Finite Group Databasebeta

← #29742872

Subgroups — #29742872

Order 15616.

812 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840070C211yesmaximal, characteristic, complemented
2C2×#16839804C211yesmaximal, characteristic
3#21449532C211yesmaximal, characteristic
4#21448822C211yesmaximal, characteristic
5#21447356C211yesmaximal, characteristic, complemented
6#21447307C211yesmaximal, characteristic, complemented
7#21447199C211yesmaximal, characteristic, complemented
8#21447158C211yesmaximal, characteristic, complemented
9#21446578C211yesmaximal, characteristic, complemented
10#21446398C211yesmaximal, characteristic, complemented
11#21446252C211yesmaximal, characteristic
12#21446129C211yesmaximal, characteristic
13#21446076C211yesmaximal, characteristic, complemented
14#21446009C211yesmaximal, characteristic
15C61×#1851C211yesmaximal, characteristic
16C2×#14519769C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21#16840070—24no—
22#16839804—24no—
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519711C2211yescharacteristic
26C2×#14519711C2211yescharacteristic
27C2×#14519709C2211yescharacteristic
28C2×#14519709C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33#16839698—21no—
34#16839685—21no—
35#16839668C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839659—21no—
40#16839659—21no—
41#16839649—21no—
42#16839645—21no—
43#16839634—21no—
44#16839632C2211yescharacteristic
45#16839622C2211yescharacteristic
46C4×C4⋊Dic61C2211yescharacteristic
47C22⋊C4×Dic61—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C23×Dic61—21no—
63#14519769—22no—
64#14519769—41no—
65#14519756—22no—
66#14519756Q814yes—
67C4×Dic122—22no—
68C4×Dic122—41no—
69#14519736—22no—
70#14519736—41no—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—41no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96#14519711—22no—
97#14519711—22no—
98#14519711—22no—
99#14519711—41no—
100#14519709—22no—
101#14519709D414yes—
102#14519702—22no—
103#14519702—22no—
104#14519702—22no—
105#14519702—41no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C23×C4×C61C2311yescharacteristic
114C2×M16×C61—22no—
115C2×M16×C61—22no—
116C2×M16×C61—22no—
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C22⋊C4×C61D411yescharacteristic
122C2×C22⋊C4×C61D411yescharacteristic
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C4⋊C8×C61—22no—
126C4⋊C8×C61—22no—
127C22⋊C8×C61—22no—
128#95×C61D411yescharacteristic
129#95×C61D411yescharacteristic
130C24×C61C2×D411yescharacteristic
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×Q812yes—
141C22×C4×C61#4112yes—
142C22×C4×C61C2411yescharacteristic
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—42no—
152C22×Dic61—42no—
153C22×Dic61—81no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122C2×Q812yes—
160M16×C61—28no—
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×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61C2×D412yes—
172C2×C8×C61#4112yes—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—41no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C22⋊Dic61—24no—
180C22⋊Dic61—42no—
181C22⋊Dic61—81no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
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—21no—
193C4⋊Dic61—42no—
194C4⋊Dic61—42no—
195C4⋊Dic61—81no—
196C4⋊Dic61C2×D412yes—
197C4⋊Dic61C2×D412yes—
198C4⋊Dic61C2×Q812yes—
199#11758196—24no—
200#11758196—42no—
201#11758196—42no—
202#11758196—42no—
203#11758196—42no—
204#11758196—81no—
205#11758196—81no—
206C4×Dic61—42no—
207C4×Dic61—42no—
208C4×Dic61—81no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61C22⋊Q812yes—
216C23×C61C22×D411yescharacteristic
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
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×C61C22⋊Q812yes—
235C2×C4×C61#13712yes—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×Q811yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×C4×C612−1+411yescharacteristic
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
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—84no—
267Dic122—22no—
268Dic122—22no—
269Dic122—41no—
270Dic122—41no—
271C8×C61—22no—
272C8×C61—22no—
273C8×C61—41no—
274C8×C61—41no—
275#26362—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61C2×C22⋊Q811yescharacteristic
284C22×C61D4211yescharacteristic
285C22×C61#54711yescharacteristic
286C22×C61C2×#13711yescharacteristic
287C22×C61#57511yescharacteristic
288C22×C61#57611yescharacteristic
289C22×C61#57811yescharacteristic
290C4×C61—22no—
291C4×C61—22no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61#52511yescharacteristic
296C4×C61#53911yescharacteristic
297C4×C61D4×Q811yescharacteristic
298C4×C61#55411yescharacteristic
299Dic61—42no—
300Dic61—42no—
301Dic61—42no—
302Dic61—42no—
303Dic61—81no—
304Dic61—81no—
305Dic61—81no—
306Dic61—81no—
307C2×#479—611no—
308C2×#428—611no—
309#2441—611no—
310#2360—611no—
311#2095—611no—
312#2086—611no—
313#2066—611no—
314#2059—611no—
315#1947—611no—
316#1919—611no—
317#1894—611no—
318#1873—611no—
319#1863—611no—
320#1852—611no—
321#1851D6111yescharacteristic
322C2×C61—42no—
323C2×C61#244911yescharacteristic
324C2×C61#307811yescharacteristic
325C2×C61#308311yescharacteristic
326C2×C61#326811yescharacteristic
