Finite Group Databasebeta

← #29835239

Subgroups — #29835239

Order 15616.

520 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456479C211yesmaximal, characteristic
2#21454682C211yesmaximal, characteristic
3#21448030C211yesmaximal, characteristic
4#21448029C211yesmaximal, characteristic
5#21447980C211yesmaximal, characteristic, complemented
6#21447870C211yesmaximal, characteristic, complemented
7#21447869C211yesmaximal, characteristic, complemented
8#21447754C211yesmaximal, characteristic
9#21447754C211yesmaximal, characteristic
10#21447689C211yesmaximal, characteristic, complemented
11#21447687C211yesmaximal, characteristic, complemented
12#21447677C211yesmaximal, characteristic, complemented
13#21447675C211yesmaximal, characteristic, complemented
14#21447625C211yesmaximal, characteristic
15C61×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17#16840375—21no—
18#16840238—21no—
19C2×Dic488C2211yescharacteristic
20C2×Dic488C2211yescharacteristic
21C2×#14519723C2211yescharacteristic
22C2×#14519723C2211yescharacteristic
23#16840142C2211yescharacteristic
24#16840132—21no—
25#16840021—21no—
26#16840004C2211yescharacteristic
27#16840004C2211yescharacteristic
28#16839868—21no—
29#16839867—21no—
30#16839866—21no—
31C4×Dic244C2211yescharacteristic
32Q16×Dic61C2211yescharacteristic
33#16839856C2211yescharacteristic
34#16839856C2211yescharacteristic
35#16839856C2211yescharacteristic
36#16839799C2211yescharacteristic
37#16839769—21no—
38#16839716C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839541C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Q8×D61—21no—
60C2×Dic244—21no—
61C2×Dic244C2311yescharacteristic
62C2×Dic244C2311yescharacteristic
63C2×Dic244C2311yescharacteristic
64C2×#11758202—21no—
65Q16×D61—22no—
66Q16×D61—22no—
67C2×#11758189D411yescharacteristic
68C2×C8×D61C2311yescharacteristic
69#14519777—21no—
70#14519772—41no—
71#14519772—41no—
72#14519768—41no—
73#14519768—41no—
74#14519757—21no—
75#14519757—21no—
76Q8×Dic61—21no—
77C4×Dic122—21no—
78C4×Dic122—41no—
79#14519742—21no—
80#14519742—21no—
81#14519742—21no—
82#14519742—41no—
83#14519735—21no—
84#14519735—41no—
85#14519734—41no—
86#14519734D411yescharacteristic
87Dic488—22no—
88Dic488—22no—
89#14519723—22no—
90#14519723—22no—
91C2×#11758185C2311yescharacteristic
92C2×#11758185C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519708—21no—
95#14519702—21no—
96#14519701—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519688D411yescharacteristic
103#14519687D411yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106#125×C61—21no—
107C4×Q8×C61—21no—
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#106×C61—21no—
114#103×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117Q8×D61—24no—
118Q8×D61—42no—
119C2×C4×D61—41no—
120C2×C4×D61C2×D411yescharacteristic
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—21no—
124C2×Dic122—41no—
125Q16×C61—21no—
126Q16×C61#4112yes—
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2411yescharacteristic
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C42×C61—41no—
136C42×C61C2×D411yescharacteristic
137#11758202—24no—
138#11758198—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198D811yescharacteristic
142#11758198D811yescharacteristic
143C4⋊Dic61—21no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196D811yescharacteristic
154#11758196D811yescharacteristic
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164Dic244—21no—
165Dic244—21no—
166Dic244—21no—
167Dic244—21no—
168Dic244—21no—
169Dic244—42no—
170Dic244#4112yes—
171#11758189—41no—
172C8×D61—21no—
173C8×D61—21no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C22×D61C2×D811yescharacteristic
179Q8×C61—22no—
180Q8×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61C2×D811yescharacteristic
193C2×Dic61C2×D811yescharacteristic
194C2×Dic61C2×D811yescharacteristic
195C4×D61—21no—
196C4×D61—21no—
197C4×D61—44no—
198Dic122—22no—
199Dic122—44no—
200Dic122—41no—
201Dic122—41no—
202Dic122—41no—
203Dic122—41no—
204Dic122—41no—
205C8×C61—21no—
206C8×C61C2×#4111yescharacteristic
207C8×C61C2×#4111yescharacteristic
208#92418—21no—
209#92418—21no—
210#33687—611nomaximal, Sylow
211C22×C61C22×D811yescharacteristic
212C2×D61—21no—
213C2×D61—21no—
214C2×D61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—42no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61—81no—
221C4×C61#52511yescharacteristic
222C4×C61#57511yescharacteristic
223Dic61—21no—
224Dic61—21no—
225Dic61—21no—
226Dic61—42no—
227Dic61—81no—
228Dic61—81no—
229Dic61—81no—
230#3177—611no—
231#2950—611no—
232#2237—611no—
233#2237—611no—
234#2229—611no—
235#2229D6111yescharacteristic, complemented
