Finite Group Databasebeta

← C2×#21444337 #29647132

Subgroups — C2×#21444337 #29647132

Order 15616.

1554 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×C22⋊Q8×D61C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic
3C2×#16839609C211yesmaximal, characteristic
4#21444337C218yesmaximal, direct product factor
5C2×#16839500C211yesmaximal, characteristic, complemented
6C2×#16839499C211yesmaximal, characteristic, complemented
7C2×#16839498C211yesmaximal, characteristic, complemented
8C2×C61×#328C211yesmaximal, characteristic, complemented
9C22×Q8×D61C411yescharacteristic, complemented
10C23×C4×D61C2211yescharacteristic
11C22×#11758189—21no—
12C2×#14519757C411yescharacteristic, complemented
13C2×#14519756C2211yescharacteristic
14C2×#14519755—21no—
15C2×#14519754—21no—
16C2×#14519753C411yescharacteristic, complemented
17C22⋊Q8×D61—22no—
18C22⋊Q8×D61—22no—
19C22⋊Q8×D61C414yescomplemented
20C22⋊Q8×D61C2214yes—
21C2×C4⋊C4×D61—21no—
22C2×C4⋊C4×D61C411yescharacteristic, complemented
23C22×#11758198—21no—
24C2×C22⋊C4×D61—21no—
25C22×C4×Dic61—21no—
26#16839724—22no—
27#16839724C2214yes—
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519689—21no—
30#16839609—22no—
31#16839609C2214yes—
32C2×#14519684C2211yescharacteristic
33#16839500C2214yescomplemented
34#16839499C2214yescomplemented
35#16839498C2214yescomplemented
36C2×C22⋊Q8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C61×#328C2214yescomplemented
40C24×D61D411yescharacteristic
41C22×Dic122—21no—
42C22×Dic122C2×C411yescharacteristic
43C2×Q8×D61—22no—
44C2×Q8×D61—44no—
45C2×Q8×D61C2×C414yescomplemented
46C23×Dic61—21no—
47C23×Dic61D411yescharacteristic
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61—44no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C412yes—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D412yes—
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D412yes—
58C22×C4×D61C2312yes—
59C2×#11758189—24no—
60C2×#11758189—44no—
61C22×#92418—21no—
62#14519757—22no—
63#14519757C2×C414yescomplemented
64#14519756—21no—
65#14519756—21no—
66#14519756C2×C412yes—
67#14519756C2312yes—
68#14519755—24no—
69#14519755—24no—
70#14519754—24no—
71#14519754—24no—
72#14519753—22no—
73#14519753C2×C414yescomplemented
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61—22no—
81C4⋊C4×D61—24no—
82C4⋊C4×D61C2×C414yescomplemented
83C2×C22⋊Dic61—21no—
84C2×#11758198—28no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—24no—
88C22⋊C4×D61—24no—
89C22⋊C4×D61—24no—
90C2×C4×Dic61—24no—
91C2×C4×Dic61—44no—
92C22⋊#92418—21no—
93C22⋊#92418C2312yes—
94#14519689—24no—
95#14519684—21no—
96#14519684C2312yes—
97C22×Q8×C61C2×C411yescharacteristic
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100C22×C8×C61—21no—
101C22⋊Q8×C61—21no—
102C22⋊Q8×C61—21no—
103C22⋊Q8×C61C2×C412yes—
104C22⋊Q8×C61C2312yes—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61C2×C411yescharacteristic
107C2×C22⋊C4×C61—21no—
108C22⋊C8×C61—21no—
109C22⋊C8×C61C2312yes—
110#95×C61—21no—
111#95×C61C2312yes—
112C24×C61C2×D411yescharacteristic
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—24no—
116C23×D61—42no—
117C23×D61C22⋊C411yescharacteristic
118C23×D61C22⋊C412yes—
119C23×D61C22⋊C411yescharacteristic
120C23×D61C2×D412yes—
121C2×Q8×C61—21no—
122C2×Q8×C61—42no—
