Finite Group Databasebeta

← C2×#21445806 #29679407

Subgroups — C2×#21445806 #29679407

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C22×#14519691C212yesmaximal
3C2×#16839620C212yesmaximal, complemented
4#21445806C218yesmaximal, direct product factor
5C2×#16839529C211yesmaximal, characteristic, complemented
6C2×C61×#342C211yesmaximal, characteristic, complemented
7C23×C22⋊D61C2211yescharacteristic
8C24×Dic61C2211yescharacteristic
9C23×C4×D61C411yescharacteristic, complemented
10C2×#14519737—22no—
11C2×#14519737—22no—
12C2×#14519737—24no—
13C2×#14519737C414yescomplemented
14C2×#14519737C2214yes—
15C22×#11758196—22no—
16C22×#11758196C411yescharacteristic, complemented
17C22×C22⋊Dic61C2212yes—
18C22×#11758198C411yescharacteristic, complemented
19C22×C4×Dic61C411yescharacteristic, complemented
20C2×#14519691—28no—
21C2×#14519691C2218yes—
22#16839620—24no—
23#16839620C2218yescomplemented
24C2×#14519684—22no—
25#16839529C2214yescomplemented
26C22×C22⋊C4×C61C2212yes—
27C22×C22⋊C4×C61C2211yescharacteristic
28C61×#342C2214yescomplemented
29C24×D61C2×C411yescharacteristic
30C22×C22⋊D61—22no—
31C22×C22⋊D61—22no—
32C22×C22⋊D61—24no—
33C22×C22⋊D61C2×C412yes—
34C22×C22⋊D61D414yes—
35C22×C22⋊D61Q814yes—
36C22×C22⋊D61C2312yes—
37C23×Dic61—22no—
38C23×Dic61—44no—
39C23×Dic61C2×C411yescharacteristic
40C23×Dic61C2×C411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C412yes—
43C23×Dic61D412yes—
44C23×Dic61D412yes—
45C23×Dic61D414yes—
46C23×Dic61C2312yes—
47C22×C4×D61—22no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61—44no—
51C22×C4×D61C2×C414yescomplemented
52#14519737—28no—
53#14519737—28no—
54#14519737—28no—
55#14519737—28no—
56C2×#11758196—22no—
57C2×#11758196—22no—
58C2×#11758196—28no—
59C2×#11758196—48no—
60C2×#11758196C2×C414yescomplemented
61C2×C22⋊Dic61—24no—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61C2314yes—
65C2×#11758198—22no—
66C2×#11758198—22no—
67C2×#11758198C2×C414yescomplemented
68C2×C4×Dic61—22no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61—21no—
71C2×C4×Dic61C2×C414yescomplemented
72#14519691—216no—
73#14519684—28no—
74C25×C61C2311yescharacteristic
75C23×C4×C61—22no—
76C23×C4×C61C2×C411yescharacteristic
77C23×C4×C61C2×C411yescharacteristic
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—24no—
81C2×C22⋊C4×C61—24no—
82C2×C22⋊C4×C61—22no—
83C2×C22⋊C4×C61C2×C412yes—
84C2×C22⋊C4×C61C2314yes—
85C2×C22⋊C4×C61C2312yes—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61C22×C411yescharacteristic
89C24×C61C22×C411yescharacteristic
90C24×C61C2×D412yes—
91C24×C61C2×D412yes—
92C24×C61C2×D412yes—
93C24×C61C2×Q812yes—
94C24×C61#4114yes—
95C24×C61C2411yescharacteristic
96C23×D61—21no—
97C23×D61—21no—
98C23×D61—22no—
99C23×D61—42no—
100C23×D61—42no—
101C23×D61C4⋊C414yescomplemented
102C23×D61C22×C412yes—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—24no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61—44no—
111C22×C4×C61—44no—
112C22×C4×C61—44no—
113C22×C4×C61C22×C412yes—
114C22×C4×C61C22×C412yes—
115C2×C22⋊D61—24no—
116C2×C22⋊D61—24no—
117C2×C22⋊D61—28no—
118C2×C22⋊D61—28no—
119C2×C22⋊D61—28no—
120C2×C22⋊D61—28no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61—24no—
123C2×C22⋊D61C4⋊C418yescomplemented
124C2×C22⋊D61C2×D414yes—
125C2×C22⋊D61C2×Q814yes—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—22no—
