Finite Group Databasebeta

← #29742943

Subgroups — #29742943

Order 15616.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840069C211yesmaximal, characteristic, complemented
2C2×#16839805C211yesmaximal, characteristic
3#21449543C211yesmaximal, characteristic
4#21447367C211yesmaximal, characteristic, complemented
5#21447315C211yesmaximal, characteristic, complemented
6#21447214C211yesmaximal, characteristic, complemented
7#21447157C211yesmaximal, characteristic, complemented
8#21446587C211yesmaximal, characteristic, complemented
9#21446397C211yesmaximal, characteristic, complemented
10#21446253C211yesmaximal, characteristic
11#21446127C211yesmaximal, characteristic
12#21446087C211yesmaximal, characteristic, complemented
13#21446018C211yesmaximal, characteristic
14#21446004C211yesmaximal, characteristic
15C61×#2362C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19#16840069—24no—
20#16839805—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
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×C22⋊Q8×C61C2211yescharacteristic
51C2×C4×Q8×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C61×#391C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#388—21no—
56C61×#388—21no—
57C61×#387—21no—
58C4×C4⋊C4×C61—21no—
59C4×C4⋊C4×C61C2211yescharacteristic
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—22no—
85#14519710—22no—
86#14519708—22no—
87#14519708—41no—
88#14519708D414yes—
89C4⋊#92418—22no—
90C4⋊#92418—22no—
91#14519701—22no—
92#14519701—22no—
93#14519701—22no—
94#14519701—41no—
95C22⋊#92418—22no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101C22×Q8×C61C2311yescharacteristic
102C23×C4×C61C2311yescharacteristic
103C22⋊Q8×C61—22no—
104C22⋊Q8×C61Q814yes—
105C4×Q8×C61—22no—
106C4×Q8×C61—41no—
107#117×C61—22no—
108#117×C61—41no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
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×C61D411yescharacteristic
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C42×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61—21no—
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61D411yescharacteristic
129#95×C61D411yescharacteristic
130C24×C61C2×D411yescharacteristic
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61C2×Q812yes—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×Q812yes—
151C22×C4×C61#4112yes—
152C22×C4×C61C2411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—42no—
158C22×Dic61—42no—
159C22×Dic61—81no—
160C4⋊C4×C61—24no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—42no—
166C4⋊C4×C61—42no—
167C4⋊C4×C61C2×D412yes—
168C4⋊C4×C61C2×Q812yes—
169C22⋊C4×C61—24no—
170C22⋊C4×C61—41no—
171C22⋊C4×C61—41no—
172C22⋊C4×C61—42no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—42no—
178C42×C61—42no—
179C42×C61—42no—
180C22⋊Dic61—42no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—42no—
189C4⋊Dic61C2×D412yes—
190#11758196—42no—
191#11758196—42no—
192#11758196—81no—
193#11758196—81no—
194#11758194—28no—
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×#92418—21no—
204C2×#92418—21no—
205C2×#92418C2×D412yes—
206C2×#92418#4112yes—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61C22⋊Q812yes—
214C23×C61C22×D411yescharacteristic
215Q8×C61—22no—
216Q8×C61—22no—
217Q8×C61—41no—
218Q8×C61—41no—
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—22no—
226C2×C4×C61—22no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—22no—
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—21no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61C22⋊Q812yes—
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×Q811yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×C4×C612−1+411yescharacteristic
256C2×Dic61—22no—
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—
269#92418—22no—
270#92418—22no—
271#92418—41no—
272#92418—41no—
273#26367—611nomaximal, Sylow
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61C2×C22⋊Q811yescharacteristic
282C22×C61D4211yescharacteristic
283C22×C61#54711yescharacteristic
284C22×C61#57511yescharacteristic
285C22×C61#57511yescharacteristic
286C22×C61#57711yescharacteristic
287C22×C61#57811yescharacteristic
288C4×C61—22no—
289C4×C61—42no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—42no—
293C4×C61—41no—
294C4×C61—42no—
295C4×C61—41no—
296C4×C61—81no—
297C4×C61#52511yescharacteristic
298C4×C61#53911yescharacteristic
299C4×C61D4×Q811yescharacteristic
300C4×C61#55411yescharacteristic
301Dic61—42no—
302Dic61—81no—
303Dic61—81no—
304Dic61—81no—
305C2×#479—611no—
306C2×#428—611no—
307#2442—611no—
308#2362D6111yescharacteristic
309#2097—611no—
310#2087—611no—
311#2068—611no—
312#2059—611no—
313#1949—611no—
314#1919—611no—
315#1894—611no—
316#1872—611no—
317#1865—611no—
318#1854—611no—
319#1851—611no—
320C2×C61—42no—
321C2×C61#244911yescharacteristic
322C2×C61#308011yescharacteristic
323C2×C61#308211yescharacteristic
324C2×C61#326911yescharacteristic
325C2×C61#327511yescharacteristic
