Finite Group Databasebeta

← #29576332

Subgroups — #29576332

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
1C2×#16839907C211yesmaximal, characteristic
2#21454268C211yesmaximal, characteristic, complemented
3#21444334C211yesmaximal, characteristic, complemented
4#21444180C211yesmaximal, characteristic, complemented
5#21443695C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#1789C211yesmaximal, characteristic, complemented
8C22×#11758201C411yescharacteristic, complemented
9C22×#11758199C411yescharacteristic, complemented
10C2×#14519784—21no—
11C2×#14519751C2211yescharacteristic
12#16839907—21no—
13#16839907—21no—
14#16839907—21no—
15#16839907—21no—
16C2×#14519701C411yescharacteristic, complemented
17C2×#14519698C411yescharacteristic, complemented
18#16839729—22no—
19#16839729—21no—
20#16839726—21no—
21#16839726C2211yescharacteristic
22C2×C22⋊#92418—21no—
23C2×C22⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25#16839495—22no—
26#16839485—21no—
27#16839485—21no—
28C22×#41×C61C2211yescharacteristic
29C2×#104×C61—21no—
30C2×#104×C61—21no—
31C61×#407C2211yescharacteristic
32C4×C22⋊C4×C61C2211yescharacteristic
33C22×D244C2×C411yescharacteristic
34C22×C22⋊D61—21no—
35C2×#11758201—21no—
36C2×#11758201—21no—
37C2×#11758201—42no—
38C2×#11758199—21no—
39C2×#11758199—21no—
40C2×#11758199—42no—
41#14519784—42no—
42#14519784—42no—
43C2×#11758194—22no—
44C2×#11758194—21no—
45C22×#92418—22no—
46C22×#92418—21no—
47C22×#92418C2×C411yescharacteristic
48C22×#92418C2×C411yescharacteristic
49#14519751—21no—
50#14519751—21no—
51#14519751—21no—
52#14519751—21no—
53C2×C4⋊Dic61C2×C411yescharacteristic
54C2×#11758198—21no—
55#14519701—21no—
56#14519701—21no—
57#14519698—21no—
58#14519698—21no—
59C22⋊#92418—22no—
60C22⋊#92418—22no—
61C22⋊#92418—21no—
62C22⋊#92418—21no—
63C22⋊#92418—21no—
64C22⋊#92418—21no—
65C22⋊#92418D411yescharacteristic
66C22⋊#92418D411yescharacteristic
67C22⋊#92418D412yes—
68C2×#41×C61—21no—
69C2×#41×C61—21no—
70C2×#41×C61—42no—
71C2×#41×C61—42no—
72C2×#41×C61D411yescharacteristic
73C2×#41×C61D411yescharacteristic
74C2×#41×C61D411yescharacteristic
75C2×#41×C61D411yescharacteristic
76C22×Q8×C61C2×C411yescharacteristic
77C22×D4×C61—21no—
78C22×D4×C61C2×C411yescharacteristic
79C23×C4×C61—21no—
80C23×C4×C61C2311yescharacteristic
81C2×M16×C61—21no—
82C2×C22⋊C4×C61—21no—
83C2×C42×C61—21no—
84#104×C61—42no—
85#104×C61—42no—
86C22⋊C8×C61—21no—
87C22⋊C8×C61—21no—
88#95×C61—21no—
89C24×C61—21no—
90C24×C61#4111yescharacteristic
91C23×D61—21no—
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—41no—
114C2×D4×C61—44no—
115C2×D4×C61C22⋊C411yescharacteristic
116C2×D4×C61C22⋊C411yescharacteristic
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61—44no—
125C22×C4×C61—41no—
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61#4111yescharacteristic
132C2×C22⋊D61—41no—
133C2×C22⋊D61—41no—
134C2×C22⋊D61—82no—
135C22×Dic61—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—41no—
139C2×D244—41no—
140M16×C61—41no—
141M16×C61—41no—
142C2×C8×C61—41no—
143C22⋊C4×C61—22no—
144C22⋊C4×C61—41no—
145C42×C61—41no—
146C42×C61—41no—
147#11758201—42no—
148#11758201—42no—
149#11758199—42no—
150#11758199—42no—
151#11758198—41no—
152#11758198—41no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155#11758194—44no—
156#11758194—41no—
157#11758194—41no—
158C2×#92418—21no—
159C2×#92418—21no—
160C2×#92418—21no—
161C2×#92418—22no—
162C2×#92418—21no—
163C2×#92418—44no—
164C2×#92418—41no—
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—81no—
178C23×C61C4×D411yescharacteristic
179C23×C61#12111yescharacteristic
180C23×C61#12311yescharacteristic
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—81no—
185C22×D61—81no—
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#9912yes—
200C2×C4×C61—24no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—81no—
218C2×C4×C61—81no—
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C22⋊D61—82no—
224C22⋊D61—82no—
225C2×Dic61—41no—
226C2×Dic61—81no—
227D244—41no—
228D244—41no—
229D244—81no—
230C8×C61—81no—
231#92418—41no—
232#92418—42no—
233#92418—41no—
234#92418—41no—
235#92418—41no—
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#38611yescharacteristic
256C22×C61#44311yescharacteristic
257C22×C61#44411yescharacteristic
258C2×D61—81no—
259C2×D61—81no—
260C2×D61—81no—
261C2×D61—161no—
262C2×D61—161no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—22no—
267C4×C61—41no—
268C4×C61—82no—
269C4×C61C2×#9911yescharacteristic
270C4×C61C2×#9911yescharacteristic
271Dic61—81no—
272C2×#449—611no—
273#2880—611no—
274#1789D6111yescharacteristic, complemented
