Finite Group Databasebeta

← C2×#21455292 #30546853

Subgroups — C2×#21455292 #30546853

Order 15616.

2810 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C212yesmaximal, complemented
2C2×#16840313C211yesmaximal, characteristic
3C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
4#21455292C2116yesmaximal, direct product factor
5C2×#16839987C212yesmaximal, complemented
6C2×#16839986C212yesmaximal, complemented
7C2×#16839969C211yesmaximal, characteristic, complemented
8C2×#16839963C211yesmaximal, characteristic, complemented
9C2×#16839962C211yesmaximal, characteristic, complemented
10C2×#16839784C211yesmaximal, characteristic, complemented
11C2×#16839762C212yesmaximal, complemented
12C2×C61×#462C211yesmaximal, characteristic, complemented
13C22×#11758226C2212yes—
14C22×Q8×D61C2211yescharacteristic
15C2×#14519809—216no—
16C2×#14519809C22116yescomplemented
17C22×#11758202C2212yes—
18C22×#11758190C2212yes—
19C22×#11758201C2212yes—
20C22×#11758189C2212yes—
21#16840313—24no—
22#16840313C2218yes—
23C2×#14519774C2211yescharacteristic
24C2×#14519766C2212yes—
25C2×#14519752—21no—
26C2×#14519752—21no—
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×Dic122—21no—
29C2×C4×Dic122C2211yescharacteristic
30C2×#14519742—21no—
31C2×#14519742C2211yescharacteristic
32C4×Q8×D61—24no—
33C4×Q8×D61C2218yescomplemented
34C2×#14519739—21no—
35C2×#14519739—21no—
36C2×C4⋊C4×D61—21no—
37C2×C4⋊C4×D61C2211yescharacteristic
38C2×C42×D61—21no—
39C2×C42×D61C2211yescharacteristic
40#16839987C22116yescomplemented
41#16839986C22116yescomplemented
42#16839969C2218yescomplemented
43#16839963C2218yescomplemented
44#16839962C2218yescomplemented
45#16839784C2218yescomplemented
46C2×C4⋊#92418C2211yescharacteristic
47C2×#14519706C2212yes—
48#16839762C22116yescomplemented
49C2×#14519701C2212yes—
50C2×#14519699C2212yes—
51C2×#14519697C2212yes—
52C22×Q16×C61C2212yes—
53C2×C4⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C61×#462C2218yescomplemented
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×#103×C61C2212yes—
58C2×#11758226—24no—
59C2×#11758226—28no—
60C2×#11758226—28no—
61C2×#11758226C2318yes—
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C2×Q8×D61—22no—
65C2×Q8×D61—24no—
66C2×Q8×D61D418yescomplemented
67C2×Q8×D61C2314yes—
68C22×D244—22no—
69C22×D244—21no—
70C22×D244—21no—
71C22×D244C2312yes—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—22no—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78#14519809—264no—
79C2×#11758202—28no—
80C2×#11758202C2318yes—
81C2×#11758190—28no—
82C2×#11758190C2318yes—
83C2×#11758201—28no—
84C2×#11758201C2318yes—
85C2×#11758189—28no—
86C2×#11758189C2318yes—
87C22×#92418C2312yes—
88#14519774—22no—
89#14519774C2314yes—
90#14519766—24no—
91#14519766C2318yes—
92#14519752—28no—
93#14519752—28no—
94Q8×Dic61—22no—
95Q8×Dic61C2314yes—
96C4×Dic122—22no—
97C4×Dic122—28no—
98C4×Dic122C2314yes—
99#14519742—22no—
100#14519742—28no—
101#14519742C2314yes—
102#14519739—28no—
103#14519739—28no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C4⋊C4×D61—28no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61C2314yes—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×C4×Dic61—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#14519701C2318yes—
126#14519699C2318yes—
127#14519697C2318yes—
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—22no—
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—21no—
162C22×Dic61—21no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166#11758226—216no—
