Finite Group Databasebeta

← #30610459

Subgroups — #30610459

Order 15616.

1246 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic, complemented
2#21462495C211yesmaximal, characteristic, complemented
3#21461154C214yesmaximal, complemented
4#21461150C214yesmaximal, complemented
5#21461121C212yesmaximal, complemented
6#21461118C212yesmaximal, complemented
7C2×#41×Dic61C211yesmaximal, characteristic
8#16840783—21no—
9#16840783C2212yescomplemented
10#16840782—21no—
11#16840782—21no—
12#16840779—21no—
13#16840779C2212yescomplemented
14#16840778C2212yes—
15#16840778C2212yes—
16#16840765—21no—
17#16840765C2212yescomplemented
18#16840732—21no—
19#16840732—21no—
20C4×#11758217—21no—
21C4×#11758217C2212yescomplemented
22Q8⋊#92420C2218yescomplemented
23D4⋊#92420C2218yescomplemented
24#41×Dic61—21no—
25#41×Dic61—21no—
26#41×Dic61—21no—
27#41×Dic61—21no—
28#41×Dic61C412yes—
29#41×Dic61C412yes—
30#41×Dic61C2212yes—
31#41×Dic61C2212yes—
32C2×Q8×Dic61C411yescharacteristic
33C2×Q8×Dic61C2211yescharacteristic
34C2×D4×Dic61—21no—
35C2×D4×Dic61—21no—
36C2×D4×Dic61C411yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519736—21no—
39C2×#14519736C411yescharacteristic
40C22×C4×Dic61—21no—
41C22×C4×Dic61C2211yescharacteristic
42C22×#41×C61C411yescharacteristic
43C2×#11758217—22no—
44C2×#11758217—22no—
45#14519844—22no—
46#14519844—22no—
47C4⋊#92420—22no—
48C4⋊#92420C2314yes—
49C22⋊#92420—22no—
50C22⋊#92420—22no—
51C22⋊#92420—22no—
52C22⋊#92420—22no—
53#14519832—22no—
54#14519832—22no—
55C4×#92420—22no—
56C4×#92420C2314yes—
57C23×Dic61—21no—
58C23×Dic61—21no—
59C23×Dic61D411yescharacteristic
60C23×Dic61D411yescharacteristic
61Q8×Dic61—21no—
62Q8×Dic61—21no—
63Q8×Dic61—21no—
64Q8×Dic61—21no—
65Q8×Dic61C2×C412yes—
66Q8×Dic61C2×C412yes—
67Q8×Dic61C2×C412yes—
68Q8×Dic61C2312yes—
69D4×Dic61—22no—
70D4×Dic61—22no—
71D4×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61—22no—
74D4×Dic61—22no—
75D4×Dic61—22no—
76D4×Dic61—22no—
77D4×Dic61—21no—
78D4×Dic61—21no—
79D4×Dic61—21no—
80D4×Dic61—21no—
81D4×Dic61C2×C412yes—
82D4×Dic61C2×C412yes—
83D4×Dic61C2×C412yes—
84D4×Dic61C2312yes—
85#14519736—21no—
86#14519736—21no—
87#14519736—22no—
88#14519736—22no—
89#14519736—22no—
90#14519736—22no—
91#14519736C2×C412yes—
92#14519736C2×C412yes—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C2×#41×C61—24no—
120C2×#41×C61—24no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61C2×C412yes—
124C2×#41×C61C2×C412yes—
125C22×Q8×C61C2×C411yescharacteristic
126C22×D4×C61—21no—
127C22×D4×C61C2×C411yescharacteristic
128C23×C4×C61—21no—
129C23×C4×C61C2×C411yescharacteristic
130C24×C61—21no—
131C24×C61C22⋊C411yescharacteristic
132#41×C61—28no—
133#41×C61—28no—
134#41×C61—24no—
135#41×C61—24no—
136#41×C61—24no—
137#41×C61—24no—
138C2×Q8×C61—21no—
139C2×Q8×C61—22no—
140C2×Q8×C61M1614yescomplemented
141C2×Q8×C61C22×C412yes—
142C2×D4×C61—28no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—22no—
147C2×D4×C61M1614yescomplemented
148C2×D4×C61C22×C412yes—
149C22×C4×C61—28no—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61C22⋊C411yescharacteristic
156C22×C4×C61C22⋊C411yescharacteristic
157C22×C4×C61C22⋊C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—42no—
168C22×Dic61—42no—
169C22×Dic61—44no—
170C22×Dic61—44no—
171C22×Dic61C22⋊C411yescharacteristic
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183#11758217—44no—
184#11758217—44no—
185C2×#92420—24no—
186C2×#92420—24no—
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—22no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61C22×C412yes—
