Finite Group Databasebeta

← D61×#2088 #29709055

Subgroups — D61×#2088 #29709055

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D61C211yesmaximal, characteristic
2C2×C4⋊C8×D61C211yesmaximal, characteristic
3#389×D61C211yesmaximal, characteristic
4#389×D61C211yesmaximal, characteristic
5#21447323C211yesmaximal, characteristic, complemented
6#21447322C211yesmaximal, characteristic, complemented
7#21447321C211yesmaximal, characteristic, complemented
8#21447320C211yesmaximal, characteristic, complemented
9#21447319C211yesmaximal, characteristic, complemented
10#21447318C211yesmaximal, characteristic, complemented
11#21447317C211yesmaximal, characteristic, complemented
12#340×D61C211yesmaximal, characteristic
13#340×D61C211yesmaximal, characteristic
14#340×D61C211yesmaximal, characteristic
15C61×#2088C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4⋊C4×D61—21no—
19C2×C4⋊C4×D61—21no—
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24C2×C42×D61C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28#106×D61—24no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C4⋊C8×D61—24no—
33#16839661C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839659—21no—
38#16839659—21no—
39#16839658C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839657—21no—
42#16839657—21no—
43#95×D61—21no—
44#95×D61—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75C2×C8×D61D414yes—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C4⋊C4×D61—22no—
91C4⋊C4×D61—22no—
92C4⋊C4×D61—22no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—44no—
97C4⋊C4×D61—44no—
98C4⋊C4×D61Q814yes—
99C4⋊C4×D61Q814yes—
100C2×C4×Dic61D411yescharacteristic
101C2×C4×Dic61D411yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C42×D61—22no—
104C42×D61—22no—
105#14519709—22no—
106#14519708—22no—
107#14519708—22no—
108C4⋊#92418—22no—
109#14519706—22no—
110#14519706—22no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126#106×C61—22no—
127C4⋊C8×C61—22no—
128#95×C61—21no—
129#95×C61—21no—
130C23×D61C2×D411yescharacteristic
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61SD1614yes—
163C2×C4×D61C2×D412yes—
164C2×C4×D61C2×Q812yes—
165C2×C4×D61C2×Q812yes—
166C2×C4×D61#4112yes—
167C2×C4×D61#4112yes—
168C2×C4×D61#4112yes—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61C2×D412yes—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—42no—
182C4⋊C4×C61—42no—
183C4⋊C4×C61C2×Q812yes—
184C4⋊C4×C61C2×Q812yes—
185C42×C61—21no—
186C42×C61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—42no—
194C4⋊Dic61—42no—
195C4⋊Dic61C2×Q812yes—
196C4⋊Dic61C2×Q812yes—
197#11758196—24no—
198#11758196—24no—
199#11758196—42no—
200#11758196—42no—
201#11758196—42no—
202#11758196—42no—
203#11758196—42no—
204#11758196—42no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418C2×D412yes—
215C8×D61—28no—
216C8×D61—44no—
217C23×C61C22×D411yescharacteristic
218C22×D61#12112yes—
219C22×D61C22⋊Q812yes—
220C22×D61C22⋊Q812yes—
221C22×D61C2×SD1612yes—
222C22×D61#13512yes—
223C22×D61AGL(1,ℤ/8)12yes—
224C22×D61#13712yes—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61C2×SD1612yes—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×Q811yescharacteristic
245C2×C4×C61C22×Q811yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61#12112yes—
267C2×Dic61C22⋊Q812yes—
268C2×Dic61C22⋊Q812yes—
269C2×Dic61C2×SD1612yes—
270C4×D61—28no—
