Finite Group Databasebeta

← #30617902

Subgroups — #30617902

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic
2#21462268C211yesmaximal, characteristic
3#21462002C214yesmaximal, complemented
4#21461999C214yesmaximal, complemented
5#21461723C212yesmaximal
6#21461722C212yesmaximal
7C2×#125×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840785—21no—
10#16840784—21no—
11#16840783—21no—
12#16840782—21no—
13D61⋊(C4⋊C8)C2212yes—
14D61⋊(C22⋊C8)C2212yes—
15#16840721C2212yes—
16#16840708C2212yes—
17#16840706—21no—
18#16840704—21no—
19#16840704C2212yes—
20C4×C4⋊#6923—21no—
21C4×C4⋊#6923C2212yes—
22#16840635C2218yes—
23#16840635C2218yes—
24C2×#14519769C411yescharacteristic, complemented
25C2×#14519768C411yescharacteristic, complemented
26C2×#14519768C411yescharacteristic, complemented
27C2×#14519767—21no—
28C2×#14519767—21no—
29#125×D61—21no—
30#125×D61—21no—
31#125×D61—21no—
32#125×D61—21no—
33#125×D61C412yescomplemented
34#125×D61C412yescomplemented
35#125×D61C2212yes—
36#125×D61C2212yes—
37C2×C4⋊C4×D61—21no—
38C2×C4⋊C4×D61—21no—
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C42×D61C2211yescharacteristic
42C2×#125×C61C411yescharacteristic, complemented
43C2×D61⋊C8C2314yes—
44#14519856—44no—
45C2×C4⋊#6923—22no—
46C2×C4⋊#6923—22no—
47C2×C4⋊#6923C2314yes—
48C2×C22⋊#6923—22no—
49C2×C4×#6923—22no—
50#14519844—22no—
51C4⋊#92420—22no—
52#14519834—22no—
53C22⋊#92420—22no—
54#14519832—22no—
55#14519832—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4—22no—
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63#14519769—21no—
64#14519769—21no—
65#14519769C2×C412yes—
66#14519769C2×C412yes—
67#14519768—21no—
68#14519768—21no—
69#14519768—21no—
70#14519768—21no—
71#14519768C2×C412yes—
72#14519768C2×C412yes—
73#14519768C2×C412yes—
74#14519768C2×C412yes—
75#14519767—22no—
76#14519767—22no—
77#14519767—22no—
78#14519767—22no—
79#14519767—22no—
80#14519767—22no—
81#14519767—22no—
82#14519767—22no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61—22no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—21no—
105C4⋊C4×D61C2×C412yes—
106C4⋊C4×D61C2×C412yes—
107C4⋊C4×D61C2312yes—
108C4⋊C4×D61C2312yes—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120#125×C61—21no—
121#125×C61—21no—
122#125×C61C2×C412yes—
123#125×C61C2×C412yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C42×C61C2×C411yescharacteristic
129C23×D61C2×D411yescharacteristic
130C22×#6923—24no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61C22⋊C411yescharacteristic
134C22×C4×C61C22⋊C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—24no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—42no—
149C2×C4×D61—44no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22×C411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2411yescharacteristic
164C22⋊#6923—44no—
165C2×#92420—24no—
166C4⋊#6923—28no—
167C4⋊#6923—44no—
168C4⋊#6923—44no—
169C4×#6923—44no—
170D61⋊C8—28no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C412yes—
178C4⋊C4×C61C22×C412yes—
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22⋊C411yescharacteristic
181C42×C61C22×C411yescharacteristic
182C42×C61C22×C411yescharacteristic
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—22no—
186C4⋊Dic61—22no—
187C4⋊Dic61—22no—
188C4⋊Dic61—22no—
189C4⋊Dic61C22×C412yes—
190C4⋊Dic61C22×C412yes—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22×C411yescharacteristic
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C23×C61C2×C22⋊C411yescharacteristic
216C22×D61—22no—
217C22×D61—22no—
218C22×D61C2×C22⋊C411yescharacteristic
219C22×D61AGL(1,ℤ/8)12yes—
220C22×D61#13712yes—
221C22×D61C22×D411yescharacteristic
222C2×#6923—44no—
223C2×#6923—44no—
224C2×#6923—44no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—41no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—41no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C2×C22⋊C411yescharacteristic
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C22×D411yescharacteristic
251C4×D61—22no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—44no—
265C4×D61—42no—
266C4×D61—42no—
267C4×D61—44no—
268C4×D61—44no—
269C4×D612−1+414yes—
270#92420—44no—
271#21838—611nomaximal, Sylow
272C22×C61—21no—
273C22×C61—21no—
274C22×C61#41712yes—
275C22×C61C22×C22⋊C411yescharacteristic
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—24no—
279C2×D61—24no—
280C2×D61#41712yes—
281C2×D61#53612yes—
282C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
283C2×D61C2×#13711yescharacteristic
284C2×D61#57512yes—
285#6923—84no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—42no—
292C4×C61—42no—
293C4×C61#51912yes—
294Dic61—21no—
295Dic61—21no—
296Dic61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—42no—
300Dic61—42no—
