Finite Group Databasebeta

← #29574869

Subgroups — #29574869

Order 15616.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455815C211yesmaximal, characteristic
2#21454554C211yesmaximal, characteristic, complemented
3#21446739C211yesmaximal, characteristic, complemented
4C4×#14519699C211yesmaximal, characteristic, complemented
5#21443720C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C61×#1492C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C4×D244C2211yescharacteristic
10#16840073—21no—
11#16840039C411yescharacteristic, complemented
12#16840039C411yescharacteristic, complemented
13#16839954C411yescharacteristic, complemented
14#16839954C411yescharacteristic, complemented
15#16839895—21no—
16C4×#11758199—21no—
17C4×#11758199—21no—
18#16839839—21no—
19#16839832—22no—
20#16839827—21no—
21#16839815C2211yescharacteristic
22C2×#14519704—21no—
23C2×#14519704—21no—
24C2×#14519699—21no—
25#16839725—21no—
26C4×#11758194C2211yescharacteristic
27C4×C4⋊Dic61C2211yescharacteristic
28#16839525—21no—
29C61×#532C2211yescharacteristic
30C61×#423C2211yescharacteristic
31C2×C4×C8×C61C2211yescharacteristic
32C61×D4⋊C8—22no—
33C22×D244D411yescharacteristic
34C22×C4×D61—21no—
35C2×#11758199—21no—
36C2×#11758199—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#14519710—21no—
54#14519710—21no—
55C4⋊#92418C2×C411yescharacteristic
56C4⋊#92418C2×C411yescharacteristic
57#14519704—42no—
58#14519704—42no—
59#14519699—24no—
60#14519698—21no—
61#14519698—21no—
62#14519697—21no—
63#14519697—21no—
64C22⋊#92418—21no—
65#14519689—22no—
66#14519689—22no—
67#14519688—21no—
68C4×#92418—21no—
69C4×#92418—21no—
70#14519684—21no—
71C2×#41×C61—21no—
72C2×M16×C61—21no—
73C22×C8×C61—21no—
74C4⋊Q8×C61C2×C411yescharacteristic
75#127×C61C2×C411yescharacteristic
76#124×C61—21no—
77#121×C61—21no—
78#121×C61—21no—
79C4×D4×C61—21no—
80C4×D4×C61—21no—
81C2×C42×C61C2311yescharacteristic
82C4⋊C8×C61—21no—
83C4⋊C8×C61D412yes—
84C4×C8×C61—21no—
85C4×C8×C61—21no—
86C23×D61—21no—
87#41×C61—41no—
88#41×C61—41no—
89#41×C61—41no—
90#41×C61—41no—
91C2×Q8×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C22×Dic61—21no—
101C22×Dic61—41no—
102C2×D244—22no—
103C2×D244—21no—
104C2×D244—41no—
105C2×D244C22⋊C411yescharacteristic
106C2×D244C22⋊C411yescharacteristic
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115M16×C61—41no—
116M16×C61—41no—
117C2×C8×C61—22no—
118C2×C8×C61—22no—
119C2×C8×C61—41no—
120C2×C8×C61—41no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C42×C61C22×C411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61#4111yescharacteristic
129#11758199—42no—
130#11758199—42no—
131#11758198—21no—
132#11758198—21no—
133#11758198—21no—
134#11758198—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—22no—
137C4⋊Dic61—41no—
138C4⋊Dic61C22⋊C411yescharacteristic
139C4⋊Dic61C22⋊C411yescharacteristic
140C4×Dic61—41no—
141C4×Dic61—41no—
142#11758194—21no—
143#11758194—21no—
144#11758194—21no—
145#11758194D812yescomplemented
146C2×#92418—21no—
147C2×#92418—21no—
148C2×#92418—21no—
149C2×#92418—21no—
150#11758189—44no—
151C8×D61—44no—
152C23×C61—41no—
153C23×C61#12111yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—42no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—81no—
160Q8×C61—41no—
161Q8×C61—41no—
162D4×C61—42no—
163D4×C61—41no—
