Finite Group Databasebeta

← #29724347

Subgroups — #29724347

Order 15616.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450127C211yesmaximal, characteristic
2#21447376C211yesmaximal, characteristic, complemented
3#21447291C211yesmaximal, characteristic, complemented
4#21447245C211yesmaximal, characteristic, complemented
5#21447245C211yesmaximal, characteristic, complemented
6#21446390C211yesmaximal, characteristic, complemented
7#21446390C211yesmaximal, characteristic, complemented
8#21446112C211yesmaximal, characteristic
9#21446007C211yesmaximal, characteristic, complemented
10#21446007C211yesmaximal, characteristic, complemented
11#21445905C211yesmaximal, characteristic, complemented
12#21445903C211yesmaximal, characteristic, complemented
13#21445846C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C61C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519758—21no—
18C22×C4⋊Dic61C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26#16839692—21no—
27#16839687—21no—
28#16839660C2211yescharacteristic
29#16839660C2211yescharacteristic
30#16839623—21no—
31#16839622C2211yescharacteristic
32#16839622C2211yescharacteristic
33#16839622C2211yescharacteristic
34#16839524C2211yescharacteristic
35#16839524C2211yescharacteristic
36#16839524C2211yescharacteristic
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4×D4×C61—21no—
49C2×C4×D4×C61C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C61×#389—21no—
53C61×#385—21no—
54C61×#385—21no—
55C61×#384C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C23×Dic61—21no—
60C22×#92418—22no—
61C22×#92418—22no—
62C22×#92418—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519758—44no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80#14519710—22no—
81#14519710—22no—
82#14519710—41no—
83#14519710—41no—
84C22⋊#92418—22no—
85C22⋊#92418—22no—
86C22⋊#92418—41no—
87#14519684—21no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92C22×D4×C61D411yescharacteristic
93C23×C4×C61—21no—
94C23×C4×C61—21no—
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C4×D4×C61—22no—
98C4×D4×C61—22no—
99C4×D4×C61—44no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—41no—
107C2×C4⋊C4×C61—41no—
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61D411yescharacteristic
116C2×C22⋊C4×C61D411yescharacteristic
117C2×C42×C61—21no—
118C2×C42×C61C2311yescharacteristic
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122C24×C61C2×D411yescharacteristic
123C24×C61C2×D411yescharacteristic
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C2×D4×C61D814yes—
127C22×C4×C61—21no—
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×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—42no—
142C22×C4×C61—42no—
143C22×C4×C61—42no—
144C22×C4×C61—42no—
145C22×C4×C61—81no—
146C22×C4×C61—81no—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4112yes—
152C22×C4×C61#4112yes—
153C22×C4×C61C2411yescharacteristic
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—42no—
159C22×Dic61—42no—
160C22×Dic61—42no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—42no—
170C4⋊C4×C61—42no—
171C4⋊C4×C61—42no—
172C4⋊C4×C61—81no—
173C4⋊C4×C61#4112yes—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—42no—
177C22⋊C4×C61—42no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—42no—
181C22⋊Dic61—42no—
182C22⋊Dic61—42no—
183C22⋊Dic61—42no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—42no—
193#11758196—42no—
194#11758196—42no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—44no—
207C2×#92418#4112yes—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61#12312yes—
219C23×C61C2×D812yes—
220C23×C61C2×D812yes—
221C23×C61#13712yes—
222C23×C61C22×D411yescharacteristic
223D4×C61—28no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—22no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
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—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—84no—
255C2×C4×C61—84no—
256C2×C4×C61#12312yes—
257C2×C4×C61C2×D812yes—
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61H(5,𝔽2)11yescharacteristic
263C2×C4×C612−1+411yescharacteristic
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—84no—
277#92418—22no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#24933—611nomaximal, Sylow
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61#48014yes—
296C22×C61C2×#12311yescharacteristic
297C22×C61#54611yescharacteristic
298C22×C61#54711yescharacteristic
299C22×C61C22×D811yescharacteristic
300C22×C61C2×#13711yescharacteristic
301C22×C61#57711yescharacteristic
302C22×C61#57811yescharacteristic
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—41no—
306C4×C61—41no—
307C4×C61—42no—
308C4×C61—81no—
309C4×C61—81no—
310C4×C61—81no—
311C4×C61#52911yescharacteristic
312C4×C61#53911yescharacteristic
313C4×C61#55111yescharacteristic
314C4×C61#55211yescharacteristic
315Dic61—81no—
316Dic61—81no—
317Dic61—81no—
318Dic61—81no—
319#2486—611no—
320D4×C4⋊C4D6111yescharacteristic
321#2099—611no—
322#2083—611no—
323#2075—611no—
324#2075—611no—
325#1918—611no—
326#1918—611no—
327#1869—611no—
328#1852—611no—
