Finite Group Databasebeta

← #29568142

Subgroups — #29568142

Order 15616.

892 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#390×D61C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic, complemented
3#21445511C211yesmaximal, characteristic, complemented
4#21443640C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic, complemented
8C22×D4×D61C411yescharacteristic
9C22×#11758189—21no—
10C2×C4⋊C4×D61C411yescharacteristic
11C2×C22⋊C4×D61—21no—
12C2×C22⋊C4×D61—21no—
13C2×C42×D61C2211yescharacteristic
14C2×#14519689—21no—
15#16839665C411yescharacteristic
16#16839664C2211yescharacteristic
17#16839663C411yescharacteristic
18#16839662—21no—
19#16839662—21no—
20#16839517C2211yescharacteristic, complemented
21#16839517C2211yescharacteristic, complemented
22#16839516—21no—
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic, complemented
26C61×#336C2211yescharacteristic, complemented
27C24×D61—21no—
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C2×D4×D61—22no—
31C2×D4×D61—22no—
32C2×D4×D61—42no—
33C2×D4×D61—42no—
34C22×C4×D61—21no—
35C22×C4×D61C2×C411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C2×#11758189—24no—
39C2×#11758189—42no—
40C2×#11758189—42no—
41C22×#92418—21no—
42C22×#92418—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C4⋊C4×D61—42no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C22⋊C4×D61—42no—
53C22⋊C4×D61—42no—
54C22⋊C4×D61—42no—
55C22⋊C4×D61—42no—
56C2×C4×Dic61C2×C411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59C42×D61—42no—
60#14519689—42no—
61C22×D4×C61C2×C411yescharacteristic
62C22×C8×C61—21no—
63C22×C8×C61—21no—
64C2×C4⋊C4×C61C2×C411yescharacteristic
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C24×C61—21no—
69C23×D61—24no—
70C23×D61—21no—
71C23×D61—42no—
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61—42no—
76C23×D61—42no—
77C23×D61C22⋊C411yescharacteristic
78C2×D4×C61—21no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61M1612yescomplemented
82C22×C4×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C2×C22⋊D61—24no—
87C2×C22⋊D61—42no—
88C2×C22⋊D61—42no—
89C22×Dic61—21no—
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93D4×D61—48no—
94D4×D61—48no—
95C2×D244—21no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244M1612yescomplemented
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—41no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61D812yes—
113C2×C4×D61SD1612yes—
114C2×C8×C61—22no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C2×C8×C61—41no—
120C4⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C42×C61—41no—
126C22⋊Dic61—42no—
127C22⋊Dic61—42no—
128#11758198—42no—
129#11758198—41no—
130#11758198—41no—
131#11758198—41no—
132#11758198—41no—
133#11758198—42no—
134C4⋊Dic61—41no—
135#11758196—42no—
136C4×Dic61—41no—
137C4×Dic61—41no—
138C4×Dic61—41no—
139C2×#92418—22no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145#11758189—48no—
146C23×C61—22no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61C2×C22⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—22no—
159C22×D61—48no—
160C22×D61—48no—
161C22×D61—48no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—84no—
169C22×D61—84no—
170C22×D61—84no—
171C22×D61—84no—
172C22×D61#9912yes—
173C22×D61#10212yes—
174C22×D61#10412yes—
175D4×C61—42no—
176D4×C61—42no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61C2×M1611yescharacteristic
187C2×C4×C61C2×M1611yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C2×SD1611yescharacteristic
190C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C22⋊D61—48no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61#10012yes—
204C2×Dic61#10212yes—
205D244—42no—
206D244—42no—
207C4×D61—24no—
208C4×D61—24no—
209C4×D61—24no—
210C4×D61—24no—
211C4×D61—42no—
212C4×D61—42no—
213C4×D61—84no—
214C8×C61—42no—
215C8×C61—81no—
216#92418—42no—
217#92418—81no—
218#7606—611nomaximal, Sylow
219C22×C61—42no—
220C22×C61—42no—
221C22×C61—42no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61#40711yescharacteristic
227C22×C61C2×#9911yescharacteristic
228C22×C61C2×#10011yescharacteristic
229C22×C61C2×#10211yescharacteristic
230C22×C61#41811yescharacteristic
231C22×C61C2×#10411yescharacteristic
232C22×C61#42111yescharacteristic
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—42no—
240C2×D61—42no—
241C2×D61—42no—
242C2×D61—816no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61#32714yes—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—81no—
255Dic61—22no—
256Dic61—22no—
257Dic61—41no—
258Dic61—81no—
259C2×#390—611no—
260#1817—611no—
261#1728—611no—
262#1270—611no—
263#1270—611no—
264#1270—611no—
265#1270D6111yescharacteristic, complemented
266C2×C61—82no—
267C2×C61#146211yescharacteristic
268C2×C61#148611yescharacteristic
269C2×C61#149011yescharacteristic
270C2×C61C2×#32711yescharacteristic
271C2×C61#151011yescharacteristic
272C2×C61#152711yescharacteristic
273C2×C61#154511yescharacteristic
274D61—24no—
275D61—82no—
276C23×D4—611no—
277C22×M16—1221no—
278C22×C4⋊C4—611no—
