Finite Group Databasebeta

← #29580430

Subgroups — #29580430

Order 15616.

1060 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456567C211yesmaximal, characteristic, complemented
2#21449452C211yesmaximal, characteristic, complemented
3#21446656C211yesmaximal, characteristic, complemented
4#21445750C211yesmaximal, characteristic, complemented
5#21444388C211yesmaximal, characteristic, complemented
6#21443665C211yesmaximal, characteristic, complemented
7C2×C61×#447C211yesmaximal, characteristic, complemented
8C2×#14519773—21no—
9C2×#14519751C2211yescharacteristic
10C2×#14519746—22no—
11#16840075—21no—
12#16840073—21no—
13#16839996—22no—
14#16839896—21no—
15#16839895—21no—
16C2×#14519698—22no—
17C2×#14519692—22no—
18C2×C22⋊#92418C2211yescharacteristic
19#16839670—22no—
20#16839665—21no—
21#16839622C2211yescharacteristic
22C4×C22⋊Dic61C2211yescharacteristic
23#16839497—22no—
24C23×D4×C61C2211yescharacteristic
25C22×D8×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C61×#447—22no—
28C61×#447—22no—
29C2×#102×C61—21no—
30C2×C22⋊C8×C61C2211yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—24no—
34C2×#11758199—22no—
35C22×#92418D412yescomplemented
36#14519773—44no—
37#14519751—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41#14519746—44no—
42#14519746—44no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C22⋊Dic61—24no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61D412yes—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50#14519710—22no—
51#14519698—22no—
52#14519698—44no—
53#14519697—22no—
54#14519692—44no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57#14519684—21no—
58#14519684—21no—
59C25×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—44no—
67C22×D4×C61D412yes—
68C22×D4×C61D411yescharacteristic, complemented
69C23×C4×C61C2311yescharacteristic
70C2×D8×C61—24no—
71C2×D8×C61—44no—
72C22×C8×C61—21no—
73#121×C61—21no—
74#121×C61—21no—
75#121×C61—21no—
76#121×C61—21no—
77C2×C4⋊C4×C61D411yescharacteristic, complemented
78C2×C22⋊C4×C61—21no—
79#102×C61—24no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61D412yescomplemented
82C24×C61—22no—
83C24×C61—21no—
84C24×C61—44no—
85C24×C61—41no—
86C24×C61—41no—
87C24×C61—42no—
88C24×C61—42no—
89C24×C61—82no—
90C24×C61C2×D411yescharacteristic
91C23×D61—21no—
92C2×D4×C61—24no—
93C2×D4×C61—24no—
94C2×D4×C61—24no—
95C2×D4×C61—22no—
96C2×D4×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61—22no—
99C2×D4×C61—42no—
100C2×D4×C61—42no—
101C2×D4×C61—42no—
102C2×D4×C61—42no—
103C2×D4×C61—44no—
104C2×D4×C61—44no—
105C2×D4×C61—44no—
106C2×D4×C61—41no—
107C2×D4×C61—41no—
108C2×D4×C61—42no—
109C2×D4×C61—42no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C22×C4×C61—21no—
113C22×C4×C61—42no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C2×C22⋊D61—48no—
121C2×C22⋊D61—48no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—42no—
125C2×C22⋊D61—42no—
126C2×C22⋊D61—84no—
127C22×Dic61—22no—
128C22×Dic61—21no—
129C22×Dic61—41no—
130C2×D244—21no—
131C2×D244—21no—
132C2×D244—42no—
133D8×C61—48no—
134C2×C8×C61—22no—
135C2×C8×C61—42no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊Dic61—22no—
141C22⋊Dic61—48no—
142C22⋊Dic61—42no—
143C22⋊Dic61D814yescomplemented
144#11758199—82no—
145#11758198—41no—
146#11758198—41no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—42no—
150C4×Dic61—42no—
151C2×#92418—22no—
152C2×#92418—42no—
153C23×C61—24no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—44no—
157C23×C61—44no—
158C23×C61—44no—
159C23×C61—42no—
160C23×C61—42no—
161C23×C61—44no—