123C2×Q8×C61C22×C412yes—
124C22×C4×C61—24no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C22×Dic61—24no—
138C22×Dic61—24no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—22no—
142C22×Dic61—42no—
143C22×Dic61—42no—
144C22×Dic61C22⋊C411yescharacteristic
145C22×Dic61C22⋊C412yes—
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C2×D412yes—
148Q8×D61—48no—
149Q8×D61—48no—
150C2×C4×D61—24no—
151C2×C4×D61—24no—
152C2×C4×D61—24no—
153C2×C4×D61—24no—
154C2×C4×D61—44no—
155C2×C4×D61—44no—
156C2×C4×D61—44no—
157C2×C4×D61—44no—
158C2×C4×D61—42no—
159C2×C4×D61—42no—
160C2×C4×D61—44no—
161C2×C4×D61—44no—
162C2×C4×D61C22⋊C412yes—
163C2×C4×D61C22⋊C412yes—
164C2×C4×D61C22⋊C412yes—
165C2×C4×D61C22⋊C412yes—
166C2×C4×D61C22×C412yes—
167C2×C4×D61C22×C412yes—
168C2×C4×D61C2×D412yes—
169C2×C4×D61C2×D412yes—
170C2×Dic122—21no—
171C2×Dic122—24no—
172C2×Dic122—44no—
173C2×Dic122—42no—
174C2×Dic122C22×C412yes—
175C2×C8×C61—22no—
176C2×C8×C61—42no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61C22×C412yes—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185#11758198—216no—
186#11758198—24no—
187#11758198—24no—
188C4⋊Dic61—21no—
189C4⋊Dic61—24no—
190C4⋊Dic61C22×C412yes—
191#11758196—22no—
192#11758196—22no—
193#11758196—24no—
194#11758196—24no—
195C4×Dic61—48no—
196C2×#92418—22no—
197C2×#92418—42no—
198#11758189—48no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61C2×C22⋊C411yescharacteristic
202C23×C61C2×C22⋊C411yescharacteristic
203C23×C61#13712yes—
204C23×C61#13712yes—
205C23×C61C22×D411yescharacteristic
206C22×D61—22no—
207C22×D61—22no—
208C22×D61—22no—
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—24no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—24no—
215C22×D61—24no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—48no—
219C22×D61—48no—
220C22×D61#10414yes—
221C22×D61C2×C22⋊C412yes—
222C22×D61C2×C22⋊C412yes—
223Q8×C61—42no—
224Q8×C61—42no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—48no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C23×C411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—24no—
246C2×Dic61—24no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—42no—
250C2×Dic61—48no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61#9914yes—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C2×C22⋊C412yes—
257C4×D61—24no—
258C4×D61—24no—
259C4×D61—24no—
260C4×D61—24no—
261C4×D61—42no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—48no—
266C4×D61—48no—
267Dic122—42no—
268Dic122—48no—
269Dic122—42no—
270C8×C61—42no—
271#92418—42no—
272C2×#1508—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—24no—
278C22×C61—24no—
279C22×C61C2×#9912yes—
280C22×C61#41912yes—
281C22×C61#41912yes—
282C22×C61C2×#10412yes—
283C22×C61C22×C22⋊C411yescharacteristic
284C22×C61C2×#13711yescharacteristic
285C22×C61C2×#13711yescharacteristic
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—28no—
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—44no—
293C2×D61—44no—
294C2×D61—48no—
295C2×D61—44no—
296C2×D61C2×#10414yes—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—44no—
302C4×C61—42no—
303C4×C61—42no—
304Dic61—22no—
305Dic61—44no—
306Dic61—42no—
307Dic61—42no—
308Dic61C2×#9914yes—
309C22×C22⋊Q8—611no—
310C2×#407—611no—
311C2×C4×C22⋊C4—611no—