200C4⋊Dic61C22×C412yes—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2411yescharacteristic
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—24no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61C2×C22⋊C411yescharacteristic
231C23×C61C2×C22⋊C411yescharacteristic
232C23×C61C2×C22⋊C411yescharacteristic
233Q8×C61—22no—
234Q8×C61—24no—
235Q8×C61C2×M1614yes—
236D4×C61—28no—
237D4×C61—28no—
238D4×C61—22no—
239D4×C61—24no—
240D4×C61C2×M1614yes—
241C2×C4×C61—28no—
242C2×C4×C61—28no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—24no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C2×M1612yes—
256C2×C4×C61C2×M1612yes—
257C2×C4×C61C23×C411yescharacteristic
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—44no—
273C2×Dic61—44no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—44no—
277C2×Dic61—44no—
278C2×Dic61C2×C22⋊C411yescharacteristic
279C2×Dic61C2×C22⋊C411yescharacteristic
280C2×Dic61C2×C22⋊C411yescharacteristic
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C22×D411yescharacteristic
285C2×Dic61C22×D411yescharacteristic
286#92420—44no—
287#92420—44no—
288#17450—611nomaximal, Sylow
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—24no—
294C22×C61—21no—
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—44no—
299C22×C61—48no—
300C22×C61—42no—
301C22×C61—42no—
302C22×C61#40712yes—
303C22×C61C22×C22⋊C411yescharacteristic
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—24no—
307C4×C61#40712yes—
308C4×C61C22×M1611yescharacteristic
309C4×C61C22×M1611yescharacteristic
310Dic61—21no—
311Dic61—21no—
312Dic61—21no—
313Dic61—21no—
314Dic61—21no—
315Dic61—21no—
316Dic61—42no—
317Dic61—42no—
318Dic61#42112yes—
319Dic61#57512yes—
320C2×C4×#41—611no—
321#2920—611no—
322#2920—611no—
323#1489—614no—
324#1488—614no—
325#1479—612no—
326#1478—612no—
327C2×C61—22no—
328C2×C61—41no—
329C2×C61—41no—
330C2×C61—44no—
331C2×C61C2×#40711yescharacteristic
332C2×C61#289611yescharacteristic
333C2×C61C2×#42111yescharacteristic
334C22×#41#692311yescharacteristic
335C4×#41—612no—
336C4×#41—612no—
337C4×#41—612no—
338C4×#41—612no—
339C4×#41—1221no—
340C4×#41—1221no—
341C4×#41—1221no—
342C4×#41—1221no—
343C2×C4×Q8—611no—
344C2×C4×Q8—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—1221no—
348C2×C4×D4—1221no—
349C2×#117—611no—
350C2×#117—1221no—
351C22×C42—611no—
352C22×C42—1221no—
353#432—612no—
354#432—1221no—
355#432—1221no—
356#432—1221no—
357#431—612no—
358#431—612no—
359#431—612no—
360#431—1221no—
361#423—612no—
362#423—1221no—
363#407—1221no—
364#407—1221no—
365C4×M16—612no—
366C4×M16—1221no—
367Q8⋊C8—618no—
368D4⋊C8—618no—
369C61#1745011yescharacteristic, complemented, Sylow
370C2×#41—24no—
371C2×#41—24no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41C2×#692312yes—
375C2×#41C2×#692312yes—
376C22×Q8C2×#692311yescharacteristic
377C22×D4—21no—
378C22×D4C2×#692311yescharacteristic
379C23×C4—21no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—1221no—
383C23×C4—1221no—
384C23×C4C2×#692311yescharacteristic
385C2×M16—1222no—
386C2×M16—1222no—
387C4×Q8—612no—
388C4×Q8—612no—
389C4×Q8—612no—
390C4×Q8—612no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×D4—612no—
396C4×D4—612no—
397C4×D4—612no—
398C4×D4—612no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4—1221no—
402C4×D4—1221no—
403C4×D4—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410C4×D4—1222no—
411#117—612no—
412#117—612no—
413#117—1222no—
414#117—1222no—
415#117—1222no—
416#117—1222no—
417#117—1221no—
