Finite Group Databasebeta

← C2×#21455608 #30547515

Subgroups — C2×#21455608 #30547515

Order 15616.

2162 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2C2×C4×#11758224C211yesmaximal, characteristic
3#21455608C2116yesmaximal, direct product factor
4C2×#16840072C212yesmaximal, complemented
5C2×#16840054C211yesmaximal, characteristic, complemented
6C2×#16840048C211yesmaximal, characteristic, complemented
7C2×#16840064C212yesmaximal, complemented
8C2×#16840042C211yesmaximal, characteristic, complemented
9C2×#16839797C212yesmaximal, complemented
10C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
11C2×#16839755C212yesmaximal
12C2×C61×#476C211yesmaximal, characteristic, complemented
13C22×#11758224C2211yescharacteristic
14C22×C8×D61C2212yes—
15#16840317—24no—
16#16840317C2218yescomplemented
17C2×#14519777C2211yescharacteristic
18C2×#14519768C2212yes—
19C2×#14519757—21no—
20C2×#14519753—21no—
21C4×#11758224—24no—
22C4×#11758224C2218yes—
23C2×Q8×Dic61—21no—
24C2×C4×Dic122C2211yescharacteristic
25C2×#14519742—21no—
26C2×#14519742C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×#14519737—21no—
30C2×#14519735C2211yescharacteristic
31C2×#14519735C2212yes—
32C2×#14519733—21no—
33C22×C4×Dic61—21no—
34C2×C42×D61C2211yescharacteristic
35#16840072C22116yescomplemented
36#16840064C22116yescomplemented
37#16840054C2218yescomplemented
38#16840048C2218yescomplemented
39#16840042C2218yescomplemented
40#16839797C22116yescomplemented
41C2×#14519710C2212yes—
42C2×#14519710C2212yes—
43C2×#14519709C2212yes—
44C2×C4⋊#92418C2211yescharacteristic
45C2×#14519706C2212yes—
46C4⋊C8×D61C2218yescomplemented
47#16839755C22116yes—
48C2×#14519702C2212yes—
49C2×#14519700C2212yes—
50C2×#14519698C2212yes—
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#476C2218yescomplemented
54C2×#106×C61C2212yes—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2212yes—
57C2×#11758224—22no—
58C2×#11758224—24no—
59C2×#11758224Q818yescomplemented
60C2×#11758224C2314yes—
61C22×Dic122—21no—
62C22×Dic122C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C22×#92418C2312yes—
70C2×C8×D61—28no—
71C2×C8×D61C2318yes—
72#14519777—22no—
73#14519777C2314yes—
74#14519768—24no—
75#14519768C2318yes—
76#14519757—28no—
77#14519753—28no—
78Q8×Dic61—28no—
79C4×Dic122—22no—
80C4×Dic122C2314yes—
81#14519742—28no—
82#14519742—22no—
83#14519742C2314yes—
84D4×Dic61—22no—
85D4×Dic61C2314yes—
86C4×C22⋊D61—28no—
87#14519737—28no—
88#14519735—22no—
89#14519735—24no—
90#14519735C2314yes—
91#14519735C2318yes—
92#14519733—28no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2312yes—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—22no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—22no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—28no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61D414yes—
112C42×D61C2314yes—
113#14519710C2318yes—
114#14519710C2318yes—
115#14519709C2318yes—
116C4⋊#92418C2314yes—
117#14519706C2318yes—
118#14519702C2318yes—
119#14519700C2318yes—
120#14519698C2318yes—
121C22×Q8×C61—21no—
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C22×C8×C61C2312yes—
125C4⋊Q8×C61—22no—
126C4⋊Q8×C61C2314yes—
127C4×D4×C61—22no—
128C4×D4×C61C2314yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61C2312yes—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#106×C61C2318yes—