129C22×Dic61—24no—
130C22×Dic61—28no—
131C22×Dic61—24no—
132C22×Dic61—44no—
133C22×Dic61—48no—
134C22×Dic61—44no—
135C22×Dic61—42no—
136C22×Dic61—44no—
137C22×Dic61—44no—
138C22×Dic61—44no—
139C22×Dic61—44no—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C412yes—
142C22×Dic61C22⋊C412yes—
143C22×Dic61C22⋊C414yes—
144C22×Dic61C22⋊C412yes—
145C22×Dic61C22⋊C414yes—
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C4⋊C414yescomplemented
148C22×Dic61C22×C412yes—
149C22×Dic61C22×C412yes—
150C22×Dic61C22×C412yes—
151C22×Dic61C2×D414yes—
152C22×Dic61C2×D414yes—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—44no—
156C2×C4×D61—48no—
157C2×C4×D61—44no—
158C2×C4×D61—48no—
159C22⋊C4×C61—24no—
160C22⋊C4×C61—24no—
161C22⋊C4×C61—24no—
162C22⋊C4×C61—24no—
163C22⋊C4×C61—44no—
164C22⋊Dic61—24no—
165C22⋊Dic61—24no—
166C22⋊Dic61—44no—
167#11758198—28no—
168#11758196—28no—
169#11758196—416no—
170C4×Dic61—24no—
171C4×Dic61—24no—
172C23×C61—24no—
173C23×C61—22no—
174C23×C61—24no—
175C23×C61—22no—
176C23×C61—41no—
177C23×C61—42no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—44no—
181C23×C61—42no—
182C23×C61—44no—
183C23×C61—48no—
184C23×C61—41no—
185C23×C61C2×C22⋊C412yes—
186C23×C61C2×C22⋊C411yescharacteristic
187C23×C61C2×C22⋊C411yescharacteristic
188C23×C61C2×C4⋊C412yes—
189C23×C61C2×C4⋊C412yes—
190C23×C61#11712yes—
191C23×C61#11712yes—
192C23×C61#12114yes—
193C23×C61#12114yes—
194C23×C61C22⋊Q814yes—
195C23×C61C22⋊Q814yes—
196C23×C61C23×C411yescharacteristic
197C23×C61C22×D412yes—
198C23×C61C22×D411yescharacteristic
199C23×C61C22×Q811yescharacteristic
200C23×C61C2×#4112yes—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—24no—
204C22×D61—24no—
205C22×D61—42no—
206C22×D61—48no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—48no—
212C22×D61—42no—
213C22×D61C2×C4⋊C414yescomplemented
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—44no—
223C2×C4×C61—44no—
224C2×C4×C61—44no—
225C2×C4×C61—88no—
226C22⋊D61—28no—
227C22⋊D61—28no—
228C22⋊D61—216no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—24no—
232C2×Dic61—24no—
233C2×Dic61—22no—
234C2×Dic61—24no—
235C2×Dic61—28no—
236C2×Dic61—24no—
237C2×Dic61—24no—
238C2×Dic61—28no—
239C2×Dic61—44no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—44no—
243C2×Dic61—44no—
244C2×Dic61—44no—
245C2×Dic61—44no—
246C2×Dic61—88no—
247C2×Dic61#9914yescomplemented
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C414yes—
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C2×C4⋊C414yescomplemented
252C4×D61—48no—
253C4×D61—48no—
254C2×#1799—611nomaximal, Sylow
255C22×C61—28no—
256C22×C61—24no—
257C22×C61—24no—
258C22×C61—28no—
259C22×C61—22no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—22no—
263C22×C61—22no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—22no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—44no—
270C22×C61—44no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—42no—
274C22×C61#38012yes—
275C22×C61#38014yes—
276C22×C61#38012yes—
277C22×C61C2×#9912yes—
278C22×C61#41012yes—
279C22×C61C22×C22⋊C411yescharacteristic
280C22×C61C22×C4⋊C411yescharacteristic
281C22×C61C2×#11711yescharacteristic
282C22×C61C2×#12112yes—
283C22×C61C2×C22⋊Q812yes—
284C2×D61—24no—
285C2×D61—44no—
286C2×D61—48no—
287C2×D61—48no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—44no—
291C4×C61—42no—