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#187611yescharacteristic
286C2×C61#189811yescharacteristic
287C2×C61#190311yescharacteristic
288D61—161no—
289C22×#41C2×D6111yescharacteristic
290C22×SD16—611no—
291C22×D8—611no—
292C2×#131—1221no—
293C2×#121—611no—
294#449—1221no—
295#449—1221no—
296#449—1221no—
297#449—1221no—
298C2×#104—21no—
299C2×#104—21no—
300C2×#103—611no—
301C2×#102—611no—
302#408—1222no—
303#408—1221no—
304#407—611no—
305#407—1221no—
306#407C2×D6111yescharacteristic
307C2×C22⋊C8—611no—
308C2×C22⋊C8—611no—
309C2×C22⋊C8—1221no—
310C4×C22⋊C4C2×D6111yescharacteristic
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×#41D24411yescharacteristic
320C2×#41D24411yescharacteristic
321C2×#41C22⋊D6111yescharacteristic
322C2×#41C22⋊D6111yescharacteristic
323C22×Q8C4×D6111yescharacteristic
324C22×D4—21no—
325C22×D4—611no—
326C22×D4—1221no—
327C22×D4C4×D6111yescharacteristic
328C23×C4—21no—
329C23×C4C22×D6111yescharacteristic
330C2×SD16—1221no—
331C2×SD16—1221no—
332C2×SD16—2442no—
333C2×D8—1221no—
334C2×D8—1221no—
335C2×D8—2442no—
336#131—2442no—
337#131—2442no—
338C2×M16—21no—
339C2×M16—1222no—
340C2×M16—1221no—
341C22×C8—611no—
342C22×C8—611no—
343C22×C8—1222no—
344C22×C8—1221no—
345#121—1221no—
346#121—1221no—
347#121—1221no—
348#121—1221no—
349C2×C4⋊C4—611no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—1221no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—1221no—
356#103—1221no—
357#102—1221no—
358#102—1221no—
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—21no—
371C24—21no—
372C24—1221no—
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×Q8#1175819811yescharacteristic
388C2×Q8#1175819811yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—44no—
397C2×D4—1221no—
398C2×D4—1221no—
399C2×D4—4882no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C2×D4—2441no—
404C2×D4#1175819811yescharacteristic
405C2×D4#1175819811yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—44no—
414C22×C4—41no—
415C22×C4—1221no—
416C22×C4C2×C4×D6111yescharacteristic
417C22×C4C2×D24411yescharacteristic
418C22×C4D4×D6111yescharacteristic
419C22×C4D4×D6111yescharacteristic
420C22×C4#1175822411yescharacteristic
421C22×C4C2×C22⋊D6111yescharacteristic
422SD16—2442no—
423SD16—2442no—
424D8—2442no—
425D8—2442no—
426M16—41no—
427M16—41no—
428M16—2444no—
429M16—2441no—
430M16—2441no—
431C2×C8—41no—
432C2×C8—1221no—
433C2×C8—1221no—
434C2×C8—1221no—
435C2×C8—1221no—
436C2×C8—1222no—
437C2×C8—2444no—
438C2×C8—2441no—
439C2×C8—2441no—
440C2×C8—2441no—
441C2×C8—2441no—
442C4⋊C4—1221no—
443C4⋊C4—1221no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—2441no—
447C22⋊C4—2441no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—81no—
460C23—4881no—
461C23—4881no—
462C23—2441no—
463C23—2441no—
464C23—2441no—
465C23#1451973711yescharacteristic
466C23#1451974911yescharacteristic
467C23#1451976111yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#1451969112yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—4881no—
482D4—4882no—
483D4—4882no—
484D4—2441no—
485D4—2441no—
486D4#1451969112yes—
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—42no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—4881no—
507C2×C4—2441no—
508C2×C4C2×#1175819811yescharacteristic
509C2×C4#1451973711yescharacteristic
510C2×C4#1451974711yescharacteristic
511C2×C4#1451974911yescharacteristic
512C8—81no—
513C8—2441no—
514C8—2441no—
515C8—2442no—
516C8—2441no—
517C8—2441no—
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—9761no—
537C22—9761no—
538C22—4881no—
539C22—4881no—
540C22—4881no—
541C22#1683963911yescharacteristic
542C22#1683987611yescharacteristic
543C22#1683988111yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—4881no—
551C4C2×#1451969111yescharacteristic
552C4C2×#1451969111yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—9761no—
560C2#2144614411yescharacteristic
561C2#2144627011yescharacteristic
562C2#2144629711yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1789C2
socleC22×C61#386
prime radicalC2×#16839907C2
cosocleC23×C4×C61C23
hypercenter#1789D61
hypocenterC61#9241
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #21454268C2semidirect
3. #21444334C2semidirect
4. #21444180C2semidirect
5. #21443695C2semidirect
6. #21443667C2semidirect
7. C61×#1789C2semidirect
8. C22×#11758201C4semidirect
9. C22×#11758199C4semidirect
16. C2×#14519701C4semidirect
17. C2×#14519698C4semidirect
274. #1789D61semidirect
314. C61#9241semidirect

Maximal subgroups

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

subgroupindex
C2×#168399072
#214542682
#214443342
#214441802
#214436952
#214436672
C61×#17892
#924161