Finite Group Databasebeta

← C2×#21454690 #30544163

Subgroups — C2×#21454690 #30544163

Order 15616.

2806 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic
2C2×#16840245C211yesmaximal, characteristic, complemented
3C2×#16840243C211yesmaximal, characteristic, complemented
4#21454690C2116yesmaximal, direct product factor
5C2×#16839865C212yesmaximal, complemented
6C2×#16839859C212yesmaximal, complemented
7C2×#16839854C212yesmaximal, complemented
8C2×#16839842C212yesmaximal, complemented
9C22×#14519710C211yesmaximal, characteristic, complemented
10C2×#16839764C211yesmaximal, characteristic, complemented
11C2×#16839720C211yesmaximal, characteristic, complemented
12C2×C61×#417C211yesmaximal, characteristic, complemented
13C22×#11758222C2211yescharacteristic
14C2×#14519797C4116yescomplemented
15C2×#14519797C2218yes—
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21#16840245—24no—
22#16840245C2218yescomplemented
23#16840243—24no—
24#16840243C2218yescomplemented
25C2×Q8×Dic61C2212yes—
26C2×#14519742C2212yes—
27C2×D4×Dic61—22no—
28C2×D4×Dic61C2212yes—
29C2×#14519739C2212yes—
30C2×C4×C22⋊D61—22no—
31C2×#14519736—21no—
32C2×#14519736C2211yescharacteristic
33C2×#14519735—21no—
34C22×C4⋊Dic61—21no—
35C22×C4⋊Dic61C2211yescharacteristic
36C2×C4⋊C4×D61—21no—
37#16839865C22116yescomplemented
38#16839859C22116yescomplemented
39#16839854C22116yescomplemented
40#16839842C22116yescomplemented
41C2×#14519710C2212yes—
42C2×#14519710C2212yes—
43C2×#14519710C2218yescomplemented
44#16839764C2218yescomplemented
45C2×#14519702C2212yes—
46C2×#14519699C2212yes—
47#16839720C2218yescomplemented
48C2×#14519687C2212yes—
49C2×C8×Dic61C2212yes—
50C22×#41×C61C2211yescharacteristic
51C22×M16×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C61×#417C2218yescomplemented
54C2×#103×C61C2212yes—
55C2×#102×C61C2212yes—
56C2×#11758222—22no—
57C2×#11758222—24no—
58C2×#11758222C2×C418yescomplemented
59C2×#11758222C2314yes—
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C23×Dic61—21no—
64C23×Dic61—22no—
65C22×C4×D61—21no—
66C22×C4×D61—22no—
67#14519797C2×C4164yescomplemented
68C2×#11758202C2×C418yescomplemented
69C2×#11758202C2314yes—
70C2×#11758200C2×C418yescomplemented
71C2×#11758200C2314yes—
72C2×#11758201C2×C418yescomplemented
73C2×#11758201C2314yes—
74C2×#11758199C2×C418yescomplemented
75C2×#11758199C2314yes—
76C22×#92418C2×C418yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2314yes—
80Q8×Dic61—24no—
81Q8×Dic61C2318yes—
82#14519742—24no—
83#14519742C2318yes—
84D4×Dic61—216no—
85D4×Dic61—24no—
86D4×Dic61C2318yes—
87#14519739—24no—
88#14519739C2318yes—
89C4×C22⋊D61—216no—
90#14519736—28no—
91#14519736D414yes—
92#14519736C2314yes—
93#14519735—28no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—28no—
98C2×C4⋊Dic61D411yescharacteristic
99C2×C4⋊Dic61D411yescharacteristic
100C2×C4⋊Dic61C2312yes—
101C2×C4⋊Dic61C2314yes—
102C2×#11758196—22no—
103C4⋊C4×D61—28no—
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61D412yes—
