Finite Group Databasebeta

← C2×#21461205 #30610942

Subgroups — C2×#21461205 #30610942

Order 15616.

1834 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840734C211yesmaximal, characteristic, complemented
2C22×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
3#21461205C218yesmaximal, direct product factor
4C2×#16840616C212yesmaximal, complemented
5C2×#16840613C212yesmaximal, complemented
6C2×#16840269C211yesmaximal, characteristic
7C24×#6923—21no—
8C22×#11758217—21no—
9#16840734—22no—
10#16840734C2214yescomplemented
11C2×#14519834—21no—
12C2×#14519834C2212yes—
13C2×(C2×#6923)⋊C4—21no—
14C2×(C2×#6923)⋊C4—22no—
15C2×(C2×#6923)⋊C4C2212yes—
16C2×(C2×#6923)⋊C4C2214yescomplemented
17#16840616C2218yescomplemented
18#16840613C2218yescomplemented
19C23×C4×D61C2211yescharacteristic
20#16840269—22no—
21#16840269—22no—
22#16840269C414yescomplemented
23#16840269C2214yes—
24C2×#14519758—21no—
25C2×#14519753C411yescharacteristic, complemented
26C2×#14519753C2211yescharacteristic
27C2×#14519748C411yescharacteristic, complemented
28C2×#14519748C2211yescharacteristic
29C2×#14519745—21no—
30C2×C4×C22⋊D61—21no—
31C2×C4×C22⋊D61—21no—
32C2×#14519736C411yescharacteristic, complemented
33C22×#41×C61C411yescharacteristic, complemented
34C23×#6923—28no—
35C23×#6923—22no—
36C23×#6923—24no—
37C23×#6923—44no—
38C23×#6923—44no—
39C2×#11758217—24no—
40C2×#11758217—44no—
41C22×#92420—22no—
42#14519834—24no—
43#14519834—22no—
44#14519834C2314yes—
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—24no—
47(C2×#6923)⋊C4C2314yes—
48C24×D61D411yescharacteristic
49C22×C22⋊D61—21no—
50C22×C22⋊D61—21no—
51C23×Dic61D411yescharacteristic
52C22×C4×D61—44no—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C412yes—
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D412yes—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D412yes—
59C22×C4×D61C2311yescharacteristic
60C22×C4×D61C2312yes—
61#14519758—24no—
62#14519758—24no—
63#14519753—22no—
64#14519753—21no—
65#14519753—21no—
66#14519753C2×C414yescomplemented
67#14519753C2×C412yescomplemented
68#14519753C2312yes—
69#14519748—22no—
70#14519748—21no—
71#14519748—21no—
72#14519748C2×C414yescomplemented
73#14519748C2×C412yescomplemented
74#14519748C2312yes—
75#14519745—24no—
76#14519745—24no—
77C4×C22⋊D61—24no—
78C4×C22⋊D61—24no—
79C4×C22⋊D61—24no—
80C4×C22⋊D61—24no—
81#14519736—22no—
82#14519736C2×C414yescomplemented
83C2×C4⋊Dic61C2×C411yescharacteristic, complemented
84C2×C4⋊Dic61C2×C411yescharacteristic, complemented
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×C4×Dic61—21no—
93C2×#41×C61—22no—
94C2×#41×C61—44no—
95C2×#41×C61C2×C414yescomplemented
96C22×Q8×C61C2×C411yescharacteristic, complemented
97C22×D4×C61—21no—
98C22×D4×C61C2×C411yescharacteristic, complemented
99C23×C4×C61—21no—
100C23×C4×C61C2×C411yescharacteristic
101C24×C61—21no—
102C24×C61C22⋊C411yescharacteristic
103C23×D61—24no—
104C23×D61—24no—
105C23×D61—22no—
106C23×D61—22no—
107C23×D61C22⋊C412yes—
108C23×D61C22⋊C411yescharacteristic
109C23×D61C2×D412yes—
110C23×D61C2×D411yescharacteristic
111C22×#6923—28no—
112C22×#6923—216no—
113C22×#6923—24no—
114C22×#6923—432no—
115C22×#6923—44no—
116C22×#6923—48no—
117C22×#6923—48no—
118C22×#6923—44no—
119#41×C61—48no—
120#41×C61—48no—
121C2×Q8×C61—21no—
122C2×Q8×C61—42no—
123C2×Q8×C61C22×C412yescomplemented
124C2×D4×C61—24no—
125C2×D4×C61—21no—
126C2×D4×C61—42no—
127C2×D4×C61—44no—
