Finite Group Databasebeta

← C2×#21455984 #30548154

Subgroups — C2×#21455984 #30548154

Order 15616.

2150 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2C2×C4×#11758226C211yesmaximal, characteristic
3#21455984C2116yesmaximal, direct product factor
4C2×#16840105C212yesmaximal, complemented
5C2×#16840049C211yesmaximal, characteristic, complemented
6C2×#16839972C211yesmaximal, characteristic, complemented
7C2×#16839968C211yesmaximal, characteristic, complemented
8C2×#16839927C212yesmaximal
9C2×#16839866C212yesmaximal, complemented
10C2×#16839861C212yesmaximal, complemented
11C2×#16839818C211yesmaximal, characteristic, complemented
12C2×C61×#477C211yesmaximal, characteristic, complemented
13C22×#11758226C2211yescharacteristic
14C22×#11758202C2212yes—
15C22×#11758190C2212yes—
16#16840317—24no—
17#16840317C2218yescomplemented
18C2×#14519777C2211yescharacteristic
19C2×#14519768—21no—
20C2×#14519757C2212yes—
21C2×#14519753—21no—
22C4×#11758226—24no—
23C4×#11758226C2218yes—
24C2×Q8×Dic61—21no—
25C2×Q8×Dic61C2211yescharacteristic
26C2×#14519742C2212yes—
27C2×C4×D244—21no—
28C2×C4×D244C2211yescharacteristic
29C2×#14519739—21no—
30C2×#14519739C2211yescharacteristic
31C2×#14519735—21no—
32C2×#14519735—21no—
33C2×#14519735C2211yescharacteristic
34C2×C42×D61—21no—
35C2×C42×D61C2211yescharacteristic
36#16840105C22116yescomplemented
37#16840049C2218yescomplemented
38#16839972C2218yescomplemented
39#16839968C2218yescomplemented
40#16839927C22116yes—
41#16839866C22116yescomplemented
42#16839861C22116yescomplemented
43#16839818C2218yescomplemented
44C2×#14519708C2212yes—
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519702C2212yes—
47C2×#14519700C2212yes—
48C2×#14519697C2212yes—
49C2×#14519689C2212yes—
50C2×#14519687C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C61×#477C2218yescomplemented
54C2×#107×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C2×#11758226—24no—
58C2×#11758226—24no—
59C2×#11758226—22no—
60C2×#11758226C2314yes—
61C22×Dic122C2312yes—
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758202—28no—
71C2×#11758202C2318yes—
72C2×#11758190—28no—
73C2×#11758190C2318yes—
74C22×#92418C2312yes—
75#14519777—22no—
76#14519777C2314yes—
77#14519768—28no—
78#14519757—24no—
79#14519757C2318yes—
80#14519753—28no—
81Q8×Dic61—28no—
82Q8×Dic61—22no—
83Q8×Dic61C2314yes—
84#14519742—24no—
85#14519742C2318yes—
86C4×D244—28no—
87C4×D244—22no—
88C4×D244C2314yes—
89#14519739—28no—
90#14519739—22no—
91#14519739C2314yes—
92#14519735—28no—
93#14519735—22no—
94#14519735—28no—
95#14519735C2314yes—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—22no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—22no—
102C2×#11758198—22no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61—28no—
113C42×D61D414yes—
114C42×D61C2314yes—
115#14519708C2318yes—
116C4⋊#92418C2314yes—
117#14519702C2318yes—
118#14519700C2318yes—
119#14519697C2318yes—
120#14519689C2318yes—
121#14519687C2318yes—
122C22×Q8×C61—21no—
123C22×Q8×C61C2311yescharacteristic
124C22×C8×C61C2312yes—
125C4⋊Q8×C61—22no—
126C4⋊Q8×C61C2314yes—
127C4×Q8×C61—22no—
128C4×Q8×C61C2314yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61C2318yes—
