Finite Group Databasebeta

← C2×#21446828 #29706810

Subgroups — C2×#21446828 #29706810

Order 15616.

2182 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758202C211yesmaximal, characteristic, complemented
2C22×#14519757C211yesmaximal, characteristic
3C22×#14519753C211yesmaximal, characteristic
4C22×#14519702C211yesmaximal, characteristic, complemented
5C22×#14519689C211yesmaximal, characteristic
6#21446828C218yesmaximal, direct product factor
7C2×#16839524C211yesmaximal, characteristic, complemented
8C22×#103×C61C211yesmaximal, characteristic, complemented
9C23×Dic122C2211yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C22×#11758202—24no—
12C22×#11758202—24no—
13C22×#11758202—24no—
14C22×#11758202C2214yescomplemented
15C23×#92418C2211yescharacteristic
16C2×#14519757—24no—
17C2×#14519757—24no—
18C2×#14519757—22no—
19C2×#14519757C2214yes—
20C2×#14519753—24no—
21C2×#14519753—24no—
22C2×#14519753—22no—
23C2×#14519753C2214yes—
24C22×C4⋊Dic61—21no—
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196—21no—
27C22×#11758198—21no—
28C22×#11758198—21no—
29C2×#14519702—24no—
30C2×#14519702C2214yescomplemented
31C2×#14519689—24no—
32C2×#14519689C2214yes—
33#16839524C2214yescomplemented
34C23×Q8×C61C2211yescharacteristic
35C23×C8×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C2×#103×C61—24no—
38C2×#103×C61C2214yescomplemented
39C24×D61D411yescharacteristic
40C22×Dic122—22no—
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122—22no—
44C22×Dic122—21no—
45C22×Dic122—22no—
46C22×Dic122D414yes—
47C22×Dic122C2312yes—
48C23×Dic61—21no—
49C23×Dic61—21no—
50C23×Dic61D411yescharacteristic
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—22no—
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61D412yes—
58C22×C4×D61C2312yes—
59C2×#11758202—232no—
60C2×#11758202—28no—
61C2×#11758202—28no—
62C2×#11758202—28no—
63C22×#92418—22no—
64C22×#92418—22no—
65C22×#92418D414yes—
66C22×#92418C2312yes—
67#14519757—216no—
68#14519757—28no—
69#14519757—28no—
70#14519753—216no—
71#14519753—28no—
72#14519753—28no—
73C2×C4⋊Dic61—28no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—24no—
77C2×C4⋊Dic61D414yes—
78C2×C4⋊Dic61C2312yes—
79C2×#11758196—28no—
80C2×#11758196—24no—
81C2×#11758198—28no—
82C2×#11758198—28no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85#14519702—28no—
86#14519689—28no—
87C22×Q8×C61—22no—
88C22×Q8×C61—21no—
89C22×Q8×C61—22no—
90C22×Q8×C61—22no—
91C22×Q8×C61—22no—
92C22×Q8×C61—22no—
93C22×Q8×C61D414yes—
94C22×Q8×C61C2312yes—
95C23×C4×C61—21no—
96C23×C4×C61—21no—
97C23×C4×C61C2311yescharacteristic
98C22×C8×C61—22no—
99C22×C8×C61—22no—
100C22×C8×C61—22no—
101C22×C8×C61C2312yes—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61D414yes—
105C2×C4⋊C4×C61C2312yes—
106#103×C61—28no—
107C24×C61C2×D411yescharacteristic
108C23×D61—22no—
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61Q1614yescomplemented
115C23×D61C2×D412yes—
116C2×Q8×C61—24no—
117C2×Q8×C61—22no—
118C2×Q8×C61—28no—
119C2×Q8×C61—28no—
120C2×Q8×C61—22no—
121C2×Q8×C61—22no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—42no—
125C2×Q8×C61—42no—
126C2×Q8×C61—44no—
127C2×Q8×C61—44no—
128C2×Q8×C61C2×D414yes—
129C22×C4×C61—24no—
130C22×C4×C61—24no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61—42no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2×D412yes—