312#1508—618no—
313C2×#328—611no—
314C2×#328—611no—
315C2×#328—611no—
316C2×#328D6111yescharacteristic, complemented
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—22no—
320C2×C61#150814yescomplemented
321C2×C61C22×#9911yescharacteristic
322C2×C61C2×#41911yescharacteristic
323C2×C61C22×#10411yescharacteristic
324D61—24no—
325D61—42no—
326C23×Q8—611no—
327C24×C4—611no—
328C22×M16—1221no—
329C2×C22⋊Q8—611no—
330C2×C22⋊Q8—611no—
331C2×C22⋊Q8—614no—
332C2×C22⋊Q8—614no—
333C2×C22⋊Q8—611no—
334C2×C22⋊Q8—1221no—
335C2×C22⋊Q8—1221no—
336C2×C22⋊Q8—1222no—
337C2×C22⋊Q8—1222no—
338C2×C22⋊Q8C2×D6111yescharacteristic
339C22×C4⋊C4—611no—
340C22×C4⋊C4—1221no—
341C22×C22⋊C4—1221no—
342C22×C22⋊C4—1221no—
343C22×C42—1221no—
344#407—614no—
345#407—1222no—
346C2×C22⋊C8—611no—
347C2×C22⋊C8—1221no—
348C2×C22⋊C8C2×D6111yescharacteristic
349C4×C22⋊C4—614no—
350C4×C22⋊C4—1222no—
351C2×#95—611no—
352C2×#95C2×D6111yescharacteristic
353#328—614no—
354#328—614no—
355#328—614no—
356#328C2×D6114yescomplemented
357C61C2×#150811yescharacteristic, complemented, Sylow
358C25—611no—
359C22×Q8—614no—
360C22×Q8—611no—
361C22×Q8—1221no—
362C22×Q8—1222no—
363C22×Q8—2444no—
364C22×Q8C4×D6111yescharacteristic
365C23×C4—21no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—612no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—612no—
373C23×C4—612no—
374C23×C4—612no—
375C23×C4—1221no—
376C23×C4—1221no—
377C23×C4—1221no—
378C23×C4—2444no—
379C23×C4C22×D6111yescharacteristic
380C2×M16—1224no—
381C2×M16—2444no—
382C22×C8—21no—
383C22×C8—1221no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—614no—
387C22⋊Q8—612no—
388C22⋊Q8—612no—
389C22⋊Q8—614no—
390C22⋊Q8—1224no—
391C22⋊Q8—1224no—
392C22⋊Q8—1224no—
393C22⋊Q8—1224no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398C22⋊Q8C4×D6112yes—
399C22⋊Q8C22×D6112yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—614no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1224no—
405C2×C4⋊C4—1224no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4C4×D6111yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—1224no—
413C2×C22⋊C4—1224no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1224no—
417C2×C22⋊C4—1228no—
418C2×C22⋊C4—1221no—
419C2×C42—1224no—
420C2×C42—2444no—
421C22⋊C8—21no—
422C22⋊C8—612no—
423C22⋊C8—1224no—
424C22⋊C8—1221no—
425C22⋊C8C22×D6112yes—
426#95—21no—
427#95—612no—
428#95—1221no—
429#95C22×D6112yes—
430C24—611no—
431C24—611no—
432C24—612no—
433C24—612no—
434C24—1224no—
435C24—1222no—
436C24—1222no—
437C24—2442no—
438C24D4×D6111yescharacteristic
439C2×Q8—21no—
440C2×Q8—42no—
441C2×Q8—612no—
442C2×Q8—1224no—
443C2×Q8—1221no—
444C2×Q8—2442no—
445C2×Q8—2444no—
446C2×Q8—2448no—
447C2×Q8—2448no—
448C2×Q8C2×C4×D6112yes—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—611no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—611no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—1224no—
469C22×C4—1224no—
470C22×C4—1224no—
471C22×C4—1224no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—1222no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2444no—
480C22×C4—2444no—
481C22×C4—2444no—
482C22×C4—2444no—
483C22×C4—2444no—
484C22×C4—2444no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4C2×C4×D6111yescharacteristic
488C22×C4C2×C4×D6111yescharacteristic
