Finite Group Databasebeta

← C2×#21447791 #29833945

Subgroups — C2×#21447791 #29833945

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×#16840564C211yesmaximal, characteristic
2C2×#16840202C211yesmaximal, characteristic, complemented
3C22×#14519722C211yesmaximal, characteristic, complemented
4C2×#16840038C211yesmaximal, characteristic, complemented
5#21447791C218yesmaximal, direct product factor
6C2×#16839574C211yesmaximal, characteristic, complemented
7C2×#16839545C211yesmaximal, characteristic, complemented
8C2×C61×#359C211yesmaximal, characteristic, complemented
9C2×#14519823—21no—
10#16840564—22no—
11#16840564—22no—
12#16840564—22no—
13#16840564C2214yes—
14C2×#14519810—21no—
15C2×#14519804—22no—
16C2×#14519802—21no—
17C2×#14519800—21no—
18C22×Dic244C2211yescharacteristic, complemented
19C22×D488C2211yescharacteristic
20C2×D8×D61—21no—
21C2×#14519783C2211yescharacteristic
22#16840202—22no—
23#16840202C2214yescomplemented
24C2×#14519723—21no—
25C2×#14519722—22no—
26C2×#14519722—22no—
27C2×#14519722C2214yescomplemented
28C2×#14519721—21no—
29C2×#14519717C2211yescharacteristic, complemented
30#16840038—22no—
31#16840038C2214yescomplemented
32C2×#14519695—21no—
33#16839574C2214yescomplemented
34#16839545C2214yescomplemented
35C2×#135×C61C2211yescharacteristic
36C22×C16×C61C2211yescharacteristic, complemented
37C2×#108×C61C2211yescharacteristic, complemented
38C61×#359C2214yescomplemented
39#14519823—24no—
40#14519823—24no—
41#14519823—42no—
42#14519823—42no—
43C2×#11758226—22no—
44C2×#11758222—41no—
45C2×#11758222D411yescharacteristic
46C22×Dic122—21no—
47C22×D244—21no—
48C22×D244—41no—
49C2×D4×D61—22no—
50C2×D4×D61—42no—
51#14519810—24no—
52#14519810—42no—
53#14519804—28no—
54#14519804—28no—
55#14519802—24no—
56#14519802—24no—
57#14519800—24no—
58#14519800—24no—
59C2×Dic244—21no—
60C2×Dic244—21no—
61C2×Dic244—21no—
62C2×Dic244—21no—
63C2×Dic244—21no—
64C2×Dic244—41no—
65C2×Dic244C2312yescomplemented
66C2×#11758190—41no—
67C2×#11758201—22no—
68C2×D488—21no—
69C2×D488—21no—
70C2×D488—21no—
71C2×D488D412yes—
72C2×D488D412yes—
73C2×D488C2312yes—
74C2×#11758199—22no—
75D8×D61—24no—
76D8×D61—24no—
77#14519783—21no—
78#14519783—21no—
79#14519783D412yes—
80#14519783C2312yes—
81C2×#11758194D411yescharacteristic
82C2×#11758189—21no—
83C2×C8×D61—21no—
84#14519723—24no—
85#14519722—28no—
86#14519721—24no—
87#14519717—21no—
88#14519717C2312yescomplemented
89C2×#11758185—21no—
90#14519695—24no—
91C2×#41×C61—21no—
92#135×C61—21no—
93#135×C61—21no—
94#135×C61D412yes—
95#135×C61C2312yes—
96C2×Q16×C61D411yescharacteristic
97C2×SD16×C61—21no—
98C2×D8×C61D411yescharacteristic
99C2×M16×C61—21no—
100C22×C8×C61C2311yescharacteristic
101C2×C16×C61—21no—
102C2×C16×C61—21no—
103C2×C16×C61C2312yescomplemented
104#108×C61—21no—
105#108×C61C2312yescomplemented
106C23×D61—42no—
107C23×D61—41no—
108#41×C61—22no—
109#41×C61—22no—
110#41×C61—41no—
111#41×C61—41no—
112C2×Q8×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—21no—
118C2×C22⋊D61—42no—
