Finite Group Databasebeta

← C2×#21459445 #30587117

Subgroups — C2×#21459445 #30587117

Order 15616.

8418 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459445C2132yesmaximal, direct product factor
2C2×Q8×Dic122C211yesmaximal, characteristic, complemented
3C2×#16840477C213yesmaximal, complemented
4C2×#16840475C216yesmaximal, complemented
5C2×#16840434C211yesmaximal, characteristic, complemented
6C2×#16840433C213yesmaximal, complemented
7C2×#16840431C212yesmaximal, complemented
8C2×#16840312C213yesmaximal, complemented
9C2×#16840309C216yesmaximal, complemented
10C2×C4×#11758226C212yesmaximal, complemented
11C2×C4×#11758222C213yesmaximal, complemented
12C2×C4×#41×C61C211yesmaximal, characteristic, complemented
13C22×#11758226C2212yes—
14C22×#11758222C2213yes—
15C22×#11758222C2216yes—
16Q8×Dic122C22116yescomplemented
17#16840477C22148yescomplemented
18#16840475C22196yescomplemented
19#16840434C22116yescomplemented
20#16840433C22148yescomplemented
21#16840431C22132yescomplemented
22#16840312C22148yescomplemented
23#16840309C22196yescomplemented
24C2×#14519777C2213yes—
25C2×#14519776C2216yes—
26C2×#14519774C2213yes—
27C2×#14519773C2216yes—
28C2×#14519765C2216yes—
29C2×#14519763C22112yes—
30C2×#14519752C2216yes—
31C2×#14519751C2216yes—
32C2×#14519751C2216yes—
33C2×#14519750C22112yes—
34C2×#14519748C2216yes—
35C4×#11758226C22132yescomplemented
36C4×#11758222C22148yescomplemented
37C2×Q8×Dic61C2212yes—
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×Dic122C2213yes—
40C2×C4×D244C2213yes—
41C2×C4×D244C2213yes—
42C2×C4×D244C2216yes—
43C2×#14519739C2216yes—
44C2×C4×C22⋊D61C2216yes—
45C2×C4×C22⋊D61C2216yes—
46C2×#14519736C2213yes—
47C2×#14519735C2216yes—
48C2×#14519734C2216yes—
49C2×C42×D61C2216yes—
50C22×#41×C61C2211yescharacteristic
51C4×#41×C61C22116yescomplemented
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2213yes—
55C2×C4×D4×C61C2213yes—
56C2×#117×C61C2213yes—
57C22×C42×C61C2213yes—
58C2×#11758226—216no—
59C2×#11758226C23116yes—
60C2×#11758222—224no—
61C2×#11758222—424no—
62C2×#11758222C23124yes—
63C2×#11758222C23148yes—
64C22×Dic122C2316yes—
65C22×Dic122C2311yescharacteristic
66C22×D244C2316yes—
67C22×D244C2313yes—
68C22×D244C2316yes—
69C22×C22⋊D61C2316yes—
70C22×C22⋊D61C23112yes—
71C22×C4×D61C2316yes—
72C22×C4×D61C2316yes—
73C22×C4×D61C2316yes—
74#14519777C23124yes—
75#14519776C23148yes—
76#14519774C23124yes—
77#14519773C23148yes—
78#14519765C23148yes—
79#14519763C23196yes—
80#14519752C23148yes—
81#14519751C23148yes—
82#14519751C23148yes—
83#14519750C23196yes—
84#14519748C23148yes—
85Q8×Dic61C23116yes—
86C4×Dic122C2318yes—
87C4×Dic122C23124yes—
88C4×D244C23124yes—
