Finite Group Databasebeta

← #29697806

Subgroups — #29697806

Order 15616.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448222C211yesmaximal, characteristic
2#21446534C211yesmaximal, characteristic, complemented
3#21446534C211yesmaximal, characteristic, complemented
4#21446381C211yesmaximal, characteristic, complemented
5#21446380C211yesmaximal, characteristic, complemented
6#21446374C211yesmaximal, characteristic, complemented
7#21446373C211yesmaximal, characteristic, complemented
8#21445801C211yesmaximal, characteristic
9#21445797C211yesmaximal, characteristic
10#21445685C211yesmaximal, characteristic, complemented
11#21445680C211yesmaximal, characteristic, complemented
12#21445587C211yesmaximal, characteristic
13#21445585C211yesmaximal, characteristic
14C22⋊C8×Dic61C211yesmaximal, characteristic
15C61×#1798C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18C2×#14519706C2211yescharacteristic
19C2×#14519706C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519688C2211yescharacteristic
25C2×#14519687C2211yescharacteristic
26C2×C4×#92418C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30#16839631C411yescharacteristic
31#16839631C411yescharacteristic
32#16839627C411yescharacteristic
33#16839627C411yescharacteristic
34#16839620C411yescharacteristic
35#16839620C411yescharacteristic
36#16839620C411yescharacteristic
37#16839620C411yescharacteristic
38C4×#11758196C2211yescharacteristic
39C4×#11758196C2211yescharacteristic
40C4×#11758196C2211yescharacteristic
41C4×#11758196C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C23×Dic61C2×C411yescharacteristic
60C23×Dic61C2×C411yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519736—41no—
66#14519736—41no—
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×#11758196C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2×C411yescharacteristic
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×C22⋊Dic61C2×C411yescharacteristic
78C2×C22⋊Dic61C2×C411yescharacteristic
79C2×C4×Dic61—22no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87#14519706—22no—
88#14519706—22no—
89#14519706—41no—
90#14519706—41no—
91C22⋊#92418—22no—
92C22⋊#92418Q814yes—
93#14519688—41no—
94#14519687—41no—
95C4×#92418—41no—
96C8×Dic61—22no—
97C8×Dic61—22no—
98C8×Dic61—41no—
99#14519684C2×C411yescharacteristic
100#14519684C2×C411yescharacteristic
101#14519684C2×C411yescharacteristic
102#14519684C2×C411yescharacteristic
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#117×C61—41no—
113#117×C61—41no—
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C4⋊C4×C61C2×C411yescharacteristic
116C2×C22⋊C4×C61C2×C411yescharacteristic
117C2×C22⋊C4×C61C2×C411yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—41no—
121C4⋊C8×C61—41no—
122C22⋊C8×C61—22no—
123C22⋊C8×C61—22no—
124C24×C61C22×C411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2×Q812yes—
135C22×C4×C61#4112yes—
136C22×C4×C61C2411yescharacteristic
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—41no—
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C4⋊C4×C61—41no—
164C4⋊C4×C61—41no—
165C22⋊C4×C61—41no—
166C22⋊C4×C61—41no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C22⋊Dic61—41no—
172C22⋊Dic61—41no—
173C4⋊Dic61—41no—
174C4⋊Dic61—41no—
175#11758196—22no—
176#11758196—22no—
177#11758196—22no—
178#11758196—22no—
179#11758196—22no—
180#11758196—22no—
181#11758196—41no—
182#11758196—41no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—21no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61#4112yes—
192C4×Dic61#4112yes—
193C2×#92418—21no—
194C2×#92418—21no—
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×#92418C2×Q812yes—
204C2×#92418C2×Q812yes—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61C4×Q812yes—
212C23×C61C23×C411yescharacteristic
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61C4×Q812yes—
232C2×C4×C61C22×Q811yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61H(5,𝔽2)11yescharacteristic
237C2×C4×C61H(5,𝔽2)11yescharacteristic
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—44no—
258C2×Dic61—44no—
259C2×Dic61#11712yes—
260C2×Dic61#11712yes—
261C2×Dic61#13112yes—
262C2×Dic61#13112yes—
263C2×Dic61#13112yes—
264C8×C61—41no—
265C8×C61—41no—
266C8×C61—41no—
267C8×C61—41no—
268#92418—22no—
269#92418—22no—
270#92418—41no—
271#92418—41no—
272#22626—611nomaximal, Sylow
273C22×C61—22no—
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61C2×#11711yescharacteristic
281C22×C61C2×C4×Q811yescharacteristic
282C22×C61#51811yescharacteristic
283C22×C61C2×#13111yescharacteristic
284C22×C61C2×#13111yescharacteristic
285C22×C61C2×#13111yescharacteristic
286C22×C61#56811yescharacteristic
287C4×C61—22no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61#55311yescharacteristic
293C4×C61#55311yescharacteristic
294C4×C61#55411yescharacteristic
295C4×C61#55411yescharacteristic
296Dic61—22no—
297Dic61—22no—
298Dic61—41no—
299Dic61—41no—
300Dic61—41no—
301Dic61—41no—
302Dic61—41no—
303Dic61#43314yes—
304#2285—611no—
305#1939—611no—
306#1939—611no—
307#1917—611no—
308#1917—611no—
309#1916—611no—
310#1916—611no—
311#1798—611no—
