Finite Group Databasebeta

← #29742883

Subgroups — #29742883

Order 15616.

860 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840062C211yesmaximal, characteristic, complemented
2C2×#16839805C211yesmaximal, characteristic, complemented
3#21449543C211yesmaximal, characteristic, complemented
4#21447340C211yesmaximal, characteristic, complemented
5#21447320C211yesmaximal, characteristic, complemented
6#21447193C211yesmaximal, characteristic, complemented
7#21447157C211yesmaximal, characteristic, complemented
8#21446587C211yesmaximal, characteristic, complemented
9#21446390C211yesmaximal, characteristic, complemented
10#21446258C211yesmaximal, characteristic
11#21446137C211yesmaximal, characteristic
12#21446066C211yesmaximal, characteristic, complemented
13#21446018C211yesmaximal, characteristic, complemented
14#21446004C211yesmaximal, characteristic, complemented
15C61×#2363C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19#16840062—24no—
20#16839805—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34#16839704—21no—
35#16839696—21no—
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839634—21no—
39#16839628C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839620—21no—
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#121×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C61×#390—21no—
54C61×#390C2211yescharacteristic
55C61×#389C2211yescharacteristic
56C61×#388—21no—
57C61×#386—21no—
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C22⋊C4×C61—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C23×Dic61—21no—
62C2×#11758194—22no—
63C2×#11758194—22no—
64C2×#11758194—22no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519769—22no—
70#14519769—41no—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—41no—
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×C22⋊Dic61—21no—
83#14519710—22no—
84#14519710—41no—
85#14519710D414yescomplemented
86#14519708—22no—
87#14519708—22no—
88#14519708—22no—
89C4⋊#92418—22no—
90C4⋊#92418—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—41no—
95C22⋊#92418—22no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101C22×D4×C61—21no—
102C22×D4×C61C2311yescharacteristic
103C23×C4×C61—21no—
104C23×C4×C61C2311yescharacteristic
105#121×C61—22no—
106#121×C61Q814yes—
107C4×D4×C61—22no—
108C4×D4×C61—41no—
109#117×C61—22no—
110#117×C61—41no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61D411yescharacteristic
121C2×C22⋊C4×C61D411yescharacteristic
122C2×C42×C61—21no—
123C2×C42×C61—21no—
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126#95×C61—21no—
127#95×C61—21no—
128#95×C61D411yescharacteristic
129#95×C61D411yescharacteristic
130C24×C61—21no—
131C24×C61C2×D411yescharacteristic
132C2×D4×C61—24no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—81no—
139C2×D4×C61—81no—
140C2×D4×C61C2×Q812yes—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61—81no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×Q812yes—
157C22×C4×C61#4112yes—
158C22×C4×C61C2411yescharacteristic
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—42no—
164C22×Dic61—42no—
165C22×Dic61—81no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—81no—
171C4⋊C4×C61C2×D412yes—
172C4⋊C4×C61C2×Q812yes—
173C22⋊C4×C61—24no—
174C22⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—42no—
177C22⋊C4×C61—42no—
178C22⋊C4×C61—42no—
179C22⋊C4×C61—81no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—42no—
185C42×C61—81no—
186C22⋊Dic61—42no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—42no—
195C4⋊Dic61C2×D412yes—
196#11758196—42no—
197#11758196—42no—
198#11758196—81no—
199#11758196—81no—
200#11758194—28no—
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—21no—
211C2×#92418C2×D412yes—
212C2×#92418#4112yes—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—22no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61C22⋊Q812yes—
227C23×C61C22×D411yescharacteristic
228D4×C61—22no—
229D4×C61—22no—
230D4×C61—41no—
231D4×C61—41no—
232D4×C61—84no—
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—21no—
241C2×C4×C61—21no—
242C2×C4×C61—22no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—84no—
261C2×C4×C61C22⋊Q812yes—
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×Q811yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61H(5,𝔽2)11yescharacteristic
267C2×C4×C612−1+411yescharacteristic
268C2×Dic61—22no—
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—84no—
281#92418—22no—
282#92418—22no—
283#92418—41no—
284#92418—41no—
285#26363—611nomaximal, Sylow
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—81no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61—81no—
300C22×C61C2×C22⋊Q811yescharacteristic
301C22×C61D4211yescharacteristic
302C22×C61#54711yescharacteristic
303C22×C61#57511yescharacteristic
304C22×C61#57511yescharacteristic
305C22×C61#57611yescharacteristic
306C22×C61#57711yescharacteristic
307C4×C61—22no—
308C4×C61—42no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—42no—
314C4×C61—81no—
315C4×C61#52511yescharacteristic
316C4×C61#53911yescharacteristic
317C4×C61D4×Q811yescharacteristic
318C4×C61#55411yescharacteristic
319Dic61—42no—
320Dic61—81no—
321Dic61—81no—
322Dic61—81no—
323C2×#478—611no—
324C2×#428—611no—
325#2442—611no—
326#2363D6111yescharacteristic
327#2092—611no—
328#2088—611no—
329#2065—611no—
330#2059—611no—
331#1949—611no—
332#1918—611no—
333#1895—611no—
334#1874—611no—
335#1862—611no—
336#1854—611no—
337#1851—611no—
338C2×C61—42no—
339C2×C61—82no—
340C2×C61#244911yescharacteristic
