Finite Group Databasebeta

← #29837593

Subgroups — #29837593

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458190C211yesmaximal, characteristic
2#21458182C211yesmaximal, characteristic
3#21448097C211yesmaximal, characteristic, complemented
4#21448025C211yesmaximal, characteristic, complemented
5#21448024C211yesmaximal, characteristic, complemented
6#21448020C211yesmaximal, characteristic, complemented
7#21448019C211yesmaximal, characteristic, complemented
8#21447985C211yesmaximal, characteristic, complemented
9#21447981C211yesmaximal, characteristic, complemented
10#21447924C211yesmaximal, characteristic, complemented
11Q32×Dic61C211yesmaximal, characteristic, complemented
12#21447649C211yesmaximal, characteristic
13#21447607C211yesmaximal, characteristic, complemented
14#21447606C211yesmaximal, characteristic, complemented
15C61×#2219C211yesmaximal, characteristic, complemented
16#16840454—21no—
17#16840446—21no—
18C2×#14519716C2211yescharacteristic
19#16840163C2211yescharacteristic
20#16840163C2211yescharacteristic
21#16840102—21no—
22#16840100—21no—
23#16840091—21no—
24#16840090—21no—
25#16840071—21no—
26#16840067—21no—
27#16840000C2211yescharacteristic
28#16840000C2211yescharacteristic
29Q16×Dic61C2211yescharacteristic
30Q16×Dic61C2211yescharacteristic
31C8×C22⋊D61C2211yescharacteristic
32#16839800C2211yescharacteristic
33#16839799C2211yescharacteristic
34C2×#14519711C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#16839590C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839566C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C2×M32×C61C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C61×#467C2211yescharacteristic
56C61×#367C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×C8×D61C2311yescharacteristic
60#14519772—41no—
61#14519770—41no—
62#14519768—21no—
63#14519768—21no—
64#14519768—41no—
65#14519767—41no—
66#14519761—41no—
67#14519759—41no—
68#14519753—21no—
69#14519753—21no—
70Q8×Dic61—21no—
71Q8×Dic61—21no—
72C4×C22⋊D61D411yescharacteristic
73#14519736—21no—
74#14519735—21no—
75#14519735—41no—
76#14519733—41no—
77C2×C4⋊Dic61—21no—
78C4⋊C4×D61—21no—
79#14519716—22no—
80C2×#11758185C2311yescharacteristic
81C2×#11758185C2311yescharacteristic
82#14519711—21no—
83#14519711C2311yescharacteristic
84#14519711C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519710—21no—
88#14519709—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519706D411yescharacteristic
93#14519701—21no—
94#14519701—21no—
95#14519701—21no—
96#14519701—21no—
97C22⋊#92418D411yescharacteristic
98#14519689D411yescharacteristic
99C8×Dic61C2311yescharacteristic
100C2×Q16×C61C2311yescharacteristic
101C2×Q16×C61C2311yescharacteristic
102C22×C8×C61C2311yescharacteristic
103C22⋊Q8×C61—21no—
104C22⋊Q8×C61—21no—
105Q32×C61—22no—
106M32×C61—22no—
107C2×C16×C61C2311yescharacteristic
108C2×C16×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#103×C61—21no—
112#103×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C22×C4×C61C2×D411yescharacteristic
116C2×C22⋊D61D811yescharacteristic
117C22×Dic61—41no—
118C2×C4×D61—41no—
119C2×C4×D61C2×D411yescharacteristic
120Q16×C61—21no—
121Q16×C61—21no—
122Q16×C61—21no—
123Q16×C61—21no—
124C2×C8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2411yescharacteristic
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊Dic61—41no—
135C22⋊Dic61D811yescharacteristic
136#11758198—41no—
137#11758198—41no—
138#11758198—41no—
139#11758198D811yescharacteristic
140C4⋊Dic61—21no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
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#11758196—41no—
154#11758196D811yescharacteristic
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162C8×D61—21no—
163C8×D61—21no—
164C16×C61—21no—
165C16×C61#4112yes—
166#11758185—21no—
167#11758185—21no—
168C23×C61C2×D811yescharacteristic
169C22×D61C2×D811yescharacteristic
170Q8×C61—41no—
171Q8×C61—41no—
172Q8×C61—41no—
173Q8×C61—41no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C22⋊D61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—82no—
188C2×Dic61C2×D811yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190C2×Dic61C2×D811yescharacteristic
191C4×D61—21no—
192C4×D61—21no—
193C4×D61—82no—
194C8×C61—21no—
195C8×C61C2×#4111yescharacteristic
196C8×C612−1+411yescharacteristic
197#92418—21no—
198#92418—21no—
199#33919—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61C22×D811yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C4×C61—21no—
208C4×C61—81no—
209C4×C61—81no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61#54711yescharacteristic
213C4×C61#57811yescharacteristic
214Dic61—21no—
215Dic61—21no—
216Dic61—21no—
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220Dic61—81no—
