Finite Group Databasebeta

← C2×#21457177 #30552853

Subgroups — C2×#21457177 #30552853

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840310C211yesmaximal, characteristic, complemented
2C2×#16840294C211yesmaximal, characteristic, complemented
3#21457177C2116yesmaximal, direct product factor
4C2×#16840048C211yesmaximal, characteristic, complemented
5C2×#16840064C212yesmaximal, complemented
6C2×#16840042C211yesmaximal, characteristic, complemented
7C2×#16840012C212yesmaximal, complemented
8C2×#16840007C212yesmaximal, complemented
9C2×#16839959C211yesmaximal, characteristic, complemented
10C2×#16839975C212yesmaximal, complemented
11C2×#16839784C211yesmaximal, characteristic, complemented
12C2×C61×#459C211yesmaximal, characteristic, complemented
13C22×#11758224—21no—
14C22×#11758200C2212yes—
15C22×#11758189C2212yes—
16#16840310—24no—
17#16840310C2218yescomplemented
18C2×#14519777C2211yescharacteristic
19#16840294—24no—
20#16840294C2218yescomplemented
21C2×#14519770—21no—
22C2×#14519768C2211yescharacteristic
23C2×#14519764—21no—
24C2×#14519764C2211yescharacteristic
25C2×#14519759—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519748—21no—
28C2×#14519748C2212yes—
29C2×#14519748C2211yescharacteristic
30C2×C4×Dic122C2211yescharacteristic
31C2×D4×Dic61—21no—
32C2×D4×Dic61C2212yes—
33C2×C4×C22⋊D61—21no—
34C2×#14519736—21no—
35C2×C42×D61C2211yescharacteristic
36#16840064C22116yescomplemented
37#16840048C2218yescomplemented
38#16840042C2218yescomplemented
39#16840012C22116yescomplemented
40#16840007C22116yescomplemented
41#16839975C22116yescomplemented
42#16839959C2218yescomplemented
43C2×#14519710C2212yes—
44C2×#14519709C2212yes—
45#16839784C2218yescomplemented
46C2×C4⋊#92418C2211yescharacteristic
47C2×#14519706C2212yes—
48C2×#14519702C2212yes—
49C2×#14519698C2212yes—
50C2×#14519698C2212yes—
51C22×D8×C61C2212yes—
52C2×#127×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#459C2218yescomplemented
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2212yes—
57C2×#11758224—28no—
58C2×#11758224—48no—
59C22×Dic122—21no—
60C22×Dic122C2311yescharacteristic
61C22×C22⋊D61—21no—
62C22×C22⋊D61—22no—
63C23×Dic61—22no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758200—44no—
68C2×#11758200C2318yes—
69C2×#11758189—44no—
70C2×#11758189C2318yes—
71C22×#92418C2312yes—
72#14519777—22no—
73#14519777C2314yes—
74#14519770—28no—
75#14519768—22no—
76#14519768C2314yes—
77#14519764—28no—
78#14519764—22no—
79#14519764C2314yes—
80#14519759—28no—
81#14519757—22no—
82#14519757C2314yes—
83#14519748—28no—
84#14519748—22no—
85#14519748—24no—
86#14519748C2318yes—
87#14519748C2314yes—
88C4×Dic122—22no—
89C4×Dic122C2314yes—
90D4×Dic61—28no—
91D4×Dic61—24no—
92D4×Dic61C2318yes—
93C4×C22⋊D61—28no—
94#14519736—28no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2312yes—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—22no—
107C2×#11758198—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61D414yes—
113C42×D61C2314yes—
114#14519710C2318yes—
115#14519709C2318yes—
116C4⋊#92418C2314yes—
117#14519706C2318yes—
118#14519702C2318yes—
119#14519698C2318yes—
120#14519698C2318yes—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61C2312yes—
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C2×D8×C61—44no—
127C2×D8×C61C2318yes—
128C22×C8×C61C2312yes—
129#127×C61—22no—
130#127×C61C2314yes—
131C4×D4×C61—22no—
