Finite Group Databasebeta

← C2×#21455640 #30547551

Subgroups — C2×#21455640 #30547551

Order 15616.

2142 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519768C211yesmaximal, characteristic, complemented
2C2×#16840230C211yesmaximal, characteristic
3#21455640C2116yesmaximal, direct product factor
4C2×#16840072C212yesmaximal, complemented
5C2×#16840068C212yesmaximal, complemented
6C2×#16840065C212yesmaximal, complemented
7C2×#16840061C212yesmaximal, complemented
8C2×#16839805C211yesmaximal, characteristic, complemented
9C2×#16839785C211yesmaximal, characteristic, complemented
10C2×#16839764C211yesmaximal, characteristic
11C2×#16839761C211yesmaximal, characteristic
12C2×C61×#428C211yesmaximal, characteristic, complemented
13C22×#11758222C2211yescharacteristic
14C22×#11758194C2211yescharacteristic
15C2×#14519768—21no—
16C2×#14519768—21no—
17C2×#14519768—24no—
18C2×#14519768C2212yes—
19C2×#14519768C2212yes—
20C2×#14519768C2218yescomplemented
21#16840230—24no—
22#16840230C2218yes—
23C2×#14519742C2211yescharacteristic
24C2×#14519742C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×#14519739C2211yescharacteristic
27C2×#14519737—21no—
28C2×#14519737—21no—
29C2×#14519734—21no—
30C22×C4⋊Dic61—21no—
31C22×C4⋊Dic61C2211yescharacteristic
32C22×#11758196—21no—
33C22×C4×Dic61C2211yescharacteristic
34C2×C42×D61—21no—
35#16840072C22116yescomplemented
36#16840068C22116yescomplemented
37#16840065C22116yescomplemented
38#16840061C22116yescomplemented
39#16839805C2218yescomplemented
40C2×#14519710C2212yes—
41C2×#14519708C2212yes—
42#16839785C2218yescomplemented
43C2×#14519706C2212yes—
44C2×#14519706C2212yes—
45#16839764C2218yes—
46#16839761C2218yes—
47C2×#14519702C2212yes—
48C2×#14519700C2212yes—
49C2×#14519699C2212yes—
50C2×#14519697C2212yes—
51C22×M16×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C61×#428C2218yescomplemented
55C2×#107×C61C2212yes—
56C2×#106×C61C2212yes—
57C2×#11758222—22no—
58C2×#11758222—24no—
59C2×#11758222Q818yes—
60C2×#11758222C2314yes—
61C22×Dic122C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C23×Dic61D411yescharacteristic
66C23×Dic61D411yescharacteristic
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C2×#11758194—24no—
71C2×#11758194C2314yes—
72C22×#92418C2312yes—
73#14519768—24no—
74#14519768—24no—
75#14519768—28no—
76#14519768—28no—
77#14519768C2318yes—
78#14519768C2318yes—
79#14519742—22no—
80#14519742—22no—
81#14519742C2314yes—
82#14519742C2314yes—
83#14519739—22no—
84#14519739—22no—
85#14519739C2314yes—
86#14519739C2314yes—
87#14519737—28no—
88#14519737—28no—
89#14519734—28no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—28no—
95C2×C4⋊Dic61C2312yes—
96C2×C4⋊Dic61C2314yes—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—28no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D414yes—
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2314yes—
112C42×D61—28no—
113#14519710C2318yes—
114#14519708C2318yes—
115#14519706C2318yes—
116#14519706C2318yes—
117#14519702C2318yes—
118#14519700C2318yes—
119#14519699C2318yes—
120#14519697C2318yes—
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C2×M16×C61—24no—
124C2×M16×C61C2314yes—
125C22×C8×C61C2312yes—
126#117×C61—22no—
