Finite Group Databasebeta

← #29689572

Subgroups — #29689572

Order 15616.

1100 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic
3C4×#14519734C211yesmaximal, characteristic
4#21446797C211yesmaximal, characteristic, complemented
5#21446796C211yesmaximal, characteristic, complemented
6#21446795C211yesmaximal, characteristic, complemented
7#21446761C214yesmaximal, complemented
8#21445917C214yesmaximal
9C61×#1994C211yesmaximal, 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—
26C2×#14519734—21no—
27#117×D61C2212yes—
28C2×C42×D61C2211yescharacteristic
29#16839818—21no—
30#16839818—21no—
31#16839814—21no—
32#16839814—21no—
33#16839786C2211yescharacteristic
34#16839725C2212yes—
35M16×Dic61C2212yes—
36C4×#11758196—21no—
37C4×#11758196C2212yes—
38C4×#11758198—21no—
39C4×#11758198C2212yes—
40#16839608—21no—
41C42×Dic61C2211yescharacteristic
42#16839523C2214yes—
43#16839522C2214yes—
44#16839521C2214yes—
45C61×#533C2211yescharacteristic
46C61×#423C2211yescharacteristic
47C43×C61C2211yescharacteristic
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—28no—
92#14519734—22no—
93#14519733—22no—
94C2×#11758196—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61C2×C412yes—
100C4⋊C4×D61C2×C412yes—
101C2×#11758198—22no—
102C22⋊C4×D61—22no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61C2312yes—
108C2×C4×Dic61C2311yescharacteristic
109C42×D61—22no—
110C42×D61C2×C411yescharacteristic
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C4⋊#92418—21no—
119C4⋊#92418—21no—
120#14519689—22no—
121#14519689—22no—
122#14519687—22no—
123C8×Dic61—22no—
124#14519684—22no—
125#14519684—22no—
126C2×M16×C61C2312yes—
127C4⋊Q8×C61C2×C411yescharacteristic
128C4⋊Q8×C61C2×C411yescharacteristic
129#125×C61C2×C412yes—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C4×Q8×C61—21no—
133C4×Q8×C61—21no—
134#117×C61C2312yes—
135C2×C42×C61—21no—
136C2×C42×C61—21no—
137C2×C42×C61C2312yes—
138C2×C42×C61C2311yescharacteristic
139C4⋊C8×C61—21no—
140C4⋊C8×C61—21no—
141C23×D61C2×D411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2411yescharacteristic
148C22×Dic61—22no—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152Q8×D61—44no—
153Q8×D61—44no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—24no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176M16×C61—24no—
177C2×C8×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22×C412yes—
183C4⋊C4×C61C22×C412yes—
184C22⋊C4×C61—22no—
185C42×C61—24no—
186C42×C61—22no—
187C42×C61—22no—
188C42×C61—22no—
189C42×C61—42no—
190C42×C61C22×C411yescharacteristic
191C42×C61C22×C411yescharacteristic
192C42×C61C2×D411yescharacteristic
193C42×C61C2×D411yescharacteristic
194C22⋊Dic61—22no—
195#11758198—28no—
196#11758198—22no—
197#11758198—22no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61C22×C412yes—
203C4⋊Dic61C22×C412yes—
204#11758196—28no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213C4×Dic61—24no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—42no—
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22×C411yescharacteristic
229C4×Dic61C22×C411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232#11758194—24no—
233C2×#92418—22no—
234C23×C61C22×D411yescharacteristic
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—41no—
238C22×D61C2×C22⋊C411yescharacteristic
239C22×D61C2×C22⋊C411yescharacteristic
240Q8×C61—42no—
