Finite Group Databasebeta

← #29580249

Subgroups — #29580249

Order 15616.

856 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840078C211yesmaximal, characteristic, complemented
2C2×#16839698C211yesmaximal, characteristic, complemented
3#21445907C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic, complemented
5C2×#16839486C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#2617C211yesmaximal, characteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C22×#11758196—21no—
10C22×C22⋊Dic61—21no—
11#16840078—22no—
12#16840078—22no—
13C2×#14519708—21no—
14C2×#14519698—21no—
15C2×C22⋊#92418C2211yescharacteristic
16C2×C22⋊#92418C2211yescharacteristic
17#16839698—22no—
18#16839698—22no—
19C2×#14519684C2211yescharacteristic
20#16839524—22no—
21#16839496—22no—
22#16839486—22no—
23C2×#121×C61C2211yescharacteristic
24C2×#120×C61—21no—
25C22×C22⋊C4×C61C2211yescharacteristic
26C61×#397—21no—
27C61×#394—22no—
28C61×#392—21no—
29C61×#386—21no—
30C61×#380C2211yescharacteristic
31C23×Dic61—21no—
32C23×Dic61—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D412yescomplemented
41C2×#11758196—24no—
42C2×#11758196—44no—
43C2×C22⋊Dic61—24no—
44C2×C22⋊Dic61—44no—
45#14519708—24no—
46#14519698—24no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418D412yescomplemented
51#14519684—21no—
52#14519684D412yescomplemented
53C25×C61D411yescharacteristic
54C22×D4×C61—21no—
55C22×D4×C61—22no—
56C22×D4×C61D411yescharacteristic
57C23×C4×C61D411yescharacteristic
58C23×C4×C61C2311yescharacteristic
59#121×C61—21no—
60#121×C61—21no—
61#121×C61—21no—
62#121×C61—21no—
63#120×C61—42no—
64#120×C61—42no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C4⋊C4×C61D412yes—
67C2×C22⋊C4×C61—22no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×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—
76C2×C22⋊C4×C61—22no—
77#95×C61—22no—
78#95×C61—21no—
79C24×C61—21no—
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61SD1612yes—
89C24×C61C2×D411yescharacteristic
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—42no—
93C2×D4×C61—44no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—82no—
101C2×D4×C61—82no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×Dic61—24no—
116C22×Dic61—22no—
117C22×Dic61—22no—
118C22×Dic61—42no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—42no—
122C22×Dic61—42no—
123C22×Dic61—41no—
124C22×Dic61—41no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—42no—
128C22⋊C4×C61—44no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—82no—
138C22⋊Dic61—48no—
139C4⋊Dic61—22no—
140C4⋊Dic61—22no—
141C4⋊Dic61—41no—
142C4⋊Dic61—41no—
143#11758196—48no—
144C2×#92418—22no—
145C2×#92418—42no—
146C2×#92418—42no—
147C2×#92418—41no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—44no—
154C23×C61—42no—
155C23×C61—44no—
156C23×C61—42no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—42no—
161C23×C61—42no—
162C23×C61—41no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61—82no—
169C23×C61—82no—
170C23×C61—81no—
171C23×C61—81no—
172C23×C61#12011yescharacteristic
173C23×C61#12011yescharacteristic
174C23×C61#12111yescharacteristic
175C23×C61C2×SD1611yescharacteristic
176C23×C61#13511yescharacteristic
177C23×C61AGL(1,ℤ/8)11yescharacteristic
178C23×C61#13711yescharacteristic
179D4×C61—42no—
180D4×C61—81no—
181D4×C61—88no—
182D4×C61—81no—
183D4×C61—81no—
184D4×C61—81no—
185D4×C61—81no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—42no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—81no—
202C2×C4×C61#12011yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12111yescharacteristic
205C2×C4×C61#12711yescharacteristic
206C2×Dic61—24no—
207C2×Dic61—44no—
208C2×Dic61—44no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—82no—
215C2×Dic61—82no—
216#92418—42no—
217#92418—81no—
218#9920—611nomaximal, Sylow
219C22×C61—22no—
220C22×C61—22no—
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—44no—
228C22×C61—44no—
229C22×C61—42no—
230C22×C61—82no—
231C22×C61—82no—
232C22×C61—82no—
233C22×C61—82no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—82no—
237C22×C61—82no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—81no—
241C22×C61#39211yescharacteristic
242C22×C61#44811yescharacteristic
243C22×C61#44911yescharacteristic
244C22×C61#45011yescharacteristic
245C22×C61#45211yescharacteristic
246C22×C61#45312yes—
247C22×C61#45812yes—
248C22×C61#46511yescharacteristic
249C22×C61#46811yescharacteristic
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—82no—
255C4×C61—81no—
256C4×C61—81no—
257Dic61—44no—
258Dic61—82no—
259C2×#481—611no—
260#2617D6111yescharacteristic
261C2×#399—611no—
262#1824—611no—
263C2×#327—611no—
264C2×#323—611no—
265#1294—611no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—21no—
269C2×C61—21no—
270C2×C61—82no—
271C2×C61—161no—