89C4×D244C23124yes—
90C4×D244C23148yes—
91#14519739C23148yes—
92C4×C22⋊D61C23148yes—
93C4×C22⋊D61C23148yes—
94#14519736C23124yes—
95#14519735C23148yes—
96#14519734C23148yes—
97C2×C4⋊Dic61C2316yes—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2313yes—
100C2×#11758196C2312yes—
101C2×#11758196C2316yes—
102C2×C22⋊Dic61C2316yes—
103C2×#11758198C2316yes—
104C2×#11758198C2316yes—
105C2×#11758198C23112yes—
106C2×C4×Dic61C2312yes—
107C2×C4×Dic61C2316yes—
108C2×C4×Dic61C2316yes—
109C42×D61C23148yes—
110C2×#41×C61—28no—
111C2×#41×C61C2318yes—
112C22×Q8×C61C2311yescharacteristic
113C22×D4×C61C2313yes—
114C23×C4×C61C2313yes—
115C23×C4×C61C2313yes—
116C23×C4×C61C2313yes—
117C4×Q8×C61C2318yes—
118C4×Q8×C61C2318yes—
119C4×D4×C61C23124yes—
120C4×D4×C61C23124yes—
121#117×C61C23124yes—
122C2×C4⋊C4×C61C2313yes—
123C2×C4⋊C4×C61C2313yes—
124C2×C22⋊C4×C61C2316yes—
125C2×C42×C61C2313yes—
126C2×C42×C61C2313yes—
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2313yes—
129C2×C42×C61C23124yes—
130C24×C61C2413yes—
131C23×D61C2416yes—
132#41×C61—232no—
133C2×Q8×C61#4118yescomplemented
134C2×Q8×C61C2414yes—
135C2×D4×C61—212no—
136C2×D4×C61C24112yes—
137C22×C4×C61—212no—
138C22×C4×C61—212no—
139C22×C4×C61—212no—
140C22×C4×C61C2413yes—
141C22×C4×C61C2413yes—
142C22×C4×C61C24112yes—
143C22×C4×C61C24112yes—
144C22×C4×C61C2411yescharacteristic
145C22×C4×C61C24112yes—
146C22×C4×C61C2413yes—
147C22×C4×C61C2411yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C2×C22⋊D61—224no—
150C2×C22⋊D61—424no—
151C2×C22⋊D61C24124yes—
152C2×C22⋊D61C24148yes—
153C22×Dic61C2412yes—
154C22×Dic61C2416yes—
155C22×Dic61C2412yes—
156#11758226—264no—
157#11758222—296no—
158#11758222—496no—
159C2×D244—212no—
160C2×D244—224no—
161C2×D244—412no—
162C2×D244C24112yes—
163C2×D244C24124yes—
164C2×D244C24124yes—
165C2×C4×D61—224no—
166C2×C4×D61—224no—
167C2×C4×D61—224no—
168C2×C4×D61C24124yes—
169C2×C4×D61C24124yes—
170C2×C4×D61C24124yes—
171C2×Dic122—412no—
172C2×Dic122#4118yescomplemented
173C2×Dic122C24124yes—
174C2×Dic122C2414yes—
175C4⋊C4×C61C24112yes—
176C4⋊C4×C61C24112yes—
177C22⋊C4×C61C24124yes—
178C42×C61C2414yes—
179C42×C61C24112yes—
180C42×C61C24112yes—
181C42×C61C24112yes—
182C22⋊Dic61C24124yes—
183#11758198C24124yes—
184#11758198C24124yes—
185#11758198C24148yes—
186C4⋊Dic61C24124yes—
187C4⋊Dic61C2414yes—
188C4⋊Dic61C24112yes—
189#11758196C2418yes—
190#11758196C24124yes—
191C4×Dic61C2418yes—
192C4×Dic61C24124yes—
193C4×Dic61C24124yes—
194C23×C61—26no—
195C23×C61—26no—
196C23×C61—26no—
197C23×C61C2516yes—
198C23×C61C2511yescharacteristic
199C22×D61—212no—
200C22×D61—212no—
201C22×D61—212no—
202C22×D61C25112yes—
