Finite Group Databasebeta

← C2×#21446611 #29683590

Subgroups — C2×#21446611 #29683590

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C22×#14519706C211yesmaximal, characteristic, complemented
3C22×C22⋊#92418C211yesmaximal, characteristic, complemented
4C22×#14519689C211yesmaximal, characteristic, complemented
5C22×#14519689C211yesmaximal, characteristic, complemented
6C22×C8×Dic61C211yesmaximal, characteristic, complemented
7#21446611C218yesmaximal, direct product factor
8C22×C22⋊C8×C61C211yesmaximal, characteristic, complemented
9C23×C22⋊D61C411yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12C23×#92418C2211yescharacteristic
13C2×C4×C22⋊D61—24no—
14C2×C4×C22⋊D61—24no—
15C2×C4×C22⋊D61C414yes—
16C2×C4×C22⋊D61C2214yes—
17C22×#11758196C411yescharacteristic
18C22×C22⋊Dic61C411yescharacteristic
19C22×#11758198C411yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21C2×#14519706—24no—
22C2×#14519706C2214yescomplemented
23C2×C22⋊#92418—24no—
24C2×C22⋊#92418C2214yescomplemented
25C2×#14519689—24no—
26C2×#14519689—24no—
27C2×#14519689C2214yescomplemented
28C2×#14519689C2214yescomplemented
29C2×C8×Dic61—24no—
30C2×C8×Dic61C2214yescomplemented
31C24×C4×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C23×C8×C61C2211yescharacteristic
34C2×C22⋊C8×C61—24no—
35C2×C22⋊C8×C61C2214yescomplemented
36C24×D61C2×C411yescharacteristic
37C22×C22⋊D61—24no—
38C22×C22⋊D61—24no—
39C22×C22⋊D61C818yescomplemented
40C22×C22⋊D61C2×C414yes—
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C411yescharacteristic
44C22×C4×D61—22no—
45C22×C4×D61—22no—
46C22×C4×D61—22no—
47C22×C4×D61—22no—
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61C2×C412yes—
51C22×C4×D61C2312yes—
52C22×#92418—22no—
53C22×#92418—22no—
54C22×#92418—22no—
55C22×#92418—22no—
56C22×#92418—22no—
57C22×#92418D414yescomplemented
58C22×#92418C2312yes—
59C22×#92418C2312yes—
60C4×C22⋊D61—216no—
61C4×C22⋊D61—28no—
62C4×C22⋊D61—28no—
63C2×#11758196—24no—
64C2×#11758196C2×C414yes—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61C2×C414yes—
67C2×#11758198—24no—
68C2×#11758198C2×C414yes—
69C2×C4×Dic61C2×C412yes—
70C2×C4×Dic61D414yes—
71C2×C4×Dic61D414yes—
72C2×C4×Dic61C2312yes—
73#14519706—28no—
74C22⋊#92418—28no—
75#14519689—28no—
76#14519689—28no—
77C8×Dic61—28no—
78C25×C61C2×C411yescharacteristic
79C23×C4×C61—22no—
80C23×C4×C61—22no—
81C23×C4×C61—22no—
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61C2×C411yescharacteristic
86C23×C4×C61C2×C412yes—
87C23×C4×C61C2312yes—
88C23×C4×C61C2311yescharacteristic
89C22×C8×C61—22no—
90C22×C8×C61—22no—
91C22×C8×C61—22no—
92C22×C8×C61—22no—
93C22×C8×C61—22no—
94C22×C8×C61D414yescomplemented
95C22×C8×C61C2312yes—
96C22×C8×C61C2312yes—
97C22⋊C8×C61—28no—
98C24×C61—22no—
99C24×C61—22no—
100C24×C61—22no—
101C24×C61—22no—
102C24×C61—22no—
103C24×C61—22no—
104C24×C61C2×C814yes—
105C24×C61C22×C412yes—
106C24×C61C22×C411yescharacteristic
107C23×D61—22no—
108C23×D61—22no—
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61C2×C814yes—
114C23×D61C22×C412yes—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—24no—
119C22×C4×C61—24no—
120C22×C4×C61—24no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—44no—
128C22×C4×C61—44no—
129C22×C4×C61—44no—
130C22×C4×C61—44no—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61#4112yes—
138C22×C4×C61#4112yes—
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—232no—
141C2×C22⋊D61—28no—
142C2×C22⋊D61—28no—