312#1798D6111yescharacteristic
313#1797—611no—
314#1770—611no—
315C8×C4⋊C4—611no—
316#1750—611no—
317#1750—611no—
318C4×C22⋊C8—611no—
319C2×C61—42no—
320C2×C61#234511yescharacteristic
321C2×C61C2×#43311yescharacteristic
322C2×C61#292411yescharacteristic
323C2×C61#296011yescharacteristic
324C2×C61#296211yescharacteristic
325C2×C61#297911yescharacteristic
326C2×C61#298111yescharacteristic
327C2×#117—611no—
328C2×#117C2×D6111yescharacteristic
329C22×C42—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8C2×D6111yescharacteristic
335C2×C4⋊C8C2×D6111yescharacteristic
336C2×C22⋊C8—611no—
337C2×C22⋊C8—611no—
338C2×C22⋊C8C2×D6111yescharacteristic
339C2×C22⋊C8C2×D6111yescharacteristic
340C2×#97—611no—
341C2×#97—611no—
342C2×C4×C8—611no—
343C2×C4×C8—611no—
344C2×C4×C8—611no—
345C2×C4×C8—611no—
346#384—611no—
347#384—611no—
348#382—611no—
349#382—611no—
350#380—611no—
351#380—611no—
352#380—611no—
353#380—611no—
354C4×C4⋊C4—611no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4—611no—
358#336—611no—
359#336—611no—
360#336—611no—
361#336—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368#336C2×D6111yescharacteristic
369#336C2×D6111yescharacteristic
370C61#2262611yescharacteristic, complemented, Sylow
371C23×C4—611no—
372C23×C4—611no—
373C23×C4C22×D6111yescharacteristic
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8C22×D6111yescharacteristic
379C22×C8C22×D6111yescharacteristic
380C22×C8C22×D6111yescharacteristic
381C22×C8C22×D6111yescharacteristic
382#117—41no—
383#117—41no—
384#117—2441no—
385#117—2441no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4C4×D6111yescharacteristic
397C2×C4⋊C4C4×D6111yescharacteristic
398C2×C22⋊C4—611no—
399C2×C22⋊C4—611no—
400C2×C22⋊C4C4×D6111yescharacteristic
401C2×C22⋊C4C4×D6111yescharacteristic
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—1222no—
409C2×C42—1222no—
410C2×C42C22×D6111yescharacteristic
411C2×C42C22×D6111yescharacteristic
412C4⋊C8—41no—
413C4⋊C8—41no—
414C4⋊C8—1222no—
415C4⋊C8—1222no—
416C4⋊C8—2441no—
417C4⋊C8—2441no—
418C22⋊C8—22no—
419C22⋊C8—22no—
420C22⋊C8—614no—
421C22⋊C8—1222no—
422#97—2441no—
423#97—2441no—
424C4×C8—1222no—
425C4×C8—1222no—
426C4×C8—2441no—
427C4×C8—2441no—
428#95—611no—
429#95—611no—
430#95—611no—
431#95—611no—
432#95—611no—
433#95—611no—
434#95—611no—
435#95—611no—
436C24C2×C4×D6111yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—2441no—
455C22×C4C2×C4×D6111yescharacteristic
456C22×C4C2×C4×D6111yescharacteristic
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4C2×C4×D6111yescharacteristic
459C22×C4C2×C4×D6111yescharacteristic
460C22×C4#1175822412yes—
461C22×C4Q8×D6112yes—
462C22×C4C23×D6111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—612no—
476C2×C8—612no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—2441no—
496C4⋊C4—2441no—
497C4⋊C4—2441no—
498C4⋊C4—2441no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—612no—
508C42—612no—
509C42—1222no—
510C42—1222no—
511C42—1221no—
512C42—1221no—
513C42—1221no—
514C42—1221no—
515C42—1221no—
516C42—1221no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#1451974212yes—
524C23C22×C4×D6111yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—612no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—2444no—
568C2×C4—2444no—
569C2×C4#1451974212yes—
570C2×C4C2×Q8×D6111yescharacteristic
571C2×C4#41×D6111yescharacteristic
572C2×C4#41×D6111yescharacteristic
573C2×C4C2×#1175822411yescharacteristic
574C2×C4#1451982211yescharacteristic
575C2×C4#1451982211yescharacteristic
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—1222no—
581C8—1222no—
582C8—2441no—
583C8—2441no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22#117×D6111yescharacteristic
592C22C2×#1451974211yescharacteristic
593C22#1684023511yescharacteristic
594C22#131×D6111yescharacteristic
595C22#131×D6111yescharacteristic
596C22#131×D6111yescharacteristic
597C22#1684052711yescharacteristic
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—614no—
604C4—1222no—
605C4—1222no—
606C4—2441no—
607C4—2441no—
608C4—2441no—
609C4—2441no—
610C4—2441no—
611C4#1684045511yescharacteristic
612C4#1684045511yescharacteristic
613C4#1684046611yescharacteristic
614C4#1684046611yescharacteristic
615C2—42no—
616C2#2144869111yescharacteristic
617C2#433×D6111yescharacteristic
618C2#2145447511yescharacteristic
619C2#2145475211yescharacteristic
620C2#2145476511yescharacteristic
621C2#2145488311yescharacteristic
622C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1798C2
prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenter#1798D61
hypocenterC61#22626
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #21446534C2semidirect
3. #21446534C2semidirect
4. #21446381C2semidirect
5. #21446380C2semidirect
6. #21446374C2semidirect
7. #21446373C2semidirect
10. #21445685C2semidirect
11. #21445680C2semidirect
370. C61#22626semidirect

Maximal subgroups

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

subgroupindex
#214482222
#214465342
#214463812
#214463802
#214463742
#214463732
#214458012
#214457972
#214456852
#214456802
#214455872
#214455852
C22⋊C8×Dic612
C61×#17982
#2262661