203Q8×C61C2×#41116yescomplemented
204D4×C61—224no—
205C2×C4×C61—26no—
206C2×C4×C61—22no—
207C2×C4×C61—26no—
208C2×C4×C61—224no—
209C2×C4×C61—224no—
210C2×C4×C61—224no—
211C2×C4×C61C2×#4114yes—
212C2×C4×C61C2×#41112yes—
213C2×C4×C61H(5,𝔽2)14yes—
214C2×C4×C61C2516yes—
215C2×C4×C61C2512yes—
216C2×C4×C61C2516yes—
217C2×C4×C61C2516yes—
218C2×C4×C61C2512yes—
219C2×C4×C61C2512yes—
220C22⋊D61—248no—
221C22⋊D61—448no—
222C2×Dic61—24no—
223C2×Dic61—212no—
224C2×Dic61C2×#4118yes—
225C2×Dic61C2514yes—
226C2×Dic61C25112yes—
227C2×Dic61C2514yes—
228D244—224no—
229D244—248no—
230D244—424no—
231C4×D61—248no—
232C4×D61—248no—
233C4×D61—248no—
234Dic122—424no—
235Dic122C2×#41116yescomplemented
236C2×#3483—611nomaximal, Sylow
237C22×C61—26no—
238C22×C61—26no—
239C22×C61—26no—
240C22×C61—412no—
241C22×C61C22×#4112yes—
242C22×C61C22×#4112yes—
243C22×C61C2×H(5,𝔽2)12yes—
244C22×C61C2611yescharacteristic
245C2×D61—212no—
246C2×D61—212no—
247C2×D61—212no—
248C2×D61—424no—
249C4×C61—26no—
250C4×C61—22no—
251C4×C61—26no—
252C4×C61C22×#4114yes—
253C4×C61C22×#41112yes—
254C4×C61C2×H(5,𝔽2)14yes—
255Dic61—24no—
256Dic61—212no—
257Dic61C22×#4118yes—
258#3483—6132no—
259C2×Q82—611no—
260C2×#555—613no—
261C2×#555—616no—
262C2×#550—612no—
263C2×#550—611no—
264C2×#550—613no—
265C2×#532—613no—
266C2×#532—616no—
267C2×C4×#41—613no—
268C2×C4×#41—612no—
269C2×C4×#41D6111yescharacteristic, complemented
270C2×C61—46no—
271C2×C61#348314yescomplemented
272C2×C61C23×#4111yescharacteristic
273C2×C61C23×#4111yescharacteristic
274C2×C61C22×H(5,𝔽2)11yescharacteristic
275D61—412no—
276C22×#41—612no—
277C22×#41—613no—
278C22×#41—616no—
279C22×#41C2×D6111yescharacteristic
280Q82—6116no—
281#555—6148no—
282#555—6196no—
283#550—6132no—
284#550—6116no—
285#550—6148no—
286#532—6196no—
287#532—6148no—
288C2×C4⋊Q8—616no—
289C2×C4⋊Q8—613no—
290C2×#127—616no—
291C2×#127—613no—
292C2×#124—6112no—
293C2×#124—616no—
294C2×#121—616no—
295C2×#121—616no—
296C2×#121—616no—
297C2×#121—616no—
298C2×#121—6112no—
299C4×#41—6132no—
300C4×#41—6148no—
301C4×#41C2×D61116yescomplemented
302C2×C4×Q8—612no—
303C2×C4×Q8—611no—
304C2×C4×Q8—613no—
305C2×C4×Q8C2×D6111yescharacteristic
306C2×C4×Q8C2×D6111yescharacteristic
307C2×C4×D4—616no—
308C2×C4×D4—616no—
309C2×C4×D4—616no—
310C2×C4×D4—613no—
311C2×C4×D4—616no—
312C2×C4×D4—613no—
313C2×C4×D4C2×D6113yes—
314C2×C4×D4C2×D6113yes—
315C2×#117—613no—
316C2×#117—616no—
317C2×#117—616no—
318C2×#117C2×D6113yes—
319C22×C42—616no—
320C22×C42C2×D6113yes—
321C61C2×#348311yescharacteristic, complemented, Sylow
322C2×#41—28no—
323C2×#41—6116no—
324C2×#41—6124no—
325C2×#41—6148no—
326C2×#41—12224no—
327C2×#41—12216no—
