Finite Group Databasebeta

← #30617900

Subgroups — #30617900

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#431C211yesmaximal, characteristic
2#21462266C211yesmaximal, characteristic
3#21462001C214yesmaximal, complemented
4#21461999C214yesmaximal, complemented
5#21461723C212yesmaximal
6#21461722C212yesmaximal
7C2×#125×D61C211yesmaximal, characteristic
8#16840781—21no—
9#16840780—21no—
10#16840779—21no—
11#16840778—21no—
12D61⋊(C4⋊C8)C2212yes—
13D61⋊(C22⋊C8)C2212yes—
14C4×D61⋊C8C2212yes—
15#16840707—21no—
16#16840706C2212yes—
17#16840705—21no—
18#16840704C2212yes—
19C4×C4⋊#6923C2212yes—
20C4×C22⋊#6923—21no—
21#16840698—21no—
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—
44C2×C4⋊#6923C2314yes—
45C2×C22⋊#6923—22no—
46C2×C4×#6923—22no—
47#14519844—22no—
48C4⋊#92420—22no—
49#14519834—22no—
50C22⋊#92420—22no—
51C4×#92420—22no—
52C4×#92420—22no—
53(C2×#6923)⋊C4—22no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4—22no—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62#14519769—21no—
63#14519769—21no—
64#14519769C2×C412yes—
65#14519769C2×C412yes—
66#14519768—21no—
67#14519768—21no—
68#14519768—21no—
69#14519768—21no—
70#14519768C2×C412yes—
71#14519768C2×C412yes—
72#14519768C2×C412yes—
73#14519768C2×C412yes—
74#14519767—22no—
75#14519767—22no—
76#14519767—22no—
77#14519767—22no—
78#14519767—22no—
79#14519767—22no—
80#14519767—22no—
81#14519767—22no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C4⋊C4×D61—22no—
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—21no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61C2×C412yes—
105C4⋊C4×D61C2×C412yes—
106C4⋊C4×D61C2312yes—
107C4⋊C4×D61C2312yes—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61C2311yescharacteristic
118C42×D61C2311yescharacteristic
119#125×C61—21no—
120#125×C61—21no—
121#125×C61C2×C412yes—
122#125×C61C2×C412yes—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61C2×C411yescharacteristic
128C23×D61C2×D411yescharacteristic
129C22×#6923—24no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61C22⋊C411yescharacteristic
133C22×C4×C61C22⋊C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C2×C4×D61—24no—
141C2×C4×D61—24no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—42no—
147C2×C4×D61—44no—
148C2×C4×D61—44no—
149C2×C4×D61C22⋊C411yescharacteristic
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22×C411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2411yescharacteristic
161C22⋊#6923—44no—
162C2×#92420—24no—
163C4⋊#6923—28no—
164C4×#6923—44no—
165D61⋊C8—28no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C412yes—
173C4⋊C4×C61C22×C412yes—
174C42×C61C22⋊C411yescharacteristic
175C42×C61C22⋊C411yescharacteristic
176C42×C61C22×C411yescharacteristic
177C42×C61C22×C411yescharacteristic
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61C22×C412yes—
185C4⋊Dic61C22×C412yes—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198C4×Dic61C22⋊C411yescharacteristic
199C4×Dic61C22⋊C411yescharacteristic
200C4×Dic61C22⋊C411yescharacteristic
201C4×Dic61C22⋊C411yescharacteristic
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22×C411yescharacteristic
205C4×Dic61C22×C411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C23×C61C2×C22⋊C411yescharacteristic
211C22×D61—22no—
212C22×D61—22no—
213C22×D61C2×C22⋊C411yescharacteristic
214C22×D61#13514yes—
215C22×D61C22×D411yescharacteristic
216C2×#6923—44no—
217C2×#6923—44no—
218C2×#6923—44no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—41no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—41no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61C2×C22⋊C411yescharacteristic
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61C2×C22⋊C411yescharacteristic
242C2×Dic61C2×C22⋊C411yescharacteristic
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C22×D411yescharacteristic
245C4×D61—22no—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—22no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—44no—
257C4×D61—44no—
258C4×D61—44no—
259C4×D61—44no—
260C4×D612−1+414yes—
261#92420—44no—
262#21836—611nomaximal, Sylow
263C22×C61—21no—
264C22×C61—21no—
265C22×C61#41612yes—
266C22×C61C22×C22⋊C411yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—28no—
270C2×D61#41612yes—
271C2×D61#53612yes—
272C2×D61C2×#13512yes—
273C2×D61#57512yes—
274#6923—84no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—42no—
281C4×C61—42no—
282C4×C61#51912yes—
283Dic61—21no—
284Dic61—21no—
285Dic61—21no—
286Dic61—21no—
287Dic61—21no—
288Dic61—42no—
289Dic61—42no—
290Dic61#53612yes—
291C22×#125—611no—
292C2×#431—611no—
293#2283—611no—
294#1991—614no—
295#1989—614no—
296#1824—612no—
297#1823—612no—
298C2×C61—22no—