127#117×C61C2314yes—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2312yes—
133C2×C4⋊C4×C61C2314yes—
134C2×C22⋊C4×C61—21no—
135C2×C42×C61—21no—
136#107×C61C2318yes—
137#106×C61C2318yes—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—24no—
143C22×C4×C61—22no—
144C22×C4×C61—44no—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D412yes—
147C22×C4×C61C2×Q814yes—
148C22×C4×C61#4114yes—
149C22×C4×C61C2411yescharacteristic
150C22×C4×C61C2412yes—
151C2×C22⋊D61—28no—
152C2×C22⋊D61—24no—
153C22×Dic61—21no—
154C22×Dic61—24no—
155C22×Dic61—22no—
156C22×Dic61—42no—
157C22×Dic61—42no—
158C22×Dic61—44no—
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D414yes—
164C22×Dic61C2×D414yes—
165#11758222—216no—
166#11758222—28no—
167#11758222C2×Q8116yes—
168C2×D244—21no—
169C2×D244—22no—
170C2×D244C2×Q814yes—
171C2×D244C2412yes—
172C2×C4×D61—28no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—24no—
176C2×C4×D61—44no—
177C2×C4×D61—44no—
178C2×Dic122—21no—
179C2×Dic122—22no—
180C2×Dic122C2×Q814yes—
181C2×Dic122C2412yes—
182M16×C61—28no—
183C2×C8×C61—24no—
184C2×C8×C61C2414yes—
185C4⋊C4×C61—24no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C2412yes—
190C4⋊C4×C61C2414yes—
191C4⋊C4×C61C2412yes—
192C22⋊C4×C61—24no—
193C42×C61—24no—
194#11758198—24no—
195#11758198—24no—
196C4⋊Dic61—24no—
197C4⋊Dic61—22no—
198C4⋊Dic61—28no—
199C4⋊Dic61—28no—
200C4⋊Dic61C2414yes—
201#11758196—28no—
202#11758196—28no—
203#11758196—24no—
204#11758196—24no—
205C4×Dic61—24no—
206C4×Dic61—24no—
207C4×Dic61C2×D414yes—
208C4×Dic61C2×D414yes—
209C4×Dic61C2×D412yes—
210C4×Dic61C2×D412yes—
211C4×Dic61C2412yes—
212C4×Dic61C2412yes—
213#11758194—28no—
214C2×#92418—24no—
215C2×#92418C2414yes—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61C22⋊Q814yes—
219C23×C61C22×D412yes—
220C23×C61C22×D411yescharacteristic
221C22×D61—24no—
222C22×D61—22no—
223C22×D61—42no—
224C22×D61—42no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—48no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—44no—
232C2×C4×C61C22⋊Q814yes—
233C2×C4×C61C22⋊Q818yes—
234C2×C4×C61C22×D412yes—
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×Q812yes—
237C2×C4×C61C22×Q814yes—
238C2×C4×C61C2×#4112yes—
239C2×C4×C61C2×#4114yes—
240C2×C4×C61C2511yescharacteristic
241C22⋊D61—216no—
242C2×Dic61—24no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—44no—
250C2×Dic61—44no—
251C2×Dic61—48no—
252C2×Dic61—44no—
253C2×Dic61C22×D412yes—
254C2×Dic61C22×D412yes—
255C2×Dic61C22×D412yes—
256C2×Dic61C22×D412yes—
257D244—24no—
258D244—22no—
259D244C22×Q814yes—
260C4×D61—216no—
261C4×D61—48no—
262C4×D61—48no—
263Dic122—24no—
264Dic122—22no—
265Dic122C22×Q814yes—
266C8×C61—24no—
267#92418—24no—
268C2×#3080—611nomaximal, Sylow
269C22×C61—28no—
270C22×C61—22no—
271C22×C61—22no—
272C22×C61C2×C22⋊Q814yes—
273C22×C61C2×C22⋊Q812yes—
274C22×C61#57512yes—
275C22×C61#57512yes—
276C22×C61C23×D411yescharacteristic
277C2×D61—24no—
278C2×D61—48no—
279C2×D61—42no—
280C2×D61—42no—
281C4×C61—42no—
282C4×C61—42no—
283C4×C61—44no—
284C4×C61C2×C22⋊Q812yes—
285C4×C61C2×C22⋊Q814yes—
286C4×C61C23×Q811yescharacteristic
287C4×C61C22×#4111yescharacteristic
288Dic61—24no—
289Dic61—22no—
290Dic61—22no—
291Dic61—22no—
292Dic61—22no—
293Dic61—44no—
