Finite Group Databasebeta

← #29575306

Subgroups — #29575306

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840135C211yesmaximal, characteristic
2#21448883C211yesmaximal, characteristic
3#21446767C211yesmaximal, characteristic, complemented
4#21446766C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C22×#11758190—22no—
9C2×#14519777C2211yescharacteristic
10C2×#14519774C2211yescharacteristic
11C2×C4×D244—21no—
12C2×#14519739—21no—
13#16840135—22no—
14#16840135C414yescomplemented
15C2×C4⋊#92418C2211yescharacteristic
16#16839664—21no—
17#16839663—21no—
18#16839640—22no—
19C4×C4⋊Dic61C2211yescharacteristic
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839524—21no—
24#16839505—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4×C8×C61C2211yescharacteristic
27C4×C4⋊C4×C61C2211yescharacteristic
28C22×Dic122—21no—
29C22×D244—21no—
30C22×D244—21no—
31C22×D244D412yes—
32C22×C4×D61—22no—
33C2×#11758190—28no—
34C2×#11758190—44no—
35C2×#11758190—44no—
36C22×#92418—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777C2×C412yescomplemented
41#14519774—21no—
42#14519774—21no—
43#14519774C2×C412yes—
44#14519774D412yes—
45C4×D244—42no—
46C4×D244—42no—
47#14519739—42no—
48#14519739—42no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61D411yescharacteristic
52C2×C4⋊Dic61D411yescharacteristic
53C2×#11758198—22no—
54C2×#11758198—22no—
55C2×#11758198—22no—
56C2×C4×Dic61—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59#14519684—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4×C8×C61—21no—
69C4×C8×C61C2×C412yescomplemented
70#95×C61—21no—
71C23×D61—22no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—42no—
94C2×D244—42no—
95C2×D244C22⋊C414yes—
96C2×C4×D61—44no—
97C2×C4×D61—44no—
98C2×C4×D61—82no—
99C2×Dic122—22no—
100C2×Dic122—42no—
101C2×Dic122—42no—
102C2×Dic122—41no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61SD1612yescomplemented
113C42×C61—41no—
114C42×C61—41no—
115C42×C61C22×C411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C42×C61#4111yescharacteristic
119#11758198—44no—
120#11758198—44no—
121#11758198—82no—
122C4⋊Dic61—21no—
123C4⋊Dic61—22no—
124C4⋊Dic61—22no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—41no—
128C4⋊Dic61—41no—
129C4⋊Dic61SD1612yescomplemented
130C4×Dic61—41no—
131C4×Dic61—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135#11758190—416no—
136C23×C61#12011yescharacteristic
137C22×D61—24no—
138C22×D61—42no—
139C22×D61—42no—
140C22×D61—42no—
141C22×D61—42no—
142C22×D61—42no—
143C22×D61—42no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61C2×C22⋊C411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×C4×C61C2×SD1611yescharacteristic
159C2×C4×C61C2×SD1611yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61#13511yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61#13711yescharacteristic
165C2×C4×C61#13711yescharacteristic
166C2×Dic61—22no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—42no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—81no—
174C2×Dic61—81no—
175D244—44no—
176D244—42no—
177D244—42no—
178D244—42no—
179D244—42no—
180D244—42no—
181D244—42no—
182D244—42no—
183D244—42no—
184D244—82no—
185C4×D61—88no—
186Dic122—44no—
187Dic122—82no—
188C8×C61—24no—
189C8×C61—81no—
190#92418—81no—
191#9064—611nomaximal, Sylow
192C22×C61#38611yescharacteristic
193C22×C61#45011yescharacteristic
194C22×C61#45011yescharacteristic
195C22×C61#45211yescharacteristic
196C22×C61#45211yescharacteristic
197C22×C61#45311yescharacteristic
198C22×C61#45311yescharacteristic
199C2×D61—44no—
200C2×D61—44no—
201C2×D61—44no—
202C2×D61—82no—
203C2×D61—82no—
204C2×D61—82no—
205C2×D61—82no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—42no—
209C4×C61—81no—
210C4×C61C4×SD1611yescharacteristic
211C4×C61C4×SD1611yescharacteristic
212C4×C61#44011yescharacteristic
213C4×C61#44011yescharacteristic
214C4×C61#46111yescharacteristic
215C4×C61#46111yescharacteristic
216C4×C61#46311yescharacteristic
217C4×C61#46311yescharacteristic
218Dic61—42no—
219Dic61—81no—
220Dic61—82no—
221C2×#492—611no—
222#2366—611no—
223#1987—611no—
224#1987—611no—
225C2×#331—611no—
226#1279—611no—
227#1279D6111yescharacteristic, complemented
228C2×C61#162911yescharacteristic
229C2×C61#163011yescharacteristic
230C2×C61#163111yescharacteristic
231C2×C61#163111yescharacteristic
232C2×C61#187711yescharacteristic
233C2×C61#187711yescharacteristic
234C2×C61#188711yescharacteristic
235D61—84no—
236C22×SD16—1222no—
237C2×C4⋊Q8—611no—
238C2×#127—611no—
239C2×C4×D4—1221no—
240C2×C4×D4—1221no—
241#492—614no—
242#492—1222no—
243C2×C4⋊C8—611no—
244C2×C4⋊C8C2×D6111yescharacteristic
245C2×C4×C8C2×D6111yescharacteristic
246#390—1221no—
247#390—1221no—
