Finite Group Databasebeta

← #29835166

Subgroups — #29835166

Order 15616.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456458C211yesmaximal, characteristic
2#21448027C211yesmaximal, characteristic, complemented
3#21448010C211yesmaximal, characteristic
4#21447971C211yesmaximal, characteristic, complemented
5#21447961C211yesmaximal, characteristic, complemented
6#21447881C211yesmaximal, characteristic, complemented
7#21447881C211yesmaximal, characteristic, complemented
8#21447753C211yesmaximal, characteristic, complemented
9#21447736C211yesmaximal, characteristic
10#21447688C211yesmaximal, characteristic, complemented
11#21447681C211yesmaximal, characteristic, complemented
12C4×#14519723C211yesmaximal, characteristic, complemented
13C4×#14519720C211yesmaximal, characteristic, complemented
14#21447626C211yesmaximal, characteristic, complemented
15C61×#2950C211yesmaximal, characteristic, complemented
16#16840383—21no—
17C2×#14519723C2211yescharacteristic
18C2×#14519723C2211yescharacteristic
19C2×#14519720C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21#16840167C2211yescharacteristic
22#16840146C2211yescharacteristic
23#16840122—21no—
24#16840008—21no—
25#16840003C2211yescharacteristic
26#16839998C2211yescharacteristic
27#16839864—21no—
28C4×Dic244C2211yescharacteristic
29C4×D488C2211yescharacteristic
30#16839589C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839587C2211yescharacteristic
33#16839587C2211yescharacteristic
34C4⋊#11758185C2211yescharacteristic
35C4⋊#11758185C2211yescharacteristic
36#16839566C2211yescharacteristic
37#16839566C2211yescharacteristic
38#16839566C2211yescharacteristic
39#16839566C2211yescharacteristic
40#16839565C2211yescharacteristic
41#16839565C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44C22⋊#11758185C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46#16839538C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C22×Q16×C61C2211yescharacteristic
49C61×#519—21no—
50C61×#441—21no—
51C61×#441—21no—
52C4×Q16×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C4×Q16×C61C2211yescharacteristic
55C4×Q16×C61C2211yescharacteristic
56C61×#427C2211yescharacteristic
57C61×#419—21no—
58C61×#405C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758190—21no—
61C2×D488C2311yescharacteristic
62#14519777—21no—
63#14519772—41no—
64#14519765—21no—
65#14519763—41no—
66#14519759—41no—
67#14519756—21no—
68#14519755—41no—
69#14519751—21no—
70C4×Dic122—21no—
71C4×D244—21no—
72#14519723—22no—
73#14519723—22no—
74#14519720—22no—
75#14519720—22no—
76C2×#11758185C2311yescharacteristic
77C2×#11758185C2311yescharacteristic
78C2×#11758185C2311yescharacteristic
79C2×#11758185C2311yescharacteristic
80#14519711—21no—
81#14519711C2311yescharacteristic
82#14519711C2311yescharacteristic
83#14519702—21no—
84#14519702—21no—
85#14519699—21no—
86#14519699—21no—
87C22×Q8×C61—21no—
88C2×Q16×C61—22no—
89C2×Q16×C61—22no—
90C2×Q16×C61—21no—
91C2×Q16×C61C2311yescharacteristic
92C2×Q16×C61C2311yescharacteristic
93C2×M16×C61D411yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C4×Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×Q8×C61—21no—
98C4×Q8×C61—21no—
99C4×Q8×C61—41no—
100C4×Q8×C61—41no—
101#117×C61—21no—
102#117×C61—41no—
103#117×C61—41no—
104#117×C61D411yescharacteristic
105#107×C61C2311yescharacteristic
106#107×C61C2311yescharacteristic
107#106×C61—21no—
108#103×C61—21no—
109#103×C61—21no—
110#103×C61—21no—
111#103×C61—21no—
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—24no—
117C2×Q8×C61—21no—
118C2×Q8×C61—21no—
119C2×Q8×C61—42no—
120C2×Q8×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61C2×D411yescharacteristic
123C2×C22⋊D61—41no—
124C2×D244—21no—
125C2×C4×D61—41no—
126C2×Dic122—21no—
127C2×Dic122—41no—
128Q16×C61—24no—
129Q16×C61—21no—
130Q16×C61—21no—
131Q16×C61#4112yes—
132Q16×C61#4112yes—
133M16×C61—41no—
134C2×C8×C61—21no—
135C2×C8×C61—21no—
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2411yescharacteristic
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61D811yescharacteristic
147C4⋊C4×C61D811yescharacteristic
148C22⋊C4×C61—41no—
149C22⋊C4×C61D811yescharacteristic
150C22⋊C4×C61D811yescharacteristic
151C42×C61—41no—
152C42×C61—41no—
153C42×C61—41no—
154C42×C61—41no—
155C42×C61—41no—
156C42×C61C2×D411yescharacteristic
157C42×C61C2×D411yescharacteristic
158C22⋊Dic61—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198—41no—
162#11758198—41no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166#11758196—41no—
167#11758196—41no—
168C4×Dic61—41no—
169Dic244—21no—
170Dic244—21no—
171D488—21no—
172D488—21no—
173#11758190—42no—
174#11758185—21no—
