Finite Group Databasebeta

← #29836444

Subgroups — #29836444

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456479C211yesmaximal, characteristic
2#21456474C211yesmaximal, characteristic
3#21447986C211yesmaximal, characteristic, complemented
4#21447982C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447928C211yesmaximal, characteristic
7#21447926C211yesmaximal, characteristic
8#21447911C211yesmaximal, characteristic
9#21447909C211yesmaximal, characteristic
10#21447870C211yesmaximal, characteristic, complemented
11#21447869C211yesmaximal, characteristic, complemented
12#21447868C211yesmaximal, characteristic, complemented
13#21447868C211yesmaximal, characteristic, complemented
14#21447576C211yesmaximal, characteristic
15C61×#2229C211yesmaximal, characteristic, complemented
16#16840375—21no—
17#16840370—21no—
18C2×Dic488C2211yescharacteristic
19C2×Dic488C2211yescharacteristic
20C2×#14519723C2211yescharacteristic
21C2×#14519723C2211yescharacteristic
22C2×#14519716C2211yescharacteristic
23C2×C16×D61C2211yescharacteristic
24#16840163C2211yescharacteristic
25#16840142C2211yescharacteristic
26#16840140C2211yescharacteristic
27#16840132—21no—
28#16840129—21no—
29#16840021—21no—
30#16840019—21no—
31#16840004C2211yescharacteristic
32#16840004C2211yescharacteristic
33#16840004C2211yescharacteristic
34#16840000C2211yescharacteristic
35#16839868—21no—
36#16839867—21no—
37C4×Dic244C2211yescharacteristic
38#16839856C2211yescharacteristic
39#16839856C2211yescharacteristic
40#16839716C2211yescharacteristic
41#16839589C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839565C2211yescharacteristic
50#16839565C2211yescharacteristic
51#16839565C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Dic244—21no—
60C2×Dic244C2311yescharacteristic
61C2×Dic244C2311yescharacteristic
62C2×Dic244C2311yescharacteristic
63C2×#11758202—21no—
64C2×#11758189D411yescharacteristic
65C2×C8×D61C2311yescharacteristic
66#14519777—21no—
67#14519775—21no—
68#14519772—41no—
69#14519772—41no—
70#14519772—41no—
71#14519771—41no—
72#14519769—41no—
73#14519768—21no—
74#14519768—41no—
75#14519768—41no—
76#14519767—41no—
77#14519757—21no—
78#14519757—21no—
79#14519757—21no—
80#14519753—21no—
81C4×Dic122—21no—
82#14519742—21no—
83#14519742—21no—
84#14519734D411yescharacteristic
85Dic488—41no—
86Dic488—41no—
87#14519723—41no—
88#14519723—41no—
89#14519716—41no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92C16×D61—41no—
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—
117C2×C4×D61C2×D411yescharacteristic
118C2×Dic122—21no—
119C2×Dic122—21no—
120C2×Dic122—21no—
121Q16×C61—21no—
122Q16×C61—21no—
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2411yescharacteristic
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—41no—
131C42×C61—41no—
132C42×C61C2×D411yescharacteristic
133#11758202—42no—
134#11758198—41no—
135#11758198—41no—
136#11758198—41no—
137#11758198—41no—
138#11758198D811yescharacteristic
139#11758198D811yescharacteristic
140C4⋊Dic61—21no—
141C4⋊Dic61—41no—
142C4⋊Dic61—41no—
143C4⋊Dic61—41no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196D811yescharacteristic
155#11758196D811yescharacteristic
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162Dic244—21no—
163Dic244—21no—
164Dic244—21no—
165Dic244—21no—
166Dic244—21no—
167Dic244—21no—
168Dic244—42no—
169#11758189—41no—
170C8×D61—21no—
171C8×D61—21no—
172C16×C61—21no—
173C16×C61—21no—
174#11758185—21no—
175#11758185—21no—
176C22×D61C2×D811yescharacteristic
177Q8×C61—41no—
178Q8×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61C2×D811yescharacteristic
191C2×Dic61C2×D811yescharacteristic
192C2×Dic61C2×D811yescharacteristic
193C4×D61—21no—
194C4×D61—21no—
195Dic122—41no—
196Dic122—41no—
197Dic122—41no—
198Dic122—41no—
199Dic122—41no—
200Dic122—41no—
201C8×C61—21no—
202C8×C61H(5,𝔽2)11yescharacteristic
203C8×C612−1+411yescharacteristic
204#92418—21no—
205#92418—21no—
206#33827—611nomaximal, Sylow
207C22×C61C22×D811yescharacteristic
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61#53711yescharacteristic
218C4×C61#57511yescharacteristic
219Dic61—21no—
220Dic61—21no—
221Dic61—21no—
222Dic61—81no—
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226#3177—611no—
227#3177—611no—
228#2229—611no—
229#2229—611no—
230#2229—611no—
