Finite Group Databasebeta

← C2×#21444324 #29647154

Subgroups — C2×#21444324 #29647154

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×#16840273C211yesmaximal, characteristic
2C22×#14519684C211yesmaximal, characteristic, complemented
3#21444324C218yesmaximal, direct product factor
4C2×#16839500C212yesmaximal, complemented
5C2×#16839497C212yesmaximal, complemented
6C2×C61×#407C211yesmaximal, characteristic, complemented
7C22×#11758222C411yescharacteristic, complemented
8C24×Dic61—21no—
9#16840273—22no—
10#16840273—22no—
11#16840273C414yescomplemented
12#16840273C2214yes—
13C2×#14519760—21no—
14C2×#14519756C411yescharacteristic, complemented
15C2×#14519756C2211yescharacteristic
16C2×#14519751C411yescharacteristic, complemented
17C2×#14519751C2211yescharacteristic
18C2×#14519746—21no—
19C2×C4×C22⋊D61—21no—
20C2×C4×C22⋊D61—21no—
21C2×#14519736C411yescharacteristic, complemented
22C2×#14519684—21no—
23C2×#14519684—22no—
24C2×#14519684C2212yes—
25C2×#14519684C2214yescomplemented
26#16839500C2218yescomplemented
27#16839497C2218yescomplemented
28C24×C4×C61C2211yescharacteristic
29C22×M16×C61—21no—
30C61×#407—22no—
31C61×#407C2214yescomplemented
32C2×C22⋊C8×C61—21no—
33C2×C22⋊C8×C61C2212yes—
34C2×#11758222—22no—
35C2×#11758222—44no—
36C2×#11758222C2×C414yescomplemented
37C22×Dic122C2×C411yescharacteristic, complemented
38C22×D244C2×C411yescharacteristic, complemented
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C22⋊D61—21no—
42C23×Dic61—28no—
43C23×Dic61—22no—
44C23×Dic61—24no—
45C23×Dic61—44no—
46C23×Dic61—44no—
47C22×C4×D61—21no—
48#14519760—24no—
49#14519760—24no—
50#14519756—22no—
51#14519756—21no—
52#14519756—21no—
53#14519756C2×C414yescomplemented
54#14519756C2×C412yescomplemented
55#14519756C2312yes—
56#14519751—22no—
57#14519751—21no—
58#14519751—21no—
59#14519751C2×C414yescomplemented
60#14519751C2×C412yescomplemented
61#14519751C2312yes—
62#14519746—24no—
63#14519746—24no—
64C4×C22⋊D61—24no—
65C4×C22⋊D61—24no—
66C4×C22⋊D61—24no—
67C4×C22⋊D61—24no—
68#14519736—22no—
69#14519736C2×C414yescomplemented
70C2×C4⋊Dic61C2×C411yescharacteristic, complemented
71C2×C4⋊Dic61C2×C411yescharacteristic, complemented
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×C4×Dic61—21no—
80#14519684—22no—
81#14519684—24no—
82#14519684C2314yes—
83C25×C61D411yescharacteristic
84C23×C4×C61—44no—
85C23×C4×C61C2×C411yescharacteristic
86C23×C4×C61C2×C411yescharacteristic
87C23×C4×C61C2×C412yes—
88C23×C4×C61D411yescharacteristic
89C23×C4×C61D412yes—
90C23×C4×C61D411yescharacteristic
91C23×C4×C61D411yescharacteristic
92C23×C4×C61D412yes—
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2312yes—
95C2×M16×C61—24no—
96C2×M16×C61—44no—
97C22×C8×C61—22no—
98C22⋊C8×C61—24no—
99C22⋊C8×C61—22no—
100C22⋊C8×C61C2314yes—
101C24×C61—24no—
102C24×C61—24no—
103C24×C61—22no—
104C24×C61—22no—
105C24×C61C22⋊C412yes—
106C24×C61C22⋊C411yescharacteristic
107C24×C61C22⋊C411yescharacteristic
108C24×C61C2×D412yes—
109C24×C61C2×D411yescharacteristic
110C23×D61—21no—
111C22×C4×C61—24no—
112C22×C4×C61—24no—
113C22×C4×C61—42no—
114C22×C4×C61—44no—
115C22×C4×C61—42no—
116C22×C4×C61—44no—
117C22×C4×C61—42no—
118C22×C4×C61—44no—
119C22×C4×C61—42no—
120C22×C4×C61—44no—
121C22×C4×C61C22⋊C411yescharacteristic