106C2×#11758198—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61C2312yes—
110#14519710C2318yes—
111#14519710C2318yes—
112#14519702C2318yes—
113#14519699C2318yes—
114#14519687C2318yes—
115C8×Dic61C2318yes—
116C2×#41×C61—22no—
117C2×#41×C61—24no—
118C2×#41×C61C2×C418yescomplemented
119C2×#41×C61C2314yes—
120C22×Q8×C61C2311yescharacteristic
121C22×D4×C61—21no—
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C23×C4×C61—21no—
125C23×C4×C61C2311yescharacteristic
126C2×M16×C61—24no—
127C2×M16×C61C2314yes—
128C22×C8×C61C2312yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61C2312yes—
132C2×C4⋊C4×C61C2314yes—
133#103×C61C2318yes—
134#102×C61C2318yes—
135C24×C61—21no—
136C24×C61C2×D411yescharacteristic
137C23×D61—21no—
138#41×C61—216no—
139#41×C61—28no—
140#41×C61C22×C4116yescomplemented
141C2×Q8×C61—21no—
142C2×Q8×C61—22no—
143C2×Q8×C61C22×C414yes—
144C2×Q8×C61C2412yes—
145C2×D4×C61—28no—
146C2×D4×C61—24no—
147C2×D4×C61—21no—
148C2×D4×C61—22no—
149C2×D4×C61C22×C414yes—
150C2×D4×C61C2412yes—
151C22×C4×C61—21no—
152C22×C4×C61—28no—
153C22×C4×C61—24no—
154C22×C4×C61—22no—
155C22×C4×C61—24no—
156C22×C4×C61—82no—
157C22×C4×C61C22×C414yes—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D412yes—
160C22×C4×C61#4114yes—
161C22×C4×C61C2411yescharacteristic
162C22×C4×C61C2412yes—
163C2×C22⋊D61—28no—
164C2×C22⋊D61—24no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—24no—
168C22×Dic61—28no—
169C22×Dic61—84no—
170C22×Dic61—82no—
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D412yes—
173#11758222—216no—
174#11758222—28no—
175#11758222C22×C4116yescomplemented
176C2×D244—21no—
177C2×D244—22no—
178C2×D244C22×C414yes—
179C2×D244C2412yes—
180C2×C4×D61—28no—
181C2×C4×D61—24no—
182C2×C4×D61—28no—
183C2×C4×D61—84no—
184C2×Dic122—21no—
185C2×Dic122—22no—
186C2×Dic122C22×C414yes—
187C2×Dic122C2412yes—
188M16×C61—28no—
189C2×C8×C61—24no—
190C2×C8×C61C2414yes—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61C2414yes—
194C22⋊Dic61—28no—
195C22⋊Dic61C2×D418yes—
196#11758202C22×C4116yescomplemented
197#11758201C22×C4116yescomplemented
198#11758200C22×C4116yescomplemented
199#11758199C22×C4116yescomplemented
200#11758198—28no—
201C4⋊Dic61—24no—
202C4⋊Dic61—22no—
203C4⋊Dic61—28no—
204C4⋊Dic61C2×D414yes—
205C4⋊Dic61C2×D414yes—
206C4⋊Dic61C2414yes—
207#11758196—28no—
208C4×Dic61—28no—
209C4×Dic61—28no—
210C4×Dic61C2×D414yes—
211C4×Dic61C2414yes—
212C2×#92418C22×C414yes—
213C2×#92418C22×C414yes—
214C2×#92418C22×C4116yescomplemented
215C2×#92418C2412yes—
216C2×#92418C2412yes—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—24no—
220C23×C61—22no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61C4×D414yes—
224C23×C61C22×D412yes—
225C23×C61C22×D411yescharacteristic
226C22×D61—24no—
227C22×D61—22no—
228C22×D61—42no—
229C22×D61—42no—
230Q8×C61—24no—
231Q8×C61—22no—
232Q8×C61C23×C414yes—
233D4×C61—216no—
234D4×C61—24no—
235D4×C61—22no—
236D4×C61C23×C414yes—
237C2×C4×C61—24no—
238C2×C4×C61—22no—
239C2×C4×C61—216no—