292C4×C61—42no—
293C4×C61—84no—
294Dic61—22no—
295Dic61—24no—
296Dic61—24no—
297Dic61—84no—
298Dic61C2×#9914yescomplemented
299C22×C4×D4—611no—
300C22×#99—612no—
301C2×#380—612no—
302#1799—618no—
303C2×#342—611no—
304C2×#342D6111yescharacteristic, complemented
305C2×C61—22no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—22no—
309C2×C61—22no—
310C2×C61—24no—
311C2×C61#179914yescomplemented
312C2×C61C2×#38011yescharacteristic
313C2×C61C22×#9911yescharacteristic
314C2×C61C2×#41011yescharacteristic
315D61—44no—
316C23×D4—611no—
317C24×C4—611no—
318C24×C4—611no—
319C2×C4×D4—614no—
320C2×C4×D4—614no—
321C2×C4×D4—1222no—
322C2×C4×D4—1222no—
323C2×C4×D4—1224no—
324C22×C4⋊C4—611no—
325C22×C4⋊C4—1222no—
326C22×C22⋊C4—611no—
327C22×C22⋊C4—612no—
328C22×C22⋊C4C2×D6112yes—
329C22×C22⋊C4C2×D6111yescharacteristic
330C22×C42—611no—
331C2×#99—618no—
332C2×#99—1228no—
333#380—618no—
334#380—1224no—
335C2×#95—1222no—
336#342—614no—
337#342C2×D6114yescomplemented
338C61C2×#179911yescharacteristic, complemented, Sylow
339C25—611no—
340C25C22×D6111yescharacteristic
341C22×D4—612no—
342C22×D4—614no—
343C22×D4—614no—
344C22×D4—612no—
345C22×D4—1224no—
346C22×D4—1222no—
347C22×D4—1222no—
348C23×C4—22no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—612no—
352C23×C4—611no—
353C23×C4—612no—
354C23×C4—612no—
355C23×C4—614no—
356C23×C4—612no—
357C23×C4—614no—
358C23×C4—1222no—
359C23×C4—1221no—
360C23×C4—1221no—
361C23×C4—1222no—
362C23×C4—2444no—
363C23×C4—2444no—
364C23×C4C4×D6111yescharacteristic
365C23×C4C4×D6111yescharacteristic
366C4×D4—1228no—
367C4×D4—1228no—
368C4×D4—1228no—
369C4×D4—1228no—
370C2×C4⋊C4—614no—
371C2×C4⋊C4—1222no—
372C2×C4⋊C4—1222no—
373C2×C4⋊C4—1228no—
374C2×C4⋊C4—2448no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—614no—
381C2×C22⋊C4—614no—
382C2×C22⋊C4—1222no—
383C2×C22⋊C4—1222no—
384C2×C22⋊C4—1224no—
385C2×C22⋊C4—1224no—
386C2×C22⋊C4—1222no—
387C2×C22⋊C4C4×D6112yes—
388C2×C22⋊C4C22×D6114yes—
389C2×C22⋊C4C22×D6112yes—
390C2×C42—614no—
391C2×C42—1222no—
392C2×C42—1221no—
393C2×C42—1221no—
394#99—12216no—
395#95—1228no—
396C24—42no—
397C24—42no—
398C24—612no—
399C24—614no—
400C24—1221no—
401C24—1221no—
402C24—1222no—
403C24—2442no—
404C24—2442no—
405C24C2×C4×D6111yescharacteristic
406C24C2×C4×D6111yescharacteristic
407C24#1175822214yes—
408C24D4×D6112yes—
409C24D4×D6112yes—
410C24D4×D6112yes—
411C24Q8×D6112yes—
412C24C23×D6111yescharacteristic
413C2×D4—614no—
414C2×D4—614no—
415C2×D4—618no—
416C2×D4—1224no—
417C2×D4—1224no—
418C2×D4—1224no—
419C2×D4—1224no—
420C2×D4—1228no—
421C2×D4—1228no—
422C2×D4—1228no—
423C2×D4—1228no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—611no—
435C22×C4—612no—
436C22×C4—612no—
437C22×C4—614no—
438C22×C4—612no—
439C22×C4—614no—
440C22×C4—611no—
441C22×C4—612no—
442C22×C4—614no—
443C22×C4—612no—
444C22×C4—614no—
445C22×C4—612no—
446C22×C4—614no—
447C22×C4—1224no—
448C22×C4—1224no—
449C22×C4—1228no—
450C22×C4—1224no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1222no—
454C22×C4—1224no—
455C22×C4—2444no—
456C22×C4—2448no—
457C22×C4—2444no—
458C22×C4—2448no—
459C22×C4—2444no—
460C22×C4—2448no—
461C22×C4—2444no—
462C22×C4—2442no—
463C22×C4—2444no—
464C22×C4—2444no—
465C22×C4—2444no—
466C22×C4—2444no—
467C22×C4C2×C4×D6112yes—
468C22×C4C2×C4×D6112yes—
469C4⋊C4—1228no—
