Finite Group Databasebeta

← C2×#21446991 #29707437

Subgroups — C2×#21446991 #29707437

Order 15616.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840319C211yesmaximal, characteristic, complemented
2C2×#16839779C211yesmaximal, characteristic
3C2×#16839736C211yesmaximal, characteristic
4#21446991C218yesmaximal, direct product factor
5C2×#16839534C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C2×#16839519C211yesmaximal, characteristic, complemented
8C22×#104×C61C211yesmaximal, characteristic
9C22×#11758194C2211yescharacteristic
10#16840319—22no—
11#16840319—22no—
12#16840319—22no—
13#16840319C2214yescomplemented
14C2×#14519777—21no—
15C2×#14519769—21no—
16C2×#14519756—22no—
17C2×C4×Dic122—22no—
18C2×#14519736C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839779—22no—
22#16839779C2214yes—
23C2×#14519704—22no—
24#16839736—22no—
25#16839736C2214yes—
26C2×#14519692—22no—
27#16839534C2214yescomplemented
28#16839522C2214yescomplemented
29#16839519C2214yescomplemented
30C22×#41×C61C2211yescharacteristic
31C22×M16×C61C2211yescharacteristic
32C22×C42×C61C2211yescharacteristic
33C2×#104×C61—21no—
34C2×#104×C61—21no—
35C2×#104×C61—22no—
36C2×#104×C61C2214yes—
37C22×Dic122—22no—
38C2×#11758194—21no—
39C2×#11758194—21no—
40C2×#11758194—21no—
41C2×#11758194—21no—
42C2×#11758194—21no—
43C2×#11758194C2312yes—
44C22×#92418—21no—
45#14519777—24no—
46#14519777—24no—
47#14519769—24no—
48#14519769—24no—
49#14519756—28no—
50#14519756—28no—
51C4×Dic122—28no—
52C4×Dic122—28no—
53#14519736—21no—
54#14519736—21no—
55#14519736—21no—
56#14519736—21no—
57#14519736—21no—
58#14519736—21no—
59#14519736—21no—
60#14519736D412yes—
61#14519736D412yes—
62#14519736C2312yes—
63#14519736C2312yes—
64#14519736C2312yes—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×#11758196—24no—
70C2×C22⋊Dic61—21no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61D412yes—
73C2×C4×Dic61—21no—
74C2×C4×Dic61—21no—
75C2×C4×Dic61D412yes—
76#14519704—28no—
77#14519692—28no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—21no—
84C2×#41×C61—21no—
85C2×#41×C61—21no—
86C2×#41×C61—21no—
87C2×#41×C61—21no—
88C2×#41×C61Q812yescomplemented
89C2×#41×C61C2312yes—
90C22×Q8×C61Q811yescharacteristic, complemented
91C22×D4×C61—21no—
92C22×D4×C61Q811yescharacteristic, complemented
93C23×C4×C61—21no—
94C23×C4×C61—21no—
95C23×C4×C61C2311yescharacteristic
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C2×M16×C61—21no—
99C2×M16×C61—21no—
100C2×M16×C61—21no—
101C2×M16×C61C2312yes—
102C22×C8×C61—21no—
103C2×C42×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61—21no—
106C2×C42×C61D411yescharacteristic
107C2×C42×C61D411yescharacteristic
108C2×C42×C61D412yes—
109C2×C42×C61C2312yes—
110#104×C61—24no—
111#104×C61—24no—
112C24×C61—21no—
113C24×C61C2×D411yescharacteristic
114#41×C61—22no—
115#41×C61—22no—
116#41×C61—22no—
117#41×C61—22no—
118#41×C61—22no—
119#41×C61—22no—
120#41×C61—22no—
121#41×C61—22no—
122#41×C61—41no—
123#41×C61—41no—
124#41×C61—41no—
125#41×C61—41no—
126#41×C61—41no—
127#41×C61—41no—
128#41×C61—41no—
129#41×C61—41no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61C2×Q812yescomplemented
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—41no—
144C2×D4×C61—41no—
145C2×D4×C61—41no—
146C2×D4×C61—41no—
147C2×D4×C61C2×Q812yescomplemented
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—44no—
156C22×C4×C61—41no—
157C22×C4×C61—41no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×Q811yescharacteristic
166C22×C4×C61C2×Q811yescharacteristic
167C22×C4×C61#4111yescharacteristic
168C22×C4×C61#4111yescharacteristic
