Finite Group Databasebeta

← #29689578

Subgroups — #29689578

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic
3#21448211C211yesmaximal, characteristic
4#21446801C211yesmaximal, characteristic, complemented
5#21446800C211yesmaximal, characteristic, complemented
6#21446799C211yesmaximal, characteristic, complemented
7#21446761C214yesmaximal, complemented
8#21445917C214yesmaximal
9C61×#1995C211yesmaximal, characteristic, complemented
10#16840319C2211yescharacteristic
11#16840318C412yescomplemented
12#16840317C411yescharacteristic, complemented
13#16840317C411yescharacteristic, complemented
14#16840316—21no—
15#16840316—21no—
16#16840315C2212yes—
17#16840314—21no—
18#16840314—21no—
19C4⋊Q8×D61C411yescharacteristic, complemented
20C4⋊Q8×D61C411yescharacteristic, complemented
21#125×D61C412yescomplemented
22C22⋊Q8×D61—21no—
23C22⋊Q8×D61—21no—
24C4×Q8×D61—21no—
25C4×Q8×D61—21no—
26#117×D61C2212yes—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839818—21no—
30#16839814—21no—
31#16839814—21no—
32#16839786C2211yescharacteristic
33#16839725C2212yes—
34M16×Dic61C2212yes—
35#16839629—21no—
36#16839626—21no—
37#16839624—21no—
38#16839621—21no—
39C4×#11758196C2212yes—
40C4×#11758198C2212yes—
41#16839608C2211yescharacteristic
42#16839523C2214yes—
43#16839522C2214yes—
44#16839521C2214yes—
45C61×#533C2211yescharacteristic
46C61×#423C2211yescharacteristic
47C61×#376C2211yescharacteristic
48C61×#339C2214yes—
49C2×Q8×D61—21no—
50C2×Q8×D61—21no—
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C2×#11758194C2312yes—
55#14519777C2×C411yescharacteristic
56#14519777C2×C411yescharacteristic
57#14519776—21no—
58#14519776—21no—
59#14519776C2×C412yes—
60#14519776C2×C412yes—
61#14519775—21no—
62#14519775—21no—
63#14519769C2×C412yes—
64#14519768C2×C412yes—
65#14519768C2×C412yes—
66#14519767—22no—
67#14519767—22no—
68#14519757—21no—
69#14519757—21no—
70#14519756—21no—
71#14519756—21no—
72#14519755—22no—
73#14519755—22no—
74#14519754—22no—
75#14519754—22no—
76#14519753—21no—
77#14519753—21no—
78Q8×Dic61—21no—
79Q8×Dic61—21no—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84#14519742—21no—
85#14519742—21no—
86#14519742—22no—
87#14519742—22no—
88#14519736C2312yes—
89#14519735C2×C412yes—
90#14519735C2×C412yes—
91#14519734—22no—
92#14519733—22no—
93C2×#11758196—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61C2×C412yes—
99C4⋊C4×D61C2×C412yes—
100C2×#11758198—22no—
101C22⋊C4×D61—22no—
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61C2312yes—
105C2×C4×Dic61C2311yescharacteristic
106C42×D61—22no—
107C42×D61C2×C411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61C2×C411yescharacteristic
110C42×D61C2×C411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C4⋊#92418—21no—
116C4⋊#92418—21no—
117#14519689—22no—
118#14519689—22no—
119#14519687—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—22no—
124#14519684—22no—
125C2×M16×C61C2312yes—
126C4⋊Q8×C61C2×C411yescharacteristic
127C4⋊Q8×C61C2×C411yescharacteristic
128#125×C61C2×C412yes—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C4×Q8×C61—21no—
132C4×Q8×C61—21no—
133#117×C61C2312yes—
134C2×C42×C61C2312yes—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140C23×D61C2×D411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C22×C4×C61—22no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C22×Dic61—22no—
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151Q8×D61—44no—
152Q8×D61—44no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C22×C411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×Dic122—21no—
172C2×Dic122—21no—
173C2×Dic122—22no—
174C2×Dic122—22no—
175M16×C61—24no—
