Finite Group Databasebeta

← #29602524

Subgroups — #29602524

Order 15616.

1226 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic61C211yesmaximal, characteristic
2#21444080C212yesmaximal
3#21444079C212yesmaximal
4#21444049C211yesmaximal, characteristic
5#21444048C211yesmaximal, characteristic
6#21444048C211yesmaximal, characteristic
7#21444048C211yesmaximal, characteristic
8#21444044C212yesmaximal
9#21444043C212yesmaximal
10C4×#14519684C211yesmaximal, characteristic
11C61×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15C22×C4×Dic61C2211yescharacteristic
16C22×C4×Dic61C2212yes—
17C4⋊C4×Dic61C418yescomplemented
18C2×#14519684C2211yescharacteristic
19C2×#14519684C2211yescharacteristic
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2211yescharacteristic
31C22×C4⋊C4×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C42×C61C2211yescharacteristic
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C23×Dic61C2312yes—
37C23×Dic61C2312yes—
38C23×Dic61C2311yescharacteristic
39C23×Dic61C2311yescharacteristic
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2311yescharacteristic
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61C2×C414yes—
48C2×C4×Dic61—22no—
49C2×C4×Dic61—22no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—22no—
52C2×C4×Dic61—22no—
53C2×C4×Dic61—42no—
54C2×C4×Dic61—42no—
55C2×C4×Dic61C2×C414yes—
56C2×C4×Dic61C2×C418yes—
57#14519684—22no—
58#14519684—22no—
59#14519684—22no—
60#14519684—24no—
61#14519684—24no—
62#14519684—42no—
63#14519684—42no—
64#14519684—42no—
65#14519684—42no—
66#14519684—42no—
67#14519684—42no—
68#14519684C2×C418yes—
69#14519684Q814yes—
70C23×C4×C61C2312yes—
71C23×C4×C61C2312yes—
72C23×C4×C61C2311yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C2×C4⋊C4×C61—22no—
76C2×C4⋊C4×C61—22no—
77C2×C4⋊C4×C61—22no—
78C2×C4⋊C4×C61—22no—
79C2×C4⋊C4×C61—22no—
80C2×C4⋊C4×C61C2×C414yes—
81C2×C42×C61—22no—
82C2×C42×C61—22no—
83C2×C42×C61—22no—
84#95×C61—24no—
85#95×C61—42no—
86C24×C61C2411yescharacteristic
87C22×C4×C61—22no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—22no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61C22×C414yes—
113C22×C4×C61C22×C412yes—
114C22×C4×C61C2×Q812yes—
115C22×C4×C61#4112yes—
116C22×C4×C61#4112yes—
117C22×C4×C61#4112yes—
118C22×C4×C61#4112yes—
119C22×C4×C61#4112yes—
120C22×C4×C61#4112yes—
121C22×C4×C61#4112yes—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61C22×C412yes—
158C22×Dic61C22×C414yes—
159C22×Dic61C22×C412yes—
160C22×Dic61C2×Q812yes—
161C22×Dic61C2×Q812yes—
162C22×Dic61#4112yes—
163C22×Dic61#4112yes—
164C4⋊C4×C61—28no—
165C4⋊C4×C61—44no—
166C42×C61—44no—
167C4⋊Dic61—28no—
168C4⋊Dic61—44no—
169C4×Dic61—28no—
170C4×Dic61—48no—
171C4×Dic61—44no—
172C23×C61C23×C411yescharacteristic
173C23×C61C22×Q811yescharacteristic
174C23×C61C2×#4111yescharacteristic
175C23×C61C2×#4111yescharacteristic
176C23×C61C2×#4111yescharacteristic
177C23×C61C2×#4111yescharacteristic
178C23×C61C2×#4111yescharacteristic
179C23×C61C2×#4111yescharacteristic
180C23×C61C2×#4111yescharacteristic
181C23×C61C2×#4111yescharacteristic
182C23×C61C2×#4111yescharacteristic
183C23×C61H(5,𝔽2)11yescharacteristic
184C23×C61H(5,𝔽2)11yescharacteristic
185C23×C61H(5,𝔽2)11yescharacteristic
186C23×C612−1+411yescharacteristic
187C2×C4×C61—24no—
188C2×C4×C61—24no—
189C2×C4×C61—24no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61#11714yes—
216C2×C4×C61#11714yes—
217C2×C4×C61#11714yes—
218C2×C4×C61#12614yes—
219C2×C4×C61#12614yes—
220C2×C4×C61#12614yes—
221C2×C4×C61#12614yes—
222C2×Dic61—22no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—24no—
230C2×Dic61—22no—
231C2×Dic61—24no—
232C2×Dic61—24no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—41no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61C4×Q814yes—
