Finite Group Databasebeta

← #29834666

Subgroups — #29834666

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456332C211yesmaximal, characteristic, complemented
2C4×D8×D61C211yesmaximal, characteristic
3#21447977C211yesmaximal, characteristic, complemented
4#21447976C211yesmaximal, characteristic, complemented
5#21447973C211yesmaximal, characteristic, complemented
6#21447965C211yesmaximal, characteristic, complemented
7#21447964C211yesmaximal, characteristic, complemented
8#21447955C211yesmaximal, characteristic, complemented
9#21447954C211yesmaximal, characteristic, complemented
10#21447606C211yesmaximal, characteristic, complemented
11#21447604C211yesmaximal, characteristic, complemented
12#21447573C211yesmaximal, characteristic, complemented
13#21447533C211yesmaximal, characteristic
14#21447533C211yesmaximal, characteristic
15C61×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17#16840318—21no—
18C4×D4×D61—21no—
19C2×#14519716C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21#16840166C2211yescharacteristic, complemented
22#16840166C2211yescharacteristic, complemented
23#16840164C2211yescharacteristic, complemented
24#16840161—21no—
25#16840159—21no—
26C4×D488C2211yescharacteristic
27D8×Dic61C2211yescharacteristic
28#16839844C2211yescharacteristic
29C4×#11758199—21no—
30#16839842—21no—
31#16839799C2211yescharacteristic
32#16839799C2211yescharacteristic
33#16839797—21no—
34#107×D61C2211yescharacteristic
35#102×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839590C2211yescharacteristic, complemented
38#16839589C2211yescharacteristic, complemented
39#16839589C2211yescharacteristic, complemented
40#16839588C2211yescharacteristic, complemented
41#16839587C2211yescharacteristic, complemented
42#16839587C2211yescharacteristic, complemented
43C4⋊#11758185C2211yescharacteristic, complemented
44#16839580C2211yescharacteristic, complemented
45#16839580C2211yescharacteristic, complemented
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839563C2211yescharacteristic
50#16839562C2211yescharacteristic
51#16839562C2211yescharacteristic
52C61×#499C2211yescharacteristic, complemented
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic, complemented
55C61×#366C2211yescharacteristic, complemented
56C61×C4⋊C16C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×D4×D61—21no—
60C22×C4×D61—41no—
61C2×D488C2311yescharacteristic
62C2×#11758199—21no—
63D8×D61—22no—
64D8×D61Q814yescomplemented
65C2×C8×D61D411yescharacteristic
66C2×C8×D61C2311yescharacteristic
67#14519776—21no—
68#14519776—21no—
69#14519769—21no—
70#14519755—41no—
71#14519755—41no—
72#14519742—41no—
73#14519742—41no—
74C4×D244—21no—
75D4×Dic61—21no—
76#14519739—21no—
77C4×C22⋊D61—41no—
78#14519737—41no—
79#14519735—21no—
80#14519735—21no—
81C4⋊C4×D61—21no—
82C22⋊C4×D61—41no—
83C42×D61D411yescharacteristic
84#14519716—22no—
85#14519716—22no—
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519710—21no—
93#14519710—21no—
94#14519709—21no—
95#14519708—21no—
96#14519708—21no—
97#14519699—21no—
98#14519698—21no—
99#14519697—21no—
100C4×#92418D411yescharacteristic
101C8×Dic61D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×D8×C61C2311yescharacteristic
104#125×C61—21no—
105C4×D4×C61—21no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#106×C61—21no—
112#102×C61—21no—
113C4×C8×C61C2311yescharacteristic
114C23×D61—41no—
115C2×D4×C61—21no—
116C22×C4×C61—41no—
117C2×C22⋊D61—41no—
118C22×Dic61—41no—
119D4×D61—24no—
120D4×D61—42no—
121C2×D244—21no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61—84no—
126C2×C4×D61D811yescharacteristic
127C2×C4×D61D811yescharacteristic
128C2×C4×D61C2×D411yescharacteristic
129C2×Dic122—41no—
130C2×Dic122—41no—
131D8×C61—21no—
