Finite Group Databasebeta

← C2×#21459441 #30587111

Subgroups — C2×#21459441 #30587111

Order 15616.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459441C2132yesmaximal, direct product factor
2C2×#16840491C211yesmaximal, characteristic, complemented
3C2×#16840482C213yesmaximal, complemented
4C2×#16840451C216yesmaximal, complemented
5C2×Q8×D244C211yesmaximal, characteristic, complemented
6C2×#16840419C212yesmaximal, complemented
7C2×#16840417C213yesmaximal, complemented
8C2×#16840319C213yesmaximal, complemented
9C2×#16840294C216yesmaximal, complemented
10C2×C4×#11758222C213yesmaximal, complemented
11C2×C4×Q8×D61C212yesmaximal, complemented
12C2×C4×#41×C61C211yesmaximal, characteristic, complemented
13C22×#11758222C2213yes—
14C22×Q8×D61C2212yes—
15#16840491C22116yescomplemented
16#16840482C22148yescomplemented
17#16840451C22196yescomplemented
18Q8×D244C22116yescomplemented
19#16840419C22132yescomplemented
20#16840417C22148yescomplemented
21#16840319C22148yescomplemented
22C2×#14519777C2213yes—
23C2×#14519777C2213yes—
24#16840294C22196yescomplemented
25C2×#14519770C22112yes—
26C2×#14519769C2216yes—
27C2×#14519768C2216yes—
28C2×#14519764C2216yes—
29C2×#14519759C22112yes—
30C2×#14519757C2216yes—
31C2×#14519756C2216yes—
32C2×#14519756C2216yes—
33C2×#14519748C2216yes—
34C4×#11758222C22148yescomplemented
35C2×Q8×Dic61C2212yes—
36C2×C4×Dic122C2216yes—
37C2×C4×Dic122C2213yes—
38C2×C4×Dic122C2213yes—
39C2×#14519742C2216yes—
40C4×Q8×D61C22132yescomplemented
41C2×C4×D244C2211yescharacteristic
42C2×C4×D244C2213yes—
43C2×C4×C22⋊D61C2216yes—
44C2×C4×C22⋊D61C2216yes—
45C2×#14519736C2213yes—
46C2×#14519736C2216yes—
47C2×#14519734C2216yes—
48C2×C4⋊C4×D61C2216yes—
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×#11758222—224no—
59C2×#11758222C23124yes—
60C22×Dic122C2316yes—
61C22×Dic122C2313yes—
62C2×Q8×D61—216no—
63C2×Q8×D61C23116yes—
64C22×D244C2311yescharacteristic
65C22×C22⋊D61C2316yes—
66C22×C4×D61C2312yes—
67C22×C4×D61C2316yes—
68C22×C4×D61C2316yes—
69#14519777C23124yes—
70#14519777C23124yes—
71#14519770C23196yes—
72#14519769C23148yes—
73#14519768C23148yes—
74#14519764C23148yes—
75#14519759C23196yes—
76#14519757C23148yes—
77#14519756C23148yes—
78#14519756C23148yes—
79#14519748C23148yes—
80Q8×Dic61C23116yes—
81C4×Dic122C23148yes—
82C4×Dic122C23124yes—
83C4×Dic122C23124yes—
84#14519742C23148yes—
85C4×D244C2318yes—
86C4×D244C23124yes—
87C4×C22⋊D61C23148yes—
88C4×C22⋊D61C23148yes—
89#14519736C23124yes—
90#14519736C23148yes—
91#14519734C23148yes—
