Finite Group Databasebeta

← C2×#21446883 #29707028

Subgroups — C2×#21446883 #29707028

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C212yesmaximal, complemented
2C2×#16839779C212yesmaximal, complemented
3C2×#16839725C211yesmaximal, characteristic, complemented
4#21446883C218yesmaximal, direct product factor
5C2×#16839519C211yesmaximal, characteristic, complemented
6C2×C61×#575C211yesmaximal, characteristic, complemented
7C23×C4×D61C2211yescharacteristic
8C22×#11758194C2211yescharacteristic
9#16840269—24no—
10#16840269—24no—
11#16840269—24no—
12#16840269C2218yescomplemented
13C2×#14519758—22no—
14C2×#14519753—22no—
15C2×#14519748—22no—
16C2×#14519745—22no—
17C2×C4×C22⋊D61—24no—
18C2×#14519736C2212yes—
19#16839779—24no—
20#16839779C2218yescomplemented
21C2×#14519704—24no—
22#16839725—22no—
23#16839725C2214yescomplemented
24C2×#14519689—22no—
25#16839519C2214yescomplemented
26C22×#41×C61C2212yes—
27C61×#575—24no—
28C61×#575—22no—
29C61×#575C2214yescomplemented
30C2×#137×C61—22no—
31C2×AGL(1,ℤ/8)×C61—22no—
32C2×#135×C61—22no—
33C22×M16×C61C2211yescharacteristic
34C24×D61D411yescharacteristic
35C22×C22⋊D61—24no—
36C23×Dic61D411yescharacteristic
37C22×C4×D61—22no—
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61—22no—
41C22×C4×D61—22no—
42C22×C4×D61—22no—
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61D412yes—
46C22×C4×D61C2312yes—
47C2×#11758194—21no—
48C2×#11758194—22no—
49C2×#11758194—22no—
50C2×#11758194C2312yes—
51C22×#92418—21no—
52#14519758—28no—
53#14519758—28no—
54#14519753—28no—
55#14519753—28no—
56#14519748—28no—
57#14519748—28no—
58#14519745—28no—
59#14519745—28no—
60C4×C22⋊D61—216no—
61C4×C22⋊D61—216no—
62#14519736—22no—
63#14519736—22no—
64#14519736D414yescomplemented
65#14519736C2314yes—
66C2×C4⋊Dic61—22no—
67C2×#11758196—24no—
68C2×C22⋊Dic61—24no—
69C2×C22⋊Dic61—22no—
70C2×#11758198—24no—
71C2×C4×Dic61D414yescomplemented
72#14519704—216no—
73#14519689—28no—
74C2×#41×C61—22no—
75C2×#41×C61—22no—
76C2×#41×C61—22no—
77C2×#41×C61—22no—
78C2×#41×C61—22no—
79C2×#41×C61—22no—
80C2×#41×C61—22no—
81C2×#41×C61—22no—
82C2×#41×C61—22no—
83C2×#41×C61—22no—
84C2×#41×C61D414yescomplemented
85C2×#41×C61C2314yes—
86C22×Q8×C61D412yescomplemented
87C22×D4×C61—22no—
88C22×D4×C61D412yescomplemented
89C23×C4×C61—22no—
90C23×C4×C61C2311yescharacteristic
91#137×C61—28no—
92#137×C61—28no—
93AGL(1,ℤ/8)×C61—28no—
94AGL(1,ℤ/8)×C61—28no—
95#135×C61—28no—
96#135×C61—28no—
97C2×Q16×C61—22no—
98C2×SD16×C61—24no—
99C2×D8×C61—22no—
100C2×M16×C61—22no—
101C2×M16×C61—22no—
102C2×M16×C61D412yescomplemented
103C2×M16×C61C2312yes—
104C22×C8×C61D412yescomplemented
105C24×C61—22no—
106C24×C61C2×D411yescharacteristic
107C23×D61—22no—
108C23×D61—21no—
109C23×D61—22no—
110C23×D61—21no—
111C23×D61—44no—
112C23×D61C2×D412yes—
