Finite Group Databasebeta

← #29835593

Subgroups — #29835593

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456402C211yesmaximal, characteristic, complemented
2#21456392C211yesmaximal, characteristic
3#21448103C211yesmaximal, characteristic, complemented
4#21448087C211yesmaximal, characteristic, complemented
5#21448063C211yesmaximal, characteristic, complemented
6#21448057C211yesmaximal, characteristic, complemented
7#21447935C211yesmaximal, characteristic
8#21447933C211yesmaximal, characteristic
9#21447926C211yesmaximal, characteristic, complemented
10#21447924C211yesmaximal, characteristic, complemented
11C4×#14519723C211yesmaximal, characteristic, complemented
12C4×#14519722C211yesmaximal, characteristic, complemented
13C4×#14519720C211yesmaximal, characteristic, complemented
14C4×#14519716C211yesmaximal, characteristic, complemented
15C4×Q32×C61C211yesmaximal, characteristic, complemented
16#16840316—21no—
17#16840299—21no—
18C2×#14519723C2211yescharacteristic
19C2×#14519722C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21C2×#14519716C2211yescharacteristic
22C2×#14519716C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840163C2211yescharacteristic
25#16840147C2211yescharacteristic
26#16840140C2211yescharacteristic
27#16840118—21no—
28#16840111—21no—
29#16840004C2211yescharacteristic
30#16840002—21no—
31#16840000C2211yescharacteristic
32#16840000C2211yescharacteristic
33#16839999C2211yescharacteristic
34#16839994—21no—
35C4×Dic244C2211yescharacteristic
36C4×#11758202—21no—
37C4×#11758201—21no—
38C4×D488C2211yescharacteristic
39C4×C8×D61C2211yescharacteristic
40#16839590C2211yescharacteristic
41#16839589C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839537C2211yescharacteristic
50#16839537C2211yescharacteristic
51C4×#11758185C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C4×Q16×C61C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758202—21no—
61C2×#11758201—21no—
62C2×D488C2311yescharacteristic
63C2×C8×D61D411yescharacteristic
64C2×C8×D61C2311yescharacteristic
65#14519776—21no—
66#14519775—21no—
67#14519772—41no—
68#14519768—21no—
69#14519767—41no—
70#14519766—21no—
71#14519762—41no—
72#14519757—21no—
73#14519755—41no—
74#14519753—21no—
75#14519753—21no—
76#14519752—21no—
77C4×Dic122—21no—
78C4×Dic122—41no—
79C4×D244—21no—
80C4×D244—41no—
81#14519734—41no—
82#14519734—41no—
83C42×D61D411yescharacteristic
84#14519723—22no—
85#14519722—22no—
86#14519720—22no—
87#14519716—22no—
88#14519716—22no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519708—21no—
95#14519702—21no—
96#14519701—21no—
97#14519701—21no—
98#14519700—21no—
99#14519699—21no—
100#14519697—21no—
101C4×#92418D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×Q16×C61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C4×Q8×C61—21no—
107C4×Q8×C61—21no—
108Q32×C61—22no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#103×C61—21no—
114#103×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×D244—21no—
119C2×D244—41no—
120C2×C4×D61—41no—
121C2×C4×D61D811yescharacteristic
122C2×C4×D61D811yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×Dic122—21no—
125C2×Dic122—41no—
126Q16×C61—21no—
127Q16×C61—21no—
128Q16×C61—21no—
129Q16×C61—21no—
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2411yescharacteristic
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C42×C61—41no—
137C42×C61—41no—
138C42×C61C2×D411yescharacteristic
139#11758202—42no—
140#11758201—42no—
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147#11758198—41no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—41no—
151C4⋊Dic61—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159C4×Dic61—41no—
160C4×Dic61D811yescharacteristic
161C4×Dic61D811yescharacteristic
162C4×Dic61C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164C2×#92418C2×D411yescharacteristic
165Dic244—21no—
166Dic244—21no—
167D488—21no—
168D488—21no—
169C8×D61—21no—
170C8×D61—21no—
171C8×D61—22no—
172C16×C61—21no—
173C16×C61#4112yes—
174#11758185—21no—
175#11758185#4112yes—
176C22×D61—41no—
177C22×D61C2×D811yescharacteristic
178Q8×C61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61C2×D811yescharacteristic
193C2×Dic61C2×D811yescharacteristic
194C2×Dic61C2×D811yescharacteristic
195D244—41no—
196D244—41no—
197D244—82no—
198C4×D61—21no—
199C4×D61—21no—
200C4×D61—22no—
201C4×D61—41no—
202C4×D61—82no—
203Dic122—41no—
204Dic122—41no—
205Dic122—82no—
206C8×C61—21no—
207C8×C61C2×#4111yescharacteristic
208C8×C61C2×#4111yescharacteristic
209#92418—21no—
210#92418#13512yes—
211#33738—611nomaximal, Sylow
212C22×C61C22×D811yescharacteristic
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—21no—
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—81no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61#51012yes—
225C4×C61#53211yescharacteristic
226C4×C61C2×#13511yescharacteristic
227Dic61—21no—
228Dic61—21no—
229Dic61—21no—
230Dic61—81no—
231Dic61—81no—
232Dic61—81no—
233#3170—611no—
234#3168—611no—
235#2255—611no—
236#2251—611no—