241Q8×C61—42no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—24no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C23×C411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C612−1+412yes—
256C2×C4×C612−1+412yes—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—24no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—21no—
275C4×D61—21no—
276C4×D61—21no—
277C4×D61—21no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—44no—
285C4×D61—44no—
286C4×D61#10414yes—
287Dic122—44no—
288Dic122—42no—
289Dic122—42no—
290Dic122—44no—
291C8×C61—42no—
292#92418—42no—
293#21844—611nomaximal, Sylow
294C22×C61—21no—
295C22×C61—21no—
296C22×C61C22×C22⋊C411yescharacteristic
297C22×C61#53612yes—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—44no—
304C2×D61C2×#10412yes—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—44no—
308C4×C61—42no—
309C4×C61—42no—
310C4×C61C2×#10412yes—
311C4×C61#42112yes—
312C4×C61#51912yes—
313C4×C61#53611yescharacteristic
314C4×C61#53611yescharacteristic
315Dic61—21no—
316Dic61—21no—
317Dic61—21no—
318Dic61—21no—
319Dic61—21no—
320Dic61—44no—
321Dic61—42no—
322Dic61—42no—
323Dic61C2×#10412yes—
324C2×#533—611no—
325#2920—611no—
326C4×#117—611no—
327#1994—611no—
328#1994—611no—
329#1994—611no—
330#1994D6111yescharacteristic, complemented
331#1986—614no—
332#1826—614no—
333C2×C61—22no—
334C2×C61#231011yescharacteristic
335C2×C61C22×#10411yescharacteristic
336C2×C61C2×#42111yescharacteristic
337D61—22no—
338D61—41no—
339#533—611no—
340#533—611no—
341#533—612no—
342#533—612no—
343#533—611no—
344#533—1221no—
345#533—1221no—
346#533—1221no—
347#533—1221no—
348#533C2×D6111yescharacteristic
349C2×C4⋊Q8—611no—
350C2×C4⋊Q8—611no—
351C2×#125—612no—
352C2×C22⋊Q8—1221no—
353C2×C22⋊Q8—1221no—
354C2×C4×Q8—1221no—
355C2×C4×Q8—1221no—
356C2×#117—612no—
357C2×#117—1221no—
358C22×C42—611no—
359#432—1221no—
360#432—1221no—
361#431—1221no—
362#431—1221no—
363#423—611no—
364#423C2×D6111yescharacteristic
365#407—612no—
366C4×M16—612no—
367C4×C4⋊C4—612no—
368C4×C4⋊C4—1221no—
369C4×C22⋊C4—612no—
370C4×C22⋊C4—1221no—
371#376—1221no—
372C43—611no—
373C43C2×D6111yescharacteristic
374#339—614no—
375#339—614no—
376#339—614no—
377#339C2×D6114yes—
378C61#2184411yescharacteristic, complemented, Sylow
379C22×Q8—1221no—
380C22×Q8—1221no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C2×M16—612no—
385C2×M16C22×D6112yes—
386C4⋊Q8—612no—
387C4⋊Q8—612no—
388C4⋊Q8—611no—
389C4⋊Q8—611no—
390C4⋊Q8—1221no—
391C4⋊Q8—1221no—
392C4⋊Q8—1221no—
393C4⋊Q8—1221no—
394C4⋊Q8C4×D6111yescharacteristic
395C4⋊Q8C4×D6111yescharacteristic
396#125—612no—
397#125—612no—
398#125—612no—
399#125—1222no—
400#125—1222no—
401#125C4×D6112yes—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—1222no—
405C22⋊Q8—1222no—
406C22⋊Q8—1222no—
407C22⋊Q8—1222no—
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410C22⋊Q8—1221no—
411C22⋊Q8—1221no—
412C22⋊Q8—1221no—
413C22⋊Q8—1221no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—1222no—
417C4×Q8—1222no—
418C4×Q8—1222no—
419C4×Q8—1222no—
420C4×Q8—1221no—
421C4×Q8—1221no—
422C4×Q8—1221no—
423C4×Q8—1221no—
424C4×Q8—1221no—
425C4×Q8—1221no—
426#117—612no—
427#117—612no—
428#117—612no—
429#117—1222no—
430#117—1228no—
431#117—1222no—
432#117C22×D6112yes—
433C2×C4⋊C4—612no—
434C2×C4⋊C4—612no—
435C2×C4⋊C4—1222no—
436C2×C4⋊C4—1222no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1222no—
440C2×C22⋊C4—1222no—
441C2×C22⋊C4—1222no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—612no—
456C2×C42—1222no—
457C2×C42—1221no—
458C2×C42—1221no—