143C2×C22⋊D61C2×C8116yescomplemented
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61C22⋊C414yes—
150C22×Dic61C22⋊C414yes—
151C22×Dic61C2×C814yes—
152C22×Dic61M1614yes—
153C22×Dic61C22×C412yes—
154C22×Dic61C22×C412yes—
155C22×Dic61C22×C412yes—
156C2×C4×D61—24no—
157C2×C4×D61—24no—
158C2×C4×D61—24no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—44no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61—44no—
169C2×C8×C61—28no—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C2×C8×C61—44no—
176C2×C8×C61C2×D414yescomplemented
177C22⋊Dic61—28no—
178#11758198—28no—
179#11758196—28no—
180C4×Dic61C22⋊C418yes—
181C4×Dic61C2×D414yes—
182C4×Dic61C2×D414yes—
183C2×#92418—28no—
184C2×#92418—22no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—22no—
189C2×#92418—44no—
190C2×#92418C2×D414yescomplemented
191C23×C61—22no—
192C23×C61—22no—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61—28no—
198C23×C61—28no—
199C23×C61—28no—
200C23×C61—44no—
201C23×C61—44no—
202C23×C61—44no—
203C23×C61—44no—
204C23×C61C2×C22⋊C412yes—
205C23×C61C4×D412yes—
206C23×C61C4×D412yes—
207C23×C61C22×C814yes—
208C23×C61C22×C812yes—
209C23×C61C2×M1612yes—
210C23×C61#13112yes—
211C23×C61#13112yes—
212C23×C61C23×C411yescharacteristic
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61—28no—
220C22×D61—28no—
221C22×D61—28no—
222C22×D61—44no—
223C22×D61—44no—
224C22×D61—44no—
225C22×D61—44no—
226C22×D61C22×C814yes—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—44no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—48no—
236C2×C4×C61C2×C22⋊C412yes—
237C2×C4×C61C4×D412yes—
238C2×C4×C61C4×D412yes—
239C2×C4×C61#12114yes—
240C2×C4×C61#12114yes—
241C2×C4×C61#12414yes—
242C2×C4×C61#12714yes—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C22⋊D61—232no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—28no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—44no—
257C2×Dic61C22⋊C8116yescomplemented
258C2×Dic61C2×C22⋊C414yes—
259C2×Dic61C2×C22⋊C414yes—
260C2×Dic61C22×C814yes—
261C2×Dic61C2×M1614yes—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—48no—
267C8×C61—24no—
268C8×C61—42no—
269#92418—24no—
270#92418—42no—
271C2×#1954—611nomaximal, Sylow
272C22×C61—24no—
273C22×C61—24no—
274C22×C61—24no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—416no—
279C22×C61—42no—
280C22×C61#39014yes—
281C22×C61C2×C22⋊C814yes—
282C22×C61#40814yes—
283C22×C61C8×D414yes—
284C22×C61C8×D414yes—
285C22×C61#43614yes—
286C22×C61#43614yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61C2×C4×D411yescharacteristic
289C22×C61C2×C4×D411yescharacteristic
290C22×C61C23×C811yescharacteristic
291C22×C61C22×M1611yescharacteristic
292C22×C61C2×#13111yescharacteristic
293C22×C61C2×#13111yescharacteristic
294C2×D61—24no—
295C2×D61—24no—
296C2×D61—24no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—416no—
301C2×D61—42no—
302C4×C61—42no—
303C4×C61#39014yes—
304C4×C61C2×#12111yescharacteristic
305C4×C61C2×#12111yescharacteristic
306C4×C61C2×#12411yescharacteristic
307C4×C61C2×#12711yescharacteristic
308Dic61—24no—
309Dic61—42no—
310Dic61C2×C22⋊C818yescomplemented
311C22×C4×D4—611no—
312C22×C4⋊C8—611no—
313C22×C22⋊C8—611no—
314C22×C22⋊C8—611no—
315C22×C22⋊C8—611no—
316C22×C22⋊C8D6111yescharacteristic, complemented
317C22×C4×C8—611no—
318#1954—618no—
319C2×C61—44no—
320C2×C61#195418yescomplemented
321C2×C61C2×#39011yescharacteristic
322C2×C61C22×C22⋊C811yescharacteristic
323C2×C61C2×#40811yescharacteristic
