Finite Group Databasebeta

← C2×#21455980 #30548150

Subgroups — C2×#21455980 #30548150

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#21455980C2116yesmaximal, direct product factor
4C2×#16840101C212yesmaximal, complemented
5C2×#16840057C211yesmaximal, characteristic, complemented
6C2×#16840053C211yesmaximal, characteristic, complemented
7C2×#16839964C211yesmaximal, characteristic, complemented
8C2×#16839923C212yesmaximal
9C2×#16839869C212yesmaximal, complemented
10C2×#16839865C212yesmaximal, complemented
11C2×#16839818C211yesmaximal, characteristic, complemented
12C2×C61×#462C211yesmaximal, characteristic, complemented
13C22×#11758226C2211yescharacteristic
14C22×#11758201C2212yes—
15#16840317—24no—
16#16840317C2218yescomplemented
17C2×#14519777C2211yescharacteristic
18C2×#14519768—21no—
19C2×#14519757—21no—
20C2×#14519753C2212yes—
21C4×#11758226—24no—
22C4×#11758226C2218yes—
23C2×Q8×Dic61C2212yes—
24C2×Q8×Dic61C2211yescharacteristic
25C2×#14519742—21no—
26C2×C4×D244—21no—
27C2×C4×D244C2211yescharacteristic
28C2×#14519739—21no—
29C2×#14519739C2211yescharacteristic
30C2×#14519735—21no—
31C2×#14519735—21no—
32C2×#14519735C2211yescharacteristic
33C2×C42×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16840101C22116yescomplemented
36#16840057C2218yescomplemented
37#16840053C2218yescomplemented
38#16839964C2218yescomplemented
39#16839923C22116yes—
40#16839869C22116yescomplemented
41#16839865C22116yescomplemented
42#16839818C2218yescomplemented
43C2×#14519710C2212yes—
44C2×#14519709C2212yes—
45C2×C4⋊#92418C2211yescharacteristic
46C2×#14519701C2212yes—
47C2×#14519701C2212yes—
48C2×#14519699C2212yes—
49C2×#14519689C2212yes—
50C2×#14519687C2212yes—
51C22×Q16×C61C2212yes—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#462C2218yescomplemented
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#103×C61C2212yes—
57C2×#11758226—24no—
58C2×#11758226—24no—
59C2×#11758226—22no—
60C2×#11758226C2314yes—
61C22×Dic122—21no—
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×#11758201—28no—
71C2×#11758201C2318yes—
72C22×#92418C2312yes—
73#14519777—22no—
74#14519777C2314yes—
75#14519768—28no—
76#14519757—28no—
77#14519753—24no—
78#14519753C2318yes—
79Q8×Dic61—22no—
80Q8×Dic61—24no—
81Q8×Dic61C2314yes—
82Q8×Dic61C2318yes—
83#14519742—28no—
84C4×D244—28no—
85C4×D244—22no—
86C4×D244C2314yes—
87#14519739—28no—
88#14519739—22no—
89#14519739C2314yes—
90#14519735—28no—
91#14519735—22no—
92#14519735—28no—
93#14519735C2314yes—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2312yes—
99C2×#11758196—22no—
100C2×#11758198—22no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C42×D61—28no—
111C42×D61D414yes—
112C42×D61C2314yes—
113#14519710C2318yes—
114#14519709C2318yes—
115C4⋊#92418C2314yes—
116#14519701C2318yes—
117#14519701C2318yes—
118#14519699C2318yes—
119#14519689C2318yes—
120#14519687C2318yes—
121C22×Q8×C61C2312yes—
122C22×Q8×C61C2311yescharacteristic
123C2×Q16×C61—28no—
124C2×Q16×C61C2318yes—
125C22×C8×C61C2312yes—
126C4⋊Q8×C61—22no—
127C4⋊Q8×C61C2314yes—
128C4×Q8×C61—22no—
129C4×Q8×C61C2314yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2314yes—
137#103×C61C2318yes—
138C23×D61—21no—
139C23×D61C2×D411yescharacteristic
140C2×Q8×C61—21no—
141C2×Q8×C61—22no—
142C2×Q8×C61—22no—
143C2×Q8×C61—24no—
144C2×Q8×C61—24no—
145C2×Q8×C61#4114yes—
146C2×Q8×C61C2414yes—
147C2×Q8×C61C2412yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C22×Dic61—21no—
155C22×Dic61—22no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159#11758226—216no—
160#11758226—28no—
161#11758226—28no—
162C2×D244—28no—
163C2×D244—24no—
164C2×D244—21no—
165C2×D244—22no—
166C2×D244#4114yes—
167C2×D244C2412yes—
168C2×C4×D61—28no—
169C2×C4×D61—24no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—42no—
176C2×C4×D61—44no—
177C2×C4×D61—44no—
178C2×C4×D61C2×D414yes—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D414yes—
181C2×C4×D61C2412yes—
182C2×Dic122—24no—
183C2×Dic122—44no—
184Q16×C61—216no—
185C2×C8×C61—24no—
186C2×C8×C61C2414yes—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61C2412yes—
192C42×C61—24no—
193C42×C61C2×D412yes—
194C42×C61C2412yes—
195#11758201—216no—
196#11758198—28no—
197#11758198—24no—
198#11758198—24no—
199#11758198—24no—
200C4⋊Dic61—24no—
201C4⋊Dic61—21no—
202C4⋊Dic61—22no—
203C4⋊Dic61—24no—
204C4⋊Dic61—28no—
205C4⋊Dic61C2414yes—
206C4⋊Dic61C2412yes—
207#11758196—28no—
208C4×Dic61—24no—
209C4×Dic61—24no—
210C4×Dic61—28no—
211C4×Dic61C2×D414yes—
212C4×Dic61C2×D412yes—
213C4×Dic61C2×D414yes—
214C4×Dic61C2412yes—
215C2×#92418—24no—
216C2×#92418C2414yes—
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—24no—
229Q8×C61—24no—
