Finite Group Databasebeta

← #29724348

Subgroups — #29724348

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#21450123C211yesmaximal, characteristic
2#21448715C211yesmaximal, characteristic
3#21447379C211yesmaximal, characteristic, complemented
4#21447293C211yesmaximal, characteristic, complemented
5#21447245C211yesmaximal, characteristic, complemented
6#21446393C211yesmaximal, characteristic, complemented
7#21446388C211yesmaximal, characteristic, complemented
8#21446108C211yesmaximal, characteristic
9#21446006C211yesmaximal, characteristic, complemented
10#21446005C211yesmaximal, characteristic, complemented
11#21445906C211yesmaximal, characteristic, complemented
12#21445904C211yesmaximal, characteristic, complemented
13#21445847C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#2075C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519759—21no—
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519737—21no—
20C22×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28#16839696—21no—
29#16839690—21no—
30#16839661C2211yescharacteristic
31#16839659—21no—
32#16839658C2211yescharacteristic
33#16839636—21no—
34#16839634—21no—
35#16839631C2211yescharacteristic
36#16839624—21no—
37#16839622C2211yescharacteristic
38#16839619C2211yescharacteristic
39#16839619C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41#16839525C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#107×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C61×#380C2211yescharacteristic
55C61×#380C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×C22⋊D61D411yescharacteristic
60C23×Dic61—21no—
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C2×C8×D61—22no—
67C2×C8×D61—22no—
68C2×C8×D61—41no—
69#14519759—44no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72#14519737—44no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—41no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196D411yescharacteristic
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—41no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61D411yescharacteristic
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198D411yescharacteristic
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98#14519710—22no—
99#14519710—22no—
100#14519710—41no—
101C22⋊#92418—22no—
102#14519689—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C23×C4×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118#107×C61—41no—
119C22⋊C8×C61—41no—
120#95×C61—21no—
121#95×C61—21no—
122C24×C61C2×D411yescharacteristic
123C23×D61C2×D411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—22no—
137C2×C22⋊D61—22no—
138C2×C22⋊D61D814yes—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—42no—
144C22×Dic61—42no—
145C22×Dic61—81no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61—81no—
159C2×C4×D61#4112yes—
160C2×C4×D61#4112yes—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C22⋊C4×C61—42no—
176C22⋊C4×C61—42no—
177C22⋊Dic61—22no—
178C22⋊Dic61—42no—
179#11758198—22no—
180#11758198—42no—
181#11758198—42no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—42no—
190C4⋊Dic61—42no—
191C4⋊Dic61#4112yes—
192#11758196—22no—
193#11758196—42no—
194#11758196—42no—
195#11758196—42no—
196#11758196—42no—
197#11758196—81no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—42no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418#4112yes—
207C8×D61—44no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61C2×D812yes—
215C23×C61C22×D411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61#12312yes—
221C22×D61C2×D812yes—
222C22×D61#13712yes—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61H(5,𝔽2)11yescharacteristic
247C2×C4×C612−1+411yescharacteristic
248C22⋊D61—28no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—84no—
269C2×Dic61#12312yes—
270C2×Dic61C2×D812yes—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—84no—
276C4×D61—84no—
277C8×C61—41no—
278C8×C61—41no—
279#92418—22no—
280#92418—41no—
281#24933—611nomaximal, Sylow
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61C2×#12311yescharacteristic
290C22×C61#54611yescharacteristic
291C22×C61#54711yescharacteristic
292C22×C61C22×D811yescharacteristic
293C22×C61C2×#13711yescharacteristic
294C22×C61#57711yescharacteristic
295C22×C61#57811yescharacteristic
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61#48014yes—
303C4×C61—41no—
304C4×C61—81no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61#52911yescharacteristic
309C4×C61#53911yescharacteristic
310C4×C61#55111yescharacteristic
311C4×C61#55211yescharacteristic
312Dic61—22no—
313Dic61—22no—
314Dic61—41no—
315Dic61—42no—
316Dic61—81no—
317Dic61—81no—
318Dic61—81no—
319#2486—611no—
320D4×C4⋊C4—611no—
321#2099—611no—
322#2083—611no—
323#2075—611no—
324#2075D6111yescharacteristic, complemented
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—42no—
335C2×C61#241911yescharacteristic
336C2×C61C2×#48011yescharacteristic
337C2×C61#309711yescharacteristic
338C2×C61#329411yescharacteristic
339C2×C61#331211yescharacteristic
340C2×C61#333411yescharacteristic
341C2×C61#334411yescharacteristic