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2×D412yes—
143C22×C4×C61#4112yes—
144C22×C4×C61C2411yescharacteristic
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—24no—
148C22×Dic61—24no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—42no—
153C22×Dic61—42no—
154C22×Dic61—42no—
155C22×Dic61—42no—
156C22×Dic61C2×D412yes—
157C2×C4×D61—24no—
158C2×C4×D61—24no—
159C2×C4×D61—24no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61—44no—
169C2×C4×D61—44no—
170C2×Dic122—28no—
171C2×Dic122—28no—
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—24no—
177C2×Dic122—22no—
178C2×Dic122—42no—
179C2×Dic122—44no—
180C2×Dic122—42no—
181C2×Dic122—44no—
182C2×Dic122C2×D414yes—
183C2×C8×C61—22no—
184C2×C8×C61—22no—
185C2×C8×C61—22no—
186C2×C8×C61—44no—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61C2×D414yes—
190#11758202—232no—
191#11758198—216no—
192#11758198—216no—
193C4⋊Dic61—216no—
194C4⋊Dic61—24no—
195C4⋊Dic61—22no—
196C4⋊Dic61C2×D414yes—
197#11758196—216no—
198C2×#92418—28no—
199C2×#92418—22no—
200C2×#92418—22no—
201C2×#92418C2×D414yes—
202C23×C61#12012yes—
203C23×C61#12012yes—
204C23×C61#12112yes—
205C23×C61C2×Q1612yes—
206C23×C61#13512yes—
207C23×C61#13712yes—
208C23×C61#13712yes—
209C23×C61C22×D411yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—28no—
217C22×D61—28no—
218C22×D61—28no—
219C22×D61—44no—
220C22×D61—44no—
221C22×D61—44no—
222C22×D61—44no—
223C22×D61C2×Q1614yescomplemented
224Q8×C61—24no—
225Q8×C61—24no—
226Q8×C61—42no—
227Q8×C61—42no—
228Q8×C61—48no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—48no—
236C2×C4×C61—48no—
237C2×C4×C61#12014yes—
238C2×C4×C61#12012yes—
239C2×C4×C61#12012yes—
240C2×C4×C61#12114yes—
241C2×C4×C61#12114yes—
242C2×C4×C61#12112yes—
243C2×C4×C61#12714yes—
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×Dic61—22no—
251C2×Dic61—24no—
252C2×Dic61—22no—
253C2×Dic61—24no—
254C2×Dic61—22no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—48no—
260C2×Dic61—44no—
261C2×Dic61—48no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—48no—
267Dic122—24no—
268Dic122—24no—
269Dic122—42no—
270Dic122—42no—
271Dic122—48no—
272C8×C61—42no—
273#92418—24no—
274C2×#2001—611nomaximal, Sylow
275C22×C61#39214yes—
276C22×C61#45114yes—
277C22×C61#45114yes—
278C22×C61#45214yes—
279C22×C61#45214yes—
280C22×C61#46714yes—
281C22×C61#47014yes—
282C22×C61C2×#12011yescharacteristic
283C22×C61C2×#12011yescharacteristic
284C22×C61C2×#12111yescharacteristic
285C22×C61C22×Q1611yescharacteristic
286C22×C61C2×#13511yescharacteristic
287C22×C61C2×#13711yescharacteristic
288C22×C61C2×#13711yescharacteristic
289C2×D61—24no—
290C2×D61—24no—
291C2×D61—24no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—416no—
296C2×D61—42no—
297C4×C61—44no—
298C4×C61—44no—
299C4×C61#39214yes—
300C4×C61C2×#12011yescharacteristic
301C4×C61C2×#12111yescharacteristic
302C4×C61C2×#12111yescharacteristic
303C4×C61C2×#12711yescharacteristic
304Dic61—44no—
305Dic61—42no—
306Dic61—44no—
307C23×Q16—611no—
308C22×C22⋊Q8—611no—
309C22×C22⋊Q8—611no—
310C22×#103—611no—
311C22×#103D6111yescharacteristic, complemented
312C22×C22⋊C8—611no—
313#2001—618no—
314C2×#340—611no—
315C2×C61#200118yescomplemented
316C2×C61C2×#39211yescharacteristic
317C2×C61C2×#45111yescharacteristic
318C2×C61C2×#45111yescharacteristic
319C2×C61C2×#45211yescharacteristic