324C2×C61C2×C8×D411yescharacteristic
325C2×C61C2×C8×D411yescharacteristic
326C2×C61C2×#43611yescharacteristic
327C2×C61C2×#43611yescharacteristic
328D61—44no—
329C23×D4—611no—
330C24×C4—611no—
331C24×C4C2×D6111yescharacteristic
332C23×C8—611no—
333C23×C8—611no—
334C23×C8C2×D6111yescharacteristic
335C23×C8C2×D6111yescharacteristic
336C2×C4×D4—614no—
337C2×C4×D4—614no—
338C2×C4×D4—1224no—
339C2×C4×D4—1224no—
340C22×C4⋊C4—611no—
341C22×C22⋊C4—611no—
342C22×C22⋊C4—611no—
343C22×C42—611no—
344C2×C4⋊C8—614no—
345C2×C4⋊C8—1224no—
346C2×C22⋊C8—24no—
347C2×C22⋊C8—614no—
348C2×C22⋊C8—614no—
349C2×C22⋊C8—614no—
350C2×C22⋊C8—1224no—
351C2×C22⋊C8—1224no—
352C2×C22⋊C8—1224no—
353C2×C22⋊C8C2×D6114yescomplemented
354C2×C4×C8—614no—
355C2×C4×C8—1224no—
356C61C2×#195411yescharacteristic, complemented, Sylow
357C25—611no—
358C25C4×D6111yescharacteristic
359C22×D4—618no—
360C22×D4—614no—
361C22×D4—1224no—
362C22×D4—1224no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—612no—
373C23×C4—612no—
374C23×C4—1222no—
375C23×C4—1222no—
376C23×C4—1222no—
377C23×C4—1222no—
378C23×C4—1222no—
379C23×C4—1222no—
380C23×C4C4×D6111yescharacteristic
381C23×C4C4×D6112yes—
382C23×C4C22×D6112yes—
383C23×C4C22×D6111yescharacteristic
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—614no—
390C22×C8—612no—
391C22×C8—612no—
392C22×C8—1222no—
393C22×C8—1222no—
394C22×C8—1222no—
395C22×C8—1222no—
396C22×C8—1222no—
397C22×C8C22⋊D6114yescomplemented
398C22×C8C22×D6112yes—
399C22×C8C22×D6112yes—
400C4×D4—1228no—
401C4×D4—1228no—
402C4×D4—12216no—
403C2×C4⋊C4—614no—
404C2×C4⋊C4—1224no—
405C2×C22⋊C4—614no—
406C2×C22⋊C4—614no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—1224no—
409C2×C42—612no—
410C2×C42—614no—
411C2×C42—614no—
412C2×C42—612no—
413C4⋊C8—1228no—
414C22⋊C8—28no—
415C22⋊C8—1228no—
416C22⋊C8—1228no—
417C22⋊C8—1228no—
418C4×C8—1228no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—612no—
426C24—614no—
427C24—1222no—
428C24—1222no—
429C24—1222no—
430C24—1222no—
431C24—1222no—
432C24—1222no—
433C24C8×D6114yes—
434C24C2×C4×D6112yes—
435C24C2×C4×D6111yescharacteristic
436C2×D4—6116no—
437C2×D4—1228no—
438C2×D4—12232no—
439C2×D4—1228no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—612no—
457C22×C4—614no—
458C22×C4—614no—
459C22×C4—614no—
460C22×C4—612no—
461C22×C4—614no—
462C22×C4—612no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1224no—
475C22×C4—1224no—
476C22×C4—1224no—
477C22×C4—2444no—
478C22×C4—2444no—
479C22×C4—2444no—
480C22×C4—2444no—
481C22×C4C2×C4×D6112yes—
482C22×C4C2×C4×D6111yescharacteristic
483C22×C4#1175822212yes—
484C22×C4D4×D6112yes—
485C22×C4D4×D6112yes—
486C22×C4D4×D6112yes—
487C22×C4#1175822412yes—
488C22×C4C2×C22⋊D6112yes—
489C22×C4C23×D6111yescharacteristic
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—28no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—44no—
497C2×C8—614no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—1228no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—2444no—
505C2×C8C2×C22⋊D6114yescomplemented
506C4⋊C4—1228no—
507C22⋊C4—1228no—
508C22⋊C4—1228no—
509C42—614no—
510C42—614no—
511C42—618no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—28no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—28no—
520C23—28no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—614no—
526C23—1222no—
527C23—1222no—
528C23—1222no—
529C23—1228no—
530C23—1222no—
531C23—1222no—
532C23—1222no—
533C23—1228no—
