Finite Group Databasebeta

← C2×#21457188 #30552865

Subgroups — C2×#21457188 #30552865

Order 15616.

1898 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2C2×#16840294C211yesmaximal, characteristic
3#21457188C2116yesmaximal, direct product factor
4C2×#16840071C212yesmaximal, complemented
5C2×#16840058C211yesmaximal, characteristic, complemented
6C2×#16840052C211yesmaximal, characteristic, complemented
7C2×#16840019C212yesmaximal, complemented
8C2×#16840005C212yesmaximal
9C2×#16839982C212yesmaximal, complemented
10C2×#16839969C211yesmaximal, characteristic, complemented
11C2×#16839784C211yesmaximal, characteristic, complemented
12C2×C61×#461C211yesmaximal, characteristic, complemented
13C22×#11758202C2212yes—
14C22×#11758189C2212yes—
15#16840317—24no—
16#16840317C2218yescomplemented
17C2×#14519777C2211yescharacteristic
18#16840294—24no—
19#16840294C2218yes—
20C2×#14519770—21no—
21C2×#14519768—21no—
22C2×#14519768C2211yescharacteristic
23C2×#14519764C2211yescharacteristic
24C2×#14519759—21no—
25C2×#14519757—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519753C2212yes—
28C2×#14519748C2211yescharacteristic
29C2×Q8×Dic61C2212yes—
30C2×C4×Dic122C2211yescharacteristic
31C2×#14519742—21no—
32C2×C4×C22⋊D61—21no—
33C2×#14519736—21no—
34C2×#14519735—21no—
35C2×C42×D61C2211yescharacteristic
36#16840071C22116yescomplemented
37#16840058C2218yescomplemented
38#16840052C2218yescomplemented
39#16840019C22116yescomplemented
40#16840005C22116yes—
41#16839982C22116yescomplemented
42#16839969C2218yescomplemented
43C2×#14519711C2212yes—
44C2×#14519708C2212yes—
45#16839784C2218yescomplemented
46C2×C4⋊#92418C2211yescharacteristic
47C2×#14519706C2212yes—
48C2×#14519702C2212yes—
49C2×#14519701C2212yes—
50C2×#14519698C2212yes—
51C22×SD16×C61C2212yes—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#461C2218yescomplemented
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C22×Dic122—21no—
58C22×Dic122C2311yescharacteristic
59C22×C22⋊D61—21no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C2×#11758202—44no—
64C2×#11758202C2318yes—
65C2×#11758189—44no—
66C2×#11758189C2318yes—
67C22×#92418C2312yes—
68#14519777—22no—
69#14519777C2314yes—
70#14519770—28no—
71#14519768—28no—
72#14519768—22no—
73#14519768C2314yes—
74#14519764—22no—
75#14519764C2314yes—
76#14519759—28no—
77#14519757—28no—
78#14519757—22no—
79#14519757C2314yes—
80#14519753—24no—
81#14519753C2318yes—
82#14519748—22no—
83#14519748C2314yes—
84Q8×Dic61—24no—
85Q8×Dic61C2318yes—
86C4×Dic122—22no—
87C4×Dic122C2314yes—
88#14519742—28no—
89C4×C22⋊D61—28no—
90#14519736—28no—
91#14519735—28no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2312yes—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—22no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—22no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61D414yes—
112C42×D61C2314yes—
113#14519711C2318yes—
114#14519708C2318yes—
115C4⋊#92418C2314yes—
116#14519706C2318yes—
117#14519702C2318yes—
118#14519701C2318yes—
119#14519698C2318yes—
120C22×Q8×C61C2312yes—
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61—21no—
123C2×SD16×C61—44no—
124C2×SD16×C61C2318yes—