327C2×C61#327611yescharacteristic
328C2×C61#334611yescharacteristic
329C2×C61#335211yescharacteristic
330C22×M16C2×D6111yescharacteristic
331C2×#125—611no—
332C2×C22⋊Q8—611no—
333C2×C4×Q8—611no—
334C2×#117—611no—
335C22×C4⋊C4—611no—
336#479—1224no—
337#428—1224no—
338C2×#107—611no—
339C2×#107—611no—
340C2×#107—611no—
341C2×#107—611no—
342C2×#106—611no—
343C2×#106—611no—
344C2×C4⋊C8C2×D6111yescharacteristic
345C2×C4⋊C8C2×D6111yescharacteristic
346C2×#103—611no—
347C2×#103—611no—
348C2×#103—611no—
349C2×#103—611no—
350C2×C22⋊C8C2×D6111yescharacteristic
351#399—1221no—
352#396—1221no—
353#391—611no—
354#389—611no—
355#389—611no—
356#389—611no—
357#389—1221no—
358#389—1221no—
359#387—1221no—
360#387—1221no—
361#385—1221no—
362#384—611no—
363#380—611no—
364C4×C4⋊C4—611no—
365C4×C22⋊C4—1221no—
366C4×C22⋊C4C2×D6111yescharacteristic
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#336C2×D6111yescharacteristic
374#336C2×D6111yescharacteristic
375C61#2636211yescharacteristic, complemented, Sylow
376C22×Q8—611no—
377C23×C4—1221no—
378C23×C4C22×D6111yescharacteristic
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C22×C8C22×D6111yescharacteristic
383C22×C8C22×D6111yescharacteristic
384C22×C8C22×D6111yescharacteristic
385C22×C8C22×D6111yescharacteristic
386#125—1222no—
387#125—2441no—
388C22⋊Q8—614no—
389C22⋊Q8—1222no—
390C4×Q8—1222no—
391C4×Q8—2441no—
392#117—1222no—
393#117—2441no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—2441no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4D24411yescharacteristic
417C2×C22⋊C4D24411yescharacteristic
418C2×C42—1221no—
419C2×C42—1221no—
420C2×C42—1221no—
421C2×C42C22×D6111yescharacteristic
422C2×C42C22×D6111yescharacteristic
423#107—1222no—
424#107—1222no—
425#107—1222no—
426#107—2441no—
427#106—614no—
428#106—1222no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431#103—1222no—
432#103—1222no—
433#103—1222no—
434#103—2441no—
435C22⋊C8—22no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95D24411yescharacteristic
444#95D24411yescharacteristic
445C24C2×D24411yescharacteristic
446C2×Q8—612no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×Q8—1221no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—4881no—
465C22×C4—2442no—
466C22×C4—2442no—
467C22×C4C2×D24411yescharacteristic
468C22×C4C2×D24411yescharacteristic
469C22×C4C2×D24411yescharacteristic
470C22×C4C2×D24411yescharacteristic
471C22×C4C2×D24411yescharacteristic
472C22×C4#1175822412yes—
473C22×C4Q8×D6112yes—
474C22×C4C23×D6111yescharacteristic
475M16—28no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8D4×D6112yes—
487C2×C8#1175822412yes—
488C4⋊C4—612no—
489C4⋊C4—612no—
490C4⋊C4—612no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1224no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—4881no—
504C4⋊C4—4881no—
505C4⋊C4—4881no—
506C4⋊C4—2442no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C22⋊C4—22no—
513C22⋊C4—41no—
514C22⋊C4—1224no—
515C22⋊C4—4881no—
516C22⋊C4—2442no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—4881no—
522C42—2442no—
523C42—2442no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#1451975712yes—
531C23C22×D24411yescharacteristic
532Q8—1222no—
533Q8—1222no—
534Q8—2441no—
535Q8—2441no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
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—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—4884no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4#1451975712yes—
579C2×C4#1451981012yes—
580C2×C4C2×D4×D6111yescharacteristic
581C2×C4C2×Q8×D6111yescharacteristic
582C2×C4C2×#1175822411yescharacteristic
583C2×C4C2×#1175822411yescharacteristic
584C2×C4#1451982311yescharacteristic
585C2×C4#1451982411yescharacteristic
586C8—22no—
587C8—22no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22C2×#1451975711yescharacteristic
598C22D4×D24411yescharacteristic
599C22#1684041611yescharacteristic
600C22C2×#1451981011yescharacteristic
601C22#1684056211yescharacteristic
602C22#1684056711yescharacteristic
603C22#1684057911yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—4881no—
610C4—4881no—
611C4—4881no—
612C4—4881no—
613C4—2442no—
614C4—2442no—
615C4—2442no—
616C4—2442no—
617C4#1684026811yescharacteristic
618C4#1684035611yescharacteristic
619C4#1684042511yescharacteristic
620C4#1684047011yescharacteristic
621C2—42no—
622C2#2144962611yescharacteristic
623C2#2145562611yescharacteristic
624C2#2145567211yescharacteristic
625C2#2145736411yescharacteristic
626C2#2145746711yescharacteristic
627C2#2145830611yescharacteristic
628C2#2145839311yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1851C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#1851D61
hypocenterC61#26362
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#16840070C2semidirect
5. #21447356C2semidirect
6. #21447307C2semidirect
7. #21447199C2semidirect
8. #21447158C2semidirect
9. #21446578C2semidirect
10. #21446398C2semidirect
13. #21446076C2semidirect
375. C61#26362semidirect

Maximal subgroups

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

subgroupindex
C2×#168400702
C2×#168398042
#214495322
#214488222
#214473562
#214473072
#214471992
#214471582
#214465782
#214463982
#214462522
#214461292
#214460762
#214460092
C61×#18512
#2636261