167#11758226—216no—
168#11758226—416no—
169Q8×D61—216no—
170Q8×D61—28no—
171Q8×D61C2×D4116yescomplemented
172C2×D244—24no—
173C2×D244—24no—
174C2×D244—28no—
175C2×D244—24no—
176C2×D244—24no—
177C2×D244—22no—
178C2×D244—44no—
179C2×D244—48no—
180C2×D244—44no—
181C2×D244C2414yes—
182C2×C4×D61—28no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—24no—
186C2×C4×D61—28no—
187C2×C4×D61—42no—
188C2×C4×D61—44no—
189C2×C4×D61—48no—
190C2×C4×D61C2×D414yes—
191C2×C4×D61C2×D414yes—
192C2×C4×D61C2×D412yes—
193C2×C4×D61C2×D414yes—
194C2×C4×D61#4114yes—
195C2×C4×D61C2412yes—
196C2×Dic122—21no—
197C2×Dic122—22no—
198C2×Dic122—28no—
199C2×Dic122—24no—
200C2×Dic122C2×D414yes—
201C2×Dic122C2412yes—
202Q16×C61—216no—
203C2×C8×C61—24no—
204C2×C8×C61C2414yes—
205C4⋊C4×C61—24no—
206C4⋊C4×C61—24no—
207C4⋊C4×C61—24no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61C2412yes—
210C42×C61—24no—
211C42×C61C2×D412yes—
212C42×C61C2412yes—
213#11758202—216no—
214#11758201—216no—
215#11758198—28no—
216#11758198—28no—
217C4⋊Dic61—21no—
218C4⋊Dic61—24no—
219C4⋊Dic61C2412yes—
220#11758196—24no—
221#11758196—24no—
222#11758196—24no—
223C4×Dic61—24no—
224C4×Dic61—24no—
225C4×Dic61—24no—
226C4×Dic61C2×D412yes—
227C4×Dic61C2×D414yes—
228C4×Dic61C2×D414yes—
229C4×Dic61C2412yes—
230C2×#92418—24no—
231C2×#92418C2414yes—
232#11758190—216no—
233#11758189—216no—
234C23×C61C22×D411yescharacteristic
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—24no—
238C22×D61—44no—
239C22×D61—44no—
240C22×D61—44no—
241C22×D61#12114yes—
242C22×D61C22×D412yes—
243Q8×C61—24no—
244Q8×C61—22no—
245Q8×C61—24no—
246Q8×C61—24no—
247Q8×C61—44no—
248Q8×C61C22×D414yes—
249C2×C4×C61—24no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—24no—
254C2×C4×C61—44no—
255C2×C4×C61—42no—
256C2×C4×C61#13714yescomplemented
257C2×C4×C61C22×D412yes—
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D412yes—
260C2×C4×C61C22×D412yes—
261C2×C4×C61C2×#4112yes—
262C2×C4×C61C2511yescharacteristic
263C2×Dic61—24no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—42no—
269C2×Dic61#12114yes—
270C2×Dic61C22×D412yes—
271C2×Dic61C22×D412yes—
272C2×Dic61C22×D412yes—
273D244—24no—
274D244—24no—
275D244—48no—
276D244—416no—
277D244—44no—
278D244—48no—
279C4×D61—216no—
280C4×D61—28no—
281C4×D61—44no—
282C4×D61—48no—
283C4×D61—416no—
284C4×D61#12118yes—
285C4×D61C22×D414yes—
286C4×D61C2×#4114yes—
287Dic122—24no—
288Dic122—22no—
289Dic122—216no—
290Dic122C22×D414yes—
291C8×C61—24no—
292#92418—24no—
293C2×#3037—611nomaximal, Sylow
294C22×C61C2×#12112yes—
295C22×C61C2×#13712yes—
296C22×C61#57512yes—
297C22×C61C23×D411yescharacteristic
298C2×D61—28no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—44no—
302C2×D61—44no—
303C2×D61—44no—
304C2×D61—88no—
305C2×D61C2×#12114yes—
306C4×C61—24no—
307C4×C61—22no—
308C4×C61—44no—
309C4×C61—42no—
310C4×C61C2×#12112yes—
311C4×C61C2×#13714yescomplemented
312C4×C61C23×D411yescharacteristic
313C4×C61C22×#4111yescharacteristic
314Dic61—24no—
315Dic61—22no—
316Dic61—22no—
317Dic61—42no—
318Dic61C2×#12114yes—
319C22×#137—612no—
320C2×#532—611no—
321C22×C4×Q8—611no—
322#3037—6116no—
323C2×#464—612no—
324C2×#464—612no—
325C2×#462—611no—
326C2×#462D6111yescharacteristic, complemented
327C2×#460—611no—
328C2×#460—611no—
329C2×#423—611no—
330C2×#417—612no—
331C2×C61#303714yescomplemented
332C2×C61C22×#12111yescharacteristic
333C2×C61C22×#13711yescharacteristic
334C2×C61C2×#57511yescharacteristic