125C22×C8×C61C2312yes—
126C4⋊Q8×C61—22no—
127C4⋊Q8×C61C2314yes—
128C4×D4×C61—22no—
129C4×D4×C61C2314yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61C2314yes—
136#103×C61C2318yes—
137C24×C61—21no—
138C23×D61C2×D411yescharacteristic
139C2×Q8×C61—22no—
140C2×Q8×C61—24no—
141C2×Q8×C61—24no—
142C2×Q8×C61C2414yes—
143C2×D4×C61—21no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61C2412yes—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—24no—
150C22×C4×C61—44no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—24no—
155C2×C22⋊D61—44no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—21no—
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C2×C4×D61—24no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—42no—
166C2×C4×D61C2×D414yes—
167C2×C4×D61C2×D412yes—
168C2×C4×D61C2×D414yes—
169C2×C4×D61C2412yes—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122—24no—
173C2×Dic122—21no—
174C2×Dic122—44no—
175C2×Dic122C2412yes—
176SD16×C61—48no—
177C2×C8×C61—24no—
178C2×C8×C61C2414yes—
179C4⋊C4×C61—24no—
180C4⋊C4×C61—24no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C2412yes—
183C22⋊C4×C61—24no—
184C42×C61C2×D412yes—
185C42×C61C2412yes—
186C22⋊Dic61—24no—
187C22⋊Dic61—24no—
188C22⋊Dic61—24no—
189#11758202—48no—
190#11758198—28no—
191#11758198—24no—
192C4⋊Dic61—24no—
193C4⋊Dic61—21no—
194C4⋊Dic61—22no—
195C4⋊Dic61—24no—
196C4⋊Dic61—24no—
197C4⋊Dic61—28no—
198C4⋊Dic61C2414yes—
199C4⋊Dic61C2412yes—
200#11758196—24no—
201#11758196—24no—
202#11758196—28no—
203C4×Dic61—24no—
204C4×Dic61—28no—
205C4×Dic61C2×D412yes—
206C4×Dic61C2×D414yes—
207C4×Dic61C2×D414yes—
208C4×Dic61C2412yes—
209C2×#92418—24no—
210C2×#92418C2414yes—
211#11758189—48no—
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×D61C22×D412yes—
221Q8×C61—24no—
222Q8×C61—24no—
223Q8×C61—44no—
224D4×C61—22no—
225D4×C61—22no—
226D4×C61—42no—
227C2×C4×C61—22no—
228C2×C4×C61—24no—
229C2×C4×C61—22no—
230C2×C4×C61—44no—
231C2×C4×C61—42no—
232C2×C4×C61—48no—
233C2×C4×C61#13714yes—
234C2×C4×C61C22×D412yes—
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D412yes—
237C2×C4×C61H(5,𝔽2)12yes—
238C2×C4×C612−1+412yes—
239C2×C4×C61C2511yescharacteristic
240C22⋊D61—48no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—42no—
248C2×Dic61—44no—
249C2×Dic61—42no—
250C2×Dic61C22×D412yes—
251C2×Dic61C22×D412yes—
252C2×Dic61C22×D412yes—
253C4×D61—24no—
254C4×D61—28no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—44no—
258Dic122—22no—
259Dic122—22no—
260Dic122—48no—
261Dic122—42no—
262C8×C61—24no—
263#92418—24no—
264C2×#3252—611nomaximal, Sylow
265C22×C61—42no—
266C22×C61—42no—
267C22×C61—42no—
268C22×C61—84no—
269C22×C61#53712yes—
270C22×C61C2×#13712yes—
271C22×C61#57512yes—
272C22×C61C23×D411yescharacteristic
273C2×D61—22no—
274C2×D61—22no—
275C2×D61—22no—
276C2×D61—44no—
277C4×C61—22no—
278C4×C61—44no—
279C4×C61—42no—
280C4×C61#53712yes—
281C4×C61C2×#13714yes—
282C4×C61C2×H(5,𝔽2)11yescharacteristic
283C4×C61C2×2−1+411yescharacteristic
284Dic61—22no—
285Dic61—22no—
286Dic61—22no—
287Dic61—42no—
288Dic61—44no—
289Dic61—42no—
290C2×#533—611no—
291C2×#529—611no—
292#3252—6116no—
293C2×#479—612no—