132D8×C61C2×Q812yes—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C22⋊C4×C61—41no—
141C42×C61C2×D411yescharacteristic
142C22⋊Dic61—41no—
143#11758199—24no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147#11758198—41no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61D811yescharacteristic
159C4×Dic61D811yescharacteristic
160C4×Dic61C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163D488—21no—
164D488C2×Q812yes—
165C8×D61—22no—
166C8×D61C2×Q812yes—
167C8×D61#4112yes—
168C16×C61—21no—
169C16×C61—21no—
170#11758185—21no—
171#11758185—21no—
172C23×C61—41no—
173C22×D61—41no—
174C22×D61—44no—
175C22×D61—82no—
176C22×D61—82no—
177C22×D61C2×D811yescharacteristic
178D4×C61—22no—
179D4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—82no—
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C22⋊D61—44no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—82no—
192C2×Dic61C2×D811yescharacteristic
193C2×Dic61C2×D811yescharacteristic
194C2×Dic61C2×D811yescharacteristic
195D244—22no—
196D244—41no—
197C4×D61—22no—
198C4×D61—41no—
199C4×D61—82no—
200C4×D61—82no—
201C4×D61—82no—
202C4×D61C22⋊Q812yes—
203C4×D61#13712yes—
204Dic122—82no—
205Dic122—82no—
206C8×C61—21no—
207C8×C61C22×Q811yescharacteristic
208C8×C61C2×#4111yescharacteristic
209#92418—21no—
210#92418C22⋊Q812yes—
211#33627—611nomaximal, Sylow
212C22×C61—42no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61C22×D811yescharacteristic
216C2×D61—21no—
217C2×D61—21no—
218C2×D61—42no—
219C2×D61—88no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61#47412yes—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61C2×C22⋊Q811yescharacteristic
229C4×C61C2×#13711yescharacteristic
230Dic61—21no—
231Dic61—81no—
232Dic61—81no—
233Dic61—81no—
234Dic61#47412yes—
235Dic61#50912yes—
236#3160—611no—
237C2×C4×D8—611no—
238#2228—611no—
239#2228—611no—
240#2228—611no—
241#2228D6111yescharacteristic, complemented
242#2226—611no—
243#2226—611no—
244#2224—611no—
245#2224—611no—
246#2159—611no—
247#2159—611no—
248#2150—611no—
249#2140—611no—
250#2140—611no—
251C2×C61—82no—
252C2×C61C2×#47411yescharacteristic
253C2×C61C2×#50911yescharacteristic
254C2×C61#341411yescharacteristic
255D61—22no—
256D61—82no—
257C22×D8—611no—
258#533—1221no—
259C2×C4×D4—1221no—
260C2×M32—611no—
261C2×M32—611no—
262#500—611no—
263#500—611no—
264#499—611no—
265#499—1221no—
266#499C2×D6111yescharacteristic, complemented
267#498—1221no—
268C4×D8—611no—
269C4×D8—611no—
270C4×D8—611no—
271C4×D8—1221no—
272C4×D8—1221no—
273C4×D8C2×D6111yescharacteristic
274#427—611no—
275#427—611no—
276#427—1221no—
277C2×#107—611no—
278C2×#102—1221no—
279C2×C4×C8—611no—
280#367—611no—
281#367—611no—
282#367—611no—
283#367C2×D6111yescharacteristic, complemented
284#366—611no—
285#366—611no—
286#366—611no—
287#366C2×D6111yescharacteristic, complemented
288C4⋊C16—611no—
289C4⋊C16—611no—
290C4⋊C16—611no—
291C4⋊C16C2×D6111yescharacteristic, complemented
292#357—611no—
293#357—611no—
294#357—611no—
295#357—611no—
296#357—611no—
297#357—611no—
298#357C2×D6111yescharacteristic
299#357C2×D6111yescharacteristic
300C61#3362711yescharacteristic, complemented, Sylow
301C22×D4—1221no—
302C23×C4—2441no—
303C2×D8—614no—
304C2×D8—611no—
305C2×D8—1222no—
306C2×D8—1221no—
307C2×D8C22×D6111yescharacteristic
308C22×C8—611no—
309C22×C8—611no—
310C4⋊Q8—1221no—
311C4⋊Q8—1221no—
312#125—21no—
313#125—1221no—
314C22⋊Q8—2441no—
315C22⋊Q8—2441no—
316C4×Q8—2441no—
317C4×Q8—2441no—
318C4×D4—21no—
319C4×D4—1221no—
320C4×D4—1221no—
321C4×D4—1221no—
322C4×D4—2441no—
323C4×D4—2441no—
324#117—1221no—
325#117—1221no—
326C2×C4⋊C4—1221no—
327C2×C22⋊C4—2441no—
328C2×C42—611no—
329M32—1222no—
330M32—1222no—
331C2×C16—611no—
332C2×C16—611no—
333C2×C16C22×D6111yescharacteristic