335D61—24no—
336D61—84no—
337C22×#41—612no—
338C23×Q8—611no—
339C2×#137—6116no—
340C2×#137—12216no—
341C22×Q16—612no—
342C22×Q16C2×D6112yes—
343C22×SD16—612no—
344C22×SD16—612no—
345C22×M16—612no—
346#532—618no—
347#532—1224no—
348C2×C4⋊Q8C2×D6111yescharacteristic
349C2×#127—611no—
350C2×#124—612no—
351C2×#121—1221no—
352C2×#121—1221no—
353C2×C4×Q8—611no—
354C2×C4×Q8—618no—
355C2×C4×Q8—611no—
356C2×C4×Q8—611no—
357C2×C4×Q8—1221no—
358C2×C4×Q8—1221no—
359C2×C4×Q8—1224no—
360C2×C4×Q8C2×D6111yescharacteristic
361C2×C4×D4—1221no—
362C2×C4×D4—1221no—
363C22×C4⋊C4—611no—
364C22×C4⋊C4—1221no—
365C22×C42—611no—
366C22×C42—1221no—
367#464—6116no—
368#464—6116no—
369#462—618no—
370#462C2×D6118yescomplemented
371#460—618no—
372#460—618no—
373#423—618no—
374C2×C4⋊C8—612no—
375C2×C4⋊C8—611no—
376C2×C4⋊C8C2×D6111yescharacteristic
377#417—6116no—
378C2×#103—612no—
379C2×#103C2×D6112yes—
380C2×#102—612no—
381C2×#102—612no—
382C61C2×#303711yescharacteristic, complemented, Sylow
383C2×#41—618no—
384C2×#41—1224no—
385C2×#41—1228no—
386C2×#41—1228no—
387C22×Q8—618no—
388C22×Q8—614no—
389C22×Q8—611no—
390C22×Q8—1221no—
391C22×Q8—1222no—
392C22×Q8—1224no—
393C22×Q8C22×D6112yes—
394C22×Q8C22×D6111yescharacteristic
395C22×D4—612no—
396C22×D4—1222no—
397C22×D4—1221no—
398C22×D4—1221no—
399C23×C4—611no—
400C23×C4—611no—
401C23×C4—611no—
402C23×C4—1222no—
403C23×C4—1221no—
404C23×C4—1221no—
405#137—12264no—
406C2×Q16—28no—
407C2×Q16—618no—
408C2×Q16—1228no—
409C2×Q16C22×D6118yes—
410C2×SD16—618no—
411C2×SD16—618no—
412C2×SD16—1228no—
413C2×SD16—1228no—
414C2×M16—618no—
415C2×M16—1228no—
416C22×C8—612no—
417C22×C8C22×D6112yes—
418C4⋊Q8—22no—
419C4⋊Q8C22×D6114yes—
420#127—614no—
421#127—1222no—
422#124—618no—
423#124—1224no—
424#121—1228no—
425#121—1228no—
426C4×Q8—22no—
427C4×Q8—614no—
428C4×Q8—614no—
429C4×Q8—614no—
430C4×Q8—1228no—
431C4×Q8—1228no—
432C4×Q8—1222no—
433C4×Q8—1222no—
434C4×Q8—1222no—
435C4×Q8C22×D6114yes—
436C4×D4—1228no—
437C4×D4—1228no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—614no—
443C2×C4⋊C4—1222no—
444C2×C4⋊C4—1228no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—1221no—
449C2×C4⋊C4C22×D6111yescharacteristic
450C2×C22⋊C4—1222no—
451C2×C22⋊C4—1222no—
452C2×C42—21no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—614no—
457C2×C42—614no—
458C2×C42—1228no—
459C2×C42—1221no—
460C2×C42—1221no—
461C2×C42—1221no—
462C2×C42C22×D6111yescharacteristic
463C4⋊C8—618no—
464C4⋊C8—614no—
465C4⋊C8C22×D6114yes—
466#103—618no—
467#103C22×D6118yes—
468#102—618no—
469#102—618no—
470C24—611no—
471C24—1222no—
472#41—12216no—
473#41—12216no—
474#41—24416no—
475C2×Q8—21no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—6116no—
481C2×Q8—614no—
482C2×Q8—612no—
483C2×Q8—1224no—
484C2×Q8—1228no—
485C2×Q8—12216no—
486C2×Q8—1228no—
487C2×Q8—1221no—
488C2×Q8—1222no—
489C2×Q8D4×D6114yes—
490C2×Q8C23×D6114yes—
491C2×Q8C23×D6112yes—
492C2×D4—614no—
493C2×D4—1228no—
494C2×D4—1224no—
495C2×D4—1224no—
496C2×D4—1224no—
497C2×D4—1222no—
498C2×D4—1224no—
499C2×D4—2444no—
500C2×D4—2448no—
501C2×D4—2444no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—611no—
506C22×C4—612no—
507C22×C4—614no—
508C22×C4—614no—
509C22×C4—612no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—614no—
513C22×C4—614no—
514C22×C4—1228no—
515C22×C4—1224no—
516C22×C4—1228no—
517C22×C4—1224no—
518C22×C4—1221no—
519C22×C4—1224no—
520C22×C4—1221no—
521C22×C4—2442no—
522C22×C4—2448no—
523C22×C4—2444no—
