Finite Group Databasebeta

← #29740620

Subgroups — #29740620

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#21449264C211yesmaximal, characteristic
2C4⋊C4×C22⋊D61C211yesmaximal, characteristic
3#21447380C211yesmaximal, characteristic, complemented
4#21447258C211yesmaximal, characteristic, complemented
5#21447231C211yesmaximal, characteristic, complemented
6#21447018C211yesmaximal, characteristic, complemented
7#21446451C211yesmaximal, characteristic, complemented
8#21446407C211yesmaximal, characteristic, complemented
9#21446242C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21446111C211yesmaximal, characteristic
13#21446012C211yesmaximal, characteristic, complemented
14#21445904C211yesmaximal, characteristic, complemented
15C2×C61×#340C211yesmaximal, characteristic, complemented
16C2×#14519757C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519702C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30#16839692—21no—
31#16839684—21no—
32#16839667C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839657—21no—
35#16839641—21no—
36#16839635—21no—
37#16839633—21no—
38#16839631C2211yescharacteristic
39#16839622—21no—
40#16839622C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C23×C8×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C22×C4⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×C22⋊D61D411yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519757—22no—
66#14519757—41no—
67#14519756—22no—
68#14519756—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—44no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196D411yescharacteristic
82C4⋊C4×D61—22no—
83C4⋊C4×D61—41no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61D411yescharacteristic
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198D411yescharacteristic
91C2×C4×Dic61—21no—
92C2×C4×Dic61C2311yescharacteristic
93#14519708—22no—
94#14519708—41no—
95#14519702—41no—
96#14519702—41no—
97#14519700—22no—
98#14519700—41no—
99C22⋊#92418—22no—
100#14519689—41no—
101#14519689—41no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C23×C4×C61—21no—
110C23×C4×C61—21no—
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61—22no—
113C22×C8×C61—41no—
114C22×C8×C61—41no—
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C2×C4⋊C4×C61—22no—
118C2×C4⋊C4×C61—22no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—41no—
122C2×C4⋊C4×C61—41no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C24×C61C2×D411yescharacteristic
128C23×D61C2×D411yescharacteristic
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—42no—
138C22×C4×C61—42no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61—81no—
142C22×C4×C61—81no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61#4112yes—
145C22×C4×C61#4112yes—
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61SD1614yes—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—81no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—44no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—42no—
186C4⋊C4×C61—42no—
187C4⋊C4×C61#4112yes—
188C4⋊C4×C61#4112yes—
189C22⋊Dic61—22no—
190C22⋊Dic61—42no—
191C22⋊Dic61—42no—
192#11758198—22no—
193#11758198—42no—
194#11758198—42no—
195#11758198—81no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—42no—
203C4⋊Dic61—81no—
204#11758196—22no—
205#11758196—42no—
206#11758196—42no—
207#11758196—42no—
208#11758196—81no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—42no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61#12312yes—
223C23×C61C2×SD1612yes—
224C23×C61#13712yes—
225C23×C61C22×D411yescharacteristic
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61C2×SD1612yes—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—41no—
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—84no—
252C2×C4×C61—84no—
253C2×C4×C61#12312yes—
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61H(5,𝔽2)11yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C22⋊D61—28no—
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—41no—
270C2×Dic61—41no—
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×Dic61C2×SD1612yes—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—84no—
287Dic122—41no—
288Dic122—41no—
289Dic122—41no—
290Dic122—41no—
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—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61#48314yes—
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—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—22no—
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—41no—
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#1872—611no—
344#1869—611no—
345#1853—611no—
346#1823—611no—
347C2×#340D6111yescharacteristic, complemented
348C2×C61—24no—
349C2×C61#244411yescharacteristic
350C2×C61C2×#48311yescharacteristic
351C2×C61#309811yescharacteristic
352C2×C61#329511yescharacteristic
353C2×C61#329811yescharacteristic
354C2×C61#331211yescharacteristic
355C2×C61#331411yescharacteristic
356D61—42no—
357C23×C8C2×D6111yescharacteristic
358C2×C22⋊Q8—611no—
359C2×C22⋊Q8—611no—
