Finite Group Databasebeta

← #29575545

Subgroups — #29575545

Order 15616.

674 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#21454841C211yesmaximal, characteristic, complemented
2#21448477C211yesmaximal, characteristic
3#21444135C211yesmaximal, characteristic, complemented
4C2×#16839486C211yesmaximal, characteristic, complemented
5#21443666C211yesmaximal, characteristic, complemented
6#21443665C211yesmaximal, characteristic, complemented
7C2×C61×#323C211yesmaximal, characteristic, complemented
8C2×#14519746C411yescharacteristic
9C2×C4×C22⋊D61C2211yescharacteristic
10C8×C22⋊D61—22no—
11#16839825—22no—
12#16839812—21no—
13C2×C22⋊#92418C2211yescharacteristic
14C2×C22⋊#92418C2211yescharacteristic
15C22⋊C8×D61—21no—
16#16839662—21no—
17#16839656—21no—
18#16839650—21no—
19#16839641C411yescharacteristic
20#16839638—21no—
21#16839635C411yescharacteristic
22#16839618C411yescharacteristic
23C4×C22⋊Dic61C2211yescharacteristic
24#16839487—21no—
25#16839486—22no—
26#16839485—21no—
27C22×C22⋊C4×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C61×#323—22no—
31C22×C22⋊D61—21no—
32C22×C22⋊D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×#92418—21no—
35C22×#92418—21no—
36C2×C8×D61—22no—
37#14519746—22no—
38#14519746C814yescomplemented
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43C2×#11758196—21no—
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61C2×C411yescharacteristic
49C2×C22⋊Dic61C2×C411yescharacteristic
50C2×C22⋊Dic61C2×C411yescharacteristic
51C2×#11758198—21no—
52C2×#11758198D411yescharacteristic
53C2×C4×Dic61—21no—
54C2×C4×Dic61D411yescharacteristic
55#14519706—22no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22⋊#92418D412yescomplemented
60#14519689—22no—
61C8×Dic61—22no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65C25×C61C2×C411yescharacteristic
66C23×C4×C61C2×C411yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61D412yescomplemented
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—81no—
87C24×C61—81no—
88C24×C61C2×C812yescomplemented
89C24×C61C22×C411yescharacteristic
90C23×D61C22⋊C411yescharacteristic
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—81no—
95C22×C4×C61—81no—
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C2×C22⋊D61—21no—
103C2×C22⋊D61—21no—
104C2×C22⋊D61—21no—
105C2×C22⋊D61—21no—
106C2×C22⋊D61—24no—
107C2×C22⋊D61—81no—
108C2×C22⋊D61—81no—
109C2×C22⋊D61C2×C812yes—
110C2×C22⋊D61M1612yes—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C22⋊C411yescharacteristic
115C22×Dic61C22⋊C411yescharacteristic
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—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊Dic61—21no—
128C22⋊Dic61—21no—
129C22⋊Dic61—21no—
130C22⋊Dic61—24no—
131C22⋊Dic61—21no—
132C22⋊Dic61—21no—
133C22⋊Dic61—81no—
134C22⋊Dic61—81no—
135C22⋊Dic61C2×C812yescomplemented
136#11758198—21no—
137#11758198—21no—
138#11758198—81no—
139#11758196—21no—
140#11758196—21no—
141#11758196—81no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C4×Dic61—81no—
145C2×#92418—22no—
146C2×#92418—41no—
147C2×#92418—81no—
148C2×#92418—81no—
149C8×D61—82no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61—41no—
162C23×C61—41no—
163C23×C61—81no—
164C23×C61—81no—
165C23×C61—81no—
166C23×C61—81no—
167C23×C61—82no—
168C23×C61—82no—
169C23×C61—82no—
170C23×C61—82no—
171C23×C61C2×C22⋊C411yescharacteristic
172C23×C61C4×D411yescharacteristic
173C23×C61C4×D411yescharacteristic
174C23×C61C22×C811yescharacteristic
175C23×C61C2×M1611yescharacteristic
176C23×C61#13111yescharacteristic
177C23×C61#13111yescharacteristic
178C22×D61—21no—
179C22×D61—21no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61C22⋊C812yes—
183C2×C4×C61—41no—
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—81no—
193C2×C4×C61—81no—
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61#12311yescharacteristic
198C22⋊D61—22no—
199C22⋊D61—22no—
200C22⋊D61—22no—
201C22⋊D61—22no—
202C22⋊D61—84no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—22no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61C22⋊C812yes—
216C4×D61—42no—
217C4×D61—81no—
218C8×C61—42no—
219C8×C61—81no—
220#92418—42no—
221#92418—81no—
222#9107—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—42no—
234C22×C61—42no—
235C22×C61—42no—
236C22×C61—82no—
237C22×C61—82no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—82no—
241C22×C61—82no—
242C22×C61—81no—
243C22×C61—81no—
244C22×C61#38611yescharacteristic
245C22×C61C2×C22⋊C811yescharacteristic
246C22×C61#40811yescharacteristic
247C22×C61C8×D411yescharacteristic
248C22×C61C8×D411yescharacteristic
249C22×C61#43511yescharacteristic
250C22×C61#43511yescharacteristic
251C2×D61—22no—
252C2×D61—41no—
253C2×D61—41no—
254C2×D61—42no—
255C2×D61—81no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—81no—
261Dic61—22no—
262Dic61—42no—
263Dic61—41no—
264Dic61—41no—
265Dic61—81no—
266#2972—611no—
267#2321—611no—
268#1459—611no—
269C2×#323—611no—
