Finite Group Databasebeta

← #29837600

Subgroups — #29837600

Order 15616.

502 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458246C211yesmaximal, characteristic, complemented
2#21458164C211yesmaximal, characteristic
3#21448093C211yesmaximal, characteristic, complemented
4#21448020C211yesmaximal, characteristic, complemented
5#21448013C211yesmaximal, characteristic, complemented
6#21448011C211yesmaximal, characteristic, complemented
7#21447959C211yesmaximal, characteristic, complemented
8#21447955C211yesmaximal, characteristic, complemented
9#21447935C211yesmaximal, characteristic, complemented
10#21447934C211yesmaximal, characteristic, complemented
11#21447668C211yesmaximal, characteristic, complemented
12#21447648C211yesmaximal, characteristic, complemented
13#21447605C211yesmaximal, characteristic, complemented
14#21447604C211yesmaximal, characteristic, complemented
15C61×#2236C211yesmaximal, characteristic, complemented
16#16840483—21no—
17#16840413—21no—
18C2×#14519720C2211yescharacteristic
19C2×#14519717C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840101—21no—
24#16840100—21no—
25#16840077—21no—
26#16840075—21no—
27#16840045—21no—
28#16840041—21no—
29#16840000C2211yescharacteristic
30#16839999C2211yescharacteristic
31#16839998C2211yescharacteristic
32Q16×Dic61C2211yescharacteristic
33#16839844C2211yescharacteristic
34C8×C22⋊D61C2211yescharacteristic
35#16839800C2211yescharacteristic
36#16839799C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839587C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#366C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758222—41no—
60C2×D488C2311yescharacteristic
61C2×C8×D61C2311yescharacteristic
62#14519776—21no—
63#14519776—21no—
64#14519772—41no—
65#14519770—41no—
66#14519763—41no—
67#14519762—41no—
68#14519760—41no—
69#14519755—41no—
70#14519753—21no—
71#14519752—21no—
72#14519751—21no—
73Q8×Dic61—21no—
74#14519742—41no—
75#14519739—21no—
76C4×C22⋊D61D411yescharacteristic
77#14519736—21no—
78#14519735—21no—
79C4⋊C4×D61—21no—
80#14519720—22no—
81#14519717—22no—
82#14519716—22no—
83C2×#11758185C2311yescharacteristic
84C2×#11758185C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519710—21no—
89#14519710—21no—
90#14519710—21no—
91#14519709—21no—
92#14519708—21no—
93#14519706D411yescharacteristic
94#14519701—21no—
95#14519701—21no—
96#14519699—21no—
97#14519697—21no—
98#14519697—21no—
99C22⋊#92418D411yescharacteristic
100#14519689D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C2×Q16×C61C2311yescharacteristic
103C22×C8×C61C2311yescharacteristic
104C22⋊Q8×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61—21no—
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#103×C61—21no—
113C2×Q8×C61—21no—
114C22×C4×C61—41no—
115C22×C4×C61C2×D411yescharacteristic
116C2×C22⋊D61—41no—
117C2×C22⋊D61D811yescharacteristic
118#11758222—84no—
119C2×D244—21no—
120C2×D244—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61C2×D411yescharacteristic
124C2×Dic122—41no—
125C2×Dic122—41no—
126Q16×C61—21no—
127Q16×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2411yescharacteristic
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61D811yescharacteristic
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144#11758198—41no—
145#11758198D811yescharacteristic
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196D811yescharacteristic
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161D488—21no—
162D488—21no—
163C8×D61—21no—
164C8×D61—21no—
165C16×C61—21no—
166C16×C61—21no—
167#11758185—21no—
168#11758185#4112yescomplemented
169C23×C61C2×D811yescharacteristic
170C22×D61—41no—
171C22×D61C2×D811yescharacteristic
172Q8×C61—41no—
173Q8×C61—41no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—82no—
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C22×D411yescharacteristic
183C22⋊D61—22no—
184C22⋊D61—82no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61C2×D811yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190C2×Dic61C2×D811yescharacteristic
191D244—41no—
192D244—41no—
193D244—82no—
194C4×D61—21no—
195C4×D61—21no—
196C4×D61—82no—
197C4×D61—82no—
198Dic122—82no—
199Dic122—82no—
200C8×C61—21no—
201C8×C61C2×#4111yescharacteristic
202C8×C612−1+411yescharacteristic
203#92418—21no—
204#92418—21no—
205#33920—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61C22×D811yescharacteristic
210C2×D61—21no—
211C2×D61—21no—
212C2×D61—21no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C4×C61—21no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61—81no—
221C4×C61#54711yescharacteristic
222C4×C61#57811yescharacteristic
223Dic61—21no—
224Dic61—21no—
225Dic61—81no—
226Dic61—81no—
227Dic61—81no—
228Dic61#50912yes—
229#3342—611no—
230#3334—611no—
231#2252—611no—
232#2236—611no—
233#2236D6111yescharacteristic, complemented
234#2234—611no—
235#2234—611no—
236#2225—611no—
237#2224—611no—
238#2220—611no—
