Finite Group Databasebeta

← C2×#21446266 #29681771

Subgroups — C2×#21446266 #29681771

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840274C211yesmaximal, characteristic
2C22×#14519734C211yesmaximal, characteristic, complemented
3C22×#14519705C211yesmaximal, characteristic, complemented
4C22×#14519703C211yesmaximal, characteristic, complemented
5C2×#16839725C211yesmaximal, characteristic, complemented
6#21446266C218yesmaximal, direct product factor
7C2×#16839521C211yesmaximal, characteristic, complemented
8C2×C61×#339C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16840274—22no—
13#16840274—22no—
14#16840274C414yescomplemented
15#16840274C2214yes—
16C2×#14519761—21no—
17C2×#14519757C412yescomplemented
18C2×#14519752C412yescomplemented
19C2×#14519747—21no—
20C2×C4×D244—22no—
21C2×#14519734—24no—
22C2×#14519734—24no—
23C2×#14519734—22no—
24C2×#14519734C2214yescomplemented
25C22×#11758196—21no—
26C22×#11758198—21no—
27C22×C4×Dic61C2211yescharacteristic
28C2×#14519705—24no—
29C2×#14519705C2214yescomplemented
30C2×#14519703—24no—
31C2×#14519703C2214yescomplemented
32#16839725—22no—
33#16839725C2214yescomplemented
34C2×#14519689—22no—
35#16839521C2214yescomplemented
36C22×M16×C61C2211yescharacteristic
37C2×#117×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C61×#339C2214yescomplemented
40C24×D61D411yescharacteristic
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—22no—
44C2×#11758222—22no—
45C2×#11758222—22no—
46C2×#11758222—22no—
47C2×#11758222C2×C412yes—
48C2×#11758222C2312yes—
49C22×Dic122C2×C411yescharacteristic
50C22×D244—22no—
51C22×D244C2×C411yescharacteristic
52C22×C22⋊D61—21no—
53C23×Dic61—21no—
54C23×Dic61D411yescharacteristic
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—21no—
60C22×C4×D61C2×C412yes—
61C22×C4×D61C2×C412yes—
62C22×C4×D61D412yes—
63C22×C4×D61D412yes—
64C22×C4×D61D412yes—
65C22×C4×D61C2312yes—
66C2×#11758194—21no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194C2312yes—
70C22×#92418—21no—
71#14519761—24no—
72#14519761—24no—
73#14519757—24no—
74#14519757C2×C418yescomplemented
75#14519752—24no—
76#14519752C2×C418yescomplemented
77#14519747—24no—
78#14519747—24no—
79C4×D244—28no—
80C4×D244—28no—
81#14519734—216no—
82#14519734—28no—
83#14519734—28no—
84C2×C4⋊Dic61—22no—
85C2×#11758196—28no—
86C2×#11758196—24no—
87C2×#11758198—28no—
88C2×#11758198—22no—
89C2×#11758198—24no—
90C2×#11758198—22no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61D414yescomplemented
94C2×C4×Dic61C2312yes—
95#14519705—28no—
96#14519703—28no—
97#14519689—28no—
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100C2×M16×C61—21no—
101C2×M16×C61—22no—
102C2×M16×C61—22no—
103C2×M16×C61C2312yes—
104C22×C8×C61—21no—
105#117×C61—21no—
106#117×C61—21no—
107#117×C61C2×C412yes—
108#117×C61C2312yes—
109C2×C4⋊C4×C61C2×C412yes—
110C2×C22⋊C4×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61—22no—
113C2×C42×C61—21no—
114C2×C42×C61D414yescomplemented
115C2×C42×C61C2312yes—
116C24×C61C2×D411yescharacteristic
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—21no—
120C23×D61—44no—
121C23×D61C22⋊C412yes—
122C23×D61C22⋊C412yes—
123C23×D61C2×D412yes—
124C22×C4×C61—22no—
125C22×C4×C61—24no—
126C22×C4×C61—22no—
127C22×C4×C61—44no—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61#4112yes—
136C22×C4×C61#4112yes—
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—21no—
145C22×Dic61—24no—
146C22×Dic61—22no—
147C22×Dic61—44no—
148C22×Dic61C22⋊C412yes—
149C22×Dic61C22⋊C412yes—
150C22×Dic61C2×D412yes—
151#11758222—24no—
152#11758222—24no—
153#11758222—22no—
154#11758222—22no—
155#11758222—22no—
156#11758222—22no—
