Finite Group Databasebeta

← #29576336

Subgroups — #29576336

Order 15616.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454268C211yesmaximal, characteristic, complemented
2#21445763C211yesmaximal, characteristic, complemented
3#21444335C211yesmaximal, characteristic, complemented
4#21444179C211yesmaximal, characteristic, complemented
5#21443696C211yesmaximal, characteristic, complemented
6#21443666C211yesmaximal, characteristic, complemented
7C2×C61×#449C211yesmaximal, characteristic
8C2×#14519784—21no—
9C2×#14519704—21no—
10C2×#14519704—21no—
11#16839729—22no—
12#16839729—21no—
13#16839726—21no—
14#16839726C2211yescharacteristic
15#16839726C2211yescharacteristic
16C2×C22⋊#92418—21no—
17C2×C22⋊#92418C2211yescharacteristic
18C4×C22⋊Dic61C2211yescharacteristic
19#16839496—22no—
20#16839486—21no—
21#16839486—21no—
22C22×#41×C61C2211yescharacteristic
23C22×SD16×C61C411yescharacteristic, complemented
24C22×D8×C61C411yescharacteristic, complemented
25C2×#121×C61C2211yescharacteristic
26C61×#449—21no—
27C61×#449—21no—
28C61×#449—21no—
29C61×#449—21no—
30C2×#103×C61C411yescharacteristic, complemented
31C2×#102×C61C411yescharacteristic, complemented
32C2×C22⋊C8×C61C2211yescharacteristic
33#14519784—42no—
34#14519784—42no—
35C2×#11758194—22no—
36C2×#11758194—21no—
37C2×#11758194—21no—
38C22×#92418—22no—
39C22×#92418—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—21no—
42#14519704—42no—
43#14519704—42no—
44C22⋊#92418—22no—
45C22⋊#92418—22no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418D411yescharacteristic
51C22⋊#92418D411yescharacteristic
52C22⋊#92418D412yes—
53#14519684—21no—
54C2×#41×C61—21no—
55C2×#41×C61—21no—
56C2×#41×C61—42no—
57C2×#41×C61—42no—
58C2×#41×C61D411yescharacteristic
59C2×#41×C61D411yescharacteristic
60C2×#41×C61D411yescharacteristic
61C2×#41×C61D411yescharacteristic
62C22×Q8×C61C2×C411yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61C2×C411yescharacteristic
66C22×D4×C61C2×C411yescharacteristic
67C23×C4×C61—21no—
68C23×C4×C61C2311yescharacteristic
69C2×SD16×C61—21no—
70C2×SD16×C61—21no—
71C2×SD16×C61—42no—
72C2×D8×C61—21no—
73C2×D8×C61—21no—
74C2×D8×C61—42no—
75C22×C8×C61C2×C411yescharacteristic
76C22×C8×C61C2×C411yescharacteristic
77#121×C61—21no—
78#121×C61—21no—
79#121×C61—21no—
80#121×C61—21no—
81C2×C4⋊C4×C61C2×C411yescharacteristic
82C2×C22⋊C4×C61—21no—
83#103×C61—21no—
84#103×C61—21no—
85#102×C61—21no—
86#102×C61—21no—
87C22⋊C8×C61—21no—
88C22⋊C8×C61—21no—
89C24×C61—21no—
90C24×C61—21no—
91C24×C61#4111yescharacteristic
92#41×C61—22no—
93#41×C61—22no—
94#41×C61—22no—
95#41×C61—22no—
96#41×C61—41no—
97#41×C61—41no—
98#41×C61—41no—
99#41×C61—41no—
100#41×C61—44no—
101#41×C61—44no—
102C2×Q8×C61—21no—
103C2×Q8×C61—22no—
104C2×Q8×C61—41no—
105C2×Q8×C61C22⋊C411yescharacteristic
106C2×Q8×C61C22⋊C411yescharacteristic
107C2×D4×C61—21no—
108C2×D4×C61—22no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—41no—
116C2×D4×C61—41no—
117C2×D4×C61—41no—
118C2×D4×C61—44no—
119C2×D4×C61—41no—
120C2×D4×C61—41no—
121C2×D4×C61—82no—
122C2×D4×C61C22⋊C411yescharacteristic
123C2×D4×C61C22⋊C411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61—44no—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61#4111yescharacteristic
139C22×Dic61—41no—
140SD16×C61—42no—
141SD16×C61—42no—
142D8×C61—42no—
143D8×C61—42no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—41no—
147C2×C8×C61—41no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C22⋊Dic61—22no—
