Finite Group Databasebeta

← #29836456

Subgroups — #29836456

Order 15616.

488 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#21456458C211yesmaximal, characteristic, complemented
2#21447966C211yesmaximal, characteristic, complemented
3#21447963C211yesmaximal, characteristic, complemented
4#21447961C211yesmaximal, characteristic, complemented
5#21447958C211yesmaximal, characteristic, complemented
6#21447925C211yesmaximal, characteristic, complemented
7#21447920C211yesmaximal, characteristic
8#21447917C211yesmaximal, characteristic, complemented
9#21447913C211yesmaximal, characteristic, complemented
10#21447881C211yesmaximal, characteristic, complemented
11#21447878C211yesmaximal, characteristic, complemented
12#21447874C211yesmaximal, characteristic, complemented
13#21447871C211yesmaximal, characteristic, complemented
14#21447578C211yesmaximal, characteristic, complemented
15C61×#3175C211yesmaximal, characteristic, complemented
16#16840383—21no—
17C2×#14519723C2211yescharacteristic
18C2×#14519721C2211yescharacteristic
19C2×#14519720C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C2×#14519717C2211yescharacteristic
22C22×#11758185C2211yescharacteristic
23#16840167C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840122—21no—
26#16840008—21no—
27#16840003C2211yescharacteristic
28#16839998C2211yescharacteristic
29#16839864—21no—
30C4×Dic244C2211yescharacteristic
31C4×D488C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839589C2211yescharacteristic
34#16839589C2211yescharacteristic
35#16839589C2211yescharacteristic
36C4⋊#11758185C2211yescharacteristic
37C4⋊#11758185C2211yescharacteristic
38C4⋊#11758185C2211yescharacteristic
39C4⋊#11758185C2211yescharacteristic
40#16839566C2211yescharacteristic
41#16839566C2211yescharacteristic
42#16839565C2211yescharacteristic
43#16839565C2211yescharacteristic
44#16839563C2211yescharacteristic
45#16839563C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48C61×#542—21no—
49C61×#500C2211yescharacteristic
50C61×#495C2211yescharacteristic
51C61×#489—21no—
52C61×#468—21no—
53C61×#467C2211yescharacteristic
54C61×#466C2211yescharacteristic
55C61×#440—21no—
56C4×Q16×C61C2211yescharacteristic
57C4×D8×C61C2211yescharacteristic
58C61×#405C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758190—21no—
61C2×D488C2311yescharacteristic
62#14519777—21no—
63#14519772—41no—
64#14519765—21no—
65#14519763—41no—
66#14519759—41no—
67#14519756—21no—
68#14519755—41no—
69#14519751—21no—
70C4×Dic122—21no—
71C4×D244—21no—
72#14519723—41no—
73#14519721—41no—
74#14519720—41no—
75#14519718—41no—
76#14519717—41no—
77C2×#11758185—41no—
78C2×#11758185C2311yescharacteristic
79C2×#11758185C2311yescharacteristic
80C2×#11758185C2311yescharacteristic
81C2×#11758185C2311yescharacteristic
82#14519711—21no—
83#14519711C2311yescharacteristic
84#14519711C2311yescharacteristic
85#14519702—21no—
86#14519702—21no—
87#14519699—21no—
88#14519699—21no—
89C2×Q16×C61C2311yescharacteristic
90C2×SD16×C61—21no—
91C2×D8×C61C2311yescharacteristic
92C2×M16×C61D411yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C4⋊Q8×C61—21no—
95#126×C61—41no—
96#124×C61—21no—
97#124×C61—41no—
98#123×C61—41no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—41no—
101#121×C61—21no—
102C4×Q8×C61—21no—
103C4×D4×C61—21no—
104#117×C61D411yescharacteristic
105#107×C61—21no—
106#107×C61C2311yescharacteristic
107#107×C61C2311yescharacteristic
108#103×C61—21no—
109#103×C61—21no—
110#102×C61—21no—
111#102×C61—21no—
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—41no—
118C2×D4×C61—21no—
119C2×D4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—41no—