169C22×C4×C61#4111yescharacteristic
170C22×C4×C61#4111yescharacteristic
171C22×C4×C61#4111yescharacteristic
172C22×C4×C61#4111yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—41no—
177C2×Dic122—28no—
178C2×Dic122—48no—
179M16×C61—22no—
180M16×C61—22no—
181M16×C61—41no—
182M16×C61—41no—
183C2×C8×C61—22no—
184C2×C8×C61—41no—
185C2×C8×C61—41no—
186C42×C61—22no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—22no—
190C42×C61C2×D412yes—
191C42×C61C2×D412yes—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—41no—
197C22⋊Dic61C2×D414yes—
198C4⋊Dic61—28no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204C4⋊Dic61—41no—
205#11758196—216no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—41no—
211C4×Dic61C2×D414yes—
212#11758194—22no—
213#11758194—22no—
214#11758194—41no—
215#11758194—41no—
216C2×#92418—22no—
217C2×#92418—41no—
218C2×#92418—41no—
219C23×C61—22no—
220C23×C61—42no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—82no—
224C23×C61#12011yescharacteristic
225C23×C61#12011yescharacteristic
226C23×C61C22⋊Q811yescharacteristic
227C23×C61C22⋊Q811yescharacteristic
228C23×C61#12411yescharacteristic
229C23×C61#12411yescharacteristic
230C23×C61C22×D411yescharacteristic
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—41no—
234Q8×C61—41no—
235D4×C61—22no—
236D4×C61—22no—
237D4×C61—42no—
238D4×C61—42no—
239D4×C61—42no—
240D4×C61—42no—
241D4×C61—41no—
242D4×C61—41no—
243C2×C4×C61—24no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—44no—
248C2×C4×C61—44no—
249C2×C4×C61—42no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61#12011yescharacteristic
257C2×C4×C61#12011yescharacteristic
258C2×C4×C61C22⋊Q811yescharacteristic
259C2×C4×C61C22⋊Q811yescharacteristic
260C2×C4×C61C22⋊Q811yescharacteristic
261C2×C4×C61C22⋊Q811yescharacteristic
262C2×C4×C61C22⋊Q811yescharacteristic
263C2×C4×C61C22⋊Q811yescharacteristic
264C2×C4×C61C22⋊Q811yescharacteristic
265C2×C4×C61C22⋊Q811yescharacteristic
266C2×C4×C61C22⋊Q811yescharacteristic
267C2×C4×C61C22⋊Q811yescharacteristic
268C2×C4×C61#12411yescharacteristic
269C2×C4×C61#12411yescharacteristic
270C2×C4×C61#12411yescharacteristic
271C2×C4×C61#12411yescharacteristic
272C2×C4×C61#12411yescharacteristic
273C2×C4×C61#12411yescharacteristic
274C2×C4×C61#12411yescharacteristic
275C2×C4×C61#12411yescharacteristic
276C2×C4×C61#12411yescharacteristic
277C2×C4×C61#12411yescharacteristic
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C22×Q811yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×Dic61—24no—
285C2×Dic61—24no—
286C2×Dic61—44no—
287C2×Dic61—44no—
288C2×Dic61—42no—
289C2×Dic61—82no—
290Dic122—416no—
291C8×C61—42no—
292#92418—42no—
293C2×#2031—611nomaximal, Sylow
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—42no—
302C22×C61—82no—
303C22×C61—82no—
304C22×C61—82no—
305C22×C61#39311yescharacteristic
306C22×C61#39311yescharacteristic
307C22×C61#39311yescharacteristic
308C22×C61#39311yescharacteristic
309C22×C61C2×#12011yescharacteristic
310C22×C61C2×C22⋊Q811yescharacteristic
311C22×C61C2×#12411yescharacteristic
312C4×C61—24no—
313C4×C61—42no—
314C4×C61—42no—
315C4×C61#39311yescharacteristic
316C4×C61#39311yescharacteristic
317C4×C61#39311yescharacteristic
318C4×C61#39311yescharacteristic
319C4×C61C2×C22⋊Q811yescharacteristic
320C4×C61C2×C22⋊Q811yescharacteristic
321C4×C61C2×#12411yescharacteristic
322C4×C61C2×#12411yescharacteristic
323Dic61—44no—
324Dic61—44no—
325Dic61—82no—
326C2×#533—611no—
327C2×#421—611no—
328C22×#104D6111yescharacteristic
329C2×#410—611no—
330#2031—618no—
331C2×#344—611no—