221#3336—611no—
222#3336—611no—
223#2253—611no—
224#2237—611no—
225#2237—611no—
226#2236—611no—
227#2236—611no—
228#2229—611no—
229#2229—611no—
230#2219—611no—
231#2219D6111yescharacteristic, complemented
232C4×Q32—611no—
233#2169—611no—
234#2159—611no—
235#2159—611no—
236C2×C61—41no—
237C2×C61#333411yescharacteristic
238C2×C61#341411yescharacteristic
239C2×C61#341711yescharacteristic
240D61—41no—
241#552—1221no—
242#552—1221no—
243C2×Q32C2×D6111yescharacteristic
244C2×M32—611no—
245C2×M32C2×D6111yescharacteristic
246#499—611no—
247#499—611no—
248#485—1221no—
249#485—1221no—
250#483—1221no—
251#483—1221no—
252#479—1221no—
253#479—1221no—
254#467—611no—
255#467—611no—
256#467C2×D6111yescharacteristic
257#467C2×D6111yescharacteristic
258C4×Q16—611no—
259C4×Q16—611no—
260C8×D4—611no—
261#427—611no—
262#427—611no—
263C2×#107—611no—
264C2×#107—611no—
265#367—611no—
266#367—611no—
267#367—611no—
268#367C2×D6111yescharacteristic
269#366—611no—
270#366—611no—
271#366—611no—
272#366—611no—
273#366—611no—
274C4⋊C16—611no—
275#358—611no—
276#358—611no—
277#358—611no—
278#358—611no—
279#358C2×D6111yescharacteristic
280#358C2×D6111yescharacteristic
281C22⋊C16—611no—
282C22⋊C16—611no—
283C4×C16—611no—
284C61#3391911yescharacteristic, complemented, Sylow
285C2×Q16C22×D6111yescharacteristic
286C2×Q16C22×D6111yescharacteristic
287C22×C8—611no—
288C22×C8C22×D6111yescharacteristic
289#126—2441no—
290#126—2441no—
291#125—1221no—
292#125—1221no—
293#125—2441no—
294#125—2441no—
295#123—2441no—
296#123—2441no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—1221no—
300C22⋊Q8—1221no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×D4—611no—
304#117—1221no—
305#117—1221no—
306#117—2441no—
307#117—2441no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310Q32—22no—
311M32—22no—
312M32—1222no—
313C2×C16—611no—
314C2×C16—611no—
315C2×C16C22×D6111yescharacteristic
316C2×C16C22×D6111yescharacteristic
317#107—611no—
318#107—611no—
319#107—611no—
320#107—611no—
321#107—1221no—
322#107—1221no—
323#107C22×D6111yescharacteristic
324#107C22×D6111yescharacteristic
325#106—1221no—
326#106—1221no—
327#106—1221no—
328#106—1221no—
329C4⋊C8—611no—
330#103—21no—
331#103—21no—
332#103—1221no—
333#103—1221no—
334#103—1221no—
335#103—1221no—
336C22⋊C8—611no—
337C22⋊C8—611no—
338C4×C8—611no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×D4—611no—
342C22×C4—611no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4D4×D6111yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—611no—
353C2×C8—611no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8D4×D6111yescharacteristic
357C2×C8C23×D6111yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—611no—
363C4⋊C4—1221no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—611no—
380C22⋊C4—611no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C42—611no—
386C42—2441no—
387C42—2441no—
388C42—2441no—
389C42—2441no—
390C16—21no—
391C16—1221no—
392C16—1221no—
393C16#1175822412yes—
394C23—611no—
395C23D8×D6111yescharacteristic
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400D4—2441no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—611no—
408C2×C4—611no—
409C2×C4—611no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—4882no—
413C2×C4—4882no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4D8×D6111yescharacteristic
419C2×C4C2×D4×D6111yescharacteristic
420C8—21no—
421C8—1221no—
422C8—1221no—
423C8C2×#1175822411yescharacteristic
424C8#1451982411yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—1221no—
429C22—1221no—
430C22—1221no—
431C22C2×D8×D6111yescharacteristic
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—1221no—
438C4—1221no—
439C4—1221no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C4—4881no—
444C4#1684041211yescharacteristic
445C4#1684057611yescharacteristic
446C2—41no—
447C2—2441no—
448C2#2145816311yescharacteristic
449C2#2145895411yescharacteristic
450C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2219C2
socleC22×C61C22×D8
prime radicalC2×C22⋊D61D8
hypercenter#2219D61
hypocenterC61#33919
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
3. #21448097C2semidirect
4. #21448025C2semidirect
5. #21448024C2semidirect
6. #21448020C2semidirect
7. #21448019C2semidirect
8. #21447985C2semidirect
9. #21447981C2semidirect
10. #21447924C2semidirect
11. Q32×Dic61C2semidirect
13. #21447607C2semidirect
14. #21447606C2semidirect
15. C61×#2219C2semidirect
231. #2219D61semidirect
284. C61#33919semidirect

Maximal subgroups

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

subgroupindex
#214581902
#214581822
#214480972
#214480252
#214480242
#214480202
#214480192
#214479852
#214479812
#214479242
Q32×Dic612
#214476492
#214476072
#214476062
C61×#22192
#3391961