122C22×C4×C61C22⋊C412yes—
123C22×C4×C61C22⋊C411yescharacteristic
124C22×C4×C61C22⋊C412yes—
125C22×C4×C61C22⋊C412yes—
126C22×C4×C61C22⋊C412yes—
127C22×C4×C61C22⋊C412yes—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C412yes—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—24no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—44no—
144C2×C22⋊D61—44no—
145C2×C22⋊D61—42no—
146C2×C22⋊D61—42no—
147C22×Dic61—28no—
148C22×Dic61—216no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—24no—
153C22×Dic61—432no—
154C22×Dic61—44no—
155C22×Dic61—48no—
156C22×Dic61—48no—
157C22×Dic61—44no—
158#11758222—48no—
159#11758222—48no—
160C2×D244—21no—
161C2×D244—42no—
162C2×D244C22×C412yescomplemented
163C2×C4×D61—24no—
164C2×C4×D61—44no—
165C2×Dic122—21no—
166C2×Dic122—42no—
167C2×Dic122C22×C412yescomplemented
168M16×C61—48no—
169C2×C8×C61—24no—
170C2×C8×C61—44no—
171C22⋊Dic61—24no—
172C22⋊Dic61—22no—
173C22⋊Dic61—24no—
174C22⋊Dic61—22no—
175#11758198—24no—
176#11758198—22no—
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—216no—
187C23×C61—216no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—24no—
191C23×C61—22no—
192C23×C61—24no—
193C23×C61—22no—
194C23×C61—24no—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61—24no—
198C23×C61—22no—
199C23×C61—24no—
200C23×C61—22no—
201C23×C61#9914yes—
202C23×C61#10414yes—
203C23×C61C2×C22⋊C412yes—
204C23×C61C2×C22⋊C411yescharacteristic
205C23×C61C2×C22⋊C412yes—
206C23×C61C2×C22⋊C411yescharacteristic
207C23×C61AGL(1,ℤ/8)12yes—
208C23×C61#13712yes—
209C23×C61C22×D411yescharacteristic
210C22×D61—22no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—42no—
214C2×C4×C61—22no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—24no—
221C2×C4×C61—22no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—41no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—42no—
229C2×C4×C61—41no—
230C2×C4×C61—42no—
231C2×C4×C61—41no—
232C2×C4×C61C2×C22⋊C412yes—
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C22⋊D61—42no—
239C22⋊D61—42no—
240C22⋊D61—48no—
241C22⋊D61—44no—
242C22⋊D61—48no—
243C2×Dic61—28no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—432no—
248C2×Dic61—44no—
249C2×Dic61—416no—
250C2×Dic61—44no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254D244—42no—
255D244—42no—
256C4×D61—48no—
257Dic122—42no—
258Dic122—42no—
259C8×C61—44no—
260C2×#1504—611nomaximal, Sylow
261C22×C61—28no—
262C22×C61—28no—
263C22×C61—216no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—22no—
267C22×C61—22no—
268C22×C61—22no—
269C22×C61—21no—
270C22×C61—22no—
271C22×C61—21no—
272C22×C61—24no—
273C22×C61—28no—
274C22×C61—28no—
275C22×C61—24no—
276C22×C61C2×#9914yes—
277C22×C61C2×#9912yes—
278C22×C61#41712yes—
279C22×C61#41712yes—
280C22×C61C2×#10414yes—
281C22×C61C2×#10412yes—
282C22×C61C22×C22⋊C411yescharacteristic
283C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C61C2×#13711yescharacteristic
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—84no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—22no—
293C4×C61—21no—
294C4×C61—22no—
295Dic61—48no—
296Dic61—42no—
297Dic61—42no—
298Dic61—42no—
299C2×#525—611no—
300C2×#407D6111yescharacteristic, complemented
301C22×#95—611no—
302#1504—618no—
303C2×#328—612no—
