Finite Group Databasebeta

← #29574855

Subgroups — #29574855

Order 15616.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455823C211yesmaximal, characteristic
2#21454554C211yesmaximal, characteristic
3#21446764C211yesmaximal, characteristic, complemented
4C4×#14519699C211yesmaximal, characteristic
5#21443720C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C61×#1493C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C4×D244C2211yescharacteristic
10#16840090—21no—
11#16840049C411yescharacteristic, complemented
12#16840049C411yescharacteristic, complemented
13#16839964C411yescharacteristic, complemented
14#16839964C411yescharacteristic, complemented
15#16839912—21no—
16C4×#11758201—21no—
17C4×#11758201—21no—
18#16839839—21no—
19#16839832—22no—
20#16839827—21no—
21#16839815C2211yescharacteristic
22C2×#14519699—21no—
23#16839725—21no—
24C4×#11758194C2211yescharacteristic
25C4×C4⋊Dic61C2211yescharacteristic
26#16839525—21no—
27#16839521—21no—
28#16839521—21no—
29C61×#533C2211yescharacteristic
30C61×#423C2211yescharacteristic
31C2×C4×C8×C61C2211yescharacteristic
32C61×Q8⋊C8—22no—
33C22×D244D411yescharacteristic
34C22×C4×D61—21no—
35C2×#11758201—21no—
36C2×#11758201—21no—
37C2×#11758194D411yescharacteristic
38C2×#11758194D411yescharacteristic
39C2×#11758189—22no—
40M16×D61—42no—
41M16×D61—42no—
42C2×C8×D61—22no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244C2×C411yescharacteristic
46C4×D244C2×C411yescharacteristic
47C4×D244D411yescharacteristic
48C4×D244D411yescharacteristic
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61D411yescharacteristic
51C2×#11758198—21no—
52C2×C4×Dic61—21no—
53#14519708—21no—
54#14519708—21no—
55C4⋊#92418C2×C411yescharacteristic
56C4⋊#92418C2×C411yescharacteristic
57#14519701—21no—
58#14519701—21no—
59#14519699—24no—
60#14519697—21no—
61#14519697—21no—
62C22⋊#92418—21no—
63#14519689—22no—
64#14519689—22no—
65#14519688—21no—
66C4×#92418—21no—
67C4×#92418—21no—
68#14519684—21no—
69C2×M16×C61—21no—
70C22×C8×C61—21no—
71C4⋊Q8×C61C2×C411yescharacteristic
72C4⋊Q8×C61C2×C411yescharacteristic
73#125×C61—21no—
74C22⋊Q8×C61—21no—
75C22⋊Q8×C61—21no—
76C4×Q8×C61—21no—
77C4×Q8×C61—21no—
78#117×C61—21no—
79C2×C42×C61C2311yescharacteristic
80C4⋊C8×C61—21no—
81C4⋊C8×C61D412yes—
82C4×C8×C61—21no—
83C4×C8×C61—21no—
84C23×D61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—41no—
92C2×D244—22no—
93C2×D244—21no—
94C2×D244—41no—
95C2×D244C22⋊C411yescharacteristic
96C2×D244C22⋊C411yescharacteristic
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—22no—
108C2×C8×C61—22no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61—41no—
119C42×C61C22×C411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123#11758201—42no—
124#11758201—42no—
125#11758198—21no—
126#11758198—21no—
127#11758198—21no—
128#11758198—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—22no—
131C4⋊Dic61—41no—
132C4⋊Dic61C22⋊C411yescharacteristic
133C4⋊Dic61C22⋊C411yescharacteristic
134C4×Dic61—41no—
135C4×Dic61—41no—
136#11758194—21no—
137#11758194—21no—
138#11758194—21no—
139#11758194SD1612yescomplemented
140C2×#92418—21no—
141C2×#92418—21no—
142C2×#92418—21no—
143C2×#92418—21no—
144#11758189—44no—
145C8×D61—44no—
146C23×C61#12111yescharacteristic
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—42no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—81no—
153Q8×C61—42no—
154Q8×C61—41no—
155Q8×C61—41no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61C2×C22⋊C411yescharacteristic
162C2×C4×C61C4×D411yescharacteristic
163C2×C4×C61C4×D411yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12311yescharacteristic
167C2×C4×C61C2×SD1611yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61#13711yescharacteristic
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—42no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178D244—21no—
179D244—21no—
180D244—21no—
181D244—42no—
182D244#10412yes—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186C4×D61—41no—
187C4×D61—41no—
188C4×D61—41no—
189C4×D61—41no—
190C4×D61—41no—
191C8×C61—42no—
192C8×C61—42no—
193#92418—22no—
194#92418—41no—
195#92418—41no—
196#92418—41no—
197#8989—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61#38611yescharacteristic
201C22×C61#46111yescharacteristic
202C22×C61#46311yescharacteristic
203C2×D61—22no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—82no—
210C2×D61—82no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61C2×#10411yescharacteristic
217C4×C61#42111yescharacteristic
218C4×C61C4×SD1611yescharacteristic
219C4×C61#44011yescharacteristic
220C4×C61#45011yescharacteristic
221C4×C61#45211yescharacteristic
222Dic61—41no—
223Dic61—41no—
224Dic61—82no—
225#3101—611no—
