Finite Group Databasebeta

← #29834657

Subgroups — #29834657

Order 15616.

546 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#21456331C211yesmaximal, characteristic, complemented
2#21454590C211yesmaximal, characteristic
3#21447986C211yesmaximal, characteristic, complemented
4#21447982C211yesmaximal, characteristic, complemented
5#21447979C211yesmaximal, characteristic, complemented
6#21447975C211yesmaximal, characteristic, complemented
7#21447970C211yesmaximal, characteristic, complemented
8#21447965C211yesmaximal, characteristic, complemented
9#21447960C211yesmaximal, characteristic, complemented
10#21447955C211yesmaximal, characteristic, complemented
11#21447601C211yesmaximal, characteristic, complemented
12C2×#16839580C211yesmaximal, characteristic, complemented
13#21447527C211yesmaximal, characteristic
14#21447524C211yesmaximal, characteristic
15C61×#2158C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17#16840315—21no—
18#16840230—21no—
19C22×#11758185C2211yescharacteristic
20#16840166C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840162—21no—
25#16840159—21no—
26#16839856C2211yescharacteristic
27#16839856C2211yescharacteristic
28#16839849—21no—
29#16839849—21no—
30#16839844C2211yescharacteristic
31#16839844C2211yescharacteristic
32#16839800C2211yescharacteristic
33#16839798—21no—
34#16839756—21no—
35C2×C8×Dic61C2211yescharacteristic
36#16839589C2211yescharacteristic
37#16839589C2211yescharacteristic
38#16839587C2211yescharacteristic
39#16839587C2211yescharacteristic
40#16839580C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839580C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839562C2211yescharacteristic
51#16839562C2211yescharacteristic
52C22×C16×C61C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#427C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#367C2211yescharacteristic
57C61×#366C2211yescharacteristic
58C61×#366C2211yescharacteristic
59C2×#11758222—21no—
60#14519799—22no—
61#14519799Q814yescomplemented
62C2×Dic244C2311yescharacteristic
63C2×#11758190—21no—
64C2×D488C2311yescharacteristic
65C22×#92418D411yescharacteristic
66#14519776—21no—
67#14519776—21no—
68#14519768—21no—
69#14519768—21no—
70#14519754—41no—
71#14519754—41no—
72C4×Dic122—41no—
73C4×Dic122—41no—
74#14519742—21no—
75#14519742—21no—
76#14519739—21no—
77#14519739—21no—
78#14519737—41no—
79#14519737—41no—
80#14519736—21no—
81#14519734—41no—
82C2×C4×Dic61D411yescharacteristic
83C42×D61—41no—
84C2×#11758185—22no—
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519710—21no—
90#14519710—21no—
91#14519709—21no—
92#14519708—21no—
93#14519708—21no—
94#14519700—21no—
95#14519700—21no—
96#14519697—21no—
97#14519697—21no—
98C8×Dic61D411yescharacteristic
99C8×Dic61D411yescharacteristic
100C8×Dic61C2311yescharacteristic
101C8×Dic61C2311yescharacteristic
102C22×C8×C61C2311yescharacteristic
103#117×C61—21no—
104#117×C61—21no—
105C2×C16×C61—22no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#106×C61—21no—
113#106×C61—21no—
114C22×C4×C61C2×D411yescharacteristic
115C2×C22⋊D61—41no—
116C22×Dic61D811yescharacteristic
117C22×Dic61D811yescharacteristic
118#11758222—24no—
119#11758222—42no—
120C2×D244—21no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×Dic122—21no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×Q812yes—
129C2×C8×C61#4112yes—
130C2×C8×C61C2411yescharacteristic