128C2×D4×C61C22×C412yescomplemented
129C22×C4×C61—24no—
130C22×C4×C61—21no—
131C22×C4×C61—24no—
132C22×C4×C61—44no—
133C22×C4×C61C22⋊C411yescharacteristic
134C22×C4×C61C22⋊C412yes—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C412yes—
137C2×C22⋊D61—22no—
138C2×C22⋊D61—24no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—44no—
141C2×C22⋊D61—42no—
142C2×C22⋊D61—42no—
143C22×Dic61—24no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C22⋊C412yes—
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D412yes—
150C2×C4×D61—42no—
151C2×C4×D61—44no—
152C2×C4×D61—42no—
153C2×C4×D61—44no—
154C2×C4×D61—42no—
155C2×C4×D61—44no—
156C2×C4×D61—42no—
157C2×C4×D61—44no—
158C2×C4×D61C22⋊C412yes—
159C2×C4×D61C22⋊C412yes—
160C2×C4×D61C22⋊C412yes—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C22×C412yes—
163C2×C4×D61C2×D412yes—
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2411yescharacteristic
168#11758217—48no—
169C2×#92420—24no—
170C2×#92420—44no—
171C22⋊Dic61—24no—
172C22⋊Dic61—24no—
173C22⋊Dic61—22no—
174C22⋊Dic61—22no—
175#11758198—22no—
176#11758198—24no—
177#11758198—22no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61C22×C412yescomplemented
181C4⋊Dic61C22×C412yescomplemented
182#11758196—24no—
183#11758196—22no—
184#11758196—22no—
185C4×Dic61—24no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61#9914yes—
193C23×C61C2×C22⋊C412yes—
194C23×C61C2×C22⋊C411yescharacteristic
195C22×D61—216no—
196C22×D61—216no—
197C22×D61—24no—
198C22×D61—22no—
199C22×D61—24no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—22no—
204C22×D61—22no—
205C22×D61—24no—
206C22×D61—24no—
207C22×D61—24no—
208C22×D61#10414yes—
209C22×D61C2×C22⋊C411yescharacteristic
210C22×D61C2×C22⋊C412yes—
211C22×D61AGL(1,ℤ/8)12yes—
212C22×D61#13712yes—
213C22×D61C22×D411yescharacteristic
214C2×#6923—28no—
215C2×#6923—432no—
216C2×#6923—44no—
217C2×#6923—416no—
218C2×#6923—44no—
219Q8×C61—42no—
220Q8×C61—42no—
221D4×C61—42no—
222D4×C61—42no—
223D4×C61—48no—
224C2×C4×C61—22no—
225C2×C4×C61—24no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—22no—
229C2×C4×C61—48no—
230C2×C4×C61—42no—
231C2×C4×C61C2×C22⋊C412yes—
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C23×C411yescharacteristic
234C22⋊D61—42no—
235C22⋊D61—42no—
236C22⋊D61—44no—
237C22⋊D61—48no—
238C2×Dic61—22no—
239C2×Dic61—24no—
240C2×Dic61—24no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C2×C22⋊C412yes—
248C2×Dic61C22×D411yescharacteristic
249C4×D61—42no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—41no—
253C4×D61—42no—
254C4×D61—42no—
255C4×D61—41no—
256C4×D61—42no—
257C4×D61—41no—
258C4×D61—41no—
259#92420—44no—
260C2×#1504—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—28no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61—42no—
267C22×C61—84no—
268C22×C61C2×#9914yes—
269C22×C61C2×#9912yes—
270C22×C61#41712yes—
271C22×C61C2×#10412yes—
272C22×C61C22×C22⋊C411yescharacteristic
273C2×D61—28no—
274C2×D61—28no—
275C2×D61—216no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—24no—
283C2×D61—28no—
284C2×D61—24no—
285C2×D61#41712yes—
286C2×D61C2×#10414yes—
287C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
288C2×D61C2×#13711yescharacteristic
289#6923—48no—
290C4×C61—22no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—42no—
294Dic61—21no—
295Dic61—21no—
296Dic61—22no—
297Dic61—42no—
298Dic61—42no—
299C2×#525—611no—
300C2×#407—611no—
301C22×#95—611no—
302#1504—618no—