113#41×C61—24no—
114#41×C61—24no—
115#41×C61—24no—
116#41×C61—24no—
117#41×C61—24no—
118#41×C61—24no—
119#41×C61—24no—
120#41×C61—24no—
121#41×C61—42no—
122#41×C61—42no—
123#41×C61—42no—
124#41×C61—42no—
125#41×C61—42no—
126#41×C61—42no—
127#41×C61—42no—
128#41×C61—42no—
129C2×Q8×C61—22no—
130C2×Q8×C61—22no—
131C2×Q8×C61—22no—
132C2×Q8×C61—22no—
133C2×Q8×C61—22no—
134C2×Q8×C61C2×D414yescomplemented
135C2×D4×C61—24no—
136C2×D4×C61—24no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—42no—
143C2×D4×C61—42no—
144C2×D4×C61—42no—
145C2×D4×C61—42no—
146C2×D4×C61C2×D414yescomplemented
147C22×C4×C61—22no—
148C22×C4×C61—24no—
149C22×C4×C61—24no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61#4111yescharacteristic
162C22×C4×C61#4111yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—216no—
165C2×C22⋊D61—416no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—24no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61C2×D412yes—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—22no—
180C2×C4×D61—41no—
181C2×C4×D61—41no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—41no—
188C2×C4×D61—42no—
189C2×C4×D61—41no—
190Q16×C61—28no—
191SD16×C61—216no—
192D8×C61—28no—
193M16×C61—24no—
194M16×C61—24no—
195C2×C8×C61—22no—
196C2×C8×C61—22no—
197C2×C8×C61C2×D414yescomplemented
198C22⋊Dic61—216no—
199C22⋊Dic61—24no—
200C22⋊Dic61—24no—
201#11758198—216no—
202C4⋊Dic61—24no—
203C4⋊Dic61—24no—
204#11758196—216no—
205C4×Dic61—24no—
206C4×Dic61C2×D418yescomplemented
207#11758194—24no—
208#11758194—42no—
209C2×#92418—22no—
210C2×#92418—41no—
211C2×#92418—41no—
212C23×C61—24no—
213C23×C61—42no—
214C23×C61—48no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61#12012yes—
218C23×C61#12012yes—
219C23×C61#12111yescharacteristic
220C23×C61#12111yescharacteristic
221C23×C61C22×D411yescharacteristic
222C22×D61—28no—
223C22×D61—24no—
224C22×D61—24no—
225C22×D61—22no—
226C22×D61—44no—
227C22×D61—48no—
228C22×D61—44no—
229C22×D61—44no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61—41no—
233C22×D61—41no—
234Q8×C61—24no—
235Q8×C61—24no—
236Q8×C61—42no—
237Q8×C61—42no—
238D4×C61—24no—
239D4×C61—24no—
240D4×C61—44no—
241D4×C61—44no—
242D4×C61—44no—
243D4×C61—44no—
244D4×C61—42no—
245D4×C61—42no—
246C2×C4×C61—24no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—44no—
250C2×C4×C61—44no—
251C2×C4×C61—44no—
252C2×C4×C61—44no—
253C2×C4×C61#12011yescharacteristic
254C2×C4×C61#12011yescharacteristic
255C2×C4×C61#12012yes—
256C2×C4×C61#12012yes—
257C2×C4×C61#12012yes—
258C2×C4×C61#12112yes—
259C2×C4×C61#12112yes—
260C2×C4×C61#12112yes—
261C2×C4×C61#12112yes—
262C2×C4×C61#12111yescharacteristic
263C2×C4×C61#12111yescharacteristic
264C2×C4×C61#12711yescharacteristic
265C2×C4×C61#12712yes—
266C2×C4×C61#12711yescharacteristic