136C4⋊C8×C61C2314yes—
137#103×C61C2318yes—
138C23×D61—21no—
139C23×D61C2×D411yescharacteristic
140C2×Q8×C61—21no—
141C2×Q8×C61—24no—
142C2×Q8×C61—22no—
143C2×Q8×C61—44no—
144C2×Q8×C61#4114yes—
145C2×Q8×C61C2412yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157#11758226—216no—
158#11758226—28no—
159#11758226—28no—
160C2×D244—28no—
161C2×D244—24no—
162C2×D244—21no—
163C2×D244—22no—
164C2×D244#4114yes—
165C2×D244C2412yes—
166C2×C4×D61—28no—
167C2×C4×D61—24no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—24no—
173C2×C4×D61—42no—
174C2×C4×D61—44no—
175C2×C4×D61—44no—
176C2×C4×D61C2×D414yes—
177C2×C4×D61C2×D412yes—
178C2×C4×D61C2×D414yes—
179C2×C4×D61C2412yes—
180C2×Dic122—24no—
181C2×Dic122—24no—
182C2×Dic122—22no—
183C2×Dic122C2414yes—
184C2×C8×C61—24no—
185C2×C8×C61C2414yes—
186C4⋊C4×C61—24no—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61C2414yes—
191C4⋊C4×C61C2412yes—
192C42×C61—24no—
193C42×C61C2×D412yes—
194C42×C61C2412yes—
195#11758202—216no—
196#11758198—28no—
197#11758198—24no—
198#11758198—24no—
199#11758198—24no—
200C4⋊Dic61—24no—
201C4⋊Dic61—24no—
202C4⋊Dic61—21no—
203C4⋊Dic61—24no—
204C4⋊Dic61—28no—
205C4⋊Dic61C2412yes—
206#11758196—28no—
207C4×Dic61—24no—
208C4×Dic61—24no—
209C4×Dic61—28no—
210C4×Dic61C2×D414yes—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D414yes—
213C4×Dic61C2412yes—
214C2×#92418—24no—
215C2×#92418C2414yes—
216#11758190—216no—
217C23×C61C22×D411yescharacteristic
218C22×D61—22no—
219C22×D61—24no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61C22×D412yes—
226Q8×C61—24no—
227Q8×C61—22no—
228Q8×C61—48no—
229Q8×C61C2×#4114yes—
230C2×C4×C61—24no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—42no—
236C2×C4×C61—44no—
237C2×C4×C61#13714yes—
238C2×C4×C61C22×D412yes—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D412yes—
241C2×C4×C61C2×#4112yes—
242C2×C4×C61C2×#4112yes—
243C2×C4×C61C2511yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—44no—
250C2×Dic61—42no—
251C2×Dic61C22×D412yes—
252C2×Dic61C22×D412yes—
253C2×Dic61C22×D412yes—
254D244—216no—
255D244—24no—
256D244—22no—
257D244C2×#4114yes—
258C4×D61—216no—
259C4×D61—24no—
260C4×D61—28no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—44no—
264C4×D61—48no—
265C4×D61—48no—
266Dic122—24no—
267Dic122—24no—
268Dic122—44no—
269C8×C61—24no—
270#92418—24no—
271C2×#3116—611nomaximal, Sylow
272C22×C61#52512yes—
273C22×C61C2×#13712yes—
274C22×C61#57512yes—
275C22×C61C23×D411yescharacteristic
276C2×D61—22no—
277C2×D61—24no—
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—44no—
281C2×D61—48no—
282C2×D61—42no—
283C2×D61—42no—
284C4×C61—24no—
285C4×C61—22no—
286C4×C61—42no—
287C4×C61—44no—
288C4×C61#52512yes—
289C4×C61C2×#13714yes—
290C4×C61C22×#4111yescharacteristic
291C4×C61C22×#4111yescharacteristic
292Dic61—22no—
293Dic61—22no—
294Dic61—22no—
295Dic61—44no—
296Dic61—42no—
297C2×#533—611no—
298C2×C4×#41—611no—
299#3116—6116no—
300C2×#485—612no—
301C2×#477D6111yescharacteristic, complemented
302C2×#476—611no—
303C2×#462—611no—
304C2×#461—611no—
305C2×#452—612no—
306C2×#441—612no—
307C2×#440—612no—
308C2×#432—611no—
309C2×C61#311614yescomplemented