153C22⋊Dic61—41no—
154C4×Dic61—41no—
155C4×Dic61—41no—
156#11758194—44no—
157#11758194—41no—
158#11758194—41no—
159#11758194—41no—
160#11758194—41no—
161C2×#92418—21no—
162C2×#92418—22no—
163C2×#92418—21no—
164C2×#92418—44no—
165C2×#92418—41no—
166C2×#92418—41no—
167C2×#92418—41no—
168C23×C61—21no—
169C23×C61—21no—
170C23×C61—21no—
171C23×C61—21no—
172C23×C61—41no—
173C23×C61—41no—
174C23×C61—42no—
175C23×C61—41no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—81no—
181C23×C61—81no—
182C23×C61—81no—
183C23×C61C4×D411yescharacteristic
184C23×C61#12111yescharacteristic
185C23×C61#12311yescharacteristic
186Q8×C61—21no—
187Q8×C61—21no—
188Q8×C61—21no—
189Q8×C61—42no—
190Q8×C61#9912yes—
191D4×C61—24no—
192D4×C61—21no—
193D4×C61—21no—
194D4×C61—21no—
195D4×C61—42no—
196D4×C61—42no—
197D4×C61—42no—
198D4×C61—42no—
199D4×C61—41no—
200D4×C61—41no—
201D4×C61—81no—
202D4×C61—82no—
203D4×C61—82no—
204D4×C61#9912yes—
205C2×C4×C61—24no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—41no—
222C2×C4×C61—81no—
223C2×C4×C61C2×C22⋊C411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61#12011yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×Dic61—42no—
228C2×Dic61—81no—
229C2×Dic61—81no—
230C8×C61—41no—
231C8×C61—41no—
232#92418—41no—
233#92418—42no—
234#92418—41no—
235#92418—81no—
236#9241—611nomaximal, Sylow
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—22no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—41no—
247C22×C61—41no—
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—81no—
252C22×C61—81no—
253C22×C61—82no—
254C22×C61—82no—
255C22×C61—81no—
256C22×C61—81no—
257C22×C61—81no—
258C22×C61—161no—
259C22×C61—161no—
260C22×C61#38611yescharacteristic
261C22×C61#44311yescharacteristic
262C22×C61#44411yescharacteristic
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—22no—
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—81no—
269C4×C61C2×#9911yescharacteristic
270C4×C61C2×#9911yescharacteristic
271Dic61—82no—
272C2×#449D6111yescharacteristic
273#2880—611no—
274#1789—611no—
275#1507—611no—
276#1471—611no—
277#1293—611no—
278#1282—611no—
279C2×C61—21no—
280C2×C61—21no—
281C2×C61—41no—
282C2×C61—41no—
283C2×C61—42no—
284C2×C61—81no—
285C2×C61—161no—
286C2×C61#187611yescharacteristic
287C2×C61#189811yescharacteristic
288C2×C61#190311yescharacteristic
289C22×#41C2×D6111yescharacteristic
290C22×SD16Dic6111yescharacteristic, complemented
291C22×D8Dic6111yescharacteristic, complemented
292C2×#131—1221no—
293C2×#121C2×D6111yescharacteristic
294#449—21no—
295#449—21no—
296#449—21no—
297#449—21no—
298C2×#104—1221no—
299C2×#104—1221no—
300C2×#103Dic6111yescharacteristic, complemented
301C2×#102Dic6111yescharacteristic, complemented
302#408—1222no—
303#408—1221no—
304#407—611no—
305#407—611no—
306#407—1221no—
307C2×C22⋊C8—611no—
308C2×C22⋊C8—1221no—
309C2×C22⋊C8C2×D6111yescharacteristic
310C4×C22⋊C4—611no—
311#327—1222no—
312#323—1221no—
313#323—1221no—
314C61#924111yescharacteristic, complemented, Sylow
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41C22⋊D6111yescharacteristic
320C2×#41C22⋊D6111yescharacteristic
321C2×#41C22⋊D6111yescharacteristic
322C2×#41C22⋊D6111yescharacteristic
323C22×Q8C2×Dic6111yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×Dic6111yescharacteristic
327C22×D4C2×Dic6111yescharacteristic
328C23×C4—21no—