341C2×C61#308011yescharacteristic
342C2×C61#308111yescharacteristic
343C2×C61#327111yescharacteristic
344C2×C61#327311yescharacteristic
345C2×C61#334811yescharacteristic
346C2×C61#335511yescharacteristic
347C22×M16—611no—
348C2×#125—611no—
349C2×#121C2×D6111yescharacteristic
350C2×C4×D4C2×D6111yescharacteristic
351C2×#117C2×D6111yescharacteristic
352C22×C4⋊C4—611no—
353#478—1224no—
354#428—1224no—
355C2×#107—611no—
356C2×#107—611no—
357C2×#107—611no—
358C2×#106—611no—
359C2×#106—611no—
360C2×#106—611no—
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×#102—611no—
364C2×#102—611no—
365C2×#102—611no—
366C2×#102—611no—
367C2×C22⋊C8—611no—
368#400—1221no—
369#398—1221no—
370#390—21no—
371#390C2×D6111yescharacteristic
372#389—611no—
373#389—611no—
374#389C2×D6111yescharacteristic
375#388—21no—
376#386—21no—
377#385—1221no—
378#382—611no—
379#380—611no—
380#380—1221no—
381C4×C4⋊C4C2×D6111yescharacteristic
382C4×C22⋊C4—21no—
383C4×C22⋊C4C2×D6111yescharacteristic
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#336—611no—
391#336—611no—
392C61#2636311yescharacteristic, complemented, Sylow
393C22×D4—21no—
394C22×D4C22×D6111yescharacteristic
395C23×C4—21no—
396C23×C4—1221no—
397C23×C4C22×D6111yescharacteristic
398C2×M16—1222no—
399C2×M16—1222no—
400C2×M16—1222no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—611no—
405#125—1222no—
406#125—2441no—
407#121—22no—
408#121Dic12214yes—
409C4×D4—22no—
410C4×D4—41no—
411#117—22no—
412#117—41no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—1222no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—2441no—
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C4⋊C4C22×D6111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4C22⋊D6111yescharacteristic
435C2×C22⋊C4C22⋊D6111yescharacteristic
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C22×D6111yescharacteristic
439C2×C42C22×D6111yescharacteristic
440#107—614no—
441#107—1222no—
442#107—2441no—
443#106—1222no—
444#106—1222no—
445#106—1222no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448#102—1222no—
449#102—1222no—
450#102—1222no—
451#102—2441no—
452C22⋊C8—1222no—
453#95—21no—
454#95—21no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460#95C22⋊D6111yescharacteristic
461#95C22⋊D6111yescharacteristic
462C24—21no—
463C24C2×C22⋊D6111yescharacteristic
464C2×D4—24no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×Dic12212yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—4881no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4C2×Dic12212yes—
491C22×C4#1175822212yes—
492C22×C4C2×C22⋊D6111yescharacteristic
493C22×C4C2×C22⋊D6111yescharacteristic
494C22×C4C2×C22⋊D6111yescharacteristic
495C22×C4C2×C22⋊D6111yescharacteristic
496C22×C4C2×C22⋊D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498M16—1228no—
499C2×C8—612no—
500C2×C8—612no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—81no—
516C4⋊C4—612no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—4881no—
525C4⋊C4—4881no—
526C4⋊C4—2442no—
527C4⋊C4—2442no—
528C4⋊C4—2442no—
529C4⋊C4C2×Dic12212yes—
530C4⋊C4D4×D6112yes—
531C22⋊C4—24no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—81no—
538C22⋊C4—2442no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—42no—
544C42—81no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23#1451975612yes—
559C23C22×C22⋊D6111yescharacteristic
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—84no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
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—84no—
593C2×C4—1222no—
594C2×C4—4884no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4#1451975612yes—
607C2×C4C2×D4×D6111yescharacteristic
608C2×C4C22×Dic12211yescharacteristic
609C2×C4#41×D6111yescharacteristic
610C2×C4C2×#1175822211yescharacteristic
611C2×C4#1451982211yescharacteristic
612C2×C4#1451982411yescharacteristic
613C8—1222no—
614C8—1222no—
615C8—2441no—
616C8—2441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×#1451975611yescharacteristic
632C22D4×C22⋊D6111yescharacteristic
633C22#1684041111yescharacteristic
634C22#1684056011yescharacteristic
635C22#1684056011yescharacteristic
636C22#1684056511yescharacteristic
637C22#1684057311yescharacteristic
638C4—22no—
639C4—41no—
640C4—42no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—4881no—
647C4—4881no—
648C4—4881no—
649C4—2442no—
650C4#1684027111yescharacteristic
651C4#1684035411yescharacteristic
652C4D4×Dic12211yescharacteristic
653C4#1684047111yescharacteristic
654C2—42no—
655C2—82no—
656C2#2144962211yescharacteristic
657C2#2145564111yescharacteristic
658C2#2145565011yescharacteristic
659C2#2145740011yescharacteristic
660C2#2145742611yescharacteristic
661C2#2145833411yescharacteristic
662C2#2145841911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2363C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenter#2363D61
hypocenterC61#26363
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. C2×#16840062C2semidirect
2. C2×#16839805C2semidirect
3. #21449543C2semidirect
4. #21447340C2semidirect
5. #21447320C2semidirect
6. #21447193C2semidirect
7. #21447157C2semidirect
8. #21446587C2semidirect
9. #21446390C2semidirect
12. #21446066C2semidirect
13. #21446018C2semidirect
14. #21446004C2semidirect
85. #14519710D4semidirect
392. C61#26363semidirect

Maximal subgroups

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

subgroupindex
C2×#168400622
C2×#168398052
#214495432
#214473402
#214473202
#214471932
#214471572
#214465872
#214463902
#214462582
#214461372
#214460662
#214460182
#214460042
C61×#23632
#2636361