Finite Group Databasebeta

← #29689605

Subgroups — #29689605

Order 15616.

1386 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic
2C2×#16839812C211yesmaximal, characteristic, complemented
3C2×#16839785C211yesmaximal, characteristic, complemented
4#21446753C212yesmaximal, complemented
5#21446611C212yesmaximal, complemented
6#21446117C211yesmaximal, characteristic, complemented
7#21446116C211yesmaximal, characteristic, complemented
8#21446114C211yesmaximal, characteristic, complemented
9#21445798C212yesmaximal, complemented
10#21445797C212yesmaximal, complemented
11C61×#1870C211yesmaximal, characteristic, complemented
12C22×#11758224C411yescharacteristic
13C22×#11758194C2211yescharacteristic
14C4×#11758224—24no—
15C4×#11758224—24no—
16C2×C4×Dic122C2211yescharacteristic
17C2×#14519742C411yescharacteristic
18C2×D4×Dic61C411yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×#14519737C411yescharacteristic
22C2×#14519737C411yescharacteristic
23C2×#14519735C411yescharacteristic
24C2×#14519733C411yescharacteristic
25C2×#14519733C411yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29#16839812—24no—
30#16839785—24no—
31C2×#14519706C2212yes—
32C2×#14519706C2212yes—
33C2×#14519706C2212yes—
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2212yes—
36C2×#14519689C2212yes—
37C2×#14519689C2212yes—
38C2×C8×Dic61C2212yes—
39#16839517C2212yes—
40#16839516C2212yes—
41#16839516C2212yes—
42C22×M16×C61C2211yescharacteristic
43C2×C4×D4×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2212yes—
46C61×#336C2212yes—
47C2×#11758224—24no—
48C2×#11758224—24no—
49C2×#11758224—24no—
50C22×Dic122C2×C411yescharacteristic
51C22×C22⋊D61C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758194—22no—
61C2×#11758194—42no—
62C22×#92418C2312yes—
63C22×#92418C2312yes—
64C4×Dic122—22no—
65C4×Dic122—22no—
66#14519742—24no—
67D4×Dic61—24no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72#14519737—24no—
73#14519737—24no—
74#14519735—24no—
75#14519733—24no—
76#14519733—24no—
77C2×C4⋊Dic61C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×C4×Dic61—22no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61D414yes—
95C2×C4×Dic61D414yes—
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C42×D61—22no—
100C42×D61—22no—
101#14519706—24no—
102#14519706—24no—
103#14519706—24no—
104C22⋊#92418—22no—
105C22⋊#92418—42no—
106#14519689—42no—
107#14519689—42no—
108C8×Dic61—24no—
109C22×D4×C61C2×C411yescharacteristic
110C23×C4×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C2×M16×C61—22no—
113C2×M16×C61—42no—
114C22×C8×C61C2312yes—
115C22×C8×C61C2312yes—
116C4×D4×C61—22no—
117C4×D4×C61—22no—
118C2×C4⋊C4×C61C2×C411yescharacteristic
119C2×C22⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2×C411yescharacteristic
121C2×C42×C61C2311yescharacteristic
122C22⋊C8×C61—22no—
123C22⋊C8×C61—42no—
124C24×C61C22×C411yescharacteristic
125C24×C61C22×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C2×D4×C61—22no—
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C2×D412yes—
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2411yescharacteristic
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61M1614yescomplemented
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—24no—
155C22×Dic61—22no—
156C22×Dic61—24no—
157C22×Dic61C22⋊C414yes—
158C22×Dic61C22⋊C414yes—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166#11758224—232no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—24no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122M1614yescomplemented
179M16×C61—44no—
180C2×C8×C61—22no—
181C2×C8×C61—22no—
182C2×C8×C61—22no—
183C2×C8×C61—22no—
184C2×C8×C61—22no—
185C2×C8×C61—22no—
186C4⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C42×C61—21no—
190C42×C61—21no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61C22⋊C414yes—
207C4×Dic61C22⋊C414yes—
208C4×Dic61C2×D412yes—
209C4×Dic61C2×D412yes—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D412yes—
212#11758194—44no—
213C2×#92418—22no—
214C2×#92418—22no—