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C22⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C42×C61—41no—
138C42×C61—41no—
139C22⋊Dic61—41no—
140#11758198—41no—
141#11758198—41no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146#11758196—41no—
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152C4×Dic61—41no—
153C4×Dic61—41no—
154C4×Dic61—41no—
155C4×Dic61D811yescharacteristic
156C4×Dic61D811yescharacteristic
157C4×Dic61C2×D411yescharacteristic
158C4×Dic61C2×D411yescharacteristic
159C2×#92418—22no—
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162Dic244—21no—
163Dic244C2×Q812yes—
164D488—21no—
165D488C2×Q812yes—
166#11758190—24no—
167C16×C61—21no—
168C16×C61—21no—
169#11758185—21no—
170#11758185—21no—
171C23×C61C2×D811yescharacteristic
172C22×D61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61C22⋊Q812yes—
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61#13712yes—
180C2×C4×C61C22×D411yescharacteristic
181C22⋊D61—44no—
182C2×Dic61—22no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61C2×D811yescharacteristic
188C2×Dic61C2×D811yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190C2×Dic61C2×D811yescharacteristic
191D244—22no—
192D244—41no—
193C4×D61—44no—
194C4×D61—82no—
195C4×D61—82no—
196Dic122—22no—
197Dic122—41no—
198Dic122—82no—
199Dic122—82no—
200C8×C61C22⋊Q812yes—
201C8×C61C22×Q811yescharacteristic
202C8×C61C2×#4111yescharacteristic
203#92418—21no—
204#92418—21no—
205#33626—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61#47412yes—
209C22×C61C22×D811yescharacteristic
210C2×D61—42no—
211C2×D61—81no—
212C2×D61—81no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61#47412yes—
218C4×C61C2×C22⋊Q811yescharacteristic
219C4×C61C2×#13711yescharacteristic
220Dic61—21no—
221Dic61—21no—
222Dic61—21no—
223Dic61—42no—
224Dic61—81no—
225Dic61—81no—
226Dic61#50812yes—
227#3160—611no—
228C4×#135—611no—
229#2229—611no—
230#2229—611no—
231#2228—611no—
232#2228—611no—
233#2227—611no—
234#2226—611no—
235#2225—611no—
236#2224—611no—
237#2158—611no—
238#2158D6111yescharacteristic, complemented
239C2×C4⋊C16—611no—
240#2138—611no—
241#2138—611no—
242C2×C61—22no—
243C2×C61C2×#47411yescharacteristic
244C2×C61C2×#50811yescharacteristic
245C2×C61#341411yescharacteristic
246D61—82no—
247C2×#135—611no—
248#533—1221no—
249C4×#41—1221no—
250C22×C16—611no—
251C22×C16C2×D6111yescharacteristic
252#500—611no—
253#500—611no—
254#499—611no—
255#499—611no—
256#499—1221no—
257#498—1221no—
258C4×Q16—611no—
259C4×Q16—611no—
260C4×SD16—1221no—
261C4×SD16—1221no—
262C4×D8—611no—
263C4×D8—611no—
264#427—611no—
265#427—1221no—
266#427C2×D6111yescharacteristic
267#427C2×D6111yescharacteristic
268#416—1221no—
269C2×C4×C8—611no—
270#367—611no—
271#367—611no—
272#367C2×D6111yescharacteristic
273#367C2×D6111yescharacteristic
274#366—611no—
275#366—611no—
276#366C2×D6111yescharacteristic
277#366C2×D6111yescharacteristic
278C4⋊C16—611no—
279C4⋊C16—611no—
280C4⋊C16—611no—
281C4⋊C16—611no—
282#358—611no—
283#358—611no—
284#358—611no—
285#358—611no—
286#357—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290C61#3362611yescharacteristic, complemented, Sylow
291C2×#41—1221no—
292#135—614no—
293#135—1222no—
294C2×Q16—611no—
295C2×SD16—1221no—
296C2×D8—611no—
297C22×C8—611no—
298C22×C8C22×D6111yescharacteristic
299C4⋊Q8—1221no—
300C4⋊Q8—1221no—
301#125—1221no—
302#125—1221no—
303C22⋊Q8—2441no—
304C22⋊Q8—2441no—
305C4×Q8—1221no—
306C4×Q8—1221no—
307C4×Q8—2441no—