236#2209—611no—
237#2209—611no—
238#2188—611no—
239#2188—611no—
240#2176—611no—
241#2176—611no—
242C4×Q32—611no—
243C4×Q32—611no—
244#2164—611no—
245C2×C61#310011yescharacteristic
246C2×C61#341711yescharacteristic
247C2×C61#341711yescharacteristic
248D61—41no—
249C22×Q16—611no—
250#541—1221no—
251#519—1221no—
252C2×Q32—611no—
253C2×Q32—611no—
254C2×Q32—611no—
255C2×Q32—611no—
256#499C2×D6111yescharacteristic
257#494—611no—
258#491—1221no—
259#470—1221no—
260#467—611no—
261#467—611no—
262#441—1221no—
263#441—1221no—
264#441—1221no—
265C4×Q16—611no—
266C4×Q16—611no—
267C4×Q16—611no—
268C4×Q16—611no—
269C4×Q16—611no—
270C4×Q16C2×D6111yescharacteristic
271#427—611no—
272#419—1221no—
273#405—611no—
274#367—611no—
275#367C2×D6111yescharacteristic
276#366—611no—
277#366C2×D6111yescharacteristic
278C4⋊C16—611no—
279C4⋊C16C2×D6111yescharacteristic
280#358—611no—
281#358—611no—
282#358—611no—
283#358—611no—
284#358—611no—
285#358—611no—
286#358C2×D6111yescharacteristic
287#358C2×D6111yescharacteristic
288C22⋊C16—611no—
289C22⋊C16—611no—
290#346—611no—
291C4×C16—611no—
292C61#3368711yescharacteristic, complemented, Sylow
293C22×Q8—1221no—
294C2×Q16—611no—
295C2×Q16—611no—
296C2×Q16—611no—
297C2×Q16—1221no—
298C2×Q16—1222no—
299C2×Q16—1222no—
300C2×Q16—1221no—
301C2×Q16C22×D6111yescharacteristic
302C2×M16—611no—
303C22×C8—611no—
304C4⋊Q8—1221no—
305#126—2441no—
306#126—2441no—
307#125—21no—
308#125—2441no—
309#125—2441no—
310C22⋊Q8—1221no—
311C22⋊Q8—1221no—
312C4×Q8—21no—
313C4×Q8—1221no—
314C4×Q8—1221no—
315C4×Q8—1221no—
316C4×Q8—1221no—
317C4×Q8—1221no—
318C4×Q8—2441no—
319C4×Q8—2441no—
320#117—611no—
321#117—1221no—
322#117—2441no—
323#117—2441no—
324Q32—1222no—
325Q32—1222no—
326Q32—1222no—
327Q32—1222no—
328C2×C16—611no—
329C2×C16—611no—
330C2×C16C22×D6111yescharacteristic
331C2×C16C22×D6111yescharacteristic
332#107—611no—
333#107C22×D6111yescharacteristic
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#106—21no—
337#106—1221no—
338#103—21no—
339#103—1221no—
340#103—1221no—
341#103—1221no—
342#103—1221no—
343#103—1221no—
344#103—1221no—
345#103—1221no—
346#97—611no—
347#97—611no—
348C4×C8—611no—
349C4×C8C22×D6111yescharacteristic
350C2×Q8—21no—
351C2×Q8—1224no—
352C2×Q8—1221no—
353C2×Q8—1221no—
354C2×Q8—1221no—
355C2×Q8—2441no—
356C2×Q8—2442no—
357C22×C4—611no—
358C22×C4—2441no—
359Q16—21no—
360Q16—612no—
361Q16—1224no—
362Q16—1221no—
363Q16—1221no—
364Q16—1221no—
365Q16—1221no—
366Q16—1221no—
367Q16—2442no—
368Q16#1175822612yes—
369M16—2441no—
370C2×C8—611no—
371C2×C8—611no—
372C2×C8—1221no—
373C2×C8—1221no—
374C2×C8D4×D6111yescharacteristic
375C2×C8C23×D6111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—611no—
383C4⋊C4—611no—
384C4⋊C4—1221no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C22⋊C4—611no—
395C22⋊C4—611no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C42—41no—
400C42—611no—
401C42—2441no—
402C42—2441no—
403C42—2441no—
404C42—2441no—
405C42—2441no—
406C42—2441no—
407C42D4×D6111yescharacteristic
408C16—21no—
409C16—21no—
410C16—1221no—
411C16—1221no—
412C23—611no—
413Q8—22no—
414Q8—41no—
415Q8—1222no—
416Q8—2444no—
417Q8—2441no—
418Q8—2441no—
419Q8—2441no—
420Q8—2441no—
421Q8—2441no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—611no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—2444no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4D8×D6111yescharacteristic
437C2×C4D8×D6111yescharacteristic
438C2×C4C2×D4×D6111yescharacteristic
439C8—21no—
440C8—1221no—
441C8—1221no—
442C8#41×D6111yescharacteristic
443C8C2×#1175822611yescharacteristic
444C22—1221no—
445C22—1221no—
446C22—1221no—
447C22C2×D8×D6111yescharacteristic
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—1221no—
455C4—1221no—
456C4—1221no—
457C4—4881no—
458C4—4881no—
459C4—4881no—
460C4—2442no—
461C4#1684027511yescharacteristic
462C4#1684056111yescharacteristic
463C2—2441no—
464C2#2145582111yescharacteristic
465C2#2145896911yescharacteristic
466C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2229C2
socleC22×C61C22×D8
prime radicalC22×D61C2×D8
hypercenter#2229D61
hypocenterC61#33687
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
5. #21447980C2semidirect
6. #21447870C2semidirect
7. #21447869C2semidirect
10. #21447689C2semidirect
11. #21447687C2semidirect
12. #21447677C2semidirect
13. #21447675C2semidirect
15. C61×#2229C2semidirect
235. #2229D61semidirect
292. C61#33687semidirect

Maximal subgroups

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

subgroupindex
#214564792
#214546822
#214480302
#214480292
#214479802
#214478702
#214478692
#214477542
#214476892
#214476872
#214476772
#214476752
#214476252
C61×#22292
#3368761