294C22×#125—611no—
295C2×C4×#41—611no—
296#3080—6116no—
297C2×#479—612no—
298C2×#479—612no—
299C2×#478—612no—
300C2×#478—612no—
301C2×#428—611no—
302C2×#428D6111yescharacteristic, complemented
303C2×#423—611no—
304C2×#417—611no—
305C2×#417—611no—
306C2×C61—24no—
307C2×C61#308014yescomplemented
308C2×C61C22×C22⋊Q811yescharacteristic
309C2×C61C2×#57511yescharacteristic
310C2×C61C2×#57511yescharacteristic
311D61—44no—
312C22×#41—611no—
313C22×M16—611no—
314C22×M16C2×D6111yescharacteristic
315C2×#125—612no—
316C2×#125—612no—
317C2×#125—618no—
318C2×#125—1221no—
319C2×#125—1224no—
320C2×#125—1221no—
321C4×#41—618no—
322C4×#41—1224no—
323C2×C4×Q8—611no—
324C2×C4×Q8—611no—
325C2×C4×D4—611no—
326C2×C4×D4—611no—
327C2×C4×D4—1221no—
328C2×C4×D4—1221no—
329C2×#117—1221no—
330C2×#117C2×D6111yescharacteristic
331C22×C4⋊C4—611no—
332C22×C4⋊C4—1221no—
333C22×C4⋊C4—1221no—
334C22×C4⋊C4C2×D6111yescharacteristic
335C22×C42—611no—
336C22×C42—1221no—
337#479—6116no—
338#479—6116no—
339#478—6116no—
340#478—6116no—
341#428—618no—
342#428C2×D6118yescomplemented
343C2×#107—612no—
344C2×#107C2×D6112yes—
345C2×#106—612no—
346C2×#106C2×D6112yes—
347#423—618no—
348C2×C4⋊C8—612no—
349C2×C4⋊C8—612no—
350#417—618no—
351#417—618no—
352C2×#103—612no—
353C2×#103—612no—
354C2×#102—612no—
355C2×#102—612no—
356C61C2×#308011yescharacteristic, complemented, Sylow
357C2×#41—618no—
358C2×#41—614no—
359C2×#41—1224no—
360C2×#41—1222no—
361C22×Q8—611no—
362C22×D4—611no—
363C22×D4—1221no—
364C23×C4—21no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—1221no—
368C23×C4—1221no—
369C23×C4—1221no—
370C23×C4—1221no—
371C23×C4C22×D6111yescharacteristic
372C2×M16—24no—
373C2×M16—614no—
374C2×M16—1224no—
375C2×M16C22×D6114yes—
376C22×C8—612no—
377C22×C8C22×D6112yes—
378#125—618no—
379#125—618no—
380#125—1228no—
381#125—1228no—
382#125—1224no—
383#125—1224no—
384C4×Q8—614no—
385C4×Q8—614no—
386C4×Q8—1222no—
387C4×Q8—1222no—
388C4×D4—614no—
389C4×D4—614no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1228no—
393C4×D4—1228no—
394#117—22no—
395#117—1228no—
396#117C22×D6114yes—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—614no—
401C2×C4⋊C4—1228no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1228no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4C22×D6112yes—
412C2×C4⋊C4C22×D6114yes—
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C42—21no—
419C2×C42—611no—
420C2×C42—614no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—614no—
425C2×C42—1228no—
426C2×C42—1221no—
427C2×C42—1221no—
428#107—618no—
429#107C22×D6118yes—
430#106—618no—
431#106C22×D6118yes—
432C4⋊C8—618no—
433C4⋊C8—618no—
434#103—618no—
435#103—618no—
436#102—618no—
437#102—618no—
438C24—1221no—
439C24D4×D6111yescharacteristic
440#41—6116no—
441#41—1228no—
442#41—12216no—
443C2×Q8—614no—
444C2×Q8—612no—
445C2×Q8—1221no—
446C2×Q8—1222no—
447C2×D4—614no—
448C2×D4—612no—
449C2×D4—1224no—
450C2×D4—1228no—
451C2×D4—1221no—
452C2×D4—1222no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—44no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—614no—
463C22×C4—614no—
464C22×C4—1224no—
465C22×C4—1224no—
466C22×C4—1221no—
467C22×C4—1224no—
468C22×C4—1228no—
469C22×C4—1224no—
470C22×C4—1222no—