123C2×D244—21no—
124C2×C4×D61—41no—
125C2×Dic122—21no—
126C2×Dic122—41no—
127Q16×C61—21no—
128Q16×C61—21no—
129SD16×C61—42no—
130D8×C61—21no—
131D8×C61—21no—
132M16×C61—41no—
133C2×C8×C61—21no—
134C2×C8×C61—21no—
135C2×C8×C61C2×D411yescharacteristic
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2411yescharacteristic
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61D811yescharacteristic
145C4⋊C4×C61D811yescharacteristic
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61D811yescharacteristic
152C22⋊C4×C61D811yescharacteristic
153C42×C61—41no—
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C22⋊Dic61—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161C4⋊Dic61—21no—
162C4⋊Dic61—21no—
163C4⋊Dic61—41no—
164#11758196—41no—
165#11758196—41no—
166C4×Dic61—41no—
167Dic244—21no—
168Dic244—21no—
169D488—21no—
170D488—21no—
171#11758190—42no—
172#11758185—21no—
173#11758185—21no—
174#11758185—21no—
175#11758185—21no—
176C23×C61—41no—
177C23×C61C2×D811yescharacteristic
178C22×D61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181Q8×C61—161no—
182D4×C61—41no—
183D4×C61—41no—
184D4×C61—161no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—161no—
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C22⋊D61—161no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201D244—41no—
202D244—41no—
203C4×D61—161no—
204Dic122—41no—
205Dic122—41no—
206Dic122—161no—
207C8×C61—21no—
208C8×C61—21no—
209C8×C61—21no—
210C8×C61H(5,𝔽2)11yescharacteristic
211C8×C612−1+411yescharacteristic
212#33829—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61C22×D811yescharacteristic
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—81no—
229C4×C61—81no—
230C4×C61—81no—
231C4×C61#53711yescharacteristic
232C4×C61#57511yescharacteristic
233Dic61—81no—
234Dic61—81no—
235Dic61—81no—
236#3175—611no—
237#3175D6111yescharacteristic, complemented
238#2226—611no—
239#2226—611no—
240#2225—611no—
241#2225—611no—
242#2219—611no—
243#2218—611no—
244#2217—611no—
245#2217—611no—
246#2211—611no—
247#2211—611no—
248#2210—611no—
249#2210—611no—
250#2151—611no—
251C2×C61—41no—
252C2×C61—161no—
253C2×C61#324511yescharacteristic
254C2×C61#341611yescharacteristic
255C2×C61#341611yescharacteristic
256D61—161no—
257#542—21no—
258#542—1221no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262C2×D16—611no—
263C2×M32—611no—
264C22×C16—611no—
265#500—611no—
266#500C2×D6111yescharacteristic
267#495—611no—
268#495C2×D6111yescharacteristic
269#489—21no—
270#489—1221no—
271#468—21no—
272#468—1221no—
273#467—611no—
274#467C2×D6111yescharacteristic
275#466—611no—
276#466C2×D6111yescharacteristic
277#440—21no—
278#440—1221no—
279C4×Q16—611no—
280C4×Q16C2×D6111yescharacteristic
281C4×D8—611no—
282C4×D8C2×D6111yescharacteristic
283#405C2×D6111yescharacteristic
284#367—611no—
285#367—611no—
286#367—611no—
287#367—611no—
288C4⋊C16—611no—
289C4⋊C16—611no—
290C4⋊C16—611no—
291C4⋊C16—611no—
292#358—611no—
293#358—611no—
294#358—611no—
295#358—611no—
296#357—611no—
297#357—611no—
298#357—611no—
299#357—611no—
300C61#3382911yescharacteristic, complemented, Sylow
301C2×Q16—611no—
302C2×Q16C22×D6111yescharacteristic
303C2×SD16—21no—
304C2×SD16—1221no—
305C2×D8—611no—
306C2×D8C22×D6111yescharacteristic
307C2×M16C22⋊D6111yescharacteristic
308C22×C8C22×D6111yescharacteristic
309C4⋊Q8—21no—
310C4⋊Q8—1221no—
311#126—41no—
312#126—2441no—
313#124—21no—
314#124—41no—
315#124—1221no—
316#124—2441no—
317#123—41no—
318#123—2441no—
319C22⋊Q8—21no—
320C22⋊Q8—41no—
321C22⋊Q8—1221no—
322C22⋊Q8—2441no—
323#121—21no—
324#121—1221no—
325C4×Q8—21no—
326C4×Q8—1221no—
327C4×D4—21no—
