no—
268C2×#350—611no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—42no—
272C2×C61#219412yescomplemented
273C2×C61C2×#44711yescharacteristic
274D61—84no—
275D61—82no—
276C2×H(5,𝔽2)—1221no—
277#576—614no—
278#576—1222no—
279#576—1222no—
280#576—1222no—
281C2×#137—21no—
282C2×AGL(1,ℤ/8)—1222no—
283C2×AGL(1,ℤ/8)—1221no—
284C2×#135—611no—
285C2×#135—1221no—
286C22×Q16C2×D6111yescharacteristic, complemented
287C22×D8—611no—
288C22×D8—1221no—
289C2×#131C2×D6111yescharacteristic
290#510—614no—
291#510—1222no—
292C2×Q32—1221no—
293C2×SD32—614no—
294C2×SD32—1222no—
295C2×SD32—1222no—
296C2×SD32—1221no—
297C2×M32—611no—
298C22×C16—611no—
299#473—22no—
300#473C2×D6114yescomplemented
301C2×#108C2×D6111yescharacteristic, complemented
302C2×#101—21no—
303#361—614no—
304#359—614no—
305#350—614no—
306C61C2×#219411yescharacteristic, complemented, Sylow
307H(5,𝔽2)—1224no—
308H(5,𝔽2)—1224no—
309H(5,𝔽2)—2442no—
310H(5,𝔽2)—2442no—
311C2×#41—1222no—
312C2×#41—1221no—
313C2×#41—2441no—
314C2×#41C22⋊D6111yescharacteristic
315C22×Q8—21no—
316C22×D4—1222no—
317C22×D4—1221no—
318C22×D4—2442no—
319C22×D4—2441no—
320#137—24no—
321#137—42no—
322AGL(1,ℤ/8)—1228no—
323AGL(1,ℤ/8)—1224no—
324AGL(1,ℤ/8)—1228no—
325AGL(1,ℤ/8)—1224no—
326#135—612no—
327#135—612no—
328#135—1224no—
329#135—1224no—
330#135—1221no—
331#135—1221no—
332C2×Q16—21no—
333C2×Q16—21no—
334C2×Q16—21no—
335C2×Q16—21no—
336C2×Q16—21no—
337C2×Q16—41no—
338C2×Q16—611no—
339C2×Q16C22×D6112yescomplemented
340C2×SD16—41no—
341C2×SD16—1222no—
342C2×SD16—1221no—
343C2×D8—612no—
344C2×D8—612no—
345C2×D8—611no—
346C2×D8—612no—
347C2×D8—1224no—
348C2×D8—1222no—
349C2×D8—1224no—
350C2×D8—1221no—
351C2×D8—1221no—
352C2×D8—1221no—
353#131—21no—
354#131—21no—
355#131C22⋊D6112yes—
356#131C22×D6112yes—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16C22⋊D6111yescharacteristic
360C22×C8—21no—
361C22×C8C22×D6111yescharacteristic
362Q32—1224no—
363SD32—1228no—
364SD32—1224no—
365M32—612no—
366M32—1221no—
367C2×C16—612no—
368C2×C16—1221no—
369C2×C16—1221no—
370C2×C16—1221no—
371#108—21no—
372#108C22×D6112yescomplemented
373#101—24no—
374C24—2442no—
375C24—2441no—
376#41—21no—
377#41—21no—
378#41—1228no—
379#41—1222no—
380#41—1222no—
381#41—2444no—
382#41—2444no—
383#41—2444no—
384#41—2441no—
385#41—2441no—
386#41#1175819912yes—
387#41C2×C22⋊D6112yes—
388C2×Q8—22no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—1221no—
395C2×Q8#1175819911yescharacteristic
396C2×D4—21no—
397C2×D4—1228no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—1221no—
401C2×D4—1222no—
402C2×D4—2442no—
403C2×D4—2444no—
404C2×D4—2448no—
405C2×D4—2448no—
406C2×D4—2444no—
407C2×D4—2442no—
408C2×D4—2441no—
409C2×D4—2444no—
410C2×D4—2441no—
411C2×D4—2441no—
412C2×D4—2441no—
413C2×D4#1175819911yescharacteristic
414C22×C4—21no—
415C22×C4—41no—
416C22×C4—2442no—
417C22×C4—2441no—
418C22×C4C2×C22⋊D6111yescharacteristic
419Q16—22no—
420Q16—22no—
421Q16—44no—
422Q16—41no—
423Q16—41no—
424Q16—612no—
425Q16—1221no—
426SD16—44no—
427SD16—1228no—
428SD16—1222no—
429SD16—1222no—
430D8—614no—
431D8—612no—
432D8—1228no—
433D8—1222no—
434D8—1222no—
435D8—1221no—
436D8—1222no—
437M16—21no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—41no—