310C2×C61C2×#52511yescharacteristic
311C2×C61C22×#13711yescharacteristic
312C2×C61C2×#57511yescharacteristic
313D61—42no—
314D61—44no—
315C22×#41—611no—
316C22×Q16—612no—
317C22×SD16—612no—
318#533—618no—
319#533—1224no—
320C2×C4⋊Q8—611no—
321C2×C4⋊Q8C2×D6111yescharacteristic
322C2×#125—1221no—
323C2×C22⋊Q8—612no—
324C2×C22⋊Q8—1221no—
325C4×#41—618no—
326C4×#41—1224no—
327C2×C4×Q8—611no—
328C2×C4×Q8—612no—
329C2×C4×Q8—1221no—
330C2×C4×Q8C2×D6111yescharacteristic
331C2×C4×D4—611no—
332C2×C4×D4—611no—
333C2×C4×D4—1221no—
334C2×C4×D4—1221no—
335C2×#117—611no—
336C2×#117—1221no—
337C2×#117—1221no—
338C22×C42—611no—
339C22×C42—1221no—
340#485—6116no—
341#477C2×D6118yescomplemented
342#476—618no—
343#462—618no—
344#461—618no—
345#452—6116no—
346#441—6116no—
347#440—6116no—
348#432—618no—
349C2×#107C2×D6112yes—
350C2×#106—612no—
351C2×C4⋊C8—611no—
352C2×C4⋊C8C2×D6111yescharacteristic
353C2×#103—612no—
354C2×#103—612no—
355C2×#103C2×D6112yes—
356C2×#102—612no—
357C2×C22⋊C8—612no—
358C2×#97—612no—
359C61C2×#311611yescharacteristic, complemented, Sylow
360C2×#41—614no—
361C2×#41—1222no—
362C2×#41—1224no—
363C2×#41—1224no—
364C22×Q8—21no—
365C22×Q8—612no—
366C22×Q8C22×D6111yescharacteristic
367C22×D4—611no—
368C22×D4—1221no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1221no—
373C23×C4—1221no—
374C23×C4—1221no—
375C2×Q16—618no—
376C2×Q16—1228no—
377C2×SD16—618no—
378C2×SD16—1228no—
379C22×C8—612no—
380C22×C8C22×D6112yes—
381C4⋊Q8—22no—
382C4⋊Q8—614no—
383C4⋊Q8—1222no—
384C4⋊Q8C22×D6114yes—
385#125—1228no—
386C22⋊Q8—618no—
387C22⋊Q8—1224no—
388C22⋊Q8—1228no—
389C4×Q8—22no—
390C4×Q8—614no—
391C4×Q8—618no—
392C4×Q8—1224no—
393C4×Q8—1222no—
394C4×Q8—1228no—
395C4×Q8C22×D6114yes—
396C4×D4—614no—
397C4×D4—614no—
398C4×D4—1228no—
399C4×D4—1222no—
400C4×D4—1228no—
401C4×D4—1222no—
402#117—614no—
403#117—1228no—
404#117—1222no—
405#117—1228no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1222no—
411C2×C4⋊C4—1222no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6112yes—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1222no—
419C2×C22⋊C4—1221no—
420C2×C42—21no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—614no—
425C2×C42—614no—
426C2×C42—1228no—
427C2×C42—1221no—
428C2×C42—1222no—
429C2×C42—1221no—
430C2×C42C22×D6111yescharacteristic
431#107C22×D6118yes—
432#106—618no—
433C4⋊C8—614no—
434C4⋊C8C22×D6114yes—
435#103—618no—
436#103—618no—
437#103C22×D6118yes—
438#102—618no—
439C22⋊C8—618no—
440#97—618no—
441C24—611no—
442C24—1221no—
443#41—1228no—
444#41—12216no—
445#41—1228no—
446C2×Q8—21no—
447C2×Q8—24no—
448C2×Q8—22no—
449C2×Q8—44no—
450C2×Q8—614no—
451C2×Q8—1222no—
452C2×Q8—1224no—
453C2×Q8—1224no—
454C2×Q8#1175822614yes—
455C2×Q8C23×D6112yes—
456C2×D4—614no—
457C2×D4—612no—
458C2×D4—1224no—
459C2×D4—1228no—
460C2×D4—1221no—
461C2×D4—1222no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—614no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—614no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—1228no—
475C22×C4—1224no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1221no—
479C22×C4—1222no—
480C22×C4—1224no—
481C22×C4—2442no—
482C22×C4—2444no—
