Finite Group Databasebeta

← #29837744

Subgroups — #29837744

Order 15616.

508 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#21458807C211yesmaximal, characteristic, complemented
2#21458671C211yesmaximal, characteristic, complemented
3#21448058C211yesmaximal, characteristic, complemented
4#21448057C211yesmaximal, characteristic, complemented
5#21448045C211yesmaximal, characteristic, complemented
6#21447970C211yesmaximal, characteristic, complemented
7#21447955C211yesmaximal, characteristic, complemented
8#21447877C211yesmaximal, characteristic
9#21447875C211yesmaximal, characteristic
10#21447863C211yesmaximal, characteristic, complemented
11#21447726C211yesmaximal, characteristic, complemented
12#21447682C211yesmaximal, characteristic, complemented
13#21447681C211yesmaximal, characteristic, complemented
14#21447665C211yesmaximal, characteristic
15C61×#2227C211yesmaximal, characteristic, complemented
16#16840484—21no—
17#16840427—21no—
18C2×#14519722C2211yescharacteristic
19C2×#14519720C2211yescharacteristic
20C2×D976C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840147C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840140C2211yescharacteristic
26#16840041—21no—
27#16840041—21no—
28#16840039—21no—
29#16839987—21no—
30#16839984—21no—
31#16839966—21no—
32C8×Dic122C2211yescharacteristic
33#16839856C2211yescharacteristic
34C4×D488C2211yescharacteristic
35#16839844C2211yescharacteristic
36#16839844C2211yescharacteristic
37#16839844C2211yescharacteristic
38#16839587C2211yescharacteristic
39#16839580C2211yescharacteristic
40#16839580C2211yescharacteristic
41#16839567C2211yescharacteristic
42#16839566C2211yescharacteristic
43#16839565C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839538C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#500C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C61×#366C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Q8×D61—41no—
60C2×Dic244C2311yescharacteristic
61C2×#11758202—21no—
62C2×#11758190—21no—
63C2×#11758201—21no—
64C2×D488C2311yescharacteristic
65C2×D488C2311yescharacteristic
66#14519776—21no—
67#14519776—21no—
68#14519775—21no—
69#14519772—41no—
70#14519771—41no—
71#14519766—21no—
72#14519765—21no—
73#14519755—41no—
74#14519755—41no—
75#14519755—41no—
76#14519753—41no—
77C4×Dic122D411yescharacteristic
78#14519742—21no—
79C4×D244—21no—
80#14519739—21no—
81#14519739—21no—
82#14519739—21no—
83#14519734—41no—
84#14519722—22no—
85#14519720—22no—
86D976—22no—
87C2×#11758185C2311yescharacteristic
88C2×#11758185C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519710—21no—
91#14519710—21no—
92C4⋊#92418D411yescharacteristic
93#14519706D411yescharacteristic
94#14519706D411yescharacteristic
95#14519700—21no—
96#14519699—21no—
97#14519697—21no—
98#14519697—21no—
99#14519697—21no—
100C8×Dic61C2311yescharacteristic
101C8×Dic61C2311yescharacteristic
102C2×Q16×C61C2311yescharacteristic
103C4⋊Q8×C61—21no—
104C4×Q8×C61—21no—
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107#107×C61—21no—
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#103×C61—21no—
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×Q8×C61—41no—
115Q8×D61—84no—
116C2×D244—21no—
117C2×D244—21no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×Dic122—21no—
123C2×Dic122—41no—
124C2×Dic122—41no—
125C2×Dic122D811yescharacteristic