442M16C2×C22⋊D6112yes—
443C2×C8—21no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—41no—
447C2×C8D4×D6111yescharacteristic
448C2×C8D4×D6111yescharacteristic
449C2×C8D4×D6111yescharacteristic
450C2×C8D4×D6111yescharacteristic
451C2×C8C2×C22⋊D6111yescharacteristic
452C2×C8C23×D6111yescharacteristic
453C16—1222no—
454C16—1222no—
455C23—21no—
456C23—9762no—
457C23—9764no—
458C23—2448no—
459C23—2442no—
460C23—2442no—
461C23—2442no—
462C23—2441no—
463C23#1451980211yescharacteristic
464Q8—21no—
465Q8—42no—
466Q8—42no—
467Q8—81no—
468Q8—81no—
469Q8—1222no—
470Q8—2441no—
471Q8C2×#1175819912yes—
472D4—22no—
473D4—22no—
474D4—21no—
475D4—1224no—
476D4—1222no—
477D4—2448no—
478D4—2448no—
479D4—2442no—
480D4—2442no—
481D4—2442no—
482D4—2441no—
483D4—2442no—
484D4—2442no—
485D4C2×#1175819912yes—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—42no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—2448no—
493C2×C4—2441no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4#1451974511yescharacteristic
497C2×C4#1451974511yescharacteristic
498C2×C4C2×#1175819911yescharacteristic
499C2×C4C2×#1175819911yescharacteristic
500C2×C4#1451980211yescharacteristic
501C2×C4C22×C22⋊D6111yescharacteristic
502C8—22no—
503C8—42no—
504C8#1451974511yescharacteristic
505C8#1451974511yescharacteristic
506C8C2×D4×D6111yescharacteristic
507C8C2×D4×D6111yescharacteristic
508C22—22no—
509C22—22no—
510C22—42no—
511C22—9762no—
512C22—9762no—
513C22—9768no—
514C22—4884no—
515C22—4882no—
516C22—2444no—
517C22—2442no—
518C22#1683989511yescharacteristic
519C22#1683989511yescharacteristic
520C22C2×#1451980211yescharacteristic
521C4—22no—
522C4—82no—
523C4—2442no—
524C4#1683989511yescharacteristic
525C4#1683989511yescharacteristic
526C4C2×#1451974511yescharacteristic
527C4C22×#1175819911yescharacteristic
528C2—21no—
529C2—21no—
530C2—42no—
531C2—4884no—
532C2—4882no—
533C2#2144778812yesdirect product factor
534C2C2×#1683989511yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#473C2
socleC22×C61#447
prime radicalC2×#16840567C2
hypercenterC2×#473D61
hypocenterC61C2×#2194
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
2. C2×#16840203C2semidirect
3. C22×#14519720C2semidirect
4. #21447788C2direct (N × H)
5. C2×#16839574C2semidirect
6. C2×#16839568C2semidirect
7. C2×#16839546C2semidirect
8. C2×C61×#473C2semidirect
21. #16840203C22semidirect
26. C2×#14519720C22semidirect
27. C2×#14519717C22semidirect
28. C22×#11758185C22semidirect
29. #16839574C22semidirect
30. #16839568C22semidirect
31. #16839546C22semidirect
33. C22×Q16×C61C22semidirect
36. C61×#473C22semidirect
37. C2×#108×C61C22semidirect
77. #14519717C23semidirect
81. C2×#11758185C23semidirect
92. C2×Q16×C61C23semidirect
104. #108×C61C23semidirect
264. C2×#473D61semidirect
272. C2×C61#2194semidirect
286. C22×Q16C2×D61semidirect
300. #473C2×D61semidirect
301. C2×#108C2×D61semidirect
306. C61C2×#2194semidirect
339. C2×Q16C22×D61semidirect
372. #108C22×D61semidirect
533. C2#21447788direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405672
C2×#168402032
C22×#145197202
#214477882
C2×#168395742
C2×#168395682
C2×#168395462
C2×C61×#4732
C2×#219461