119C22×Dic61—41no—
120#11758226—28no—
121#11758226—44no—
122D4×D61—28no—
123D4×D61—44no—
124D4×D61—48no—
125D4×D61—48no—
126#11758222—21no—
127#11758222—21no—
128#11758222—44no—
129#11758222—44no—
130#11758222D812yes—
131#11758222C2×D412yes—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—44no—
136C2×D244—42no—
137C2×D244—41no—
138C2×D244—41no—
139C2×D244—41no—
140C2×D244—44no—
141C2×D244D811yescharacteristic
142C2×C4×D61—21no—
143C2×C4×D61—42no—
144C2×Dic122—22no—
145C2×Dic122—41no—
146C2×Dic122—41no—
147C2×Dic122—41no—
148C2×Dic122—41no—
149C2×Dic122—41no—
150C2×Dic122D811yescharacteristic
151Q16×C61—21no—
152Q16×C61C2×D412yes—
153SD16×C61—22no—
154SD16×C61—22no—
155D8×C61—21no—
156D8×C61C2×D412yes—
157M16×C61—22no—
158M16×C61—41no—
159C2×C8×C61—41no—
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2411yescharacteristic
166#11758201—28no—
167#11758199—28no—
168#11758194—21no—
169#11758194C2×D412yes—
170C2×#92418—21no—
171Dic244—22no—
172Dic244—22no—
173Dic244—44no—
174Dic244—41no—
175Dic244—41no—
176D488—22no—
177D488—22no—
178D488—22no—
179D488C2×D414yes—
180#11758190—44no—
181#11758189—22no—
182#11758189—22no—
183C8×D61—22no—
184C8×D61—22no—
185C16×C61—22no—
186#11758185—22no—
187C23×C61—41no—
188C23×C61AGL(1,ℤ/8)11yescharacteristic
189C22×D61—21no—
190C22×D61—48no—
191C22×D61—42no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—164no—
195C22×D61—162no—
196Q8×C61—22no—
197Q8×C61—41no—
198D4×C61—22no—
199D4×C61—42no—
200D4×C61—42no—
201D4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61#12011yescharacteristic
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61C2×D811yescharacteristic
208C2×C4×C61C2×D811yescharacteristic
209C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C22⋊D61—22no—
212C22⋊D61—22no—
213C22⋊D61—48no—
214C2×Dic61—21no—
215C2×Dic61—42no—
216C2×Dic61—81no—
217C2×Dic61—81no—
218D244—24no—
219D244—21no—
220D244—48no—
221D244—42no—
222D244—42no—
223D244—42no—
224D244C2×D812yes—
225C4×D61—22no—
226C4×D61—22no—
227C4×D61—48no—
228Dic122—21no—
229Dic122—42no—
230Dic122—42no—
231Dic122—81no—
232Dic122—81no—
233Dic122C2×D812yes—
234C8×C61—42no—
235C8×C61#12011yescharacteristic
236C8×C61#12011yescharacteristic
237C8×C61C22×D411yescharacteristic
238C8×C61C22×D411yescharacteristic
239#92418—22no—
240C2×#2194—611nomaximal, Sylow
241C22×C61—22no—
242C22×C61—42no—
243C22×C61—82no—
244C22×C61#44711yescharacteristic
245C22×C61#44711yescharacteristic
246C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
247C2×D61—22no—
248C2×D61—42no—
249C2×D61—44no—
250C2×D61—84no—
251C2×D61—168no—
252C2×D61—162no—
253C2×D61—162no—
254C4×C61—42no—
255C4×C61#44711yescharacteristic
256C4×C61#44711yescharacteristic
257C4×C61C2×#12011yescharacteristic
258C4×C61C22×D811yescharacteristic
259Dic61—22no—
260Dic61—82no—
261C2×#576—611no—
262C2×#510—611no—
263C22×SD32—611no—
264C2×#473—611no—
265#2194—618no—
266C2×#361—611no—
267C2×#359D6111yescharacteristic, complemented
268C2×#350—611no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—82no—