524C22×C4D4×D6111yescharacteristic
525C22×C4D4×D6111yescharacteristic
526C22×C4C23×D6111yescharacteristic
527Q16—216no—
528Q16—12216no—
529SD16—12216no—
530SD16—12216no—
531M16—12216no—
532C2×C8—24no—
533C2×C8—614no—
534C2×C8—1224no—
535C2×C8C23×D6114yes—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—612no—
541C4⋊C4—1224no—
542C4⋊C4—1224no—
543C4⋊C4—1224no—
544C4⋊C4—1221no—
545C4⋊C4—1224no—
546C4⋊C4C23×D6112yes—
547C22⋊C4—1228no—
548C22⋊C4—1228no—
549C42—24no—
550C42—614no—
551C42—614no—
552C42—612no—
553C42—612no—
554C42—1224no—
555C42—1224no—
556C42—1224no—
557C42D4×D6112yes—
558C42C23×D6112yes—
559C23—614no—
560C23—612no—
561C23—1222no—
562C23—1222no—
563C23—1224no—
564C23—2444no—
565C23—2444no—
566C23—2444no—
567C23C2×D4×D6111yescharacteristic
568Q8—24no—
569Q8—22no—
570Q8—24no—
571Q8—24no—
572Q8—44no—
573Q8—614no—
574Q8—12216no—
575Q8—1224no—
576Q8—1222no—
577Q8C2×D4×D6114yes—
578D4—1224no—
579D4—1224no—
580D4—2448no—
581D4—24416no—
582D4—2444no—
583D4—2448no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—44no—
590C2×C4—42no—
591C2×C4—614no—
592C2×C4—612no—
593C2×C4—618no—
594C2×C4—614no—
595C2×C4—614no—
596C2×C4—612no—
597C2×C4—612no—
598C2×C4—12216no—
599C2×C4—1224no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1228no—
604C2×C4—1222no—
605C2×C4—2444no—
606C2×C4—24416no—
607C2×C4—2448no—
608C2×C4—2442no—
609C2×C4#1451980914yescomplemented
610C2×C4C2×D4×D6112yes—
611C2×C4C2×D4×D6111yescharacteristic
612C2×C4C2×D4×D6112yes—
613C2×C4C2×D4×D6112yes—
614C2×C4#41×D6112yes—
615C2×C4C24×D6111yescharacteristic
616C8—24no—
617C8—1224no—
618C22—614no—
619C22—1222no—
620C22—1222no—
621C22—1228no—
622C22—4888no—
623C22—2444no—
624C22—2444no—
625C22—2444no—
626C22#121×D6112yes—
627C22C2×#1451980912yes—
628C22#1684056112yes—
629C22C22×D4×D6111yescharacteristic
630C4—22no—
631C4—24no—
632C4—42no—
633C4—44no—
634C4—614no—
635C4—1222no—
636C4—1222no—
637C4—1224no—
638C4—2442no—
639C4#121×D6112yes—
640C4C2×#1451980914yescomplemented
641C4C22×D4×D6111yescharacteristic
642C4C2×#41×D6111yescharacteristic
643C2—1224no—
644C2—4884no—
645C2#2145529214yesdirect product factor
646C2C2×#121×D6111yescharacteristic
647C2C22×#1451980911yescharacteristic
648C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC2×#16840313C2
hypercenterC2×#462D61
hypocenterC61C2×#3037
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. C22×#14519809C2semidirect
3. C2×C4×Q8×D61C2semidirect
4. #21455292C2direct (N × H)
5. C2×#16839987C2semidirect
6. C2×#16839986C2semidirect
7. C2×#16839969C2semidirect
8. C2×#16839963C2semidirect
9. C2×#16839962C2semidirect
10. C2×#16839784C2semidirect
11. C2×#16839762C2semidirect
12. C2×C61×#462C2semidirect
16. C2×#14519809C22semidirect
33. C4×Q8×D61C22semidirect
40. #16839987C22semidirect
41. #16839986C22semidirect
42. #16839969C22semidirect
43. #16839963C22semidirect
44. #16839962C22semidirect
45. #16839784C22semidirect
48. #16839762C22semidirect
55. C61×#462C22semidirect
66. C2×Q8×D61D4semidirect
171. Q8×D61C2×D4semidirect
256. C2×C4×C61#137semidirect
311. C4×C61C2×#137semidirect
326. C2×#462D61semidirect
331. C2×C61#3037semidirect
370. #462C2×D61semidirect
382. C61C2×#3037semidirect
609. C2×C4#14519809semidirect
640. C4C2×#14519809semidirect
645. C2#21455292direct (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×#168403132
C2×C4×Q8×D612
#214552922
C2×#168399872
C2×#168399862
C2×#168399692
C2×#168399632
C2×#168399622
C2×#168397842
C2×#168397622
C2×C61×#4622
C2×#303761