92C2×C4⋊Dic61C2316yes—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2313yes—
95C2×C4⋊Dic61C2316yes—
96C2×C4⋊Dic61C2316yes—
97C2×#11758196C23112yes—
98C2×#11758196C2316yes—
99C2×#11758196C2316yes—
100C4⋊C4×D61C23148yes—
101C2×C22⋊Dic61C2316yes—
102C2×C22⋊Dic61C23112yes—
103C2×#11758198C2312yes—
104C2×#11758198C2316yes—
105C2×C4×Dic61C2316yes—
106C2×C4×Dic61C2316yes—
107C2×C4×Dic61C2316yes—
108C42×D61C23148yes—
109C2×#41×C61—28no—
110C2×#41×C61C2318yes—
111C22×Q8×C61C2311yescharacteristic
112C22×D4×C61C2313yes—
113C23×C4×C61C2313yes—
114C23×C4×C61C2313yes—
115C23×C4×C61C2313yes—
116C4×Q8×C61C2318yes—
117C4×Q8×C61C2318yes—
118C4×D4×C61C23124yes—
119C4×D4×C61C23124yes—
120#117×C61C23124yes—
121C2×C4⋊C4×C61C2313yes—
122C2×C4⋊C4×C61C2313yes—
123C2×C22⋊C4×C61C2316yes—
124C2×C42×C61C2313yes—
125C2×C42×C61C2313yes—
126C2×C42×C61C2311yescharacteristic
127C2×C42×C61C2313yes—
128C2×C42×C61C23124yes—
129C24×C61C2413yes—
130C23×D61C2412yes—
131#41×C61—232no—
132C2×Q8×C61#4118yescomplemented
133C2×Q8×C61C2414yes—
134C2×D4×C61—212no—
135C2×D4×C61C24112yes—
136C22×C4×C61—212no—
137C22×C4×C61—212no—
138C22×C4×C61—212no—
139C22×C4×C61C2413yes—
140C22×C4×C61C24112yes—
141C22×C4×C61C2411yescharacteristic
142C22×C4×C61C2413yes—
143C22×C4×C61C24112yes—
144C22×C4×C61C24112yes—
145C22×C4×C61C2413yes—
146C22×C4×C61C2411yescharacteristic
147C22×C4×C61C2411yescharacteristic
148C2×C22⋊D61—224no—
149C2×C22⋊D61C24124yes—
150C22×Dic61C2416yes—
151C22×Dic61C2416yes—
152C22×Dic61C2412yes—
153Q8×D61—264no—
154#11758222—296no—
155C2×D244#4118yescomplemented
156C2×D244C2414yes—
157C2×C4×D61—224no—
158C2×C4×D61—224no—
159C2×C4×D61—28no—
160C2×C4×D61C24124yes—
161C2×C4×D61C24124yes—
162C2×C4×D61C2418yes—
163C2×Dic122—224no—
164C2×Dic122—212no—
165C2×Dic122C24124yes—
166C2×Dic122C24112yes—
167C4⋊C4×C61C24112yes—
168C4⋊C4×C61C24112yes—
169C22⋊C4×C61C24124yes—
170C42×C61C2414yes—
171C42×C61C24112yes—
172C42×C61C24112yes—
173C42×C61C24112yes—
174C22⋊Dic61C24124yes—
175C22⋊Dic61C24148yes—
176#11758198C2418yes—
177#11758198C24124yes—
178C4⋊Dic61C24124yes—
179C4⋊Dic61C2414yes—
180C4⋊Dic61C24112yes—
181C4⋊Dic61C24124yes—
182C4⋊Dic61C24124yes—
183#11758196C24148yes—
184#11758196C24124yes—
185#11758196C24124yes—
186C4×Dic61C24124yes—
187C4×Dic61C24124yes—
188C4×Dic61C24124yes—
189C23×C61—26no—
190C23×C61—26no—
191C23×C61—26no—
192C23×C61C2516yes—
193C23×C61C2511yescharacteristic
194C22×D61—24no—
195C22×D61—24no—
196C22×D61C2×#4118yes—
197C22×D61C2514yes—
198Q8×C61C2×#41116yescomplemented
199D4×C61—224no—
200C2×C4×C61—26no—
201C2×C4×C61—22no—
202C2×C4×C61—26no—
