Finite Group Databasebeta

← C2×#21446491 #29682597

Subgroups — C2×#21446491 #29682597

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839810C211yesmaximal, characteristic, complemented
2C22×#14519704C211yesmaximal, characteristic
3C2×#16839746C211yesmaximal, characteristic
4C2×M16×Dic61C211yesmaximal, characteristic, complemented
5#21446491C218yesmaximal, direct product factor
6C2×#16839532C211yesmaximal, characteristic, complemented
7C2×#16839521C211yesmaximal, characteristic, complemented
8C2×C61×#421C211yesmaximal, characteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12C22×C4×Dic61C2211yescharacteristic
13#16839810—22no—
14#16839810C2214yescomplemented
15C2×#14519712—22no—
16C2×#14519704—21no—
17C2×#14519704—21no—
18C2×#14519704—22no—
19C2×#14519704C2214yes—
20#16839746C414yescomplemented
21#16839746C2214yes—
22C2×#14519696C412yescomplemented
23C2×#14519694C412yescomplemented
24M16×Dic61—22no—
25M16×Dic61C2214yescomplemented
26C2×#14519687—21no—
27C2×C8×Dic61—21no—
28#16839532C2214yescomplemented
29#16839521C2214yescomplemented
30C22×#41×C61C2211yescharacteristic
31C22×M16×C61C2211yescharacteristic
32C2×#117×C61C2211yescharacteristic
33C61×#421—22no—
34C61×#421C2214yes—
35C2×#104×C61—22no—
36C23×Dic61—21no—
37C2×#11758194—21no—
38C2×#11758194—21no—
39C2×#11758194—21no—
40C2×#11758194—21no—
41C2×#11758194—21no—
42C2×#11758194—21no—
43C2×#11758194—21no—
44C2×#11758194—21no—
45C2×#11758194—21no—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194C2×C412yes—
49C2×#11758194C2×C412yes—
50C2×#11758194C2×C412yes—
51C2×#11758194C2×C412yes—
52C2×#11758194C2312yes—
53C2×#11758194C2312yes—
54C2×#11758194C2312yes—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C2×C4×Dic61—21no—
59C2×C4×Dic61—21no—
60C2×C4×Dic61—21no—
61C2×C4×Dic61D411yescharacteristic
62C2×C4×Dic61D411yescharacteristic
63C2×C4×Dic61D412yes—
64C2×C4×Dic61C2312yes—
65#14519712—28no—
66#14519704—24no—
67#14519704—24no—
68#14519696C2×C418yescomplemented
69#14519694C2×C418yescomplemented
70#14519687—24no—
71C8×Dic61—24no—
72C2×#41×C61—21no—
73C2×#41×C61—21no—
74C2×#41×C61—21no—
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61C2×C412yes—
83C2×#41×C61C2312yes—
84C22×Q8×C61C2×C411yescharacteristic
85C22×D4×C61—21no—
86C22×D4×C61C2×C411yescharacteristic
87C23×C4×C61—21no—
88C23×C4×C61C2311yescharacteristic
89C2×M16×C61—21no—
90C2×M16×C61—21no—
91C2×M16×C61—21no—
92C2×M16×C61D412yes—
93C2×M16×C61D412yes—
94C2×M16×C61C2312yes—
95C22×C8×C61—21no—
96#117×C61—21no—
97#117×C61—21no—
98#117×C61—21no—
99#117×C61C2312yes—
100C2×C4⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C42×C61—21no—
103#104×C61—28no—
104C24×C61—21no—
105C24×C61#4111yescharacteristic
106#41×C61—22no—
107#41×C61—22no—
108#41×C61—22no—
109#41×C61—22no—
110#41×C61—22no—
111#41×C61—22no—
112#41×C61—22no—
113#41×C61—22no—
114#41×C61—41no—
115#41×C61—41no—
116#41×C61—41no—
117#41×C61—41no—
118#41×C61—41no—
119#41×C61—41no—
120#41×C61—41no—
121#41×C61—41no—
122C2×Q8×C61—21no—
123C2×Q8×C61—21no—
124C2×Q8×C61—21no—
125C2×Q8×C61—21no—
126C2×Q8×C61—21no—
127C2×Q8×C61C22×C412yes—
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—41no—
136C2×D4×C61—41no—
137C2×D4×C61—41no—
138C2×D4×C61—41no—
139C2×D4×C61C22×C412yes—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—41no—
