Finite Group Databasebeta

← C2×#21455303 #30546866

Subgroups — C2×#21455303 #30546866

Order 15616.

2790 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C212yesmaximal
2C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3C2×C4×#11758226C211yesmaximal, characteristic
4#21455303C2116yesmaximal, direct product factor
5C2×#16839972C211yesmaximal, characteristic, complemented
6C2×#16839970C212yesmaximal, complemented
7C2×#16839968C211yesmaximal, characteristic, complemented
8C2×#16839966C212yesmaximal, complemented
9C2×#16839964C211yesmaximal, characteristic, complemented
10C2×#16839784C211yesmaximal, characteristic, complemented
11C2×#16839769C212yesmaximal, complemented
12C2×C61×#462C211yesmaximal, characteristic, complemented
13C22×#11758226C2211yescharacteristic
14C22×Q8×D61C2212yes—
15C2×#14519809—216no—
16C2×#14519809C22116yes—
17C22×#11758202C2212yes—
18C22×#11758190C2212yes—
19C22×#11758201C2212yes—
20C22×#11758189C2212yes—
21C2×#14519777C2211yescharacteristic
22C2×#14519776—21no—
23C2×#14519776—21no—
24C2×#14519775C2212yes—
25C4⋊Q8×D61—24no—
26C4⋊Q8×D61C2218yescomplemented
27C4×#11758226—24no—
28C4×#11758226C2218yes—
29C2×Q8×Dic61C2211yescharacteristic
30C2×C4×D244—21no—
31C2×C4×D244C2211yescharacteristic
32C2×#14519739—21no—
33C2×#14519739C2211yescharacteristic
34C2×#14519735—21no—
35C2×#14519735C2211yescharacteristic
36C2×C4⋊C4×D61—21no—
37C2×C4⋊C4×D61—21no—
38C2×C42×D61—21no—
39C2×C42×D61C2211yescharacteristic
40#16839972C2218yescomplemented
41#16839970C22116yescomplemented
42#16839968C2218yescomplemented
43#16839966C22116yescomplemented
44#16839964C2218yescomplemented
45#16839784C2218yescomplemented
46C2×C4⋊#92418C2211yescharacteristic
47C2×#14519706C2212yes—
48#16839769C22116yescomplemented
49C2×#14519702C2212yes—
50C2×#14519701C2212yes—
51C2×#14519700C2212yes—
52C22×Q16×C61C2212yes—
53C2×C4⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C61×#462C2218yescomplemented
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×#103×C61C2212yes—
58C2×#11758226—22no—
59C2×#11758226—24no—
60C2×#11758226D418yes—
61C2×#11758226C2314yes—
62C22×Dic122—22no—
63C22×Dic122C2312yes—
64C2×Q8×D61—24no—
65C2×Q8×D61—28no—
66C2×Q8×D61—28no—
67C2×Q8×D61C2318yes—
68C22×D244—21no—
69C22×D244C2311yescharacteristic
70C22×C4×D61—21no—
71C22×C4×D61—22no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519809—264no—
78C2×#11758202—28no—
79C2×#11758202C2318yes—
80C2×#11758190—28no—
81C2×#11758190C2318yes—
82C2×#11758201—28no—
83C2×#11758201C2318yes—
84C2×#11758189—28no—
85C2×#11758189C2318yes—
86C22×#92418C2312yes—
87#14519777—22no—
88#14519777C2314yes—
89#14519776—28no—
90#14519776—28no—
91#14519775—24no—
92#14519775C2318yes—
93Q8×Dic61—22no—
94Q8×Dic61C2314yes—
95C4×D244—28no—
96C4×D244—22no—
97C4×D244C2314yes—
98#14519739—28no—
99#14519739—22no—