332C2×#339—611no—
333C2×H(3,ℤ/4)—611no—
334C2×C61—21no—
335C2×C61—21no—
336C2×C61—21no—
337C2×C61—21no—
338C2×C61—21no—
339C2×C61—21no—
340C2×C61—82no—
341C2×C61#203112yescomplemented
342C2×C61C2×#39311yescharacteristic
343C22×#41C2×D6111yescharacteristic
344C22×M16—611no—
345C22×M16C2×D6111yescharacteristic
346#533—614no—
347#533—1222no—
348#533—1222no—
349#533—1222no—
350C2×C4⋊Q8—1221no—
351C2×#125—1221no—
352C2×C22⋊Q8—1222no—
353C2×C4×Q8—1222no—
354C2×#117—611no—
355C2×#117—611no—
356C2×#117—611no—
357C22×C42C2×D6111yescharacteristic
358#421—614no—
359#421—1222no—
360C2×#104—21no—
361C2×#104—21no—
362C2×#104—22no—
363C2×#104—1222no—
364C2×#104C2×D6114yes—
365#410—614no—
366#410—1222no—
367C2×#99—1222no—
368#344—614no—
369#339—614no—
370H(3,ℤ/4)—614no—
371C61C2×#203111yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41Dic12212yescomplemented
383C2×#41C22×D6112yes—
384C22×Q8—1222no—
385C22×Q8Dic12211yescharacteristic, complemented
386C22×D4—21no—
387C22×D4Dic12211yescharacteristic, complemented
388C23×C4—21no—
389C23×C4—21no—
390C23×C4C22×D6111yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—612no—
397C2×M16—1221no—
398C2×M16—1221no—
399C2×M16—1221no—
400C2×M16—1221no—
401C2×M16—1221no—
402C2×M16C22×D6112yes—
403C22×C8—21no—
404C22×C8—1221no—
405C4⋊Q8—1224no—
406C4⋊Q8—1224no—
407#125—1224no—
408#125—1224no—
409C22⋊Q8—1228no—
410C22⋊Q8—1228no—
411C4×Q8—1228no—
412C4×Q8—1228no—
413#117—612no—
414#117—612no—
415#117—612no—
416#117—612no—
417#117—612no—
418#117—1221no—
419#117—1221no—
420#117—1221no—
421#117—1221no—
422#117—1221no—
423#117—1221no—
424#117—1221no—
425C2×C4⋊C4—1224no—
426C2×C4⋊C4—1222no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C22⋊C4—612no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—612no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42C22⋊D6111yescharacteristic
440C2×C42C22⋊D6111yescharacteristic
441C2×C42C22⋊D6112yes—
442C2×C42C22×D6112yes—
443#104—24no—
444#104—24no—
445#104—1228no—
446#99—1228no—
447C24—21no—
448C24D4×D6111yescharacteristic
449#41—22no—
450#41—22no—
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—41no—
458#41—41no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—1228no—
471C2×Q8—2448no—
472C2×Q8C2×Dic12212yescomplemented
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4C2×Dic12212yescomplemented
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—44no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—2441no—
500C22×C4C2×Dic12211yescharacteristic
501C22×C4C2×Dic12211yescharacteristic
502C22×C4#1175822211yescharacteristic
503C22×C4#1175822211yescharacteristic
504C22×C4D4×D6111yescharacteristic
505C22×C4D4×D6111yescharacteristic
506C22×C4D4×D6111yescharacteristic
507C22×C4#1175822411yescharacteristic
508C22×C4#1175822411yescharacteristic
509C22×C4#1175822411yescharacteristic
510C22×C4#1175822411yescharacteristic
511C22×C4C2×C22⋊D6111yescharacteristic
512C22×C4C2×C22⋊D6111yescharacteristic
513C22×C4C23×D6111yescharacteristic
514M16—22no—
515M16—22no—
516M16—41no—
517M16—41no—
518M16—1222no—
519M16—1222no—
520M16—2441no—
521M16—2441no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—1222no—
526C2×C8—2441no—
527C2×C8—2441no—
528C4⋊C4—12216no—
529C4⋊C4—1228no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1222no—
533C4⋊C4—1222no—
534C4⋊C4—1222no—
535C4⋊C4—2441no—
536C22⋊C4—614no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—2441no—
542C42—22no—
543C42—22no—
544C42—21no—
545C42—21no—
546C42—614no—
547C42—1222no—
548C42—1222no—
549C42—1222no—
550C42—1222no—
551C42—2441no—
552C42C2×C22⋊D6112yes—
