Finite Group Databasebeta

← C2×#21461905 #30615937

Subgroups — C2×#21461905 #30615937

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840773C211yesmaximal, characteristic, complemented
2C2×#16840754C211yesmaximal, characteristic
3C22×#14519839C211yesmaximal, characteristic
4C2×#16840728C211yesmaximal, characteristic, complemented
5#21461905C218yesmaximal, direct product factor
6C2×#16840641C211yesmaximal, characteristic, complemented
7C2×#16840637C211yesmaximal, characteristic, complemented
8C2×#100×D61C211yesmaximal, characteristic
9C2×D61⋊M16C2211yescharacteristic
10C22×D61⋊C8C2211yescharacteristic
11C2×#14519856C2211yescharacteristic
12C22×C4⋊#6923C2211yescharacteristic
13#16840773—22no—
14#16840773C2214yescomplemented
15C2×#14519846—21no—
16C2×#14519845—21no—
17#16840754—22no—
18#16840754C2214yes—
19C2×#14519839—21no—
20C2×#14519839—21no—
21C2×#14519839—22no—
22C2×#14519839—21no—
23C2×#14519839—21no—
24C2×#14519839C2214yes—
25#16840728—22no—
26#16840728C2214yescomplemented
27C2×#14519831—21no—
28C2×C8×#6923—21no—
29#16840641C2214yescomplemented
30#16840637C2214yescomplemented
31C22×D4×D61C2211yescharacteristic
32C2×M16×D61C2211yescharacteristic
33C2×M16×D61C2211yescharacteristic
34C2×#14519694C411yescharacteristic, complemented
35C2×#14519693C411yescharacteristic, complemented
36C2×#14519693C411yescharacteristic, complemented
37#100×D61C414yescomplemented
38#100×D61C2214yes—
39C2×#100×C61C411yescharacteristic, complemented
40C23×#6923—21no—
41C2×#11758213—21no—
42D61⋊M16—21no—
43D61⋊M16—21no—
44D61⋊M16—21no—
45D61⋊M16C2312yes—
46C2×#11758217—21no—
47C2×D61⋊C8—21no—
48C2×D61⋊C8—21no—
49C2×D61⋊C8—21no—
50C2×D61⋊C8—21no—
51C2×D61⋊C8D411yescharacteristic
52C2×D61⋊C8D411yescharacteristic
53C2×D61⋊C8D412yes—
54C2×D61⋊C8C2312yes—
55C22×#92420—21no—
56#14519856—21no—
57#14519856—21no—
58#14519856D412yes—
59#14519856C2312yes—
60C2×C4⋊#6923—21no—
61C2×C4⋊#6923—21no—
62C2×C4⋊#6923—21no—
63C2×C4⋊#6923—21no—
64C2×C4⋊#6923—21no—
65C2×C4⋊#6923D411yescharacteristic
66C2×C4⋊#6923D411yescharacteristic
67C2×C4⋊#6923C2312yes—
68C2×C22⋊#6923—21no—
69C2×C4×#6923—21no—
70#14519846—24no—
71#14519845—24no—
72#14519839—24no—
73#14519839—24no—
74#14519839—24no—
75#14519839—24no—
76#14519831—24no—
77C8×#6923—24no—
78C24×D61—21no—
79C22×D244C2×C411yescharacteristic
80C22×C22⋊D61—21no—
81C2×D4×D61—21no—
82C2×D4×D61—21no—
83C2×D4×D61—21no—
84C2×D4×D61—21no—
85C2×D4×D61—21no—
86C2×D4×D61—21no—
87C2×D4×D61—21no—
88C2×D4×D61—21no—
89C2×D4×D61—21no—
90C2×D4×D61—21no—
91C2×D4×D61C2×C412yes—
92C2×D4×D61C2312yes—
93C22×C4×D61C2311yescharacteristic
94C2×#11758194C2×C411yescharacteristic
95C2×#11758194C2×C411yescharacteristic
96C2×#11758189—21no—
97C2×#11758189—21no—
98M16×D61—21no—
99M16×D61—21no—
100M16×D61—21no—
101M16×D61—21no—
102M16×D61C2×C412yes—
103M16×D61C2×C412yes—
104M16×D61C2312yes—
105M16×D61C2312yes—
106C2×C8×D61—21no—
107C2×C8×D61—21no—
108#14519694C2×C414yescomplemented
109#14519693C2×C414yescomplemented
110#14519693C2×C414yescomplemented
111C22×D4×C61C2×C411yescharacteristic
112C2×M16×C61C2×C411yescharacteristic
113C2×M16×C61C2×C411yescharacteristic