100#14519739C2314yes—
101#14519735—22no—
102#14519735—28no—
103#14519735C2314yes—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—22no—
109C2×#11758196—22no—
110C4⋊C4×D61—28no—
111C4⋊C4×D61—28no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C42×D61—28no—
121C42×D61D414yes—
122C42×D61C2314yes—
123C4⋊#92418C2314yes—
124#14519706C2318yes—
125#14519702C2318yes—
126#14519701C2318yes—
127#14519700C2318yes—
128C22×Q8×C61C2312yes—
129C22×Q8×C61C2311yescharacteristic
130C2×Q16×C61—28no—
131C2×Q16×C61C2318yes—
132C22×C8×C61C2312yes—
133C4⋊Q8×C61—22no—
134C4⋊Q8×C61C2314yes—
135C4×Q8×C61—22no—
136C4×Q8×C61C2314yes—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C42×C61—21no—
142C2×C42×C61C2311yescharacteristic
143C4⋊C8×C61C2314yes—
144#103×C61C2318yes—
145C23×D61—21no—
146C23×D61C2×D411yescharacteristic
147C2×Q8×C61—21no—
148C2×Q8×C61—22no—
149C2×Q8×C61—22no—
150C2×Q8×C61—24no—
151C2×Q8×C61—24no—
152C2×Q8×C61C2×D414yes—
153C2×Q8×C61C2414yes—
154C2×Q8×C61C2412yes—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—21no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166#11758226—216no—
167#11758226—28no—
168#11758226C2×D4116yes—
169Q8×D61—216no—
170Q8×D61—216no—
171Q8×D61—416no—
172C2×D244—28no—
173C2×D244—24no—
174C2×D244—21no—
175C2×D244—22no—
176C2×D244C2×D414yes—
177C2×D244C2412yes—
178C2×C4×D61—24no—
179C2×C4×D61—28no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—28no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—48no—
186C2×C4×D61—44no—
187C2×C4×D61—44no—
188C2×C4×D61C2×D414yes—
189C2×C4×D61C2×D414yes—
190C2×C4×D61C2×D412yes—
191C2×C4×D61C2×D414yes—
192C2×C4×D61#4114yes—
193C2×C4×D61C2412yes—
194C2×Dic122—24no—
195C2×Dic122—24no—
196C2×Dic122—22no—
197C2×Dic122—28no—
198C2×Dic122—48no—
199C2×Dic122C2414yes—
200Q16×C61—216no—
201C2×C8×C61—24no—
202C2×C8×C61C2414yes—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—24no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C2412yes—
208C42×C61—24no—
209C42×C61C2×D412yes—
210C42×C61C2412yes—
211#11758202—216no—
212#11758201—216no—
213#11758198—24no—
214#11758198—24no—
215#11758198—24no—
216C4⋊Dic61—24no—
217C4⋊Dic61—24no—
218C4⋊Dic61—21no—
219C4⋊Dic61—24no—
220C4⋊Dic61C2412yes—
221#11758196—28no—
222#11758196—28no—
223C4×Dic61—24no—
224C4×Dic61—24no—
225C4×Dic61C2×D414yes—
226C4×Dic61C2×D412yes—
227C4×Dic61C2×D414yes—
228C4×Dic61C2412yes—
229C2×#92418—24no—
230C2×#92418C2414yes—
231#11758190—216no—
232#11758189—216no—
233C23×C61C22×D411yescharacteristic
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—24no—
237C22×D61—22no—
238C22×D61—42no—
239C22×D61—42no—
240C22×D61#12114yes—
241C22×D61C22×D412yes—
242Q8×C61—24no—
243Q8×C61—22no—
244Q8×C61—24no—
245Q8×C61—24no—
246Q8×C61—44no—
247Q8×C61C22×D414yes—
248C2×C4×C61—24no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—24no—
