Finite Group Databasebeta

← #29682083

Subgroups — #29682083

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839787C211yesmaximal, characteristic
2C2×C4×#11758189C211yesmaximal, characteristic
3#21448299C211yesmaximal, characteristic
4#21446386C211yesmaximal, characteristic, complemented
5#21446384C211yesmaximal, characteristic, complemented
6#21446382C211yesmaximal, characteristic, complemented
7#21446380C211yesmaximal, characteristic, complemented
8#21446378C211yesmaximal, characteristic, complemented
9#21446376C211yesmaximal, characteristic, complemented
10#21446374C211yesmaximal, characteristic, complemented
11#21445514C211yesmaximal, characteristic
12#21445514C211yesmaximal, characteristic
13#21445514C211yesmaximal, characteristic
14#336×D61C211yesmaximal, characteristic
15C61×#1916C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22C2×C42×D61C2211yescharacteristic
23#16839787—24no—
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C4×#11758189—24no—
28C2×#14519687C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31#16839659C411yescharacteristic
32#16839659C411yescharacteristic
33#16839657C411yescharacteristic
34#16839657C411yescharacteristic
35#16839636C411yescharacteristic
36#16839636C411yescharacteristic
37#16839633C411yescharacteristic
38#16839633C411yescharacteristic
39C4×#11758196C2211yescharacteristic
40C4×#11758196C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758189—22no—
65C2×#11758189—22no—
66C2×#11758189—22no—
67C2×#11758189—22no—
68C2×#11758189D414yes—
69C2×#11758189Q814yes—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C2×C8×D61—22no—
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—22no—
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80#14519734—22no—
81#14519734—22no—
82#14519734—22no—
83#14519734—22no—
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×#11758196C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C42×D61—22no—
104C42×D61—22no—
105C4⋊#92418—22no—
106#14519706—22no—
107#14519706—22no—
108#14519687—22no—
109#14519687—22no—
110C4×#92418—22no—
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2×C411yescharacteristic
122C2×C4⋊C4×C61C2×C411yescharacteristic
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126C4⋊C8×C61—22no—
127C4×C8×C61—22no—
128#95×C61C2×C411yescharacteristic
129#95×C61C2×C411yescharacteristic
130C23×D61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61C2×D412yes—
152C2×C4×D61C2×Q812yes—
153C2×C4×D61#4112yes—
154C2×C4×D61#4112yes—
155C2×C4×D61#4112yes—
156C2×C4×D61#4112yes—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61C2×D412yes—
168C2×C8×C61C2×Q812yes—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177#11758198—22no—
178#11758198—22no—
179#11758198—22no—
180#11758198—22no—
181C4⋊Dic61—41no—
182C4⋊Dic61—41no—
183#11758196—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—41no—
190#11758196—41no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C2×#92418—21no—
200C2×#92418—21no—
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×#92418C2×D412yes—
210C2×#92418C2×Q812yes—
211#11758189—28no—
212#11758189—28no—
213C8×D61—44no—
214C8×D61—44no—
215C23×C61C23×C411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61#11712yes—
221C22×D61C4×D412yes—
222C22×D61C4×Q812yes—
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×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61#13112yes—
240C2×C4×C61#13112yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×Q811yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
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—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61#11712yes—
266C2×Dic61C4×D412yes—
267C2×Dic61C4×Q812yes—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61C22⋊Q814yes—
271C4×D61#12314yes—
272C4×D61#12514yes—
273C4×D61#12614yes—
274C8×C61—22no—
275C8×C61—22no—
276C8×C61—41no—
277C8×C61—41no—
278#92418—22no—
279#92418—22no—
280#92418—41no—
281#92418—41no—
282#21022—611nomaximal, Sylow
283C22×C61C2×#11711yescharacteristic
284C22×C61C2×C4×D411yescharacteristic
285C22×C61C2×C4×Q811yescharacteristic
286C22×C61C2×#13111yescharacteristic
287C22×C61C2×#13111yescharacteristic
288C22×C61#56811yescharacteristic
289C22×C61#56811yescharacteristic
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61#38714yes—
297C4×C61—22no—
298C4×C61—22no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61C2×C22⋊Q811yescharacteristic
304C4×C61C2×#12311yescharacteristic
305C4×C61C2×#12511yescharacteristic
306C4×C61C2×#12611yescharacteristic
307Dic61—41no—
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61—41no—
312Dic61—41no—
313Dic61#38714yes—
314C2×#424—611no—
315C2×C4×M16—611no—
316#2296—611no—
317#1917—611no—
318#1917—611no—
319#1917—611no—
320#1917—611no—
321#1916—611no—
322#1916—611no—
323#1916—611no—
324#1916D6111yescharacteristic, complemented
325#1729—611no—
326#1729—611no—
327#1729—611no—
328C2×#336—611no—
329C2×C61C2×#38711yescharacteristic
330C2×C61#292211yescharacteristic
331C2×C61#292311yescharacteristic
332C2×C61#293311yescharacteristic
333C2×C61#293311yescharacteristic
334C2×C61#296211yescharacteristic
335C2×C61#296211yescharacteristic
336D61—24no—
337C22×M16—611no—
