Finite Group Databasebeta

← C2×#21455990 #30548161

Subgroups — C2×#21455990 #30548161

Order 15616.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2#21455990C2116yesmaximal, direct product factor
3C2×#16840097C211yesmaximal, characteristic, complemented
4C2×#16840080C211yesmaximal, characteristic
5C2×#16840069C212yesmaximal, complemented
6C2×#16839984C212yesmaximal, complemented
7C2×#16839918C211yesmaximal, characteristic, complemented
8C2×#16839901C211yesmaximal, characteristic
9C2×#16839867C212yesmaximal, complemented
10C2×#16839860C212yesmaximal, complemented
11C2×#16839819C211yesmaximal, characteristic, complemented
12C22×C4×Q8×C61C211yesmaximal, characteristic, complemented
13C22×#11758202C2212yes—
14C22×#11758201C2212yes—
15#16840296—24no—
16#16840296C2218yes—
17C2×#14519771—21no—
18C2×#14519769C2211yescharacteristic
19C2×#14519765C2211yescharacteristic
20C2×#14519760—21no—
21C2×#14519756C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×C22⋊D61—21no—
26C2×#14519734—21no—
27#16840097C2218yescomplemented
28#16840080C2218yes—
29#16840069C22116yescomplemented
30#16839984C22116yescomplemented
31#16839918C2218yescomplemented
32#16839901C2218yes—
33#16839867C22116yescomplemented
34#16839860C22116yescomplemented
35#16839819C2218yescomplemented
36C2×#14519710C2212yes—
37C2×#14519708C2212yes—
38C2×C4⋊#92418C2212yes—
39C2×#14519701C2212yes—
40C2×#14519701C2212yes—
41C2×#14519700C2212yes—
42C2×#14519697C2212yes—
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519688C2212yes—
46C23×Q8×C61C2211yescharacteristic
47C2×C4×Q8×C61—21no—
48C2×C4×Q8×C61—21no—
49C2×C4×Q8×C61—24no—
50C2×C4×Q8×C61C2212yes—
51C2×C4×Q8×C61C2212yes—
52C2×C4×Q8×C61C2218yescomplemented
53C22×C4⋊C4×C61—21no—
54C22×C4⋊C4×C61C2211yescharacteristic
55C22×C42×C61—21no—
56C22×C42×C61C2211yescharacteristic
57C22×Dic122C2311yescharacteristic
58C22×D244C2311yescharacteristic
59C22×C22⋊D61—21no—
60C22×C4×D61—21no—
61C2×#11758202—28no—
62C2×#11758202C2318yes—
63C2×#11758201—28no—
64C2×#11758201C2318yes—
65C22×#92418C2312yes—
66C22×#92418C2312yes—
67#14519771—28no—
68#14519769—22no—
69#14519769C2314yes—
70#14519765—22no—
71#14519765C2314yes—
72#14519760—28no—
73#14519756—22no—
74#14519756C2314yes—
75#14519751—22no—
76#14519751C2314yes—
77C4×Dic122—22no—
78C4×Dic122C2314yes—
79C4×D244—22no—
80C4×D244C2314yes—
81C4×C22⋊D61—28no—
82#14519734—28no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×C4×Dic61—21no—
95#14519710C2318yes—
96#14519708C2318yes—
97C4⋊#92418C2318yes—
98#14519701C2318yes—
99#14519701C2318yes—
100#14519700C2318yes—
101#14519697C2318yes—
102C22⋊#92418C2314yes—
103C22⋊#92418C2314yes—
104#14519688C2318yes—
105C22×Q8×C61—28no—
106C22×Q8×C61—21no—
107C22×Q8×C61—22no—
108C22×Q8×C61C2314yes—
109C22×Q8×C61C2312yes—
110C23×C4×C61—21no—
111C23×C4×C61—21no—
112C23×C4×C61D411yescharacteristic
113C23×C4×C61D411yescharacteristic
114C23×C4×C61C2311yescharacteristic
115C4×Q8×C61—24no—
116C4×Q8×C61—24no—
117C4×Q8×C61—28no—
118C4×Q8×C61—28no—
119C4×Q8×C61C2318yes—
120C4×Q8×C61C2318yes—
121C2×C4⋊C4×C61—22no—
122C2×C4⋊C4×C61—22no—
123C2×C4⋊C4×C61—28no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61C2312yes—