253C2×C4×C61—44no—
254C2×C4×C61—42no—
255C2×C4×C61#13714yescomplemented
256C2×C4×C61C22×D412yes—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C22×D412yes—
259C2×C4×C61C22×D412yes—
260C2×C4×C61C2×#4112yes—
261C2×C4×C61C2511yescharacteristic
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—24no—
265C2×Dic61—44no—
266C2×Dic61—42no—
267C2×Dic61#12114yes—
268C2×Dic61#13714yescomplemented
269C2×Dic61C22×D412yes—
270C2×Dic61C22×D412yes—
271C2×Dic61C22×D412yes—
272D244—216no—
273D244—24no—
274D244—22no—
275D244C22×D414yes—
276C4×D61—28no—
277C4×D61—216no—
278C4×D61—28no—
279C4×D61—416no—
280C4×D61—48no—
281C4×D61—48no—
282C4×D61#12118yes—
283C4×D61C22×D414yes—
284C4×D61C2×#4114yes—
285Dic122—24no—
286Dic122—24no—
287Dic122—44no—
288Dic122—416no—
289C8×C61—24no—
290#92418—24no—
291C2×#3039—611nomaximal, Sylow
292C22×C61C2×#12112yes—
293C22×C61C2×#13712yes—
294C22×C61C2×#13712yes—
295C22×C61C23×D411yescharacteristic
296C2×D61—28no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—24no—
300C2×D61—48no—
301C2×D61—42no—
302C2×D61—42no—
303C2×D61C2×#12114yes—
304C4×C61—24no—
305C4×C61—22no—
306C4×C61—44no—
307C4×C61—42no—
308C4×C61C2×#12112yes—
309C4×C61C2×#13714yescomplemented
310C4×C61C23×D411yescharacteristic
311C4×C61C22×#4111yescharacteristic
312Dic61—22no—
313Dic61—44no—
314Dic61—42no—
315Dic61C2×#12114yes—
316Dic61C2×#13714yescomplemented
317C22×#137—612no—
318C22×C4⋊Q8—611no—
319C2×C4×#41—611no—
320#3039—6116no—
321C2×#462—612no—
322C2×#462—611no—
323C2×#462D6111yescharacteristic, complemented
324C2×#461—611no—
325C2×#461—612no—
326C2×#461—611no—
327C2×#423—611no—
328C2×#419—612no—
329C2×C61#303914yescomplemented
330C2×C61C22×#12111yescharacteristic
331C2×C61C22×#13711yescharacteristic
332C2×C61C22×#13711yescharacteristic
333D61—24no—
334D61—44no—
335C22×#41—611no—
336C23×Q8—612no—
337C2×#137—6116no—
338C2×#137—12216no—
339C22×Q16—612no—
340C22×Q16C2×D6112yes—
341C22×SD16—612no—
342C22×SD16—612no—
343C22×M16—612no—
344C2×C4⋊Q8—612no—
345C2×C4⋊Q8—618no—
346C2×C4⋊Q8—611no—
347C2×C4⋊Q8—1221no—
348C2×C4⋊Q8—1221no—
349C2×C4⋊Q8—1224no—
350C2×C4⋊Q8C2×D6111yescharacteristic
351C4×#41—618no—
352C4×#41—1224no—
353C2×C4×Q8—611no—
354C2×C4×Q8C2×D6111yescharacteristic
355C2×C4×D4—611no—
356C2×C4×D4—611no—
357C2×C4×D4—1221no—
358C2×C4×D4—1221no—
359C2×#117—611no—
360C2×#117—1221no—
361C22×C4⋊C4—1221no—
362C22×C4⋊C4—1221no—
363C22×C42—611no—
364C22×C42—1221no—
365#462—6116no—
366#462—618no—
367#462C2×D6118yescomplemented
368#461—618no—
369#461—618no—
370#461—6116no—
371#423—618no—
372C2×C4⋊C8—612no—
373C2×C4⋊C8—611no—
374C2×C4⋊C8C2×D6111yescharacteristic
375#419—6116no—
376C2×#103—612no—
377C2×#103—612no—
378C2×#103—612no—
379C2×#103C2×D6112yes—
380C61C2×#303911yescharacteristic, complemented, Sylow
381C2×#41—618no—
382C2×#41—614no—
383C2×#41—1222no—
384C2×#41—1224no—