157#11758222—42no—
158#11758222—42no—
159#11758222—42no—
160#11758222—42no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—28no—
164C2×D244—21no—
165C2×D244—48no—
166C2×D244C22×C412yes—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—24no—
176C2×C4×D61—24no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61C22⋊C414yes—
186C2×C4×D61C22⋊C414yes—
187C2×C4×D61C22×C414yes—
188C2×C4×D61C2×D414yes—
189C2×Dic122—22no—
190C2×Dic122—22no—
191C2×Dic122—21no—
192C2×Dic122C22×C412yes—
193M16×C61—22no—
194M16×C61—22no—
195M16×C61—42no—
196C2×C8×C61—22no—
197C2×C8×C61—42no—
198C4⋊C4×C61—22no—
199C4⋊C4×C61C22×C414yes—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C42×C61—22no—
203C42×C61—24no—
204C42×C61—22no—
205C42×C61—22no—
206C42×C61C2×D414yescomplemented
207#11758198—216no—
208#11758198—28no—
209#11758198—28no—
210C4⋊Dic61—28no—
211#11758196—216no—
212C4×Dic61—24no—
213C4×Dic61—22no—
214C4×Dic61C2×D414yescomplemented
215#11758194—22no—
216#11758194—22no—
217#11758194—42no—
218C2×#92418—22no—
219C2×#92418—42no—
220C23×C61—24no—
221C23×C61C2×C22⋊C411yescharacteristic
222C23×C61C2×C22⋊C411yescharacteristic
223C23×C61#12012yes—
224C23×C61#12312yes—
225C23×C61C22×D411yescharacteristic
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—24no—
229C22×D61—24no—
230C22×D61—24no—
231C22×D61—24no—
232C22×D61—22no—
233C22×D61—44no—
234C22×D61—44no—
235C22×D61—48no—
236C22×D61—48no—
237C22×D61—42no—
238C22×D61—44no—
239C22×D61C2×C22⋊C414yes—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—44no—
243C2×C4×C61—48no—
244C2×C4×C61—44no—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C4×D412yes—
248C2×C4×C61C4×D412yes—
249C2×C4×C61C4×D412yes—
250C2×C4×C61C4×D412yes—
251C2×C4×C61#12012yes—
252C2×C4×C61#12112yes—
253C2×C4×C61#12112yes—
254C2×C4×C61#12112yes—
255C2×C4×C61#12112yes—
256C2×C4×C61#12312yes—
257C2×C4×C61C23×C411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C22⋊D61—42no—
264C22⋊D61—42no—
265C22⋊D61—44no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—22no—
271C2×Dic61—24no—
272C2×Dic61—44no—
273C2×Dic61—48no—
274C2×Dic61—42no—
275C2×Dic61C2×C22⋊C414yes—
276D244—22no—
277D244—22no—
278D244—416no—
279D244—42no—
280C4×D61—24no—
281C4×D61—24no—
282C4×D61—24no—
283C4×D61—24no—
284C4×D61—28no—
285C4×D61—28no—
286C4×D61—42no—
287C4×D61—42no—
288C4×D61—44no—
289Dic122—22no—
290Dic122—22no—
291Dic122—42no—
292C8×C61—42no—
293#92418—42no—
294C2×#1897—611nomaximal, Sylow
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—24no—
298C22×C61—24no—
299C22×C61#38612yes—
300C22×C61#38612yes—
301C22×C61#42114yes—
302C22×C61C22×C22⋊C411yescharacteristic
303C22×C61C2×#12011yescharacteristic
304C22×C61C2×#12311yescharacteristic
305C2×D61—24no—
306C2×D61—24no—
307C2×D61—24no—
308C2×D61—44no—
309C2×D61—44no—
310C2×D61—48no—
311C2×D61—48no—
312C2×D61—44no—
313C2×D61—42no—
314C2×D61—84no—
315C4×C61—44no—
316C4×C61—44no—
317C4×C61#38612yes—
318C4×C61#38612yes—
319C4×C61C2×C4×D411yescharacteristic
320C4×C61C2×C4×D411yescharacteristic
321C4×C61C2×#12111yescharacteristic
322C4×C61C2×#12111yescharacteristic
323Dic61—24no—
324Dic61—44no—
325Dic61—42no—
326C2×#525—611no—
327C22×#117—611no—
328C22×#104—611no—
329C22×#104—611no—
330C2×#407—611no—
331#1897—618no—
332C2×#339—611no—
333C2×#339D6111yescharacteristic, complemented
334C2×C61—21no—
335C2×C61—21no—
336C2×C61—22no—
337C2×C61#189714yescomplemented
338C2×C61C2×#38611yescharacteristic
339C2×C61C2×#42112yes—
340D61—44no—
341D61—82no—
342C22×#41—611no—
343C24×C4—611no—
344C22×M16—611no—
345C22×M16C2×D6111yescharacteristic
346#525—614no—
347#525—614no—
348#525—1222no—
349#525—1222no—