320C2×C61C2×#45211yescharacteristic
321C2×C61C2×#46711yescharacteristic
322C2×C61C2×#47011yescharacteristic
323D61—44no—
324C23×Q8—611no—
325C23×Q8C2×D6111yescharacteristic
326C24×C4—611no—
327C22×Q16—614no—
328C22×Q16—1224no—
329C22×Q16—1224no—
330C22×Q16—1224no—
331C23×C8—611no—
332C23×C8C2×D6111yescharacteristic
333C2×C22⋊Q8—614no—
334C2×C22⋊Q8—614no—
335C2×C22⋊Q8—1222no—
336C2×C22⋊Q8—1224no—
337C2×C22⋊Q8—1224no—
338C2×C22⋊Q8—1222no—
339C2×C22⋊Q8—1224no—
340C2×C22⋊Q8—1224no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—1221no—
343C22×C4⋊C4—1221no—
344C22×C4⋊C4C2×D6111yescharacteristic
345C22×C22⋊C4—1221no—
346C22×C22⋊C4—1221no—
347C2×#103—24no—
348C2×#103—614no—
349C2×#103—1224no—
350C2×#103C2×D6114yescomplemented
351C2×C22⋊C8—614no—
352C2×C22⋊C8—1224no—
353#340—614no—
354C61C2×#200111yescharacteristic, complemented, Sylow
355C25—611no—
356C22×Q8—21no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—614no—
363C22×Q8—612no—
364C22×Q8—1221no—
365C22×Q8—1222no—
366C22×Q8—1222no—
367C22×Q8—1222no—
368C22×Q8—1222no—
369C22×Q8—1222no—
370C22×Q8D24414yes—
371C22×Q8C22×D6112yes—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—611no—
375C23×C4—612no—
376C23×C4—612no—
377C23×C4—1221no—
378C23×C4—1221no—
379C23×C4—1222no—
380C23×C4—1222no—
381C23×C4—1222no—
382C23×C4—1222no—
383C23×C4—1222no—
384C23×C4—1222no—
385C23×C4C22×D6111yescharacteristic
386C2×Q16—1228no—
387C2×Q16—1228no—
388C2×Q16—12232no—
389C2×Q16—1228no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—614no—
394C22×C8—612no—
395C22×C8—1222no—
396C22×C8—1222no—
397C22×C8C22×D6112yes—
398C22⋊Q8—1228no—
399C22⋊Q8—12216no—
400C22⋊Q8—1228no—
401C22⋊Q8—12216no—
402C22⋊Q8—1228no—
403C22⋊Q8—1228no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—614no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4—1224no—
409C2×C4⋊C4—1224no—
410C2×C4⋊C4—1228no—
411C2×C4⋊C4—1228no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C22⋊D6114yes—
415C2×C4⋊C4C22×D6112yes—
416C2×C22⋊C4—1224no—
417C2×C22⋊C4—1224no—
418C2×C22⋊C4—1228no—
419C2×C22⋊C4—1228no—
420#103—28no—
421#103—1228no—
422C22⋊C8—1228no—
423C24—612no—
424C24—614no—
425C24—1222no—
426C24—1222no—
427C24—1222no—
428C24—1222no—
429C24—1222no—
430C24—1222no—
431C24D4×D6111yescharacteristic
432C2×Q8—22no—
433C2×Q8—24no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—614no—
445C2×Q8—1222no—
446C2×Q8—1224no—
447C2×Q8—1222no—
448C2×Q8—1222no—
449C2×Q8—1222no—
450C2×Q8—1222no—
451C2×Q8—1228no—
452C2×Q8—1228no—
453C2×Q8—2442no—
454C2×Q8—2442no—
455C2×Q8—2444no—
456C2×Q8—2444no—
457C2×Q8C2×D24414yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—612no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1224no—
470C22×C4—1222no—
471C22×C4—1224no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1224no—
481C22×C4—1224no—
482C22×C4—1224no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4—2444no—
488C22×C4—2444no—
489C22×C4—2444no—
490C22×C4—2444no—
491C22×C4C2×D24412yes—
492C22×C4#1175822212yes—
493C22×C4D4×D6112yes—
494C22×C4D4×D6112yes—
495C22×C4D4×D6112yes—
496C22×C4D4×D6111yescharacteristic
497C22×C4C2×C22⋊D6112yes—
498C22×C4C23×D6111yescharacteristic
499Q16—12232no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—44no—
504C2×C8—614no—
505C2×C8—1222no—
506C2×C8—1222no—
507C2×C8—1228no—
508C4⋊C4—22no—