114#100×C61C2×C414yescomplemented
115C24×C61—21no—
116C23×D61—21no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—41no—
120C23×D61—41no—
121C23×D61—41no—
122C23×D61—41no—
123C23×D61—82no—
124C23×D61—82no—
125C23×D61#4111yescharacteristic
126C22×#6923—21no—
127C22×#6923—21no—
128C22×#6923—22no—
129C22×#6923—41no—
130C22×#6923—41no—
131C22×#6923—82no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61C22×C412yes—
138C22×C4×C61C22×C411yescharacteristic
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—41no—
142C2×C22⋊D61—41no—
143C2×C22⋊D61—41no—
144C2×C22⋊D61—41no—
145C22×Dic61#4111yescharacteristic
146D4×D61—22no—
147D4×D61—22no—
148D4×D61—22no—
149D4×D61—22no—
150D4×D61—22no—
151D4×D61—22no—
152D4×D61—22no—
153D4×D61—22no—
154D4×D61—41no—
155D4×D61—41no—
156D4×D61—41no—
157D4×D61—41no—
158D4×D61—41no—
159D4×D61—41no—
160D4×D61—41no—
161D4×D61—41no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244C22×C412yes—
168C2×C4×D61C22×C411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61#4111yescharacteristic
174C2×C4×D61#4111yescharacteristic
175C2×C4×D61#4111yescharacteristic
176C2×C4×D61#4111yescharacteristic
177C2×C4×D61#4111yescharacteristic
178C2×C4×D61#4111yescharacteristic
179C2×C4×D61C2411yescharacteristic
180C22⋊#6923—22no—
181C22⋊#6923—22no—
182#11758217—22no—
183#11758217—41no—
184C2×#92420—21no—
185C2×#92420—21no—
186C2×#92420—22no—
187C2×#92420—22no—
188C2×#92420—41no—
189C4⋊#6923—21no—
190C4⋊#6923—21no—
191C4⋊#6923—22no—
192C4⋊#6923—22no—
193C4⋊#6923—41no—
194C4⋊#6923—41no—
195C4⋊#6923C2×D412yes—
196C4⋊#6923C2×D412yes—
197C4×#6923—22no—
198C4×#6923—22no—
199#11758213—22no—
200#11758213—41no—
201D61⋊C8—21no—
202D61⋊C8—21no—
203D61⋊C8—22no—
204D61⋊C8—22no—
205D61⋊C8—22no—
206D61⋊C8—41no—
207D61⋊C8C2×D412yes—
208D61⋊C8C2×D412yes—
209M16×C61—21no—
210M16×C61—21no—
211M16×C61C22×C412yes—
212M16×C61C22×C412yes—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215#11758194—21no—
216#11758194—21no—
217#11758194C22×C412yes—
218#11758194C22×C412yes—
219C2×#92418—21no—
220C2×#92418—21no—
221#11758189—22no—
222#11758189—22no—
223#11758189—22no—
224#11758189—22no—
225C8×D61—22no—
226C8×D61—22no—
227C8×D61—22no—
228C8×D61—22no—
229C23×C61—22no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—82no—
233C23×C61#11711yescharacteristic
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—42no—
240C22×D61—42no—
241C22×D61—42no—
242C22×D61—42no—
243C22×D61—84no—
244C22×D61—84no—
245C22×D61—82no—
246C22×D61—82no—
247C22×D61—84no—
248C22×D61—82no—
249C22×D61—82no—
250C22×D61—82no—
251C22×D61—82no—
252C22×D61—82no—
253C22×D61#11711yescharacteristic
254C22×D61#12111yescharacteristic
255C22×D61#12111yescharacteristic
256C22×D61#12611yescharacteristic
257C22×D61#12611yescharacteristic
258C22×D61C2×#4111yescharacteristic
259C2×#6923—22no—
260C2×#6923—22no—
261C2×#6923—42no—
262C2×#6923—42no—
263C2×#6923—42no—
264C2×#6923—82no—
265C2×#6923—82no—
266C2×#6923—82no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—41no—
270D4×C61—41no—
271C2×C4×C61#11711yescharacteristic
272C2×C4×C61C4×D411yescharacteristic
273C2×C4×C61C4×D411yescharacteristic