270C2×#323D6111yescharacteristic, complemented
271#1282—611no—
272#1282—611no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—82no—
280C2×C61#186911yescharacteristic
281C2×C61#191311yescharacteristic
282C2×C61#191411yescharacteristic
283D61—42no—
284C2×#120—611no—
285C2×C4×D4—611no—
286C22×C22⋊C4C2×D6111yescharacteristic
287C8×D4—1222no—
288C8×D4—1222no—
289#431—1221no—
290C2×C22⋊C8—611no—
291C2×C22⋊C8—611no—
292C2×C22⋊C8—1221no—
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⋊C4—611no—
303#324—1221no—
304#323—22no—
305#323—1221no—
306#323—1222no—
307C61#910711yescharacteristic, complemented, Sylow
308C25C4×D6111yescharacteristic
309C22×D4—611no—
310C22×D4—1221no—
311C23×C4—611no—
312C23×C4C4×D6111yescharacteristic
313C23×C4C22×D6111yescharacteristic
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—1222no—
317C22×C8—1221no—
318C22×C8—1221no—
319#120—614no—
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—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—611no—
334C2×C22⋊C4—611no—
335C2×C22⋊C4—611no—
336C2×C22⋊C4—611no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—1221no—
341C2×C42—611no—
342C2×C42—1221no—
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⋊C8C22⋊D6112yescomplemented
353C4×C8—1222no—
354#95—1221no—
355#95—1221no—
356#95—1221no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—81no—
364C24—81no—
365C24—611no—
366C24C8×D6112yescomplemented
367C24C2×C4×D6111yescharacteristic
368C2×D4—612no—
369C2×D4—612no—
370C2×D4—1221no—
371C2×D4—1221no—
372C2×D4—1221no—
373C2×D4—1221no—
374C2×D4—1224no—
375C2×D4—4881no—
376C2×D4—4881no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—81no—
381C22×C4—81no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—4881no—
390C22×C4#1175822211yescharacteristic
391C22×C4D4×D6111yescharacteristic
392C22×C4D4×D6111yescharacteristic
393C22×C4D4×D6111yescharacteristic
394C22×C4#1175822411yescharacteristic
395C22×C4C2×C22⋊D6111yescharacteristic
396C2×C8—22no—
397C2×C8—41no—
398C2×C8—81no—
399C2×C8—81no—
400C2×C8—1222no—
401C2×C8—4882no—
402C2×C8—4881no—
403C2×C8—4881no—
404C2×C8—2441no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—4881no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—612no—
413C22⋊C4—1224no—
414C22⋊C4—1221no—
415C22⋊C4—1221no—
416C22⋊C4—1221no—
417C22⋊C4—1221no—
418C22⋊C4—1221no—
419C22⋊C4—1221no—
420C22⋊C4—1221no—
421C22⋊C4—4881no—
422C22⋊C4—4881no—
423C22⋊C4—4881no—
424C42—1221no—
425C42—1221no—
426C42—4881no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—81no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—612no—
449C23—1221no—
450C23—1221no—
451C23—2441no—
452C23—2441no—
453C23C22⋊C4×D6111yescharacteristic
454C23#1451973711yescharacteristic
455C23C4×C22⋊D6111yescharacteristic
456C23C2×C8×D6111yescharacteristic
457C23M16×D6111yescharacteristic
458C23#1451978311yescharacteristic
459C23#1451978511yescharacteristic
460D4—1222no—
461D4—1222no—
462D4—1222no—
463D4—1222no—
464D4—4884no—
465C2×C4—41no—
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—81no—
475C2×C4—81no—
476C2×C4—612no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1222no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—4881no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4#1451974511yescharacteristic
492C2×C4#1451974811yescharacteristic
493C2×C4#1451975011yescharacteristic
494C2×C4#1451975911yescharacteristic
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—42no—
510C22—42no—
511C22—42no—
512C22—82no—
513C22—82no—
514C22—81no—
515C22—81no—
516C22—82no—
517C22—82no—
518C22—81no—
519C22—81no—
520C22—1222no—
521C22—4881no—
522C22—2442no—
523C22—2441no—
524C22—2441no—
525C22#1683963811yescharacteristic
526C22C22⋊C8×D6111yescharacteristic
527C22#1683972711yescharacteristic
528C22#1683982511yescharacteristic
529C22C8×C22⋊D6111yescharacteristic
530C22#1683983111yescharacteristic
531C22#1683983611yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—81no—
537C4—1222no—
538C4—4881no—
539C4—2442no—
540C4—2441no—
541C4—2441no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—82no—
549C2—2442no—
550C2#2144610811yescharacteristic
551C2#2144635811yescharacteristic
552C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC2×C61×#323C2
socleC22×C61#386
prime radicalC2×#14519746C4
cosocleC23×C4×C61C23
hypercenterC2×#323D61
hypocenterC61#9107
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
1. #21454841C2semidirect
3. #21444135C2semidirect
4. C2×#16839486C2semidirect
5. #21443666C2semidirect
6. #21443665C2semidirect
7. C2×C61×#323C2semidirect
38. #14519746C8semidirect
59. C22⋊#92418D4semidirect
79. C22⋊C8×C61D4semidirect
88. C24×C61C2×C8semidirect
135. C22⋊Dic61C2×C8semidirect
270. C2×#323D61semidirect
307. C61#9107semidirect
352. C22⋊C8C22⋊D61semidirect
366. C24C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214548412
#214484772
#214441352
C2×#168394862
#214436662
#214436652
C2×C61×#3232
#910761