203C2×C4×C61—224no—
204C2×C4×C61—224no—
205C2×C4×C61—224no—
206C2×C4×C61C2×#4114yes—
207C2×C4×C61C2×#41112yes—
208C2×C4×C612−1+414yes—
209C2×C4×C61C2516yes—
210C2×C4×C61C2512yes—
211C2×C4×C61C2516yes—
212C2×C4×C61C2516yes—
213C2×C4×C61C2512yes—
214C2×C4×C61C2512yes—
215C22⋊D61—248no—
216C2×Dic61—212no—
217C2×Dic61—212no—
218C2×Dic61—24no—
219C2×Dic61C2514yes—
220C2×Dic61C25112yes—
221C2×Dic61C25112yes—
222D244C2×#41116yescomplemented
223C4×D61—248no—
224C4×D61—248no—
225C4×D61—216no—
226Dic122—224no—
227Dic122—248no—
228C2×#3482—611nomaximal, Sylow
229C22×C61—26no—
230C22×C61—26no—
231C22×C61—26no—
232C22×C61—412no—
233C22×C61C22×#4112yes—
234C22×C61C22×#4112yes—
235C22×C61C2×2−1+412yes—
236C22×C61C2611yescharacteristic
237C2×D61—24no—
238C2×D61—24no—
239C2×D61—216no—
240C2×D61C22×#4118yes—
241C4×C61—26no—
242C4×C61—22no—
243C4×C61—26no—
244C4×C61C22×#4114yes—
245C4×C61C22×#41112yes—
246C4×C61C2×2−1+414yes—
247Dic61—212no—
248Dic61—212no—
249Dic61—24no—
250#3482—6132no—
251C2×#557—611no—
252C2×#556—613no—
253C2×#552—616no—
254C2×D4×Q8—611no—
255C2×#548—612no—
256C2×#547—613no—
257C2×#533—613no—
258C2×#529—616no—
259C2×C4×#41—613no—
260C2×C4×#41D6111yescharacteristic, complemented
261C22×C4×Q8—612no—
262C2×C61—46no—
263C2×C61#348214yescomplemented
264C2×C61C23×#4111yescharacteristic
265C2×C61C23×#4111yescharacteristic
266C2×C61C22×2−1+411yescharacteristic
267D61—28no—
268C22×#41—613no—
269C22×#41C2×D6111yescharacteristic
270C23×Q8—612no—
271#557—6116no—
272#556—6148no—
273#552—6196no—
274D4×Q8—6116no—
275#548—6132no—
276#547—6148no—
277#533—6148no—
278C2×C4⋊Q8—613no—
279C2×C4⋊Q8—613no—
280#529—6196no—
281C2×#126—6112no—
282C2×#125—616no—
283C2×#125—616no—
284C2×#124—616no—
285C2×#123—6112no—
286C2×C22⋊Q8—616no—
287C2×C22⋊Q8—616no—
288C2×C22⋊Q8—616no—
289C2×#121—616no—
290C4×#41—6148no—
291C4×#41C2×D61116yescomplemented
292C2×C4×Q8—612no—
293C2×C4×Q8—6132no—
294C2×C4×Q8—616no—
295C2×C4×Q8—616no—
296C2×C4×Q8—613no—
297C2×C4×Q8—613no—
298C2×C4×Q8C2×D6111yescharacteristic
299C2×C4×Q8C2×D6111yescharacteristic
300C2×C4×D4—616no—
301C2×C4×D4—616no—
302C2×C4×D4—611no—
303C2×C4×D4—613no—
304C2×C4×D4C2×D6113yes—
305C2×C4×D4C2×D6113yes—
306C2×#117—613no—
307C2×#117—616no—
308C2×#117—616no—
309C2×#117C2×D6113yes—
310C22×C4⋊C4—616no—
311C22×C42—616no—
312C22×C42C2×D6113yes—
313C61C2×#348211yescharacteristic, complemented, Sylow
314C2×#41—28no—
315C2×#41—6124no—
316C2×#41—12224no—
317C2×#41C22×D6118yes—
318C22×Q8—6116no—
319C22×Q8—616no—
320C22×Q8—613no—
321C22×Q8—12216no—
322C22×Q8C22×D6111yescharacteristic