132C4×D4×C61C2314yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2314yes—
137#102×C61C2318yes—
138C24×C61—22no—
139C24×C61—21no—
140C23×D61C2×D411yescharacteristic
141C2×D4×C61—24no—
142C2×D4×C61—21no—
143C2×D4×C61—22no—
144C2×D4×C61—24no—
145C2×D4×C61—22no—
146C2×D4×C61—24no—
147C2×D4×C61—24no—
148C2×D4×C61—22no—
149C2×D4×C61—44no—
150C2×D4×C61—44no—
151C2×D4×C61C2414yes—
152C2×D4×C61C2412yes—
153C22×C4×C61—21no—
154C22×C4×C61—24no—
155C22×C4×C61—44no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—28no—
160C2×C22⋊D61—24no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—48no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—28no—
167C22×Dic61—48no—
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171#11758224—432no—
172C2×C4×D61—24no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—42no—
176C2×C4×D61C2×D414yes—
177C2×C4×D61C2×D412yes—
178C2×C4×D61C2×D414yes—
179C2×C4×D61C2412yes—
180C2×Dic122—22no—
181C2×Dic122—22no—
182C2×Dic122—24no—
183C2×Dic122—21no—
184C2×Dic122—44no—
185C2×Dic122C2412yes—
186D8×C61—48no—
187C2×C8×C61—24no—
188C2×C8×C61C2414yes—
189C4⋊C4×C61—21no—
190C4⋊C4×C61C2412yes—
191C22⋊C4×C61—24no—
192C42×C61C2×D412yes—
193C42×C61C2412yes—
194C22⋊Dic61—24no—
195C22⋊Dic61—24no—
196C22⋊Dic61—24no—
197C22⋊Dic61—28no—
198C22⋊Dic61—28no—
199#11758200—48no—
200#11758198—24no—
201C4⋊Dic61—24no—
202C4⋊Dic61—22no—
203C4⋊Dic61—21no—
204C4⋊Dic61—24no—
205C4⋊Dic61—24no—
206C4⋊Dic61C2412yes—
207C4⋊Dic61C2414yes—
208#11758196—24no—
209#11758196—24no—
210C4×Dic61—24no—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2×D414yes—
214C4×Dic61C2412yes—
215C2×#92418—24no—
216C2×#92418C2414yes—
217#11758189—48no—
218C23×C61—22no—
219C23×C61—24no—
220C23×C61—42no—
221C23×C61—44no—
222C23×C61—44no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—44no—
226C23×C61C22×D411yescharacteristic
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—22no—
230C22×D61C22×D412yes—
231D4×C61—24no—
232D4×C61—22no—
233D4×C61—24no—
234D4×C61—22no—
235D4×C61—48no—
236D4×C61—42no—
237D4×C61—44no—
238D4×C61—48no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—42no—
242C2×C4×C61—48no—
243C2×C4×C61AGL(1,ℤ/8)14yes—
244C2×C4×C61C22×D412yes—
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D412yes—
247C2×C4×C61H(5,𝔽2)12yes—
248C2×C4×C612−1+412yes—
249C2×C4×C61C2511yescharacteristic
250C22⋊D61—416no—
251C22⋊D61—48no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—24no—
258C2×Dic61—416no—
259C2×Dic61—42no—
260C2×Dic61—44no—
261C2×Dic61—42no—
262C2×Dic61C22×D412yes—
263C2×Dic61C22×D412yes—
264C2×Dic61C22×D412yes—
265C4×D61—24no—
266C4×D61—28no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—44no—
270Dic122—22no—
271Dic122—22no—
272Dic122—42no—
273Dic122—48no—
274C8×C61—24no—
275#92418—24no—
276C2×#3251—611nomaximal, Sylow
277C22×C61—44no—
278C22×C61—42no—
279C22×C61—44no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—44no—
283C22×C61—88no—
284C22×C61—84no—
285C22×C61#53712yes—
286C22×C61C2×AGL(1,ℤ/8)12yes—
287C22×C61#57512yes—
288C22×C61C23×D411yescharacteristic
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—44no—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61#53712yes—
296C4×C61C2×AGL(1,ℤ/8)14yes—
297C4×C61C2×H(5,𝔽2)11yescharacteristic
298C4×C61C2×2−1+411yescharacteristic
299Dic61—22no—
300Dic61—22no—
301Dic61—22no—
302Dic61—42no—
303Dic61—44no—
304Dic61—42no—
305C2×#532—611no—
306C2×#529—611no—
307#3251—6116no—