135C4⋊C8×C61C2314yes—
136#102×C61C2318yes—
137C24×C61—21no—
138C23×D61C2×D411yescharacteristic
139C2×Q8×C61—24no—
140C2×Q8×C61—44no—
141C2×D4×C61—21no—
142C2×D4×C61—22no—
143C2×D4×C61C2×Q814yes—
144C2×D4×C61C2412yes—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—24no—
148C22×C4×C61—44no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—28no—
153C2×C22⋊D61—24no—
154C22×Dic61—21no—
155C22×Dic61—28no—
156C22×Dic61—24no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—24no—
160C22×Dic61—44no—
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164#11758224—216no—
165#11758224—28no—
166#11758224C2×Q8116yescomplemented
167C2×C4×D61—24no—
168C2×C4×D61—42no—
169C2×C4×D61C2×D414yes—
170C2×C4×D61C2×D414yes—
171C2×C4×D61C2×D412yes—
172C2×C4×D61C2×Q814yes—
173C2×C4×D61#4114yes—
174C2×C4×D61C2412yes—
175C2×Dic122—21no—
176C2×Dic122—22no—
177C2×Dic122—24no—
178C2×Dic122—44no—
179C2×Dic122C2×Q814yes—
180C2×Dic122C2412yes—
181C2×C8×C61—24no—
182C2×C8×C61C2414yes—
183C4⋊C4×C61—24no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61C2414yes—
187C4⋊C4×C61C2412yes—
188C22⋊C4×C61—24no—
189C42×C61C2×D412yes—
190C42×C61C2412yes—
191C22⋊Dic61—24no—
192#11758198—24no—
193#11758198—28no—
194C4⋊Dic61—24no—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—28no—
198C4⋊Dic61C2414yes—
199C4⋊Dic61C2412yes—
200#11758196—24no—
201#11758196—24no—
202#11758196—28no—
203C4×Dic61—24no—
204C4×Dic61—24no—
205C4×Dic61—24no—
206C4×Dic61—28no—
207C4×Dic61C2×D412yes—
208C4×Dic61C2×D414yes—
209C4×Dic61C2×D414yes—
210C4×Dic61C2412yes—
211C2×#92418—24no—
212C2×#92418C2414yes—
213C8×D61—216no—
214C23×C61—24no—
215C23×C61—22no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—22no—
221C22×D61C22⋊Q814yes—
222C22×D61C22×D412yes—
223Q8×C61—48no—
224D4×C61—24no—
225D4×C61—22no—
226D4×C61C22×Q814yes—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—24no—
230C2×C4×C61—42no—
231C2×C4×C61—44no—
232C2×C4×C61—48no—
233C2×C4×C61#13514yes—
234C2×C4×C61C22×D412yes—
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D412yes—
237C2×C4×C61C22×Q812yes—
238C2×C4×C61C2×#4112yes—
239C2×C4×C61C2511yescharacteristic
240C22⋊D61—216no—
241C2×Dic61—24no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—216no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—48no—
249C2×Dic61—44no—
250C2×Dic61—42no—
251C2×Dic61C22⋊Q814yes—
252C2×Dic61C22×D412yes—
253C2×Dic61C22×D412yes—
254C2×Dic61C22×D412yes—
255C4×D61—28no—
256C4×D61—44no—
257C4×D61C22⋊Q818yes—
258C4×D61C22×Q814yes—
259C4×D61C2×#4114yes—
260Dic122—24no—
261Dic122—22no—
262Dic122—48no—
263Dic122C22×Q814yes—
264C8×C61—24no—
265#92418—24no—
266C2×#3076—611nomaximal, Sylow
267C22×C61—24no—
268C22×C61—48no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61C2×C22⋊Q812yes—
272C22×C61C2×#13512yes—
273C22×C61#57512yes—
274C22×C61C23×D411yescharacteristic
275C2×D61—28no—
276C2×D61—22no—
277C2×D61—22no—
278C2×D61C2×C22⋊Q814yes—
279C4×C61—22no—
280C4×C61—42no—
281C4×C61—44no—
282C4×C61C2×C22⋊Q812yes—
283C4×C61C2×#13514yes—
284C4×C61C23×Q811yescharacteristic
285C4×C61C22×#4111yescharacteristic
286Dic61—24no—
287Dic61—22no—
288Dic61—22no—
289Dic61—44no—
290Dic61—42no—
291Dic61C2×C22⋊Q814yes—
292C2×#533—611no—
293C2×C4×#41—611no—
294#3076—6116no—
295C2×#479—612no—
296C2×#477—611no—
297C2×#475—611no—