328C2×#41—24424no—
329C2×#41C22×D6118yes—
330C22×Q8—611no—
331C22×Q8—616no—
332C22×Q8C22×D6111yescharacteristic
333C22×D4—616no—
334C22×D4—6112no—
335C22×D4—613no—
336C22×D4—616no—
337C22×D4—616no—
338C22×D4C22×D6113yes—
339C23×C4—616no—
340C23×C4—616no—
341C23×C4—616no—
342C23×C4C22×D6113yes—
343C23×C4C22×D6113yes—
344C23×C4C22×D6113yes—
345C4⋊Q8—6148no—
346C4⋊Q8—6124no—
347#127—6148no—
348#127—6124no—
349#124—6196no—
350#124—6148no—
351#121—6148no—
352#121—6148no—
353#121—6148no—
354#121—6148no—
355#121—6196no—
356C4×Q8—6116no—
357C4×Q8—618no—
358C4×Q8—6124no—
359C4×Q8C22×D6118yes—
360C4×Q8C22×D6118yes—
361C4×D4—6148no—
362C4×D4—6148no—
363C4×D4—6148no—
364C4×D4—6148no—
365C4×D4—6124no—
366C4×D4—6124no—
367C4×D4C22×D61124yes—
368C4×D4C22×D61124yes—
369#117—6124no—
370#117—6148no—
371#117—6148no—
372#117C22×D61124yes—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—616no—
376C2×C4⋊C4—613no—
377C2×C4⋊C4—616no—
378C2×C4⋊C4C22×D6113yes—
379C2×C4⋊C4C22×D6113yes—
380C2×C22⋊C4—616no—
381C2×C22⋊C4—616no—
382C2×C22⋊C4—6112no—
383C2×C22⋊C4—616no—
384C2×C22⋊C4C22×D6116yes—
385C2×C42—616no—
386C2×C42—616no—
387C2×C42—612no—
388C2×C42—6148no—
389C2×C42C22×D6113yes—
390C2×C42C22×D6113yes—
391C2×C42C22×D61124yes—
392C2×C42C22×D6111yescharacteristic
393C2×C42C22×D6113yes—
394C24—616no—
395C24C23×D6113yes—
396#41—232no—
397#41—12296no—
398#41—12264no—
399#41—24496no—
400C2×Q8—618no—
401C2×Q8—614no—
402C2×Q8—6124no—
403C2×Q8—24412no—
404C2×Q8#1175822218yescomplemented
405C2×Q8C23×D6114yes—
406C2×D4—212no—
407C2×D4—6124no—
408C2×D4—6148no—
409C2×D4—6112no—
410C2×D4—6124no—
411C2×D4—6124no—
412C2×D4—12224no—
413C2×D4—12212no—
414C2×D4—12224no—
415C2×D4—24412no—
416C2×D4—24424no—
417C2×D4C23×D61112yes—
418C22×C4—212no—
419C22×C4—212no—
420C22×C4—212no—
421C22×C4—612no—
422C22×C4—612no—
423C22×C4—616no—
424C22×C4—6124no—
425C22×C4—6124no—
426C22×C4—6124no—
427C22×C4—12224no—
428C22×C4—12224no—
429C22×C4—12224no—
430C22×C4C23×D6113yes—
431C22×C4C23×D6111yescharacteristic
432C22×C4C23×D6113yes—
433C22×C4C23×D61112yes—
434C22×C4C23×D61112yes—
435C22×C4C23×D61112yes—
436C22×C4C23×D6111yescharacteristic
437C22×C4C23×D6113yes—
438C22×C4C23×D6111yescharacteristic
439C4⋊C4—618no—
440C4⋊C4—6124no—
441C4⋊C4—614no—
442C4⋊C4—6112no—
443C4⋊C4—6124no—
444C4⋊C4C23×D61112yes—
445C4⋊C4C23×D61112yes—
446C22⋊C4—6124no—
447C22⋊C4—6124no—
448C22⋊C4—6148no—
449C22⋊C4—6124no—
450C22⋊C4C23×D61124yes—
451C42—618no—
452C42—6124no—
453C42—6124no—
454C42C23×D61112yes—
455C42C23×D6114yes—
456C42C23×D61112yes—
457C42C23×D61112yes—
458C23—26no—
459C23—26no—
460C23—26no—
461C23—6112no—
462C23—12212no—
463C23—12212no—