272C2×C61#161312yes—
273C2×C61#161812yes—
274C2×C61#200011yescharacteristic
275C2×C61#200211yescharacteristic
276C2×C61#202211yescharacteristic
277C2×#121C2×D6111yescharacteristic
278C2×#120—21no—
279C22×C4⋊C4—611no—
280C22×C4⋊C4—1221no—
281C22×C22⋊C4—1221no—
282C22×C22⋊C4C2×D6111yescharacteristic
283#481—1222no—
284#481—1222no—
285C2×#106—1221no—
286C2×#102—1221no—
287C2×C22⋊C8—611no—
288C2×C22⋊C8—611no—
289#399—1222no—
290#399—1222no—
291#397—21no—
292#394—22no—
293#392—21no—
294#386—21no—
295#380C2×D6111yescharacteristic
296C2×#95—611no—
297#340—1222no—
298#327—1222no—
299#323—1222no—
300C61#992011yescharacteristic, complemented, Sylow
301C25C22⋊D6111yescharacteristic
302C22×D4—21no—
303C22×D4—22no—
304C22×D4C22⋊D6111yescharacteristic
305C23×C4—1221no—
306C23×C4—1221no—
307C23×C4C22⋊D6111yescharacteristic
308C23×C4C22×D6111yescharacteristic
309C22×C8—1221no—
310C22×C8—1221no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#120—42no—
316#120—42no—
317C2×C4⋊C4—612no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1224no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—2444no—
325C2×C4⋊C4C22⋊D6111yescharacteristic
326C2×C4⋊C4C22⋊D6112yes—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—1224no—
338C2×C22⋊C4—2444no—
339#106—1224no—
340#102—1224no—
341C22⋊C8—612no—
342C22⋊C8—1221no—
343C22⋊C8—1221no—
344C22⋊C8—1221no—
345#95—22no—
346#95—21no—
347#95—612no—
348#95—1221no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—42no—
357C24—42no—
358C24#1175820012yes—
359C24C2×C22⋊D6111yescharacteristic
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—42no—
363C2×D4—44no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—82no—
371C2×D4—82no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—1224no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2442no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4D4×D6111yescharacteristic
390C22×C4D4×D6111yescharacteristic
391C22×C4D4×D6111yescharacteristic
392C22×C4#1175822411yescharacteristic
393C22×C4C2×C22⋊D6111yescharacteristic
394C22×C4C2×C22⋊D6111yescharacteristic
395C2×C8—1222no—
396C2×C8—2442no—
397C2×C8—2441no—
398C2×C8—2442no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—42no—
402C4⋊C4—1222no—
403C4⋊C4—1222no—
404C4⋊C4—2448no—
405C4⋊C4—2441no—
406C4⋊C4—2441no—
407C22⋊C4—44no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—82no—
417C22⋊C4—2448no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—44no—
424C23—42no—
425C23—44no—
426C23—42no—
427C23—42no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—82no—
439C23—82no—
440C23—81no—
441C23—81no—
442C23#1451974511yescharacteristic
443C23#1451974611yescharacteristic
444C23#1451974911yescharacteristic
445C23C2×#1175820011yescharacteristic
446C23#1451979711yescharacteristic
447C23#1451980311yescharacteristic
448C23#1451980711yescharacteristic
449D4—42no—
450D4—81no—
451D4—88no—
452D4—81no—
453D4—81no—
454D4—81no—
455D4—81no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—81no—
472C2×C4—1224no—
473C2×C4—4882no—
474C2×C4—4882no—
475C2×C4—2442no—
476C2×C4—2442no—
477C2×C4—2442no—
478C2×C4—2444no—
479C2×C4—2442no—
480C2×C4—2444no—
481C2×C4—2442no—
482C2×C4#1451974511yescharacteristic
483C2×C4#1451974811yescharacteristic
484C2×C4#1451974911yescharacteristic
485C2×C4#1451977311yescharacteristic
486C8—4881no—
487C8—2442no—
488C22—22no—
489C22—22no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—22no—
496C22—44no—
497C22—42no—
498C22—44no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—81no—
504C22—81no—
505C22—82no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—82no—
510C22#1683967011yescharacteristic
511C22#1683990011yescharacteristic
512C22#1683990511yescharacteristic
513C22#1683991311yescharacteristic
514C22#1683992411yescharacteristic
515C22#1683993012yes—
516C22#1683995212yes—
517C22#1683998911yescharacteristic
518C22#1684000611yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—81no—
524C4—81no—
525C4—82no—
526C4—4882no—
527C4—2444no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—161no—
534C2#2144483912yes—
535C2#2144486712yes—
536C2#2144682211yescharacteristic
537C2#2144683211yescharacteristic
538C2#2144694811yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#2617C2
socleC23×C61#120
hypercenter#2617D61
hypocenterC61#9920
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. C2×#16840078C2semidirect
2. C2×#16839698C2semidirect
3. #21445907C2semidirect
4. C2×#16839496C2semidirect
5. C2×#16839486C2semidirect
6. #21443697C2semidirect
40. C2×C4⋊Dic61D4semidirect
50. C22⋊#92418D4semidirect
52. #14519684D4semidirect
300. C61#9920semidirect

Maximal subgroups

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

subgroupindex
C2×#168400782
C2×#168396982
#214459072
C2×#168394962
C2×#168394862
#214436972
C61×#26172
#992061