267C2×C4×C61C22×D412yes—
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D412yes—
270C2×C4×C61C2×#4111yescharacteristic
271C22⋊D61—432no—
272C2×Dic61—28no—
273C2×Dic61—24no—
274C2×Dic61—22no—
275C2×Dic61—48no—
276C2×Dic61—42no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C4×D61—42no—
280C4×D61—44no—
281C4×D61—42no—
282C4×D61—42no—
283C4×D61—44no—
284C4×D61—42no—
285C8×C61—24no—
286#92418—42no—
287C2×#2010—611nomaximal, Sylow
288C22×C61—24no—
289C22×C61—22no—
290C22×C61—42no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—48no—
294C22×C61—44no—
295C22×C61—84no—
296C22×C61—84no—
297C22×C61#39212yes—
298C22×C61#39211yescharacteristic
299C22×C61#39211yescharacteristic
300C22×C61C2×#12012yes—
301C22×C61C2×#12111yescharacteristic
302C2×D61—28no—
303C2×D61—24no—
304C2×D61—44no—
305C2×D61—42no—
306C2×D61—48no—
307C2×D61—44no—
308C2×D61—42no—
309C2×D61—44no—
310C4×C61—44no—
311C4×C61#39211yescharacteristic
312C4×C61#39212yes—
313C4×C61#39211yescharacteristic
314C4×C61C2×#12011yescharacteristic
315C4×C61C2×#12112yes—
316C4×C61C2×#12711yescharacteristic
317Dic61—48no—
318Dic61—42no—
319C2×#575D6111yescharacteristic, complemented
320C2×#525—612no—
321C2×#421—612no—
322C2×#407—611no—
323#2010—618no—
324C2×H(3,ℤ/4)—611no—
325C2×C61—22no—
326C2×C61—21no—
327C2×C61—22no—
328C2×C61—21no—
329C2×C61—84no—
330C2×C61#201012yescomplemented
331C2×C61C2×#39211yescharacteristic
332D61—44no—
333C22×#41C2×D6112yes—
334C24×C4—611no—
335#575—24no—
336#575—22no—
337#575C2×D6114yescomplemented
338C2×#137—22no—
339C2×AGL(1,ℤ/8)—22no—
340C2×#135—22no—
341C22×M16—611no—
342C22×M16C2×D6111yescharacteristic
343#525—618no—
344#525—1224no—
345#525—1224no—
346#525—1224no—
347C2×#123—1222no—
348C2×C22⋊Q8—1222no—
349C2×#121—1222no—
350C2×#120—1222no—
351C2×C4×D4—1224no—
352C2×#117—612no—
353#421—618no—
354#421—1224no—
355C2×#104—1224no—
356#407—614no—
357#407—1222no—
358C2×C22⋊C8—1222no—
359H(3,ℤ/4)—614no—
360C61C2×#201011yescharacteristic, complemented, Sylow
361C25—611no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41C22⋊D6114yescomplemented
373C2×#41C22×D6114yes—
374C22×Q8C22⋊D6112yescomplemented
375C22×D4—22no—
376C22×D4—1224no—
377C22×D4C22⋊D6112yescomplemented
378C23×C4—22no—
379C23×C4—611no—
380C23×C4—612no—
381C23×C4—612no—
382C23×C4—1222no—
383C23×C4—1222no—
384C23×C4—1221no—
385C23×C4—1221no—
386C23×C4—1222no—
387C23×C4—1222no—
388C23×C4—1221no—
389C23×C4—1221no—
390C23×C4C22×D6111yescharacteristic
391#137—28no—
392#137—28no—
393AGL(1,ℤ/8)—28no—
394AGL(1,ℤ/8)—28no—
395#135—28no—
396#135—28no—
397C2×Q16—22no—
398C2×SD16—24no—
399C2×D8—22no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—612no—
403C2×M16—1221no—
404C2×M16—1222no—
405C2×M16—1222no—
406C2×M16C22⋊D6112yescomplemented
407C2×M16C22×D6112yes—
408C22×C8—1221no—