127C2×C4⋊C4×C61C2314yes—
128C2×C42×C61—22no—
129C2×C42×C61—22no—
130C2×C42×C61—28no—
131C2×C42×C61D411yescharacteristic
132C2×C42×C61D411yescharacteristic
133C2×C42×C61D414yes—
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2314yes—
137C24×C61C2×D411yescharacteristic
138C23×D61—21no—
139C2×Q8×C61—216no—
140C2×Q8×C61—28no—
141C2×Q8×C61—216no—
142C2×Q8×C61—24no—
143C2×Q8×C61—22no—
144C2×Q8×C61—24no—
145C2×Q8×C61#4118yes—
146C2×Q8×C61C2414yes—
147C22×C4×C61—28no—
148C22×C4×C61—24no—
149C22×C4×C61—24no—
150C22×C4×C61—22no—
151C22×C4×C61—24no—
152C22×C4×C61—24no—
153C22×C4×C61—22no—
154C22×C4×C61—42no—
155C22×C4×C61—44no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D414yes—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D414yes—
164C22×C4×C61C2412yes—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—44no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C2×D244—24no—
172C2×D244—21no—
173C2×D244C2412yes—
174C2×C4×D61—24no—
175C2×C4×D61—44no—
176C2×Dic122—24no—
177C2×Dic122—21no—
178C2×Dic122C2412yes—
179C4⋊C4×C61—28no—
180C4⋊C4×C61—28no—
181C4⋊C4×C61—24no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61C2414yes—
184C42×C61—28no—
185C42×C61—28no—
186C42×C61C2×D414yes—
187C42×C61C2×D412yes—
188C42×C61C2×D412yes—
189C42×C61C2×D414yes—
190C42×C61C2412yes—
191C42×C61C2412yes—
192C22⋊Dic61—24no—
193#11758202—216no—
194#11758201—216no—
195#11758198—24no—
196#11758198—24no—
197#11758198—24no—
198#11758198—24no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C2412yes—
202C4⋊Dic61C2412yes—
203#11758196—24no—
204#11758196—24no—
205#11758196—24no—
206#11758196—24no—
207C4×Dic61—24no—
208C2×#92418—24no—
209C2×#92418—24no—
210C2×#92418C2414yes—
211C2×#92418C2414yes—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61#13714yes—
215C23×C61C22×D412yes—
216C23×C61C22×D411yescharacteristic
217C22×D61—22no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221Q8×C61—216no—
222Q8×C61—28no—
223Q8×C61—24no—
224Q8×C61C2×#4118yes—
225C2×C4×C61—216no—
226C2×C4×C61—28no—
227C2×C4×C61—22no—
228C2×C4×C61—28no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—44no—
238C2×C4×C61—48no—
239C2×C4×C61—44no—
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×D412yes—
242C2×C4×C61C22×D412yes—
243C2×C4×C61C22×D412yes—
244C2×C4×C61C22×D412yes—
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C2×#4114yes—
247C2×C4×C61C2511yescharacteristic
248C22⋊D61—48no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255D244—24no—
256D244—42no—
257C4×D61—48no—
258Dic122—24no—
259Dic122—42no—
260#92418—24no—
261#92418—24no—
262C2×#3117—611nomaximal, Sylow
263C22×C61—28no—
264C22×C61—22no—
265C22×C61—22no—
266C22×C61#52512yes—
267C22×C61C2×#13714yes—
268C22×C61C2×#13712yes—
269C22×C61#57512yes—
270C22×C61C23×D411yescharacteristic
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—84no—
275C4×C61—28no—
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—22no—
281C4×C61—44no—
282C4×C61#52512yes—
283C4×C61C22×#4112yes—
284Dic61—42no—
285Dic61—42no—
286Dic61—42no—
287C2×#529—611no—
288C22×C4×Q8D6111yescharacteristic, complemented
289#3117—6116no—
290C2×#484—611no—
291C2×#481—611no—
