Finite Group Databasebeta

← #29836419

Subgroups — #29836419

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456478C211yesmaximal, characteristic, complemented
2#21456458C211yesmaximal, characteristic
3#21447984C211yesmaximal, characteristic, complemented
4#21447977C211yesmaximal, characteristic, complemented
5#21447972C211yesmaximal, characteristic, complemented
6#21447962C211yesmaximal, characteristic, complemented
7#21447932C211yesmaximal, characteristic
8#21447927C211yesmaximal, characteristic, complemented
9#21447915C211yesmaximal, characteristic
10#21447910C211yesmaximal, characteristic, complemented
11#21447882C211yesmaximal, characteristic, complemented
12#21447882C211yesmaximal, characteristic, complemented
13#21447870C211yesmaximal, characteristic, complemented
14#21447865C211yesmaximal, characteristic, complemented
15C61×#2151C211yesmaximal, characteristic, complemented
16#16840383—21no—
17#16840374—21no—
18C2×Dic488C2211yescharacteristic
19C2×Dic488C2211yescharacteristic
20C2×#14519722C2211yescharacteristic
21C2×#14519722C2211yescharacteristic
22#16840167C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840142C2211yescharacteristic
26#16840131—21no—
27#16840122—21no—
28#16840020—21no—
29#16840008—21no—
30#16840003C2211yescharacteristic
31#16840003C2211yescharacteristic
32#16840003C2211yescharacteristic
33#16839998C2211yescharacteristic
34#16839870—21no—
35#16839864—21no—
36C4×Dic244C2211yescharacteristic
37C4×Dic244C2211yescharacteristic
38C4×Dic244C2211yescharacteristic
39C4×D488C2211yescharacteristic
40#16839590C2211yescharacteristic
41#16839590C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839588C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839567C2211yescharacteristic
49#16839567C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C2×M32×C61C2211yescharacteristic
53C22×C16×C61C2211yescharacteristic
54C61×#405C2211yescharacteristic
55C61×C4⋊C16C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×C4⋊C16C2211yescharacteristic
58C61×C4⋊C16C2211yescharacteristic
59C2×Dic244—21no—
60C2×Dic244C2311yescharacteristic
61C2×Dic244C2311yescharacteristic
62C2×Dic244C2311yescharacteristic
63C2×#11758190—21no—
64C2×D488C2311yescharacteristic
65#14519777—21no—
66#14519777—21no—
67#14519772—41no—
68#14519770—41no—
69#14519770—41no—
70#14519769—21no—
71#14519767—41no—
72#14519767—41no—
73#14519765—21no—
74#14519763—41no—
75#14519759—41no—
76#14519756—21no—
77#14519756—21no—
78#14519756—21no—
79#14519755—41no—
80#14519751—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×D244—21no—
85Dic488—41no—
86Dic488—41no—
87#14519722—41no—
88#14519722—41no—
89#14519711—21no—
90#14519711C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519709—21no—
95#14519702—21no—
96#14519702—21no—
97#14519702—21no—
98#14519702—21no—
99#14519702—21no—
100#14519702—21no—
101#14519699—21no—
102#14519699—21no—
103C2×M16×C61D411yescharacteristic
104C22×C8×C61C2311yescharacteristic
105#117×C61D411yescharacteristic
106M32×C61—41no—
107C2×C16×C61—41no—
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C2×D244—21no—
119C2×C4×D61—41no—
120C2×Dic122—21no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—41no—
124M16×C61—41no—
125C2×C8×C61—21no—
126C2×C8×C61—21no—
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2411yescharacteristic
