Finite Group Databasebeta

← #29740617

Subgroups — #29740617

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449266C211yesmaximal, characteristic
2C4⋊C4×C22⋊D61C211yesmaximal, characteristic
3#21447380C211yesmaximal, characteristic, complemented
4#21447252C211yesmaximal, characteristic, complemented
5#21447230C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21446455C211yesmaximal, characteristic, complemented
8#21446407C211yesmaximal, characteristic, complemented
9#21446239C211yesmaximal, characteristic, complemented
10#21446123C211yesmaximal, characteristic, complemented
11#21446108C211yesmaximal, characteristic
12#21446013C211yesmaximal, characteristic, complemented
13#21445905C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519753C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28#16839693—21no—
29#16839685—21no—
30#16839669C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839657—21no—
33#16839638—21no—
34#16839635—21no—
35#16839633—21no—
36#16839631C2211yescharacteristic
37#16839622C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839619—21no—
40#16839619C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×C22⋊D61D411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C2×C8×D61—22no—
66C2×C8×D61—41no—
67C2×C8×D61—41no—
68#14519753—22no—
69#14519753—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72C4×C22⋊D61—44no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196D411yescharacteristic
84C4⋊C4×D61—22no—
85C4⋊C4×D61—22no—
86C4⋊C4×D61—41no—
87C4⋊C4×D61—41no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61D411yescharacteristic
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198D411yescharacteristic
94C2×C4×Dic61—21no—
95C2×C4×Dic61C2311yescharacteristic
96#14519709—41no—
97#14519708—22no—
98#14519701—41no—
99#14519701—41no—
100C22⋊#92418—41no—
101#14519689—22no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×Q8×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61—41no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—41no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C22⋊C4×C61—21no—
124#103×C61—22no—
125#103×C61—41no—
126C22⋊C8×C61—41no—
127C24×C61C2×D411yescharacteristic
128C23×D61C2×D411yescharacteristic
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—42no—
146C22×C4×C61—42no—
147C22×C4×C61—81no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61SD1614yes—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61—42no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×C4×D61#4112yes—
171C2×C4×D61#4112yes—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—42no—
183C4⋊C4×C61—42no—
184C4⋊C4×C61#4112yes—
185C4⋊C4×C61#4112yes—
186C22⋊C4×C61—42no—
187C22⋊Dic61—22no—
188C22⋊Dic61—42no—
189C22⋊Dic61—81no—
190#11758198—22no—
191#11758198—42no—
192#11758198—42no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—81no—
202#11758196—22no—
203#11758196—42no—
204#11758196—42no—
205#11758196—42no—
206#11758196—42no—
207#11758196—81no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—42no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C8×D61—44no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61C2×SD1612yes—
225C23×C61C22×D411yescharacteristic
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61#12312yes—
231C22×D61C2×SD1612yes—
232C22×D61#13712yes—
233Q8×C61—41no—
234Q8×C61—41no—
235Q8×C61—41no—
236Q8×C61—41no—
237C2×C4×C61—21no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—84no—
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61H(5,𝔽2)11yescharacteristic
262C2×C4×C61H(5,𝔽2)11yescharacteristic
263C22⋊D61—28no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61#12312yes—
284C2×Dic61C2×SD1612yes—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—84no—
290C4×D61—84no—
291C8×C61—41no—
292C8×C61—41no—
293#92418—41no—
294#92418—41no—
295#26200—611nomaximal, Sylow
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61C2×#12311yescharacteristic
304C22×C61#54611yescharacteristic
305C22×C61#54611yescharacteristic
306C22×C61C22×SD1611yescharacteristic
307C22×C61C2×#13711yescharacteristic
308C22×C61#57611yescharacteristic
309C22×C61#57811yescharacteristic
310C2×D61—22no—
311C2×D61—22no—
312C2×D61—22no—
313C2×D61—22no—
314C2×D61—22no—
315C2×D61—22no—
316C2×D61#48314yes—
317C4×C61—41no—
318C4×C61—42no—
319C4×C61—42no—
320C4×C61—81no—
321C4×C61—81no—
322C4×C61#52911yescharacteristic
323C4×C61#53811yescharacteristic
324C4×C61#55311yescharacteristic
325C4×C61#55311yescharacteristic
326Dic61—22no—
327Dic61—22no—
328Dic61—41no—
329Dic61—81no—
330Dic61—81no—
331Dic61—81no—
332Dic61—81no—
333#2417—611no—
334D4×C4⋊C4—611no—
335#2099—611no—
336#2077—611no—
337#2072—611no—
338#2035—611no—
339#1927—611no—
340#1920—611no—
341#1892—611no—
342#1872—611no—
343#1872D6111yescharacteristic, complemented
344#1869—611no—
345#1853—611no—
346#1823—611no—
347C2×#340—611no—
348C2×C61—42no—
349C2×C61#244411yescharacteristic
350C2×C61C2×#48311yescharacteristic
351C2×C61#309811yescharacteristic
352C2×C61#329511yescharacteristic
353C2×C61#329811yescharacteristic
354C2×C61#331211yescharacteristic
355C2×C61#331411yescharacteristic
356D61—24no—
357C23×C8—611no—