459C2×C42C22×D6112yes—
460C2×C42C22×D6111yescharacteristic
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465C22⋊C8—1222no—
466C22⋊C8—1222no—
467#97—1222no—
468C4×C8—1222no—
469#95—1222no—
470#95—1222no—
471C24—611no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—1222no—
475C2×Q8—1222no—
476C2×Q8—1221no—
477C2×Q8—1221no—
478C2×Q8—2444no—
479C2×Q8—2444no—
480C22×C4—22no—
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—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—1224no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—2442no—
503C22×C4D4×D6111yescharacteristic
504C22×C4D4×D6111yescharacteristic
505C22×C4C23×D6111yescharacteristic
506M16—24no—
507M16—1224no—
508C2×C8—22no—
509C2×C8—1222no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—612no—
515C4⋊C4—612no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1228no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4C2×C4×D6112yes—
530C4⋊C4C2×C4×D6112yes—
531C22⋊C4—22no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1228no—
535C22⋊C4—1222no—
536C42—24no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—42no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—1222no—
554C42—1222no—
555C42—1224no—
556C42—1222no—
557C42—1222no—
558C42—1222no—
559C42—2442no—
560C42C2×C4×D6111yescharacteristic
561C42C2×C4×D6111yescharacteristic
562C42D4×D6111yescharacteristic
563C42D4×D6111yescharacteristic
564C23—611no—
565C23—611no—
566C23—1222no—
567C23—1222no—
568C23—2441no—
569C23C2×D4×D6111yescharacteristic
570Q8—42no—
571Q8—42no—
572Q8—2444no—
573Q8—2444no—
574Q8—2442no—
575Q8—2442no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—611no—
584C2×C4—614no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1224no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2444no—
609C2×C4—2444no—
610C2×C4—2441no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4C22⋊C4×D6111yescharacteristic
614C2×C4C22⋊C4×D6111yescharacteristic
615C2×C4C22⋊C4×D6111yescharacteristic
616C2×C4C22⋊C4×D6111yescharacteristic
617C2×C4C22×C4×D6111yescharacteristic
618C2×C4C2×D4×D6111yescharacteristic
619C2×C4#1451982412yes—
620C2×C4#1451982512yes—
621C8—42no—
622C8—2442no—
623C22—21no—
624C22—21no—
625C22—612no—
626C22—1221no—
627C22—1221no—
628C22—1221no—
629C22—1221no—
630C22—1221no—
631C22—2444no—
632C22C2×C22⋊C4×D6111yescharacteristic
633C22#1684033512yes—
634C4—21no—
635C4—21no—
636C4—44no—
637C4—42no—
638C4—42no—
639C4—612no—
640C4—1221no—
641C4—1221no—
642C4—1221no—
643C4—1221no—
644C4—1221no—
645C4—2444no—
646C4—2442no—
647C4—2442no—
648C4#104×D6112yes—
649C4#1683977712yes—
650C4#1684023812yes—
651C4#1684033211yescharacteristic
652C4#1684033711yescharacteristic
653C2—22no—
654C2—1222no—
655C2—2441no—
656C2#2144840211yescharacteristic
657C2C2×#104×D6111yescharacteristic
658C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1994C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1994D61
hypocenterC61#21844
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
4. #21446797C2semidirect
5. #21446796C2semidirect
6. #21446795C2semidirect
7. #21446761C2semidirect
9. C61×#1994C2semidirect
11. #16840318C4semidirect
12. #16840317C4semidirect
13. #16840317C4semidirect
19. C4⋊Q8×D61C4semidirect
20. C4⋊Q8×D61C4semidirect
21. #125×D61C4semidirect
330. #1994D61semidirect
378. C61#21844semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214544512
C4×#145197342
#214467972
#214467962
#214467952
#214467612
#214459172
C61×#19942
#2184461