Finite Group Databasebeta

← C2×#21457016 #30552155

Subgroups — C2×#21457016 #30552155

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2C2×#16840309C211yesmaximal, characteristic
3#21457016C2116yesmaximal, direct product factor
4C2×#16840170C212yesmaximal, complemented
5C2×#16840125C212yesmaximal, complemented
6C2×#16840089C212yesmaximal, complemented
7C2×#16840085C212yesmaximal, complemented
8C2×#16840053C211yesmaximal, characteristic, complemented
9C2×#16840052C211yesmaximal, characteristic, complemented
10C2×#16840039C211yesmaximal, characteristic, complemented
11C2×#16839818C211yesmaximal, characteristic, complemented
12C2×C61×#474C211yesmaximal, characteristic, complemented
13C22×#11758222—21no—
14#16840317—24no—
15#16840317C2218yescomplemented
16#16840309—24no—
17#16840309C2218yes—
18C2×#14519777C2211yescharacteristic
19C2×#14519776C2211yescharacteristic
20C2×#14519773C2211yescharacteristic
21C2×#14519768C2212yes—
22C2×#14519763—21no—
23C2×#14519757—21no—
24C2×#14519753—21no—
25C2×#14519752C2211yescharacteristic
26C2×#14519750—21no—
27C2×#14519748C2211yescharacteristic
28C2×Q8×Dic61—21no—
29C2×#14519742—21no—
30C2×C4×D244C2211yescharacteristic
31C2×C4×C22⋊D61—21no—
32C2×#14519735C2212yes—
33C2×C42×D61C2211yescharacteristic
34#16840170C22116yescomplemented
35#16840125C22116yescomplemented
36#16840089C22116yescomplemented
37#16840085C22116yescomplemented
38#16840053C2218yescomplemented
39#16840052C2218yescomplemented
40#16840039C2218yescomplemented
41#16839818C2218yescomplemented
42C2×#14519710C2212yes—
43C2×#14519709C2212yes—
44C2×#14519708C2212yes—
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519699C2212yes—
47C2×#14519698C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×#14519687C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#474C2218yescomplemented
54C2×#107×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2212yes—
57C2×#11758222—28no—
58C2×#11758222—48no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×D244—21no—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C22×#92418C2312yes—
71#14519777—22no—
72#14519777C2314yes—
73#14519776—22no—
74#14519776C2314yes—
75#14519773—22no—
76#14519773C2314yes—
77#14519768—24no—
78#14519768C2318yes—
79#14519763—28no—
80#14519757—28no—
81#14519753—28no—
82#14519752—22no—
83#14519752C2314yes—
84#14519750—28no—
85#14519748—22no—
86#14519748C2314yes—
87Q8×Dic61—28no—
88#14519742—28no—
89C4×D244—22no—
90C4×D244C2314yes—
91C4×C22⋊D61—28no—
92#14519735—24no—
93#14519735C2318yes—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61C2312yes—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—22no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—22no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C42×D61D414yes—
109C42×D61C2314yes—
110#14519710C2318yes—
111#14519709C2318yes—
112#14519708C2318yes—
113C4⋊#92418C2314yes—
114#14519699C2318yes—
115#14519698C2318yes—
116#14519697C2318yes—
117#14519689C2318yes—
118#14519687C2318yes—
119C22×Q8×C61—21no—
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—21no—
122C22×C8×C61C2312yes—
123C4⋊Q8×C61—22no—
124C4⋊Q8×C61C2314yes—
125C4×D4×C61—22no—
126C4×D4×C61C2314yes—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2312yes—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61C2318yes—