176C2×C8×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C412yes—
182C4⋊C4×C61C22×C412yes—
183C22⋊C4×C61—22no—
184C42×C61—22no—
185C42×C61—22no—
186C42×C61—22no—
187C42×C61C22×C411yescharacteristic
188C42×C61C22×C411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C22⋊Dic61—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—44no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61C22×C412yes—
200C4⋊Dic61C22×C412yes—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—44no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22×C411yescharacteristic
224C4×Dic61C22×C411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227#11758194—24no—
228C2×#92418—22no—
229C23×C61C22×D411yescharacteristic
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—41no—
233C22×D61C2×C22⋊C411yescharacteristic
234C22×D61C2×C22⋊C411yescharacteristic
235Q8×C61—42no—
236Q8×C61—42no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C23×C411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C612−1+412yes—
251C2×C4×C612−1+412yes—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—41no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—21no—
271C4×D61—21no—
272C4×D61—21no—
273C4×D61—21no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—44no—
281C4×D61—44no—
282Dic122—44no—
283Dic122—42no—
284Dic122—42no—
285Dic122—44no—
286C8×C61—42no—
287#92418—42no—
288#21845—611nomaximal, Sylow
289C22×C61—21no—
290C22×C61—21no—
291C22×C61C22×C22⋊C411yescharacteristic
292C22×C61#53612yes—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—44no—
299C2×D61#42112yes—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—42no—
305C4×C61—42no—
306C4×C61—82no—
307C4×C61#51912yes—
308C4×C61#53611yescharacteristic
309C4×C61#53611yescharacteristic
310Dic61—21no—
311Dic61—21no—
312Dic61—21no—
313Dic61—21no—
314Dic61—21no—
315Dic61—42no—
316Dic61—42no—
317Dic61—82no—
318Dic61#42112yes—
319C2×#533—611no—
320#2920—611no—
321#2283—611no—
322#1995—611no—
323#1995—611no—
324#1995—611no—
325#1995D6111yescharacteristic, complemented
326#1986—614no—
327#1826—614no—
328C2×C61—22no—
329C2×C61#231011yescharacteristic
330C2×C61C2×#42111yescharacteristic
331C2×C61C2×#42111yescharacteristic
332D61—22no—
333D61—41no—
334#533—611no—
335#533—611no—
336#533—612no—
337#533—612no—
338#533—611no—
339#533—1221no—
340#533—1221no—
341#533—1221no—
342#533—1221no—
343#533C2×D6111yescharacteristic
344C2×C4⋊Q8—611no—
345C2×C4⋊Q8—611no—
346C2×#125—612no—
347C2×C22⋊Q8—1221no—
348C2×C22⋊Q8—1221no—
349C2×C4×Q8—1221no—
350C2×C4×Q8—1221no—
351C2×#117—612no—
352C22×C42—611no—
353#432—1221no—
354#432—1221no—
355#431—1221no—
356#431—1221no—
357#423—611no—
358#423C2×D6111yescharacteristic
359#407—612no—
360C4×M16—612no—
361#383—1221no—
362#382—1221no—
363#381—1221no—
364#380—1221no—
365C4×C4⋊C4—612no—
366C4×C22⋊C4—612no—
367#376—611no—
368#376C2×D6111yescharacteristic
369#339—614no—
370#339—614no—
371#339—614no—
372#339C2×D6114yes—
373C61#2184511yescharacteristic, complemented, Sylow
374C22×Q8—1221no—
375C22×Q8—1221no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C2×M16—612no—
380C2×M16C22×D6112yes—
381C4⋊Q8—612no—
382C4⋊Q8—612no—
383C4⋊Q8—611no—
384C4⋊Q8—611no—
385C4⋊Q8—1221no—
386C4⋊Q8—1221no—
387C4⋊Q8—1221no—
388C4⋊Q8—1221no—
389C4⋊Q8C4×D6111yescharacteristic
390C4⋊Q8C4×D6111yescharacteristic
391#125—612no—
392#125—612no—
393#125—612no—
394#125—1222no—
395#125—1222no—
396#125C4×D6112yes—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—1222no—
400C22⋊Q8—1222no—
401C22⋊Q8—1222no—
402C22⋊Q8—1222no—
403C22⋊Q8—1221no—
404C22⋊Q8—1221no—
405C22⋊Q8—1221no—
406C22⋊Q8—1221no—
407C22⋊Q8—1221no—
