Finite Group Databasebeta

← #29575557

Subgroups — #29575557

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454845C211yesmaximal, characteristic, complemented
2#21448479C211yesmaximal, characteristic
3#21444135C211yesmaximal, characteristic, complemented
4C2×#16839485C211yesmaximal, characteristic, complemented
5C2×#16839485C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C2×#14519747C411yescharacteristic
9C2×C4×C22⋊D61C2211yescharacteristic
10C22×#11758198C2211yescharacteristic
11#16839833—22no—
12#16839830—22no—
13#16839816—21no—
14#16839724—21no—
15C2×C22⋊#92418C2211yescharacteristic
16C2×C22⋊#92418C2211yescharacteristic
17#16839664—21no—
18#16839654—21no—
19#16839653—21no—
20#16839640—21no—
21#16839639C411yescharacteristic
22#16839637C411yescharacteristic
23#16839617C411yescharacteristic
24#16839487—21no—
25#16839485—21no—
26#16839485—22no—
27#16839485—22no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C24×D61C2×C411yescharacteristic
32C22×D244—21no—
33C22×C22⋊D61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758189—22no—
37C22×#92418—21no—
38C22×#92418—21no—
39#14519747—22no—
40#14519747—22no—
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45C2×C4⋊Dic61—21no—
46C2×#11758196D411yescharacteristic
47C2×C22⋊Dic61C2×C411yescharacteristic
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×#11758198D411yescharacteristic
59C2×C4×Dic61D411yescharacteristic
60#14519706—22no—
61C22⋊#92418—21no—
62C22⋊#92418—21no—
63C22⋊#92418—21no—
64C22⋊#92418D412yescomplemented
65#14519689—22no—
66#14519687—22no—
67#14519684—21no—
68#14519684—21no—
69C23×C4×C61C2311yescharacteristic
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C2×C22⋊C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61C2×C411yescharacteristic
74C2×C42×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61D412yescomplemented
79#95×C61—21no—
80C24×C61C22×C411yescharacteristic
81C23×D61—21no—
82C23×D61—21no—
83C23×D61—21no—
84C23×D61—21no—
85C23×D61—21no—
86C23×D61—21no—
87C23×D61—81no—
88C23×D61—81no—
89C23×D61C22⋊C411yescharacteristic
90C23×D61M1612yescomplemented
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—81no—
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C2×C22⋊D61—21no—
101C2×C22⋊D61—21no—
102C2×C22⋊D61—21no—
103C2×C22⋊D61—21no—
104C2×C22⋊D61—21no—
105C2×C22⋊D61—21no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—81no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C22⋊C411yescharacteristic
113C2×D244—24no—
114C2×D244—81no—
115C2×D244—81no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61—81no—
119C2×C8×C61—22no—
120C2×C8×C61—41no—
121C2×C8×C61—81no—
122C2×C8×C61—81no—
123C22⋊C4×C61—21no—
124C22⋊C4×C61—21no—
125C22⋊C4×C61—21no—
126C22⋊C4×C61M1612yescomplemented
127C42×C61—81no—
128C22⋊Dic61—21no—
129C22⋊Dic61—21no—
130#11758198—24no—
131#11758198—21no—
132#11758198—21no—
133#11758198—41no—
134#11758198—41no—
135#11758198—41no—
136#11758198—41no—
137#11758198—81no—
138#11758198—81no—
139#11758198—81no—
140C4⋊Dic61—81no—
141#11758196—21no—
142#11758196—21no—
143C4×Dic61—21no—
144C4×Dic61—21no—
145C2×#92418—22no—
146C2×#92418—41no—
147C2×#92418—81no—
148C2×#92418—81no—
149#11758189—82no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61C2×C22⋊C411yescharacteristic
153C23×C61C4×D411yescharacteristic
154C23×C61C4×D411yescharacteristic
155C23×C61C2×M1611yescharacteristic