418#117—1221no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—1222no—
439C2×C42—1222no—
440C2×C42—1222no—
441C2×C42—1222no—
442C2×C42—1221no—
443C2×C42—1221no—
444C2×C42—1221no—
445C4⋊C8—614no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1222no—
453#97—1222no—
454#97—1222no—
455C4×C8—614no—
456C4×C8—1222no—
457C24—21no—
458C24C22⋊#692311yescharacteristic
459#41—28no—
460#41—28no—
461#41—24no—
462#41—24no—
463#41—24no—
464#41—24no—
465C2×Q8—21no—
466C2×Q8—22no—
467C2×Q8#1175821714yescomplemented
468C2×Q8C22×#692312yes—
469C2×D4—28no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4#1175821714yescomplemented
475C2×D4C22×#692312yes—
476C22×C4—28no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
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—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4—2444no—
503C22×C4—2444no—
504C22×C4C22⋊#692311yescharacteristic
505C22×C4C22⋊#692311yescharacteristic
506C22×C4C22⋊#692311yescharacteristic
507C22×C4C22×#692311yescharacteristic
508C22×C4C22×#692311yescharacteristic
509C22×C4C22×#692311yescharacteristic
510M16—2444no—
511M16—2444no—
512C2×C8—1224no—
513C2×C8—1224no—
514C4⋊C4—612no—
515C4⋊C4—612no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—1222no—
545C42—1222no—
546C42—1222no—
547C42—1222no—
548C42—1222no—
549C42—1222no—
550C23—22no—
551C23—24no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—42no—
556C23—42no—
557C23C2×C22⋊#692311yescharacteristic
558C23C2×C22⋊#692311yescharacteristic
559C23C2×C22⋊#692311yescharacteristic
560Q8—24no—
561Q8—22no—
562Q8C2×#1175821714yes—
563D4—28no—
564D4—28no—
565D4—24no—
566D4—22no—
567D4C2×#1175821714yes—
568C2×C4—28no—
569C2×C4—28no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—611no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—2444no—
596C2×C4—2444no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2444no—
604C2×C4—2444no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4C2×C22⋊#692311yescharacteristic
608C2×C4C2×C22⋊#692311yescharacteristic
609C2×C4C2×C22⋊#692311yescharacteristic
610C2×C4C2×#1175821712yes—
611C2×C4C2×#1175821712yes—
612C2×C4C23×#692311yescharacteristic
613C8—2444no—
614C8—2444no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—24no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—44no—
625C22—48no—
626C22—42no—
627C22—42no—
628C22#1684073212yes—
629C22C22×C22⋊#692311yescharacteristic
630C4—21no—
631C4—21no—
632C4—24no—
633C4—612no—
634C4—612no—
635C4—1221no—
636C4—1221no—
637C4—1221no—
638C4—1221no—
639C4—1221no—
640C4—1221no—
641C4—2442no—
642C4—2442no—
643C4#1684073212yes—
644C4C22×#1175821711yescharacteristic
645C4C22×#1175821711yescharacteristic
646C2—22no—
647C2—41no—
648C2—41no—
649C2—44no—
650C2C2×#1684073211yescharacteristic
651C2#2146243911yescharacteristic
652C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
Fitting, prime radicalC22×#41×C61C4
socleC22×C61C22×C22⋊C4
cosocleC4×Dic61C24
hypercenterC22×#41#6923
hypocenterC61#17450
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. #21462495C2semidirect
3. #21461154C2semidirect
4. #21461150C2semidirect
5. #21461121C2semidirect
6. #21461118C2semidirect
9. #16840783C22semidirect
13. #16840779C22semidirect
17. #16840765C22semidirect
21. C4×#11758217C22semidirect
22. Q8⋊#92420C22semidirect
23. D4⋊#92420C22semidirect
140. C2×Q8×C61M16semidirect
147. C2×D4×C61M16semidirect
369. C61#17450semidirect
467. C2×Q8#11758217semidirect
474. C2×D4#11758217semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214611542
#214611502
#214611212
#214611182
C2×#41×Dic612
#1745061