131C4⋊C4×C61D811yescharacteristic
132C4⋊C4×C61D811yescharacteristic
133C22⋊C4×C61D811yescharacteristic
134C22⋊C4×C61D811yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61—41no—
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151#11758196—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×Dic61—41no—
161C4×Dic61—41no—
162Dic244—21no—
163Dic244—21no—
164Dic244—21no—
165Dic244—21no—
166Dic244—21no—
167Dic244—21no—
168Dic244—42no—
169D488—21no—
170D488—21no—
171#11758190—42no—
172C16×C61—21no—
173C16×C61—21no—
174C16×C61—21no—
175C16×C61—21no—
176C23×C61C2×D811yescharacteristic
177C22×D61—41no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C2×D811yescharacteristic
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C22⋊D61—161no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194D244—41no—
195D244—41no—
196C4×D61—161no—
197Dic122—41no—
198Dic122—41no—
199Dic122—41no—
200Dic122—41no—
201Dic122—41no—
202Dic122—41no—
203Dic122—161no—
204C8×C61—21no—
205C8×C61—21no—
206C8×C61—21no—
207C8×C61H(5,𝔽2)11yescharacteristic
208C8×C612−1+411yescharacteristic
209#33824—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61C22×D811yescharacteristic
214C2×D61—81no—
215C2×D61—81no—
216C2×D61—81no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61#53711yescharacteristic
223C4×C61#57511yescharacteristic
224Dic61—81no—
225Dic61—81no—
226Dic61—81no—
227Dic61—81no—
228Dic61—81no—
229Dic61—81no—
230Dic61—81no—
231#3177—611no—
232#3175—611no—
233#2229—611no—
234#2228—611no—
235#2227—611no—
236#2225—611no—
237#2220—611no—
238#2219—611no—
239#2217—611no—
240#2216—611no—
241#2211—611no—
242#2211—611no—
243#2209—611no—
244#2208—611no—
245#2151D6111yescharacteristic, complemented
246C2×C61—41no—
247C2×C61#324511yescharacteristic
248C2×C61#341611yescharacteristic
249C2×C61#341711yescharacteristic
250D61—161no—
251#542—1221no—
252#541—1221no—
253C2×Q32—611no—
254C2×Q32—611no—
255C2×SD32—611no—
256C2×SD32—611no—
257C2×M32C2×D6111yescharacteristic
258C22×C16C2×D6111yescharacteristic
259#500—611no—
260#499—611no—
261#495—611no—
262#494—611no—
263#491—1221no—
264#489—1221no—
265#470—1221no—
266#468—1221no—
267#467—611no—
268#467—611no—
269#467—611no—
270#466—611no—
271#441—1221no—
272#440—1221no—
273C4×Q16—611no—
274C4×Q16—611no—
275C4×Q16—611no—
276C4×D8—611no—
277#405C2×D6111yescharacteristic
278#367—611no—
279#367—611no—
280#366—611no—
281#366—611no—
282C4⋊C16C2×D6111yescharacteristic
283C4⋊C16C2×D6111yescharacteristic
284C4⋊C16C2×D6111yescharacteristic
285C4⋊C16C2×D6111yescharacteristic
286#358—611no—
287#358—611no—
288#358—611no—
289#358—611no—
290#358—611no—
291#358—611no—
292#357—611no—
293#357—611no—
294C61#3382411yescharacteristic, complemented, Sylow
295C2×Q16—611no—
296C2×Q16—611no—
297C2×Q16—611no—
298C2×Q16—1221no—
299C2×SD16—1221no—
300C2×D8—611no—
301C2×M16D24411yescharacteristic
302C22×C8C22×D6111yescharacteristic
303C4⋊Q8—1221no—
304C4⋊Q8—1221no—
305#126—2441no—
306#126—2441no—
307#126—2441no—
308#125—1221no—
309#125—2441no—
310#125—2441no—
311#124—1221no—
312#124—2441no—
313#123—2441no—
314C22⋊Q8—1221no—
315C22⋊Q8—1221no—
316C22⋊Q8—1221no—
317C22⋊Q8—2441no—
318#121—1221no—
319C4×Q8—1221no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×D4—1221no—
323#117D24411yescharacteristic
324Q32—2441no—
325Q32—2441no—
326SD32—2441no—