304C2×#327—612no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—24no—
308C2×C61—22no—
309C2×C61—24no—
310C2×C61#150414yescomplemented
311C2×C61C22×#9911yescharacteristic
312C2×C61C2×#41711yescharacteristic
313C2×C61C22×#10411yescharacteristic
314D61—82no—
315C22×#41—611no—
316C24×C4—1221no—
317C24×C4C2×D6111yescharacteristic
318C22×M16—21no—
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—22no—
333#407C2×D6114yescomplemented
334C2×C22⋊C8—21no—
335C2×C22⋊C8C2×D6112yes—
336C2×#95—612no—
337C2×#95—614no—
338C2×#95—1221no—
339C2×#95—1222no—
340#328—618no—
341#327—618no—
342C61C2×#150411yescharacteristic, complemented, Sylow
343C25D24411yescharacteristic
344C2×#41—614no—
345C2×#41—1222no—
346C2×#41—2444no—
347C22×Q8—611no—
348C22×D4—611no—
349C22×D4—1221no—
350C22×D4—1221no—
351C22×D4—1221no—
352C23×C4—44no—
353C23×C4—1228no—
354C23×C4—1224no—
355C23×C4—1222no—
356C23×C4—1221no—
357C23×C4—2444no—
358C23×C4—2444no—
359C23×C4C4×D6111yescharacteristic
360C23×C4C4×D6111yescharacteristic
361C23×C4C4×D6112yes—
362C23×C4D24411yescharacteristic
363C23×C4D24412yes—
364C23×C4C22⋊D6111yescharacteristic
365C23×C4C22⋊D6111yescharacteristic
366C23×C4C22⋊D6112yes—
367C23×C4C22×D6111yescharacteristic
368C23×C4C22×D6112yes—
369C2×M16—24no—
370C2×M16—44no—
371C22×C8—22no—
372#123—1224no—
373#123—1224no—
374C22⋊Q8—614no—
375C22⋊Q8—612no—
376C22⋊Q8—612no—
377C22⋊Q8—1222no—
378C22⋊Q8—1221no—
379C22⋊Q8—1221no—
380#121—614no—
381#121—612no—
382#121—612no—
383#121—1222no—
384#121—1221no—
385#121—1221no—
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—24no—
405C22⋊C8—22no—
406C22⋊C8C22×D6114yes—
407#95—614no—
408#95—1224no—
409#95—1222no—
410C24—22no—
411C24—24no—
412C24—24no—
413C24—22no—
414C24—1221no—
415C24#1175819812yes—
416C24#1175819811yescharacteristic
417C24#1175819811yescharacteristic
418C24C2×D24412yes—
419C24C2×D24411yescharacteristic
420#41—2448no—
421#41—2448no—
422C2×Q8—612no—
423C2×Q8—1221no—
424C2×Q8—2442no—
425C2×D4—612no—
426C2×D4—1222no—
427C2×D4—1222no—
428C2×D4—1224no—
429C2×D4—1224no—
430C2×D4—1221no—
431C2×D4—2442no—
432C2×D4—2442no—
433C2×D4—2444no—
434C2×D4—2444no—
435C2×D4—2442no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—42no—
439C22×C4—44no—
440C22×C4—42no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—44no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—12216no—
447C22×C4—1228no—
448C22×C4—1224no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1224no—
453C22×C4—2444no—
454C22×C4—24432no—
455C22×C4—2448no—
456C22×C4—2444no—
457C22×C4—2448no—
458C22×C4—2444no—
459C22×C4#1175819812yes—
460C22×C4#1175819812yes—
461C22×C4#1175819811yescharacteristic
462C22×C4#1175819811yescharacteristic
463C22×C4#1175819812yes—
464C22×C4#1175819812yes—
465C22×C4#1175819812yes—
466C22×C4C2×C4×D6112yes—
467C22×C4C2×C4×D6111yescharacteristic
468C22×C4C2×C4×D6111yescharacteristic
469C22×C4C2×C4×D6112yes—
470C22×C4C2×D24412yes—
471C22×C4C2×D24411yescharacteristic
472C22×C4C2×C22⋊D6112yes—
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6112yes—
475C22×C4C2×C22⋊D6111yescharacteristic
476C22×C4C23×D6111yescharacteristic
477M16—48no—
478C2×C8—24no—
479C2×C8—44no—
480C4⋊C4—612no—
481C4⋊C4—612no—
482C4⋊C4—1222no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1224no—