385C22×Q8—618no—
386C22×Q8—612no—
387C22×Q8—1222no—
388C22×Q8—1224no—
389C22×Q8—1228no—
390C22×Q8—1228no—
391C22×Q8C22×D6112yes—
392C22×Q8C22×D6111yescharacteristic
393C22×D4—611no—
394C22×D4—1221no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—1221no—
399C23×C4—1221no—
400C23×C4—1222no—
401C23×C4—1221no—
402#137—12264no—
403C2×Q16—28no—
404C2×Q16—618no—
405C2×Q16—1228no—
406C2×Q16C22×D6118yes—
407C2×SD16—618no—
408C2×SD16—618no—
409C2×SD16—1228no—
410C2×SD16—1228no—
411C2×M16—618no—
412C2×M16—1228no—
413C22×C8—612no—
414C22×C8C22×D6112yes—
415C4⋊Q8—22no—
416C4⋊Q8—618no—
417C4⋊Q8—614no—
418C4⋊Q8—1228no—
419C4⋊Q8—1228no—
420C4⋊Q8—1224no—
421C4⋊Q8—1222no—
422C4⋊Q8C22×D6114yes—
423C4×Q8—22no—
424C4×Q8—614no—
425C4×Q8—1222no—
426C4×Q8C22×D6114yes—
427C4×D4—614no—
428C4×D4—614no—
429C4×D4—1228no—
430C4×D4—1222no—
431C4×D4—1228no—
432C4×D4—1222no—
433#117—614no—
434#117—1228no—
435#117—1222no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—1228no—
441C2×C4⋊C4—1228no—
442C2×C4⋊C4—1222no—
443C2×C4⋊C4—1222no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C42—21no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—614no—
456C2×C42—614no—
457C2×C42—1228no—
458C2×C42—1221no—
459C2×C42—1221no—
460C2×C42C22×D6111yescharacteristic
461C4⋊C8—618no—
462C4⋊C8—614no—
463C4⋊C8C22×D6114yes—
464#103—618no—
465#103—618no—
466#103—618no—
467#103C22×D6118yes—
468C24—611no—
469C24—1221no—
470#41—6116no—
471#41—12216no—
472#41—1228no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—614no—
479C2×Q8—1228no—
480C2×Q8—12216no—
481C2×Q8—12216no—
482C2×Q8—1222no—
483C2×Q8—1224no—
484C2×Q8—1224no—
485C2×Q8—2448no—
486C2×Q8—24416no—
487C2×Q8D4×D6114yes—
488C2×Q8C23×D6114yes—
489C2×Q8C23×D6112yes—
490C2×D4—614no—
491C2×D4—612no—
492C2×D4—1224no—
493C2×D4—1228no—
494C2×D4—1221no—
495C2×D4—1222no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—612no—
502C22×C4—614no—
503C22×C4—614no—
504C22×C4—612no—
505C22×C4—611no—
506C22×C4—614no—
507C22×C4—614no—
508C22×C4—1224no—
509C22×C4—1224no—
510C22×C4—1228no—
511C22×C4—1224no—
512C22×C4—1228no—
513C22×C4—1224no—
514C22×C4—1221no—
515C22×C4—1222no—
516C22×C4—1224no—
517C22×C4—2444no—
518C22×C4—2448no—
519C22×C4—2444no—
520C22×C4D4×D6111yescharacteristic
521C22×C4D4×D6111yescharacteristic
522C22×C4C23×D6111yescharacteristic
523Q16—216no—
524Q16—12216no—
525SD16—12216no—
526SD16—12216no—
527M16—12216no—
528C2×C8—24no—
529C2×C8—614no—
530C2×C8—1224no—
531C2×C8C23×D6114yes—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—21no—
536C4⋊C4—612no—
537C4⋊C4—1228no—
538C4⋊C4—1228no—
539C4⋊C4—1224no—
540C4⋊C4—1221no—
541C4⋊C4—1224no—
542C4⋊C4—1224no—
543C4⋊C4C23×D6112yes—
544C22⋊C4—1224no—
545C22⋊C4—1224no—
546C22⋊C4—1224no—
547C42—24no—
548C42—614no—
549C42—614no—
550C42—612no—
551C42—612no—
552C42—1224no—
553C42—1224no—