360C2×C4×D4—611no—
361C2×C4×D4—1221no—
362C22×C4⋊C4—611no—
363C22×C4⋊C4C2×D6111yescharacteristic
364C22×C4⋊C4C2×D6111yescharacteristic
365C2×#106—611no—
366C2×#106—611no—
367C2×#103—611no—
368C2×#103—611no—
369C2×#103—611no—
370C2×#103—611no—
371C2×C22⋊C8—611no—
372C2×C22⋊C8—611no—
373C2×C22⋊C8—611no—
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#340C2×D6111yescharacteristic
395#340C2×D6111yescharacteristic
396#340C2×D6111yescharacteristic
397#340C2×D6111yescharacteristic
398#336—611no—
399#336—611no—
400C61#2620011yescharacteristic, complemented, Sylow
401C22×Q8—611no—
402C22×D4—611no—
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—611no—
406C23×C4—1221no—
407C23×C4C22×D6111yescharacteristic
408C22×C8—22no—
409C22×C8—41no—
410C22×C8—41no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8C22×D6111yescharacteristic
414C22×C8C22×D6111yescharacteristic
415C22⋊Q8—1222no—
416C22⋊Q8—1222no—
417C22⋊Q8—1222no—
418C22⋊Q8—2441no—
419C4×D4—1222no—
420C4×D4—1222no—
421C4×D4—2444no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
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⋊C4C22×D6111yescharacteristic
441C2×C4⋊C4C22×D6111yescharacteristic
442C2×C4⋊C4C22×D6111yescharacteristic
443C2×C4⋊C4C22×D6111yescharacteristic
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—1221no—
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—1222no—
456#103—2441no—
457#103—2441no—
458#103—2441no—
459C22⋊C8—1222no—
460C22⋊C8—2441no—
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—1221no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×Q8—1221no—
475C2×Q8—1221no—
476C2×Q8—1221no—
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—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—1221no—
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—1221no—
507C22×C4—4881no—
508C22×C4—2442no—
509C22×C4—2442no—
510C22×C4#1175822212yes—
511C22×C4D4×D6111yescharacteristic
512C22×C4#1175822612yes—
513C22×C4C23×D6111yescharacteristic
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—44no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—1222no—
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#1175822212yes—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—4881no—
553C22⋊C4—2442no—
554C22⋊C4—2442no—
555C22⋊C4—2442no—
556C22⋊C4—2442no—
557C42—1221no—
558C42—1221no—
559C42—2442no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—612no—
565C23—1221no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23—1221no—
571C23#1451976212yes—
572C23SD16×D6112yes—
573C23#1451980612yes—
574C23C2×D4×D6111yescharacteristic
575Q8—2441no—
576Q8—2441no—
577Q8—2441no—
578Q8—2441no—
579D4—1228no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
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—84no—
599C2×C4—84no—
600C2×C4—612no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—4884no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
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#1451976212yes—
627C2×C4C2×#1175822211yescharacteristic
628C2×C4C2×#1175822211yescharacteristic
629C2×C4C2×#1175822211yescharacteristic
630C2×C4C2×#1175822611yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982211yescharacteristic
633C8—41no—
634C8—41no—
635C8—2441no—
636C8—2441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—1222no—
644C22—1222no—
645C22—1222no—
646C22—2441no—
647C22—2441no—
648C22—2441no—
649C22—2441no—
650C22#1684009414yes—
651C22C2×#1451976211yescharacteristic
652C22#1684040211yescharacteristic
653C22#1684040211yescharacteristic
654C22C2×SD16×D6111yescharacteristic
655C22C2×#1451980611yescharacteristic
656C22#1684056311yescharacteristic
657C22#1684057511yescharacteristic
658C4—22no—
659C4—42no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—1222no—
664C4—4881no—
665C4—4881no—
666C4—4881no—
667C4—4881no—
668C4—2441no—
669C4—2441no—
670C4#1684029611yescharacteristic
671C4#1684035011yescharacteristic
672C4#1684046011yescharacteristic
673C4#1684046011yescharacteristic
674C2—24no—
675C2—2442no—
676C2#2144956911yescharacteristic
677C2C2×#1684009411yescharacteristic
678C2#2145580211yescharacteristic
679C2#2145763911yescharacteristic
680C2#2145768011yescharacteristic
681C2#2145786611yescharacteristic
682C2#2145789611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#340D61
hypocenterC61#26200
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #21447380C2semidirect
4. #21447258C2semidirect
5. #21447231C2semidirect
6. #21447018C2semidirect
7. #21446451C2semidirect
8. #21446407C2semidirect
9. #21446242C2semidirect
10. #21446126C2semidirect
11. #21446125C2semidirect
13. #21446012C2semidirect
14. #21445904C2semidirect
15. C2×C61×#340C2semidirect
347. C2×#340D61semidirect
400. C61#26200semidirect

Maximal subgroups

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

subgroupindex
#214492642
C4⋊C4×C22⋊D612
#214473802
#214472582
#214472312
#214470182
#214464512
#214464072
#214462422
#214461262
#214461252
#214461112
#214460122
#214459042
C2×C61×#3402
#2620061