271C4×D61—44no—
272C4×D61—48no—
273C4×D61—48no—
274C4×D61—84no—
275C4×D61—84no—
276C4×D61#12314yes—
277C4×D61#12514yes—
278C4×D61#12514yes—
279C4×D61C4⋊Q814yes—
280C8×C61—22no—
281C8×C61—41no—
282#92418—22no—
283#92418—41no—
284C2×#2088—611nomaximal, Sylow
285C22×C61C2×#12111yescharacteristic
286C22×C61C2×C22⋊Q811yescharacteristic
287C22×C61C2×C22⋊Q811yescharacteristic
288C22×C61C22×SD1611yescharacteristic
289C22×C61C2×#13511yescharacteristic
290C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C61C2×#13711yescharacteristic
292C2×D61#39814yes—
293C2×D61#46514yes—
294C2×D61#46814yes—
295C2×D61#47514yes—
296C2×D61#47614yes—
297C2×D61#47814yes—
298C2×D61#47914yes—
299C4×C61—22no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61—42no—
303C4×C61—81no—
304C4×C61—81no—
305C4×C61C2×#12311yescharacteristic
306C4×C61C2×#12511yescharacteristic
307C4×C61C2×#12511yescharacteristic
308C4×C61C2×C4⋊Q811yescharacteristic
309Dic61—22no—
310Dic61—42no—
311Dic61—41no—
312Dic61—42no—
313Dic61—81no—
314Dic61—81no—
315Dic61#39814yes—
316C22×#106—611no—
317C22×C4⋊C8—611no—
318C2×#389—611no—
319C2×#389—611no—
320#2088—611no—
321#2088—611no—
322#2088—611no—
323#2088—611no—
324#2088—611no—
325#2088—611no—
326#2088—611no—
327#2088D6111yescharacteristic, direct product factor
328C2×#340—611no—
329C2×#340—611no—
330C2×#340—611no—
331C2×C61C2×#39811yescharacteristic
332C2×C61C2×#46511yescharacteristic
333C2×C61C2×#46811yescharacteristic
334C2×C61C2×#47611yescharacteristic
335C2×C61C2×#47811yescharacteristic
336C2×C61C2×#47511yescharacteristic
337C2×C61C2×#47911yescharacteristic
338D61#208818yesdirect product factor
339C23×C8—611no—
340C23×C8—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—611no—
343C22×C4⋊C4—611no—
344C22×C4⋊C4—611no—
345C22×C4⋊C4—1221no—
346C22×C4⋊C4—1221no—
347C22×C42—611no—
348C2×#106—611no—
349C2×#106—611no—
350C2×#106—611no—
351C2×#106—1224no—
352C2×#106C2×D6111yescharacteristic
353C2×C4⋊C8—611no—
354C2×C4⋊C8—611no—
355C2×C4⋊C8—611no—
356C2×C4⋊C8—1224no—
357C2×C4⋊C8C2×D6111yescharacteristic
358#389—611no—
359#389—611no—
360#389—611no—
361#389—611no—
362#389—611no—
363#389—611no—
364#389—1221no—
365#389—1221no—
366#389—1221no—
367#389—1221no—
368#389C2×D6111yescharacteristic
369#389C2×D6111yescharacteristic
370C2×#95—1221no—
371C2×#95—1221no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340C2×D6111yescharacteristic
382#340C2×D6111yescharacteristic
383#340C2×D6111yescharacteristic
384C61C2×#208811yescharacteristic, complemented, Sylow
385C23×C4—611no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—1221no—
389C23×C4—1221no—
390C23×C4—1221no—
391C23×C4—1221no—
392C22×C8—611no—
393C22×C8—614no—
394C22×C8—611no—
395C22×C8—1222no—
396C22×C8—1222no—
397C22×C8—1222no—
398C22×C8—1222no—
399C22×C8—1222no—
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—614no—
407C2×C4⋊C4—614no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—1222no—
411C2×C4⋊C4—1222no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1222no—
416C2×C4⋊C4—1221no—
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—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—2444no—
427C2×C4⋊C4—2444no—
428C2×C4⋊C4C22×D6111yescharacteristic
429C2×C4⋊C4C22×D6111yescharacteristic
430C2×C4⋊C4C22×D6111yescharacteristic
431C2×C4⋊C4C22×D6111yescharacteristic
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—1222no—