554C42D4×D6112yes—
555C42C23×D6112yes—
556C23—614no—
557C23—612no—
558C23—1222no—
559C23—1222no—
560C23—1224no—
561C23—1222no—
562C23—2442no—
563C23—2442no—
564C23C2×D4×D6111yescharacteristic
565Q8—24no—
566Q8—22no—
567Q8—24no—
568Q8—24no—
569Q8—44no—
570Q8—1224no—
571Q8—1224no—
572Q8—24416no—
573Q8—2444no—
574Q8C2×D4×D6114yes—
575D4—614no—
576D4—12216no—
577D4—1224no—
578D4—1222no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—614no—
587C2×C4—614no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—618no—
591C2×C4—614no—
592C2×C4—614no—
593C2×C4—612no—
594C2×C4—1228no—
595C2×C4—12216no—
596C2×C4—1222no—
597C2×C4—1228no—
598C2×C4—1222no—
599C2×C4—1224no—
600C2×C4—2448no—
601C2×C4—24416no—
602C2×C4—2444no—
603C2×C4—2442no—
604C2×C4—2448no—
605C2×C4#1451980914yescomplemented
606C2×C4C2×D4×D6112yes—
607C2×C4C2×D4×D6111yescharacteristic
608C2×C4C2×D4×D6112yes—
609C2×C4C2×D4×D6112yes—
610C2×C4#41×D6112yes—
611C2×C4C24×D6111yescharacteristic
612C8—24no—
613C8—1224no—
614C22—614no—
615C22—1222no—
616C22—1222no—
617C22—1228no—
618C22—1224no—
619C22—2442no—
620C22—2442no—
621C22—2448no—
622C22#121×D6112yes—
623C22#137×D6112yes—
624C22C2×#1451980912yes—
625C22C22×D4×D6111yescharacteristic
626C4—22no—
627C4—24no—
628C4—42no—
629C4—44no—
630C4—614no—
631C4—614no—
632C4—1222no—
633C4—2442no—
634C4—2444no—
635C4#121×D6112yes—
636C4C2×#1451980914yescomplemented
637C4C22×D4×D6111yescharacteristic
638C4C2×#41×D6111yescharacteristic
639C2—1224no—
640C2—2444no—
641C2#2145530314yesdirect product factor
642C2C2×#121×D6111yescharacteristic
643C2C2×#137×D6111yescharacteristic
644C2C22×#1451980911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
hypercenterC2×#462D61
hypocenterC61C2×#3039
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
2. C2×C4⋊Q8×D61C2semidirect
4. #21455303C2direct (N × H)
5. C2×#16839972C2semidirect
6. C2×#16839970C2semidirect
7. C2×#16839968C2semidirect
8. C2×#16839966C2semidirect
9. C2×#16839964C2semidirect
10. C2×#16839784C2semidirect
11. C2×#16839769C2semidirect
12. C2×C61×#462C2semidirect
26. C4⋊Q8×D61C22semidirect
40. #16839972C22semidirect
41. #16839970C22semidirect
42. #16839968C22semidirect
43. #16839966C22semidirect
44. #16839964C22semidirect
45. #16839784C22semidirect
48. #16839769C22semidirect
55. C61×#462C22semidirect
255. C2×C4×C61#137semidirect
268. C2×Dic61#137semidirect
309. C4×C61C2×#137semidirect
316. Dic61C2×#137semidirect
323. C2×#462D61semidirect
329. C2×C61#3039semidirect
367. #462C2×D61semidirect
380. C61C2×#3039semidirect
605. C2×C4#14519809semidirect
636. C4C2×#14519809semidirect
641. C2#21455303direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C2×C4⋊Q8×D612
C2×C4×#117582262
#214553032
C2×#168399722
C2×#168399702
C2×#168399682
C2×#168399662
C2×#168399642
C2×#168397842
C2×#168397692
C2×C61×#4622
C2×#303961