471C22×C4—2444no—
472C22×C4—2444no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4—2444no—
476C22×C4#1175822214yes—
477C22×C4D4×D6112yes—
478C22×C4D4×D6111yescharacteristic
479C22×C4Q8×D6114yes—
480C22×C4C23×D6112yes—
481C22×C4C23×D6111yescharacteristic
482M16—28no—
483M16—1228no—
484C2×C8—24no—
485C2×C8—614no—
486C2×C8—1224no—
487C2×C8C23×D6114yes—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—614no—
493C4⋊C4—1228no—
494C4⋊C4—1228no—
495C4⋊C4—1228no—
496C4⋊C4—1228no—
497C4⋊C4—1224no—
498C4⋊C4—1224no—
499C4⋊C4—1224no—
500C4⋊C4—1222no—
501C4⋊C4C23×D6114yes—
502C4⋊C4C23×D6112yes—
503C4⋊C4C23×D6112yes—
504C22⋊C4—24no—
505C22⋊C4—1224no—
506C22⋊C4—1224no—
507C42—24no—
508C42—614no—
509C42—614no—
510C42—612no—
511C42—612no—
512C42—612no—
513C42—612no—
514C42—1224no—
515C42—1224no—
516C23—22no—
517C23—22no—
518C23—1224no—
519C23—1222no—
520C23—2442no—
521C23—2442no—
522C23#1451975514yes—
523C23C2×D4×D6112yes—
524C23C2×D4×D6111yescharacteristic
525Q8—614no—
526Q8—1224no—
527Q8—1222no—
528D4—614no—
529D4—12216no—
530D4—1224no—
531D4—1222no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—48no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—1224no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—12216no—
550C2×C4—1224no—
551C2×C4—2448no—
552C2×C4—2448no—
553C2×C4—2444no—
554C2×C4—2444no—
555C2×C4—2448no—
556C2×C4—2444no—
557C2×C4#1451975514yes—
558C2×C4#1451975518yes—
559C2×C4C2×D4×D6112yes—
560C2×C4C2×D4×D6111yescharacteristic
561C2×C4C2×Q8×D6112yes—
562C2×C4C2×Q8×D6114yes—
563C2×C4C2×#1175822212yes—
564C2×C4C2×#1175822214yes—
565C2×C4C24×D6111yescharacteristic
566C8—24no—
567C8—1224no—
568C22—28no—
569C22—22no—
570C22—22no—
571C22—1224no—
572C22—2448no—
573C22—2442no—
574C22—2442no—
575C22C2×#1451975514yes—
576C22C2×#1451975512yes—
577C22#1684055812yes—
578C22#1684056112yes—
579C22C22×D4×D6111yescharacteristic
580C4—44no—
581C4—42no—
582C4—42no—
583C4—1222no—
584C4—1222no—
585C4—1222no—
586C4—1222no—
587C4—1224no—
588C4—2444no—
589C4C2×#1451975514yes—
590C4C2×#1451975512yes—
591C4C22×Q8×D6111yescharacteristic
592C4C22×#1175822211yescharacteristic
593C2—24no—
594C2—2444no—
595C2#2145564014yesdirect product factor
596C2C22×#1451975511yescharacteristic
597C2C2×#1684055811yescharacteristic
598C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#428D61
hypocenterC61C2×#3080
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C22×#14519768C2semidirect
3. #21455640C2direct (N × H)
4. C2×#16840072C2semidirect
5. C2×#16840068C2semidirect
6. C2×#16840065C2semidirect
7. C2×#16840061C2semidirect
8. C2×#16839805C2semidirect
9. C2×#16839785C2semidirect
12. C2×C61×#428C2semidirect
20. C2×#14519768C22semidirect
35. #16840072C22semidirect
36. #16840068C22semidirect
37. #16840065C22semidirect
38. #16840061C22semidirect
39. #16839805C22semidirect
42. #16839785C22semidirect
54. C61×#428C22semidirect
302. C2×#428D61semidirect
307. C2×C61#3080semidirect
342. #428C2×D61semidirect
356. C61C2×#3080semidirect
595. C2#21455640direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197682
C2×#168402302
#214556402
C2×#168400722
C2×#168400682
C2×#168400652
C2×#168400612
C2×#168398052
C2×#168397852
C2×#168397642
C2×#168397612
C2×C61×#4282
C2×#308061