133C4⋊C8×C61C2314yes—
134#102×C61C2318yes—
135C24×C61—21no—
136C23×D61—21no—
137C23×D61C2×D411yescharacteristic
138C2×Q8×C61—24no—
139C2×Q8×C61—44no—
140C2×D4×C61—21no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61C2412yes—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—24no—
147C22×C4×C61—44no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—24no—
152C2×C22⋊D61—24no—
153C2×C22⋊D61—24no—
154C2×C22⋊D61—44no—
155C2×C22⋊D61—44no—
156C2×C22⋊D61—44no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162#11758222—432no—
163C2×D244—22no—
164C2×D244—22no—
165C2×D244—24no—
166C2×D244—21no—
167C2×D244—44no—
168C2×D244C2412yes—
169C2×C4×D61—24no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—24no—
173C2×C4×D61—42no—
174C2×C4×D61—44no—
175C2×C4×D61C2×D414yes—
176C2×C4×D61C2×D412yes—
177C2×C4×D61C2×D414yes—
178C2×C4×D61C2412yes—
179C2×Dic122—24no—
180C2×Dic122—24no—
181C2×Dic122—44no—
182C2×Dic122—44no—
183C2×C8×C61—24no—
184C2×C8×C61C2414yes—
185C4⋊C4×C61—24no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61C2414yes—
189C4⋊C4×C61C2412yes—
190C22⋊C4×C61—24no—
191C42×C61C2×D412yes—
192C42×C61C2412yes—
193C22⋊Dic61—24no—
194#11758198—28no—
195#11758198—24no—
196#11758198—24no—
197C4⋊Dic61—24no—
198C4⋊Dic61—22no—
199C4⋊Dic61—21no—
200C4⋊Dic61—28no—
201C4⋊Dic61C2414yes—
202C4⋊Dic61C2412yes—
203#11758196—24no—
204#11758196—28no—
205C4×Dic61—28no—
206C4×Dic61C2×D412yes—
207C4×Dic61C2×D414yes—
208C4×Dic61C2×D414yes—
209C4×Dic61C2412yes—
210C2×#92418—24no—
211C2×#92418C2414yes—
212C23×C61—22no—
213C23×C61—42no—
214C23×C61—42no—
215C23×C61—42no—
216C23×C61C22×D411yescharacteristic
217C22×D61—22no—
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61C22×D412yes—
225Q8×C61—48no—
226D4×C61—22no—
227D4×C61—22no—
228D4×C61—42no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—22no—
232C2×C4×C61—42no—
233C2×C4×C61—44no—
234C2×C4×C61—48no—
235C2×C4×C61AGL(1,ℤ/8)14yes—
236C2×C4×C61C22×D412yes—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D412yes—
239C2×C4×C612−1+412yes—
240C2×C4×C612−1+412yes—
241C2×C4×C61C2511yescharacteristic
242C22⋊D61—48no—
243C22⋊D61—48no—
244C22⋊D61—48no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—22no—
250C2×Dic61—42no—
251C2×Dic61—44no—
252C2×Dic61C22×D412yes—
253C2×Dic61C22×D412yes—
254C2×Dic61C22×D412yes—
255D244—22no—
256D244—22no—
257D244—48no—
258D244—42no—
259C4×D61—24no—
260C4×D61—28no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—44no—
264C4×D61—48no—
265Dic122—48no—
266Dic122—48no—
267C8×C61—24no—
268#92418—24no—
269C2×#3235—611nomaximal, Sylow
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—84no—
274C22×C61#53612yes—
275C22×C61C2×AGL(1,ℤ/8)12yes—
276C22×C61#57512yes—
277C22×C61C23×D411yescharacteristic
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—22no—
281C2×D61—44no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—84no—
286C4×C61—22no—
287C4×C61—42no—
288C4×C61—44no—
289C4×C61#53612yes—
290C4×C61C2×AGL(1,ℤ/8)14yes—
291C4×C61C2×2−1+411yescharacteristic
292C4×C61C2×2−1+411yescharacteristic
293Dic61—22no—
294Dic61—22no—
295Dic61—22no—
296Dic61—42no—
297Dic61—44no—
298C2×#533—611no—
299C2×#532—611no—
300#3235—6116no—
301C2×#501—612no—
302C2×#490—612no—
303C2×#482—612no—
304C2×#482—612no—
305C2×#476—611no—
306C2×#476—611no—