156C23×C61C2×M1611yescharacteristic
157C23×C61#13111yescharacteristic
158C23×C61#13111yescharacteristic
159C22×D61—21no—
160C22×D61—22no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—82no—
176C22×D61—82no—
177C22×D61—81no—
178C22×D61—81no—
179C22×D61—81no—
180C22×D61—81no—
181C22×D61—82no—
182C22×D61—82no—
183C2×C4×C61—22no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61#12011yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61#12111yescharacteristic
198C2×C4×C61#12311yescharacteristic
199C22⋊D61—41no—
200C22⋊D61—41no—
201C22⋊D61—41no—
202C22⋊D61—41no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—81no—
214C2×Dic61—81no—
215D244—84no—
216C4×D61—42no—
217C4×D61—81no—
218C8×C61—42no—
219C8×C61—81no—
220#92418—42no—
221#92418—81no—
222#9109—611nomaximal, Sylow
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61#38611yescharacteristic
234C22×C61#40711yescharacteristic
235C22×C61#40811yescharacteristic
236C22×C61#43511yescharacteristic
237C22×C61#43511yescharacteristic
238C22×C61#43611yescharacteristic
239C22×C61#43611yescharacteristic
240C2×D61—42no—
241C2×D61—42no—
242C2×D61—42no—
243C2×D61—41no—
244C2×D61—42no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—82no—
250C2×D61—82no—
251C2×D61—81no—
252C2×D61—81no—
253C2×D61—81no—
254C2×D61—82no—
255C2×D61—82no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—42no—
261C4×C61—81no—
262Dic61—41no—
263Dic61—41no—
264Dic61—41no—
265Dic61—81no—
266#2973—611no—
267#2321—611no—
268#1459—611no—
269C2×#323—611no—
270C2×#323—611no—
271#1282—611no—
272#1282D6111yescharacteristic, complemented
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61#187011yescharacteristic
280C2×C61#191311yescharacteristic
281C2×C61#191411yescharacteristic
282D61—81no—
283D61—82no—
284C2×#120—611no—
285C2×C4×D4—611no—
286C22×C22⋊C4—611no—
287#435—1222no—
288#435—1222no—
289#432—1221no—
290#407—1221no—
291C2×C22⋊C8—611no—
292C2×C22⋊C8—611no—
293C2×C22⋊C8C2×D6111yescharacteristic
294C2×C22⋊C8C2×D6111yescharacteristic
295#390—1221no—
296#388—1221no—
297#388—1221no—
298#386—611no—
299#386—1221no—
300#385—611no—
301#379—611no—
302C4×C22⋊C4C2×D6111yescharacteristic
303#324—1221no—
304#323—1222no—
305#323—1221no—
306#323—1222no—
307C61#910911yescharacteristic, complemented, Sylow
308C25—611no—
309C22×D4—611no—
310C22×D4—1221no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4C22×D6111yescharacteristic
314C2×M16—1222no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—1221no—
318C22×C8—1221no—
319#120—1222no—
320#120—1222no—
321C4×D4—1221no—
322C4×D4—1221no—
323C4×D4—1221no—
324C4×D4—1221no—
325C2×C4⋊C4—611no—
326C2×C4⋊C4—1221no—
327C2×C22⋊C4—611no—
328C2×C22⋊C4—611no—
329C2×C22⋊C4—1221no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4C4×D6111yescharacteristic
340C2×C22⋊C4C4×D6111yescharacteristic
341C2×C42—21no—
342C2×C42—611no—
343C4⋊C8—1222no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—612no—
348C22⋊C8—1222no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351C22⋊C8—1221no—
352C22⋊C8D24412yescomplemented
353#97—1222no—
354#95—21no—
355#95—1221no—
356#95—1221no—
357C24—612no—
358C24—611no—
359C24—1221no—
360C24—1221no—
361C24—1221no—
362C24—1221no—
363C24—1221no—
364C24—1221no—
365C24—4881no—
366C24—4881no—
367C24C2×C4×D6111yescharacteristic
368C2×D4—1224no—
369C2×D4—1221no—
370C2×D4—1221no—
371C2×D4—1221no—
372C2×D4—1221no—
373C2×D4—1221no—