470C4⋊C4—24416no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—44no—
476C22⋊C4—1228no—
477C22⋊C4—1224no—
478C22⋊C4—1224no—
479C22⋊C4—2444no—
480C42—1224no—
481C42—1224no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—44no—
492C23—42no—
493C23—44no—
494C23—41no—
495C23—614no—
496C23—1222no—
497C23—1222no—
498C23—1224no—
499C23—1224no—
500C23—2442no—
501C23—2448no—
502C23—2442no—
503C23—2442no—
504C23—2448no—
505C23—2442no—
506C23—2442no—
507C23—2442no—
508C23C22⋊C4×D6112yes—
509C23C22⋊C4×D6111yescharacteristic
510C23C22⋊C4×D6111yescharacteristic
511C23C4⋊C4×D6112yes—
512C23C4⋊C4×D6112yes—
513C23#1451973412yes—
514C23#1451973412yes—
515C23#1451975014yes—
516C23#1451975014yes—
517C23#1451975514yes—
518C23#1451975514yes—
519C23C22×C4×D6111yescharacteristic
520C23C2×D4×D6112yes—
521C23C2×D4×D6111yescharacteristic
522C23C2×Q8×D6111yescharacteristic
523C23C2×#1175822212yes—
524D4—1228no—
525D4—1228no—
526D4—12216no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—88no—
539C2×C4—612no—
540C2×C4—614no—
541C2×C4—612no—
542C2×C4—614no—
543C2×C4—614no—
544C2×C4—1228no—
545C2×C4—1228no—
546C2×C4—1224no—
547C2×C4—1224no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1224no—
551C2×C4—1222no—
552C2×C4—1224no—
553C2×C4—1224no—
554C2×C4—4888no—
555C2×C4—2448no—
556C2×C4—2448no—
557C2×C4—2442no—
558C2×C4—2442no—
559C2×C4—2444no—
560C2×C4—2444no—
561C2×C4—2444no—
562C2×C4—2444no—
563C2×C4—2444no—
564C22—28no—
565C22—24no—
566C22—24no—
567C22—28no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—1224no—
584C22—2444no—
585C22—2444no—
586C22—2448no—
587C22—2448no—
588C22—2442no—
589C22—2442no—
590C22#1683962112yes—
591C22#1683962114yes—
592C22#1683962112yes—
593C22#99×D6112yes—
594C22#1683973412yes—
595C22C2×C22⋊C4×D6111yescharacteristic
596C22C2×C4⋊C4×D6111yescharacteristic
597C22C2×#1451973411yescharacteristic
598C22C2×#1451975012yes—
599C22C2×#1451975512yes—
600C4—42no—
601C4—42no—
602C4—84no—
603C4—614no—
604C4—1224no—
605C4—1222no—
606C4—1224no—
607C4—4884no—
608C2—22no—
609C2—21no—
610C2—21no—
611C2—22no—
612C2—22no—
613C2—24no—
614C2—2444no—
615C2#2144580614yesdirect product factor
616C2C2×#1683962111yescharacteristic
617C2C2×#99×D6111yescharacteristic
618C2C2×#1683973411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#342C2
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC24×C61C24
hypercenterC2×#342D61
hypocenterC61C2×#1799
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×#16839620C2semidirect
4. #21445806C2direct (N × H)
5. C2×#16839529C2semidirect
6. C2×C61×#342C2semidirect
9. C23×C4×D61C4semidirect
13. C2×#14519737C4semidirect
16. C22×#11758196C4semidirect
18. C22×#11758198C4semidirect
19. C22×C4×Dic61C4semidirect
23. #16839620C22semidirect
25. #16839529C22semidirect
28. C61×#342C22semidirect
51. C22×C4×D61C2×C4semidirect
60. C2×#11758196C2×C4semidirect
67. C2×#11758198C2×C4semidirect
71. C2×C4×Dic61C2×C4semidirect
101. C23×D61C4⋊C4semidirect
123. C2×C22⋊D61C4⋊C4semidirect
147. C22×Dic61C4⋊C4semidirect
213. C22×D61C2×C4⋊C4semidirect
247. C2×Dic61#99semidirect
251. C2×Dic61C2×C4⋊C4semidirect
298. Dic61C2×#99semidirect
304. C2×#342D61semidirect
311. C2×C61#1799semidirect
337. #342C2×D61semidirect
338. C61C2×#1799semidirect
615. C2#21445806direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
C22×#145196912
C2×#168396202
#214458062
C2×#168395292
C2×C61×#3422
C2×#179961