Finite Group Databasebeta

← #30610471

Subgroups — #30610471

Order 15616.

1248 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic, complemented
2C2×#16840783C211yesmaximal, characteristic, complemented
3#21461161C212yesmaximal, complemented
4#21461158C212yesmaximal, complemented
5#21461150C214yesmaximal, complemented
6#21461114C214yesmaximal, complemented
7C2×#41×Dic61C211yesmaximal, characteristic
8#16840783—21no—
9#16840783—21no—
10#16840783—21no—
11#16840783C2212yes—
12#16840783C2212yescomplemented
13#16840782—21no—
14#16840779C2212yescomplemented
15#16840778C2212yescomplemented
16#16840765—21no—
17C2×C4⋊#92420C2212yescomplemented
18#16840732—21no—
19C2×C22⋊#92420—21no—
20C4×#11758217C2212yes—
21C2×#14519832—21no—
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—
44C22×#92420—22no—
45#14519844—22no—
46C4⋊#92420—22no—
47C4⋊#92420—22no—
48C4⋊#92420C2314yes—
49C22⋊#92420—22no—
50C22⋊#92420—22no—
51C22⋊#92420—22no—
52C22⋊#92420—22no—
53#14519832—22no—
54#14519832—22no—
55#14519832—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—28no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C2×#41×C61C2×C412yes—
123C2×#41×C61C2×C412yes—
124C22×Q8×C61C2×C411yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61C2×C411yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61C2×C411yescharacteristic
129C24×C61—21no—
130C24×C61C22⋊C411yescharacteristic
131#41×C61—28no—
132#41×C61—28no—
133#41×C61—24no—
134#41×C61—24no—
135#41×C61—24no—
136#41×C61M1618yescomplemented
137C2×Q8×C61—24no—
138C2×Q8×C61—21no—
139C2×Q8×C61C22×C412yes—
140C2×D4×C61—28no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—24no—
144C2×D4×C61—21no—
145C2×D4×C61C22×C412yes—
146C22×C4×C61—28no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—24no—
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22⋊C411yescharacteristic
153C22×C4×C61C22⋊C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—42no—
164C22×Dic61—42no—
165C22×Dic61—44no—
166C22×Dic61—44no—
167C22×Dic61C22⋊C411yescharacteristic
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C411yescharacteristic
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179#11758217—44no—
180C2×#92420—24no—
181C2×#92420—24no—
182C2×#92420—44no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61—22no—
194C4⋊Dic61—22no—
195C4⋊Dic61C22×C412yes—
196C4⋊Dic61C22×C412yes—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—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×Dic61C22×C411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2411yescharacteristic
219C23×C61—24no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—41no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61C2×C22⋊C411yescharacteristic
227C23×C61C2×C22⋊C411yescharacteristic
228C23×C61C2×C22⋊C411yescharacteristic
229Q8×C61—24no—
230Q8×C61—22no—
231Q8×C61C2×M1614yes—
232D4×C61—28no—
233D4×C61—24no—
234D4×C61—28no—
235D4×C61—22no—
236D4×C61C2×M1614yes—
237C2×C4×C61—24no—
238C2×C4×C61—28no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—28no—
245C2×C4×C61—22no—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×M1614yes—
250C2×C4×C61C23×C411yescharacteristic
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—44no—
266C2×Dic61—44no—
267C2×Dic61—44no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—44no—
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C411yescharacteristic
277C2×Dic61C22×D411yescharacteristic
278C2×Dic61C22×D411yescharacteristic
279#92420—44no—
280#92420—44no—
281#17452—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—24no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—44no—
291C22×C61—48no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61#40712yes—
295C22×C61#42112yes—
296C22×C61C22×C22⋊C411yescharacteristic
297C4×C61—21no—
298C4×C61—24no—
299C4×C61—21no—
300C4×C61#40712yes—
301C4×C61C22×M1612yes—
302Dic61—21no—
303Dic61—21no—
304Dic61—21no—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—42no—
310Dic61—42no—
311Dic61#57512yes—
312C2×C4×#41—611no—
313#2920—611no—
314C2×#432—611no—
315#1491—612no—
316#1490—612no—
317#1488—614no—
318#1477—614no—
319C2×C61—22no—
320C2×C61—22no—
321C2×C61—41no—
322C2×C61—44no—
323C2×C61C2×#40711yescharacteristic
324C2×C61#289611yescharacteristic
325C2×C61C2×#42111yescharacteristic
326C22×#41#692311yescharacteristic
327C4×#41—612no—
328C4×#41—612no—
329C4×#41—612no—
330C4×#41—612no—
331C4×#41—1221no—
332C4×#41—1221no—
333C4×#41—1221no—
334C4×#41—1221no—
335C2×C4×Q8—611no—
336C2×C4×Q8—611no—
337C2×C4×D4—611no—
338C2×C4×D4—611no—
339C2×C4×D4—1221no—
340C2×C4×D4—1221no—
341C2×#117—611no—