326C2×C61#334911yescharacteristic
327C2×C61#335111yescharacteristic
328C22×M16—611no—
329C2×#125—611no—
330C2×C22⋊Q8C2×D6111yescharacteristic
331C2×C4×Q8C2×D6111yescharacteristic
332C2×#117C2×D6111yescharacteristic
333C22×C4⋊C4—611no—
334#479—1224no—
335#428—1224no—
336C2×#107—611no—
337C2×#107—611no—
338C2×#107—611no—
339C2×#106—611no—
340C2×#106—611no—
341C2×#106—611no—
342C2×C4⋊C8—611no—
343C2×C4⋊C8—611no—
344C2×#103—611no—
345C2×#103—611no—
346C2×#103—611no—
347C2×#103—611no—
348C2×C22⋊C8—611no—
349#400—1221no—
350#398—1221no—
351#391C2×D6111yescharacteristic
352#389—611no—
353#389—611no—
354#389C2×D6111yescharacteristic
355#388—21no—
356#388—21no—
357#387—21no—
358#385—1221no—
359#382—611no—
360#380—611no—
361#380—1221no—
362C4×C4⋊C4—21no—
363C4×C4⋊C4C2×D6111yescharacteristic
364C4×C22⋊C4C2×D6111yescharacteristic
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#336—611no—
372#336—611no—
373C61#2636711yescharacteristic, complemented, Sylow
374C22×Q8C22×D6111yescharacteristic
375C23×C4—1221no—
376C23×C4C22×D6111yescharacteristic
377C2×M16—1222no—
378C2×M16—1222no—
379C2×M16—1222no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8—611no—
383C22×C8—611no—
384#125—1222no—
385#125—2441no—
386C22⋊Q8—22no—
387C22⋊Q8Dic12214yes—
388C4×Q8—22no—
389C4×Q8—41no—
390#117—22no—
391#117—41no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—2441no—
406C2×C4⋊C4C22×D6111yescharacteristic
407C2×C4⋊C4C22×D6111yescharacteristic
408C2×C4⋊C4C22×D6111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4C22⋊D6111yescharacteristic
413C2×C22⋊C4C22⋊D6111yescharacteristic
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C22×D6111yescharacteristic
418C2×C42C22×D6111yescharacteristic
419#107—1222no—
420#107—1222no—
421#107—1222no—
422#106—614no—
423#106—1222no—
424#106—2441no—
425C4⋊C8—1222no—
426C4⋊C8—1222no—
427#103—1222no—
428#103—1222no—
429#103—1222no—
430#103—2441no—
431C22⋊C8—1222no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95C22⋊D6111yescharacteristic
442#95C22⋊D6111yescharacteristic
443C24C2×C22⋊D6111yescharacteristic
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×Dic12212yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—4881no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4C2×Dic12212yes—
466C22×C4#1175822212yes—
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C23×D6111yescharacteristic
473M16—1228no—
474C2×C8—612no—
475C2×C8—612no—
476C2×C8—1221no—
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—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—612no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—4881no—
502C4⋊C4—4881no—
503C4⋊C4—2442no—
504C4⋊C4—2442no—
505C4⋊C4—2442no—
506C4⋊C4C2×Dic12212yes—
507C4⋊C4D4×D6112yes—
508C22⋊C4—24no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—42no—
512C22⋊C4—2442no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—42no—
519C42—42no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23#1451975612yes—
527C23C22×C22⋊D6111yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—41no—
531Q8—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—1222no—
563C2×C4—4884no—
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#1451975612yes—
576C2×C4C2×D4×D6111yescharacteristic
577C2×C4C22×Dic12211yescharacteristic
578C2×C4#41×D6111yescharacteristic
579C2×C4C2×#1175822211yescharacteristic
580C2×C4#1451982211yescharacteristic
581C2×C4#1451982411yescharacteristic
582C8—1222no—
583C8—1222no—
584C8—2441no—
585C8—2441no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#1451975611yescharacteristic
594C22D4×C22⋊D6111yescharacteristic
595C22#1684041111yescharacteristic
596C22#1684056011yescharacteristic
597C22#1684056011yescharacteristic
598C22#1684057011yescharacteristic
599C22#1684057711yescharacteristic
600C4—22no—
601C4—42no—
602C4—41no—
603C4—42no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—81no—
609C4—4881no—
610C4—4881no—
611C4—4881no—
612C4—2442no—
613C4#1684027111yescharacteristic
614C4#1684035411yescharacteristic
615C4D4×Dic12211yescharacteristic
616C4#1684047111yescharacteristic
617C2—42no—
618C2#2144962211yescharacteristic
619C2#2145564111yescharacteristic
620C2#2145566111yescharacteristic
621C2#2145737011yescharacteristic
622C2#2145745111yescharacteristic
623C2#2145834311yescharacteristic
624C2#2145837911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2362C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2362D61
hypocenterC61#26367
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
1. C2×#16840069C2semidirect
4. #21447367C2semidirect
5. #21447315C2semidirect
6. #21447214C2semidirect
7. #21447157C2semidirect
8. #21446587C2semidirect
9. #21446397C2semidirect
12. #21446087C2semidirect
373. C61#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#168400692
C2×#168398052
#214495432
#214473672
#214473152
#214472142
#214471572
#214465872
#214463972
#214462532
#214461272
#214460872
#214460182
#214460042
C61×#23622
#2636761