350C2×#123—1221no—
351C2×C22⋊Q8—612no—
352C2×#121—612no—
353C2×#120—1221no—
354C2×C4×D4—1222no—
355C2×#117—614no—
356C2×#117—1224no—
357C2×#117—1222no—
358C2×#117—1224no—
359C2×#117C2×D6111yescharacteristic
360C22×C4⋊C4—1221no—
361C22×C22⋊C4—1221no—
362C22×C42—611no—
363C22×C42C2×D6111yescharacteristic
364C2×#104—614no—
365C2×#104—614no—
366C2×#104—1224no—
367C2×#104—1224no—
368#407—614no—
369#407—1222no—
370C2×C22⋊C8—1222no—
371#339—614no—
372#339C2×D6114yescomplemented
373C61C2×#189711yescharacteristic, complemented, Sylow
374C25—611no—
375C2×#41—612no—
376C2×#41—612no—
377C2×#41—1221no—
378C2×#41—1221no—
379C2×#41—1222no—
380C2×#41—1222no—
381C2×#41—1222no—
382C2×#41—1222no—
383C22×Q8—611no—
384C22×D4—611no—
385C22×D4—1222no—
386C22×D4—1221no—
387C23×C4—21no—
388C23×C4—611no—
389C23×C4—612no—
390C23×C4—612no—
391C23×C4—612no—
392C23×C4—612no—
393C23×C4—612no—
394C23×C4—612no—
395C23×C4—1222no—
396C23×C4—1222no—
397C23×C4—1222no—
398C23×C4—1222no—
399C23×C4—1221no—
400C23×C4—1221no—
401C23×C4C22×D6111yescharacteristic
402C2×M16—21no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—612no—
406C2×M16—1221no—
407C2×M16—1222no—
408C2×M16—1222no—
409C2×M16C22×D6112yes—
410C22×C8—21no—
411C22×C8—1221no—
412#123—1224no—
413#123—1224no—
414C22⋊Q8—618no—
415C22⋊Q8—1224no—
416#121—618no—
417#121—1224no—
418#120—1224no—
419#120—1224no—
420C4×D4—1228no—
421C4×D4—1228no—
422#117—21no—
423#117—21no—
424#117—1228no—
425#117—12216no—
426#117—1228no—
427#117C4×D6112yes—
428#117C22×D6112yes—
429C2×C4⋊C4—1224no—
430C2×C4⋊C4—1222no—
431C2×C4⋊C4—1228no—
432C2×C4⋊C4C4×D6112yes—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—1222no—
435C2×C22⋊C4—1224no—
436C2×C22⋊C4—1222no—
437C2×C22⋊C4—1228no—
438C2×C42—22no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—614no—
442C2×C42—612no—
443C2×C42—1222no—
444C2×C42—1221no—
445C2×C42D24414yescomplemented
446C2×C42C22×D6112yes—
447#104—1228no—
448#104—1228no—
449C22⋊C8—1228no—
450C24—612no—
451C24—612no—
452C24—612no—
453C24—1222no—
454C24—1222no—
455C24—1221no—
456C24—2444no—
457C24D4×D6111yescharacteristic
458#41—1222no—
459#41—1222no—
460#41—1222no—
461#41—1222no—
462#41—1224no—
463#41—1224no—
464#41—2442no—
465#41—2442no—
466#41—2442no—
467#41—2442no—
468C2×Q8—612no—
469C2×Q8—1221no—
470C2×Q8—1222no—
471C2×Q8—1222no—
472C2×D4—612no—
473C2×D4—1228no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—1221no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—2448no—
480C2×D4—2442no—
481C2×D4—2442no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—44no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—614no—
490C22×C4—614no—
491C22×C4—614no—
492C22×C4—614no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1224no—
500C22×C4—1224no—
501C22×C4—1224no—
502C22×C4—1224no—
503C22×C4—1224no—
504C22×C4—1224no—
505C22×C4—1224no—
506C22×C4—1224no—
507C22×C4—1224no—
508C22×C4—1224no—
509C22×C4—1222no—
510C22×C4—1221no—
511C22×C4—1224no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—2444no—
515C22×C4—2442no—
516C22×C4—2442no—
517C22×C4C2×C4×D6111yescharacteristic
518C22×C4C2×C4×D6111yescharacteristic
519C22×C4C2×D24412yes—
520C22×C4#1175822212yes—
521C22×C4D4×D6111yescharacteristic
522C22×C4D4×D6112yes—
523C22×C4D4×D6111yescharacteristic
524C22×C4D4×D6111yescharacteristic
525C22×C4#1175822612yes—
526C22×C4C23×D6111yescharacteristic
527M16—22no—
528M16—22no—
529M16—42no—
530M16—1222no—
531M16—1222no—
532M16—2442no—
533C2×C8—22no—
534C2×C8—42no—
535C2×C8—1222no—
536C2×C8—2442no—
537C4⋊C4—22no—
538C4⋊C4—1228no—
539C4⋊C4—12216no—
540C4⋊C4C2×C4×D6114yes—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—1228no—