338C22×M16—611no—
339C23×C8—611no—
340C23×C8—611no—
341C2×#117—611no—
342C2×#117—611no—
343C22×C42—611no—
344#424—1224no—
345C2×C4⋊C8—611no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8C2×D6111yescharacteristic
349C4×M16—1224no—
350C2×#97—611no—
351C2×#97—611no—
352C2×C4×C8—611no—
353C2×C4×C8C2×D6111yescharacteristic
354#389—611no—
355#389—611no—
356#389—611no—
357#389—611no—
358#385—611no—
359#385—611no—
360#385—611no—
361#385—611no—
362C4×C4⋊C4—611no—
363C4×C4⋊C4—611no—
364C4×C4⋊C4—611no—
365C4×C4⋊C4C2×D6111yescharacteristic
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370#336—611no—
371#336—611no—
372#336—611no—
373#336—611no—
374#336—611no—
375#336—611no—
376#336—611no—
377#336—611no—
378#336C2×D6111yescharacteristic
379#336C2×D6111yescharacteristic
380#336C2×D6111yescharacteristic
381#336C2×D6111yescharacteristic
382C61#2102211yescharacteristic, complemented, Sylow
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—611no—
386C2×M16—614no—
387C2×M16—614no—
388C2×M16—1222no—
389C2×M16—1222no—
390C2×M16—1222no—
391C2×M16—1222no—
392C22×C8—611no—
393C22×C8—611no—
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—1222no—
397C22×C8—1222no—
398C22×C8—1222no—
399C22×C8—1222no—
400C22×C8—1222no—
401C22×C8—1222no—
402C22×C8C22×D6111yescharacteristic
403C22×C8C22×D6111yescharacteristic
404C22×C8C22×D6111yescharacteristic
405C22×C8C22×D6111yescharacteristic
406#117—1222no—
407#117—1222no—
408#117—1222no—
409#117—1222no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4C4×D6111yescharacteristic
421C2×C4⋊C4C4×D6111yescharacteristic
422C2×C22⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42C22×D6111yescharacteristic
434C2×C42C22×D6111yescharacteristic
435C2×C42C22×D6111yescharacteristic
436C4⋊C8—22no—
437C4⋊C8—1222no—
438C4⋊C8—1222no—
439C4⋊C8—1222no—
440#97—1222no—
441#97—1222no—
442C4×C8—22no—
443C4×C8—1222no—
444#95—611no—
445#95—611no—
446#95—611no—
447#95—611no—
448#95—611no—
449#95—611no—
450#95C4×D6111yescharacteristic
451#95C4×D6111yescharacteristic
452C24—611no—
453C22×C4—611no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—2441no—
471C22×C4—2441no—
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4C2×C4×D6111yescharacteristic
475C22×C4C2×C4×D6111yescharacteristic
476C22×C4C2×C4×D6111yescharacteristic
477C22×C4C2×C4×D6111yescharacteristic
478C22×C4C23×D6111yescharacteristic
479M16—1228no—
480M16—1228no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—612no—
492C2×C8—612no—
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—1221no—
502C2×C8—1221no—
503C2×C8—2444no—
504C2×C8—2444no—
505C2×C8D4×D6112yes—
506C2×C8Q8×D6112yes—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—2441no—
516C4⋊C4—2441no—
517C4⋊C4—2441no—
518C4⋊C4—2441no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—1222no—
530C42—1222no—
531C42—1221no—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C42—1221no—
536C42—1221no—
537C23—612no—
538C23—612no—
539C23—612no—
540C23—1221no—
541C23—1221no—
542C23—1221no—
543C23—1221no—
544C23C22×C4×D6111yescharacteristic
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—612no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—614no—
565C2×C4—614no—
566C2×C4—614no—
567C2×C4—614no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—2444no—
587C2×C4—2444no—
588C2×C4#1451978312yes—
589C2×C4#1451978512yes—
590C2×C4C2×D4×D6111yescharacteristic
591C2×C4C2×Q8×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C2×C4#41×D6111yescharacteristic
595C2×C4#41×D6111yescharacteristic
596C8—22no—
597C8—22no—
598C8—41no—
599C8—41no—
600C8—1222no—
601C8—1222no—
602C8—2441no—
603C8—2441no—
604C22—614no—
605C22—1222no—
606C22—1222no—
607C22—1222no—
608C22—1222no—
609C22—1222no—
610C22—1222no—
611C22#117×D6111yescharacteristic
612C22C4×D4×D6111yescharacteristic
613C22C4×Q8×D6111yescharacteristic
614C22C2×#1451978311yescharacteristic
615C22C2×#1451978511yescharacteristic
616C22#1684052711yescharacteristic
617C22#1684052711yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—614no—
625C4—2441no—
626C4—2441no—
627C4—2441no—
628C4—2441no—
629C4—2441no—
630C4—2441no—
631C4C22⋊Q8×D6111yescharacteristic
632C4#123×D6111yescharacteristic
633C4#125×D6111yescharacteristic
634C4#126×D6111yescharacteristic
635C2—1224no—
636C2#387×D6111yescharacteristic
637C2#2145445811yescharacteristic
638C2#2145446711yescharacteristic
639C2#2145453911yescharacteristic
640C2#2145454511yescharacteristic
641C2#2145476111yescharacteristic
642C2#2145476711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1916C2
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1916D61
hypocenterC61#21022
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
4. #21446386C2semidirect
5. #21446384C2semidirect
6. #21446382C2semidirect
7. #21446380C2semidirect
8. #21446378C2semidirect
9. #21446376C2semidirect
10. #21446374C2semidirect
15. C61×#1916C2semidirect
324. #1916D61semidirect
382. C61#21022semidirect

Maximal subgroups

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

subgroupindex
C2×#168397872
C2×C4×#117581892
#214482992
#214463862
#214463842
#214463822
#214463802
#214463782
#214463762
#214463742
#214455142
#336×D612
C61×#19162
#2102261