Finite Group Databasebeta

← #29601349

Subgroups — #29601349

Order 15616.

1710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839650C212yesmaximal
2C2×C4×C22⋊Dic61C211yesmaximal, characteristic
3#21444056C212yesmaximal
4#21444054C212yesmaximal, complemented
5#21444047C211yesmaximal, characteristic, complemented
6#21444045C211yesmaximal, characteristic, complemented
7#21444045C212yesmaximal, complemented
8#21444042C211yesmaximal, characteristic
9#95×Dic61C211yesmaximal, characteristic, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic
12C22×#11758196C2212yes—
13C22×C22⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C4×Dic61C2212yes—
17C22×C4×Dic61C2211yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2212yes—
20#16839650C4116yescomplemented
21C4×C22⋊Dic61C418yescomplemented
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C24×C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2212yes—
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C23×Dic61C2312yes—
38C23×Dic61C2312yes—
39C23×Dic61C2311yescharacteristic
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2311yescharacteristic
42C23×Dic61C2311yescharacteristic
43C2×#11758196—42no—
44C2×#11758196—42no—
45C2×#11758196C2×C418yescomplemented
46C2×C22⋊Dic61—24no—
47C2×C22⋊Dic61—42no—
48C2×C22⋊Dic61—42no—
49C2×C22⋊Dic61C2×C414yes—
50C2×C22⋊Dic61C2×C418yes—
51C2×C22⋊Dic61C2×C414yes—
52C2×C22⋊Dic61C2×C418yes—
53C2×C4×Dic61—24no—
54C2×C4×Dic61—42no—
55C2×C4×Dic61—42no—
56C2×C4×Dic61—42no—
57C2×C4×Dic61—42no—
58C2×C4×Dic61—42no—
59C2×C4×Dic61—42no—
60C2×C4×Dic61C2×C414yes—
61C2×C4×Dic61C2×C414yes—
62C2×C4×Dic61C2×C418yescomplemented
63#14519684—22no—
64#14519684—22no—
65#14519684—24no—
66#14519684—42no—
67#14519684—42no—
68#14519684—42no—
69#14519684C2×C414yes—
70#14519684C2×C414yes—
71#14519684C2×C418yescomplemented
72#14519684C2×C418yescomplemented
73C25×C61C2311yescharacteristic
74C23×C4×C61—22no—
75C23×C4×C61—22no—
76C23×C4×C61—42no—
77C23×C4×C61—42no—
78C23×C4×C61C2×C414yes—
79C23×C4×C61C2312yes—
80C23×C4×C61C2312yes—
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C2×C22⋊C4×C61—42no—
84C2×C22⋊C4×C61—42no—
85C2×C22⋊C4×C61C2×C418yes—
86#95×C61—22no—
87#95×C61—22no—
88#95×C61—42no—
89C24×C61—21no—
90C24×C61—21no—
91C24×C61—22no—
92C24×C61—21no—
93C24×C61—22no—
94C24×C61—22no—
95C24×C61—21no—
96C24×C61—21no—
97C24×C61—21no—
98C24×C61C22×C414yes—
99C24×C61C22×C412yes—
100C24×C61C2411yescharacteristic
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—28no—
120C22×C4×C61—44no—
121C22×C4×C61—44no—
122C22×C4×C61—48no—
123C22×C4×C61—48no—
124C22×C4×C61C22×C414yes—
125C22×C4×C61C22×C414yes—
126C22×C4×C61C22×C412yes—
127C22×C4×C61C22×C412yes—
128C22×C4×C61#4112yes—
129C22×C4×C61#4112yes—
130C22×Dic61—22no—
131C22×Dic61—21no—
132C22×Dic61—22no—
133C22×Dic61—21no—
134C22×Dic61—22no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—21no—
154C22×Dic61—22no—
155C22×Dic61C22×C412yes—
156C22×Dic61C22×C414yes—
157C22×Dic61C22×C414yes—
158C22×Dic61C22×C412yes—
159C22×Dic61C22×C412yes—
160C22×Dic61C22×C414yes—
161C22×Dic61C22×C414yes—
162C22×Dic61C22×C412yes—
163C22×Dic61#4114yes—
164C22⋊C4×C61—48no—
165C22⋊Dic61—28no—
166C22⋊Dic61—48no—
167C22⋊Dic61C42116yescomplemented
168#11758196—48no—
169C4×Dic61—44no—
170C4×Dic61—44no—
171C4×Dic61—48no—
172C4×Dic61—48no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—24no—
176C23×C61—24no—
177C23×C61—24no—
178C23×C61—24no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—24no—
184C23×C61—24no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—41no—
190C23×C61—42no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—42no—
195C23×C61C2×C4214yes—
196C23×C61C23×C411yescharacteristic
197C23×C61C23×C412yes—
198C23×C61C2×#4111yescharacteristic
199C23×C61C2×#4111yescharacteristic
200C23×C61C2×#4112yes—
201C23×C61H(5,𝔽2)12yes—