292C2×#479—612no—
293C2×#464—612no—
294C2×#451—611no—
295C2×#448—611no—
296C2×#441—612no—
297C2×#440—612no—
298C2×#432—611no—
299C2×C61—24no—
300C2×C61#311714yescomplemented
301C2×C61C2×#52511yescharacteristic
302C2×C61C22×#13711yescharacteristic
303C2×C61C2×#57511yescharacteristic
304D61—82no—
305C23×Q8C2×D6111yescharacteristic
306C22×Q16—612no—
307C22×SD16—612no—
308#529—618no—
309#529—1224no—
310C2×#126—1221no—
311C2×#125—611no—
312C2×#124—611no—
313C2×#123—1221no—
314C2×C22⋊Q8—611no—
315C2×#121—611no—
316C2×C4×Q8—21no—
317C2×C4×Q8—21no—
318C2×C4×Q8—24no—
319C2×C4×Q8—611no—
320C2×C4×Q8C2×D6112yes—
321C2×C4×Q8C2×D6112yes—
322C2×C4×Q8C2×D6118yescomplemented
323C2×C4×D4—611no—
324C2×C4×D4—1221no—
325C2×#117—1221no—
326C22×C4⋊C4—21no—
327C22×C4⋊C4C2×D6111yescharacteristic
328C22×C42—21no—
329C22×C42C2×D6111yescharacteristic
330#484—618no—
331#481—618no—
332#479—6116no—
333#464—6116no—
334#451—618no—
335#448—618no—
336#441—6116no—
337#440—6116no—
338#432—618no—
339C2×#107—612no—
340C2×#106—612no—
341C2×C4⋊C8—612no—
342C2×#103—612no—
343C2×#103—612no—
344C2×#103—612no—
345C2×#102—612no—
346C2×C22⋊C8—611no—
347C2×C22⋊C8—611no—
348C2×#97—612no—
349C61C2×#311711yescharacteristic, complemented, Sylow
350C22×Q8—28no—
351C22×Q8—22no—
352C22×Q8—21no—
353C22×Q8—611no—
354C22×Q8C22×D6114yes—
355C22×Q8C22×D6112yes—
356C22×D4—611no—
357C22×D4—1221no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—1221no—
361C23×C4C22⋊D6111yescharacteristic
362C23×C4C22⋊D6111yescharacteristic
363C23×C4C22×D6111yescharacteristic
364C2×Q16—618no—
365C2×Q16—1228no—
366C2×SD16—618no—
367C2×SD16—1228no—
368C22×C8—612no—
369C22×C8—612no—
370#126—1228no—
371#125—614no—
372#125—1222no—
373#124—614no—
374#124—1222no—
375#123—1228no—
376C22⋊Q8—614no—
377C22⋊Q8—1222no—
378#121—614no—
379#121—1222no—
380C4×Q8—24no—
381C4×Q8—24no—
382C4×Q8—28no—
383C4×Q8—28no—
384C4×Q8—614no—
385C4×Q8—1222no—
386C4×Q8C22×D6118yes—
387C4×Q8C22×D6118yes—
388C4×D4—614no—
389C4×D4—1228no—
390C4×D4—1222no—
391#117—1228no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4C22×D6112yes—
404C2×C4⋊C4C22×D6114yes—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—28no—
413C2×C42—1221no—
414C2×C42C22⋊D6111yescharacteristic
415C2×C42C22⋊D6111yescharacteristic
416C2×C42C22⋊D6114yes—
417C2×C42C22×D6111yescharacteristic
418C2×C42C22×D6111yescharacteristic
419C2×C42C22×D6114yes—
420#107—618no—
421#106—618no—
422C4⋊C8—618no—
423#103—618no—
424#103—618no—
425#103—618no—
426#102—618no—
427C22⋊C8—614no—
428C22⋊C8—614no—
429#97—618no—
430C24—1221no—
431C24C2×C22⋊D6111yescharacteristic
432C2×Q8—216no—
433C2×Q8—28no—
434C2×Q8—216no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—24no—
438C2×Q8—612no—
439C2×Q8—1221no—
440C2×Q8—1224no—
441C2×Q8#1175822218yes—
442C2×Q8C23×D6114yes—
443C2×D4—612no—
444C2×D4—1224no—
445C2×D4—1221no—
446C2×D4—1224no—
447C2×D4—2444no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—44no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1224no—
461C22×C4—2444no—
462C22×C4C2×C22⋊D6114yes—
463C22×C4C2×C22⋊D6112yes—
464C22×C4C2×C22⋊D6111yescharacteristic
465C22×C4C2×C22⋊D6111yescharacteristic
