Finite Group Databasebeta

← #29837633

Subgroups — #29837633

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458246C211yesmaximal, characteristic
2#21458208C211yesmaximal, characteristic
3#21448100C211yesmaximal, characteristic, complemented
4#21448026C211yesmaximal, characteristic, complemented
5#21448024C211yesmaximal, characteristic, complemented
6#21448015C211yesmaximal, characteristic, complemented
7#21448014C211yesmaximal, characteristic, complemented
8#21447969C211yesmaximal, characteristic, complemented
9#21447959C211yesmaximal, 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#16840483—21no—
17#16840470—21no—
18C2×#14519716C2211yescharacteristic
19#16840166C2211yescharacteristic
20#16840166C2211yescharacteristic
21#16840101—21no—
22#16840100—21no—
23#16840096—21no—
24#16840095—21no—
25#16840055—21no—
26#16840045—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#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839588C2211yescharacteristic
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#14519776—21no—
61#14519776—21no—
62#14519772—41no—
63#14519770—41no—
64#14519767—41no—
65#14519763—41no—
66#14519757—41no—
67#14519754—41no—
68#14519753—21no—
69#14519753—21no—
70Q8×Dic61—21no—
71Q8×Dic61—21no—
72#14519742—41no—
73C4×C22⋊D61D411yescharacteristic
74#14519737—41no—
75#14519736—21no—
76#14519735—21no—
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#14519710—21no—
89#14519710—21no—
90#14519709—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
120C2×Dic122—41no—
121C2×Dic122—41no—
122Q16×C61—21no—
123Q16×C61—21no—
124Q16×C61—21no—
125Q16×C61—21no—
126C2×C8×C61—21no—
127C2×C8×C61—21no—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C22⋊Dic61—41no—
137C22⋊Dic61D811yescharacteristic
138#11758198—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198D811yescharacteristic
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
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—22no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—161no—
188C2×Dic61C2×D811yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190C2×Dic61C2×D811yescharacteristic
191C4×D61—21no—
192C4×D61—21no—
193C4×D61—161no—
194Dic122—82no—
195Dic122—161no—
196C8×C61—21no—
197C8×C61C2×#4111yescharacteristic
198C8×C612−1+411yescharacteristic
199#92418—21no—
200#92418—21no—
201#33923—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61C22×D811yescharacteristic
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—21no—
209C4×C61—21no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61—81no—
213C4×C61—81no—
214C4×C61#54711yescharacteristic
215C4×C61#57811yescharacteristic
216Dic61—21no—
217Dic61—21no—
218Dic61—81no—
219Dic61—81no—
220Dic61—81no—
221Dic61—81no—
222Dic61#51012yes—
223#3342—611no—
224#3338—611no—
225#2254—611no—
226#2237—611no—
227#2237—611no—
228#2235—611no—
229#2235—611no—
230#2227—611no—
231#2225—611no—
232#2219—611no—
233#2219D6111yescharacteristic, complemented
234C4×Q32—611no—
235#2169—611no—
236#2159—611no—
237#2159—611no—
238C2×C61—41no—
239C2×C61#333411yescharacteristic
240C2×C61C2×#51011yescharacteristic
241C2×C61#341611yescharacteristic
242D61—41no—
243#556—1221no—
244#554—1221no—
245C2×Q32C2×D6111yescharacteristic
246C2×M32—611no—
247C2×M32C2×D6111yescharacteristic
248#500—611no—
249#500—611no—
250#485—1221no—
251#485—1221no—
252#484—1221no—
253#484—1221no—
254#477—1221no—
255#475—1221no—
256#467—611no—
257#467—611no—
258#467C2×D6111yescharacteristic
259#467C2×D6111yescharacteristic
260C4×Q16—611no—
261C4×Q16—611no—
262C8×D4—611no—
263#427—611no—
264#427—611no—
265C2×#107—611no—
266C2×#107—611no—
267#367—611no—
268#367—611no—
269#367—611no—
270#367—611no—
271#367—611no—
272#367C2×D6111yescharacteristic
273#366—611no—
274#366—611no—
275#366—611no—
276C4⋊C16—611no—