126Q16×C61—21no—
127Q16×C61—21no—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C42×C61—41no—
136C42×C61C2×D411yescharacteristic
137#11758202—81no—
138#11758201—81no—
139#11758198—41no—
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147C4⋊Dic61—21no—
148C4⋊Dic61D811yescharacteristic
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196D811yescharacteristic
155#11758196D811yescharacteristic
156C4×Dic61—41no—
157C4×Dic61C2×D411yescharacteristic
158C4×Dic61C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161Dic244—21no—
162Dic244—21no—
163D488—21no—
164D488—21no—
165D488—21no—
166D488#4112yes—
167#11758190—81no—
168C16×C61—21no—
169C16×C61—21no—
170#11758185—21no—
171#11758185—21no—
172C22×D61—41no—
173C22×D61—41no—
174Q8×C61—41no—
175Q8×C61—41no—
176Q8×C61—82no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C2×D811yescharacteristic
183C2×C4×C61C22×D411yescharacteristic
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61C2×D811yescharacteristic
187C2×Dic61C2×D811yescharacteristic
188C2×Dic61C2×D811yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190D244—22no—
191D244—41no—
192D244—41no—
193D244—41no—
194C4×D61—82no—
195C4×D61—82no—
196C4×D61—82no—
197C4×D61—82no—
198Dic122—22no—
199Dic122—41no—
200Dic122—41no—
201Dic122—82no—
202Dic122—82no—
203C8×C61—21no—
204C8×C61C2×#4111yescharacteristic
205C8×C612−1+411yescharacteristic
206#92418—21no—
207#92418—21no—
208#33934—611nomaximal, Sylow
209C22×C61C22×D811yescharacteristic
210C2×D61—42no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61—81no—
221C4×C61—81no—
222C4×C61#54811yescharacteristic
223C4×C61#57711yescharacteristic
224Dic61—21no—
225Dic61—21no—
226Dic61—21no—
227Dic61—81no—
228Dic61—81no—
229Dic61#50912yes—
230#3393—611no—
231Q8×D8—611no—
232#2243—611no—
233#2243—611no—
234#2241—611no—
235#2227—611no—
236#2227D6111yescharacteristic, complemented
237#2224—611no—
238#2210—611no—
239#2210—611no—
240#2208—611no—
241#2183—611no—
242#2175—611no—
243#2175—611no—
244C4×D16—611no—
245C2×C61#335811yescharacteristic
246C2×C61C2×#50911yescharacteristic
247C2×C61#341711yescharacteristic
248D61—82no—
249D61—161no—
250#556—1221no—
251D4×Q8—1221no—
252C2×SD32—611no—
253C2×SD32—611no—
254C2×D16—611no—
255#500—611no—
256#500—611no—
257#500C2×D6111yescharacteristic
258#495—611no—
259#495—611no—
260#494—611no—
261#474—1221no—
262#474—1221no—
263#474—1221no—
264#464—1221no—
265#464—1221no—
266#461—1221no—
267C8×Q8—611no—
268C4×Q16—611no—
269C4×Q16C2×D6111yescharacteristic
270C4×D8—611no—
271C4×D8—611no—
272C4×D8—611no—
273C4×D8—611no—
274#366—611no—
275#366C2×D6111yescharacteristic
276#366C2×D6111yescharacteristic
277C4⋊C16—611no—
278C4⋊C16—611no—
279C4⋊C16C2×D6111yescharacteristic
280#358—611no—
281#358—611no—
282#358—611no—
283#358—611no—
284#358C2×D6111yescharacteristic
285#358C2×D6111yescharacteristic
286#357—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290#346—611no—
291#346—611no—
292C4×C16—611no—
293C61#3393411yescharacteristic, complemented, Sylow
294C22×Q8—2441no—
295C2×Q16—611no—
296C2×Q16—1221no—
297C2×Q16C22×D6111yescharacteristic
298C2×SD16—1221no—
299C2×SD16—1221no—
300C2×D8—611no—
301C2×D8—611no—
302C4⋊Q8—21no—
303C4⋊Q8—1221no—
304C4⋊Q8—1221no—
305C4⋊Q8—1221no—
306#126—2441no—
307#126—2441no—
308#124—1221no—
309#124—1221no—
310C22⋊Q8—2441no—