202C23×C61H(5,𝔽2)12yes—
203C23×C61H(5,𝔽2)11yescharacteristic
204C23×C61H(5,𝔽2)11yescharacteristic
205C23×C612−1+411yescharacteristic
206C23×C612−1+411yescharacteristic
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—22no—
212C2×C4×C61—24no—
213C2×C4×C61—24no—
214C2×C4×C61—24no—
215C2×C4×C61—24no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—24no—
220C2×C4×C61—416no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61#11714yes—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—24no—
236C2×Dic61—24no—
237C2×Dic61—22no—
238C2×Dic61—24no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—24no—
242C2×Dic61—24no—
243C2×Dic61—24no—
244C2×Dic61—22no—
245C2×Dic61—24no—
246C2×Dic61—24no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61C2×C4214yes—
264C2×Dic61C2×C4214yes—
265C2×Dic61#11714yes—
266#13788—611nomaximal, Sylow
267C22×C61—24no—
268C22×C61—24no—
269C22×C61—24no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—42no—
274C22×C61—44no—
275C22×C61—44no—
276C22×C61—44no—
277C22×C61—44no—
278C22×C61C22×C4211yescharacteristic
279C22×C61C2×#11711yescharacteristic
280C22×C61C2×#11711yescharacteristic
281C22×C61C4×#4112yes—
282C22×C61C4×#4112yes—
283C22×C61#51812yes—
284C22×C61#51811yescharacteristic
285C22×C61#51811yescharacteristic
286C22×C61#51812yes—
287C22×C61#52012yes—
288C22×C61#52011yescharacteristic
289C22×C61#52011yescharacteristic
290C22×C61#52012yes—
291C22×C61#53812yes—
292C22×C61#53812yes—
293C22×C61#53812yes—
294C22×C61#53912yes—
295C22×C61#54012yes—
296C22×C61#54011yescharacteristic
297C22×C61#54111yescharacteristic
298C22×C61#54211yescharacteristic
299C22×C61#54212yes—
300C22×C61#54211yescharacteristic
301C4×C61—24no—
302C4×C61—42no—
303C4×C61—44no—
304C4×C61—44no—
305Dic61—24no—
306Dic61—24no—
307Dic61—24no—
308Dic61—42no—
309Dic61—44no—
310Dic61—44no—
311C2×#388—612no—
312C2×C4×C22⋊C4—611no—
313#1437—612no—
314#1436—612no—
315C4⋊#95—611no—
316#1434—612no—
317#1434—611no—
318C22⋊#95—611no—
319C22⋊#95D6111yescharacteristic
320C4×#95—611no—
321C4×#95—611no—
322C2×C61—44no—
323C2×C61C4×#11711yescharacteristic
324C2×C61#227511yescharacteristic
325C2×C61#227511yescharacteristic
326C2×C61#231211yescharacteristic
327C2×C61#231411yescharacteristic
328C2×C61#231811yescharacteristic
329C2×C61#231911yescharacteristic
330C2×C61#233312yes—
331C2×C61#233412yes—
332C2×C61#233512yes—
333C2×C61#233712yes—
334C24×C4C2×D6111yescharacteristic
335C22×C4⋊C4—612no—
336C22×C22⋊C4—611no—
337C22×C22⋊C4—611no—
338C22×C22⋊C4—612no—
339C22×C22⋊C4C2×D6112yes—
340C22×C42—611no—
341C22×C42—612no—
342C22×C42—611no—
343C22×C42—612no—
344#388—6116no—
345C4×C22⋊C4—618no—
346C2×#95—612no—
347C2×#95—611no—
348C2×#95—612no—
349C2×#95—611no—
350C2×#95—611no—
351C2×#95—611no—
352C2×#95—612no—
353C2×#95—612no—
354C2×#95—612no—
355C2×#95—612no—
356C2×#95C2×D6111yescharacteristic
357C2×#95C2×D6111yescharacteristic
358C2×#95C2×D6112yes—
359C61#1378811yescharacteristic, complemented, Sylow
360C25C22×D6111yescharacteristic
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—612no—
369C23×C4—612no—
370C23×C4—611no—
371C23×C4C4×D6114yes—
372C23×C4C22×D6112yes—
373C23×C4C22×D6112yes—
374C23×C4C22×D6111yescharacteristic
375C23×C4C22×D6111yescharacteristic
376C2×C4⋊C4—618no—
377C2×C4⋊C4—2442no—
378C2×C4⋊C4—2442no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—614no—
382C2×C22⋊C4—618no—
383C2×C22⋊C4—614no—
384C2×C22⋊C4—618no—
385C2×C22⋊C4—1224no—
386C2×C22⋊C4—2442no—
387C2×C22⋊C4—2442no—
388C2×C22⋊C4C4×D6118yes—
389C2×C42—614no—
390C2×C42—614no—
391C2×C42—618no—
392C2×C42—1224no—
393C2×C42—2442no—
394C2×C42—2442no—
395C2×C42—2442no—
396C2×C42—2442no—
397C2×C42—2442no—
398C2×C42—2442no—
399#95—22no—
400#95—22no—
401#95—42no—
402#95—614no—
403#95—614no—
404#95—618no—
405#95—618no—
406#95—1224no—
407#95—1222no—
408#95—1222no—
409#95—2442no—