240C2×C4×C61—24no—
241C2×C4×C61—44no—
242C2×C4×C61—84no—
243C2×C4×C61C4×D414yes—
244C2×C4×C61C4×D418yes—
245C2×C4×C61C23×C412yes—
246C2×C4×C61C23×C414yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D412yes—
249C2×C4×C61C2×#4112yes—
250C2×C4×C61C2×#4114yes—
251C2×C4×C61C2511yescharacteristic
252C22⋊D61—216no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—22no—
257C2×Dic61—24no—
258C2×Dic61—44no—
259C2×Dic61—88no—
260C2×Dic61—84no—
261C2×Dic61C22×D414yes—
262C2×Dic61C22×D414yes—
263D244—24no—
264D244—22no—
265D244C23×C414yes—
266C4×D61—216no—
267C4×D61—88no—
268Dic122—24no—
269Dic122—22no—
270Dic122C23×C414yes—
271C8×C61—24no—
272#92418C23×C414yes—
273#92418C23×C414yes—
274C2×#2951—611nomaximal, Sylow
275C22×C61—28no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—24no—
279C22×C61—48no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61C2×C4×D414yes—
283C22×C61C2×C4×D412yes—
284C22×C61#57612yes—
285C22×C61#57812yes—
286C22×C61C23×D411yescharacteristic
287C2×D61—24no—
288C2×D61—48no—
289C2×D61—42no—
290C2×D61—42no—
291C4×C61—24no—
292C4×C61—44no—
293C4×C61C2×C4×D412yes—
294C4×C61C2×C4×D414yes—
295C4×C61C24×C411yescharacteristic
296C4×C61C22×#4111yescharacteristic
297Dic61—24no—
298Dic61—24no—
299Dic61—24no—
300Dic61—44no—
301C22×#135—611no—
302C2×#520—611no—
303C2×#520—611no—
304#2951—6116no—
305C2×#440—612no—
306C2×#440—612no—
307C2×C4×Q16—612no—
308C2×C4×D8—612no—
309C22×#107—611no—
310C2×#417—611no—
311C2×#417D6111yescharacteristic, complemented
312C2×#405—611no—
313C2×C61—24no—
314C2×C61—44no—
315C2×C61#295114yescomplemented
316C2×C61C22×C4×D411yescharacteristic
317C2×C61C2×#57611yescharacteristic
318C2×C61C2×#57811yescharacteristic
319D61—44no—
320C22×#41—611no—
321C22×#41C2×D6111yescharacteristic
322C2×#135—6116no—
323C2×#135—618no—
324C22×Q16—611no—
325C22×SD16—611no—
326C22×SD16—611no—
327C22×D8—611no—
328C22×M16C2×D6111yescharacteristic
329C23×C8—611no—
330#520—618no—
331#520—618no—
332#520—1224no—
333#520—1224no—
334C2×C4×Q8—612no—
335C2×C4×Q8—612no—
336C2×C4×D4—612no—
337C2×C4×D4—612no—
338C2×C4×D4—1222no—
339C2×C4×D4—1222no—
340C2×#117—611no—
341C2×#117—1221no—
342C2×#117—1221no—
343C22×C4⋊C4—611no—
344C22×C4⋊C4—1221no—
345C22×C4⋊C4—1221no—
346C22×C4⋊C4C2×D6111yescharacteristic
347#440—6116no—
348#440—6116no—
349C4×Q16—6116no—
350C4×D8—6116no—
351C2×#107—612no—
352C2×#107—612no—
353C2×#107—618no—
354#417—618no—
355#417C2×D6118yescomplemented
356C2×#103—612no—
357C2×#103C2×D6112yes—
358C2×#102—612no—
359C2×#102C2×D6112yes—
360#405—618no—
361C2×#97—612no—
362C2×C4×C8—612no—
363C61C2×#295111yescharacteristic, complemented, Sylow
364C2×#41—22no—
365C2×#41—24no—
366C2×#41—618no—
367C2×#41—614no—
368C2×#41—1222no—
369C2×#41—1224no—
370C2×#41C4×D6118yescomplemented
371C2×#41C22×D6114yes—
372C22×Q8—611no—
373C22×Q8C22×D6111yescharacteristic
374C22×D4—21no—
375C22×D4—611no—
376C22×D4—1221no—
377C22×D4C22×D6111yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—1222no—
381C23×C4—1222no—