230Q8×C61—44no—
231Q8×C61C2×#4114yes—
232C2×C4×C61—24no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—22no—
237C2×C4×C61—44no—
238C2×C4×C61—42no—
239C2×C4×C61#13714yes—
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D412yes—
243C2×C4×C61C2×#4112yes—
244C2×C4×C61C2×#4112yes—
245C2×C4×C61C2511yescharacteristic
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—42no—
252C2×Dic61—44no—
253C2×Dic61C22×D412yes—
254C2×Dic61C22×D412yes—
255C2×Dic61C22×D412yes—
256D244—216no—
257D244—24no—
258D244—22no—
259D244C2×#4114yes—
260C4×D61—216no—
261C4×D61—24no—
262C4×D61—28no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—44no—
266C4×D61—48no—
267C4×D61—48no—
268Dic122—48no—
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—44no—
287C4×C61—42no—
288C4×C61#52512yes—
289C4×C61C2×#13714yes—
290C4×C61C22×#4111yescharacteristic
291C4×C61C22×#4111yescharacteristic
292Dic61—22no—
293Dic61—22no—
294Dic61—22no—
295Dic61—42no—
296Dic61—44no—
297C2×#533—611no—
298C2×C4×#41—611no—
299#3116—6116no—
300C2×#485—612no—
301C2×#477—611no—
302C2×#476—611no—
303C2×#462D6111yescharacteristic, complemented
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×Q16C2×D6112yes—
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#477—618no—
342#476—618no—
343#462C2×D6118yescomplemented
344#461—618no—
345#452—6116no—
346#441—6116no—
347#440—6116no—
348#432—618no—
349C2×#107—612no—
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—1221no—
365C22×Q8C22×D6112yes—
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—28no—
376C2×Q16C22×D6118yes—
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—1228no—
388C22⋊Q8—1224no—
389C4×Q8—22no—
390C4×Q8—614no—
391C4×Q8—618no—
392C4×Q8—1228no—
393C4×Q8—1222no—
394C4×Q8—1224no—
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—21no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—612no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4C22×D6111yescharacteristic
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#107—618no—
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—22no—
448C2×Q8—22no—
449C2×Q8—24no—
450C2×Q8—24no—
451C2×Q8—1224no—
452C2×Q8—2444no—
453C2×Q8#1175822414yes—
454C2×Q8C23×D6114yes—
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—216no—
488SD16—12216no—
489C2×C8—24no—
490C2×C8—614no—
491C2×C8—1224no—
492C2×C8C23×D6114yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—21no—
497C4⋊C4—614no—
498C4⋊C4—612no—
499C4⋊C4—1228no—
500C4⋊C4—1224no—
501C4⋊C4—1228no—
502C4⋊C4—1221no—
503C4⋊C4—1222no—
504C4⋊C4—1224no—
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—24no—
532Q8—24no—
533Q8—44no—
534Q8—2448no—
535Q8C2×#1175822414yes—
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—44no—
546C2×C4—42no—
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—2442no—
563C2×C4—2444no—
564C2×C4—2448no—
565C2×C4#1451980914yes—
566C2×C4C2×D4×D6112yes—
567C2×C4C2×D4×D6111yescharacteristic
568C2×C4C2×D4×D6112yes—
569C2×C4#41×D6112yes—
570C2×C4C2×#1175822412yes—
571C2×C4C24×D6111yescharacteristic
572C8—24no—
573C8—1224no—
574C22—1222no—
575C22—1222no—
576C22—1224no—
577C22—1222no—
578C22—2442no—
579C22—2442no—
580C22—2444no—
581C22—2448no—
582C22#1684027212yes—
583C22C2×#1451980912yes—
584C22#1684056112yes—
585C22C22×D4×D6111yescharacteristic
586C4—22no—
587C4—24no—
588C4—42no—
589C4—44no—
590C4—1222no—
591C4—1222no—
592C4—1222no—
593C4—2442no—
594C4—2444no—
595C4#1684027212yes—
596C4C2×#1451980914yes—
597C4C2×#41×D6111yescharacteristic
598C4C22×#1175822411yescharacteristic
599C2—2442no—
600C2—2444no—
601C2#2145598014yesdirect product factor
602C2C2×#1684027211yescharacteristic
603C2C22×#1451980911yescharacteristic
604C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
hypercenterC2×#462D61
hypocenterC61C2×#3116
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21455980C2direct (N × H)
4. C2×#16840101C2semidirect
5. C2×#16840057C2semidirect
6. C2×#16840053C2semidirect
7. C2×#16839964C2semidirect
9. C2×#16839869C2semidirect
10. C2×#16839865C2semidirect
11. C2×#16839818C2semidirect
12. C2×C61×#462C2semidirect
16. #16840317C22semidirect
35. #16840101C22semidirect
36. #16840057C22semidirect
37. #16840053C22semidirect
38. #16839964C22semidirect
40. #16839869C22semidirect
41. #16839865C22semidirect
42. #16839818C22semidirect
54. C61×#462C22semidirect
303. C2×#462D61semidirect
309. C2×C61#3116semidirect
343. #462C2×D61semidirect
359. C61C2×#3116semidirect
601. C2#21455980direct (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
#214559802
C2×#168401012
C2×#168400572
C2×#168400532
C2×#168399642
C2×#168399232
C2×#168398692
C2×#168398652
C2×#168398182
C2×C61×#4622
C2×#311661