534C23—1228no—
535C23—2444no—
536C23—2444no—
537C23—2444no—
538C23—2444no—
539C23C22⋊C4×D6112yes—
540C23#1451973712yes—
541C23C4×C22⋊D6112yes—
542C23C2×C8×D6114yes—
543C23C2×C8×D6112yes—
544C23M16×D6112yes—
545C23#1451978312yes—
546C23#1451978512yes—
547C23C22×C4×D6111yescharacteristic
548D4—12232no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—48no—
558C2×C4—614no—
559C2×C4—6116no—
560C2×C4—614no—
561C2×C4—614no—
562C2×C4—614no—
563C2×C4—1228no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—2444no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2448no—
575C2×C4C22⋊C4×D6112yes—
576C2×C4#1451973712yes—
577C2×C4C4×C22⋊D6112yes—
578C2×C4#1451974914yes—
579C2×C4#1451975014yes—
580C2×C4#1451976314yes—
581C2×C4#1451977314yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4C2×D4×D6111yescharacteristic
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4C22×C22⋊D6111yescharacteristic
586C2×C4C2×#1175822411yescharacteristic
587C2×C4C2×#1175822211yescharacteristic
588C8—24no—
589C8—42no—
590C8—1224no—
591C8—2442no—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—416no—
600C22—1224no—
601C22—1224no—
602C22—1224no—
603C22—2442no—
604C22—2442no—
605C22—2442no—
606C22—2442no—
607C22—24416no—
608C22#1683966214yes—
609C22C22⋊C8×D6114yes—
610C22#1683972714yes—
611C22#1683982514yes—
612C22C8×C22⋊D6114yes—
613C22#1683983714yes—
614C22#1683983814yes—
615C22C2×C22⋊C4×D6111yescharacteristic
616C22C2×#1451973711yescharacteristic
617C22C2×C4×C22⋊D6111yescharacteristic
618C22C22×C8×D6111yescharacteristic
619C22C2×M16×D6111yescharacteristic
620C22C2×#1451978311yescharacteristic
621C22C2×#1451978511yescharacteristic
622C4—42no—
623C4—618no—
624C4—1224no—
625C4—2442no—
626C4#1683966214yes—
627C4C2×#1451974911yescharacteristic
628C4C2×#1451975011yescharacteristic
629C4C2×#1451976311yescharacteristic
630C4C2×#1451977311yescharacteristic
631C2—44no—
632C2—2444no—
633C2#2144661118yesdirect product factor
634C2C2×#1683966211yescharacteristic
635C2C2×C22⋊C8×D6111yescharacteristic
636C2C2×#1683972711yescharacteristic
637C2C2×#1683982511yescharacteristic
638C2C2×C8×C22⋊D6111yescharacteristic
639C2C2×#1683983711yescharacteristic
640C2C2×#1683983811yescharacteristic
subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C23×C8
FrattiniC22×C4C23×D61
FittingC22×C22⋊C8×C61C2
socleC24×C61C22×C4
prime radicalC23×C22⋊D61C4
cosocleC22×C4×C61C24
hypercenterC22×C22⋊C8D61
hypocenterC61C2×#1954
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#14519706C2semidirect
3. C22×C22⋊#92418C2semidirect
4. C22×#14519689C2semidirect
5. C22×#14519689C2semidirect
6. C22×C8×Dic61C2semidirect
7. #21446611C2direct (N × H)
8. C22×C22⋊C8×C61C2semidirect
22. C2×#14519706C22semidirect
24. C2×C22⋊#92418C22semidirect
27. C2×#14519689C22semidirect
28. C2×#14519689C22semidirect
30. C2×C8×Dic61C22semidirect
35. C2×C22⋊C8×C61C22semidirect
39. C22×C22⋊D61C8semidirect
57. C22×#92418D4semidirect
94. C22×C8×C61D4semidirect
143. C2×C22⋊D61C2×C8semidirect
176. C2×C8×C61C2×D4semidirect
190. C2×#92418C2×D4semidirect
257. C2×Dic61C22⋊C8semidirect
310. Dic61C2×C22⋊C8semidirect
316. C22×C22⋊C8D61semidirect
320. C2×C61#1954semidirect
353. C2×C22⋊C8C2×D61semidirect
356. C61C2×#1954semidirect
397. C22×C8C22⋊D61semidirect
505. C2×C8C2×C22⋊D61semidirect
633. C2#21446611direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C22×#145197062
C22×C22⋊#924182
C22×#145196892
C22×C8×Dic612
#214466112
C22×C22⋊C8×C612
C2×#195461