299C2×C61#231011yescharacteristic
300C2×C61C2×#41611yescharacteristic
301C2×C61#289611yescharacteristic
302D61—22no—
303D61#323214yes—
304C2×#125—612no—
305C2×#125—612no—
306C2×#125—612no—
307C2×#125—612no—
308C2×#125—611no—
309C2×#125—611no—
310C2×#125—611no—
311C2×#125—1221no—
312C2×#125—1221no—
313C2×#125—1221no—
314C2×#125—1221no—
315C2×#125—1221no—
316C2×#125—1221no—
317C2×#125#692311yescharacteristic, complemented
318C22×C4⋊C4—611no—
319C22×C4⋊C4—611no—
320C22×C4⋊C4—1221no—
321C22×C4⋊C4—1221no—
322C22×C42—611no—
323#431—1221no—
324#431—1221no—
325#431—1221no—
326#431—1221no—
327C2×C4⋊C8—612no—
328C2×C22⋊C8—612no—
329C2×C4×C8—612no—
330#383—1221no—
331#382—612no—
332#381—1221no—
333#380—612no—
334C4×C4⋊C4—612no—
335C4×C22⋊C4—1221no—
336#376—1221no—
337#340—618no—
338#340—618no—
339C61#2183611yescharacteristic, complemented, Sylow
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—1221no—
344C23×C4—1221no—
345C22×C8—614no—
346#125—21no—
347#125—21no—
348#125—612no—
349#125—612no—
350#125—612no—
351#125—612no—
352#125—612no—
353#125—612no—
354#125—1222no—
355#125—1222no—
356#125—1222no—
357#125—1222no—
358#125—1222no—
359#125—1222no—
360#125—1222no—
361#125—1222no—
362#125—1221no—
363#125—1221no—
364#125—1221no—
365#125—1221no—
366#125—1221no—
367#125—1221no—
368#125C2×#692312yes—
369#125C2×#692312yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—612no—
375C2×C4⋊C4—612no—
376C2×C4⋊C4—612no—
377C2×C4⋊C4—612no—
378C2×C4⋊C4—614no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1222no—
384C2×C4⋊C4—1222no—
385C2×C4⋊C4—1222no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1222no—
390C2×C4⋊C4—1222no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4C2×#692311yescharacteristic
400C2×C4⋊C4C2×#692311yescharacteristic
401C2×C22⋊C4—1222no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—1222no—
414C2×C42C2×#692311yescharacteristic
415C4⋊C8—1222no—
416C4⋊C8—1222no—
417C22⋊C8—1222no—
418C22⋊C8—1222no—
419C4×C8—1222no—
420C4×C8—1222no—
421#95—1222no—
422#95—1222no—
423#95—1222no—
424#95—1222no—
425C24—611no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—1224no—
444C22×C4—1224no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1224no—
452C22×C4—2442no—
453C22×C4—2444no—
454C22×C4—2444no—
455C22×C4C22⋊#692311yescharacteristic
456C22×C4C22⋊#692311yescharacteristic
457C22×C4C22×#692311yescharacteristic
458C2×C8—1224no—
459C2×C8—1228no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—612no—
467C4⋊C4—612no—
468C4⋊C4—1222no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C4⋊C4—1222no—
472C4⋊C4—1222no—
473C4⋊C4—1222no—
474C4⋊C4—1222no—
475C4⋊C4—1222no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1228no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4C22×#692312yes—
488C4⋊C4C22×#692312yes—
489C22⋊C4—2444no—
490C42—611no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—611no—
502C42—2444no—
503C42C22⋊#692311yescharacteristic
504C42C22⋊#692311yescharacteristic
505C42C22×#692311yescharacteristic
506C42C22×#692311yescharacteristic
507C23—611no—
508C23—614no—
509C23—611no—
510C23—1222no—
511C23—1222no—
512C23C2×C22⋊#692311yescharacteristic
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—611no—
521C2×C4—614no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2444no—
543C2×C4—2444no—
544C2×C4—2444no—
545C2×C4—2444no—
546C2×C4—2441no—
547C2×C4—2444no—
548C2×C4—2444no—
549C2×C4—2444no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4C2×C22⋊#692311yescharacteristic
553C2×C4C2×C22⋊#692311yescharacteristic
554C2×C4C2×C22⋊#692311yescharacteristic
555C2×C4C2×C22⋊#692311yescharacteristic
556C2×C4C2×C22⋊#692311yescharacteristic
557C2×C4C23×#692311yescharacteristic
558C8—2444no—
559C22—21no—
560C22—21no—
561C22—612no—
562C22—612no—
563C22—612no—
564C22—612no—
565C22—1228no—
566C22—1221no—
567C22—1221no—
568C22#1684075212yes—
569C22C22×C22⋊#692311yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—42no—
577C4—612no—
578C4—1221no—
579C4—1221no—
580C4—1221no—
581C4—1221no—
582C4—1221no—
583C4—4884no—
584C4—2442no—
585C4—2442no—
586C4#1684083012yes—
587C2—22no—
588C2—614no—
589C2—1222no—
590C2#2146229311yescharacteristic
591C2C2×#1684075211yescharacteristic
592C2#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#21836
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. #21462001C2semidirect
4. #21461999C2semidirect
24. C2×#14519769C4semidirect
25. C2×#14519768C4semidirect
26. C2×#14519768C4semidirect
33. #125×D61C4semidirect
34. #125×D61C4semidirect
42. C2×#125×C61C4semidirect
317. C2×#125#6923semidirect
339. C61#21836semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4312
#214622662
#214620012
#214619992
#214617232
#214617222
C2×#125×D612
#2183661