301Dic61#53612yes—
302C22×#125—611no—
303C2×#432—611no—
304#2285—611no—
305#1992—614no—
306#1989—614no—
307#1824—612no—
308#1823—612no—
309C2×C61—22no—
310C2×C61#231011yescharacteristic
311C2×C61C2×#41711yescharacteristic
312C2×C61#289611yescharacteristic
313D61—22no—
314D61#323412yes—
315D61#323612yes—
316C2×#125—612no—
317C2×#125—612no—
318C2×#125—612no—
319C2×#125—612no—
320C2×#125—611no—
321C2×#125—611no—
322C2×#125—611no—
323C2×#125—1221no—
324C2×#125—1221no—
325C2×#125—1221no—
326C2×#125—1221no—
327C2×#125—1221no—
328C2×#125—1221no—
329C2×#125#692311yescharacteristic, complemented
330C2×#117—1221no—
331C22×C4⋊C4—611no—
332C22×C4⋊C4—611no—
333C22×C4⋊C4—1221no—
334C22×C4⋊C4—1221no—
335C22×C42—611no—
336#432—1221no—
337#432—1221no—
338#432—1221no—
339#432—1221no—
340C2×C4⋊C8—612no—
341C2×C22⋊C8—612no—
342C2×#97—612no—
343#384—612no—
344#382—1221no—
345#380—612no—
346#380—1221no—
347C4×C4⋊C4—612no—
348C4×C4⋊C4—1221no—
349#340—618no—
350#340—618no—
351C61#2183811yescharacteristic, complemented, Sylow
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—1221no—
356C23×C4—1221no—
357C22×C8—614no—
358#125—21no—
359#125—21no—
360#125—612no—
361#125—612no—
362#125—612no—
363#125—612no—
364#125—612no—
365#125—612no—
366#125—1222no—
367#125—1222no—
368#125—1222no—
369#125—1222no—
370#125—1222no—
371#125—1222no—
372#125—1222no—
373#125—1222no—
374#125—1221no—
375#125—1221no—
376#125—1221no—
377#125—1221no—
378#125—1221no—
379#125—1221no—
380#125C2×#692312yes—
381#125C2×#692312yes—
382#117—2444no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—612no—
388C2×C4⋊C4—612no—
389C2×C4⋊C4—612no—
390C2×C4⋊C4—612no—
391C2×C4⋊C4—614no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4C2×#692311yescharacteristic
415C2×C4⋊C4C2×#692311yescharacteristic
416C2×C22⋊C4—1222no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—1222no—
429C2×C42C2×#692311yescharacteristic
430C4⋊C8—1222no—
431C4⋊C8—1222no—
432C22⋊C8—1222no—
433C22⋊C8—1222no—
434#97—1222no—
435#97—1222no—
436#95—1222no—
437#95—1222no—
438C24—611no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1224no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1224no—
466C22×C4—2442no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4—2444no—
470C22×C4C22⋊#692311yescharacteristic
471C22×C4C22⋊#692311yescharacteristic
472C22×C4C22×#692311yescharacteristic
473C2×C8—1224no—
474C2×C8—1228no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—612no—
482C4⋊C4—612no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1228no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—2444no—
503C4⋊C4—2444no—
504C4⋊C4C22×#692312yes—
505C4⋊C4C22×#692312yes—
506C22⋊C4—2444no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—2444no—
520C42C22⋊#692311yescharacteristic
521C42C22⋊#692311yescharacteristic
522C42C22×#692311yescharacteristic
523C42C22×#692311yescharacteristic
524C23—611no—
525C23—612no—
526C23—612no—
527C23—611no—
528C23—1222no—
529C23—1222no—
530C23C2×C22⋊#692311yescharacteristic
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—611no—
539C2×C4—614no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—1222no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2444no—
565C2×C4—2444no—
566C2×C4—2444no—
567C2×C4—2441no—
568C2×C4—2444no—
569C2×C4—2444no—
570C2×C4—2444no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4C2×C22⋊#692311yescharacteristic
574C2×C4C2×C22⋊#692311yescharacteristic
575C2×C4C2×C22⋊#692311yescharacteristic
576C2×C4C2×C22⋊#692311yescharacteristic
577C2×C4C2×C22⋊#692311yescharacteristic
578C2×C4C23×#692311yescharacteristic
579C8—2444no—
580C22—21no—
581C22—21no—
582C22—612no—
583C22—611no—
584C22—611no—
585C22—612no—
586C22—612no—
587C22—1224no—
588C22—1224no—
589C22—1221no—
590C22—1221no—
591C22#1684075312yes—
592C22C22×C22⋊#692311yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—42no—
599C4—42no—
600C4—612no—
601C4—1221no—
602C4—1221no—
603C4—1221no—
604C4—1221no—
605C4—1221no—
606C4—4884no—
607C4—2442no—
608C4—2442no—
609C4#1684083012yes—
610C2—22no—
611C2—612no—
612C2—612no—
613C2—1222no—
614C2#2146229311yescharacteristic
615C2C2×#1684075311yescharacteristic
616C2#2146243911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#125×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×#125#6923
hypocenterC61#21838
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #21462002C2semidirect
4. #21461999C2semidirect
24. C2×#14519769C4semidirect
25. C2×#14519768C4semidirect
26. C2×#14519768C4semidirect
33. #125×D61C4semidirect
34. #125×D61C4semidirect
42. C2×#125×C61C4semidirect
329. C2×#125#6923semidirect
351. C61#21838semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
#214622682
#214620022
#214619992
#214617232
#214617222
C2×#125×D612
#2183861