307C2×#474—611no—
308C2×#474D6111yescharacteristic, complemented
309C2×#432—611no—
310C2×C61—82no—
311C2×C61#323514yescomplemented
312C2×C61C2×#53611yescharacteristic
313C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
314C2×C61C2×#57511yescharacteristic
315D61—42no—
316D61—82no—
317C22×#41—1221no—
318#533—618no—
319#533—1224no—
320#532—618no—
321#532—1224no—
322C2×C4⋊Q8—611no—
323C2×C4⋊Q8—611no—
324C2×C4⋊Q8C2×D6111yescharacteristic
325C2×#127—611no—
326C2×#125—612no—
327C2×#124—1221no—
328C2×C22⋊Q8—1221no—
329C2×C22⋊Q8—1221no—
330C2×#121—611no—
331C2×#121—611no—
332C2×#121—1221no—
333C2×C4×Q8—1221no—
334C2×C4×Q8—1221no—
335C2×C4×D4—611no—
336C2×C4×D4—1221no—
337C2×C4×D4C2×D6111yescharacteristic
338C2×#117—612no—
339C22×C42—611no—
340#501—6116no—
341#490—6116no—
342#482—6116no—
343#482—6116no—
344#476—618no—
345#476—618no—
346#474—618no—
347#474C2×D6118yescomplemented
348#432—618no—
349C2×#107—612no—
350C2×#107C2×D6112yes—
351C2×#106—612no—
352C2×#106—612no—
353C2×C4⋊C8—611no—
354C2×C4⋊C8C2×D6111yescharacteristic
355C2×#102—612no—
356C2×#102—612no—
357C2×#102—612no—
358C2×#102C2×D6112yes—
359C2×C22⋊C8—612no—
360C2×#97—612no—
361C61C2×#323511yescharacteristic, complemented, Sylow
362C2×#41—1228no—
363C2×#41—2448no—
364C22×Q8—21no—
365C22×Q8—1221no—
366C22×Q8—1221no—
367C22×D4—611no—
368C22×D4—1221no—
369C22×D4—1221no—
370C22×D4—1221no—
371C22×D4—1221no—
372C22×D4C22×D6111yescharacteristic
373C23×C4—21no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—1221no—
378C22×C8—612no—
379C22×C8C22×D6112yes—
380C4⋊Q8—22no—
381C4⋊Q8—614no—
382C4⋊Q8—614no—
383C4⋊Q8—1222no—
384C4⋊Q8—1222no—
385C4⋊Q8C22×D6114yes—
386#127—614no—
387#127—1222no—
388#125—618no—
389#125—1224no—
390#124—1228no—
391C22⋊Q8—1228no—
392C22⋊Q8—1228no—
393#121—614no—
394#121—614no—
395#121—1228no—
396#121—1222no—
397#121—1222no—
398C4×Q8—1228no—
399C4×Q8—1228no—
400C4×D4—22no—
401C4×D4—614no—
402C4×D4—1228no—
403C4×D4—1222no—
404C4×D4C22×D6114yes—
405#117—618no—
406#117—1224no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1222no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C22×D6112yes—
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1222no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—614no—
425C2×C42—614no—
426C2×C42—1222no—
427C2×C42C22×D6111yescharacteristic
428#107—618no—
429#107C22×D6118yes—
430#106—618no—
431#106—618no—
432C4⋊C8—614no—
433C4⋊C8C22×D6114yes—
434#102—618no—
435#102—618no—
436#102—618no—
437#102C22×D6118yes—
438C22⋊C8—618no—
439#97—618no—
440C24—21no—
441C24—611no—
442C24—1221no—
443#41—24432no—
444C2×Q8—24no—
445C2×Q8—44no—
446C2×Q8—1224no—
447C2×Q8—1224no—
448C2×Q8—2444no—
449C2×Q8—2444no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—612no—
454C2×D4—1224no—
455C2×D4—1224no—
456C2×D4—1224no—
457C2×D4—1224no—
458C2×D4—1221no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—2444no—
462C2×D4—2444no—
463C2×D4—2444no—
464C2×D4—2444no—
465C2×D4C23×D6112yes—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—24no—
469C22×C4—44no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—612no—
474C22×C4—614no—
475C22×C4—612no—
476C22×C4—614no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1224no—
480C22×C4—1222no—
481C22×C4—1221no—
482C22×C4—1224no—
483C22×C4—2442no—
484C22×C4—2444no—