408C22⋊Q8—1221no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—1222no—
412C4×Q8—1222no—
413C4×Q8—1222no—
414C4×Q8—1222no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×Q8—1221no—
418C4×Q8—1221no—
419C4×Q8—1221no—
420C4×Q8—1221no—
421#117—612no—
422#117—612no—
423#117—612no—
424#117—1222no—
425#117—1222no—
426#117C22×D6112yes—
427C2×C4⋊C4—612no—
428C2×C4⋊C4—612no—
429C2×C4⋊C4—1222no—
430C2×C4⋊C4—1222no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1222no—
434C2×C22⋊C4—1222no—
435C2×C22⋊C4—1222no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—612no—
448C2×C42—1222no—
449C2×C42C22×D6112yes—
450C2×C42C22×D6111yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—1221no—
454C4⋊C8—1221no—
455C22⋊C8—1222no—
456C22⋊C8—1222no—
457#97—1222no—
458C4×C8—1222no—
459#95—21no—
460#95—21no—
461#95—1222no—
462#95—1222no—
463#95—1221no—
464#95—1221no—
465C24—611no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—1222no—
469C2×Q8—1222no—
470C2×Q8—1221no—
471C2×Q8—1221no—
472C2×Q8—2444no—
473C2×Q8—2444no—
474C22×C4—22no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—2442no—
496C22×C4—2442no—
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499C22×C4C23×D6111yescharacteristic
500M16—24no—
501M16—1224no—
502C2×C8—22no—
503C2×C8—1222no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—612no—
509C4⋊C4—612no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—2444no—
523C4⋊C4C2×C4×D6112yes—
524C4⋊C4C2×C4×D6112yes—
525C22⋊C4—22no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—2444no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—1222no—
546C42—1222no—
547C42—1222no—
548C42—1222no—
549C42—1222no—
550C42C2×C4×D6111yescharacteristic
551C42C2×C4×D6111yescharacteristic
552C42D4×D6111yescharacteristic
553C42D4×D6111yescharacteristic
554C23—611no—
555C23—611no—
556C23—1222no—
557C23—1222no—
558C23—2441no—
559C23C2×D4×D6111yescharacteristic
560Q8—42no—
561Q8—42no—
562Q8—2442no—
563Q8—2442no—
564Q8—2444no—
565Q8—2444no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2444no—
598C2×C4—2444no—
599C2×C4—2441no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4C22⋊C4×D6111yescharacteristic
604C2×C4C22⋊C4×D6111yescharacteristic
605C2×C4C22⋊C4×D6111yescharacteristic
606C2×C4C22⋊C4×D6111yescharacteristic
607C2×C4C22×C4×D6111yescharacteristic
608C2×C4C2×D4×D6111yescharacteristic
609C2×C4#1451982412yes—
610C2×C4#1451982512yes—
611C8—42no—
612C8—2442no—
613C22—21no—
614C22—21no—
615C22—612no—
616C22—1221no—
617C22—1221no—
618C22—1221no—
619C22—1221no—
620C22—1221no—
621C22—2444no—
622C22C2×C22⋊C4×D6111yescharacteristic
623C22#1684033512yes—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—42no—
630C4—82no—
631C4—612no—
632C4—1221no—
633C4—1221no—
634C4—1221no—
635C4—1221no—
636C4—1221no—
637C4—4882no—
638C4—2442no—
639C4—2442no—
640C4#1684023812yes—
641C4#1684033211yescharacteristic
642C4#1684033711yescharacteristic
643C2—22no—
644C2—1222no—
645C2—2441no—
646C2#2144840211yescharacteristic
647C2#421×D6111yescharacteristic
648C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1995C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1995D61
hypocenterC61#21845
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
4. #21446801C2semidirect
5. #21446800C2semidirect
6. #21446799C2semidirect
7. #21446761C2semidirect
9. C61×#1995C2semidirect
11. #16840318C4semidirect
12. #16840317C4semidirect
13. #16840317C4semidirect
19. C4⋊Q8×D61C4semidirect
20. C4⋊Q8×D61C4semidirect
21. #125×D61C4semidirect
325. #1995D61semidirect
373. C61#21845semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214544512
#214482112
#214468012
#214468002
#214467992
#214467612
#214459172
C61×#19952
#2184561