323C22×D4—616no—
324C22×D4—611no—
325C22×D4C22×D6113yes—
326C23×C4—616no—
327C23×C4—616no—
328C23×C4—612no—
329C23×C4C22×D6113yes—
330C23×C4C22×D6113yes—
331C23×C4C22×D6113yes—
332C4⋊Q8—6124no—
333C4⋊Q8—6124no—
334#126—6196no—
335#125—6148no—
336#125—6148no—
337#124—6148no—
338#123—6196no—
339C22⋊Q8—6148no—
340C22⋊Q8—6148no—
341C22⋊Q8—6148no—
342#121—6148no—
343C4×Q8—6116no—
344C4×Q8—6148no—
345C4×Q8—6148no—
346C4×Q8—6124no—
347C4×Q8—6124no—
348C4×Q8C22×D6118yes—
349C4×Q8C22×D6118yes—
350C4×D4—6148no—
351C4×D4—6148no—
352C4×D4—618no—
353C4×D4—6124no—
354C4×D4C22×D61124yes—
355C4×D4C22×D61124yes—
356#117—6124no—
357#117—6148no—
358#117—6148no—
359#117C22×D61124yes—
360C2×C4⋊C4—616no—
361C2×C4⋊C4—6112no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—616no—
364C2×C4⋊C4—613no—
365C2×C4⋊C4—616no—
366C2×C4⋊C4—616no—
367C2×C4⋊C4—616no—
368C2×C4⋊C4—6148no—
369C2×C4⋊C4C22×D6113yes—
370C2×C4⋊C4C22×D6113yes—
371C2×C22⋊C4—616no—
372C2×C22⋊C4—6112no—
373C2×C22⋊C4—612no—
374C2×C22⋊C4—616no—
375C2×C22⋊C4C22×D6116yes—
376C2×C42—616no—
377C2×C42—616no—
378C2×C42—616no—
379C2×C42—6148no—
380C2×C42C22×D6113yes—
381C2×C42C22×D6113yes—
382C2×C42C22×D61124yes—
383C2×C42C22×D6111yescharacteristic
384C2×C42C22×D6113yes—
385C24—612no—
386C24C23×D6113yes—
387#41—232no—
388#41—12296no—
389C2×Q8—6124no—
390C2×Q8—6112no—
391C2×Q8—12264no—
392C2×Q8—12212no—
393C2×Q8—12224no—
394C2×Q8#1175822218yescomplemented
395C2×Q8C23×D6114yes—
396C2×D4—212no—
397C2×D4—6124no—
398C2×D4—618no—
399C2×D4—614no—
400C2×D4—12224no—
401C2×D4C23×D61112yes—
402C22×C4—212no—
403C22×C4—212no—
404C22×C4—212no—
405C22×C4—612no—
406C22×C4—616no—
407C22×C4—616no—
408C22×C4—618no—
409C22×C4—6124no—
410C22×C4—6124no—
411C22×C4—12224no—
412C22×C4—12224no—
413C22×C4—1228no—
414C22×C4C23×D6113yes—
415C22×C4C23×D6111yescharacteristic
416C22×C4C23×D6113yes—
417C22×C4C23×D61112yes—
418C22×C4C23×D61112yes—
419C22×C4C23×D61112yes—
420C22×C4C23×D6111yescharacteristic
421C22×C4C23×D6113yes—
422C22×C4C23×D6111yescharacteristic
423C4⋊C4—6148no—
424C4⋊C4—6124no—
425C4⋊C4—6124no—
426C4⋊C4—6124no—
427C4⋊C4—614no—
428C4⋊C4—6112no—
429C4⋊C4—6124no—
430C4⋊C4—6124no—
431C4⋊C4C23×D61112yes—
432C4⋊C4C23×D61112yes—
433C22⋊C4—6124no—
434C22⋊C4—6148no—
435C22⋊C4—618no—
436C22⋊C4—6124no—
437C22⋊C4C23×D61124yes—
438C42—6124no—
439C42—6124no—
440C42—6124no—
441C42C23×D61112yes—
442C42C23×D6114yes—
443C42C23×D61112yes—
444C42C23×D61112yes—
445C23—26no—
446C23—26no—
447C23—26no—
448C23—618no—
449C23—614no—
450C23—1224no—
451C23—1224no—
452C23C24×D6116yes—