264#13936—611nomaximal, Sylow
265C22×C61C2×#11711yescharacteristic
266C22×C61C2×#11711yescharacteristic
267C22×C61C2×#11711yescharacteristic
268C22×C61C2×C4×Q811yescharacteristic
269C22×C61C4×#4111yescharacteristic
270C22×C61#51811yescharacteristic
271C22×C61#52011yescharacteristic
272C22×C61C2×#12611yescharacteristic
273C22×C61C2×#12611yescharacteristic
274C22×C61C2×#12611yescharacteristic
275C22×C61C2×#12611yescharacteristic
276C22×C61#52911yescharacteristic
277C22×C61#52911yescharacteristic
278C22×C61#53311yescharacteristic
279C22×C61#53311yescharacteristic
280C22×C61#54011yescharacteristic
281C22×C61#54011yescharacteristic
282C22×C61#54211yescharacteristic
283C22×C61#54211yescharacteristic
284C22×C61#55211yescharacteristic
285C22×C61#55211yescharacteristic
286C22×C61#55311yescharacteristic
287C22×C61#55311yescharacteristic
288C22×C61#55311yescharacteristic
289C22×C61#55311yescharacteristic
290C22×C61#55411yescharacteristic
291C22×C61#55411yescharacteristic
292C22×C61#55411yescharacteristic
293C22×C61#55511yescharacteristic
294C22×C61#55511yescharacteristic
295C22×C61#55611yescharacteristic
296C22×C61#55711yescharacteristic
297C22×C61#55911yescharacteristic
298C22×C61#55911yescharacteristic
299C22×C61#55911yescharacteristic
300C4×C61—44no—
301C4×C61—42no—
302C4×C61—42no—
303C4×C61—82no—
304C4×C61#38318yes—
305Dic61—24no—
306Dic61—44no—
307Dic61—42no—
308Dic61—42no—
309Dic61—42no—
310Dic61—82no—
311C2×C4×C4⋊C4—611no—
312#1443—612no—
313#1443—612no—
314C4⋊#95—611no—
315C4⋊#95—611no—
316C4⋊#95—611no—
317C4⋊#95—611no—
318C4⋊#95D6111yescharacteristic
319#1434—612no—
320#1434—612no—
321C4×#95—611no—
322C2×C61C2×#38311yescharacteristic
323C2×C61#229511yescharacteristic
324C2×C61#231911yescharacteristic
325C2×C61#234511yescharacteristic
326C2×C61#234611yescharacteristic
327C2×C61#235511yescharacteristic
328C2×C61#235711yescharacteristic
329C2×C61#249411yescharacteristic
330C2×C61#249411yescharacteristic
331C2×C61#249711yescharacteristic
332C2×C61#249711yescharacteristic
333C2×C61#251111yescharacteristic
334C2×C61#251111yescharacteristic
335C2×C61#251311yescharacteristic
336C2×C61#251311yescharacteristic
337C22×C4⋊C4—611no—
338C22×C4⋊C4—611no—
339C22×C4⋊C4C2×D6111yescharacteristic
340C22×C4⋊C4C2×D6111yescharacteristic
341C22×C42—611no—
342C22×C42—612no—
343C22×C42—611no—
344C22×C42C2×D6111yescharacteristic
345C4×C4⋊C4—618no—
346C2×#95—611no—
347C2×#95—612no—
348C2×#95—611no—
349C2×#95—611no—
350C2×#95—611no—
351C2×#95—612no—
352C2×#95—612no—
353C2×#95—612no—
354C2×#95—612no—
355C2×#95—612no—
356C2×#95—612no—
357C2×#95—612no—
358C2×#95—612no—
359C2×#95C2×D6112yes—
360C2×#95C2×D6112yes—
361C61#1393611yescharacteristic, complemented, Sylow
362C23×C4—611no—
363C23×C4—612no—
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—612no—
368C23×C4C22×D6112yes—
369C23×C4C22×D6112yes—
370C23×C4C22×D6111yescharacteristic
371C23×C4C22×D6111yescharacteristic
372C23×C4C22×D6111yescharacteristic
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—614no—
379C2×C4⋊C4—1222no—
380C2×C4⋊C4—1222no—
381C2×C4⋊C4—1222no—
382C2×C4⋊C4—1222no—
383C2×C4⋊C4—1222no—
384C2×C4⋊C4C4×D6114yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—614no—
389C2×C42—618no—
390C2×C42—1222no—
391C2×C42—1222no—
392C2×C42—1222no—
393C2×C42—1222no—
394C2×C42—1222no—
395C2×C42—2442no—
396C2×C42—2442no—
397#95—24no—
398#95—42no—
399#95—618no—
400#95—614no—
401#95—1222no—
402#95—1222no—
403#95—1224no—
404#95—1224no—
405#95—1222no—
406#95—2442no—
407#95—2442no—
408#95—2442no—
409#95—2442no—
410#95—2442no—
411#95—2442no—
412C24C23×D6111yescharacteristic
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—614no—
443C22×C4—612no—
444C22×C4—612no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1222no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1222no—