162C23×C61—41no—
163C23×C61—42no—
164C23×C61—82no—
165C23×C61—82no—
166C23×C61—81no—
167C23×C61—81no—
168C23×C61—88no—
169C23×C61—88no—
170C23×C61—82no—
171C23×C61—81no—
172C23×C61—81no—
173C23×C61#12011yescharacteristic
174C23×C61#12111yescharacteristic
175C23×C61#12711yescharacteristic
176C23×C61C2×D812yes—
177C23×C61AGL(1,ℤ/8)12yes—
178C22×D61—42no—
179C22×D61—42no—
180C22×D61—41no—
181C22×D61—42no—
182D4×C61—24no—
183D4×C61—24no—
184D4×C61—42no—
185D4×C61—44no—
186D4×C61—42no—
187D4×C61—42no—
188D4×C61—44no—
189D4×C61—42no—
190D4×C61—82no—
191D4×C61—81no—
192D4×C61—81no—
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—42no—
201C2×C4×C61#12011yescharacteristic
202C2×C4×C61#12011yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12111yescharacteristic
205C22⋊D61—816no—
206C22⋊D61—82no—
207C22⋊D61—81no—
208C22⋊D61—81no—
209C2×Dic61—24no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—41no—
213C2×Dic61—42no—
214C2×Dic61—81no—
215C2×Dic61—81no—
216C2×Dic61—81no—
217D244—42no—
218D244—81no—
219C8×C61—42no—
220#92418—42no—
221#9946—611nomaximal, Sylow
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—42no—
229C22×C61—42no—
230C22×C61—48no—
231C22×C61—44no—
232C22×C61—84no—
233C22×C61—84no—
234C22×C61—88no—
235C22×C61—84no—
236C22×C61—82no—
237C22×C61—82no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—81no—
241C22×C61—162no—
242C22×C61#39211yescharacteristic
243C22×C61#44712yes—
244C22×C61#45912yes—
245C22×C61#49311yescharacteristic
246C22×C61#49611yescharacteristic
247C2×D61—84no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—81no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—81no—
255C4×C61B(4,𝔽2)12yes—
256Dic61—44no—
257Dic61—81no—
258Dic61—161no—
259#3186—611no—
260C2×#447D6111yescharacteristic, complemented
261#2433—611no—
262#1964—611no—
263#1786—611no—
264#1519—611no—
265#1282—611no—
266C2×C61—22no—
267C2×C61—21no—
268C2×C61—22no—
269C2×C61—21no—
270C2×C61—84no—
271C2×C61—161no—
272C2×C61#200811yescharacteristic
273C2×C61#201111yescharacteristic
274C2×C61#202111yescharacteristic
275D61—161no—
276C23×D4C2×D6111yescharacteristic
277C22×D8—21no—
278C2×#127—1221no—
279C2×#121—611no—
280C2×#121C2×D6111yescharacteristic
281C2×#120—1222no—
282#480—1221no—
283#480—1221no—
284#466—1222no—
285#447—22no—
286#447—22no—
287#447—1221no—
288#447—1221no—
289C2×#102—21no—
290C2×#102—1222no—
291C2×#99—1222no—
292C2×C22⋊C8—611no—
293C2×C22⋊C8C2×D6111yescharacteristic
294#392—1222no—
295#390—1221no—
296#380—611no—
297C4×C22⋊C4—611no—
298#327—1222no—
299C61#994611yescharacteristic, complemented, Sylow
300C25—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—44no—
308C22×D4—611no—
309C22×D4—1224no—
310C22×D4—1221no—
311C22×D4C22⋊D6112yes—
312C22×D4C22⋊D6111yescharacteristic, complemented
313C23×C4C22×D6111yescharacteristic
314C2×D8—24no—
315C2×D8—44no—
316C2×D8—1222no—
317C22×C8—21no—
318C22×C8—612no—
319#127—2444no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—1221no—
325#121—1221no—
326#121—1221no—
327#121—1221no—
328#120—2444no—
329#120—2444no—
330C2×C4⋊C4—611no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
333C2×C22⋊C4—21no—
334C2×C22⋊C4—612no—
335C2×C22⋊C4—1224no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C42—1221no—
339#107—1222no—
340#102—24no—
341#102—1222no—
342#102—1222no—
343#102—2444no—
344#99—2444no—
345C22⋊C8—21no—
346C22⋊C8—1221no—
347C22⋊C8—1221no—
348C22⋊C8C22⋊D6112yescomplemented
349#95—1221no—
350#95—1221no—
351C24—22no—
352C24—21no—
353C24—44no—
354C24—41no—
355C24—41no—
356C24—42no—
357C24—42no—
