Finite Group Databasebeta

← #29689580

Subgroups — #29689580

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840315C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic
3#21448213C211yesmaximal, characteristic
4#21446798C214yesmaximal, complemented
5#21446761C214yesmaximal, complemented
6#21445919C211yesmaximal, characteristic
7#21445918C211yesmaximal, characteristic
8#21445916C211yesmaximal, characteristic
9C61×#1826C211yesmaximal, characteristic
10#16840315—21no—
11#16840315—21no—
12#16840315—21no—
13#16840315—21no—
14#16840315C412yescomplemented
15#16840315C412yescomplemented
16#16840315C2212yes—
17#16840315C2212yes—
18C2×#14519776C411yescharacteristic, complemented
19C2×#14519776C411yescharacteristic, complemented
20C2×#14519768C411yescharacteristic, complemented
21C2×#14519768C411yescharacteristic, complemented
22C2×#14519754—21no—
23C2×#14519754—21no—
24C2×C4×Dic122—21no—
25C2×C4×Dic122—21no—
26C2×#14519736C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839816—21no—
29#16839816—21no—
30#16839812—21no—
31#16839812—21no—
32#16839785C2212yes—
33#16839726C2211yescharacteristic
34M16×Dic61C2212yes—
35#16839629—21no—
36#16839626—21no—
37#16839623—21no—
38#16839620—21no—
39C4×#11758196C2212yes—
40C4×C22⋊Dic61C2211yescharacteristic
41#16839608C2212yes—
42#16839523C2214yes—
43#16839522C2214yes—
44#16839521C2214yes—
45C2×#117×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#339C2214yes—
49C22×Dic122—21no—
50C22×Dic122—21no—
51C23×Dic61D411yescharacteristic
52C23×Dic61D411yescharacteristic
53C2×#11758194C2312yes—
54#14519776—21no—
55#14519776—21no—
56#14519776—21no—
57#14519776—21no—
58#14519776C2×C412yes—
59#14519776C2×C412yes—
60#14519776C2×C412yes—
61#14519776C2×C412yes—
62#14519768—21no—
63#14519768—21no—
64#14519768—21no—
65#14519768—21no—
66#14519768C2×C412yes—
67#14519768C2×C412yes—
68#14519768C2×C412yes—
69#14519768C2×C412yes—
70#14519754—22no—
71#14519754—22no—
72#14519754—22no—
73#14519754—22no—
74#14519754—22no—
75#14519754—22no—
76#14519754—22no—
77#14519754—22no—
78C4×Dic122—22no—
79C4×Dic122—22no—
80C4×Dic122—22no—
81C4×Dic122—22no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86#14519736—21no—
87#14519736—21no—
88#14519736C2×C412yes—
89#14519736C2312yes—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—22no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61C2312yes—
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119#14519687—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125C23×C4×C61C2311yescharacteristic
126C2×M16×C61C2312yes—
127#117×C61—21no—
128#117×C61—21no—
129#117×C61C2×C412yes—
130#117×C61C2312yes—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C42×C61—21no—
136C2×C42×C61C2312yes—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139#95×C61—21no—
140C24×C61C2×D411yescharacteristic
141C22×C4×C61—24no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—42no—
155C22×Dic61—42no—
156C22×Dic61C22⋊C411yescharacteristic
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C2×Dic122—22no—
169C2×Dic122—22no—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122—44no—
173C2×Dic122—44no—
174M16×C61—24no—
175C2×C8×C61—22no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61C22×C412yes—
179C4⋊C4×C61C22×C412yes—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—42no—
183C42×C61—22no—
184C42×C61—22no—
185C42×C61—24no—
186C22⋊Dic61—22no—
187C22⋊Dic61—22no—
188C22⋊Dic61—42no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61—22no—
194C4⋊Dic61—22no—
195C4⋊Dic61C22×C412yes—
196C4⋊Dic61C22×C412yes—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—44no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—24no—
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C22×C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225#11758194—24no—
226C2×#92418—22no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—41no—
230C23×C61C2×C22⋊C411yescharacteristic
231C23×C61C2×C22⋊C411yescharacteristic
232C23×C61C22×D411yescharacteristic
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C23×C411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C612−1+414yes—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C411yescharacteristic
277Dic122—44no—
278Dic122—44no—
279Dic122—44no—
280Dic122—44no—
281C8×C61—42no—
282#92418—42no—
283#21845—611nomaximal, Sylow
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—44no—
292C22×C61#42112yes—
293C22×C61C22×C22⋊C411yescharacteristic
294C22×C61#53612yes—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—42no—
298C4×C61—42no—
299C4×C61—82no—
300C4×C61#51912yes—
301C4×C61#53612yes—
302Dic61—21no—
303Dic61—21no—
304Dic61—21no—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—42no—