226D4×M16—611no—
227#1986—611no—
228C4×#102—611no—
229#1493D6111yescharacteristic, complemented
230#1303—611no—
231#1278—611no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61#187111yescharacteristic
235C2×C61#187711yescharacteristic
236C2×C61#188111yescharacteristic
237D61—42no—
238D61—81no—
239C22×M16—1221no—
240#533C2×D6111yescharacteristic
241C2×C4×D4—611no—
242#483—1221no—
243#476—611no—
244#476—611no—
245#461—611no—
246#461—611no—
247#450—1221no—
248C4×SD16—1221no—
249C4×SD16—1221no—
250#436—1221no—
251#435—1222no—
252C8×D4—1221no—
253#431—611no—
254#423C2×D6111yescharacteristic
255C2×#102—1221no—
256#407—1221no—
257C4×M16—611no—
258C2×C4×C8C2×D6111yescharacteristic
259C4×C4⋊C4—611no—
260#340—1221no—
261#339—1221no—
262#339—1221no—
263Q8⋊C8—22no—
264C61#898911yescharacteristic, complemented, Sylow
265C22×D4—611no—
266C23×C4—1221no—
267C2×SD16—1221no—
268C2×SD16—1221no—
269C2×M16—21no—
270C2×M16—611no—
271C2×M16—611no—
272C2×M16—1222no—
273C2×M16—2442no—
274C2×M16—2442no—
275C22×C8—21no—
276C22×C8—1222no—
277C4⋊Q8C4×D6111yescharacteristic
278C4⋊Q8C4×D6111yescharacteristic
279#125—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—611no—
285C4×D4—611no—
286C4×D4—611no—
287C4×D4—611no—
288C4×D4—1221no—
289C4×D4—1221no—
290#117—21no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C42—1221no—
295C2×C42C22×D6111yescharacteristic
296#106—1221no—
297#106—1221no—
298C4⋊C8—21no—
299C4⋊C8—611no—
300C4⋊C8—611no—
301C4⋊C8C22⋊D6112yes—
302#103—1221no—
303#103—1221no—
304#102—1221no—
305#102—1221no—
306#102—1224no—
307C22⋊C8—1222no—
308C22⋊C8—1222no—
309C22⋊C8—1221no—
310#97—1221no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8—1221no—
314C4×C8—1221no—
315#95—1221no—
316C24—1221no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×D4—611no—
320C2×D4—611no—
321C2×D4—1222no—
322C2×D4—1221no—
323C2×D4—2441no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4#1175822211yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337SD16—2442no—
338SD16—2442no—
339M16—41no—
340M16—41no—
341M16—612no—
342M16—1221no—
343M16—1221no—
344M16—1221no—
345M16—2444no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—2444no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—611no—
362C4⋊C4—611no—
363C4⋊C4—1222no—
364C4⋊C4—1221no—
365C4⋊C4—2441no—
366C22⋊C4—41no—
367C22⋊C4—1221no—
368C22⋊C4—1221no—
369C22⋊C4—1221no—
370C22⋊C4—1221no—
371C42—41no—
372C42—2441no—
373C42—2441no—
374C42C2×C4×D6111yescharacteristic
375C42D4×D6111yescharacteristic
376C42#1175822411yescharacteristic
377C42C2×C22⋊D6111yescharacteristic
378C23—1221no—
379C23—1221no—
380C23—4881no—
381C23—2442no—
382C23—2441no—
383C23—2441no—
384C23#1451975011yescharacteristic
385Q8—42no—
386Q8—41no—
387Q8—41no—
388D4—612no—
389D4—1221no—
390D4—1221no—
391D4—1221no—
392D4—2442no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—2442no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C22⋊C4×D6111yescharacteristic
414C2×C4#1451973711yescharacteristic
415C2×C4C4×C22⋊D6111yescharacteristic
416C2×C4#1451974511yescharacteristic
417C2×C4#1451974811yescharacteristic
418C2×C4#1451975911yescharacteristic
419C2×C4SD16×D6111yescharacteristic
420C2×C4#1451980011yescharacteristic
421C2×C4#1451980411yescharacteristic
422C2×C4#1451980911yescharacteristic
423C8—42no—
424C8—42no—
425C8—1222no—
426C8—2441no—
427C8—2441no—
428C8—2441no—
429C22—21no—
430C22—21no—
431C22—1222no—
432C22—4882no—
433C22—4882no—
434C22—2441no—
435C22—2441no—
436C22—2441no—
437C22—2441no—
438C22—2441no—
439C22#1683963811yescharacteristic
440C22#1683996611yescharacteristic
441C22#1683998011yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—4882no—
448C4—2441no—
449C4—2441no—
450C4#104×D6111yescharacteristic
451C4#1683977711yescharacteristic
452C4#1683984711yescharacteristic
453C4#1683986511yescharacteristic
454C4#1683991111yescharacteristic
455C4#1683992311yescharacteristic
456C2—21no—
457C2—21no—
458C2—4881no—
459C2—2442no—
460C2#2144611811yescharacteristic
461C2#2144615011yescharacteristic
462C2#2144618411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1493C2
socleC22×C61#386
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1493D61
hypocenterC61#8989
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #21446764C2semidirect
5. #21443720C2semidirect
6. #21443656C2semidirect
7. C61×#1493C2semidirect
11. #16840049C4semidirect
12. #16840049C4semidirect
13. #16839964C4semidirect
14. #16839964C4semidirect
139. #11758194SD16semidirect
229. #1493D61semidirect
264. C61#8989semidirect

Maximal subgroups

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

subgroupindex
#214558232
#214545542
#214467642
C4×#145196992
#214437202
#214436562
C61×#14932
#898961