274C2×C4×C61C4×D411yescharacteristic
275C2×C4×C61C4×D411yescharacteristic
276C2×C4×C61C23×C411yescharacteristic
277C22⋊D61—42no—
278C22⋊D61—42no—
279C22⋊D61—42no—
280C22⋊D61—42no—
281C2×Dic61#11711yescharacteristic
282C2×Dic61#12311yescharacteristic
283C2×Dic61#12311yescharacteristic
284C2×Dic61#12411yescharacteristic
285C2×Dic61#12411yescharacteristic
286C2×Dic61C2×#4111yescharacteristic
287D244—22no—
288D244—22no—
289D244—41no—
290D244—41no—
291C4×D61C4×D411yescharacteristic
292C4×D61C4×D411yescharacteristic
293C4×D61C4×D411yescharacteristic
294C4×D61C4×D411yescharacteristic
295C4×D61#12111yescharacteristic
296C4×D61#12111yescharacteristic
297C4×D61#12311yescharacteristic
298C4×D61#12311yescharacteristic
299C4×D61#12411yescharacteristic
300C4×D61#12411yescharacteristic
301C4×D61#12611yescharacteristic
302C4×D61#12611yescharacteristic
303C4×D61C22×D411yescharacteristic
304C4×D61C22×D411yescharacteristic
305C4×D61C2×#4111yescharacteristic
306C4×D61C2×#4111yescharacteristic
307#92420—22no—
308#92420—22no—
309#92420—42no—
310C8×C61—22no—
311C8×C61—22no—
312#92418—22no—
313#92418—22no—
314C2×#1931—611nomaximal, Sylow
315C22×C61—22no—
316C22×C61—42no—
317C22×C61—82no—
318C22×C61—82no—
319C22×C61—82no—
320C22×C61#38811yescharacteristic
321C22×C61#38811yescharacteristic
322C22×C61C2×#11711yescharacteristic
323C2×D61—22no—
324C2×D61—22no—
325C2×D61—22no—
326C2×D61—21no—
327C2×D61—21no—
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—42no—
331C2×D61—84no—
332C2×D61—84no—
333C2×D61—82no—
334C2×D61—82no—
335C2×D61—84no—
336C2×D61—82no—
337C2×D61—82no—
338C2×D61—82no—
339C2×D61#38811yescharacteristic
340C2×D61#38811yescharacteristic
341C2×D61#47112yes—
342C2×D61#47212yes—
343C2×D61C2×#12111yescharacteristic
344C2×D61C2×#12611yescharacteristic
345#6923—42no—
346#6923—42no—
347#6923—82no—
348C4×C61#38811yescharacteristic
349C4×C61#38811yescharacteristic
350C4×C61C2×C4×D411yescharacteristic
351C4×C61C2×C4×D411yescharacteristic
352Dic61#38811yescharacteristic
353Dic61#38811yescharacteristic
354Dic61C2×#12311yescharacteristic
355Dic61C2×#12411yescharacteristic
356C2×#428—611no—
357C2×#418—611no—
358C22×#102—611no—
359C22×#100—611no—
360C2×#405—611no—
361#1931—618no—
362C2×#343—611no—
363C2×#341—611no—
364C2×C61—21no—
365C2×C61—21no—
366C2×C61—82no—
367C2×C61#193112yescomplemented
368C2×C61C2×#38811yescharacteristic
369D61—21no—
370D61—21no—
371D61—82no—
372D61#193112yescomplemented
373D61C2×#47111yescharacteristic
374D61C2×#47211yescharacteristic
375C23×D4—611no—
376C22×M16—611no—
377C22×M16—611no—
378C22×M16—611no—
379C23×C8—611no—
380C2×#117—611no—
381C22×C4⋊C4—611no—
382#428—614no—
383#428—1222no—
384C2×#107—1221no—
385C2×#106—1221no—
386#418—614no—
387#418—1222no—
388C2×#102—614no—
389C2×#102—1221no—
390C2×#102—1221no—
391C2×#102—1221no—
392C2×#102—1221no—
393C2×#102—1222no—
394C2×#100—611no—
395C2×#100—611no—
396C2×#100—611no—
397C2×#100—614no—
398C2×#100—614no—
399C2×#100#692311yescharacteristic, complemented
400#405—614no—
401#405—1222no—
402C2×#97—1221no—
403C2×C4×C8—1221no—
404#343—614no—
405#341—614no—
406C61C2×#193111yescharacteristic, complemented, Sylow
407C25—1221no—