239#2220—611no—
240C4×SD32—611no—
241#2169—611no—
242#2159—611no—
243#2159—611no—
244C2×C61—41no—
245C2×C61#333411yescharacteristic
246C2×C61C2×#50911yescharacteristic
247C2×C61#341711yescharacteristic
248D61—41no—
249D61—161no—
250#556—1221no—
251#547—1221no—
252C2×SD32—611no—
253C2×M32—611no—
254C2×M32—611no—
255#500—611no—
256#500—611no—
257#485—1221no—
258#485—1221no—
259#480—1221no—
260#480—1221no—
261#475—1221no—
262#474—1221no—
263#467—611no—
264#467C2×D6111yescharacteristic
265#466—611no—
266#466—611no—
267C4×Q16—611no—
268C4×D8—611no—
269C8×D4—611no—
270#427—611no—
271#427—611no—
272C2×#107—611no—
273C2×#107C2×D6111yescharacteristic
274#367—611no—
275#367—611no—
276#367—611no—
277#366—611no—
278#366—611no—
279#366—611no—
280#366—611no—
281#366C2×D6111yescharacteristic
282#366C2×D6111yescharacteristic
283C4⋊C16—611no—
284#358—611no—
285#358C2×D6111yescharacteristic
286#358C2×D6111yescharacteristic
287#357—611no—
288#357—611no—
289#357—611no—
290C22⋊C16—611no—
291C22⋊C16C2×D6111yescharacteristic
292C4×C16—611no—
293C61#3392011yescharacteristic, complemented, Sylow
294C2×#41—2441no—
295C2×Q16C22×D6111yescharacteristic
296C2×D8—611no—
297C22×C8—611no—
298C22×C8C22×D6111yescharacteristic
299C4⋊Q8—1221no—
300C4⋊Q8—1221no—
301#126—2441no—
302#126—2441no—
303#124—2441no—
304#123—2441no—
305#123—2441no—
306C22⋊Q8—21no—
307C22⋊Q8—1221no—
308C22⋊Q8—2441no—
309#121—1221no—
310#121—1221no—
311C4×Q8—1221no—
312C4×Q8—2441no—
313C4×D4—611no—
314C4×D4—1221no—
315#117—1221no—
316#117—1221no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—1221no—
319SD32—1222no—
320M32—1222no—
321M32—1222no—
322C2×C16—611no—
323C2×C16—611no—
324C2×C16C22×D6111yescharacteristic
325C2×C16C22×D6111yescharacteristic
326#107—21no—
327#107—611no—
328#107—611no—
329#107—611no—
330#107—1221no—
331#107—1221no—
332#107—1221no—
333#107C22×D6111yescharacteristic
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#106—1221no—
337#106—1221no—
338C4⋊C8—611no—
339#103—21no—
340#103—1221no—
341#103—1221no—
342#102—1221no—
343#102—1221no—
344#102—1221no—
345C22⋊C8—611no—
346C22⋊C8—611no—
347C4×C8—611no—
348#41—4884no—
349C2×Q8—21no—
350C2×Q8—2441no—
351C2×Q8—2441no—
352C2×D4—611no—
353C2×D4—1221no—
354C2×D4—2441no—
355C2×D4—2441no—
356C22×C4—41no—
357C22×C4—611no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4D4×D6111yescharacteristic
361Q16—21no—
362Q16—21no—
363D8—1221no—
364D8—1221no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—611no—
368C2×C8—611no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8D4×D6111yescharacteristic
372C2×C8C23×D6111yescharacteristic
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—611no—
379C4⋊C4—1221no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C22⋊C4—41no—
388C22⋊C4—611no—
389C22⋊C4—611no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C42—611no—
397C42—2441no—
398C42—2441no—
399C42—2441no—
400C16—21no—
401C16—21no—
402C16—612no—
403C16—1221no—
404C23—611no—
405C23—2441no—
406C23D8×D6111yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—4882no—
410Q8—4882no—
411D4—1222no—
412D4—4882no—
413D4—4882no—
414D4—2441no—
415D4—2441no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—82no—
423C2×C4—611no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—4882no—
429C2×C4—4882no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4D8×D6111yescharacteristic
434C2×C4C2×D4×D6111yescharacteristic
435C8—21no—
436C8—1221no—
437C8—1221no—
438C8#41×D6111yescharacteristic
439C8#1451982411yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—1221no—
444C22—1221no—
445C22—1221no—
446C22—4881no—
447C22—4881no—
448C22—4881no—
449C22C2×D8×D6111yescharacteristic
450C4—21no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—612no—
456C4—1221no—
457C4—1221no—
458C4—4881no—
459C4—4881no—
460C4—4881no—
461C4#1684041011yescharacteristic
462C4#1684057811yescharacteristic
463C2—41no—
464C2—9761no—
465C2—2441no—
466C2#2145816111yescharacteristic
467C2#509×D6111yescharacteristic
468C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2236C2
socleC22×C61C22×D8
prime radical#21458164C2
hypercenter#2236D61
hypocenterC61#33920
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
1. #21458246C2semidirect
3. #21448093C2semidirect
4. #21448020C2semidirect
5. #21448013C2semidirect
6. #21448011C2semidirect
7. #21447959C2semidirect
8. #21447955C2semidirect
9. #21447935C2semidirect
10. #21447934C2semidirect
11. #21447668C2semidirect
12. #21447648C2semidirect
13. #21447605C2semidirect
14. #21447604C2semidirect
15. C61×#2236C2semidirect
168. #11758185#41semidirect
233. #2236D61semidirect
293. C61#33920semidirect

Maximal subgroups

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

subgroupindex
#214582462
#214581642
#214480932
#214480202
#214480132
#214480112
#214479592
#214479552
#214479352
#214479342
#214476682
#214476482
#214476052
#214476042
C61×#22362
#3392061