553C42C2×C22⋊D6112yes—
554C23—22no—
555C23—42no—
556C23—41no—
557C23—41no—
558C23—82no—
559C23#1451974511yescharacteristic
560C23#1451974511yescharacteristic
561C23#1451975411yescharacteristic
562C23#1451975411yescharacteristic
563C23#1451976311yescharacteristic
564C23#1451976311yescharacteristic
565C23C2×D4×D6111yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—41no—
569Q8—41no—
570Q8—24416no—
571D4—22no—
572D4—22no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—42no—
577D4—41no—
578D4—41no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—4882no—
595C2×C4—2442no—
596C2×C4—2444no—
597C2×C4—2444no—
598C2×C4#1451974511yescharacteristic
599C2×C4#1451974511yescharacteristic
600C2×C4#1451975411yescharacteristic
601C2×C4#1451975411yescharacteristic
602C2×C4#1451975411yescharacteristic
603C2×C4#1451975411yescharacteristic
604C2×C4#1451975411yescharacteristic
605C2×C4#1451975411yescharacteristic
606C2×C4#1451975611yescharacteristic
607C2×C4#1451975611yescharacteristic
608C2×C4#1451975611yescharacteristic
609C2×C4#1451975611yescharacteristic
610C2×C4#1451976311yescharacteristic
611C2×C4#1451976311yescharacteristic
612C2×C4#1451976311yescharacteristic
613C2×C4#1451976311yescharacteristic
614C2×C4#1451976311yescharacteristic
615C2×C4#1451976311yescharacteristic
616C2×C4#1451976411yescharacteristic
617C2×C4#1451976411yescharacteristic
618C2×C4#1451976411yescharacteristic
619C2×C4#1451976411yescharacteristic
620C2×C4C2×D4×D6111yescharacteristic
621C2×C4C22×C22⋊D6111yescharacteristic
622C2×C4C22×Dic12211yescharacteristic
623C2×C4C2×#1175822411yescharacteristic
624C2×C4C2×#1175822411yescharacteristic
625C2×C4C2×#1175822211yescharacteristic
626C8—42no—
627C8—2442no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—42no—
636C22—82no—
637C22—82no—
638C22—82no—
639C22#1683967411yescharacteristic
640C22#1683967411yescharacteristic
641C22#1683967411yescharacteristic
642C22#1683967411yescharacteristic
643C22C2×#1451974511yescharacteristic
644C22C2×#1451975411yescharacteristic
645C22C2×#1451976311yescharacteristic
646C4—24no—
647C4—42no—
648C4—42no—
649C4—4882no—
650C4—2444no—
651C4—2444no—
652C4#1683967411yescharacteristic
653C4#1683967411yescharacteristic
654C4#1683967411yescharacteristic
655C4#1683967411yescharacteristic
656C4C2×#1451975411yescharacteristic
657C4C2×#1451975611yescharacteristic
658C4C2×#1451976311yescharacteristic
659C4C2×#1451976411yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—82no—
667C2#2144699112yesdirect product factor
668C2C2×#1683967411yescharacteristic
subgroupG/H
centerC2×C4#14519763
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#104×C61C2
socleC22×C61#393
prime radicalC22×#41×C61C22
hypercenterC22×#104D61
hypocenterC61C2×#2031
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C2×#16840319C2semidirect
4. #21446991C2direct (N × H)
5. C2×#16839534C2semidirect
6. C2×#16839522C2semidirect
7. C2×#16839519C2semidirect
13. #16840319C22semidirect
27. #16839534C22semidirect
28. #16839522C22semidirect
29. #16839519C22semidirect
88. C2×#41×C61Q8semidirect
90. C22×Q8×C61Q8semidirect
92. C22×D4×C61Q8semidirect
135. C2×Q8×C61C2×Q8semidirect
147. C2×D4×C61C2×Q8semidirect
341. C2×C61#2031semidirect
371. C61C2×#2031semidirect
382. C2×#41Dic122semidirect
385. C22×Q8Dic122semidirect
387. C22×D4Dic122semidirect
472. C2×Q8C2×Dic122semidirect
484. C2×D4C2×Dic122semidirect
667. C2#21446991direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403192
C2×#168397792
C2×#168397362
#214469912
C2×#168395342
C2×#168395222
C2×#168395192
C22×#104×C612
C2×#203161