164D4×C61—41no—
165D4×C61—41no—
166D4×C61—41no—
167D4×C61—81no—
168D4×C61—81no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—81no—
174C2×C4×C61—81no—
175C2×C4×C61C2×C22⋊C411yescharacteristic
176C2×C4×C61C4×D411yescharacteristic
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12311yescharacteristic
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61#13511yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—42no—
190C2×Dic61—81no—
191C2×Dic61—81no—
192D244—21no—
193D244—21no—
194D244—21no—
195D244—42no—
196D244#10412yescomplemented
197C4×D61—41no—
198C4×D61—41no—
199C4×D61—41no—
200C4×D61—41no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61—41no—
205C8×C61—42no—
206C8×C61—42no—
207#92418—22no—
208#92418—41no—
209#92418—41no—
210#92418—41no—
211#8991—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61#38611yescharacteristic
218C22×C61#45911yescharacteristic
219C22×C61#46311yescharacteristic
220C2×D61—22no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—82no—
227C2×D61—82no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—81no—
232C4×C61C2×#10411yescharacteristic
233C4×C61#42111yescharacteristic
234C4×C61C4×D811yescharacteristic
235C4×C61#44211yescharacteristic
236C4×C61#44711yescharacteristic
237C4×C61#44911yescharacteristic
238Dic61—41no—
239Dic61—41no—
240Dic61—82no—
241#3100—611no—
242D4×M16—611no—
243#1980—611no—
244C4×#102—611no—
245#1492D6111yescharacteristic, complemented
246#1303—611no—
247#1278—611no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—161no—
251C2×C61#187111yescharacteristic
252C2×C61#187911yescharacteristic
253C2×C61#188111yescharacteristic
254D61—42no—
255D61—81no—
256C22×M16—1221no—
257#532C2×D6111yescharacteristic
258C2×C4×D4—611no—
259#480—1221no—
260#474—611no—
261#474—611no—
262#459—611no—
263#459—611no—
264#447—1221no—
265C4×D8—1221no—
266C4×D8—1221no—
267#436—1221no—
268#435—1222no—
269C8×D4—1221no—
270#431—611no—
271#423C2×D6111yescharacteristic
272C2×#104—1221no—
273C2×#104—1221no—
274C2×#102—1221no—
275#407—1221no—
276C4×M16—611no—
277C2×C4×C8C2×D6111yescharacteristic
278C4×C4⋊C4—611no—
279#340—1221no—
280D4⋊C8—22no—
281C61#899111yescharacteristic, complemented, Sylow
282C2×#41—21no—
283C22×D4—611no—
284C23×C4—1221no—
285C2×D8—1221no—
286C2×D8—1221no—
287C2×M16—21no—
288C2×M16—611no—
289C2×M16—611no—
290C2×M16—1222no—
291C2×M16—2442no—
292C2×M16—2442no—
293C22×C8—21no—
294C22×C8—1222no—
295C4⋊Q8C4×D6111yescharacteristic
296#127C4×D6111yescharacteristic
297#124—21no—
298#121—21no—
299#121—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—611no—
303C4×D4—611no—
304C4×D4—611no—
305C4×D4—611no—
306C4×D4—1221no—
307C4×D4—1221no—
308C2×C4⋊C4—611no—
309C2×C4⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C42—1221no—
312C2×C42C22×D6111yescharacteristic
313#107—1221no—
314#107—1221no—
315C4⋊C8—21no—
316C4⋊C8—611no—
317C4⋊C8—611no—
318C4⋊C8C22⋊D6112yes—
319#104—2442no—
320#104—2442no—
321#102—1221no—
322#102—1221no—
323#102—1221no—
324#102—1221no—
325#102—1224no—
326C22⋊C8—1222no—
327C22⋊C8—1222no—
328C22⋊C8—1221no—
329#97—1221no—
330C4×C8—21no—
331C4×C8—21no—
332C4×C8—1221no—
333C4×C8—1221no—
334#95—1221no—
335C24—1221no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340C2×Q8—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—611no—