248#386—1222no—
249C4×C4⋊C4—611no—
250C4×C4⋊C4C2×D6111yescharacteristic
251#340—1221no—
252#340—1221no—
253#340—1221no—
254#340—1221no—
255#331—1222no—
256C61#906411yescharacteristic, complemented, Sylow
257C22×Q8—1221no—
258C22×D4—612no—
259C22×D4—1221no—
260C22×D4—1221no—
261C23×C4—1222no—
262C2×SD16—1228no—
263C2×SD16—2444no—
264C2×SD16—2444no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—1221no—
268C4⋊Q8—612no—
269C4⋊Q8—1221no—
270C4⋊Q8—1221no—
271C4⋊Q8—1221no—
272#127—612no—
273#127—612no—
274#127—1221no—
275#127—1221no—
276C4×D4—2442no—
277C4×D4—2442no—
278C4×D4—2442no—
279C4×D4—2442no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—611no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4D24411yescharacteristic
285C2×C4⋊C4D24411yescharacteristic
286C2×C22⋊C4—1222no—
287C2×C22⋊C4—1222no—
288C2×C22⋊C4—1222no—
289C2×C42—21no—
290C2×C42—1221no—
291C2×C42C22×D6111yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1221no—
295C4⋊C8—1221no—
296C4×C8—21no—
297C4×C8C4×D6112yescomplemented
298#95—21no—
299#95—1221no—
300C24—1222no—
301C2×Q8—1222no—
302C2×Q8—2442no—
303C2×Q8—2442no—
304C2×Q8—2441no—
305C2×D4—614no—
306C2×D4—1222no—
307C2×D4—1222no—
308C2×D4—1222no—
309C2×D4—1222no—
310C2×D4—1222no—
311C2×D4—2442no—
312C2×D4—2442no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2441no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—4882no—
326C22×C4—2444no—
327C22×C4—2444no—
328C22×C4—2441no—
329C22×C4C2×D24411yescharacteristic
330C22×C4D4×D6111yescharacteristic
331C22×C4D4×D6111yescharacteristic
332SD16—24416no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—612no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C4⋊C4—1222no—
349C4⋊C4—1222no—
350C4⋊C4—1221no—
351C4⋊C4—2441no—
352C4⋊C4—2441no—
353C4⋊C4#1175819012yescomplemented
354C22⋊C4—4882no—
355C22⋊C4—2444no—
356C22⋊C4—2444no—
357C42—41no—
358C42—41no—
359C42—2441no—
360C42—2441no—
361C42C2×C4×D6111yescharacteristic
362C42#1175822211yescharacteristic
363C42D4×D6111yescharacteristic
364C42#1175822611yescharacteristic
365C23—1224no—
366C23—2442no—
367C23—2442no—
368C23—2442no—
369C23—2442no—
370C23—2442no—
371C23—2442no—
372C23#1451974711yescharacteristic
373Q8—4882no—
374Q8—2444no—
375D4—4882no—
376D4—2444no—
377D4—2442no—
378D4—2442no—
379D4—2442no—
380D4—2442no—
381D4—2442no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—1222no—
394C2×C4—4888no—
395C2×C4—4881no—
396C2×C4—4881no—
397C2×C4—2442no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4C22⋊C4×D6111yescharacteristic
404C2×C4#1451973911yescharacteristic
405C2×C4C4×D24411yescharacteristic
406C2×C4#1451975011yescharacteristic
407C2×C4#1451975211yescharacteristic
408C2×C4#1451976211yescharacteristic
409C2×C4SD16×D6111yescharacteristic
410C2×C4C2×#1175819011yescharacteristic
411C2×C4#1451979811yescharacteristic
412C2×C4#1451979911yescharacteristic
413C2×C4#1451980111yescharacteristic
414C2×C4#1451980511yescharacteristic
415C2×C4#1451980911yescharacteristic
416C2×C4#1451981011yescharacteristic
417C8—24no—
418C8—81no—
419C8—4881no—
420C22—4882no—
421C22—4882no—
422C22—4882no—
423C22—4882no—
424C22—2444no—
425C22—2444no—
426C22—2444no—
427C22#1683964011yescharacteristic
428C22#1683991411yescharacteristic
429C22#1683991511yescharacteristic
430C22#1683992611yescharacteristic
431C22#1683992711yescharacteristic
432C22#1683993111yescharacteristic
433C22#1683993111yescharacteristic
434C4—21no—
435C4—21no—
436C4—42no—
437C4—81no—
438C4—4882no—
439C4—4881no—
440C4—2442no—
441C4#1683984911yescharacteristic
442C4C4×#1175819011yescharacteristic
443C4#1683986111yescharacteristic
444C4#1683986411yescharacteristic
445C4#1683996611yescharacteristic
446C4#1683996811yescharacteristic
447C4#1683997611yescharacteristic
448C4#1683997811yescharacteristic
449C2—4884no—
450C2#2144493711yescharacteristic
451C2#2144494211yescharacteristic
452C2#2144494811yescharacteristic
453C2#2144494911yescharacteristic
454C2#2144615211yescharacteristic
455C2#2144615411yescharacteristic
456C2#2144621611yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61#120
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#9064
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #21446767C2semidirect
4. #21446766C2semidirect
6. #21443659C2semidirect
7. C61×#1279C2semidirect
14. #16840135C4semidirect
40. #14519777C2×C4semidirect
69. C4×C8×C61C2×C4semidirect
112. C4⋊C4×C61SD16semidirect
129. C4⋊Dic61SD16semidirect
227. #1279D61semidirect
256. C61#9064semidirect
297. C4×C8C4×D61semidirect
353. C4⋊C4#11758190semidirect

Maximal subgroups

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

subgroupindex
C2×#168401352
#214488832
#214467672
#214467662
C2×#168395052
#214436592
C61×#12792
#906461