308C2×#475—611no—
309C2×#478—612no—
310C2×#474—611no—
311C2×#469—612no—
312C2×#468—612no—
313C2×#460—611no—
314C2×#463—612no—
315C2×#459D6111yescharacteristic, complemented
316C2×#423—611no—
317C2×C61—84no—
318C2×C61—82no—
319C2×C61#325114yescomplemented
320C2×C61C2×#53711yescharacteristic
321C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
322C2×C61C2×#57511yescharacteristic
323D61—42no—
324C22×#41—1221no—
325C22×SD16—612no—
326C22×D8C2×D6112yes—
327C22×M16—612no—
328#532—618no—
329#532—1224no—
330C2×C4⋊Q8—611no—
331C2×#127C2×D6111yescharacteristic
332#529—618no—
333#529—1224no—
334C2×#126—1221no—
335C2×#125—611no—
336C2×#124—611no—
337C2×#124—1221no—
338C2×#123—1221no—
339C2×C22⋊Q8—611no—
340C2×#121—611no—
341C2×#121—612no—
342C2×#121—1221no—
343C2×C4×Q8—611no—
344C2×C4×D4—612no—
345C2×C4×D4—1221no—
346C2×C4×D4—1221no—
347C2×C4×D4C2×D6111yescharacteristic
348C2×#117—1221no—
349C22×C42—611no—
350#478—6116no—
351#475—618no—
352#474—618no—
353#469—6116no—
354#468—6116no—
355#463—6116no—
356#460—618no—
357#459C2×D6118yescomplemented
358C2×#107—612no—
359C2×#106—612no—
360#423—618no—
361C2×C4⋊C8—612no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8C2×D6111yescharacteristic
364C2×#103—612no—
365C2×#102—612no—
366C2×#102—612no—
367C2×#102C2×D6112yes—
368C61C2×#325111yescharacteristic, complemented, Sylow
369C2×#41—1228no—
370C2×#41—2448no—
371C22×Q8—611no—
372C22×Q8—1221no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4—1221no—
376C22×D4—1222no—
377C22×D4C22×D6112yes—
378C22×D4C22×D6111yescharacteristic
379C23×C4—21no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—1222no—
384C2×SD16—618no—
385C2×SD16—2444no—
386C2×D8—44no—
387C2×D8C22×D6118yes—
388C2×M16—618no—
389C2×M16—2444no—
390C22×C8—612no—
391C22×C8C22×D6112yes—
392C4⋊Q8—614no—
393C4⋊Q8—1222no—
394#127—22no—
395#127C22×D6114yes—
396#126—1228no—
397#125—614no—
398#125—1222no—
399#124—614no—
400#124—1222no—
401#124—1228no—
402#123—1228no—
403C22⋊Q8—614no—
404C22⋊Q8—1222no—
405#121—614no—
406#121—618no—
407#121—1222no—
408#121—1224no—
409#121—1228no—
410C4×Q8—614no—
411C4×Q8—1222no—
412C4×D4—22no—
413C4×D4—618no—
414C4×D4—1224no—
415C4×D4—1228no—
416C4×D4—1228no—
417C4×D4C22×D6114yes—
418#117—1228no—
419C2×C4⋊C4—612no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1222no—
432C2×C22⋊C4—1222no—
433C2×C22⋊C4—1221no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—614no—
438C2×C42—614no—
439C2×C42—1221no—
440C2×C42C22×D6111yescharacteristic
441#107—618no—
442#106—618no—
443C4⋊C8—618no—
444C4⋊C8—614no—
445C4⋊C8C22×D6114yes—
446#103—618no—
447#102—618no—
448#102—618no—
449#102C22×D6118yes—
450C24—21no—
451C24—22no—
452C24—611no—
453#41—24432no—
454C2×Q8—612no—
455C2×Q8—1221no—
456C2×Q8—1224no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—2444no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—22no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—22no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—1224no—
471C2×D4—1228no—
472C2×D4—2448no—
473C2×D4—2444no—
474C2×D4C23×D6112yes—
475C2×D4C23×D6114yes—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—44no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—614no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—614no—
486C22×C4—1228no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1224no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1222no—
493C22×C4—2442no—
494C22×C4—2448no—