303C2×#328—612no—
304C2×#327—612no—
305C2×C61—24no—
306C2×C61—82no—
307C2×C61#150414yescomplemented
308C2×C61C22×#9911yescharacteristic
309C2×C61C2×#41711yescharacteristic
310C2×C61C22×#10411yescharacteristic
311D61—21no—
312D61—21no—
313D61—22no—
314D61—24no—
315C22×#41#692311yescharacteristic, complemented
316C24×C4—611no—
317C24×C4—1221no—
318C22×M16—1221no—
319#525—614no—
320#525—614no—
321#525—1222no—
322#525—1222no—
323C2×#123—1221no—
324C2×C22⋊Q8—611no—
325C2×C22⋊Q8—611no—
326C2×#121—611no—
327C2×#121—611no—
328C2×#120—1221no—
329C2×C4×D4—1221no—
330C2×C4×D4—1221no—
331C2×#117—611no—
332#407—614no—
333#407—1222no—
334C2×C22⋊C8—612no—
335C2×C22⋊C8—1221no—
336C2×#95—612no—
337C2×#95—614no—
338C2×#95—1221no—
339C2×#95—1222no—
340#328—618no—
341#327—618no—
342C61C2×#150411yescharacteristic, complemented, Sylow
343C25—611no—
344C2×#41—22no—
345C2×#41—44no—
346C2×#41C2×#692314yescomplemented
347C22×Q8C2×#692311yescharacteristic, complemented
348C22×D4—21no—
349C22×D4—1221no—
350C22×D4—1221no—
351C22×D4C2×#692311yescharacteristic, complemented
352C23×C4—21no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—612no—
357C23×C4—612no—
358C23×C4—611no—
359C23×C4—612no—
360C23×C4—611no—
361C23×C4—612no—
362C23×C4—1222no—
363C23×C4—1224no—
364C23×C4—1228no—
365C23×C4—2444no—
366C23×C4—2444no—
367C23×C4—2444no—
368C23×C4C2×#692311yescharacteristic
369C2×M16—1224no—
370C2×M16—2444no—
371C22×C8—1222no—
372#123—1224no—
373#123—1224no—
374C22⋊Q8—612no—
375C22⋊Q8—614no—
376C22⋊Q8—612no—
377C22⋊Q8—1221no—
378C22⋊Q8—1221no—
379C22⋊Q8—1222no—
380#121—612no—
381#121—614no—
382#121—612no—
383#121—1221no—
384#121—1221no—
385#121—1222no—
386#120—1224no—
387#120—1224no—
388C4×D4—1224no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1224no—
392#117—614no—
393#117—1222no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C42—1221no—
404C22⋊C8—614no—
405C22⋊C8—1222no—
406C22⋊C8—1224no—
407#95—614no—
408#95—1224no—
409#95—1222no—
410C24—21no—
411C24—611no—
412C24—611no—
413C24—612no—
414C24—612no—
415C24—1224no—
416C24—1222no—
417C24—1222no—
418C24—1224no—
419C24C22⋊#692311yescharacteristic
420#41—48no—
421#41—48no—
422C2×Q8—21no—
423C2×Q8—42no—
424C2×Q8C22×#692312yescomplemented
425C2×D4—24no—
426C2×D4—21no—
427C2×D4—42no—
428C2×D4—44no—
429C2×D4—1222no—
430C2×D4—1224no—
431C2×D4—1222no—
432C2×D4—2442no—
433C2×D4—2442no—
434C2×D4—2444no—
435C2×D4C22×#692312yescomplemented
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—44no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—612no—
445C22×C4—611no—
446C22×C4—612no—
447C22×C4—611no—
448C22×C4—612no—
449C22×C4—612no—
450C22×C4—612no—
451C22×C4—611no—
452C22×C4—612no—
453C22×C4—611no—
454C22×C4—1224no—
455C22×C4—1224no—
456C22×C4—12216no—
457C22×C4—1228no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—2442no—
461C22×C4—2442no—
462C22×C4—2444no—
463C22×C4—2444no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4—2444no—
467C22×C4—2444no—
468C22×C4—2444no—
469C22×C4—2448no—
470C22×C4—24432no—
471C22×C4—2448no—
472C22×C4—2444no—
473C22×C4C22⋊#692312yes—
474C22×C4C22⋊#692311yescharacteristic
475C22×C4C22×#692312yes—
476C22×C4C22×#692311yescharacteristic
477M16—2448no—
478C2×C8—1224no—
479C2×C8—2444no—
480C4⋊C4—612no—
481C4⋊C4—612no—
482C4⋊C4—1224no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C22⋊C4—1224no—
488C22⋊C4—1222no—
489C22⋊C4—1222no—
490C22⋊C4—1224no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1224no—