298C2×#478—612no—
299C2×#476D6111yescharacteristic, complemented
300C2×#474—611no—
301C2×#427—612no—
302C22×C4⋊C8—611no—
303C2×#416—612no—
304C2×C61—44no—
305C2×C61#307614yescomplemented
306C2×C61C22×C22⋊Q811yescharacteristic
307C2×C61C22×#13511yescharacteristic
308C2×C61C2×#57511yescharacteristic
309D61—24no—
310C22×#41—611no—
311C23×C8—612no—
312#533—618no—
313#533—1224no—
314C2×C4⋊Q8—611no—
315C2×C4⋊Q8C2×D6111yescharacteristic
316C2×#125—612no—
317C2×C22⋊Q8—1221no—
318C2×C22⋊Q8—1221no—
319C4×#41—618no—
320C4×#41—1224no—
321C2×C4×Q8—611no—
322C2×C4×Q8—611no—
323C2×C4×Q8—1221no—
324C2×C4×Q8—1221no—
325C2×C4×D4—611no—
326C2×C4×D4—1221no—
327C2×C4×D4—1221no—
328C2×C4×D4C2×D6111yescharacteristic
329C2×#117—612no—
330C2×#117—611no—
331C2×#117—1221no—
332C22×C42—611no—
333C22×C42—1221no—
334#479—6116no—
335#478—6116no—
336#477—618no—
337#476C2×D6118yescomplemented
338#475—618no—
339#474—618no—
340#427—6116no—
341C2×#107—612no—
342C2×#107—612no—
343C2×#106—612no—
344C2×#106C2×D6112yes—
345C2×C4⋊C8—612no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8—618no—
348C2×C4⋊C8C2×D6111yescharacteristic
349#416—6116no—
350C2×#103—612no—
351C2×#103—612no—
352C2×#102—612no—
353C2×#102C2×D6112yes—
354C61C2×#307611yescharacteristic, complemented, Sylow
355C2×#41—618no—
356C2×#41—614no—
357C2×#41—1222no—
358C2×#41—1224no—
359C22×Q8—21no—
360C22×Q8—611no—
361C22×Q8—1221no—
362C22×D4—1221no—
363C22×D4C22×D6111yescharacteristic
364C23×C4—21no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—1221no—
369C23×C4—1221no—
370C22×C8—612no—
371C22×C8—618no—
372C22×C8—1228no—
373C22×C8C22×D6112yes—
374C4⋊Q8—22no—
375C4⋊Q8—614no—
376C4⋊Q8—1222no—
377C4⋊Q8C22×D6114yes—
378#125—618no—
379#125—1224no—
380C22⋊Q8—1228no—
381C22⋊Q8—1228no—
382C4×Q8—614no—
383C4×Q8—614no—
384C4×Q8—1222no—
385C4×Q8—1228no—
386C4×Q8—1228no—
387C4×Q8—1222no—
388C4×D4—22no—
389C4×D4—614no—
390C4×D4—1222no—
391C4×D4—1228no—
392C4×D4—1228no—
393C4×D4C22×D6114yes—
394#117—614no—
395#117—618no—
396#117—1228no—
397#117—1222no—
398#117—1224no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—612no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4C22×D6111yescharacteristic
408C2×C4⋊C4C22×D6112yes—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1222no—
412C2×C22⋊C4—1221no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—614no—
417C2×C42—614no—
418C2×C42—1228no—
419C2×C42—1221no—
420C2×C42—1222no—
421C2×C42—1221no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#107—618no—
425#107—618no—
426#106—618no—
427#106C22×D6118yes—
428C4⋊C8—618no—
429C4⋊C8—614no—
430C4⋊C8C22×D6114yes—
431#103—618no—
432#103—618no—
433#102—618no—
434#102C22×D6118yes—
435C24—21no—
436C24—611no—
437#41—6116no—
438#41—12216no—
439#41—1228no—
440C2×Q8—24no—
441C2×Q8—44no—
442C2×Q8—614no—
443C2×Q8—612no—
444C2×Q8—1221no—
445C2×Q8—1224no—
446C2×Q8—1222no—
447C2×Q8—2444no—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—1224no—
451C2×D4—1228no—
452C2×D4Q8×D6114yes—
453C2×D4C23×D6112yes—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—44no—
458C22×C4—611no—
459C22×C4—612no—
460C22×C4—614no—
461C22×C4—614no—
462C22×C4—612no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—614no—
466C22×C4—614no—
467C22×C4—1224no—
468C22×C4—1228no—
469C22×C4—1224no—
470C22×C4—1221no—
471C22×C4—1224no—