311C22⋊Q8—2441no—
312C22⋊Q8—2441no—
313C22⋊Q8—2441no—
314C4×Q8—21no—
315C4×Q8—611no—
316C4×Q8—1221no—
317C4×D4—1221no—
318C4×D4—1221no—
319C4×D4—1221no—
320C4×D4—1221no—
321#117—2441no—
322SD32—1222no—
323SD32—1222no—
324D16—1222no—
325C2×C16—611no—
326C2×C16—611no—
327C2×C16C22×D6111yescharacteristic
328C2×C16C22×D6111yescharacteristic
329#107—21no—
330#107—611no—
331#107—1221no—
332#107—1221no—
333#107C22×D6111yescharacteristic
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336C4⋊C8—611no—
337C4⋊C8—611no—
338C4⋊C8—611no—
339#103—21no—
340#103—1221no—
341#102—1221no—
342#102—1221no—
343#102—1221no—
344#102—1221no—
345C4×C8—611no—
346C4×C8—611no—
347C4×C8C22×D6111yescharacteristic
348C2×Q8—21no—
349C2×Q8—41no—
350C2×Q8—611no—
351C2×Q8—1221no—
352C2×Q8—4884no—
353C2×Q8—2441no—
354C2×Q8—2441no—
355C2×D4—1221no—
356C2×D4—1221no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4—2441no—
361Q16—21no—
362Q16—21no—
363Q16—1221no—
364Q16—1221no—
365Q16—4881no—
366SD16—4881no—
367SD16—4881no—
368D8—612no—
369D8—1221no—
370D8—1221no—
371D8—1221no—
372C2×C8—611no—
373C2×C8—611no—
374C2×C8D4×D6111yescharacteristic
375C2×C8C23×D6111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—611no—
382C4⋊C4—611no—
383C4⋊C4—611no—
384C4⋊C4—1221no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C42—41no—
399C42—611no—
400C42—611no—
401C42—2441no—
402C42D4×D6111yescharacteristic
403C16—21no—
404C16—21no—
405C16—1221no—
406C16—1221no—
407C23—2441no—
408C23—2441no—
409Q8—41no—
410Q8—41no—
411Q8—82no—
412Q8—1222no—
413Q8—4882no—
414Q8—4882no—
415Q8—2441no—
416Q8—2441no—
417D4—1222no—
418D4—2441no—
419D4—2441no—
420D4—2441no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—611no—
426C2×C4—611no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—4882no—
430C2×C4—4882no—
431C2×C4—4882no—
432C2×C4—4882no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4D8×D6111yescharacteristic
436C2×C4D8×D6111yescharacteristic
437C2×C4C2×D4×D6111yescharacteristic
438C8—21no—
439C8—1221no—
440C8—1221no—
441C8#41×D6111yescharacteristic
442C8#1451982511yescharacteristic
443C22—4881no—
444C22—4881no—
445C22—4881no—
446C22—4881no—
447C22—4881no—
448C22—2442no—
449C22C2×D8×D6111yescharacteristic
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—612no—
457C4—1221no—
458C4—1221no—
459C4—1221no—
460C4—4881no—
461C4—4881no—
462C4#1684042211yescharacteristic
463C4#1684057111yescharacteristic
464C2—9761no—
465C2—4882no—
466C2#2145845311yescharacteristic
467C2#509×D6111yescharacteristic
468C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2227C2
socleC22×C61C22×D8
prime radicalC2×D976C22
hypercenter#2227D61
hypocenterC61#33934
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
1. #21458807C2semidirect
2. #21458671C2semidirect
3. #21448058C2semidirect
4. #21448057C2semidirect
5. #21448045C2semidirect
6. #21447970C2semidirect
7. #21447955C2semidirect
10. #21447863C2semidirect
11. #21447726C2semidirect
12. #21447682C2semidirect
13. #21447681C2semidirect
15. C61×#2227C2semidirect
236. #2227D61semidirect
293. C61#33934semidirect

Maximal subgroups

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

subgroupindex
#214588072
#214586712
#214480582
#214480572
#214480452
#214479702
#214479552
#214478772
#214478752
#214478632
#214477262
#214476822
#214476812
#214476652
C61×#22272
#3393461