334C2×C16C22×D6111yescharacteristic
335#107—611no—
336#107—611no—
337#107—611no—
338#107—1221no—
339#107—1221no—
340#107—1221no—
341#107C22×D6111yescharacteristic
342#107C22×D6111yescharacteristic
343#107C22×D6111yescharacteristic
344#106—21no—
345#106—1221no—
346#106—1221no—
347#106—1221no—
348#102—21no—
349#102—1221no—
350#102—1221no—
351#102—1221no—
352C4×C8—611no—
353C4×C8—611no—
354C4×C8—611no—
355C4×C8C22×D6111yescharacteristic
356C24—2441no—
357C2×Q8—2441no—
358C2×Q8—2441no—
359C2×D4—21no—
360C2×D4—1224no—
361C2×D4—1221no—
362C2×D4—2442no—
363C2×D4—2441no—
364C22×C4—41no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—4884no—
369C22×C4—2441no—
370C22×C4—2441no—
371C22×C4—2441no—
372C22×C4—2441no—
373D8—21no—
374D8—612no—
375D8—1224no—
376D8—1221no—
377D8Q8×D6112yes—
378C2×C8—611no—
379C2×C8—612no—
380C2×C8—612no—
381C2×C8—611no—
382C2×C8—1222no—
383C2×C8D4×D6111yescharacteristic
384C2×C8C23×D6111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—1221no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C22⋊C4—41no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C42—611no—
405C42—611no—
406C42—611no—
407C42—2441no—
408C42—2441no—
409C42D4×D6111yescharacteristic
410C16—21no—
411C16—21no—
412C16—1221no—
413C16—1221no—
414C23—41no—
415C23—611no—
416C23—4882no—
417C23—4882no—
418C23—2444no—
419C23—2441no—
420Q8—4882no—
421Q8—4882no—
422D4—22no—
423D4—41no—
424D4—1222no—
425D4—2444no—
426D4—2441no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4—611no—
432C2×C4—611no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—611no—
436C2×C4—1222no—
437C2×C4—4882no—
438C2×C4—4882no—
439C2×C4—4882no—
440C2×C4—4882no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4D8×D6111yescharacteristic
446C2×C4D8×D6111yescharacteristic
447C2×C4C2×D4×D6111yescharacteristic
448C8—21no—
449C8—612no—
450C8—1221no—
451C8C2×Q8×D6111yescharacteristic
452C8#41×D6111yescharacteristic
453C22—42no—
454C22—81no—
455C22—81no—
456C22—612no—
457C22—1221no—
458C22—1221no—
459C22—4888no—
460C22—4881no—
461C22—4881no—
462C22—2442no—
463C22C2×D8×D6111yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—612no—
470C4—612no—
471C4—1221no—
472C4—4881no—
473C4—4881no—
474C4—4881no—
475C4C22⋊Q8×D6111yescharacteristic
476C4#137×D6111yescharacteristic
477C2—82no—
478C2—1222no—
479C2—4882no—
480C2#474×D6111yescharacteristic
481C2#509×D6111yescharacteristic
482C2#2145895211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
prime radicalC2×D8×D61C22
hypercenter#2228D61
hypocenterC61#33627
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #21456332C2semidirect
3. #21447977C2semidirect
4. #21447976C2semidirect
5. #21447973C2semidirect
6. #21447965C2semidirect
7. #21447964C2semidirect
8. #21447955C2semidirect
9. #21447954C2semidirect
10. #21447606C2semidirect
11. #21447604C2semidirect
12. #21447573C2semidirect
15. C61×#2228C2semidirect
21. #16840166C22semidirect
22. #16840166C22semidirect
23. #16840164C22semidirect
37. #16839590C22semidirect
38. #16839589C22semidirect
39. #16839589C22semidirect
40. #16839588C22semidirect
41. #16839587C22semidirect
42. #16839587C22semidirect
43. C4⋊#11758185C22semidirect
44. #16839580C22semidirect
45. #16839580C22semidirect
52. C61×#499C22semidirect
54. C61×#367C22semidirect
55. C61×#366C22semidirect
56. C61×C4⋊C16C22semidirect
64. D8×D61Q8semidirect
241. #2228D61semidirect
266. #499C2×D61semidirect
283. #367C2×D61semidirect
287. #366C2×D61semidirect
291. C4⋊C16C2×D61semidirect
300. C61#33627semidirect

Maximal subgroups

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

subgroupindex
#214563322
C4×D8×D612
#214479772
#214479762
#214479732
#214479652
#214479642
#214479552
#214479542
#214476062
#214476042
#214475732
#214475332
C61×#22282
#3362761