327SD32—2441no—
328M32—41no—
329C2×C16—41no—
330C2×C16C22×D6111yescharacteristic
331C2×C16C22×D6111yescharacteristic
332C2×C16C22×D6111yescharacteristic
333C2×C16C22×D6111yescharacteristic
334#107—611no—
335#107—611no—
336#107—611no—
337#107—611no—
338#107—1221no—
339#106—1221no—
340#103—1221no—
341#103—1221no—
342#103—1221no—
343#103—1221no—
344#103—1221no—
345#103—1221no—
346#102—1221no—
347#102—1221no—
348#97D24411yescharacteristic
349#97D24411yescharacteristic
350C4×C8C22×D6111yescharacteristic
351C4×C8C22×D6111yescharacteristic
352C2×Q8—1221no—
353C2×Q8—1221no—
354C2×Q8—1221no—
355C2×Q8—2441no—
356C2×D4—1221no—
357C2×D4—2441no—
358C22×C4—2441no—
359C22×C4C2×D24411yescharacteristic
360Q16—1221no—
361Q16—1221no—
362Q16—1221no—
363Q16—1221no—
364Q16—1221no—
365Q16—1221no—
366Q16—2442no—
367SD16—2442no—
368D8—1221no—
369D8—1221no—
370M16—41no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C2×D24411yescharacteristic
374C2×C8C2×D24411yescharacteristic
375C2×C8C2×D24411yescharacteristic
376C2×C8C23×D6111yescharacteristic
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—1221no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4D48811yescharacteristic
393C4⋊C4D48811yescharacteristic
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4D48811yescharacteristic
402C22⋊C4D48811yescharacteristic
403C42—2441no—
404C42—2441no—
405C42—2441no—
406C42C2×D24411yescharacteristic
407C42C2×D24411yescharacteristic
408C16—21no—
409C16—21no—
410C16—21no—
411C16—21no—
412C23—2441no—
413C23C2×D48811yescharacteristic
414Q8—9761no—
415Q8—2441no—
416Q8—2441no—
417Q8—2441no—
418Q8—2441no—
419Q8—2441no—
420Q8—2441no—
421D4—9761no—
422D4—2441no—
423D4—2441no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—9761no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4C2×D48811yescharacteristic
435C2×C4C2×D48811yescharacteristic
436C2×C4C2×D48811yescharacteristic
437C2×C4C2×D48811yescharacteristic
438C2×C4C2×D48811yescharacteristic
439C2×C4C22×D24411yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8#1451982211yescharacteristic
444C8#1451982511yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—4881no—
449C22—4881no—
450C22—4881no—
451C22C22×D48811yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—4881no—
458C4—4881no—
459C4—4881no—
460C4—4881no—
461C4—4881no—
462C4—4881no—
463C4—4881no—
464C4#1684034311yescharacteristic
465C4#1684056211yescharacteristic
466C2—41no—
467C2—9761no—
468C2#2145712911yescharacteristic
469C2#2145896711yescharacteristic
470C2#2145897211yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2151C2
socleC22×C61C22×D8
prime radical#16839998C22
hypercenter#2151D61
hypocenterC61#33824
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #21456478C2semidirect
3. #21447984C2semidirect
4. #21447977C2semidirect
5. #21447972C2semidirect
6. #21447962C2semidirect
8. #21447927C2semidirect
10. #21447910C2semidirect
11. #21447882C2semidirect
12. #21447882C2semidirect
13. #21447870C2semidirect
14. #21447865C2semidirect
15. C61×#2151C2semidirect
245. #2151D61semidirect
294. C61#33824semidirect

Maximal subgroups

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

subgroupindex
#214564782
#214564582
#214479842
#214479772
#214479722
#214479622
#214479322
#214479272
#214479152
#214479102
#214478822
#214478702
#214478652
C61×#21512
#3382461