466C22×C4C2×C22⋊D6111yescharacteristic
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6114yes—
470C22×C4C23×D6112yes—
471C22×C4C23×D6111yescharacteristic
472Q16—12216no—
473SD16—12216no—
474C2×C8—614no—
475C2×C8—614no—
476C2×C8—1224no—
477C2×C8—1224no—
478C4⋊C4—28no—
479C4⋊C4—28no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—612no—
483C4⋊C4—612no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1224no—
487C4⋊C4—1224no—
488C4⋊C4—1224no—
489C4⋊C4—1224no—
490C4⋊C4C23×D6114yes—
491C22⋊C4—1224no—
492C22⋊C4—1224no—
493C22⋊C4—1224no—
494C22⋊C4—1224no—
495C22⋊C4—1224no—
496C42—28no—
497C42—28no—
498C42—1224no—
499C42C2×C22⋊D6114yes—
500C42C2×C22⋊D6112yes—
501C42C2×C22⋊D6112yes—
502C42C2×C22⋊D6114yes—
503C42C23×D6112yes—
504C42C23×D6112yes—
505C23—22no—
506C23—22no—
507C23—1222no—
508C23—2442no—
509C23—2442no—
510C23—2442no—
511C23#1451980814yes—
512C23C22×C22⋊D6112yes—
513C23C22×C22⋊D6111yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—1224no—
518Q8—2442no—
519Q8C2×#1175822218yes—
520D4—1224no—
521D4—2448no—
522D4—2442no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—28no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—44no—
536C2×C4—48no—
537C2×C4—44no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1222no—
541C2×C4—2448no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4C22×C22⋊D6112yes—
546C2×C4C22×C22⋊D6112yes—
547C2×C4C22×C22⋊D6112yes—
548C2×C4C22×C22⋊D6112yes—
549C2×C4C22×C22⋊D6112yes—
550C2×C4C22×C22⋊D6111yescharacteristic
551C2×C4C2×#1175822214yes—
552C2×C4C24×D6111yescharacteristic
553C8—1224no—
554C8—1224no—
555C22—22no—
556C22—22no—
557C22—28no—
558C22—4884no—
559C22—2442no—
560C22—2442no—
561C22—2442no—
562C22#1684027312yes—
563C22C2×#1451980814yes—
564C22C2×#1451980812yes—
565C22#1684056012yes—
566C22C23×C22⋊D6111yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—28no—
572C4—22no—
573C4—44no—
574C4—2442no—
575C4—2442no—
576C4—2442no—
577C4#1684027312yes—
578C4C22×#1175822212yes—
579C2—24no—
580C2—4882no—
581C2#2145599014yesdirect product factor
582C2C2×#1684027311yescharacteristic
583C2C22×#1451980811yescharacteristic
584C2C2×#1684056011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×C4×Q8×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC22×C4×Q8D61
hypocenterC61C2×#3117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #21455990C2direct (N × H)
3. C2×#16840097C2semidirect
5. C2×#16840069C2semidirect
6. C2×#16839984C2semidirect
7. C2×#16839918C2semidirect
9. C2×#16839867C2semidirect
10. C2×#16839860C2semidirect
11. C2×#16839819C2semidirect
12. C22×C4×Q8×C61C2semidirect
27. #16840097C22semidirect
29. #16840069C22semidirect
30. #16839984C22semidirect
31. #16839918C22semidirect
33. #16839867C22semidirect
34. #16839860C22semidirect
35. #16839819C22semidirect
52. C2×C4×Q8×C61C22semidirect
288. C22×C4×Q8D61semidirect
300. C2×C61#3117semidirect
322. C2×C4×Q8C2×D61semidirect
349. C61C2×#3117semidirect
581. C2#21455990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402962
#214559902
C2×#168400972
C2×#168400802
C2×#168400692
C2×#168399842
C2×#168399182
C2×#168399012
C2×#168398672
C2×#168398602
C2×#168398192
C22×C4×Q8×C612
C2×#311761