277#358—611no—
278#358—611no—
279#358—611no—
280#358—611no—
281#358C2×D6111yescharacteristic
282#358C2×D6111yescharacteristic
283C22⋊C16—611no—
284C22⋊C16—611no—
285C4×C16—611no—
286C61#3392311yescharacteristic, complemented, Sylow
287C2×Q16C22×D6111yescharacteristic
288C2×Q16C22×D6111yescharacteristic
289C22×C8—611no—
290C22×C8C22×D6111yescharacteristic
291C4⋊Q8—1221no—
292C4⋊Q8—1221no—
293#126—2441no—
294#126—2441no—
295#125—2441no—
296#124—2441no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—1221no—
300C22⋊Q8—1221no—
301C22⋊Q8—2441no—
302C22⋊Q8—2441no—
303C4×Q8—1221no—
304C4×Q8—1221no—
305C4×Q8—2441no—
306C4×D4—611no—
307C4×D4—2441no—
308#117—1221no—
309#117—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—1221no—
312Q32—22no—
313M32—22no—
314M32—1222no—
315C2×C16—611no—
316C2×C16—611no—
317C2×C16C22×D6111yescharacteristic
318C2×C16C22×D6111yescharacteristic
319#107—611no—
320#107—611no—
321#107—611no—
322#107—611no—
323#107—1221no—
324#107—1221no—
325#107—1221no—
326#107—1221no—
327#107C22×D6111yescharacteristic
328#107C22×D6111yescharacteristic
329#106—1221no—
330#106—1221no—
331C4⋊C8—611no—
332#103—21no—
333#103—21no—
334#103—1221no—
335#103—1221no—
336#103—1221no—
337#103—1221no—
338C22⋊C8—611no—
339C22⋊C8—611no—
340C4×C8—611no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—2441no—
344C2×Q8—2441no—
345C2×D4—611no—
346C22×C4—611no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4D4×D6111yescharacteristic
350Q16—21no—
351Q16—21no—
352Q16—21no—
353Q16—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—611no—
357C2×C8—611no—
358C2×C8—1221no—
359C2×C8—1221no—
360C2×C8D4×D6111yescharacteristic
361C2×C8C23×D6111yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—611no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—611no—
382C22⋊C4—611no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C42—611no—
388C42—2441no—
389C42—2441no—
390C42—2441no—
391C42—2441no—
392C16—21no—
393C16—1221no—
394C16—1221no—
395C16#1175822412yes—
396C23—611no—
397C23D8×D6111yescharacteristic
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—9761no—
403Q8—4882no—
404D4—1222no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—611no—
412C2×C4—611no—
413C2×C4—611no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—9761no—
417C2×C4—9761no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4D8×D6111yescharacteristic
423C2×C4C2×D4×D6111yescharacteristic
424C8—21no—
425C8—1221no—
426C8—1221no—
427C8C2×#1175822411yescharacteristic
428C8#1451982411yescharacteristic
429C22—21no—
430C22—21no—
431C22—21no—
432C22—1221no—
433C22—1221no—
434C22—1221no—
435C22C2×D8×D6111yescharacteristic
436C4—21no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—612no—
442C4—1221no—
443C4—1221no—
444C4—4881no—
445C4—4881no—
446C4—4881no—
447C4—4881no—
448C4#1684041211yescharacteristic
449C4#1684057611yescharacteristic
450C2—41no—
451C2—2441no—
452C2#2145816311yescharacteristic
453C2#510×D6111yescharacteristic
454C2#2145896411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2219C2
socleC22×C61C22×D8
prime radicalC2×C22⋊D61D8
hypercenter#2219D61
hypocenterC61#33923
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. #21448100C2semidirect
4. #21448026C2semidirect
5. #21448024C2semidirect
6. #21448015C2semidirect
7. #21448014C2semidirect
8. #21447969C2semidirect
9. #21447959C2semidirect
10. #21447924C2semidirect
11. Q32×Dic61C2semidirect
13. #21447607C2semidirect
14. #21447606C2semidirect
15. C61×#2219C2semidirect
233. #2219D61semidirect
286. C61#33923semidirect

Maximal subgroups

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

subgroupindex
#214582462
#214582082
#214481002
#214480262
#214480242
#214480152
#214480142
#214479692
#214479592
#214479242
Q32×Dic612
#214476492
#214476072
#214476062
C61×#22192
#3392361