308C4×Q8—2441no—
309C4×D4—1221no—
310C4×D4—1221no—
311C4×D4—2441no—
312C4×D4—2441no—
313#117—21no—
314#117—21no—
315#117—1221no—
316#117—2441no—
317C2×C42—611no—
318C2×C42—2441no—
319C2×C16—22no—
320C2×C16—611no—
321C2×C16—611no—
322C2×C16—1222no—
323C2×C16C22×D6111yescharacteristic
324C2×C16C22×D6111yescharacteristic
325#107—611no—
326#107—611no—
327#107—1221no—
328#107—1221no—
329#107C22×D6111yescharacteristic
330#107C22×D6111yescharacteristic
331#107C22×D6111yescharacteristic
332#107C22×D6111yescharacteristic
333#106—21no—
334#106—21no—
335#106—1221no—
336#106—1221no—
337#106—1221no—
338#103—1221no—
339#103—1221no—
340#102—1221no—
341#102—1221no—
342C4×C8—611no—
343C4×C8—611no—
344C4×C8—611no—
345C4×C8—611no—
346#41—1224no—
347#41—2442no—
348C2×Q8—1221no—
349C2×Q8—2441no—
350C2×Q8—2441no—
351C2×D4—1221no—
352C2×D4—2441no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4D4×D6111yescharacteristic
359Q16—612no—
360Q16—1221no—
361SD16—1224no—
362D8—612no—
363D8—1221no—
364C2×C8—611no—
365C2×C8—611no—
366C2×C8—1222no—
367C2×C8#1175822212yes—
368C2×C8D4×D6111yescharacteristic
369C2×C8Q8×D6112yes—
370C2×C8C23×D6111yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C42—41no—
391C42—41no—
392C42—611no—
393C42—611no—
394C42—611no—
395C42—611no—
396C42—2441no—
397C42—2441no—
398C42—2441no—
399C16—21no—
400C16—21no—
401C16—1221no—
402C16—1221no—
403C23—2441no—
404C23D8×D6111yescharacteristic
405Q8—1222no—
406Q8—4882no—
407Q8—4882no—
408Q8—2441no—
409D4—1222no—
410D4—2444no—
411D4—2441no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—611no—
417C2×C4—611no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—1222no—
421C2×C4—4882no—
422C2×C4—4882no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2444no—
428C2×C4#1451975512yes—
429C2×C4D8×D6111yescharacteristic
430C2×C4#1451980912yes—
431C2×C4C2×D4×D6111yescharacteristic
432C8—1221no—
433C8—1221no—
434C8#1451975512yes—
435C8C2×Q8×D6111yescharacteristic
436C8C2×#1175822211yescharacteristic
437C22—21no—
438C22—21no—
439C22—4881no—
440C22—4881no—
441C22—2442no—
442C22#1684004112yes—
443C22C2×D8×D6111yescharacteristic
444C4—81no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—612no—
449C4—1221no—
450C4—1221no—
451C4—1221no—
452C4—4881no—
453C4—4881no—
454C4—2442no—
455C4#1684004112yes—
456C4C2×#1451975511yescharacteristic
457C4C2×#1451980911yescharacteristic
458C2—22no—
459C2—4882no—
460C2C2×#1684004111yescharacteristic
461C2#508×D6111yescharacteristic
462C2#2145895211yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2158C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
hypercenter#2158D61
hypocenterC61#33626
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2158

Complements

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

NH ≅ G/Ntype
1. #21456331C2semidirect
3. #21447986C2semidirect
4. #21447982C2semidirect
5. #21447979C2semidirect
6. #21447975C2semidirect
7. #21447970C2semidirect
8. #21447965C2semidirect
9. #21447960C2semidirect
10. #21447955C2semidirect
11. #21447601C2semidirect
12. C2×#16839580C2semidirect
15. C61×#2158C2semidirect
61. #14519799Q8semidirect
238. #2158D61semidirect
290. C61#33626semidirect

Maximal subgroups

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

subgroupindex
#214563312
#214545902
#214479862
#214479822
#214479792
#214479752
#214479702
#214479652
#214479602
#214479552
#214476012
C2×#168395802
#214475272
#214475242
C61×#21582
#3362661