310Dic61—42no—
311Dic61—82no—
312Dic61#42112yes—
313C2×#533—611no—
314#2920—611no—
315#2283—611no—
316#1995—614no—
317#1986—614no—
318#1826—611no—
319#1826—611no—
320#1826—611no—
321#1826D6111yescharacteristic
322C2×C61—22no—
323C2×C61—22no—
324C2×C61—41no—
325C2×C61#231011yescharacteristic
326C2×C61C2×#42111yescharacteristic
327C2×C61C2×#42111yescharacteristic
328#533—612no—
329#533—612no—
330#533—612no—
331#533—612no—
332#533—1221no—
333#533—1221no—
334#533—1221no—
335#533—1221no—
336C2×C4⋊Q8—611no—
337C2×C4⋊Q8—611no—
338C2×#125—611no—
339C2×#125—611no—
340C2×C22⋊Q8—1221no—
341C2×C22⋊Q8—1221no—
342C2×C4×Q8—1221no—
343C2×C4×Q8—1221no—
344C2×#117—611no—
345C2×#117C2×D6111yescharacteristic
346C22×C42—611no—
347#432—1221no—
348#432—1221no—
349#431—1221no—
350#431—1221no—
351#423—612no—
352#407—611no—
353#407C2×D6111yescharacteristic
354C4×M16—612no—
355#383—1221no—
356#382—1221no—
357#381—1221no—
358#380—1221no—
359C4×C4⋊C4—612no—
360C4×C22⋊C4—611no—
361C4×C22⋊C4C2×D6111yescharacteristic
362#376—612no—
363#339—614no—
364#339—614no—
365#339—614no—
366#339C2×D6114yes—
367C61#2184511yescharacteristic, complemented, Sylow
368C22×Q8—1221no—
369C22×Q8—1221no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4C22×D6111yescharacteristic
373C2×M16—612no—
374C2×M16C22×D6112yes—
375C4⋊Q8—612no—
376C4⋊Q8—612no—
377C4⋊Q8—612no—
378C4⋊Q8—612no—
379C4⋊Q8—1221no—
380C4⋊Q8—1221no—
381C4⋊Q8—1221no—
382C4⋊Q8—1221no—
383#125—612no—
384#125—612no—
385#125—612no—
386#125—612no—
387#125—1221no—
388#125—1221no—
389#125—1221no—
390#125—1221no—
391C22⋊Q8—1222no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C22⋊Q8—1222no—
397C22⋊Q8—1222no—
398C22⋊Q8—1222no—
399C4×Q8—1222no—
400C4×Q8—1222no—
401C4×Q8—1222no—
402C4×Q8—1222no—
403C4×Q8—1222no—
404C4×Q8—1222no—
405C4×Q8—1222no—
406C4×Q8—1222no—
407#117—21no—
408#117—21no—
409#117—612no—
410#117—612no—
411#117—1221no—
412#117—1221no—
413#117C4×D6112yes—
414#117C22×D6112yes—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4C4×D6111yescharacteristic
425C2×C4⋊C4C4×D6111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C42—21no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—612no—
444C2×C42—1221no—
445C2×C42C22×D6112yes—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—1221no—
451C22⋊C8—1221no—
452#97—1222no—
453C4×C8—1222no—
454#95—21no—
455#95—1222no—
456#95—1222no—
457#95—1222no—
458#95—1221no—
459C24D4×D6111yescharacteristic
460C2×Q8—1222no—
461C2×Q8—1222no—
462C2×Q8—1222no—
463C2×Q8—1222no—
464C2×Q8—2444no—
465C2×Q8—2444no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1222no—
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—24no—
494M16—1224no—
495C2×C8—22no—
496C2×C8—1222no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—612no—
500C4⋊C4—612no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—2444no—
516C4⋊C4C2×C4×D6112yes—
517C4⋊C4C2×C4×D6112yes—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—42no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—2442no—
524C42—22no—
525C42—22no—
526C42—24no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—1222no—
544C42—1222no—
545C42—1224no—
546C23—22no—
547C23—22no—
548C23—41no—
549C23C22⋊C4×D6111yescharacteristic
550C23C22⋊C4×D6111yescharacteristic
551C23C2×D4×D6111yescharacteristic
552Q8—2444no—
553Q8—2444no—
554Q8—2444no—
555Q8—2444no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6111yescharacteristic
597C2×C4C22×C4×D6111yescharacteristic
598C2×C4C2×D4×D6111yescharacteristic
599C2×C4#1451982414yes—
600C8—42no—
601C8—2442no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—44no—
610C22#1683977712yes—
611C22C2×C22⋊C4×D6111yescharacteristic
612C22#1684033412yes—
613C4—21no—
614C4—21no—
615C4—42no—
616C4—42no—
617C4—82no—
618C4—612no—
619C4—1221no—
620C4—1221no—
621C4—1221no—
622C4—1221no—
623C4—1221no—
624C4—1221no—
625C4—1221no—
626C4—4882no—
627C4—2442no—
628C4—2442no—
629C4#1684023912yes—
630C4#1684033412yes—
631C2—22no—
632C2—22no—
633C2—41no—
634C2#2144840411yescharacteristic
635C2#421×D6111yescharacteristic
636C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1826C2
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenter#1826D61
hypocenterC61#21845
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #21446798C2semidirect
5. #21446761C2semidirect
14. #16840315C4semidirect
15. #16840315C4semidirect
18. C2×#14519776C4semidirect
19. C2×#14519776C4semidirect
20. C2×#14519768C4semidirect
21. C2×#14519768C4semidirect
367. C61#21845semidirect

Maximal subgroups

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

subgroupindex
C2×#168403152
#214544482
#214482132
#214467982
#214467612
#214459192
#214459182
#214459162
C61×#18262
#2184561