472C22×C4—1221no—
473C22×C4—1222no—
474C22×C4—2442no—
475C22×C4—2444no—
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4C23×D6111yescharacteristic
479C2×C8—24no—
480C2×C8—614no—
481C2×C8—12216no—
482C2×C8—1224no—
483C2×C8C23×D6114yes—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—614no—
488C4⋊C4—612no—
489C4⋊C4—1224no—
490C4⋊C4—1228no—
491C4⋊C4—1228no—
492C4⋊C4—1221no—
493C4⋊C4—1222no—
494C4⋊C4—1224no—
495C4⋊C4—1224no—
496C4⋊C4C23×D6114yes—
497C4⋊C4C23×D6112yes—
498C22⋊C4—24no—
499C22⋊C4—1224no—
500C22⋊C4—1228no—
501C22⋊C4—1224no—
502C42—614no—
503C42—614no—
504C42—612no—
505C42—612no—
506C42—1224no—
507C42—1224no—
508C42—1228no—
509C42—1224no—
510C42D4×D6112yes—
511C42C23×D6112yes—
512C23—24no—
513C23—22no—
514C23—42no—
515C23—42no—
516C23—614no—
517C23—612no—
518C23—1222no—
519C23—1222no—
520C23C2×D4×D6111yescharacteristic
521Q8—48no—
522Q8—614no—
523Q8—1224no—
524Q8—1222no—
525Q8—2448no—
526D4—24no—
527D4—22no—
528D4—12216no—
529D4C2×Q8×D6114yes—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—48no—
536C2×C4—614no—
537C2×C4—612no—
538C2×C4—618no—
539C2×C4—614no—
540C2×C4—614no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—12216no—
544C2×C4—1224no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1228no—
549C2×C4—1222no—
550C2×C4—1224no—
551C2×C4—2444no—
552C2×C4—2448no—
553C2×C4—2444no—
554C2×C4—2442no—
555C2×C4#1451979814yes—
556C2×C4C2×D4×D6112yes—
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4C2×D4×D6112yes—
559C2×C4C2×Q8×D6112yes—
560C2×C4#41×D6112yes—
561C2×C4C24×D6111yescharacteristic
562C8—24no—
563C8—1224no—
564C22—24no—
565C22—42no—
566C22—42no—
567C22—48no—
568C22—614no—
569C22—1222no—
570C22—1222no—
571C22—1228no—
572C22C22⋊Q8×D6112yes—
573C22C2×#1451979812yes—
574C22#1684055812yes—
575C22C22×D4×D6111yescharacteristic
576C4—22no—
577C4—42no—
578C4—44no—
579C4—614no—
580C4—1222no—
581C4—1222no—
582C4—1224no—
583C4—2444no—
584C4—2442no—
585C4C22⋊Q8×D6112yes—
586C4C2×#1451979814yes—
587C4C22×Q8×D6111yescharacteristic
588C4C2×#41×D6111yescharacteristic
589C2—44no—
590C2—1224no—
591C2#2145560814yesdirect product factor
592C2C2×C22⋊Q8×D6111yescharacteristic
593C2C22×#1451979811yescharacteristic
594C2C2×#1684055811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#476C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenterC2×#476D61
hypocenterC61C2×#3076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21455608C2direct (N × H)
4. C2×#16840072C2semidirect
5. C2×#16840054C2semidirect
6. C2×#16840048C2semidirect
7. C2×#16840064C2semidirect
8. C2×#16840042C2semidirect
9. C2×#16839797C2semidirect
10. C2×C4⋊C8×D61C2semidirect
12. C2×C61×#476C2semidirect
16. #16840317C22semidirect
35. #16840072C22semidirect
36. #16840064C22semidirect
37. #16840054C22semidirect
38. #16840048C22semidirect
39. #16840042C22semidirect
40. #16839797C22semidirect
46. C4⋊C8×D61C22semidirect
53. C61×#476C22semidirect
59. C2×#11758224Q8semidirect
166. #11758224C2×Q8semidirect
299. C2×#476D61semidirect
305. C2×C61#3076semidirect
337. #476C2×D61semidirect
354. C61C2×#3076semidirect
591. C2#21455608direct (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×#117582242
#214556082
C2×#168400722
C2×#168400542
C2×#168400482
C2×#168400642
C2×#168400422
C2×#168397972
C2×C4⋊C8×D612
C2×#168397552
C2×C61×#4762
C2×#307661