489C22×C4D4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4C23×D6111yescharacteristic
493M16—2448no—
494C2×C8—22no—
495C2×C8—42no—
496C2×C8—1222no—
497C2×C8—2442no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—612no—
502C4⋊C4—1224no—
503C4⋊C4—1224no—
504C4⋊C4—1224no—
505C4⋊C4—1222no—
506C4⋊C4—1221no—
507C4⋊C4—1222no—
508C4⋊C4C2×C4×D6112yes—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—1224no—
512C22⋊C4—1224no—
513C22⋊C4—12216no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C42—2448no—
517C23—22no—
518C23—22no—
519C23—612no—
520C23—614no—
521C23—612no—
522C23—1224no—
523C23—1224no—
524C23—1222no—
525C23—1222no—
526C23—1222no—
527C23—1224no—
528C23—1222no—
529C23—1222no—
530C23—1222no—
531C23—1222no—
532C23—2442no—
533C23—2442no—
534C23—2448no—
535C23—2448no—
536C23C22⋊C4×D6111yescharacteristic
537C23C22⋊C4×D6111yescharacteristic
538C23#1451980612yes—
539C23#1451980912yes—
540C23C2×D4×D6111yescharacteristic
541Q8—42no—
542Q8—42no—
543Q8—2442no—
544Q8—2442no—
545Q8—2448no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—612no—
561C2×C4—614no—
562C2×C4—612no—
563C2×C4—1224no—
564C2×C4—1224no—
565C2×C4—1224no—
566C2×C4—1224no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1224no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2448no—
578C2×C4—2448no—
579C2×C4—2442no—
580C2×C4—2448no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4C22⋊C4×D6111yescharacteristic
585C2×C4C22⋊C4×D6111yescharacteristic
586C2×C4C22×C4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C8—42no—
589C8—2442no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—24no—
595C22—24no—
596C22—614no—
597C22—1222no—
598C22—1228no—
599C22—1222no—
600C22—1222no—
601C22—1222no—
602C22—1222no—
603C22—2444no—
604C22—2444no—
605C22—2448no—
606C22—2444no—
607C22#99×D6112yes—
608C22#1683976912yes—
609C22#1683976912yes—
610C22#104×D6112yes—
611C22C2×C22⋊C4×D6111yescharacteristic
612C22C2×#1451980611yescharacteristic
613C22C2×#1451980911yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—614no—
622C4—1222no—
623C4—2444no—
624C4—2442no—
625C4—2442no—
626C2—21no—
627C2—21no—
628C2—22no—
629C2—1224no—
630C2—2442no—
631C2#2144433714yesdirect product factor
632C2C2×#99×D6111yescharacteristic
633C2C2×#1683976911yescharacteristic
634C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#328C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenterC2×#328D61
hypocenterC61C2×#1508
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. #21444337C2direct (N × H)
5. C2×#16839500C2semidirect
6. C2×#16839499C2semidirect
7. C2×#16839498C2semidirect
8. C2×C61×#328C2semidirect
9. C22×Q8×D61C4semidirect
12. C2×#14519757C4semidirect
16. C2×#14519753C4semidirect
19. C22⋊Q8×D61C4semidirect
22. C2×C4⋊C4×D61C4semidirect
33. #16839500C22semidirect
34. #16839499C22semidirect
35. #16839498C22semidirect
39. C61×#328C22semidirect
45. C2×Q8×D61C2×C4semidirect
63. #14519757C2×C4semidirect
73. #14519753C2×C4semidirect
82. C4⋊C4×D61C2×C4semidirect
316. C2×#328D61semidirect
320. C2×C61#1508semidirect
356. #328C2×D61semidirect
357. C61C2×#1508semidirect
631. C2#21444337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
C2×#168397242
C2×#168396092
#214443372
C2×#168395002
C2×#168394992
C2×#168394982
C2×C61×#3282
C2×#150861