279C22×C22⋊C4—1221no—
280C22×C22⋊C4—1221no—
281C22×C42—611no—
282C2×C22⋊C8—1221no—
283#390—611no—
284#390—611no—
285#390—611no—
286#390—1221no—
287#390—1221no—
288#390C2×D6111yescharacteristic
289#336—611no—
290#336—611no—
291#336—1221no—
292#336—1221no—
293#336C2×D6111yescharacteristic, complemented
294#336C2×D6111yescharacteristic, complemented
295C61#760611yescharacteristic, complemented, Sylow
296C25—1221no—
297C22×D4—611no—
298C22×D4—1221no—
299C22×D4—1222no—
300C22×D4—1222no—
301C22×D4—2442no—
302C22×D4—2442no—
303C22×D4C4×D6111yescharacteristic
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—1221no—
308C2×M16—1224no—
309C2×M16—2442no—
310C2×M16—2442no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—1221no—
314C22×C8—1221no—
315C2×C4⋊C4—611no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—2442no—
318C2×C4⋊C4C4×D6111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C22⋊C4—1221no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4—2442no—
328C2×C22⋊C4—2442no—
329C2×C22⋊C4—2442no—
330C2×C22⋊C4—2442no—
331C2×C42—611no—
332C2×C42—611no—
333C2×C42—611no—
334C2×C42—2442no—
335C2×C42C22×D6111yescharacteristic
336C22⋊C8—2442no—
337C24—21no—
338C24—611no—
339C24—1224no—
340C24—1221no—
341C24—2442no—
342C24—2442no—
343C24—2442no—
344C24—2442no—
345C24—2442no—
346C24—2442no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—612no—
351C2×D4—1224no—
352C2×D4—1221no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2442no—
356C2×D4—2448no—
357C2×D4—2448no—
358C2×D4—2442no—
359C2×D4#1175818912yescomplemented
360C22×C4—21no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—611no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—2441no—
377C22×C4—2442no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4C2×C4×D6111yescharacteristic
381C22×C4D4×D6111yescharacteristic
382C22×C4D4×D6111yescharacteristic
383M16—2448no—
384C2×C8—22no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—41no—
390C2×C8—1222no—
391C2×C8—2441no—
392C2×C8—2441no—
393C2×C8—2441no—
394C2×C8—2441no—
395C2×C8—2441no—
396C4⋊C4—41no—
397C4⋊C4—2441no—
398C4⋊C4—2442no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—2442no—
404C22⋊C4—2442no—
405C22⋊C4—2442no—
406C22⋊C4—2442no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C22⋊C4—2441no—
411C42—41no—
412C42—2441no—
413C42—2441no—
414C42—2441no—
415C23—22no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—612no—
423C23—612no—
424C23—612no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1222no—
430C23—4884no—
431C23—4884no—
432C23—4884no—
433C23—4884no—
434C23—2448no—
435C23—2448no—
436C23—2448no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23C22⋊C4×D6111yescharacteristic
444D4—42no—
445D4—42no—
446D4—2442no—
447D4—2442no—
448D4—2448no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—612no—
459C2×C4—612no—
460C2×C4—1224no—
461C2×C4—1224no—
462C2×C4—1224no—
463C2×C4—1224no—
464C2×C4—1221no—
465C2×C4—1221no—
466C2×C4—1221no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—4884no—
472C2×C4—2442no—
473C2×C4—2442no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4M16×D6111yescharacteristic
478C2×C4C2×#1175818911yescharacteristic
479C2×C4D8×D6111yescharacteristic
480C2×C4SD16×D6111yescharacteristic
481C2×C4#1451980111yescharacteristic
482C2×C4#1451980411yescharacteristic
483C8—42no—
484C8—81no—
485C8—4881no—
486C8—2442no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—614no—
495C22—1222no—
496C22—1222no—
497C22—1222no—
498C22—1222no—
499C22—1222no—
500C22—1222no—
501C22—48816no—
502C22—4881no—
503C22—4881no—
504C22—4881no—
505C22—4881no—
506C22—2442no—
507C22—2442no—
508C22—2442no—
509C22#1683972411yescharacteristic
510C22#99×D6111yescharacteristic
511C22#100×D6111yescharacteristic
512C22#102×D6111yescharacteristic
513C22#1683976511yescharacteristic
514C22#104×D6111yescharacteristic
515C22#1683977711yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—81no—
523C4—1222no—
524C4—1222no—
525C4—4881no—
526C4—2441no—
527C2—82no—
528C2—1224no—
529C2—4882no—
530C2#2144414411yescharacteristic
531C2#2144424211yescharacteristic
532C2#2144426011yescharacteristic
533C2#327×D6111yescharacteristic
534C2#2144434611yescharacteristic
535C2#2144441511yescharacteristic
536C2#2144448511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC2×C42×C61C23
hypercenter#1270D61
hypocenterC61#7606
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21445886C2semidirect
3. #21445511C2semidirect
4. #21443640C2semidirect
5. #21443639C2semidirect
6. #21443639C2semidirect
7. C61×#1270C2semidirect
20. #16839517C22semidirect
21. #16839517C22semidirect
25. C61×#336C22semidirect
26. C61×#336C22semidirect
81. C2×D4×C61M16semidirect
98. C2×D244M16semidirect
265. #1270D61semidirect
293. #336C2×D61semidirect
294. #336C2×D61semidirect
295. C61#7606semidirect
359. C2×D4#11758189semidirect

Maximal subgroups

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

subgroupindex
#390×D612
#214458862
#214455112
#214436402
#214436392
C61×#12702
#760661