382C23×C4—1221no—
383C23×C4—1221no—
384C23×C4C22×D6111yescharacteristic
385#135—6164no—
386C2×Q16—618no—
387C2×Q16—614no—
388C2×SD16—618no—
389C2×SD16—614no—
390C2×SD16—618no—
391C2×SD16—614no—
392C2×D8—618no—
393C2×D8—614no—
394C2×M16—24no—
395C2×M16C22×D6114yes—
396C22×C8—618no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—614no—
400C22×C8C22×D6112yes—
401C4×Q8—618no—
402C4×Q8—618no—
403C4×Q8—1224no—
404C4×Q8—1224no—
405C4×D4—618no—
406C4×D4—618no—
407C4×D4—1224no—
408C4×D4—1224no—
409C4×D4—12216no—
410C4×D4—12216no—
411#117—614no—
412#117—614no—
413#117—1228no—
414#117—1228no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—612no—
420C2×C4⋊C4—614no—
421C2×C4⋊C4—1228no—
422C2×C4⋊C4—1228no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1222no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1222no—
427C2×C4⋊C4C22×D6112yes—
428C2×C4⋊C4C22×D6114yes—
429C2×C22⋊C4—612no—
430C2×C22⋊C4—1222no—
431C2×C22⋊C4—1222no—
432C2×C42—612no—
433C2×C42—1222no—
434C2×C42—1222no—
435#107—618no—
436#107—618no—
437#103—618no—
438#103C22×D6118yes—
439#102—618no—
440#102C22×D6118yes—
441#97—618no—
442C4×C8—618no—
443C24—21no—
444C24—1221no—
445C24D4×D6111yescharacteristic
446#41—28no—
447#41—216no—
448#41—6116no—
449#41—1228no—
450#41—12216no—
451#41C2×C4×D61116yescomplemented
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—614no—
455C2×Q8—612no—
456C2×Q8—1221no—
457C2×Q8—1222no—
458C2×Q8C2×C4×D6114yes—
459C2×Q8C23×D6112yes—
460C2×D4—24no—
461C2×D4—28no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—614no—
465C2×D4—612no—
466C2×D4—1224no—
467C2×D4—1228no—
468C2×D4—1221no—
469C2×D4—1222no—
470C2×D4C2×C4×D6114yes—
471C2×D4C23×D6112yes—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—82no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—1228no—
481C22×C4—1228no—
482C22×C4—1221no—
483C22×C4—1224no—
484C22×C4—1228no—
485C22×C4—1224no—
486C22×C4—1222no—
487C22×C4—4884no—
488C22×C4—4884no—
489C22×C4—4882no—
490C22×C4C2×C4×D6114yes—
491C22×C4D4×D6112yes—
492C22×C4D4×D6111yescharacteristic
493C22×C4#1175822414yes—
494C22×C4C23×D6112yes—
495C22×C4C23×D6111yescharacteristic
496Q16—6116no—
497SD16—6116no—
498SD16—6116no—
499D8—6116no—
500M16—28no—
501C2×C8—24no—
502C2×C8—614no—
503C2×C8—614no—
504C2×C8—6116no—
505C2×C8—612no—
506C2×C8—612no—
507C2×C8C23×D6114yes—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—614no—
511C4⋊C4—614no—
512C4⋊C4—614no—
513C4⋊C4—1228no—
514C4⋊C4—1228no—
515C4⋊C4—1224no—
516C4⋊C4—1222no—
517C4⋊C4C23×D6114yes—
518C22⋊C4—618no—
519C22⋊C4—1228no—
520C22⋊C4—1228no—
521C42—614no—
522C42—614no—
523C42—1228no—
524C42—1228no—
525C23—22no—
526C23—22no—
527C23—24no—
528C23—22no—
529C23—42no—
530C23—42no—
531C23—1224no—
532C23—1222no—
533C23—2442no—
534C23—2442no—
535C23#1451973714yes—
536C23C2×D4×D6112yes—
537C23C2×D4×D6111yescharacteristic
538Q8—24no—
539Q8—22no—
540Q8—614no—
541Q8—1224no—
542Q8—1222no—
543Q8C22×C4×D6114yes—
544D4—216no—
545D4—24no—
546D4—22no—
547D4—614no—
