Finite Group Databasebeta

← #29575114

Subgroups — #29575114

Order 15616.

566 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
1#21454456C211yesmaximal, characteristic, complemented
2#21449057C211yesmaximal, characteristic
3#21444244C211yesmaximal, characteristic, complemented
4#21444131C211yesmaximal, characteristic, complemented
5#21443721C211yesmaximal, characteristic, complemented
6#21443720C211yesmaximal, characteristic, complemented
7C61×#1486C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61—21no—
9C2×#14519734C2211yescharacteristic
10#16839822—22no—
11#16839822—22no—
12#16839815C2211yescharacteristic
13#16839786C2211yescharacteristic
14#16839725—21no—
15M16×Dic61—21no—
16#16839693C411yescharacteristic
17#16839688C411yescharacteristic
18#16839685—21no—
19#16839678—21no—
20#16839676C411yescharacteristic
21#16839670C411yescharacteristic
22C4×C4⋊Dic61C2211yescharacteristic
23C4×C22⋊Dic61—21no—
24D4⋊#92418—22no—
25#16839487—21no—
26#16839485—21no—
27C2×C4×D4×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×C22⋊D61—21no—
32C22×C4×D61D411yescharacteristic
33C2×#11758194—21no—
34C4×C22⋊D61—42no—
35C4×C22⋊D61—42no—
36#14519734—21no—
37#14519734—21no—
38#14519734—21no—
39#14519734—21no—
40C2×C4⋊Dic61—21no—
41C2×#11758196—21no—
42C2×#11758196C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×#11758198C2×C411yescharacteristic
49C2×#11758198D411yescharacteristic
50C2×C4×Dic61—21no—
51C2×C4×Dic61D411yescharacteristic
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418D412yescomplemented
55C22⋊#92418—21no—
56#14519689—24no—
57#14519687—22no—
58C4×#92418—21no—
59C8×Dic61—22no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C22×D4×C61C2×C411yescharacteristic
65C23×C4×C61—21no—
66C2×M16×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C22⋊C4×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C4⋊C8×C61D412yescomplemented
77C22⋊C8×C61—21no—
78C4×C8×C61—21no—
79C24×C61—21no—
80C23×D61C22⋊C411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—42no—
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C2×C22⋊D61—42no—
95C2×C22⋊D61—42no—
96C2×C22⋊D61—42no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108M16×C61—41no—
109M16×C61—41no—
110C2×C8×C61—22no—
111C2×C8×C61—41no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61#4111yescharacteristic
119C42×C61#4111yescharacteristic
120C22⋊Dic61—42no—
121C22⋊Dic61—42no—
122C22⋊Dic61—42no—
123#11758198—21no—
124#11758198—21no—
125#11758198—21no—
126#11758198—21no—
127#11758198—42no—
128C4⋊Dic61—42no—
129#11758196—21no—
130#11758196—21no—
131#11758196—21no—
132#11758196—21no—
133#11758196—42no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—41no—
137C4×Dic61—41no—
138#11758194—41no—
139#11758194—41no—
140C2×#92418—22no—
141C2×#92418—41no—
142C23×C61—22no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61C2×C22⋊C411yescharacteristic
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—41no—
154C22×D61—41no—
155D4×C61—22no—
156D4×C61—22no—
157D4×C61—41no—
158D4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61C4×D411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12311yescharacteristic
174C2×C4×C61#13511yescharacteristic
175C2×C4×C61#13511yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
178C22⋊D61—48no—
179C2×Dic61—22no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C4×D61—41no—
193C4×D61—41no—
194C4×D61—41no—
195C4×D61—41no—
196C8×C61—42no—
197C8×C61—81no—
198#92418—42no—
199#92418—81no—
200#9036—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—42no—
204C22×C61—42no—
205C22×C61—42no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61#38611yescharacteristic
211C22×C61#41611yescharacteristic
212C22×C61#41811yescharacteristic
213C2×D61—42no—
214C2×D61—41no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—81no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—81no—
223C4×C61#44911yescharacteristic
224C4×C61#44911yescharacteristic
225C4×C61#48211yescharacteristic
226C4×C61#48211yescharacteristic
227Dic61—42no—
228Dic61—41no—
229Dic61—41no—
230Dic61—41no—
231Dic61—81no—
232#2921—611no—
233#2392—611no—
234#1486—611no—
235#1486D6111yescharacteristic, complemented
236#1458—611no—
237#1303—611no—
238#1303—611no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61—82no—