408C22×D4—612no—
409C22×D4—612no—
410C22×D4—611no—
411C22×D4—1221no—
412C22×D4—1221no—
413C22×D4—1221no—
414C22×D4—1221no—
415C22×D4—1221no—
416C22×D4—1221no—
417C22×D4—1221no—
418C22×D4—1221no—
419C22×D4—1221no—
420C22×D4—1221no—
421C22×D4—1221no—
422C22×D4C2×#692311yescharacteristic
423C23×C4—611no—
424C23×C4—1221no—
425C2×M16—611no—
426C2×M16—611no—
427C2×M16—612no—
428C2×M16—612no—
429C2×M16—612no—
430C2×M16—612no—
431C2×M16—612no—
432C2×M16—1221no—
433C2×M16—1221no—
434C2×M16—1221no—
435C2×M16—1221no—
436C2×M16—1221no—
437C2×M16—1221no—
438C2×M16—1221no—
439C2×M16—1221no—
440C2×M16—1221no—
441C2×M16—1221no—
442C2×M16—1221no—
443C2×M16C2×#692311yescharacteristic
444C2×M16C2×#692311yescharacteristic
445C22×C8—611no—
446C22×C8—611no—
447C22×C8—612no—
448C22×C8—612no—
449C22×C8—1221no—
450C22×C8—1221no—
451C22×C8—1221no—
452C22×C8—1221no—
453C22×C8—1221no—
454C22×C8—1221no—
455C22×C8—1221no—
456#117—612no—
457#117—612no—
458#117—1221no—
459#117—1221no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—612no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C42—1221no—
470#107—1224no—
471#106—1224no—
472#102—1224no—
473#102—1224no—
474#102—1224no—
475#102—1224no—
476#100—614no—
477#100—614no—
478#100—614no—
479#100C2×#692314yescomplemented
480#97—1224no—
481C4×C8—1224no—
482C24—21no—
483C24—611no—
484C24—1222no—
485C24—1222no—
486C24—1221no—
487C24—4882no—
488C24—4882no—
489C24—2441no—
490C24—2441no—
491C24—2441no—
492C24—2441no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—612no—
499C2×D4—1222no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1221no—
510C2×D4—1221no—
511C2×D4—1221no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—2441no—
515C2×D4—2441no—
516C2×D4—2441no—
517C2×D4—2441no—
518C2×D4—2441no—
519C2×D4—2441no—
520C2×D4—2441no—
521C2×D4—2441no—
522C2×D4—2441no—
523C2×D4—2441no—
524C2×D4—2441no—
525C2×D4—2441no—
526C2×D4C22×#692312yes—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1222no—
543C22×C4—4882no—
544C22×C4—2441no—
545C22×C4—2441no—
546C22×C4C22×#692311yescharacteristic
547M16—21no—
548M16—21no—
549M16—612no—
550M16—612no—
551M16—1222no—
552M16—1222no—
553M16—1222no—
554M16—1222no—
555M16—1221no—
556M16—1221no—
557M16—1222no—
558M16—1222no—
559M16—2441no—
560M16—2441no—
561M16C22×#692312yes—
562M16C22×#692312yes—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—612no—
566C2×C8—612no—
567C2×C8—1222no—
568C2×C8—1222no—
569C2×C8—1222no—
570C2×C8—1222no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1222no—
574C2×C8—1222no—
575C2×C8—1222no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1222no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1222no—
582C2×C8—2441no—
583C2×C8—2441no—
584C4⋊C4—612no—
585C4⋊C4—612no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1222no—
589C4⋊C4—1222no—
590C4⋊C4—2441no—
591C4⋊C4—2441no—
592C22⋊C4—1222no—
593C22⋊C4—1222no—
594C42—1222no—
595C42—1222no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—82no—
600C23—611no—
601C23—611no—
602C23—611no—
603C23—611no—
604C23—611no—
605C23—611no—
606C23—1222no—
607C23—1222no—
608C23—1222no—
609C23—4882no—
610C23—4882no—