548D4—12216no—
549D4—1224no—
550D4—1222no—
551D4C22×C4×D6114yes—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—216no—
555C2×C4—24no—
556C2×C4—44no—
557C2×C4—84no—
558C2×C4—614no—
559C2×C4—614no—
560C2×C4—1224no—
561C2×C4—1224no—
562C2×C4—1224no—
563C2×C4—1222no—
564C2×C4—12216no—
565C2×C4—1224no—
566C2×C4—4888no—
567C2×C4—4888no—
568C2×C4—4884no—
569C2×C4—2444no—
570C2×C4#1451973714yes—
571C2×C4#1451973718yes—
572C2×C4C22×C4×D6112yes—
573C2×C4C22×C4×D6114yes—
574C2×C4C2×D4×D6111yescharacteristic
575C2×C4C2×D4×D6112yes—
576C2×C4C2×#1175822412yes—
577C2×C4C2×#1175822414yes—
578C2×C4C24×D6111yescharacteristic
579C8—24no—
580C8—614no—
581C8—614no—
582C22—22no—
583C22—28no—
584C22—22no—
585C22—24no—
586C22—42no—
587C22—48no—
588C22—42no—
589C22—1224no—
590C22—2442no—
591C22—2448no—
592C22—2442no—
593C22C2×#1451973714yes—
594C22C2×#1451973712yes—
595C22#1684056612yes—
596C22#1684057812yes—
597C22C22×D4×D6111yescharacteristic
598C4—24no—
599C4—44no—
600C4—1224no—
601C4—1224no—
602C4—1224no—
603C4—2444no—
604C4C2×#1451973714yes—
605C4C2×#1451973712yes—
606C4C23×C4×D6111yescharacteristic
607C4C22×#1175822411yescharacteristic
608C2—24no—
609C2—44no—
610C2—2444no—
611C2#2145469014yesdirect product factor
612C2C22×#1451973711yescharacteristic
613C2C2×#1684056611yescharacteristic
614C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC22×#14519797C2
cosocleC2×C4×C61C25
hypercenterC2×#417D61
hypocenterC61C2×#2951
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16840245C2semidirect
3. C2×#16840243C2semidirect
4. #21454690C2direct (N × H)
5. C2×#16839865C2semidirect
6. C2×#16839859C2semidirect
7. C2×#16839854C2semidirect
8. C2×#16839842C2semidirect
9. C22×#14519710C2semidirect
10. C2×#16839764C2semidirect
11. C2×#16839720C2semidirect
12. C2×C61×#417C2semidirect
14. C2×#14519797C4semidirect
22. #16840245C22semidirect
24. #16840243C22semidirect
37. #16839865C22semidirect
38. #16839859C22semidirect
39. #16839854C22semidirect
40. #16839842C22semidirect
43. C2×#14519710C22semidirect
44. #16839764C22semidirect
47. #16839720C22semidirect
53. C61×#417C22semidirect
58. C2×#11758222C2×C4semidirect
67. #14519797C2×C4semidirect
68. C2×#11758202C2×C4semidirect
70. C2×#11758200C2×C4semidirect
72. C2×#11758201C2×C4semidirect
74. C2×#11758199C2×C4semidirect
76. C22×#92418C2×C4semidirect
118. C2×#41×C61C2×C4semidirect
140. #41×C61C22×C4semidirect
175. #11758222C22×C4semidirect
196. #11758202C22×C4semidirect
197. #11758201C22×C4semidirect
198. #11758200C22×C4semidirect
199. #11758199C22×C4semidirect
214. C2×#92418C22×C4semidirect
311. C2×#417D61semidirect
315. C2×C61#2951semidirect
355. #417C2×D61semidirect
363. C61C2×#2951semidirect
370. C2×#41C4×D61semidirect
451. #41C2×C4×D61semidirect
611. C2#21454690direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197972
C2×#168402452
C2×#168402432
#214546902
C2×#168398652
C2×#168398592
C2×#168398542
C2×#168398422
C22×#145197102
C2×#168397642
C2×#168397202
C2×C61×#4172
C2×#295161