453C23C24×D6111yescharacteristic
454Q8—12224no—
455Q8—12248no—
456Q8C2×#11758222116yescomplemented
457D4—224no—
458D4—6116no—
459D4—12248no—
460C2×C4—26no—
461C2×C4—22no—
462C2×C4—26no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—614no—
467C2×C4—6112no—
468C2×C4—6112no—
469C2×C4—12248no—
470C2×C4—12212no—
471C2×C4—12212no—
472C2×C4—1224no—
473C2×C4—12248no—
474C2×C4—12216no—
475C2×C4#41×D6114yes—
476C2×C4C2×#11758222112yes—
477C2×C4#1451982414yes—
478C2×C4C24×D6116yes—
479C2×C4C24×D6112yes—
480C2×C4C24×D6116yes—
481C2×C4C24×D6112yes—
482C2×C4C24×D6116yes—
483C2×C4C24×D6112yes—
484C22—26no—
485C22—26no—
486C22—26no—
487C22—412no—
488C22—618no—
489C22—1224no—
490C22—1224no—
491C22—12216no—
492C22C2×#41×D6112yes—
493C22C22×#1175822212yes—
494C22C2×#1451982412yes—
495C22C25×D6111yescharacteristic
496C4—26no—
497C4—22no—
498C4—26no—
499C4—12212no—
500C4—12212no—
501C4—1224no—
502C4C2×#41×D6114yes—
503C4C22×#11758222112yes—
504C4C2×#1451982414yes—
505C2—46no—
506C2—1228no—
507C2#2145944114yesdirect product factor
508C2C22×#41×D6111yescharacteristic
509C2C23×#1175822211yescharacteristic
510C2C22×#1451982411yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C4×#41×C61C2
socleC23×C61C25
hypercenterC2×C4×#41D61
hypocenterC61C2×#3482
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. #21459441C2direct (N × H)
2. C2×#16840491C2semidirect
3. C2×#16840482C2semidirect
4. C2×#16840451C2semidirect
5. C2×Q8×D244C2semidirect
6. C2×#16840419C2semidirect
7. C2×#16840417C2semidirect
8. C2×#16840319C2semidirect
9. C2×#16840294C2semidirect
10. C2×C4×#11758222C2semidirect
11. C2×C4×Q8×D61C2semidirect
12. C2×C4×#41×C61C2semidirect
15. #16840491C22semidirect
16. #16840482C22semidirect
17. #16840451C22semidirect
18. Q8×D244C22semidirect
19. #16840419C22semidirect
20. #16840417C22semidirect
21. #16840319C22semidirect
24. #16840294C22semidirect
34. C4×#11758222C22semidirect
40. C4×Q8×D61C22semidirect
51. C4×#41×C61C22semidirect
132. C2×Q8×C61#41semidirect
155. C2×D244#41semidirect
198. Q8×C61C2×#41semidirect
222. D244C2×#41semidirect
260. C2×C4×#41D61semidirect
263. C2×C61#3482semidirect
291. C4×#41C2×D61semidirect
313. C61C2×#3482semidirect
394. C2×Q8#11758222semidirect
456. Q8C2×#11758222semidirect
507. C2#21459441direct (N × H)

Maximal subgroups

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

subgroupindex
#214594412
C2×#168404912
C2×#168404822
C2×#168404512
C2×Q8×D2442
C2×#168404192
C2×#168404172
C2×#168403192
C2×#168402942
C2×C4×#117582222
C2×C4×Q8×D612
C2×C4×#41×C612
C2×#348261