509C4⋊C4—24no—
510C4⋊C4—614no—
511C4⋊C4—12216no—
512C4⋊C4—12216no—
513C4⋊C4—1222no—
514C4⋊C4—1224no—
515C4⋊C4C2×C22⋊D6114yes—
516C22⋊C4—12216no—
517C22⋊C4—12216no—
518C23—614no—
519C23—1222no—
520C23—1222no—
521C23—1222no—
522C23—1228no—
523C23—1222no—
524C23—1222no—
525C23—1222no—
526C23—1228no—
527C23—1228no—
528C23—2444no—
529C23—2444no—
530C23—2444no—
531C23—2444no—
532C23#1451974512yes—
533C23#1451974712yes—
534C23#1451975012yes—
535C23Q16×D6112yes—
536C23#1451979812yes—
537C23#1451980612yes—
538C23#1451980912yes—
539C23C2×D4×D6111yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—42no—
543Q8—42no—
544Q8—48no—
545Q8—1224no—
546Q8—1224no—
547Q8—2442no—
548Q8—2442no—
549Q8—2448no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—48no—
557C2×C4—48no—
558C2×C4—1224no—
559C2×C4—1222no—
560C2×C4—1224no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2444no—
568C2×C4—2448no—
569C2×C4—2448no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2448no—
575C2×C4#1451974512yes—
576C2×C4#1451974714yes—
577C2×C4#1451974712yes—
578C2×C4#1451975014yes—
579C2×C4#1451975012yes—
580C2×C4#1451975114yes—
581C2×C4#1451977314yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4C2×D4×D6111yescharacteristic
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4C22×C22⋊D6111yescharacteristic
586C2×C4C22×D24411yescharacteristic
587C2×C4C2×#1175822211yescharacteristic
588C8—42no—
589C8—1224no—
590C22—1224no—
591C22—1224no—
592C22—1224no—
593C22—2442no—
594C22—2442no—
595C22—24416no—
596C22—2442no—
597C22—2442no—
598C22#1683967114yes—
599C22#1683991614yes—
600C22#1683991914yes—
601C22#1683992114yes—
602C22#1683992714yes—
603C22#1684000214yes—
604C22#1684001914yes—
605C22C2×#1451974511yescharacteristic
606C22C2×#1451974711yescharacteristic
607C22C2×#1451975011yescharacteristic
608C22C2×Q16×D6111yescharacteristic
609C22C2×#1451979811yescharacteristic
610C22C2×#1451980611yescharacteristic
611C22C2×#1451980911yescharacteristic
612C4—44no—
613C4—44no—
614C4—2442no—
615C4—2444no—
616C4—2444no—
617C4#1683967114yes—
618C4C2×#1451974711yescharacteristic
619C4C2×#1451975011yescharacteristic
620C4C2×#1451975111yescharacteristic
621C4C2×#1451977311yescharacteristic
622C2—2444no—
623C2#2144682818yesdirect product factor
624C2C2×#1683967111yescharacteristic
625C2C2×#1683991611yescharacteristic
626C2C2×#1683991911yescharacteristic
627C2C2×#1683992111yescharacteristic
628C2C2×#1683992711yescharacteristic
629C2C2×#1684000211yescharacteristic
630C2C2×#1684001911yescharacteristic
subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#103×C61C2
socleC24×C61C2×D4
prime radicalC24×D61D4
hypercenterC22×#103D61
hypocenterC61C2×#2001
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C23×#11758202C2semidirect
4. C22×#14519702C2semidirect
6. #21446828C2direct (N × H)
7. C2×#16839524C2semidirect
8. C22×#103×C61C2semidirect
14. C22×#11758202C22semidirect
30. C2×#14519702C22semidirect
33. #16839524C22semidirect
38. C2×#103×C61C22semidirect
114. C23×D61Q16semidirect
223. C22×D61C2×Q16semidirect
311. C22×#103D61semidirect
315. C2×C61#2001semidirect
350. C2×#103C2×D61semidirect
354. C61C2×#2001semidirect
623. C2#21446828direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117582022
C22×#145197572
C22×#145197532
C22×#145197022
C22×#145196892
#214468282
C2×#168395242
C22×#103×C612
C2×#200161