409C22×C8C22⋊D6112yescomplemented
410#123—1228no—
411#123—1228no—
412C22⋊Q8—1228no—
413C22⋊Q8—1228no—
414#121—1228no—
415#121—1228no—
416#120—1228no—
417#120—1228no—
418C4×D4—12216no—
419C4×D4—12216no—
420#117—614no—
421#117—614no—
422#117—1222no—
423#117—1222no—
424C2×C4⋊C4—1224no—
425C2×C4⋊C4—1222no—
426C2×C22⋊C4—1224no—
427C2×C22⋊C4—1224no—
428C2×C22⋊C4—1222no—
429C2×C42—614no—
430#104—12216no—
431C22⋊C8—1228no—
432C24—22no—
433C24—612no—
434C24—1222no—
435C24—1221no—
436C24—1222no—
437C24—1221no—
438C24—2444no—
439C24D4×D6111yescharacteristic
440#41—24no—
441#41—24no—
442#41—24no—
443#41—24no—
444#41—24no—
445#41—24no—
446#41—24no—
447#41—24no—
448#41—42no—
449#41—42no—
450#41—42no—
451#41—42no—
452#41—42no—
453#41—42no—
454#41—42no—
455#41—42no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8C2×C22⋊D6114yescomplemented
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—12216no—
474C2×D4—24416no—
475C2×D4C2×C22⋊D6114yescomplemented
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—612no—
484C22×C4—1224no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1224no—
490C22×C4—1222no—
491C22×C4—1224no—
492C22×C4—1222no—
493C22×C4—1224no—
494C22×C4—1224no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—2441no—
498C22×C4—2441no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4—2442no—
503C22×C4—2442no—
504C22×C4—2441no—
505C22×C4—2442no—
506C22×C4—2441no—
507C22×C4D4×D6112yes—
508C22×C4D4×D6112yes—
509C22×C4D4×D6111yescharacteristic
510C22×C4#1175822411yescharacteristic
511C22×C4#1175822411yescharacteristic
512C22×C4C2×C22⋊D6112yes—
513C22×C4C2×C22⋊D6112yes—
514C22×C4C2×C22⋊D6111yescharacteristic
515C22×C4C2×C22⋊D6111yescharacteristic
516C22×C4C23×D6111yescharacteristic
517Q16—28no—
518SD16—216no—
519D8—28no—
520M16—24no—
521M16—24no—
522M16—1224no—
523M16—2442no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—1222no—
527C2×C8—2441no—
528C2×C8—2441no—
529C2×C8C2×C22⋊D6114yescomplemented
530C4⋊C4—12216no—
531C4⋊C4—1224no—
532C4⋊C4—1224no—
533C22⋊C4—12216no—
534C22⋊C4—12216no—
535C22⋊C4—1224no—
536C22⋊C4—1224no—
537C42—618no—
538C42—1224no—
539C23—24no—
540C23—42no—
541C23—48no—
542C23—42no—
543C23—42no—
544C23—1228no—
545C23—1224no—
546C23—1224no—
547C23—1222no—
548C23—2444no—
549C23—2442no—
550C23—2444no—
551C23—2448no—
552C23—2444no—
553C23—2442no—
554C23—2441no—
555C23—2441no—
556C23#1451974512yes—
557C23#1451974512yes—
558C23#1451974811yescharacteristic
559C23#1451974811yescharacteristic
560C23C2×D4×D6111yescharacteristic
561Q8—24no—
562Q8—24no—
563Q8—42no—
564Q8—42no—
565D4—24no—
566D4—24no—
567D4—44no—
568D4—44no—
569D4—44no—
570D4—44no—
571D4—42no—
572D4—42no—
573D4—24432no—
574C2×C4—24no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—1228no—
582C2×C4—1224no—
583C2×C4—1222no—
584C2×C4—2448no—