483C22×C4—2444no—
484C22×C4D4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C22×C4C23×D6111yescharacteristic
487Q16—12216no—
488SD16—12216no—
489C2×C8—24no—
490C2×C8—614no—
491C2×C8—1224no—
492C2×C8C23×D6114yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—612no—
498C4⋊C4—1228no—
499C4⋊C4—1224no—
500C4⋊C4—1228no—
501C4⋊C4—1221no—
502C4⋊C4—1224no—
503C4⋊C4—1224no—
504C4⋊C4C23×D6114yes—
505C4⋊C4C23×D6112yes—
506C22⋊C4—1224no—
507C22⋊C4—1224no—
508C22⋊C4—1228no—
509C22⋊C4—1224no—
510C42—24no—
511C42—614no—
512C42—614no—
513C42—612no—
514C42—612no—
515C42—1224no—
516C42—1224no—
517C42—1228no—
518C42D4×D6112yes—
519C42C23×D6112yes—
520C23—612no—
521C23—1224no—
522C23—1222no—
523C23—1222no—
524C23—1222no—
525C23—1222no—
526C23—2442no—
527C23—2442no—
528C23C2×D4×D6111yescharacteristic
529Q8—24no—
530Q8—22no—
531Q8—48no—
532Q8—1224no—
533Q8—1224no—
534Q8—2444no—
535Q8C2×#1175822614yes—
536D4—614no—
537D4—12216no—
538D4—1224no—
539D4—1222no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—612no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—12216no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1224no—
555C2×C4—1228no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1224no—
560C2×C4—2444no—
561C2×C4—2448no—
562C2×C4—2444no—
563C2×C4—2442no—
564C2×C4—2448no—
565C2×C4#1451980914yes—
566C2×C4C2×D4×D6112yes—
567C2×C4C2×D4×D6111yescharacteristic
568C2×C4C2×D4×D6112yes—
569C2×C4#41×D6112yes—
570C2×C4C2×#1175822612yes—
571C2×C4C24×D6111yescharacteristic
572C8—24no—
573C8—1224no—
574C22—1222no—
575C22—1222no—
576C22—1224no—
577C22—1222no—
578C22—2442no—
579C22—2442no—
580C22—2444no—
581C22—2448no—
582C22#1684027512yes—
583C22C2×#1451980912yes—
584C22#1684055812yes—
585C22C22×D4×D6111yescharacteristic
586C4—22no—
587C4—24no—
588C4—42no—
589C4—44no—
590C4—1222no—
591C4—1222no—
592C4—1222no—
593C4—2442no—
594C4—2444no—
595C4#1684027512yes—
596C4C2×#1451980914yes—
597C4C2×#41×D6111yescharacteristic
598C4C22×#1175822611yescharacteristic
599C2—2442no—
600C2—2444no—
601C2#2145598414yesdirect product factor
602C2C2×#1684027511yescharacteristic
603C2C22×#1451980911yescharacteristic
604C2C2×#1684055811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
hypercenterC2×#477D61
hypocenterC61C2×#3116
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21455984C2direct (N × H)
4. C2×#16840105C2semidirect
5. C2×#16840049C2semidirect
6. C2×#16839972C2semidirect
7. C2×#16839968C2semidirect
9. C2×#16839866C2semidirect
10. C2×#16839861C2semidirect
11. C2×#16839818C2semidirect
12. C2×C61×#477C2semidirect
17. #16840317C22semidirect
36. #16840105C22semidirect
37. #16840049C22semidirect
38. #16839972C22semidirect
39. #16839968C22semidirect
41. #16839866C22semidirect
42. #16839861C22semidirect
43. #16839818C22semidirect
53. C61×#477C22semidirect
301. C2×#477D61semidirect
309. C2×C61#3116semidirect
341. #477C2×D61semidirect
359. C61C2×#3116semidirect
601. C2#21455984direct (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×C4×#117582262
#214559842
C2×#168401052
C2×#168400492
C2×#168399722
C2×#168399682
C2×#168399272
C2×#168398662
C2×#168398612
C2×#168398182
C2×C61×#4772
C2×#311661