544C22⋊C4—1228no—
545C22⋊C4—12216no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—24no—
550C42—614no—
551C42—1222no—
552C42—1224no—
553C42C2×D24414yescomplemented
554C23—24no—
555C23—614no—
556C23—1222no—
557C23—1222no—
558C23—1224no—
559C23—1224no—
560C23—1224no—
561C23—1224no—
562C23—1222no—
563C23—2444no—
564C23—2444no—
565C23—2448no—
566C23—2448no—
567C23—2444no—
568C23—2442no—
569C23C22⋊C4×D6111yescharacteristic
570C23C22⋊C4×D6111yescharacteristic
571C23#1451974712yes—
572C23#1451976212yes—
573C23C2×D4×D6111yescharacteristic
574Q8—1222no—
575Q8—1222no—
576Q8—2442no—
577D4—1222no—
578D4—1222no—
579D4—24416no—
580D4—2442no—
581D4—2442no—
582D4—2444no—
583D4—2442no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—44no—
587C2×C4—48no—
588C2×C4—44no—
589C2×C4—614no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1224no—
598C2×C4—1228no—
599C2×C4—1228no—
600C2×C4—1222no—
601C2×C4—1224no—
602C2×C4—2444no—
603C2×C4—2448no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2444no—
608C2×C4C22⋊C4×D6111yescharacteristic
609C2×C4C22⋊C4×D6111yescharacteristic
610C2×C4#1451973912yes—
611C2×C4#1451973912yes—
612C2×C4C4×D24412yes—
613C2×C4C4×D24412yes—
614C2×C4#1451974712yes—
615C2×C4#1451975012yes—
616C2×C4#1451975012yes—
617C2×C4#1451975212yes—
618C2×C4#1451975212yes—
619C2×C4#1451976212yes—
620C2×C4C22×C4×D6111yescharacteristic
621C2×C4C2×D4×D6111yescharacteristic
622C2×C4C2×D4×D6111yescharacteristic
623C2×C4C22×D24411yescharacteristic
624C2×C4C2×#1175822211yescharacteristic
625C2×C4C2×#1175822611yescharacteristic
626C8—42no—
627C8—2442no—
628C22—22no—
629C22—22no—
630C22—24no—
631C22—24no—
632C22—1224no—
633C22—1224no—
634C22—1224no—
635C22—4884no—
636C22—2444no—
637C22—2444no—
638C22—2448no—
639C22—2444no—
640C22—2442no—
641C22—2448no—
642C22#1683964012yes—
643C22#1683964012yes—
644C22#1683977714yes—
645C22C2×C22⋊C4×D6111yescharacteristic
646C22C2×#1451974711yescharacteristic
647C22C2×#1451976211yescharacteristic
648C4—44no—
649C4—44no—
650C4—1224no—
651C4—2444no—
652C4—2442no—
653C4#1683964012yes—
654C4#1683964012yes—
655C4C2×#1451973911yescharacteristic
656C4C2×C4×D24411yescharacteristic
657C4C2×#1451975011yescharacteristic
658C4C2×#1451975211yescharacteristic
659C2—21no—
660C2—21no—
661C2—22no—
662C2—4882no—
663C2—2444no—
664C2#2144626614yesdirect product factor
665C2C2×#1683964011yescharacteristic
666C2C2×#1683977712yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#339C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840274C2
cosocleC22×C4×C61C24
hypercenterC2×#339D61
hypocenterC61C2×#1897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
2. C22×#14519734C2semidirect
3. C22×#14519705C2semidirect
4. C22×#14519703C2semidirect
5. C2×#16839725C2semidirect
6. #21446266C2direct (N × H)
7. C2×#16839521C2semidirect
8. C2×C61×#339C2semidirect
14. #16840274C4semidirect
17. C2×#14519757C4semidirect
18. C2×#14519752C4semidirect
24. C2×#14519734C22semidirect
29. C2×#14519705C22semidirect
31. C2×#14519703C22semidirect
33. #16839725C22semidirect
35. #16839521C22semidirect
39. C61×#339C22semidirect
74. #14519757C2×C4semidirect
76. #14519752C2×C4semidirect
93. C2×C4×Dic61D4semidirect
114. C2×C42×C61D4semidirect
206. C42×C61C2×D4semidirect
214. C4×Dic61C2×D4semidirect
333. C2×#339D61semidirect
337. C2×C61#1897semidirect
372. #339C2×D61semidirect
373. C61C2×#1897semidirect
445. C2×C42D244semidirect
553. C42C2×D244semidirect
664. C2#21446266direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402742
C22×#145197342
C22×#145197052
C22×#145197032
C2×#168397252
#214462662
C2×#168395212
C2×C61×#3392
C2×#189761