Finite Group Databasebeta

← #29576193

Subgroups — #29576193

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839958C211yesmaximal, characteristic
2C2×C8×D244C211yesmaximal, characteristic, complemented
3#21446625C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C22×D488—21no—
9C22×C8×D61—21no—
10C2×#14519774C2211yescharacteristic
11C2×C4×D244C2211yescharacteristic
12#16839958—22no—
13#16839958C414yescomplemented
14C8×D244—22no—
15C8×D244—22no—
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519699—21no—
18C2×#14519699—21no—
19C2×#14519699—21no—
20C2×#14519699—21no—
21C2×#14519689—21no—
22#16839632C2211yescharacteristic
23#16839525—21no—
24#16839505—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C22×D244—21no—
29C22×D244—21no—
30C22×D244—21no—
31C22×D244D411yescharacteristic
32C22×C4×D61—21no—
33C2×D488—24no—
34C2×D488—42no—
35C2×D488—42no—
36C22×#92418—21no—
37C2×C8×D61—24no—
38C2×C8×D61—42no—
39C2×C8×D61—42no—
40#14519774—21no—
41#14519774—21no—
42#14519774—21no—
43#14519774C2×C412yes—
44C4×D244—21no—
45C4×D244—21no—
46C4×D244C2×C412yes—
47C4×D244D412yes—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61D411yescharacteristic
52C2×#11758198—21no—
53C4⋊#92418—21no—
54C4⋊#92418D412yes—
55#14519699—24no—
56#14519699—42no—
57#14519699—42no—
58#14519699—42no—
59#14519689—24no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C22×C8×C61D411yescharacteristic
63C22×C8×C61D411yescharacteristic
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61C2×C412yes—
69C4×C8×C61—21no—
70C4×C8×C61—21no—
71C23×D61—21no—
72C23×D61—41no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—41no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—41no—
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—41no—
94C2×D244—41no—
95C2×D244—81no—
96C2×D244—81no—
97C2×D244C22⋊C412yes—
98C2×D244D812yes—
99C2×D244SD1612yes—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—22no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61D812yescomplemented
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122#11758198—22no—
123#11758198—22no—
124C4⋊Dic61—21no—
125C4⋊Dic61—41no—
126C4⋊Dic61—41no—
127C4⋊Dic61—41no—
128C4⋊Dic61—41no—
129C4⋊Dic61—81no—
130C4⋊Dic61C22⋊C412yes—
131C2×#92418—22no—
132C2×#92418—41no—
133C2×#92418—41no—
134D488—48no—
135C8×D61—48no—
136C23×C61#12111yescharacteristic
137C22×D61—22no—
138C22×D61—22no—
139C22×D61—22no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—42no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61—81no—
148C22×D61—81no—
149C22×D61—81no—
150C22×D61—81no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61C2×C22⋊C411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12311yescharacteristic
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61C2×SD1611yescharacteristic
162C2×C4×C61#13511yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61#13511yescharacteristic
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
167C2×Dic61—22no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173D244—22no—
174D244—22no—
175D244—22no—
176D244—42no—
177D244—42no—
178D244—42no—
179D244—42no—
180D244—82no—
181D244—82no—
182D244—81no—
183D244—81no—
184D244—81no—
185D244—81no—
186D244#10214yescomplemented
187C4×D61—42no—
188C4×D61—42no—
189C4×D61—42no—
190C4×D61—42no—
191C8×C61—22no—
192C8×C61—42no—
193C8×C61—41no—
194C8×C61—81no—
195#92418—42no—
196#9221—611nomaximal, Sylow
197C22×C61#38611yescharacteristic
198C22×C61#45911yescharacteristic
199C22×C61#46311yescharacteristic
200C22×C61#46511yescharacteristic
201C22×C61#46611yescharacteristic
202C22×C61#47111yescharacteristic
203C22×C61#47211yescharacteristic
204C2×D61—24no—
205C2×D61—42no—
206C2×D61—42no—
207C2×D61—42no—
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—82no—
212C2×D61—82no—
213C2×D61—82no—
214C2×D61—161no—
215C2×D61—161no—
216C2×D61—161no—
217C2×D61—161no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61C2×#10211yescharacteristic
221C4×C61#41611yescharacteristic
222C4×C61C4×D811yescharacteristic
223C4×C61#44211yescharacteristic
224C4×C61#44711yescharacteristic
225C4×C61#44911yescharacteristic
226C4×C61#46511yescharacteristic
227C4×C61#46611yescharacteristic
228Dic61—42no—
229Dic61—161no—
230C2×#459—611no—
231C2×C8×D4—611no—
232#1957—611no—
233#1802—611no—
234C2×#331—611no—
235#1296—611no—
236#1277D6111yescharacteristic, complemented
237C2×C61#166511yescharacteristic
238C2×C61#166711yescharacteristic
239C2×C61#167711yescharacteristic
240C2×C61#168111yescharacteristic
241C2×C61#187911yescharacteristic
242C2×C61#189311yescharacteristic
243C2×C61#190711yescharacteristic
244D61—44no—
245D61—162no—
246C22×D8—1221no—
247C23×C8—1221no—
248C2×#127—611no—
249C2×C4×D4—611no—
250#459—614no—
251#459—1222no—
252C8×D4—1222no—
253C8×D4—1222no—
254C2×C4⋊C8—611no—
255C2×C4⋊C8C2×D6111yescharacteristic
256C2×C4⋊C8C2×D6111yescharacteristic
257C2×#102—1221no—