585C2×C4—2442no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2442no—
589C2×C4—2444no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2444no—
593C2×C4—2442no—
594C2×C4#1451974512yes—
595C2×C4#1451974512yes—
596C2×C4#1451974611yescharacteristic
597C2×C4#1451974611yescharacteristic
598C2×C4#1451974612yes—
599C2×C4#1451974811yescharacteristic
600C2×C4#1451974811yescharacteristic
601C2×C4#1451974912yes—
602C2×C4#1451974912yes—
603C2×C4#1451974912yes—
604C2×C4#1451974912yes—
605C2×C4#1451977311yescharacteristic
606C2×C4#1451977312yes—
607C2×C4#1451977311yescharacteristic
608C2×C4C2×D4×D6112yes—
609C2×C4C22×C22⋊D6112yes—
610C2×C4C22×C22⋊D6111yescharacteristic
611C2×C4C2×#1175822411yescharacteristic
612C8—24no—
613C8—2442no—
614C22—24no—
615C22—22no—
616C22—41no—
617C22—42no—
618C22—41no—
619C22—48no—
620C22—44no—
621C22—84no—
622C22—84no—
623C22—1228no—
624C22—1224no—
625C22—2444no—
626C22—2448no—
627C22—2442no—
628C22—2444no—
629C22—2442no—
630C22—2444no—
631C22#1683967012yes—
632C22#1683967011yescharacteristic
633C22#1683967011yescharacteristic
634C22C2×#1451974512yes—
635C22C2×#1451974811yescharacteristic
636C4—44no—
637C4—2448no—
638C4—2442no—
639C4#1683967011yescharacteristic
640C4#1683967012yes—
641C4#1683967011yescharacteristic
642C4C2×#1451974611yescharacteristic
643C4C2×#1451974912yes—
644C4C2×#1451977311yescharacteristic
645C2—22no—
646C2—22no—
647C2—21no—
648C2—21no—
649C2—84no—
650C2—2444no—
651C2#2144688312yesdirect product factor
652C2C2×#1683967011yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#575C2
socleC22×C61#392
hypercenterC2×#575D61
hypocenterC61C2×#2010
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#16840269C2semidirect
2. C2×#16839779C2semidirect
3. C2×#16839725C2semidirect
4. #21446883C2direct (N × H)
5. C2×#16839519C2semidirect
6. C2×C61×#575C2semidirect
12. #16840269C22semidirect
20. #16839779C22semidirect
23. #16839725C22semidirect
25. #16839519C22semidirect
29. C61×#575C22semidirect
64. #14519736D4semidirect
71. C2×C4×Dic61D4semidirect
84. C2×#41×C61D4semidirect
86. C22×Q8×C61D4semidirect
88. C22×D4×C61D4semidirect
102. C2×M16×C61D4semidirect
104. C22×C8×C61D4semidirect
134. C2×Q8×C61C2×D4semidirect
146. C2×D4×C61C2×D4semidirect
197. C2×C8×C61C2×D4semidirect
206. C4×Dic61C2×D4semidirect
319. C2×#575D61semidirect
330. C2×C61#2010semidirect
337. #575C2×D61semidirect
360. C61C2×#2010semidirect
372. C2×#41C22⋊D61semidirect
374. C22×Q8C22⋊D61semidirect
377. C22×D4C22⋊D61semidirect
406. C2×M16C22⋊D61semidirect
409. C22×C8C22⋊D61semidirect
461. C2×Q8C2×C22⋊D61semidirect
475. C2×D4C2×C22⋊D61semidirect
529. C2×C8C2×C22⋊D61semidirect
651. C2#21446883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402692
C2×#168397792
C2×#168397252
#214468832
C2×#168395192
C2×C61×#5752
C2×#201061