272C2×C61#219412yescomplemented
273C2×C61C2×#44711yescharacteristic
274D61—42no—
275D61—84no—
276C2×H(5,𝔽2)—1221no—
277#576—614no—
278#576—1222no—
279#576—1222no—
280#576—1222no—
281C2×#137—1221no—
282C2×AGL(1,ℤ/8)—1221no—
283C2×AGL(1,ℤ/8)—1222no—
284C2×#135—1221no—
285C2×#135C2×D6111yescharacteristic
286C22×Q16—611no—
287C22×D8—611no—
288C22×D8—1221no—
289C2×#131—611no—
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×C16C2×D6111yescharacteristic, complemented
299#473—614no—
300#473—1222no—
301C2×#108C2×D6111yescharacteristic, complemented
302C2×#101—1221no—
303#361—614no—
304#359C2×D6114yescomplemented
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—21no—
312C2×#41—611no—
313C2×#41—1222no—
314C2×#41—2441no—
315C22×Q8—1221no—
316C22×D4—1222no—
317C22×D4—1221no—
318C22×D4—2441no—
319C22×D4—2442no—
320#137—1224no—
321#137—2442no—
322AGL(1,ℤ/8)—1224no—
323AGL(1,ℤ/8)—1228no—
324AGL(1,ℤ/8)—1228no—
325AGL(1,ℤ/8)—1224no—
326#135—21no—
327#135—21no—
328#135—1224no—
329#135—1224no—
330#135D24412yes—
331#135C22×D6112yes—
332C2×Q16—612no—
333C2×Q16—1221no—
334C2×Q16—1221no—
335C2×Q16—1221no—
336C2×Q16—1221no—
337C2×Q16—1221no—
338C2×Q16—2441no—
339C2×Q16D24411yescharacteristic
340C2×SD16—21no—
341C2×SD16—1222no—
342C2×SD16—2441no—
343C2×D8—612no—
344C2×D8—612no—
345C2×D8—612no—
346C2×D8—1224no—
347C2×D8—1222no—
348C2×D8—1224no—
349C2×D8—1221no—
350C2×D8—1221no—
351C2×D8—1221no—
352C2×D8D24411yescharacteristic
353#131—612no—
354#131—612no—
355#131—1221no—
356#131—1221no—
357C2×M16—21no—
358C2×M16—611no—
359C2×M16—1221no—
360C22×C8—1221no—
361C22×C8C22×D6111yescharacteristic
362Q32—1224no—
363SD32—1228no—
364SD32—1224no—
365M32—612no—
366M32—1221no—
367C2×C16—21no—
368C2×C16—21no—
369C2×C16—1221no—
370C2×C16C22×D6112yescomplemented
371#108—21no—
372#108C22×D6112yescomplemented
373#101—1224no—
374C24—2442no—
375C24—2441no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—612no—
381#41—612no—
382#41—1221no—
383#41—1221no—
384#41—1228no—
385#41—2444no—
386#41—2444no—
387#41—2444no—
388C2×Q8—21no—
389C2×Q8—611no—
390C2×Q8—1222no—
391C2×Q8—2441no—
392C2×Q8—2441no—
393C2×Q8—2441no—
394C2×Q8—2441no—
395C2×Q8—2441no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—611no—
399C2×D4—1228no—
400C2×D4—1221no—
401C2×D4—1222no—
402C2×D4—1222no—
403C2×D4—1222no—
404C2×D4—2444no—
405C2×D4—2444no—
406C2×D4—2442no—
407C2×D4—2444no—
408C2×D4—2442no—
409C2×D4—2448no—
410C2×D4—2448no—
411C2×D4—2441no—
412C2×D4—2441no—
413C2×D4—2441no—
414C22×C4—41no—
415C22×C4—1221no—
416C22×C4—2442no—
417C22×C4—2441no—
418C22×C4D4×D6111yescharacteristic
419Q16—21no—
420Q16—1222no—
421Q16—1222no—
422Q16—2444no—
423Q16—2441no—
424Q16—2441no—
425Q16C2×D24412yes—
426SD16—22no—
427SD16—22no—
428SD16—1228no—
429SD16—2444no—
430D8—21no—
431D8—614no—
432D8—1228no—
433D8—1222no—
434D8—1222no—
435D8—1222no—
436D8C2×D24412yes—
437M16—22no—
438M16—41no—
439M16—612no—
440M16—1221no—
441M16—1222no—
442M16—1222no—
443C2×C8—41no—
444C2×C8—1221no—
445C2×C8—1222no—