215C2×#92418—22no—
216C2×#92418—22no—
217C2×#92418—22no—
218C2×#92418—22no—
219C23×C61—21no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61C2×C22⋊C412yes—
228C23×C61C2×M1612yes—
229C23×C61C23×C411yescharacteristic
230C22×D61—21no—
231C22×D61—22no—
232C22×D61—21no—
233C22×D61—22no—
234C22×D61C2×M1612yes—
235D4×C61—28no—
236C2×C4×C61—21no—
237C2×C4×C61—22no—
238C2×C4×C61—21no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—24no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—42no—
249C2×C4×C61C2×C22⋊C412yes—
250C2×C4×C61C2×M1612yes—
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61H(5,𝔽2)12yes—
254C2×C4×C612−1+412yes—
255C22⋊D61—28no—
256C22⋊D61—28no—
257C2×Dic61—28no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—22no—
263C2×Dic61—28no—
264C2×Dic61—28no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—44no—
270C2×Dic61C2×C22⋊C412yes—
271C2×Dic61C2×C22⋊C412yes—
272C2×Dic61C2×C22⋊C412yes—
273C2×Dic61C2×C22⋊C412yes—
274C2×Dic61C2×M1612yes—
275C2×Dic61C2×M1612yes—
276C2×Dic61C2×M1612yes—
277C2×Dic61#13114yes—
278C4×D61—28no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—42no—
282C4×D61—44no—
283Dic122—28no—
284C8×C61—42no—
285C8×C61—42no—
286#92418—42no—
287#92418—42no—
288#21849—611nomaximal, Sylow
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—24no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61C22×C22⋊C411yescharacteristic
300C22×C61#52012yes—
301C22×C61C22×M1611yescharacteristic
302C22×C61C22×M1611yescharacteristic
303C22×C61C2×#13112yes—
304C2×D61—22no—
305C2×D61—24no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—42no—
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61#53511yescharacteristic
314C4×C61#53611yescharacteristic
315C4×C61#53712yes—
316Dic61—22no—
317Dic61—22no—
318Dic61—22no—
319Dic61—41no—
320Dic61—41no—
321Dic61#40714yes—
322Dic61#40814yes—
323C2×C4×#41—611no—
324C2×#431—611no—
325C2×#423—611no—
326#1984—612no—
327#1954—612no—
328#1870—611no—
329#1870—611no—
330#1870—611no—
331#1870D6111yescharacteristic, complemented
332#1797—612no—
333#1797—612no—
334C2×C61—42no—
335C2×C61—42no—
336C2×C61#231111yescharacteristic
337C2×C61C2×#40711yescharacteristic
338C2×C61C2×#40811yescharacteristic
339C2×C61#299012yes—
340C2×C61#299112yes—
341D61—42no—
342C22×#41—611no—
343C22×M16—611no—
344C22×M16C2×D6111yescharacteristic
345C4×#41—1224no—
346C4×#41—1224no—
347C2×C4×Q8—611no—
348C2×C4×Q8—611no—
349C2×C4×D4—611no—
350C2×C4×D4—611no—
351C2×C4×D4—611no—
352C2×C4×D4—611no—
353C2×C4×D4—611no—
354C2×C4×D4C2×D6111yescharacteristic
355C2×#117—611no—
356C2×#117—611no—
357C2×#117—611no—
358C22×C42—611no—
359C22×C42—611no—
360C22×C42—611no—
361#431—1224no—
362#423—1224no—
363C2×C4⋊C8—612no—
364C2×C4⋊C8—612no—
365C2×C4⋊C8—612no—
366C2×C22⋊C8—611no—
367C2×C22⋊C8—612no—
368C2×C22⋊C8—612no—
369C2×C22⋊C8—612no—
370C2×C22⋊C8C2×D6111yescharacteristic
371C2×C22⋊C8C2×D6112yes—
372C2×C4×C8—612no—
373#336—612no—
374#336—612no—
375#336—612no—
376#336C2×D6112yes—
377C61#2184911yescharacteristic, complemented, Sylow
378C2×#41—1224no—
379C2×#41—1224no—
380C2×#41—1224no—
381C22×Q8—611no—
382C22×D4—611no—
383C22×D4—611no—
384C22×D4C4×D6111yescharacteristic
385C23×C4—611no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4C22×D6111yescharacteristic
393C23×C4C22×D6111yescharacteristic
394C2×M16—22no—
395C2×M16—42no—
396C2×M16—1222no—
397C2×M16—2442no—
398C22×C8—612no—
399C22×C8—612no—
400C22×C8C22×D6112yes—
401C22×C8C22×D6112yes—
402C4×Q8—1222no—
403C4×Q8—1222no—
404C4×Q8—1224no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—1224no—
408C4×D4—1222no—
409C4×D4—1222no—
410C4×D4—1224no—
411C4×D4—1224no—
412C4×D4—1222no—
413C4×D4—1222no—
414#117—1224no—
415#117—1224no—
416#117—1224no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4C4×D6111yescharacteristic
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4C4×D6111yescharacteristic
428C2×C22⋊C4C4×D6111yescharacteristic
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—614no—
432C2×C42—614no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—1222no—