258C2×#102—1221no—
259C2×#102—1221no—
260C2×#102—1221no—
261C2×C22⋊C8—1221no—
262C2×C4×C8C2×D6111yescharacteristic
263#384—611no—
264#340—1221no—
265#331—1222no—
266C61#922111yescharacteristic, complemented, Sylow
267C22×D4—611no—
268C22×D4—1221no—
269C22×D4—1221no—
270C22×D4—1221no—
271C23×C4—1221no—
272C2×D8—1224no—
273C2×D8—2442no—
274C2×D8—2442no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—1224no—
278C22×C8—1221no—
279C22×C8—2442no—
280C22×C8—2442no—
281C22×C8D24411yescharacteristic
282C22×C8D24411yescharacteristic
283#127—612no—
284#127—1221no—
285#127—1221no—
286#127—1221no—
287C4×D4—612no—
288C4×D4—612no—
289C4×D4—1221no—
290C4×D4—1221no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42C22×D6111yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—612no—
301C4⋊C8—1221no—
302C4⋊C8C4×D6112yes—
303#102—1224no—
304#102—2442no—
305#102—2442no—
306#102—2442no—
307C22⋊C8—1224no—
308C4×C8—21no—
309C4×C8—21no—
310C24—1221no—
311C24—2441no—
312C2×D4—612no—
313C2×D4—612no—
314C2×D4—612no—
315C2×D4—1222no—
316C2×D4—1222no—
317C2×D4—1222no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—4881no—
322C2×D4—4881no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C2×D4—2441no—
328C2×D4—2441no—
329C2×D4—2441no—
330C2×D4—2441no—
331C2×D4—2441no—
332C2×D4—2441no—
333C2×D4—2441no—
334C22×C4—1221no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4C2×D24411yescharacteristic
343C22×C4D4×D6111yescharacteristic
344C22×C4#1175822611yescharacteristic
345D8—2448no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—1222no—
358C2×C8—2448no—
359C2×C8—2441no—
360C2×C8—2441no—
361C2×C8D48812yescomplemented
362C4⋊C4—612no—
363C4⋊C4—1221no—
364C4⋊C4—4881no—
365C4⋊C4—2441no—
366C4⋊C4—2441no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C42C2×C4×D6111yescharacteristic
372C42#1175822211yescharacteristic
373C42D4×D6111yescharacteristic
374C42D4×D6111yescharacteristic
375C23—1222no—
376C23—1222no—
377C23—1222no—
378C23—4881no—
379C23—4881no—
380C23—4881no—
381C23—4881no—
382C23—4881no—
383C23—4881no—
384C23—2442no—
385C23—2441no—
386C23—2441no—
387C23—2441no—
388C23—2441no—
389C23#1451975211yescharacteristic
390D4—614no—
391D4—1222no—
392D4—1222no—
393D4—1222no—
394D4—4882no—
395D4—4882no—
396D4—4881no—
397D4—4881no—
398D4—4881no—
399D4—4881no—
400D4—2442no—
401D4—2442no—
402D4—2442no—
403D4—2442no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—1222no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—4881no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4C22⋊C4×D6111yescharacteristic
417C2×C4#1451973911yescharacteristic
418C2×C4C4×D24411yescharacteristic
419C2×C4#1451974711yescharacteristic
420C2×C4#1451975011yescharacteristic
421C2×C4#1451976211yescharacteristic
422C2×C4D8×D6111yescharacteristic
423C2×C4C2×D48811yescharacteristic
424C2×C4SD16×D6111yescharacteristic
425C2×C4#1451979811yescharacteristic
426C2×C4#1451979911yescharacteristic
427C2×C4#1451980011yescharacteristic
428C2×C4#1451980511yescharacteristic
429C2×C4#1451980511yescharacteristic
430C8—22no—
431C8—42no—
432C8—41no—
433C8—81no—
434C8—2442no—
435C22—1224no—
436C22—9761no—
437C22—9761no—
438C22—9761no—
439C22—9761no—
440C22—4882no—
441C22—4882no—
442C22—4882no—
443C22—2442no—
444C22—2442no—
445C22—2442no—
446C22—2442no—
447C22—2442no—
448C22—2442no—
449C22#1683964011yescharacteristic
450C22#1683995811yescharacteristic
451C22#1683997811yescharacteristic
452C22#1683999211yescharacteristic
453C22#1683999911yescharacteristic
454C22#1684002611yescharacteristic
455C22#1684003311yescharacteristic
456C4—21no—
457C4—21no—
458C4—9761no—
459C4—2442no—
460C4#102×D6111yescharacteristic
461C4#1683975711yescharacteristic
462C4C4×D48811yescharacteristic
463C4#1683987511yescharacteristic
464C4#1683989811yescharacteristic
465C4#1683990911yescharacteristic
466C4#1683999411yescharacteristic
467C4#1683999711yescharacteristic
468C2—9762no—
469C2—2444no—
470C2#2144516111yescharacteristic
471C2#2144517511yescharacteristic
472C2#2144522911yescharacteristic
473C2#2144525711yescharacteristic
474C2#2144616611yescharacteristic
475C2#2144624611yescharacteristic
476C2#2144632611yescharacteristic
subgroupG/H
centerC23#14519752
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61#121
prime radicalC2×#16839958C2
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#9221
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. C2×C8×D244C2semidirect
3. #21446625C2semidirect
4. #21445820C2semidirect
5. C2×#16839505C2semidirect
6. #21443703C2semidirect
7. C61×#1277C2semidirect
13. #16839958C4semidirect
117. C2×C8×C61D8semidirect
186. D244#102semidirect
236. #1277D61semidirect
266. C61#9221semidirect
361. C2×C8D488semidirect

Maximal subgroups

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

subgroupindex
C2×#168399582
C2×C8×D2442
#214466252
#214458202
C2×#168395052
#214437032
C61×#12772
#922161