231#2229D6111yescharacteristic, complemented
232#2219—611no—
233#2219—611no—
234#2216—611no—
235#2216—611no—
236#2209—611no—
237#2209—611no—
238#2209—611no—
239#2209—611no—
240#2151—611no—
241C2×C61#324511yescharacteristic
242C2×C61#341711yescharacteristic
243C2×C61#341711yescharacteristic
244D61—41no—
245#541—1221no—
246#541—1221no—
247C2×Q32—611no—
248C2×Q32—611no—
249C2×Q32—611no—
250C2×Q32—611no—
251C2×M32—611no—
252C22×C16—611no—
253#499—611no—
254#499C2×D6111yescharacteristic
255#494—611no—
256#494—611no—
257#491—1221no—
258#491—1221no—
259#470—1221no—
260#470—1221no—
261#467—611no—
262#467—611no—
263#467—611no—
264#467—611no—
265#441—1221no—
266#441—1221no—
267C4×Q16—611no—
268C4×Q16—611no—
269C4×Q16—611no—
270C4×Q16C2×D6111yescharacteristic
271#405—611no—
272#367—611no—
273#367C2×D6111yescharacteristic
274#366—611no—
275#366C2×D6111yescharacteristic
276C4⋊C16—611no—
277C4⋊C16—611no—
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
288C61#3382711yescharacteristic, complemented, Sylow
289C2×Q16—611no—
290C2×Q16—611no—
291C2×Q16—611no—
292C2×Q16—1221no—
293C2×Q16—1221no—
294C2×Q16C22×D6111yescharacteristic
295C2×M16—611no—
296C22×C8—611no—
297C4⋊Q8—1221no—
298C4⋊Q8—1221no—
299#126—2441no—
300#126—2441no—
301#126—2441no—
302#126—2441no—
303#125—21no—
304#125—1221no—
305#125—2441no—
306#125—2441no—
307#125—2441no—
308#125—2441no—
309C22⋊Q8—1221no—
310C22⋊Q8—1221no—
311C22⋊Q8—1221no—
312C22⋊Q8—1221no—
313C4×Q8—21no—
314C4×Q8—1221no—
315C4×Q8—1221no—
316C4×Q8—1221no—
317#117—611no—
318Q32—2441no—
319Q32—2441no—
320Q32—2441no—
321Q32—2441no—
322M32—2441no—
323C2×C16—611no—
324C2×C16—611no—
325C2×C16—2441no—
326C2×C16C22×D6111yescharacteristic
327C2×C16C22×D6111yescharacteristic
328#107—611no—
329#107C22×D6111yescharacteristic
330#107C22×D6111yescharacteristic
331#107C22×D6111yescharacteristic
332#106—21no—
333#106—1221no—
334#103—21no—
335#103—1221no—
336#103—1221no—
337#103—1221no—
338#103—1221no—
339#103—1221no—
340#103—1221no—
341#103—1221no—
342#97—611no—
343#97—611no—
344C4×C8—611no—
345C4×C8C22×D6111yescharacteristic
346C2×Q8—21no—
347C2×Q8—1221no—
348C2×Q8—1221no—
349C2×Q8—1221no—
350C22×C4—611no—
351Q16—21no—
352Q16—21no—
353Q16—1221no—
354Q16—1221no—
355Q16—1221no—
356Q16—1221no—
357Q16—1221no—
358Q16—1221no—
359Q16—2442no—
360Q16—2442no—
361M16—2441no—
362C2×C8—611no—
363C2×C8—611no—
364C2×C8—1221no—
365C2×C8—1221no—
366C2×C8D4×D6111yescharacteristic
367C2×C8C23×D6111yescharacteristic
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—611no—
375C4⋊C4—611no—
376C4⋊C4—1221no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
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—
390C22⋊C4—611no—
391C22⋊C4—611no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C42—41no—
397C42—611no—
398C42—2441no—
399C42—2441no—
400C42—2441no—
401C42D4×D6111yescharacteristic
402C16—21no—
403C16—21no—
404C16—1221no—
405C16—1221no—
406C23—611no—
407Q8—41no—
408Q8—41no—
409Q8—2441no—
410Q8—2441no—
411Q8—2441no—
412Q8—2441no—
413Q8—2441no—
414Q8—2441no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4D8×D6111yescharacteristic
429C2×C4D8×D6111yescharacteristic
430C2×C4C2×D4×D6111yescharacteristic
431C8—21no—
432C8—1221no—
433C8—1221no—
434C8#1451982311yescharacteristic
435C8#1451982511yescharacteristic
436C22—1221no—
437C22—1221no—
438C22—1221no—
439C22C2×D8×D6111yescharacteristic
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—1221no—
447C4—1221no—
448C4—1221no—
449C4—4881no—
450C4—4881no—
451C4—4881no—
452C4—4881no—
453C4#1684034211yescharacteristic
454C4#1684056111yescharacteristic
455C2—2441no—
456C2#2145712811yescharacteristic
457C2#2145896911yescharacteristic
458C2#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#33827
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
3. #21447986C2semidirect
4. #21447982C2semidirect
5. #21447980C2semidirect
10. #21447870C2semidirect
11. #21447869C2semidirect
12. #21447868C2semidirect
13. #21447868C2semidirect
15. C61×#2229C2semidirect
231. #2229D61semidirect
288. C61#33827semidirect

Maximal subgroups

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

subgroupindex
#214564792
#214564742
#214479862
#214479822
#214479802
#214479282
#214479262
#214479112
#214479092
#214478702
#214478692
#214478682
#214475762
C61×#22292
#3382761