410#95—2442no—
411#95—2442no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24C2×C4×D6114yes—
422C24C2×C4×D6112yes—
423C24C23×D6111yescharacteristic
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—48no—
446C22×C4—48no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—614no—
450C22×C4—612no—
451C22×C4—614no—
452C22×C4—614no—
453C22×C4—614no—
454C22×C4—612no—
455C22×C4—614no—
456C22×C4—1222no—
457C22×C4—1221no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1221no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1222no—
481C22×C4C2×C4×D6112yes—
482C22×C4C2×C4×D6114yes—
483C22×C4C2×C4×D6114yes—
484C22×C4C2×C4×D6112yes—
485C22×C4#1175822412yes—
486C22×C4#1175822412yes—
487C4⋊C4—2448no—
488C22⋊C4—48no—
489C22⋊C4—6116no—
490C22⋊C4—1228no—
491C22⋊C4—2448no—
492C42—2444no—
493C42—2444no—
494C42—2448no—
495C42—2448no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—22no—
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—41no—
518C23C42×D6114yes—
519C23C22×C4×D6111yescharacteristic
520C23C22×C4×D6112yes—
521C23#41×D6112yes—
522C23C2×#1175822411yescharacteristic
523C23C2×#1175822411yescharacteristic
524C23#1451982212yes—
525C23#1451982212yes—
526C23#1451982211yescharacteristic
527C23#1451982311yescharacteristic
528C23#1451982411yescharacteristic
529C23#1451982511yescharacteristic
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—416no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—614no—
555C2×C4—614no—
556C2×C4—614no—
557C2×C4—1224no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1224no—
561C2×C4—1222no—
562C2×C4—1224no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1224no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1224no—
571C2×C4—1224no—
572C2×C4—1224no—
573C2×C4—1224no—
574C2×C4—1222no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4#1451973314yes—
589C22—24no—
590C22—24no—
591C22—24no—
592C22—42no—
593C22—42no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—42no—
599C22—42no—
600C22C2×C42×D6111yescharacteristic
601C22#117×D6111yescharacteristic
602C22C2×#1451973311yescharacteristic
603C22C4×#1175822412yes—
604C22C4×#1175822412yes—
605C22#1684023412yes—
606C22#1684023511yescharacteristic
607C22#1684023511yescharacteristic
608C22#1684023512yes—
609C22#1684024112yes—
610C22#1684024211yescharacteristic
611C22#1684024311yescharacteristic
612C22#1684024312yes—
613C22#1684034712yes—
614C22#1684034712yes—
615C22#1684034812yes—
616C22#1684035512yes—
617C22#1684036212yes—
618C22#1684036511yescharacteristic
619C22#1684037211yescharacteristic
620C22#1684037911yescharacteristic
621C22#1684038212yes—
622C22#1684038511yescharacteristic
623C4—24no—
624C4—44no—
625C4—44no—
626C4—42no—
627C4—1224no—
628C4—1224no—
629C4—1224no—
630C4—2442no—
631C4—2444no—
632C4—2444no—
633C2—44no—
634C2C4×#1451973311yescharacteristic
635C2#2144817711yescharacteristic
636C2#2144817811yescharacteristic
637C2#2144841511yescharacteristic
638C2#2144842611yescharacteristic
639C2#2144844811yescharacteristic
640C2#2144846111yescharacteristic
641C2#2144858012yes—
642C2#2144858912yes—
643C2#2144861012yes—
644C2#2144863312yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC22⋊#95D61
hypocenterC61#13788
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #21444054C2semidirect
5. #21444047C2semidirect
6. #21444045C2semidirect
7. #21444045C2semidirect
9. #95×Dic61C2semidirect
10. #95×Dic61C2semidirect
20. #16839650C4semidirect
21. C4×C22⋊Dic61C4semidirect
45. C2×#11758196C2×C4semidirect
62. C2×C4×Dic61C2×C4semidirect
71. #14519684C2×C4semidirect
72. #14519684C2×C4semidirect
167. C22⋊Dic61C42semidirect
359. C61#13788semidirect

Maximal subgroups

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

subgroupindex
C2×#168396502
C2×C4×C22⋊Dic612
#214440562
#214440542
#214440472
#214440452
#214440422
#95×Dic612
C61×C22⋊#952
#1378861