464C23—12212no—
465C23C24×D6116yes—
466C23C24×D6111yescharacteristic
467Q8—6116no—
468Q8—24424no—
469Q8C2×#11758222116yescomplemented
470D4—224no—
471D4—12248no—
472D4—12224no—
473D4—12248no—
474D4—24424no—
475D4—24448no—
476C2×C4—26no—
477C2×C4—22no—
478C2×C4—26no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—618no—
483C2×C4—614no—
484C2×C4—614no—
485C2×C4—6112no—
486C2×C4—12248no—
487C2×C4—1224no—
488C2×C4—12212no—
489C2×C4—12248no—
490C2×C4—12248no—
491C2×C4#41×D6114yes—
492C2×C4C2×#11758222112yes—
493C2×C4#1451982314yes—
494C2×C4C24×D6116yes—
495C2×C4C24×D6112yes—
496C2×C4C24×D6116yes—
497C2×C4C24×D6112yes—
498C2×C4C24×D6116yes—
499C2×C4C24×D6112yes—
500C22—26no—
501C22—26no—
502C22—26no—
503C22—412no—
504C22—12212no—
505C22—12212no—
506C22—12212no—
507C22—24424no—
508C22C2×#41×D6112yes—
509C22C22×#1175822212yes—
510C22C2×#1451982312yes—
511C22C25×D6111yescharacteristic
512C4—26no—
513C4—22no—
514C4—26no—
515C4—618no—
516C4—1224no—
517C4—12212no—
518C4C2×#41×D6114yes—
519C4C22×#11758222112yes—
520C4C2×#1451982314yes—
521C2—46no—
522C2—24412no—
523C2#2145944514yesdirect product factor
524C2C22×#41×D6111yescharacteristic
525C2C23×#1175822211yescharacteristic
526C2C22×#1451982311yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C4×#41×C61C2
socleC23×C61C25
hypercenterC2×C4×#41D61
hypocenterC61C2×#3483
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #21459445C2direct (N × H)
2. C2×Q8×Dic122C2semidirect
3. C2×#16840477C2semidirect
4. C2×#16840475C2semidirect
5. C2×#16840434C2semidirect
6. C2×#16840433C2semidirect
7. C2×#16840431C2semidirect
8. C2×#16840312C2semidirect
9. C2×#16840309C2semidirect
10. C2×C4×#11758226C2semidirect
11. C2×C4×#11758222C2semidirect
12. C2×C4×#41×C61C2semidirect
16. Q8×Dic122C22semidirect
17. #16840477C22semidirect
18. #16840475C22semidirect
19. #16840434C22semidirect
20. #16840433C22semidirect
21. #16840431C22semidirect
22. #16840312C22semidirect
23. #16840309C22semidirect
35. C4×#11758226C22semidirect
36. C4×#11758222C22semidirect
51. C4×#41×C61C22semidirect
133. C2×Q8×C61#41semidirect
172. C2×Dic122#41semidirect
203. Q8×C61C2×#41semidirect
235. Dic122C2×#41semidirect
269. C2×C4×#41D61semidirect
271. C2×C61#3483semidirect
301. C4×#41C2×D61semidirect
321. C61C2×#3483semidirect
404. C2×Q8#11758222semidirect
469. Q8C2×#11758222semidirect
523. C2#21459445direct (N × H)

Maximal subgroups

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

subgroupindex
#214594452
C2×Q8×Dic1222
C2×#168404772
C2×#168404752
C2×#168404342
C2×#168404332
C2×#168404312
C2×#168403122
C2×#168403092
C2×C4×#117582262
C2×C4×#117582222
C2×C4×#41×C612
C2×#348361