495C22×C4D4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498SD16—2448no—
499D8—48no—
500M16—2448no—
501C2×C8—24no—
502C2×C8—614no—
503C2×C8—1224no—
504C2×C8C23×D6114yes—
505C4⋊C4—21no—
506C4⋊C4—612no—
507C4⋊C4—614no—
508C4⋊C4—1224no—
509C4⋊C4—1224no—
510C4⋊C4—1224no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—1224no—
514C4⋊C4—1224no—
515C4⋊C4C23×D6112yes—
516C22⋊C4—24no—
517C22⋊C4—1224no—
518C22⋊C4—1224no—
519C22⋊C4—1224no—
520C22⋊C4—1228no—
521C22⋊C4—1228no—
522C22⋊C4—1224no—
523C42—614no—
524C42—612no—
525C42—614no—
526C42—612no—
527C42—1224no—
528C42D4×D6112yes—
529C42C23×D6112yes—
530C23—22no—
531C23—24no—
532C23—42no—
533C23—44no—
534C23—44no—
535C23—42no—
536C23—42no—
537C23—44no—
538C23—612no—
539C23—1222no—
540C23—1222no—
541C23—1222no—
542C23C2×D4×D6111yescharacteristic
543Q8—1222no—
544Q8—1222no—
545Q8—2448no—
546Q8—2442no—
547D4—22no—
548D4—24no—
549D4—22no—
550D4—24no—
551D4—48no—
552D4—48no—
553D4—42no—
554D4—44no—
555D4—2448no—
556D4—24416no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—48no—
561C2×C4—612no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1228no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1224no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1224no—
574C2×C4—2444no—
575C2×C4—24416no—
576C2×C4—2444no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4#1451980114yes—
580C2×C4C2×D4×D6112yes—
581C2×C4C2×D4×D6112yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4#1451982212yes—
584C2×C4#1451982412yes—
585C2×C4C24×D6111yescharacteristic
586C8—24no—
587C8—1224no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—42no—
592C22—42no—
593C22—44no—
594C22—84no—
595C22—88no—
596C22—1222no—
597C22—1222no—
598C22—1222no—
599C22—2444no—
600C22#1684034112yes—
601C22C2×#1451980112yes—
602C22#1684055812yes—
603C22C22×D4×D6111yescharacteristic
604C4—22no—
605C4—42no—
606C4—1222no—
607C4—1222no—
608C4—1222no—
609C4—2444no—
610C4—2442no—
611C4—2442no—
612C4#1684034112yes—
613C4C2×#1451980114yes—
614C4C2×#1451982211yescharacteristic
615C4C2×#1451982411yescharacteristic
616C2—82no—
617C2—84no—
618C2—2442no—
619C2#2145717714yesdirect product factor
620C2C2×#1684034111yescharacteristic
621C2C22×#1451980111yescharacteristic
622C2C2×#1684055811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#459C2
socleC23×C61C22×D4
hypercenterC2×#459D61
hypocenterC61C2×#3251
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16840310C2semidirect
2. C2×#16840294C2semidirect
3. #21457177C2direct (N × H)
4. C2×#16840048C2semidirect
5. C2×#16840064C2semidirect
6. C2×#16840042C2semidirect
7. C2×#16840012C2semidirect
8. C2×#16840007C2semidirect
9. C2×#16839959C2semidirect
10. C2×#16839975C2semidirect
11. C2×#16839784C2semidirect
12. C2×C61×#459C2semidirect
17. #16840310C22semidirect
20. #16840294C22semidirect
36. #16840064C22semidirect
37. #16840048C22semidirect
38. #16840042C22semidirect
39. #16840012C22semidirect
40. #16840007C22semidirect
41. #16839975C22semidirect
42. #16839959C22semidirect
45. #16839784C22semidirect
54. C61×#459C22semidirect
315. C2×#459D61semidirect
319. C2×C61#3251semidirect
357. #459C2×D61semidirect
368. C61C2×#3251semidirect
619. C2#21457177direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403102
C2×#168402942
#214571772
C2×#168400482
C2×#168400642
C2×#168400422
C2×#168400122
C2×#168400072
C2×#168399592
C2×#168399752
C2×#168397842
C2×C61×#4592
C2×#325161