441C2×C42—1222no—
442C2×C42—1222no—
443C2×C42—1222no—
444C2×C42C22×D6111yescharacteristic
445C4⋊C8—1224no—
446C4⋊C8—1224no—
447C4⋊C8—1224no—
448C22⋊C8—22no—
449C22⋊C8—42no—
450C22⋊C8—1222no—
451C22⋊C8—2442no—
452C22⋊C8—2442no—
453C22⋊C8—2442no—
454C4×C8—1224no—
455C24—611no—
456C24C2×C4×D6111yescharacteristic
457C24C2×C4×D6111yescharacteristic
458#41—12232no—
459C2×Q8—614no—
460C2×Q8—1222no—
461C2×Q8—1222no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—614no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1222no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—614no—
483C22×C4—614no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1224no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1224no—
495C22×C4—1222no—
496C22×C4—1224no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4C2×C4×D6111yescharacteristic
504C22×C4C2×C4×D6111yescharacteristic
505C22×C4C2×C4×D6111yescharacteristic
506C22×C4C2×C4×D6111yescharacteristic
507C22×C4D4×D6112yes—
508C22×C4D4×D6112yes—
509C22×C4C23×D6111yescharacteristic
510M16—44no—
511M16—2444no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—1222no—
519C2×C8—1222no—
520C2×C8—1222no—
521C2×C8—1222no—
522C2×C8—1222no—
523C2×C8—1222no—
524C4⋊C4—22no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—1222no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C42—21no—
537C42—21no—
538C42—612no—
539C42—612no—
540C42—612no—
541C42—612no—
542C42—614no—
543C42—614no—
544C42—1222no—
545C42—1222no—
546C42—1222no—
547C42—1222no—
548C42—1221no—
549C42—1221no—
550C23—21no—
551C23—22no—
552C23—22no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—22no—
557C23—22no—
558C23—612no—
559C23—1221no—
560C23—1222no—
561C23—1221no—
562C23—1222no—
563C23C22⋊C4×D6112yes—
564C23M16×D6112yes—
565C23C22×C4×D6111yescharacteristic
566Q8—1228no—
567D4—28no—
568D4—1228no—
569D4—1228no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—612no—
584C2×C4—612no—
585C2×C4—612no—
586C2×C4—612no—
587C2×C4—614no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—612no—
591C2×C4—1228no—
592C2×C4—1228no—
593C2×C4—1228no—
594C2×C4—1228no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1222no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—2444no—
605C2×C4—2444no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2442no—
609C2×C4C22⋊C4×D6112yes—
610C2×C4M16×D6112yes—
611C2×C4C2×D4×D6111yescharacteristic
612C2×C4C2×D4×D6111yescharacteristic
613C2×C4#1451982212yes—
614C2×C4#1451982412yes—
615C8—42no—
616C8—42no—
617C8—2442no—
618C8—2442no—
619C22—24no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—41no—
628C22—41no—
629C22—1224no—
630C22—1222no—
631C22—2442no—
632C22—2441no—
633C22—2441no—
634C22C2×C22⋊C4×D6111yescharacteristic
635C22#1684024112yes—
636C22C2×M16×D6111yescharacteristic
637C22C2×M16×D6111yescharacteristic
638C22#131×D6112yes—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—614no—
644C4—614no—
645C4—1222no—
646C4—1222no—
647C4—1222no—
648C4—2441no—
649C4—2441no—
650C4#1684032711yescharacteristic
651C4#1684033411yescharacteristic
652C4#1684033912yes—
653C2—42no—
654C2—42no—
655C2—2442no—
656C2#2144840611yescharacteristic
657C2#407×D6111yescharacteristic
658C2#408×D6111yescharacteristic
659C2#2145493912yes—
660C2#2145494712yes—
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radicalC22×#11758224C4
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#21849
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#16839812C2semidirect
3. C2×#16839785C2semidirect
4. #21446753C2semidirect
5. #21446611C2semidirect
6. #21446117C2semidirect
7. #21446116C2semidirect
8. #21446114C2semidirect
9. #21445798C2semidirect
10. #21445797C2semidirect
11. C61×#1870C2semidirect
148. C2×C22⋊D61M16semidirect
178. C2×Dic122M16semidirect
331. #1870D61semidirect
377. C61#21849semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
C2×#168398122
C2×#168397852
#214467532
#214466112
#214461172
#214461162
#214461142
#214457982
#214457972
C61×#18702
#2184961