144C22×C4×C61—41no—
145C22×C4×C61—41no—
146C22×C4×C61—41no—
147C22×C4×C61—41no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61#4111yescharacteristic
161C22×C4×C61C2411yescharacteristic
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—44no—
167M16×C61—22no—
168M16×C61—22no—
169M16×C61—22no—
170M16×C61C2×D414yes—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—41no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—41no—
178C42×C61—22no—
179C42×C61—41no—
180C4×Dic61—21no—
181C4×Dic61—22no—
182C4×Dic61—21no—
183C4×Dic61—22no—
184C4×Dic61C2×D412yes—
185C4×Dic61C2×D412yes—
186#11758194—22no—
187#11758194—22no—
188#11758194—22no—
189#11758194—22no—
190#11758194—22no—
191#11758194—22no—
192#11758194—22no—
193#11758194—22no—
194#11758194—41no—
195#11758194—41no—
196#11758194C22×C414yes—
197#11758194C22×C414yes—
198C2×#92418—22no—
199C2×#92418—22no—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—22no—
204C2×#92418—22no—
205C2×#92418—41no—
206C2×#92418—41no—
207C23×C61—22no—
208C23×C61—42no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—82no—
212C23×C61#11711yescharacteristic
213C23×C61#11711yescharacteristic
214C23×C61#12311yescharacteristic
215C23×C61#12311yescharacteristic
216C23×C61#12411yescharacteristic
217C23×C61#12411yescharacteristic
218C23×C61C2×#4111yescharacteristic
219Q8×C61—22no—
220Q8×C61—22no—
221Q8×C61—41no—
222Q8×C61—41no—
223D4×C61—22no—
224D4×C61—22no—
225D4×C61—42no—
226D4×C61—42no—
227D4×C61—42no—
228D4×C61—42no—
229D4×C61—41no—
230D4×C61—41no—
231C2×C4×C61—22no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—82no—
240C2×C4×C61#11711yescharacteristic
241C2×C4×C61#11711yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C4×D411yescharacteristic
245C2×C4×C61C4×D411yescharacteristic
246C2×C4×C61C4×D411yescharacteristic
247C2×C4×C61C4×D411yescharacteristic
248C2×C4×C61C4×D411yescharacteristic
249C2×C4×C61C4×D411yescharacteristic
250C2×C4×C61#12111yescharacteristic
251C2×C4×C61#12111yescharacteristic
252C2×C4×C61#12111yescharacteristic
253C2×C4×C61#12111yescharacteristic
254C2×C4×C61#12311yescharacteristic
255C2×C4×C61#12311yescharacteristic
256C2×C4×C61#12411yescharacteristic
257C2×C4×C61#12411yescharacteristic
258C2×C4×C61#12611yescharacteristic
259C2×C4×C61#12611yescharacteristic
260C2×C4×C61#12611yescharacteristic
261C2×C4×C61#12611yescharacteristic
262C2×C4×C61C23×C411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×Dic61—24no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—44no—
272C2×Dic61—44no—
273C2×Dic61—42no—
274C8×C61—24no—
275#92418—24no—
276#92418—24no—
277#92418—42no—
278C2×#1932—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—42no—
287C22×C61—82no—
288C22×C61—82no—
289C22×C61—82no—
290C22×C61#38811yescharacteristic
291C22×C61#38811yescharacteristic
292C22×C61#38811yescharacteristic
293C22×C61#38811yescharacteristic
294C22×C61C2×#11711yescharacteristic
295C22×C61C2×#12311yescharacteristic
296C22×C61C2×#12411yescharacteristic
297C4×C61—42no—
298C4×C61—82no—
299C4×C61#38811yescharacteristic
300C4×C61#38811yescharacteristic
301C4×C61#38811yescharacteristic
302C4×C61#38811yescharacteristic
303C4×C61C2×C4×D411yescharacteristic
304C4×C61C2×C4×D411yescharacteristic
305C4×C61C2×#12111yescharacteristic
306C4×C61C2×#12611yescharacteristic
307Dic61—24no—
308Dic61—42no—