237#2245—611no—
238#2243—611no—
239#2220—611no—
240#2220—611no—
241#2219—611no—
242#2219—611no—
243C4×Q32—611no—
244C4×Q32D6111yescharacteristic, complemented
245C4×SD32—611no—
246C4×SD32—611no—
247C4×M32—611no—
248C2×C61#316911yescharacteristic
249C2×C61C2×#51011yescharacteristic
250C2×C61#341411yescharacteristic
251D61—41no—
252D61—161no—
253#533—1221no—
254#529—1221no—
255C2×Q32—611no—
256C2×Q32C2×D6111yescharacteristic
257C2×SD32—611no—
258C2×SD32—611no—
259C2×M32—611no—
260C2×M32—611no—
261#500—611no—
262#499—611no—
263#495—611no—
264#494—611no—
265#488—1221no—
266#487—1221no—
267#467—611no—
268#467—611no—
269#467—611no—
270#467—1221no—
271#466—611no—
272#465—1221no—
273C4×Q16—611no—
274C4×Q16—1221no—
275C4×Q16C2×D6111yescharacteristic
276C4×Q16C2×D6111yescharacteristic
277C4×SD16—1221no—
278C4×D8—611no—
279C2×C4×C8—611no—
280#367—611no—
281#367—611no—
282#366—611no—
283#366C2×D6111yescharacteristic
284#358—611no—
285#358—611no—
286#358—611no—
287#358—611no—
288#358C2×D6111yescharacteristic
289#358C2×D6111yescharacteristic
290#357—611no—
291#357—611no—
292#346—611no—
293#346—611no—
294C4×C16—611no—
295C4×C16C2×D6111yescharacteristic
296C61#3373811yescharacteristic, complemented, Sylow
297C2×Q16—611no—
298C2×Q16—1221no—
299C2×Q16C22×D6111yescharacteristic
300C2×Q16C22×D6111yescharacteristic
301C2×SD16—1221no—
302C2×D8—611no—
303C22×C8—611no—
304C22×C8—611no—
305C4⋊Q8—1221no—
306C4⋊Q8—1221no—
307#126—2441no—
308#125—1221no—
309#125—2441no—
310#124—1221no—
311#123—2441no—
312C22⋊Q8—1221no—
313C22⋊Q8—1221no—
314C22⋊Q8—1221no—
315C22⋊Q8—2441no—
316#121—1221no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—1221no—
320C4×Q8—2441no—
321C4×D4—1221no—
322C4×D4—2441no—
323#117—2441no—
324#117—2441no—
325C2×C42—611no—
326Q32—22no—
327Q32—1222no—
328SD32—1222no—
329SD32—1222no—
330M32—1222no—
331M32—1222no—
332C2×C16—611no—
333C2×C16—611no—
334C2×C16C22×D6111yescharacteristic
335C2×C16C22×D6111yescharacteristic
336#107—611no—
337#107—611no—
338#107—1221no—
339#107C22×D6111yescharacteristic
340#107C22×D6111yescharacteristic
341#106—1221no—
342#103—21no—
343#103—21no—
344#103—1221no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#102—1221no—
349#102—1221no—
350C4×C8—611no—
351C4×C8—611no—
352C4×C8—611no—
353C4×C8C22×D6111yescharacteristic
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—1221no—
357C2×Q8—2441no—
358C2×D4—1221no—
359C2×D4—2441no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—2441no—
364Q16—21no—
365Q16—21no—
366Q16—21no—
367Q16—21no—
368Q16—1221no—
369Q16—1221no—
370Q16—2442no—
371SD16—2442no—
372D8—1221no—
373D8—1221no—
374C2×C8—611no—
375C2×C8—611no—
376C2×C8—1222no—
377C2×C8—1221no—
378C2×C8—1221no—
379C2×C8D4×D6111yescharacteristic
380C2×C8C23×D6111yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—1221no—
386C4⋊C4—1221no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C42—41no—
404C42—41no—
405C42—611no—
406C42—611no—
407C42—611no—
408C42—2441no—
409C42D4×D6111yescharacteristic
410C16—21no—
411C16—612no—
412C16—1221no—
413C16#1175822212yes—
414C23—611no—
415C23—2441no—
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—4882no—
421Q8—2441no—
422Q8—2441no—
423D4—4882no—
424D4—2441no—
425D4—2441no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—611no—
433C2×C4—1222no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—4882no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4D8×D6111yescharacteristic
442C2×C4D8×D6111yescharacteristic
443C2×C4C2×D4×D6111yescharacteristic
444C8—21no—
445C8—612no—
446C8—1221no—
447C8#41×D6111yescharacteristic
448C8C2×#1175822211yescharacteristic
449C22—1221no—
450C22—1221no—
451C22—1221no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22C2×D8×D6111yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—1221no—
462C4—1221no—
463C4—1221no—
464C4—4881no—
465C4—4881no—
466C4—4881no—
467C4#1684020412yes—
468C4#1684030911yescharacteristic
469C4#135×D6111yescharacteristic
470C2—9761no—
471C2—2441no—
472C2#2145639511yescharacteristic
473C2C2×#1684020411yescharacteristic
474C2#2145895211yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×Q32×C61C2
socleC22×C61C22×D8
prime radical#16839999C22
hypercenterC4×Q32D61
hypocenterC61#33738
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×Q32

Complements

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

NH ≅ G/Ntype
1. #21456402C2semidirect
3. #21448103C2semidirect
4. #21448087C2semidirect
5. #21448063C2semidirect
6. #21448057C2semidirect
9. #21447926C2semidirect
10. #21447924C2semidirect
11. C4×#14519723C2semidirect
12. C4×#14519722C2semidirect
13. C4×#14519720C2semidirect
14. C4×#14519716C2semidirect
15. C4×Q32×C61C2semidirect
244. C4×Q32D61semidirect
296. C61#33738semidirect

Maximal subgroups

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

subgroupindex
#214564022
#214563922
#214481032
#214480872
#214480632
#214480572
#214479352
#214479332
#214479262
#214479242
C4×#145197232
C4×#145197222
C4×#145197202
C4×#145197162
C4×Q32×C612
#3373861