294C2×#477—611no—
295C2×#476—611no—
296C2×#470—612no—
297C2×#468—612no—
298C2×#464—612no—
299C2×#462—611no—
300C2×#461D6111yescharacteristic, complemented
301C2×#423—611no—
302C2×C61—82no—
303C2×C61#325214yescomplemented
304C2×C61C2×#53711yescharacteristic
305C2×C61C22×#13711yescharacteristic
306C2×C61C2×#57511yescharacteristic
307D61—42no—
308C22×Q16—612no—
309C22×SD16C2×D6112yes—
310C22×M16—612no—
311#533—618no—
312#533—1224no—
313C2×C4⋊Q8—611no—
314C2×C4⋊Q8C2×D6111yescharacteristic
315#529—618no—
316#529—1224no—
317C2×#126—1221no—
318C2×#125—611no—
319C2×#125—1221no—
320C2×#124—611no—
321C2×#123—1221no—
322C2×C22⋊Q8—612no—
323C2×C22⋊Q8—611no—
324C2×C22⋊Q8—1221no—
325C2×#121—611no—
326C2×C4×Q8—612no—
327C2×C4×Q8—611no—
328C2×C4×Q8—1221no—
329C2×C4×D4—1221no—
330C2×C4×D4C2×D6111yescharacteristic
331C2×#117—1221no—
332C2×#117—1221no—
333C22×C42—611no—
334#479—6116no—
335#477—618no—
336#476—618no—
337#470—6116no—
338#468—6116no—
339#464—6116no—
340#462—618no—
341#461C2×D6118yescomplemented
342C2×#107—612no—
343C2×#106—612no—
344#423—618no—
345C2×C4⋊C8—612no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8C2×D6111yescharacteristic
348C2×#103—612no—
349C2×#103—612no—
350C2×#103C2×D6112yes—
351C2×#102—612no—
352C61C2×#325211yescharacteristic, complemented, Sylow
353C22×Q8—611no—
354C22×Q8—1221no—
355C22×Q8C22×D6112yes—
356C22×D4—1221no—
357C22×D4C22×D6111yescharacteristic
358C23×C4—21no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—611no—
362C2×Q16—618no—
363C2×Q16—2444no—
364C2×SD16—44no—
365C2×SD16C22×D6118yes—
366C2×M16—618no—
367C2×M16—2444no—
368C22×C8—612no—
369C22×C8C22×D6112yes—
370C4⋊Q8—22no—
371C4⋊Q8—614no—
372C4⋊Q8—1222no—
373C4⋊Q8C22×D6114yes—
374#126—1228no—
375#125—614no—
376#125—1222no—
377#125—1228no—
378#124—614no—
379#124—1222no—
380#123—1228no—
381C22⋊Q8—618no—
382C22⋊Q8—614no—
383C22⋊Q8—1222no—
384C22⋊Q8—1228no—
385C22⋊Q8—1224no—
386#121—614no—
387#121—1222no—
388C4×Q8—618no—
389C4×Q8—614no—
390C4×Q8—1228no—
391C4×Q8—1224no—
392C4×Q8—1222no—
393C4×D4—22no—
394C4×D4—1228no—
395C4×D4C22×D6114yes—
396#117—1228no—
397#117—1228no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—612no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—1222no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—614no—
420C2×C42—614no—
421C2×C42—1222no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#107—618no—
425#106—618no—
426C4⋊C8—618no—
427C4⋊C8—614no—
428C4⋊C8C22×D6114yes—
429#103—618no—
430#103—618no—
431#103C22×D6118yes—
432#102—618no—
433C24—21no—
434C24—611no—
435C2×Q8—22no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—612no—
439C2×Q8—1221no—
440C2×Q8—1224no—
441C2×Q8—1222no—
442C2×Q8—1222no—
443C2×Q8—2444no—
444C2×Q8C23×D6114yes—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—1224no—
449C2×D4—2444no—
450C2×D4C23×D6112yes—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—44no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—614no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—614no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1224no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1222no—
468C22×C4—2442no—