329#1852—611no—
330#1823—611no—
331#1823—611no—
332#1808—611no—
333C2×#340—611no—
334C2×C61—24no—
335C2×C61—42no—
336C2×C61#241911yescharacteristic
337C2×C61C2×#48011yescharacteristic
338C2×C61#309711yescharacteristic
339C2×C61#329411yescharacteristic
340C2×C61#331211yescharacteristic
341C2×C61#333411yescharacteristic
342C2×C61#334411yescharacteristic
343C23×C8—611no—
344C2×#123—1221no—
345C2×C4×D4—21no—
346C2×C4×D4C2×D6111yescharacteristic
347C22×C4⋊C4—611no—
348C22×C4⋊C4C2×D6111yescharacteristic
349C22×C4⋊C4C2×D6111yescharacteristic
350C2×#107—611no—
351C2×#107—611no—
352C2×#107—611no—
353C2×#107—611no—
354C2×C22⋊C8—611no—
355C2×C22⋊C8—611no—
356C2×C22⋊C8—611no—
357#398—1221no—
358#397—1221no—
359#389—21no—
360#389—611no—
361#389—611no—
362#385—21no—
363#385—21no—
364#384C2×D6111yescharacteristic
365#381—1221no—
366#380—611no—
367#380—611no—
368#380—611no—
369#380C2×D6111yescharacteristic
370#380C2×D6111yescharacteristic
371C4×C4⋊C4C2×D6111yescharacteristic
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#336—611no—
385#336—611no—
386C61#2493311yescharacteristic, complemented, Sylow
387C22×D4C22⋊D6111yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—1221no—
391C23×C4C22×D6111yescharacteristic
392C23×C4C22×D6111yescharacteristic
393C22×C8—611no—
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—611no—
397C22×C8—1222no—
398C22×C8—1222no—
399C22×C8—2441no—
400#123—2444no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—44no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—1222no—
417C2×C4⋊C4—1222no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4C22⋊D6111yescharacteristic
422C2×C4⋊C4C22×D6111yescharacteristic
423C2×C4⋊C4C22×D6111yescharacteristic
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4C22⋊D6111yescharacteristic
432C2×C22⋊C4C22⋊D6111yescharacteristic
433C2×C42—21no—
434C2×C42C22×D6111yescharacteristic
435#107—1222no—
436#107—1222no—
437#107—2441no—
438#107—2441no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441C22⋊C8—2441no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450C24C2×C22⋊D6111yescharacteristic
451C24C2×C22⋊D6111yescharacteristic
452C2×D4—22no—
453C2×D4—22no—
454C2×D4#1175819914yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4#1175822212yes—
483C22×C4#1175822212yes—
484C22×C4C2×C22⋊D6111yescharacteristic
485C22×C4C2×C22⋊D6111yescharacteristic
486C22×C4C2×C22⋊D6111yescharacteristic
487C22×C4C2×C22⋊D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489C2×C8—612no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—2444no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—81no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—2442no—
523C4⋊C4—2442no—
524C4⋊C4—2442no—
525C4⋊C4#1175822412yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—2442no—
531C22⋊C4—2442no—
532C22⋊C4—2442no—
533C42—21no—
534C42—21no—
535C42—42no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23#1451976012yes—
547C23C2×#1175819912yes—
548C23C2×#1175819912yes—
549C23#1451980812yes—
550C23C22×C22⋊D6111yescharacteristic
551D4—28no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—84no—
583C2×C4—84no—
584C2×C4—4884no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4#1451976012yes—
598C2×C4C2×#1175819912yes—
599C2×C4#41×D6111yescharacteristic
600C2×C4C2×#1175822411yescharacteristic
601C2×C4C2×#1175822211yescharacteristic
602C2×C4C2×#1175822211yescharacteristic
603C2×C4#1451982211yescharacteristic
604C2×C4#1451982411yescharacteristic
605C8—1222no—
606C8—2441no—
607C8—2441no—
608C8—2441no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22#1684007514yes—
623C22C2×#1451976011yescharacteristic
624C22#1684040611yescharacteristic
625C22#1684041111yescharacteristic
626C22C22×#1175819911yescharacteristic
627C22C2×#1451980811yescharacteristic
628C22#1684057311yescharacteristic
629C22#1684057711yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—4881no—
639C4—4881no—
640C4—4881no—
641C4—4881no—
642C4#1684029211yescharacteristic
643C4#1684035411yescharacteristic
644C4#1684044111yescharacteristic
645C4#1684045211yescharacteristic
646C2—24no—
647C2—42no—
648C2#2144929011yescharacteristic
649C2C2×#1684007511yescharacteristic
650C2#2145578811yescharacteristic
651C2#2145763211yescharacteristic
652C2#2145787011yescharacteristic
653C2#2145816211yescharacteristic
654C2#2145826811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C4⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenterD4×C4⋊C4D61
hypocenterC61#24933
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21447376C2semidirect
3. #21447291C2semidirect
4. #21447245C2semidirect
5. #21447245C2semidirect
6. #21446390C2semidirect
7. #21446390C2semidirect
9. #21446007C2semidirect
10. #21446007C2semidirect
11. #21445905C2semidirect
12. #21445903C2semidirect
13. #21445846C2semidirect
14. C2×#16839524C2semidirect
386. C61#24933semidirect

Maximal subgroups

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

subgroupindex
#214501272
#214473762
#214472912
#214472452
#214463902
#214461122
#214460072
#214459052
#214459032
#214458462
C2×#168395242
D4×C4⋊C4×C612
#2493361