Finite Group Databasebeta

← #29699563

Subgroups — #29699563

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448282C211yesmaximal, characteristic
2#21446434C211yesmaximal, characteristic, complemented
3#21446386C211yesmaximal, characteristic, complemented
4#21446373C211yesmaximal, characteristic, complemented
5#21446113C211yesmaximal, characteristic
6#21446108C211yesmaximal, characteristic
7#21445961C211yesmaximal, characteristic, complemented
8#21445888C211yesmaximal, characteristic, complemented
9#21445800C211yesmaximal, characteristic, complemented
10#21445601C211yesmaximal, characteristic, complemented
11#21445596C211yesmaximal, characteristic, complemented
12#21445587C211yesmaximal, characteristic, complemented
13#21445567C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1924C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519689C2211yescharacteristic
25C2×#14519689C2211yescharacteristic
26C2×#14519688C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839662C411yescharacteristic
30#16839662C411yescharacteristic
31#16839659C411yescharacteristic
32#16839659C411yescharacteristic
33#16839654C411yescharacteristic
34#16839654C411yescharacteristic
35#16839650C411yescharacteristic
36#16839650C411yescharacteristic
37C4×#11758196C2211yescharacteristic
38C4×#11758198C2211yescharacteristic
39C42×Dic61C2211yescharacteristic
40#16839517C2211yescharacteristic
41#16839517C2211yescharacteristic
42#16839516C2211yescharacteristic
43#16839516C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×C22⋊D61C2×C411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758189—22no—
62C2×#11758189—22no—
63C2×#11758189—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C2×C8×D61—22no—
69C2×C8×D61—22no—
70C2×C8×D61—41no—
71C4×C22⋊D61—22no—
72C4×C22⋊D61—22no—
73#14519736—41no—
74#14519736—41no—
75#14519734—41no—
76#14519734—41no—
77C2×C4⋊Dic61C2×C411yescharacteristic
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C4⋊#92418—41no—
100C22⋊#92418—22no—
101C22⋊#92418—41no—
102#14519689—22no—
103#14519689—22no—
104#14519688—22no—
105#14519687—41no—
106C8×Dic61—41no—
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C22⋊C4×C61C2×C411yescharacteristic
117C2×C22⋊C4×C61C2×C411yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—41no—
121C22⋊C8×C61—22no—
122C22⋊C8×C61—41no—
123#97×C61—22no—
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126C24×C61C22×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—41no—
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61#4112yes—
155C2×C4×D61#4112yes—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61#4112yes—
168C22⋊C4×C61—41no—
169C22⋊C4×C61—41no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C22⋊Dic61—22no—
175C22⋊Dic61—41no—
176C22⋊Dic61—41no—
177#11758198—22no—
178#11758198—41no—
179#11758198—41no—
180#11758198—41no—
181#11758198—41no—
182C4⋊Dic61—41no—
183C4⋊Dic61—41no—
184#11758196—22no—
185#11758196—22no—
186#11758196—41no—
187#11758196—41no—
188#11758196—41no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—22no—
196C4×Dic61—41no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418#4112yes—
211#11758189—44no—
212C8×D61—44no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61C23×C411yescharacteristic
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61#11712yes—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61H(5,𝔽2)11yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C22⋊D61—44no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61#11712yes—
274C2×Dic61#13112yes—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C8×C61—22no—
280C8×C61—41no—
281C8×C61—41no—
282C8×C61—41no—
283#92418—22no—
284#92418—41no—
285#92418—41no—
286#92418—41no—
287#22790—611nomaximal, Sylow
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61C2×#11711yescharacteristic
296C22×C61C4×#4111yescharacteristic
297C22×C61#51811yescharacteristic
298C22×C61C2×#13111yescharacteristic
299C22×C61#56811yescharacteristic
300C22×C61#56811yescharacteristic
301C22×C61#56811yescharacteristic
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61#55111yescharacteristic
315C4×C61#55111yescharacteristic
316C4×C61#55311yescharacteristic
317C4×C61#55311yescharacteristic
318Dic61—22no—
319Dic61—22no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323Dic61—41no—
324Dic61—41no—
325#2293—611no—
326#1924—611no—
327#1924D6111yescharacteristic, complemented
328#1917—611no—
329#1916—611no—
330#1870—611no—
331#1869—611no—
332#1839—611no—
333#1818—611no—
334#1798—611no—
335#1753—611no—
336#1752—611no—
337#1750—611no—
338#1745—611no—
339#1729—611no—
340C2×C61—81no—
341C2×C61#235311yescharacteristic
342C2×C61#292311yescharacteristic
343C2×C61#292411yescharacteristic
344C2×C61#296711yescharacteristic
345C2×C61#296911yescharacteristic
346C2×C61#298011yescharacteristic
347C2×C61#298111yescharacteristic
348D61—42no—
349C22×M16—611no—
350C23×C8—611no—
351C2×C4×D4—611no—
352C2×#117—611no—
353C2×#117—611no—
354C2×C4⋊C8—611no—
355C2×C4⋊C8C2×D6111yescharacteristic
356C2×C22⋊C8—611no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—611no—