342D61—24no—
343C23×C8—611no—
344C2×#123—1221no—
345C2×C4×D4—611no—
346C2×C4×D4—1221no—
347C22×C4⋊C4—611no—
348C22×C4⋊C4—611no—
349C22×C4⋊C4—611no—
350C2×#107—611no—
351C2×#107—611no—
352C2×#107—611no—
353C2×#107C2×D6111yescharacteristic
354C2×C22⋊C8—611no—
355C2×C22⋊C8—611no—
356C2×C22⋊C8C2×D6111yescharacteristic
357#398—1221no—
358#397—1221no—
359#389—611no—
360#389—611no—
361#389—1221no—
362#385—1221no—
363#385—1221no—
364#384—611no—
365#381—1221no—
366#380—611no—
367#380—611no—
368#380—611no—
369#380C2×D6111yescharacteristic
370#380C2×D6111yescharacteristic
371C4×C4⋊C4—611no—
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#340C2×D6111yescharacteristic
382#340C2×D6111yescharacteristic
383#340C2×D6111yescharacteristic
384#336—611no—
385#336—611no—
386C61#2493311yescharacteristic, complemented, Sylow
387C22×D4—611no—
388C23×C4—611no—
389C23×C4—1221no—
390C23×C4—1221no—
391C23×C4—1221no—
392C23×C4C22×D6111yescharacteristic
393C22×C8—611no—
394C22×C8—611no—
395C22×C8—1222no—
396C22×C8—1222no—
397C22×C8—2441no—
398C22×C8C22×D6111yescharacteristic
399C22×C8C22×D6111yescharacteristic
400#123—2444no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—2444no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4—1222no—
411C2×C4⋊C4—1222no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—2441no—
421C2×C4⋊C4—2441no—
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—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C42—611no—
434C2×C42—1221no—
435#107—41no—
436#107—1222no—
437#107—1222no—
438#107—2441no—
439C22⋊C8—41no—
440C22⋊C8—1222no—
441C22⋊C8—1222no—
442#95—21no—
443#95—21no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450C24—611no—
451C24D4×D6111yescharacteristic
452C2×D4—614no—
453C2×D4—1222no—
454C2×D4—1222no—
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—611no—
466C22×C4—611no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—611no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—4881no—
479C22×C4—4881no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4—2442no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—612no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—2444no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—612no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—4881no—
520C4⋊C4—2442no—
521C4⋊C4—2442no—
522C4⋊C4—2442no—
523C4⋊C4—2442no—
524C4⋊C4—2442no—
525C4⋊C4—2442no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—2442no—
531C22⋊C4—2442no—
532C22⋊C4—2442no—
533C42—1221no—
534C42—1221no—
535C42—2442no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—612no—
543C23—612no—
544C23—612no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23—1221no—
549C23D8×D6112yes—
550C23C2×D4×D6111yescharacteristic
551D4—1228no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—612no—
572C2×C4—612no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1222no—
585C2×C4—4884no—
586C2×C4—4884no—
587C2×C4—4884no—
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—2441no—
598C2×C4—2441no—
599C2×C4#41×D6111yescharacteristic
600C2×C4#41×D6111yescharacteristic
601C2×C4#41×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#1451982211yescharacteristic
604C2×C4#1451982411yescharacteristic
605C8—41no—
606C8—41no—
607C8—1222no—
608C8—2441no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—614no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22#123×D6111yescharacteristic
624C22#1684040111yescharacteristic
625C22#1684041011yescharacteristic
626C22C2×D8×D6111yescharacteristic
627C22#137×D6111yescharacteristic
628C22#1684056911yescharacteristic
629C22#1684057811yescharacteristic
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—1222no—
636C4—1222no—
637C4—4881no—
638C4—4881no—
639C4—4881no—
640C4—2441no—
641C4—2442no—
642C4#1684029511yescharacteristic
643C4#1684035511yescharacteristic
644C4#1684044211yescharacteristic
645C4#1684044811yescharacteristic
646C2—42no—
647C2—1224no—
648C2#2144929111yescharacteristic
649C2#480×D6111yescharacteristic
650C2#2145578511yescharacteristic
651C2#2145762711yescharacteristic
652C2#2145786511yescharacteristic
653C2#2145816111yescharacteristic
654C2#2145826711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2075C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#2075D61
hypocenterC61#24933
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2075

Complements

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

NH ≅ G/Ntype
3. #21447379C2semidirect
4. #21447293C2semidirect
5. #21447245C2semidirect
6. #21446393C2semidirect
7. #21446388C2semidirect
9. #21446006C2semidirect
10. #21446005C2semidirect
11. #21445906C2semidirect
12. #21445904C2semidirect
13. #21445847C2semidirect
14. #340×D61C2semidirect
15. C61×#2075C2semidirect
324. #2075D61semidirect
386. C61#24933semidirect

Maximal subgroups

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

subgroupindex
#214501232
#214487152
#214473792
#214472932
#214472452
#214463932
#214463882
#214461082
#214460062
#214460052
#214459062
#214459042
#214458472
#340×D612
C61×#20752
#2493361