328C4×D4—1221no—
329#117C22⋊D6111yescharacteristic
330Q32—2441no—
331SD32—2441no—
332SD32—2441no—
333D16—2441no—
334M32—2441no—
335C2×C16—611no—
336C2×C16—611no—
337C2×C16—611no—
338C2×C16—611no—
339C2×C16—2441no—
340#107—21no—
341#107—611no—
342#107—611no—
343#107—1221no—
344#107C22×D6111yescharacteristic
345#107C22×D6111yescharacteristic
346#103—21no—
347#103—21no—
348#103—1221no—
349#103—1221no—
350#102—21no—
351#102—21no—
352#102—1221no—
353#102—1221no—
354#97C22⋊D6111yescharacteristic
355#97C22⋊D6111yescharacteristic
356C4×C8C22×D6111yescharacteristic
357C4×C8C22×D6111yescharacteristic
358C2×Q8—21no—
359C2×Q8—41no—
360C2×Q8—1221no—
361C2×Q8—2441no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4—1221no—
365C2×D4—2441no—
366C22×C4—41no—
367C22×C4—2441no—
368C22×C4C2×C22⋊D6111yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—1221no—
372Q16—1221no—
373SD16—42no—
374SD16—2442no—
375D8—21no—
376D8—21no—
377D8—1221no—
378D8—1221no—
379M16—41no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8C2×C22⋊D6111yescharacteristic
383C2×C8C2×C22⋊D6111yescharacteristic
384C2×C8C2×C22⋊D6111yescharacteristic
385C2×C8C23×D6111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4#1175819911yescharacteristic
397C4⋊C4#1175819911yescharacteristic
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—2441no—
404C22⋊C4—2441no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C22⋊C4#1175819911yescharacteristic
409C22⋊C4#1175819911yescharacteristic
410C42—41no—
411C42—2441no—
412C42C2×C22⋊D6111yescharacteristic
413C42C2×C22⋊D6111yescharacteristic
414C16—1221no—
415C16—1221no—
416C16—1221no—
417C16—1221no—
418C23—41no—
419C23—2441no—
420C23C2×#1175819911yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—161no—
424Q8—9761no—
425Q8—2441no—
426Q8—2441no—
427D4—41no—
428D4—41no—
429D4—161no—
430D4—9761no—
431D4—2441no—
432D4—2441no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—161no—
439C2×C4—9761no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4C2×#1175819911yescharacteristic
444C2×C4C2×#1175819911yescharacteristic
445C2×C4C2×#1175819911yescharacteristic
446C2×C4C2×#1175819911yescharacteristic
447C2×C4C2×#1175819911yescharacteristic
448C2×C4C22×C22⋊D6111yescharacteristic
449C8—21no—
450C8—21no—
451C8—21no—
452C8#1451982311yescharacteristic
453C8#1451982411yescharacteristic
454C22—21no—
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—4881no—
461C22—4881no—
462C22—4881no—
463C22C22×#1175819911yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—4881no—
473C4—4881no—
474C4—4881no—
475C4#1684034011yescharacteristic
476C4#1684056011yescharacteristic
477C2—41no—
478C2—161no—
479C2—9761no—
480C2#2145712611yescharacteristic
481C2#2145896311yescharacteristic
482C2#2145896611yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3175C2
socleC22×C61C22×D8
prime radical#21447920C2
hypercenter#3175D61
hypocenterC61#33829
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #21456458C2semidirect
2. #21447966C2semidirect
3. #21447963C2semidirect
4. #21447961C2semidirect
5. #21447958C2semidirect
6. #21447925C2semidirect
8. #21447917C2semidirect
9. #21447913C2semidirect
10. #21447881C2semidirect
11. #21447878C2semidirect
12. #21447874C2semidirect
13. #21447871C2semidirect
14. #21447578C2semidirect
15. C61×#3175C2semidirect
237. #3175D61semidirect
300. C61#33829semidirect

Maximal subgroups

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

subgroupindex
#214564582
#214479662
#214479632
#214479612
#214479582
#214479252
#214479202
#214479172
#214479132
#214478812
#214478782
#214478742
#214478712
#214475782
C61×#31752
#3382961