446C2×C8—1222no—
447C2×C8C2×D24411yescharacteristic
448C2×C8C2×D24411yescharacteristic
449C2×C8D4×D6111yescharacteristic
450C2×C8D4×D6111yescharacteristic
451C2×C8D4×D6111yescharacteristic
452C2×C8C23×D6111yescharacteristic
453C16—22no—
454C16—1222no—
455C23—41no—
456C23—1221no—
457C23—9762no—
458C23—9764no—
459C23—2448no—
460C23—2442no—
461C23—2442no—
462C23—2442no—
463C23#1451980411yescharacteristic
464Q8—22no—
465Q8—41no—
466Q8—612no—
467Q8—1221no—
468Q8—4881no—
469Q8—4881no—
470Q8—2442no—
471Q8—2442no—
472D4—22no—
473D4—42no—
474D4—42no—
475D4—41no—
476D4—612no—
477D4—1222no—
478D4—1222no—
479D4—1224no—
480D4—1221no—
481D4—2448no—
482D4—2448no—
483D4—2442no—
484D4—2442no—
485D4—2442no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—1221no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—4881no—
493C2×C4—4881no—
494C2×C4—2448no—
495C2×C4—2442no—
496C2×C4#1451974711yescharacteristic
497C2×C4#1451974711yescharacteristic
498C2×C4D8×D6111yescharacteristic
499C2×C4D8×D6111yescharacteristic
500C2×C4#1451980411yescharacteristic
501C2×C4C2×D4×D6111yescharacteristic
502C8—42no—
503C8—1222no—
504C8#1451974711yescharacteristic
505C8#1451974711yescharacteristic
506C8C2×D4×D6111yescharacteristic
507C8C22×D24411yescharacteristic
508C22—22no—
509C22—42no—
510C22—82no—
511C22—1222no—
512C22—9762no—
513C22—9762no—
514C22—9768no—
515C22—4884no—
516C22—2444no—
517C22—2442no—
518C22#1683989711yescharacteristic
519C22#1683989711yescharacteristic
520C22C2×#1451980411yescharacteristic
521C4—42no—
522C4—1222no—
523C4—4882no—
524C4#1683989711yescharacteristic
525C4#1683989711yescharacteristic
526C4C2×#1451974711yescharacteristic
527C4C2×D8×D6111yescharacteristic
528C2—21no—
529C2—21no—
530C2—82no—
531C2—4884no—
532C2—2442no—
533C2#2144779112yesdirect product factor
534C2C2×#1683989711yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#359C2
socleC22×C61#447
prime radicalC2×#16840564C2
hypercenterC2×#359D61
hypocenterC61C2×#2194
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#16840202C2semidirect
3. C22×#14519722C2semidirect
4. C2×#16840038C2semidirect
5. #21447791C2direct (N × H)
6. C2×#16839574C2semidirect
7. C2×#16839545C2semidirect
8. C2×C61×#359C2semidirect
18. C22×Dic244C22semidirect
23. #16840202C22semidirect
27. C2×#14519722C22semidirect
29. C2×#14519717C22semidirect
31. #16840038C22semidirect
33. #16839574C22semidirect
34. #16839545C22semidirect
36. C22×C16×C61C22semidirect
37. C2×#108×C61C22semidirect
38. C61×#359C22semidirect
65. C2×Dic244C23semidirect
88. #14519717C23semidirect
103. C2×C16×C61C23semidirect
105. #108×C61C23semidirect
267. C2×#359D61semidirect
272. C2×C61#2194semidirect
298. C22×C16C2×D61semidirect
301. C2×#108C2×D61semidirect
304. #359C2×D61semidirect
306. C61C2×#2194semidirect
370. C2×C16C22×D61semidirect
372. #108C22×D61semidirect
533. C2#21447791direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405642
C2×#168402022
C22×#145197222
C2×#168400382
#214477912
C2×#168395742
C2×#168395452
C2×C61×#3592
C2×#219461