358C2×C22⋊Q8—611no—
359C2×C22⋊Q8C2×D6111yescharacteristic
360C2×C4×D4—611no—
361C2×C4×D4—1221no—
362C22×C4⋊C4—611no—
363C22×C4⋊C4—611no—
364C22×C4⋊C4C2×D6111yescharacteristic
365C2×#106—611no—
366C2×#106—611no—
367C2×#103—611no—
368C2×#103—611no—
369C2×#103C2×D6111yescharacteristic
370C2×#103C2×D6111yescharacteristic
371C2×C22⋊C8—611no—
372C2×C22⋊C8—611no—
373C2×C22⋊C8C2×D6111yescharacteristic
374#398—1221no—
375#396—1221no—
376#391—611no—
377#389—611no—
378#389—1221no—
379#386—1221no—
380#385—1221no—
381#385—1221no—
382#384—611no—
383#380—611no—
384#380—611no—
385#380—611no—
386#380—1221no—
387C4×C4⋊C4—611no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#340—611no—
395#340—611no—
396#340C2×D6111yescharacteristic
397#340C2×D6111yescharacteristic
398#336—611no—
399#336—611no—
400C61#2620011yescharacteristic, complemented, Sylow
401C22×Q8C22×D6111yescharacteristic
402C22×D4—611no—
403C23×C4—21no—
404C23×C4—611no—
405C23×C4—1221no—
406C23×C4—1221no—
407C23×C4C22×D6111yescharacteristic
408C22×C8—611no—
409C22×C8—611no—
410C22×C8—1222no—
411C22×C8—2441no—
412C22×C8—2441no—
413C22×C8C22×D6111yescharacteristic
414C22×C8C22×D6111yescharacteristic
415C22⋊Q8—22no—
416C22⋊Q8—41no—
417C22⋊Q8—1222no—
418C22⋊Q8—1222no—
419C4×D4—1222no—
420C4×D4—1222no—
421C4×D4—2444no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—1222no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—2441no—
440C2×C4⋊C4—2441no—
441C2×C4⋊C4C22×D6111yescharacteristic
442C2×C4⋊C4C22×D6111yescharacteristic
443C2×C4⋊C4C22×D6111yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C42—611no—
452C2×C42—1221no—
453#106—1222no—
454#106—2441no—
455#103—22no—
456#103—41no—
457#103—2441no—
458#103—2441no—
459C22⋊C8—41no—
460C22⋊C8—1222no—
461C22⋊C8—2441no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469C24—611no—
470C24D4×D6111yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×D4—614no—
478C2×D4—1222no—
479C2×D4—1222no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—612no—
496C22×C4—612no—
497C22×C4—611no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—4881no—
507C22×C4—4881no—
508C22×C4—2442no—
509C22×C4—2442no—
510C22×C4—2442no—
511C22×C4—2442no—
512C22×C4D4×D6111yescharacteristic
513C22×C4C23×D6111yescharacteristic
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—2444no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—1222no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—4881no—
543C4⋊C4—4881no—
544C4⋊C4—2442no—
545C4⋊C4—2442no—
546C4⋊C4—2442no—
547C4⋊C4—2442no—
548C4⋊C4#1175822212yes—
549C4⋊C4#1175822412yes—
550C22⋊C4—42no—
551C22⋊C4—1222no—
552C22⋊C4—1222no—
553C22⋊C4—4881no—
554C22⋊C4—2442no—
555C22⋊C4—2442no—
556C22⋊C4—2442no—
557C42—1221no—
558C42—1221no—
559C42—2442no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—612no—
567C23—612no—
568C23—612no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23—1221no—
573C23SD16×D6112yes—
574C23C2×D4×D6111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—1228no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—612no—
601C2×C4—612no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—4884no—
614C2×C4—4884no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4#41×D6111yescharacteristic
628C2×C4#41×D6111yescharacteristic
629C2×C4C2×#1175822411yescharacteristic
630C2×C4C2×#1175822211yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982211yescharacteristic
633C8—41no—
634C8—41no—
635C8—2441no—
636C8—2441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—614no—
645C22—1222no—
646C22—1222no—
647C22—1222no—
648C22—1222no—
649C22—1222no—
650C22—1222no—
651C22#123×D6111yescharacteristic
652C22#1684039911yescharacteristic
653C22#1684040211yescharacteristic
654C22C2×SD16×D6111yescharacteristic
655C22#137×D6111yescharacteristic
656C22#1684056611yescharacteristic
657C22#1684057511yescharacteristic
658C4—41no—
659C4—42no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—1222no—
664C4—1222no—
665C4—4881no—
666C4—4881no—
667C4—4881no—
668C4—4881no—
669C4—2441no—
670C4#1684029411yescharacteristic
671C4#1684034411yescharacteristic
672C4#1684045911yescharacteristic
673C4#1684046211yescharacteristic
674C2—42no—
675C2—1224no—
676C2#2144956611yescharacteristic
677C2#483×D6111yescharacteristic
678C2#2145579811yescharacteristic
679C2#2145763611yescharacteristic
680C2#2145768011yescharacteristic
681C2#2145786311yescharacteristic
682C2#2145790111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1872D61
hypocenterC61#26200
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. #21447380C2semidirect
4. #21447252C2semidirect
5. #21447230C2semidirect
6. #21447012C2semidirect
7. #21446455C2semidirect
8. #21446407C2semidirect
9. #21446239C2semidirect
10. #21446123C2semidirect
12. #21446013C2semidirect
13. #21445905C2semidirect
14. #340×D61C2semidirect
15. C61×#1872C2semidirect
343. #1872D61semidirect
400. C61#26200semidirect

Maximal subgroups

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

subgroupindex
#214492662
C4⋊C4×C22⋊D612
#214473802
#214472522
#214472302
#214470122
#214464552
#214464072
#214462392
#214461232
#214461082
#214460132
#214459052
#340×D612
C61×#18722
#2620061