485C22×C4D4×D6111yescharacteristic
486C22×C4D4×D6111yescharacteristic
487C22×C4C23×D6111yescharacteristic
488C2×C8—24no—
489C2×C8—614no—
490C2×C8—1224no—
491C2×C8C23×D6114yes—
492C4⋊C4—24no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—614no—
496C4⋊C4—612no—
497C4⋊C4—1224no—
498C4⋊C4—1228no—
499C4⋊C4—1228no—
500C4⋊C4—1222no—
501C4⋊C4—1221no—
502C4⋊C4—1224no—
503C4⋊C4C23×D6114yes—
504C4⋊C4C23×D6112yes—
505C22⋊C4—24no—
506C22⋊C4—1224no—
507C22⋊C4—1228no—
508C22⋊C4—1224no—
509C22⋊C4—1224no—
510C42—614no—
511C42—614no—
512C42—612no—
513C42—612no—
514C42—1228no—
515C42D4×D6112yes—
516C42C23×D6112yes—
517C23—22no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—612no—
522C23—1222no—
523C23—1222no—
524C23—1222no—
525C23—1222no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23C2×D4×D6111yescharacteristic
530Q8—48no—
531Q8—2448no—
532Q8—2448no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—1222no—
537D4—1222no—
538D4—2448no—
539D4—2448no—
540D4—2448no—
541D4—2448no—
542D4—2442no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—48no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1228no—
556C2×C4—1224no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1224no—
560C2×C4—1222no—
561C2×C4—2444no—
562C2×C4—2442no—
563C2×C4—2444no—
564C2×C4—2448no—
565C2×C4#1451980114yes—
566C2×C4C2×D4×D6112yes—
567C2×C4C2×D4×D6112yes—
568C2×C4C2×D4×D6111yescharacteristic
569C2×C4#1451982412yes—
570C2×C4#1451982512yes—
571C2×C4C24×D6111yescharacteristic
572C8—24no—
573C8—1224no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—1222no—
579C22—1222no—
580C22—1222no—
581C22—4884no—
582C22—2442no—
583C22—2442no—
584C22—2442no—
585C22—2444no—
586C22#1684033512yes—
587C22C2×#1451980112yes—
588C22#1684056112yes—
589C22C22×D4×D6111yescharacteristic
590C4—22no—
591C4—42no—
592C4—44no—
593C4—1222no—
594C4—1222no—
595C4—1222no—
596C4—2442no—
597C4—2444no—
598C4#1684033512yes—
599C4C2×#1451980114yes—
600C4C2×#1451982411yescharacteristic
601C4C2×#1451982511yescharacteristic
602C2—82no—
603C2—4882no—
604C2—2442no—
605C2#2145701614yesdirect product factor
606C2C2×#1684033511yescharacteristic
607C2C22×#1451980111yescharacteristic
608C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#474C2
socleC23×C61C22×D4
prime radicalC2×#16840309C2
hypercenterC2×#474D61
hypocenterC61C2×#3235
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21457016C2direct (N × H)
4. C2×#16840170C2semidirect
5. C2×#16840125C2semidirect
6. C2×#16840089C2semidirect
7. C2×#16840085C2semidirect
8. C2×#16840053C2semidirect
9. C2×#16840052C2semidirect
10. C2×#16840039C2semidirect
11. C2×#16839818C2semidirect
12. C2×C61×#474C2semidirect
15. #16840317C22semidirect
34. #16840170C22semidirect
35. #16840125C22semidirect
36. #16840089C22semidirect
37. #16840085C22semidirect
38. #16840053C22semidirect
39. #16840052C22semidirect
40. #16840039C22semidirect
41. #16839818C22semidirect
53. C61×#474C22semidirect
308. C2×#474D61semidirect
311. C2×C61#3235semidirect
347. #474C2×D61semidirect
361. C61C2×#3235semidirect
605. C2#21457016direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403172
C2×#168403092
#214570162
C2×#168401702
C2×#168401252
C2×#168400892
C2×#168400852
C2×#168400532
C2×#168400522
C2×#168400392
C2×#168398182
C2×C61×#4742
C2×#323561