494C42—1224no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—612no—
502C23—612no—
503C23—614no—
504C23—611no—
505C23—612no—
506C23—611no—
507C23—1224no—
508C23—1222no—
509C23—1222no—
510C23—1224no—
511C23—1224no—
512C23—12216no—
513C23—12216no—
514C23—1224no—
515C23—1222no—
516C23—1224no—
517C23—1222no—
518C23—1222no—
519C23—1222no—
520C23#1451983514yes—
521C23C2×C22⋊#692312yes—
522C23C2×C22⋊#692311yescharacteristic
523Q8—42no—
524Q8—42no—
525D4—42no—
526D4—42no—
527D4—48no—
528D4—2442no—
529D4—2442no—
530D4—2444no—
531D4—2448no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—48no—
538C2×C4—42no—
539C2×C4—612no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—1222no—
543C2×C4—1224no—
544C2×C4—1224no—
545C2×C4—1222no—
546C2×C4—1228no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2442no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2442no—
559C2×C4—2444no—
560C2×C4—24432no—
561C2×C4—2444no—
562C2×C4—24416no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4C2×C22⋊#692312yes—
566C2×C4C2×C22⋊#692311yescharacteristic
567C2×C4C23×#692311yescharacteristic
568C8—2444no—
569C22—22no—
570C22—22no—
571C22—28no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—84no—
576C22—611no—
577C22—611no—
578C22—612no—
579C22—614no—
580C22—1228no—
581C22—1228no—
582C22—12216no—
583C22—1221no—
584C22—1221no—
585C22—1222no—
586C22—1222no—
587C22—1221no—
588C22—1221no—
589C22—1224no—
590C22—1228no—
591C22—1224no—
592C22C2×#1451983514yes—
593C22C2×#1451983512yes—
594C22#1684075312yes—
595C22D61⋊#10412yes—
596C22C22×C22⋊#692311yescharacteristic
597C4—22no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—1221no—
602C4—1221no—
603C4—1222no—
604C4—2448no—
605C4—2442no—
606C4—2442no—
607C2—24no—
608C2—82no—
609C2—1221no—
610C2—1221no—
611C2—1222no—
612C2—1224no—
613C2#2146120514yesdirect product factor
614C2C22×#1451983511yescharacteristic
615C2C2×#1684075311yescharacteristic
616C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×#41×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840269C2
cosocleC2×C4×D61C24
hypercenterC22×#41#6923
hypocenterC61C2×#1504
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16840734C2semidirect
2. C22×(C2×#6923)⋊C4C2semidirect
3. #21461205C2direct (N × H)
4. C2×#16840616C2semidirect
5. C2×#16840613C2semidirect
10. #16840734C22semidirect
16. C2×(C2×#6923)⋊C4C22semidirect
17. #16840616C22semidirect
18. #16840613C22semidirect
22. #16840269C4semidirect
25. C2×#14519753C4semidirect
27. C2×#14519748C4semidirect
32. C2×#14519736C4semidirect
33. C22×#41×C61C4semidirect
66. #14519753C2×C4semidirect
67. #14519753C2×C4semidirect
72. #14519748C2×C4semidirect
73. #14519748C2×C4semidirect
82. #14519736C2×C4semidirect
83. C2×C4⋊Dic61C2×C4semidirect
84. C2×C4⋊Dic61C2×C4semidirect
95. C2×#41×C61C2×C4semidirect
96. C22×Q8×C61C2×C4semidirect
98. C22×D4×C61C2×C4semidirect
123. C2×Q8×C61C22×C4semidirect
128. C2×D4×C61C22×C4semidirect
180. C4⋊Dic61C22×C4semidirect
181. C4⋊Dic61C22×C4semidirect
307. C2×C61#1504semidirect
315. C22×#41#6923semidirect
342. C61C2×#1504semidirect
346. C2×#41C2×#6923semidirect
347. C22×Q8C2×#6923semidirect
351. C22×D4C2×#6923semidirect
424. C2×Q8C22×#6923semidirect
435. C2×D4C22×#6923semidirect
613. C2#21461205direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407342
C22×(C2×#6923)⋊C42
#214612052
C2×#168406162
C2×#168406132
C2×#168402692
C2×#150461