611C23—4882no—
612C23—4882no—
613C23—4882no—
614C23—4884no—
615C23—4882no—
616C23—4882no—
617C23—4884no—
618C23—4884no—
619C23—2442no—
620C23—2442no—
621C23—2442no—
622C23—2442no—
623C23—2441no—
624C23—2441no—
625C23#1451985611yescharacteristic
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—1222no—
631D4—1222no—
632D4—2442no—
633D4—2442no—
634D4—2442no—
635D4—2442no—
636D4—2441no—
637D4—2441no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—611no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—611no—
645C2×C4—611no—
646C2×C4—611no—
647C2×C4—611no—
648C2×C4—611no—
649C2×C4—611no—
650C2×C4—611no—
651C2×C4—611no—
652C2×C4—611no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—4882no—
663C2×C4—4882no—
664C2×C4—4882no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4#1451985611yescharacteristic
669C2×C4D4×#692311yescharacteristic
670C2×C4D4×#692311yescharacteristic
671C2×C4D4×#692311yescharacteristic
672C2×C4D4×#692311yescharacteristic
673C2×C4C23×#692311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1222no—
677C8—1222no—
678C8—1222no—
679C8—1222no—
680C8—2442no—
681C22—22no—
682C22—42no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—611no—
687C22—611no—
688C22—612no—
689C22—612no—
690C22—611no—
691C22—611no—
692C22—1221no—
693C22—1221no—
694C22—1221no—
695C22—1222no—
696C22—1221no—
697C22—1222no—
698C22—1222no—
699C22—4882no—
700C22—4882no—
701C22—4882no—
702C22—4882no—
703C22—4884no—
704C22—4884no—
705C22—4884no—
706C22—4882no—
707C22—2442no—
708C22#1684071211yescharacteristic
709C22#1684071211yescharacteristic
710C22C2×#1451985611yescharacteristic
711C4—611no—
712C4—611no—
713C4—611no—
714C4—611no—
715C4—4882no—
716C4—2442no—
717C4—2442no—
718C4#1684071211yescharacteristic
719C4#1684071211yescharacteristic
720C4C2×D4×#692311yescharacteristic
721C4C2×D4×#692311yescharacteristic
722C2—21no—
723C2—21no—
724C2—82no—
725C2—611no—
726C2—611no—
727C2—612no—
728C2—1221no—
729C2—1221no—
730C2—4882no—
731C2#2146190512yesdirect product factor
732C2C2×#1684071211yescharacteristic
subgroupG/H
centerC22#16840712
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#100×C61C4
socleC22×C61#388
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#100#6923
hypocenterC61C2×#1931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#16840773C2semidirect
4. C2×#16840728C2semidirect
5. #21461905C2direct (N × H)
6. C2×#16840641C2semidirect
7. C2×#16840637C2semidirect
14. #16840773C22semidirect
26. #16840728C22semidirect
29. #16840641C22semidirect
30. #16840637C22semidirect
34. C2×#14519694C4semidirect
35. C2×#14519693C4semidirect
36. C2×#14519693C4semidirect
37. #100×D61C4semidirect
39. C2×#100×C61C4semidirect
108. #14519694C2×C4semidirect
109. #14519693C2×C4semidirect
110. #14519693C2×C4semidirect
114. #100×C61C2×C4semidirect
367. C2×C61#1931semidirect
372. D61#1931semidirect
399. C2×#100#6923semidirect
406. C61C2×#1931semidirect
479. #100C2×#6923semidirect
731. C2#21461905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407732
C2×#168407542
C22×#145198392
C2×#168407282
#214619052
C2×#168406412
C2×#168406372
C2×#100×D612
C2×#193161