309C2×#430—611no—
310C2×#421D6111yescharacteristic
311C22×#104—611no—
312C2×#413—611no—
313C2×C4×M16—611no—
314#1932—618no—
315C2×#344—611no—
316C2×#339—611no—
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—82no—
324C2×C61#193212yescomplemented
325C2×C61C2×#38811yescharacteristic
326C22×#41C2×D6111yescharacteristic
327C22×M16—611no—
328C22×M16—611no—
329C22×M16—611no—
330C22×M16C2×D6111yescharacteristic
331C2×#117C2×D6111yescharacteristic
332C22×C42—611no—
333#430—614no—
334#430—1222no—
335C2×#108—1222no—
336#421—22no—
337#421C2×D6114yes—
338C2×#104—22no—
339C2×#104—614no—
340C2×#104—1221no—
341C2×#104—1221no—
342C2×#104—1222no—
343#413—614no—
344#413—614no—
345C2×#101—612no—
346C2×#100—612no—
347C4×M16—614no—
348C4×M16—1222no—
349C2×#97—1221no—
350C2×C4×C8—1221no—
351#344—614no—
352#339—614no—
353C61C2×#193211yescharacteristic, complemented, Sylow
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41C4×D6112yes—
365C2×#41C22×D6112yes—
366C22×Q8C4×D6111yescharacteristic
367C22×D4—21no—
368C22×D4C4×D6111yescharacteristic
369C23×C4—21no—
370C23×C4—1221no—
371C23×C4C22×D6111yescharacteristic
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—612no—
376C2×M16—612no—
377C2×M16—612no—
378C2×M16—612no—
379C2×M16—612no—
380C2×M16—612no—
381C2×M16—612no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C2×M16—1221no—
388C2×M16—1221no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C2×M16C22⋊D6112yes—
394C2×M16C22⋊D6112yes—
395C2×M16C22×D6112yes—
396C22×C8—21no—
397C22×C8—1221no—
398C22×C8—1221no—
399C22×C8—1221no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117C22×D6112yes—
404C2×C4⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C42—21no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—612no—
410C2×C42—612no—
411C2×C42—1221no—
412C2×C42—1221no—
413C2×C42—1221no—
414#108—1228no—
415#104—28no—
416#104—1224no—
417#104—1224no—
418#101—618no—
419#100—618no—
420#97—1224no—
421C4×C8—1224no—
422C24—21no—
423C24#1175822411yescharacteristic
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—41no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×C4×D6112yes—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C2×C4×D6112yes—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—1221no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1221no—
470C22×C4—2444no—
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4#1175822211yescharacteristic
474C22×C4#1175822211yescharacteristic
475C22×C4D4×D6111yescharacteristic
476C22×C4D4×D6111yescharacteristic
477C22×C4#1175822411yescharacteristic
478C22×C4#1175822411yescharacteristic
479C22×C4#1175822411yescharacteristic
480C22×C4#1175822411yescharacteristic
481C22×C4#1175822411yescharacteristic
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—614no—
489M16—614no—
490M16—1222no—
491M16—1222no—
492M16—1222no—
493M16—1222no—
494M16—1222no—
495M16—1222no—
496M16—1222no—
497M16—1222no—
498M16—2441no—
499M16—2441no—
500M16C2×C22⋊D6114yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—1222no—
505C2×C8—1222no—
506C2×C8—1222no—
507C2×C8—1222no—
508C2×C8—1222no—
509C2×C8—1222no—
510C2×C8—1222no—
511C2×C8—2441no—
512C2×C8—2441no—
513C4⋊C4—22no—
514C4⋊C4—41no—
515C22⋊C4—22no—
516C22⋊C4—41no—
517C42—22no—
518C42—41no—
519C42—612no—
520C42—612no—
521C42—1222no—