242C2×C61#187511yescharacteristic
243C2×C61#188411yescharacteristic
244C2×C61#189111yescharacteristic
245D61—81no—
246C2×C4×D4—1221no—
247C2×C4×D4C2×D6111yescharacteristic
248C2×#117—611no—
249#433—1222no—
250#433—1222no—
251#431—611no—
252#431C2×D6111yescharacteristic
253#423—611no—
254#423C2×D6111yescharacteristic
255#407—1221no—
256C4×M16—1221no—
257#398—611no—
258#397—611no—
259#396—1221no—
260#394—611no—
261#394—1221no—
262#392—611no—
263C4×C4⋊C4—611no—
264C4×C22⋊C4—1221no—
265D4⋊C8—22no—
266D4⋊C8—1222no—
267#324—1221no—
268#323—1221no—
269C61#903611yescharacteristic, complemented, Sylow
270C22×D4—1221no—
271C22×D4C4×D6111yescharacteristic
272C23×C4—21no—
273C23×C4—611no—
274C2×M16—21no—
275C2×M16—1221no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—2442no—
281C4×D4—2442no—
282#117—1221no—
283#117—1221no—
284#117—1221no—
285#117—1221no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—1221no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4C4×D6111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C22⋊C4—1221no—
297C2×C22⋊C4—1221no—
298C2×C42—611no—
299C2×C42—1221no—
300C2×C42C22×D6111yescharacteristic
301C4⋊C8—21no—
302C4⋊C8—21no—
303C4⋊C8—612no—
304C4⋊C8—1221no—
305C4⋊C8—1221no—
306C4⋊C8C22⋊D6112yescomplemented
307C22⋊C8—21no—
308C22⋊C8—1224no—
309C22⋊C8—1221no—
310#97—1222no—
311C4×C8—21no—
312C4×C8—1222no—
313C4×C8—1221no—
314#95—611no—
315#95—611no—
316#95—1221no—
317#95—1221no—
318C24—21no—
319C24—611no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—42no—
323C2×D4—2442no—
324C2×D4—2442no—
325C2×D4—2442no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4C2×C4×D6111yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4D4×D6111yescharacteristic
347M16—41no—
348M16—41no—
349M16—2441no—
350M16—2441no—
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—1222no—
354C2×C8—2441no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4—2442no—
362C4⋊C4—2442no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—1221no—
366C22⋊C4—1221no—
367C22⋊C4—1221no—
368C22⋊C4—1221no—
369C22⋊C4—2442no—
370C22⋊C4—2442no—
371C22⋊C4—2442no—
372C22⋊C4—2442no—
373C42—1221no—
374C42—1221no—
375C42—2441no—
376C42—2441no—
377C42#1175822211yescharacteristic
378C42D4×D6111yescharacteristic
379C42#1175822411yescharacteristic
380C42C2×C22⋊D6111yescharacteristic
381C23—22no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—1221no—
389C23—1221no—
390C23—1221no—
391C23—2441no—
392C23—2441no—
393C23C22⋊C4×D6111yescharacteristic
394D4—22no—
395D4—22no—
396D4—41no—
397D4—41no—
398D4—2448no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—1222no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4#1451973711yescharacteristic
426C2×C4C4×C22⋊D6111yescharacteristic
427C2×C4#1451974511yescharacteristic
428C2×C4#1451974811yescharacteristic
429C2×C4#1451975011yescharacteristic
430C2×C4#1451975911yescharacteristic
431C2×C4#1451979611yescharacteristic
432C2×C4#1451979811yescharacteristic
433C2×C4#1451980111yescharacteristic
434C2×C4#1451980411yescharacteristic
435C8—42no—
436C8—81no—
437C8—4881no—
438C8—2442no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—4881no—
449C22—2442no—
450C22—2441no—
451C22—2441no—
452C22—2441no—
453C22#1683963811yescharacteristic
454C22#1683975511yescharacteristic
455C22#1683976511yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—4881no—
462C4—2442no—
463C4—2441no—
464C4—2441no—
465C4—2441no—
466C4#1683990411yescharacteristic
467C4#1683990611yescharacteristic
468C4#1684008411yescharacteristic
469C4#1684008511yescharacteristic
470C2—21no—
471C2—21no—
472C2—82no—
473C2—4881no—
474C2#2144613811yescharacteristic
475C2#2144619911yescharacteristic
476C2#2144623411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1486C2
socleC22×C61#386
prime radical#16839670C4
cosocleC2×C42×C61C23
hypercenter#1486D61
hypocenterC61#9036
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #21454456C2semidirect
3. #21444244C2semidirect
4. #21444131C2semidirect
5. #21443721C2semidirect
6. #21443720C2semidirect
7. C61×#1486C2semidirect
54. C4⋊#92418D4semidirect
76. C4⋊C8×C61D4semidirect
235. #1486D61semidirect
269. C61#9036semidirect
306. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214544562
#214490572
#214442442
#214441312
#214437212
#214437202
C61×#14862
#903661