358C24—82no—
359C24—1221no—
360C24D4×D6111yescharacteristic
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—44no—
373C2×D4—44no—
374C2×D4—44no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—1221no—
382C2×D4—1221no—
383C2×D4—4884no—
384C2×D4—2442no—
385C2×D4—2448no—
386C2×D4—2448no—
387C2×D4—2441no—
388C2×D4—2441no—
389C2×D4—2442no—
390C2×D4—2442no—
391C22×C4—21no—
392C22×C4—42no—
393C22×C4—1222no—
394C22×C4—1221no—
395C22×C4—2441no—
396C22×C4D4×D6111yescharacteristic
397C22×C4D4×D6111yescharacteristic
398C22×C4#1175822411yescharacteristic
399C22×C4C2×C22⋊D6111yescharacteristic
400C22×C4C2×C22⋊D6111yescharacteristic
401C22×C4C2×C22⋊D6111yescharacteristic
402D8—48no—
403D8—4882no—
404C2×C8—22no—
405C2×C8—42no—
406C2×C8—1222no—
407C2×C8—2442no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—1221no—
411C4⋊C4—1221no—
412C4⋊C4—2442no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—614no—
416C22⋊C4—1222no—
417C22⋊C4—2448no—
418C22⋊C4—2442no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C42—2442no—
422C23—24no—
423C23—41no—
424C23—41no—
425C23—44no—
426C23—44no—
427C23—42no—
428C23—44no—
429C23—44no—
430C23—42no—
431C23—41no—
432C23—42no—
433C23—82no—
434C23—82no—
435C23—81no—
436C23—81no—
437C23—88no—
438C23—88no—
439C23—82no—
440C23—81no—
441C23—81no—
442C23—2442no—
443C23—2442no—
444C23—2442no—
445C23—2441no—
446C23#1451974511yescharacteristic
447C23#1451974911yescharacteristic
448C23#1451977311yescharacteristic
449C23D8×D6112yes—
450C23#1451980112yes—
451D4—24no—
452D4—24no—
453D4—42no—
454D4—44no—
455D4—42no—
456D4—42no—
457D4—44no—
458D4—42no—
459D4—81no—
460D4—82no—
461D4—81no—
462D4—4881no—
463D4—4882no—
464D4—4881no—
465D4—4881no—
466D4—48816no—
467D4—2442no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—1224no—
477C2×C4—4881no—
478C2×C4—4881no—
479C2×C4—4881no—
480C2×C4—2442no—
481C2×C4—2441no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4#1451974511yescharacteristic
485C2×C4#1451974611yescharacteristic
486C2×C4#1451974811yescharacteristic
487C2×C4#1451974911yescharacteristic
488C8—42no—
489C8—2442no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—42no—
497C22—42no—
498C22—48no—
499C22—44no—
500C22—84no—
501C22—84no—
502C22—88no—
503C22—84no—
504C22—82no—
505C22—82no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—162no—
510C22—4884no—
511C22—4881no—
512C22—4881no—
513C22—4881no—
514C22#1683967011yescharacteristic
515C22#1683989412yes—
516C22#1683995512yes—
517C22#1684013711yescharacteristic
518C22#1684015011yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—81no—
523C4—9761no—
524C4—4881no—
525C4—2444no—
526C4#1683994812yes—
527C2—21no—
528C2—22no—
529C2—22no—
530C2—21no—
531C2—84no—
532C2—161no—
533C2—9761no—
534C2#2144687011yescharacteristic
535C2#2144688811yescharacteristic
536C2#2144694211yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#447C2
socleC22×C61#392
hypercenterC2×#447D61
hypocenterC61#9946
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #21456567C2semidirect
2. #21449452C2semidirect
3. #21446656C2semidirect
4. #21445750C2semidirect
5. #21444388C2semidirect
6. #21443665C2semidirect
7. C2×C61×#447C2semidirect
35. C22×#92418D4semidirect
68. C22×D4×C61D4semidirect
77. C2×C4⋊C4×C61D4semidirect
81. C22⋊C8×C61D4semidirect
143. C22⋊Dic61D8semidirect
260. C2×#447D61semidirect
299. C61#9946semidirect
312. C22×D4C22⋊D61semidirect
332. C2×C4⋊C4C22⋊D61semidirect
348. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214565672
#214494522
#214466562
#214457502
#214443882
#214436652
C2×C61×#4472
#994661