436C2×C42—1222no—
437C2×C42C22×D6111yescharacteristic
438#106—22no—
439#106—1222no—
440#106—1222no—
441#106—1222no—
442C4⋊C8—22no—
443C4⋊C8—1222no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446#95—21no—
447#95—21no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454C24—611no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—611no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—611no—
467C22×C4—614no—
468C22×C4—611no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4C23×D6111yescharacteristic
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—612no—
499C2×C8—1228no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—2444no—
506C2×C8D4×D6112yes—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—612no—
516C4⋊C4—612no—
517C4⋊C4—1224no—
518C4⋊C4—1224no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—2442no—
526C4⋊C4—2442no—
527C4⋊C4—2442no—
528C4⋊C4—2442no—
529C4⋊C4—2442no—
530C4⋊C4—2442no—
531C4⋊C4—2442no—
532C4⋊C4—2442no—
533C4⋊C4Q8×D6112yes—
534C4⋊C4Q8×D6112yes—
535C42—21no—
536C42—21no—
537C42—1222no—
538C42—1222no—
539C42—1221no—
540C42—1221no—
541C23—612no—
542C23—612no—
543C23—612no—
544C23—612no—
545C23—612no—
546C23—612no—
547C23—612no—
548C23C2×D4×D6111yescharacteristic
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—614no—
570C2×C4—614no—
571C2×C4—614no—
572C2×C4—614no—
573C2×C4—612no—
574C2×C4—1228no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—4884no—
583C2×C4—4884no—
584C2×C4—2444no—
585C2×C4—2448no—
586C2×C4—2448no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4SD16×D6112yes—
598C2×C4C2×D4×D6111yescharacteristic
599C2×C4C2×Q8×D6111yescharacteristic
600C2×C4C2×Q8×D6111yescharacteristic
601C2×C4#41×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C8—22no—
605C8—41no—
606C8—1222no—
607C8—2441no—
608C22—614no—
609C22—614no—
610C22—614no—
611C22—614no—
612C22—614no—
613C22—614no—
614C22—614no—
615C22#121×D6111yescharacteristic
616C22C22⋊Q8×D6111yescharacteristic
617C22C22⋊Q8×D6111yescharacteristic
618C22C2×SD16×D6111yescharacteristic
619C22#135×D6111yescharacteristic
620C22AGL(1,ℤ/8)×D6111yescharacteristic
621C22#137×D6111yescharacteristic
622C4—22no—
623C4—41no—
624C4—42no—
625C4—42no—
626C4—81no—
627C4—81no—
628C4—614no—
629C4—1222no—
630C4—4881no—
631C4—4881no—
632C4—2441no—
633C4—2442no—
634C4—2442no—
635C4#123×D6111yescharacteristic
636C4#125×D6111yescharacteristic
637C4#125×D6111yescharacteristic
638C4C4⋊Q8×D6111yescharacteristic
639C2—618no—
640C2#398×D6111yescharacteristic
641C2#465×D6111yescharacteristic
642C2#468×D6111yescharacteristic
643C2#476×D6111yescharacteristic
644C2#478×D6111yescharacteristic
645C2#475×D6111yescharacteristic
646C2#479×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2088C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2088D61
hypocenterC61C2×#2088
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #21447323C2semidirect
6. #21447322C2semidirect
7. #21447321C2semidirect
8. #21447320C2semidirect
9. #21447319C2semidirect
10. #21447318C2semidirect
11. #21447317C2semidirect
15. C61×#2088C2semidirect
327. #2088D61direct (N × H)
338. D61#2088direct (N × H)
384. C61C2×#2088semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D612
C2×C4⋊C8×D612
#389×D612
#214473232
#214473222
#214473212
#214473202
#214473192
#214473182
#214473172
#340×D612
C61×#20882
C2×#208861