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4C23×D6111yescharacteristic
472Q16—2448no—
473SD16—48no—
474M16—2448no—
475C2×C8—24no—
476C2×C8—614no—
477C2×C8—1224no—
478C2×C8C23×D6114yes—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—614no—
483C4⋊C4—612no—
484C4⋊C4—1224no—
485C4⋊C4—1228no—
486C4⋊C4—1224no—
487C4⋊C4—1224no—
488C4⋊C4—1228no—
489C4⋊C4—1221no—
490C4⋊C4—1222no—
491C4⋊C4—1224no—
492C4⋊C4—1224no—
493C4⋊C4C23×D6112yes—
494C22⋊C4—24no—
495C22⋊C4—1228no—
496C22⋊C4—1224no—
497C22⋊C4—1224no—
498C22⋊C4—1224no—
499C22⋊C4—1224no—
500C42—614no—
501C42—612no—
502C42—614no—
503C42—612no—
504C42—1228no—
505C42—1224no—
506C42D4×D6112yes—
507C42C23×D6112yes—
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—612no—
513C23—1222no—
514C23—1222no—
515C23—1222no—
516C23C2×D4×D6111yescharacteristic
517Q8—24no—
518Q8—24no—
519Q8—44no—
520Q8—1222no—
521Q8—1222no—
522Q8—2448no—
523Q8—2442no—
524D4—22no—
525D4—22no—
526D4—42no—
527D4—2448no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—48no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1228no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1224no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1224no—
547C2×C4—2444no—
548C2×C4—2442no—
549C2×C4—2444no—
550C2×C4—2442no—
551C2×C4#1451980614yes—
552C2×C4C2×D4×D6112yes—
553C2×C4C2×D4×D6112yes—
554C2×C4C2×D4×D6111yescharacteristic
555C2×C4#1451982212yes—
556C2×C4#1451982412yes—
557C2×C4C24×D6111yescharacteristic
558C8—24no—
559C8—1224no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—84no—
564C22—1222no—
565C22—1222no—
566C22—1222no—
567C22—2444no—
568C22#1684034112yes—
569C22C2×#1451980612yes—
570C22#1684056112yes—
571C22C22×D4×D6111yescharacteristic
572C4—22no—
573C4—42no—
574C4—44no—
575C4—1222no—
576C4—1222no—
577C4—1222no—
578C4—2442no—
579C4—2444no—
580C4—2442no—
581C4#1684034112yes—
582C4C2×#1451980614yes—
583C4C2×#1451982211yescharacteristic
584C4C2×#1451982411yescharacteristic
585C2—82no—
586C2—2442no—
587C2#2145718814yesdirect product factor
588C2C2×#1684034111yescharacteristic
589C2C22×#1451980611yescharacteristic
590C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#461C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC2×#461D61
hypocenterC61C2×#3252
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21457188C2direct (N × H)
4. C2×#16840071C2semidirect
5. C2×#16840058C2semidirect
6. C2×#16840052C2semidirect
7. C2×#16840019C2semidirect
9. C2×#16839982C2semidirect
10. C2×#16839969C2semidirect
11. C2×#16839784C2semidirect
12. C2×C61×#461C2semidirect
16. #16840317C22semidirect
36. #16840071C22semidirect
37. #16840058C22semidirect
38. #16840052C22semidirect
39. #16840019C22semidirect
41. #16839982C22semidirect
42. #16839969C22semidirect
45. #16839784C22semidirect
54. C61×#461C22semidirect
300. C2×#461D61semidirect
303. C2×C61#3252semidirect
341. #461C2×D61semidirect
352. C61C2×#3252semidirect
587. C2#21457188direct (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×#168402942
#214571882
C2×#168400712
C2×#168400582
C2×#168400522
C2×#168400192
C2×#168400052
C2×#168399822
C2×#168399692
C2×#168397842
C2×C61×#4612
C2×#325261