346C2×D4—611no—
347C2×D4—1222no—
348C2×D4—1221no—
349C2×D4—2441no—
350C22×C4—41no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4#1175822211yescharacteristic
362C22×C4D4×D6111yescharacteristic
363C22×C4D4×D6111yescharacteristic
364D8—2442no—
365D8—2442no—
366M16—41no—
367M16—41no—
368M16—612no—
369M16—1221no—
370M16—1221no—
371M16—1221no—
372M16—2444no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—1221no—
378C2×C8—1221no—
379C2×C8—1221no—
380C2×C8—1221no—
381C2×C8—2444no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—611no—
385C4⋊C4—611no—
386C4⋊C4—1222no—
387C4⋊C4—1221no—
388C4⋊C4—2441no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—1221no—
392C22⋊C4—1221no—
393C22⋊C4—1221no—
394C22⋊C4—1221no—
395C42—2441no—
396C42—2441no—
397C42C2×C4×D6111yescharacteristic
398C42D4×D6111yescharacteristic
399C42#1175822411yescharacteristic
400C42C2×C22⋊D6111yescharacteristic
401C23—41no—
402C23—1221no—
403C23—1221no—
404C23—4881no—
405C23—2442no—
406C23—2441no—
407C23—2441no—
408C23#1451975011yescharacteristic
409Q8—41no—
410Q8—41no—
411D4—42no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—81no—
418D4—612no—
419D4—1221no—
420D4—1221no—
421D4—1221no—
422D4—2442no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—4881no—
432C2×C4—4881no—
433C2×C4—2442no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4C22⋊C4×D6111yescharacteristic
445C2×C4#1451973711yescharacteristic
446C2×C4C4×C22⋊D6111yescharacteristic
447C2×C4#1451974511yescharacteristic
448C2×C4#1451974811yescharacteristic
449C2×C4#1451975911yescharacteristic
450C2×C4D8×D6111yescharacteristic
451C2×C4#1451979811yescharacteristic
452C2×C4#1451980111yescharacteristic
453C2×C4#1451980411yescharacteristic
454C8—42no—
455C8—42no—
456C8—1222no—
457C8—2441no—
458C8—2441no—
459C8—2441no—
460C22—21no—
461C22—21no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—1222no—
466C22—4882no—
467C22—4882no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22—2441no—
472C22—2441no—
473C22#1683963811yescharacteristic
474C22#1683995611yescharacteristic
475C22#1683997611yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—81no—
480C4—4882no—
481C4—2441no—
482C4—2441no—
483C4#104×D6111yescharacteristic
484C4#1683977711yescharacteristic
485C4#1683984211yescharacteristic
486C4#1683987111yescharacteristic
487C4#1683989411yescharacteristic
488C4#1683990611yescharacteristic
489C2—21no—
490C2—21no—
491C2—161no—
492C2—4881no—
493C2—2442no—
494C2#2144611811yescharacteristic
495C2#2144616411yescharacteristic
496C2#2144618411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1492C2
socleC22×C61#386
prime radical#21455815C2
cosocleC2×C42×C61C23
hypercenter#1492D61
hypocenterC61#8991
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #21454554C2semidirect
3. #21446739C2semidirect
4. C4×#14519699C2semidirect
5. #21443720C2semidirect
6. #21443656C2semidirect
7. C61×#1492C2semidirect
11. #16840039C4semidirect
12. #16840039C4semidirect
13. #16839954C4semidirect
14. #16839954C4semidirect
145. #11758194D8semidirect
196. D244#104semidirect
245. #1492D61semidirect
281. C61#8991semidirect

Maximal subgroups

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

subgroupindex
#214558152
#214545542
#214467392
C4×#145196992
#214437202
#214436562
C61×#14922
#899161