463C22×C4—1221no—
464C22×C4—1222no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4C2×C4×D6114yes—
481C22×C4C2×C4×D6112yes—
482C22×C4#1175822212yes—
483C22×C4#1175822212yes—
484C22×C4#1175822412yes—
485C22×C4#1175822412yes—
486C22×C4#1175822412yes—
487C22×C4#1175822412yes—
488C22×C4Q8×D6112yes—
489C22×C4#1175822612yes—
490C4⋊C4—28no—
491C4⋊C4—44no—
492C4⋊C4—1228no—
493C4⋊C4—2444no—
494C42—44no—
495C42—1228no—
496C42—2448no—
497C42—2444no—
498C23C22×C4×D6111yescharacteristic
499C23C2×Q8×D6111yescharacteristic
500C23#41×D6111yescharacteristic
501C23#41×D6111yescharacteristic
502C23C2×#1175822411yescharacteristic
503C23C2×#1175822411yescharacteristic
504C23C2×#1175822411yescharacteristic
505C23C2×#1175822411yescharacteristic
506C23C2×#1175822211yescharacteristic
507C23C2×#1175822211yescharacteristic
508C23C2×#1175822611yescharacteristic
509C23#1451982211yescharacteristic
510C23#1451982311yescharacteristic
511C23#1451982311yescharacteristic
512C23#1451982511yescharacteristic
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—614no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1224no—
554C2×C4—1222no—
555C2×C4—1224no—
556C2×C4—1224no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2441no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4#1451973314yes—
584C2×C4#1451973414yes—
585C2×C4#1451973514yes—
586C2×C4#1451977014yes—
587C2×C4#1451977014yes—
588C2×C4#1451977214yes—
589C2×C4#1451977214yes—
590C22C2×#1451973311yescharacteristic
591C22C2×#1451973411yescharacteristic
592C22C2×#1451973511yescharacteristic
593C22C4×Q8×D6111yescharacteristic
594C22C4×#1175822411yescharacteristic
595C22#1684023411yescharacteristic
596C22#1684024411yescharacteristic
597C22C2×#1451977011yescharacteristic
598C22C2×#1451977011yescharacteristic
599C22C2×#1451977211yescharacteristic
600C22C2×#1451977211yescharacteristic
601C22#1684029311yescharacteristic
602C22#1684029711yescharacteristic
603C22#1684031411yescharacteristic
604C22#1684031711yescharacteristic
605C22#1684036511yescharacteristic
606C22#1684036811yescharacteristic
607C22#1684038511yescharacteristic
608C22#1684038611yescharacteristic
609C22#1684044711yescharacteristic
610C22#1684045311yescharacteristic
611C22#1684045611yescharacteristic
612C22#1684045911yescharacteristic
613C22#1684046211yescharacteristic
614C22#1684046411yescharacteristic
615C22#1684046711yescharacteristic
616C22#1684047011yescharacteristic
617C22#1684047211yescharacteristic
618C22#1684047511yescharacteristic
619C22#1684047711yescharacteristic
620C22#1684048311yescharacteristic
621C22#1684048711yescharacteristic
622C22#1684049411yescharacteristic
623C22#1684049411yescharacteristic
624C22#1684049811yescharacteristic
625C4—42no—
626C4—44no—
627C4—42no—
628C4—82no—
629C4—1224no—
630C4—4882no—
631C4—2444no—
632C4—2442no—
633C4—2442no—
634C4—2442no—
635C4#1683962918yes—
636C2C2×#1683962911yescharacteristic
637C2#2144829011yescharacteristic
638C2#2144845811yescharacteristic
639C2#2144869211yescharacteristic
640C2#2144870011yescharacteristic
641C2#2144877511yescharacteristic
642C2#2144879111yescharacteristic
643C2#2145021511yescharacteristic
644C2#2145021711yescharacteristic
645C2#2145024811yescharacteristic
646C2#2145025011yescharacteristic
647C2#2145039011yescharacteristic
648C2#2145039211yescharacteristic
649C2#2145041211yescharacteristic
650C2#2145041411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, prime radical, cosocleC24×C61C24
hypercenterC4⋊#95D61
hypocenterC61#13936
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
17. C4⋊C4×Dic61C4semidirect
361. C61#13936semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic612
#214440802
#214440792
#214440492
#214440482
#214440442
#214440432
C4×#145196842
C61×C4⋊#952
#1393661