359C2×C22⋊C8—611no—
360C2×C22⋊C8C2×D6111yescharacteristic
361C2×C22⋊C8C2×D6111yescharacteristic
362C2×#97—611no—
363C2×#97—611no—
364C2×#97C2×D6111yescharacteristic
365C2×C4×C8—611no—
366#390—611no—
367#390—611no—
368#389—611no—
369#389—611no—
370#388—611no—
371#388—611no—
372#388—611no—
373#388—611no—
374C4×C4⋊C4—611no—
375C4×C22⋊C4—611no—
376C4×C22⋊C4C2×D6111yescharacteristic
377C43—611no—
378#336—611no—
379#336—611no—
380#336—611no—
381#336—611no—
382#336—611no—
383#336—611no—
384#336—611no—
385#336—611no—
386#336—611no—
387#336—611no—
388#336—611no—
389#336—611no—
390#336C2×D6111yescharacteristic
391#336C2×D6111yescharacteristic
392C61#2279011yescharacteristic, complemented, Sylow
393C22×D4—611no—
394C23×C4—611no—
395C23×C4C22×D6111yescharacteristic
396C2×M16—1222no—
397C2×M16—1222no—
398C2×M16—2441no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8—1222no—
404C22×C8—1222no—
405C22×C8—2441no—
406C22×C8C22×D6111yescharacteristic
407C22×C8C22×D6111yescharacteristic
408C22×C8C22×D6111yescharacteristic
409C22×C8C22×D6111yescharacteristic
410C4×D4—1222no—
411C4×D4—1222no—
412#117—2441no—
413#117—2441no—
414#117—2441no—
415#117—2441no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4C4×D6111yescharacteristic
432C2×C22⋊C4C4×D6111yescharacteristic
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42C22×D6111yescharacteristic
441C2×C42C22×D6111yescharacteristic
442C4⋊C8—41no—
443C4⋊C8—2441no—
444C22⋊C8—22no—
445C22⋊C8—41no—
446C22⋊C8—1222no—
447C22⋊C8—1222no—
448C22⋊C8—1222no—
449C22⋊C8—2441no—
450#97—22no—
451#97—1222no—
452#97—2441no—
453C4×C8—2441no—
454#95—611no—
455#95—611no—
456#95—611no—
457#95—611no—
458#95C4×D6111yescharacteristic
459#95C4×D6111yescharacteristic
460C24—611no—
461C24C2×C4×D6111yescharacteristic
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—2441no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—612no—
474C22×C4—612no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4C2×C4×D6111yescharacteristic
486C22×C4C2×C4×D6111yescharacteristic
487C22×C4C2×C4×D6111yescharacteristic
488C22×C4C2×C4×D6111yescharacteristic
489C22×C4C23×D6111yescharacteristic
490M16—2444no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—612no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—2444no—
515C2×C8#1175822412yes—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—2441no—
519C4⋊C4—2441no—
520C4⋊C4—2441no—
521C4⋊C4—2441no—
522C4⋊C4—2441no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—2441no—
528C22⋊C4—2441no—
529C22⋊C4—2441no—
530C22⋊C4—2441no—
531C22⋊C4—2441no—
532C22⋊C4—2441no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—1222no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42—2441no—
545C42—2441no—
546C42—2441no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—612no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23C22×C4×D6111yescharacteristic
562D4—2444no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—612no—
583C2×C4—612no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4#41×D6111yescharacteristic
608C2×C4#41×D6111yescharacteristic
609C2×C4#41×D6111yescharacteristic
610C2×C4C2×#1175822411yescharacteristic
611C2×C4#1451982211yescharacteristic
612C2×C4#1451982311yescharacteristic
613C8—22no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—1222no—
618C8—2441no—
619C8—2441no—
620C8—2441no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—1222no—
629C22—1222no—
630C22—1222no—
631C22—2441no—
632C22—2441no—
633C22—2441no—
634C22—2441no—
635C22#117×D6111yescharacteristic
636C22C4×#1175822411yescharacteristic
637C22#1684023411yescharacteristic
638C22#131×D6111yescharacteristic
639C22#1684052711yescharacteristic
640C22#1684052811yescharacteristic
641C22#1684052811yescharacteristic
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—1222no—
648C4—1222no—
649C4—2441no—
650C4—2441no—
651C4—2441no—
652C4—2441no—
653C4—2441no—
654C4#1684043511yescharacteristic
655C4#1684044211yescharacteristic
656C4#1684045911yescharacteristic
657C4#1684046311yescharacteristic
658C2—81no—
659C2—2442no—
660C2#2144875411yescharacteristic
661C2#2145446511yescharacteristic
662C2#2145447511yescharacteristic
663C2#2145480511yescharacteristic
664C2#2145481611yescharacteristic
665C2#2145488711yescharacteristic
666C2#2145489111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1924C2
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1924D61
hypocenterC61#22790
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
2. #21446434C2semidirect
3. #21446386C2semidirect
4. #21446373C2semidirect
7. #21445961C2semidirect
8. #21445888C2semidirect
9. #21445800C2semidirect
10. #21445601C2semidirect
11. #21445596C2semidirect
12. #21445587C2semidirect
13. #21445567C2semidirect
14. #21445514C2semidirect
15. C61×#1924C2semidirect
327. #1924D61semidirect
392. C61#22790semidirect

Maximal subgroups

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

subgroupindex
#214482822
#214464342
#214463862
#214463732
#214461132
#214461082
#214459612
#214458882
#214458002
#214456012
#214455962
#214455872
#214455672
#214455142
C61×#19242
#2279061