329C23×C4C22×D6111yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—42no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—42no—
336#131—2442no—
337#131—2442no—
338C2×M16—1222no—
339C2×M16—1221no—
340C2×M16—1221no—
341C22×C8—1222no—
342C22×C8—1221no—
343C22×C8C2×Dic6111yescharacteristic
344C22×C8C2×Dic6111yescharacteristic
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349C2×C4⋊C4C2×Dic6111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—1221no—
352C2×C42—1221no—
353#104—2442no—
354#104—2442no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—611no—
362C22⋊C8—611no—
363C22⋊C8—612no—
364C22⋊C8—1222no—
365C22⋊C8—1222no—
366C22⋊C8—1221no—
367C22⋊C8—1221no—
368C22⋊C8—1221no—
369C22⋊C8—1221no—
370#95—1221no—
371C24—21no—
372C24—21no—
373C24#1175822411yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊Dic6111yescharacteristic
388C2×Q8C22⋊Dic6111yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊Dic6111yescharacteristic
405C2×D4C22⋊Dic6111yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—2441no—
416C22×C4D4×D6111yescharacteristic
417C22×C4D4×D6111yescharacteristic
418C22×C4#1175822411yescharacteristic
419C22×C4C22×Dic6111yescharacteristic
420C22×C4C2×C22⋊D6111yescharacteristic
421C22×C4C2×C22⋊D6111yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—2441no—
427M16—2441no—
428M16—2444no—
429M16—2441no—
430M16—2441no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—41no—
434C2×C8—41no—
435C2×C8—1221no—
436C2×C8—1221no—
437C2×C8—1222no—
438C2×C8—2441no—
439C2×C8—2444no—
440C2×C8—2441no—
441C2×C8—2441no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—1222no—
447C22⋊C4—2441no—
448C42—2441no—
449C42—2441no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23D4×Dic6111yescharacteristic
466C23#1451974911yescharacteristic
467C23#1451975811yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#1451969212yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#1451969212yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—81no—
505C2×C4—4881no—
506C2×C4—4881no—
507C2×C4—2442no—
508C2×C4C2×C22⋊Dic6111yescharacteristic
509C2×C4D4×Dic6111yescharacteristic
510C2×C4#1451974511yescharacteristic
511C2×C4#1451974911yescharacteristic
512C8—41no—
513C8—41no—
514C8—4881no—
515C8—2441no—
516C8—2441no—
517C8—2442no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22#1683964211yescharacteristic
542C22#1683987911yescharacteristic
543C22#1683988411yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—81no—
550C4—4882no—
551C4C2×#1451969211yescharacteristic
552C4C2×#1451969211yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2#2144614811yescharacteristic
561C2#2144627311yescharacteristic
562C2#2144630111yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC2×C61×#449C2
socleC22×C61#386
cosocleC23×C4×C61C23
hypercenterC2×#449D61
hypocenterC61#9241
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #21454268C2semidirect
2. #21445763C2semidirect
3. #21444335C2semidirect
4. #21444179C2semidirect
5. #21443696C2semidirect
6. #21443666C2semidirect
23. C22×SD16×C61C4semidirect
24. C22×D8×C61C4semidirect
30. C2×#103×C61C4semidirect
31. C2×#102×C61C4semidirect
290. C22×SD16Dic61semidirect
291. C22×D8Dic61semidirect
300. C2×#103Dic61semidirect
301. C2×#102Dic61semidirect
314. C61#9241semidirect

Maximal subgroups

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

subgroupindex
#214542682
#214457632
#214443352
#214441792
#214436962
#214436662
C2×C61×#4492
#924161