342C2×#117—1221no—
343C22×C42—611no—
344C22×C42—1221no—
345#432—612no—
346#432—612no—
347#432—1221no—
348#432—1221no—
349#432—1221no—
350#432—1221no—
351#431—612no—
352#431—612no—
353#423—1221no—
354C2×C4⋊C8—612no—
355#407—1221no—
356C2×C22⋊C8—1221no—
357C4×M16—612no—
358C2×#97—1221no—
359Q8⋊C8—618no—
360D4⋊C8—618no—
361C61#1745211yescharacteristic, complemented, Sylow
362C2×#41—28no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41C2×#692312yes—
366C2×#41C2×#692312yes—
367C22×Q8C2×#692311yescharacteristic
368C22×D4—21no—
369C22×D4C2×#692311yescharacteristic
370C23×C4—21no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—1221no—
374C23×C4—1221no—
375C23×C4C2×#692311yescharacteristic
376C2×M16—1222no—
377C22×C8—1222no—
378C4×Q8—612no—
379C4×Q8—612no—
380C4×Q8—612no—
381C4×Q8—612no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×Q8—1221no—
385C4×Q8—1221no—
386C4×D4—612no—
387C4×D4—612no—
388C4×D4—612no—
389C4×D4—612no—
390C4×D4—1221no—
391C4×D4—1221no—
392C4×D4—1221no—
393C4×D4—1221no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401C4×D4—1222no—
402#117—612no—
403#117—612no—
404#117—1222no—
405#117—1222no—
406#117—1222no—
407#117—1222no—
408#117—1221no—
409#117—1221no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
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—611no—
429C2×C42—1222no—
430C2×C42—1222no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42—1221no—
434C2×C42—1221no—
435C2×C42—1221no—
436C4⋊C8—614no—
437C4⋊C8—1222no—
438C4⋊C8—1222no—
439C4⋊C8—1222no—
440C22⋊C8—1222no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443C22⋊C8—1222no—
444#97—1222no—
445#97—1222no—
446#97—1222no—
447C4×C8—614no—
448C24—21no—
449C24C22⋊#692311yescharacteristic
450#41—28no—
451#41—28no—
452#41—24no—
453#41—24no—
454#41—24no—
455#41#1175821718yescomplemented
456C2×Q8—24no—
457C2×Q8—21no—
458C2×Q8C22×#692312yes—
459C2×D4—28no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4C22×#692312yes—
465C22×C4—28no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4—2444no—
491C22×C4—2444no—
492C22×C4C22⋊#692311yescharacteristic
493C22×C4C22⋊#692311yescharacteristic
494C22×C4C22⋊#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C22×C4C22×#692311yescharacteristic
497C22×C4C22×#692311yescharacteristic
498M16—2444no—
499C2×C8—1224no—
500C2×C8—1224no—
501C2×C8—2444no—
502C4⋊C4—612no—
503C4⋊C4—612no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—1222no—
533C42—1222no—
534C42—1222no—
535C42—1222no—
536C42—1222no—
537C42—1222no—
538C23—24no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—42no—
544C23—42no—
545C23C2×C22⋊#692311yescharacteristic
546C23C2×C22⋊#692311yescharacteristic
547C23C2×C22⋊#692311yescharacteristic
548Q8—24no—
549Q8—22no—
550Q8C2×#1175821714yes—
551D4—28no—
552D4—24no—
553D4—28no—
554D4—22no—
555D4C2×#1175821714yes—
556C2×C4—24no—
557C2×C4—28no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—28no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—2444no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2444no—
589C2×C4—2444no—
590C2×C4—2444no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4C2×C22⋊#692311yescharacteristic
594C2×C4C2×C22⋊#692311yescharacteristic
595C2×C4C2×C22⋊#692311yescharacteristic
596C2×C4C2×#1175821714yes—
597C2×C4C23×#692311yescharacteristic
598C8—2444no—
599C8—2444no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—24no—
606C22—21no—
607C22—21no—
608C22—44no—
609C22—48no—
610C22—42no—
611C22—42no—
612C22#1684073212yes—
613C22#1684075912yes—
614C22C22×C22⋊#692311yescharacteristic
615C4—21no—
616C4—24no—
617C4—21no—
618C4—612no—
619C4—1221no—
620C4—1221no—
621C4—1221no—
622C4—1221no—
623C4—1221no—
624C4—1221no—
625C4—1221no—
626C4—2442no—
627C4—2442no—
628C4#1684073212yes—
629C4C22×#1175821712yes—
630C2—22no—
631C2—22no—
632C2—41no—
633C2—44no—
634C2C2×#1684073211yescharacteristic
635C2#2146243911yescharacteristic
636C2C2×#1684075911yescharacteristic
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#17452
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. C2×#16840783C2semidirect
3. #21461161C2semidirect
4. #21461158C2semidirect
5. #21461150C2semidirect
6. #21461114C2semidirect
12. #16840783C22semidirect
14. #16840779C22semidirect
15. #16840778C22semidirect
17. C2×C4⋊#92420C22semidirect
22. Q8⋊#92420C22semidirect
23. D4⋊#92420C22semidirect
136. #41×C61M16semidirect
361. C61#17452semidirect
455. #41#11758217semidirect

Maximal subgroups

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

subgroupindex
#214624952
C2×#168407832
#214611612
#214611582
#214611502
#214611142
C2×#41×Dic612
#1745261