374C2×D4—1221no—
375C2×D4—4881no—
376C2×D4—4881no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—81no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—4881no—
389C22×C4—4881no—
390C22×C4C2×D24411yescharacteristic
391C22×C4#1175822211yescharacteristic
392C22×C4D4×D6111yescharacteristic
393C22×C4D4×D6111yescharacteristic
394C22×C4D4×D6111yescharacteristic
395C22×C4#1175822611yescharacteristic
396M16—4882no—
397C2×C8—22no—
398C2×C8—41no—
399C2×C8—81no—
400C2×C8—81no—
401C2×C8—1222no—
402C2×C8—4881no—
403C2×C8—4881no—
404C2×C8—2441no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—4881no—
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—1224no—
412C22⋊C4—1221no—
413C22⋊C4—1221no—
414C22⋊C4—1221no—
415C22⋊C4—1221no—
416C22⋊C4—4881no—
417C22⋊C4—4881no—
418C22⋊C4—4881no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C22⋊C4#1175818912yescomplemented
424C42—81no—
425C42—1221no—
426C42—1221no—
427C23—41no—
428C23—41no—
429C23—1221no—
430C23—1222no—
431C23—1222no—
432C23—1222no—
433C23—1221no—
434C23—1221no—
435C23—4881no—
436C23—4881no—
437C23—4881no—
438C23—4881no—
439C23—4882no—
440C23—4882no—
441C23—4882no—
442C23—4882no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23C22⋊C4×D6111yescharacteristic
454C23#1451973911yescharacteristic
455C23C4×D24411yescharacteristic
456C23M16×D6111yescharacteristic
457C23C2×#1175818911yescharacteristic
458C23#1451978311yescharacteristic
459C23#1451978511yescharacteristic
460D4—4884no—
461D4—2441no—
462D4—2441no—
463D4—2441no—
464D4—2441no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—4881no—
485C2×C4—2442no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4#1451974711yescharacteristic
492C2×C4#1451975011yescharacteristic
493C2×C4#1451975211yescharacteristic
494C2×C4#1451976211yescharacteristic
495C8—42no—
496C8—81no—
497C8—4881no—
498C8—2442no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—4882no—
510C22—4882no—
511C22—4881no—
512C22—4882no—
513C22—4882no—
514C22—4881no—
515C22—4881no—
516C22—4881no—
517C22—4881no—
518C22—2442no—
519C22—2442no—
520C22—2442no—
521C22—2441no—
522C22—2441no—
523C22—2441no—
524C22—2442no—
525C22#1683964011yescharacteristic
526C22#1683972411yescharacteristic
527C22#1683972711yescharacteristic
528C22#1683983211yescharacteristic
529C22#1683983511yescharacteristic
530C22#1683983911yescharacteristic
531C22#1683984111yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—42no—
537C4—81no—
538C4—4881no—
539C4—2441no—
540C4—2441no—
541C4—2441no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—4882no—
549C2—4881no—
550C2#2144611511yescharacteristic
551C2#2144636011yescharacteristic
552C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61#386
prime radicalC2×#14519747C4
cosocleC23×C4×C61C23
hypercenter#1282D61
hypocenterC61#9109
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
1. #21454845C2semidirect
3. #21444135C2semidirect
4. C2×#16839485C2semidirect
5. C2×#16839485C2semidirect
6. #21443667C2semidirect
7. C61×#1282C2semidirect
64. C22⋊#92418D4semidirect
78. C22⋊C8×C61D4semidirect
90. C23×D61M16semidirect
126. C22⋊C4×C61M16semidirect
272. #1282D61semidirect
307. C61#9109semidirect
352. C22⋊C8D244semidirect
423. C22⋊C4#11758189semidirect

Maximal subgroups

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

subgroupindex
#214548452
#214484792
#214441352
C2×#168394852
#214436672
C61×#12822
#910961