522C42—1221no—
523C42—1222no—
524C42—1221no—
525C23—22no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—82no—
530C23#1451973311yescharacteristic
531C23#1451973311yescharacteristic
532C23#1451975911yescharacteristic
533C23#1451975911yescharacteristic
534C23#1451976411yescharacteristic
535C23#1451976411yescharacteristic
536C23C2×#1175822411yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541D4—22no—
542D4—22no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—42no—
547D4—41no—
548D4—41no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—82no—
558C2×C4—1224no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—2444no—
562C2×C4—2444no—
563C2×C4—2442no—
564C2×C4#1451973311yescharacteristic
565C2×C4#1451973311yescharacteristic
566C2×C4#1451973711yescharacteristic
567C2×C4#1451973711yescharacteristic
568C2×C4#1451973711yescharacteristic
569C2×C4#1451973711yescharacteristic
570C2×C4C4×C22⋊D6111yescharacteristic
571C2×C4C4×C22⋊D6111yescharacteristic
572C2×C4C4×C22⋊D6111yescharacteristic
573C2×C4C4×C22⋊D6111yescharacteristic
574C2×C4#1451974911yescharacteristic
575C2×C4#1451974911yescharacteristic
576C2×C4#1451974911yescharacteristic
577C2×C4#1451974911yescharacteristic
578C2×C4#1451975911yescharacteristic
579C2×C4#1451975911yescharacteristic
580C2×C4#1451976411yescharacteristic
581C2×C4#1451976411yescharacteristic
582C2×C4#1451977011yescharacteristic
583C2×C4#1451977011yescharacteristic
584C2×C4#1451977011yescharacteristic
585C2×C4#1451977011yescharacteristic
586C2×C4C22×C4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C22×C22⋊D6111yescharacteristic
589C2×C4C2×#1175822411yescharacteristic
590C2×C4C2×#1175822411yescharacteristic
591C2×C4C2×#1175822211yescharacteristic
592C8—24no—
593C8—1224no—
594C8—1224no—
595C8—2442no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—42no—
604C22—82no—
605C22—82no—
606C22—82no—
607C22#1683965611yescharacteristic
608C22#1683965611yescharacteristic
609C22#1683965611yescharacteristic
610C22#1683965611yescharacteristic
611C22C2×#1451973311yescharacteristic
612C22C2×#1451975911yescharacteristic
613C22C2×#1451976411yescharacteristic
614C4—42no—
615C4—82no—
616C4—1224no—
617C4—2442no—
618C4#1683965611yescharacteristic
619C4#1683965611yescharacteristic
620C4#1683965611yescharacteristic
621C4#1683965611yescharacteristic
622C4C2×#1451973711yescharacteristic
623C4C2×C4×C22⋊D6111yescharacteristic
624C4C2×#1451974911yescharacteristic
625C4C2×#1451977011yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2#2144649112yesdirect product factor
634C2C2×#1683965611yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#388
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#16839810C2semidirect
4. C2×M16×Dic61C2semidirect
5. #21446491C2direct (N × H)
6. C2×#16839532C2semidirect
7. C2×#16839521C2semidirect
14. #16839810C22semidirect
20. #16839746C4semidirect
22. C2×#14519696C4semidirect
23. C2×#14519694C4semidirect
25. M16×Dic61C22semidirect
28. #16839532C22semidirect
29. #16839521C22semidirect
68. #14519696C2×C4semidirect
69. #14519694C2×C4semidirect
324. C2×C61#1932semidirect
353. C61C2×#1932semidirect
633. C2#21446491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168398102
C22×#145197042
C2×#168397462
C2×M16×Dic612
#214464912
C2×#168395322
C2×#168395212
C2×C61×#4212
C2×#193261