486C4⋊C4—1222no—
487C22⋊C4—1222no—
488C22⋊C4—1224no—
489C22⋊C4—1222no—
490C22⋊C4—1224no—
491C22⋊C4—1222no—
492C22⋊C4—1224no—
493C22⋊C4—1222no—
494C42—1224no—
495C23—216no—
496C23—216no—
497C23—24no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—1222no—
511C23—2442no—
512C23—2442no—
513C23—2442no—
514C23#1451969114yes—
515C23#1451970314yes—
516C23C2×#1175819812yes—
517C23C2×#1175819811yescharacteristic
518C23C2×#1175819812yes—
519C23C2×#1175819811yescharacteristic
520C23#1451980512yes—
521C23#1451981012yes—
522C23C22×D24411yescharacteristic
523Q8—2442no—
524Q8—2442no—
525D4—2442no—
526D4—2442no—
527D4—2448no—
528D4—2444no—
529D4—2448no—
530D4—2442no—
531D4—2442no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—1228no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—2448no—
555C2×C4—24432no—
556C2×C4—2444no—
557C2×C4—24416no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2444no—
562C2×C4C2×#1175819812yes—
563C2×C4C2×#1175819811yescharacteristic
564C2×C4C2×#1175819812yes—
565C2×C4C2×#1175819811yescharacteristic
566C2×C4C22×C4×D6111yescharacteristic
567C2×C4C22×C22⋊D6111yescharacteristic
568C8—44no—
569C22—28no—
570C22—216no—
571C22—28no—
572C22—21no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—22no—
578C22—24no—
579C22—24no—
580C22—28no—
581C22—28no—
582C22—22no—
583C22—22no—
584C22—4884no—
585C22—2442no—
586C22—2442no—
587C22—2442no—
588C22C2×#1451969114yes—
589C22C2×#1451969112yes—
590C22#1683976412yes—
591C22#1683976412yes—
592C22C2×#1451970314yes—
593C22C2×#1451970312yes—
594C22C22×#1175819811yescharacteristic
595C22C2×#1451980511yescharacteristic
596C22C2×#1451981011yescharacteristic
597C4—21no—
598C4—22no—
599C4—21no—
600C4—21no—
601C4—22no—
602C4—21no—
603C4—2448no—
604C4—2442no—
605C4—2442no—
606C4—2442no—
607C2—21no—
608C2—24no—
609C2—22no—
610C2—24no—
611C2—21no—
612C2—4882no—
613C2#2144432414yesdirect product factor
614C2C22×#1451969111yescharacteristic
615C2C2×#1683976411yescharacteristic
616C2C22×#1451970311yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#407C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenterC2×#407D61
hypocenterC61C2×#1504
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×#14519684C2semidirect
3. #21444324C2direct (N × H)
4. C2×#16839500C2semidirect
5. C2×#16839497C2semidirect
6. C2×C61×#407C2semidirect
7. C22×#11758222C4semidirect
11. #16840273C4semidirect
14. C2×#14519756C4semidirect
16. C2×#14519751C4semidirect
21. C2×#14519736C4semidirect
25. C2×#14519684C22semidirect
26. #16839500C22semidirect
27. #16839497C22semidirect
31. C61×#407C22semidirect
36. C2×#11758222C2×C4semidirect
37. C22×Dic122C2×C4semidirect
38. C22×D244C2×C4semidirect
53. #14519756C2×C4semidirect
54. #14519756C2×C4semidirect
59. #14519751C2×C4semidirect
60. #14519751C2×C4semidirect
69. #14519736C2×C4semidirect
70. C2×C4⋊Dic61C2×C4semidirect
71. C2×C4⋊Dic61C2×C4semidirect
162. C2×D244C22×C4semidirect
167. C2×Dic122C22×C4semidirect
180. C4⋊Dic61C22×C4semidirect
181. C4⋊Dic61C22×C4semidirect
300. C2×#407D61semidirect
310. C2×C61#1504semidirect
333. #407C2×D61semidirect
342. C61C2×#1504semidirect
613. C2#21444324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402732
C22×#145196842
#214443242
C2×#168395002
C2×#168394972
C2×C61×#4072
C2×#150461