175#11758185—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61C2×D811yescharacteristic
179C22×D61—41no—
180Q8×C61—22no—
181Q8×C61—22no—
182Q8×C61—44no—
183Q8×C61—41no—
184Q8×C61—41no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—44no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C22⋊D61—161no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202D244—41no—
203D244—41no—
204C4×D61—161no—
205Dic122—41no—
206Dic122—41no—
207Dic122—161no—
208C8×C61—21no—
209C8×C61—21no—
210C8×C61—21no—
211C8×C61C2×#4111yescharacteristic
212C8×C61C2×#4111yescharacteristic
213#33681—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61C22×D811yescharacteristic
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—42no—
227C4×C61—42no—
228C4×C61—81no—
229C4×C61—81no—
230C4×C61#52511yescharacteristic
231C4×C61#57511yescharacteristic
232Dic61—81no—
233Dic61—81no—
234Dic61—81no—
235#3175—611no—
236#2950D6111yescharacteristic, complemented
237#2237—611no—
238#2234—611no—
239#2227—611no—
240#2225—611no—
241#2211—611no—
242#2211—611no—
243#2188—611no—
244#2185—611no—
245#2176—611no—
246#2175—611no—
247C4×Q32—611no—
248C4×SD32—611no—
249#2164—611no—
250C2×C61—41no—
251C2×C61#310011yescharacteristic
252C2×C61#341611yescharacteristic
253C2×C61#341711yescharacteristic
254D61—161no—
255C22×Q16C2×D6111yescharacteristic
256#542—1221no—
257#519—21no—
258C2×Q32—611no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262#500—611no—
263#495—611no—
264#489—1221no—
265#468—1221no—
266#467—611no—
267#466—611no—
268#441—21no—
269#441—21no—
270#440—1221no—
271C4×Q16—611no—
272C4×Q16C2×D6111yescharacteristic
273C4×Q16C2×D6111yescharacteristic
274C4×Q16C2×D6111yescharacteristic
275C4×Q16C2×D6111yescharacteristic
276C4×D8—611no—
277#427C2×D6111yescharacteristic
278#419—21no—
279#405C2×D6111yescharacteristic
280#367—611no—
281#367—611no—
282#366—611no—
283#366—611no—
284C4⋊C16—611no—
285C4⋊C16—611no—
286#358—611no—
287#358—611no—
288#358—611no—
289#358—611no—
290#358—611no—
291#358—611no—
292#357—611no—
293#357—611no—
294C22⋊C16—611no—
295C22⋊C16—611no—
296#346—611no—
297C4×C16—611no—
298C61#3368111yescharacteristic, complemented, Sylow
299C22×Q8—21no—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×Q16—21no—
303C2×Q16—611no—
304C2×Q16C22×D6111yescharacteristic
305C2×Q16C22×D6111yescharacteristic
306C2×SD16—1221no—
307C2×D8—611no—
308C2×M16C22⋊D6111yescharacteristic
309C22×C8C22×D6111yescharacteristic
310C4⋊Q8—1221no—
311#126—2441no—
312#124—1221no—
313#124—2441no—
314#123—2441no—
315C22⋊Q8—1221no—
316C22⋊Q8—2441no—
317#121—1221no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—41no—
323C4×Q8—41no—
324C4×Q8—1221no—
325C4×D4—1221no—
326#117—21no—
327#117—41no—
328#117—41no—
329#117C22⋊D6111yescharacteristic
330Q32—1222no—
331Q32—1222no—
332SD32—1222no—
333SD32—1222no—
334C2×C16—611no—
335C2×C16—611no—
336C2×C16—611no—
337C2×C16—611no—
338#107—611no—
339#107—611no—
340#107—1221no—
341#107C22×D6111yescharacteristic
342#107C22×D6111yescharacteristic
343#106—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#103—21no—
348#103—1221no—
349#103—1221no—
350#102—1221no—
351#102—1221no—
352#97C22⋊D6111yescharacteristic
353#97C22⋊D6111yescharacteristic
354C4×C8C22×D6111yescharacteristic
355C4×C8C22×D6111yescharacteristic
356C2×Q8—24no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—41no—
361C2×Q8—1221no—
362C2×Q8—2441no—
363C2×D4—1221no—
364C2×D4—2441no—
365C22×C4—41no—
366C22×C4—2441no—
367C22×C4C2×C22⋊D6111yescharacteristic
368Q16—24no—
369Q16—21no—
370Q16—21no—
371Q16—1221no—
372Q16—1221no—
373Q16#1175822212yes—
374Q16#1175822212yes—
375SD16—2442no—
376D8—1221no—
377D8—1221no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D6111yescharacteristic
382C2×C8C2×C22⋊D6111yescharacteristic
383C2×C8C2×C22⋊D6111yescharacteristic
384C2×C8C23×D6111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4#1175819911yescharacteristic
397C4⋊C4#1175819911yescharacteristic
398C22⋊C4—41no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C22⋊C4#1175819911yescharacteristic
405C22⋊C4#1175819911yescharacteristic
406C42—41no—
407C42—41no—
408C42—41no—
409C42—41no—
410C42—41no—
411C42—2441no—
412C42C2×C22⋊D6111yescharacteristic
413C42C2×C22⋊D6111yescharacteristic
414C16—1221no—
415C16—1221no—
416C16—1221no—
417C16—1221no—
418C23—2441no—
419C23C2×#1175819911yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8—9761no—
426Q8—2441no—
427Q8—2441no—
428D4—9761no—
429D4—2441no—
430D4—2441no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—9761no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4C2×#1175819911yescharacteristic
443C2×C4C2×#1175819911yescharacteristic
444C2×C4C2×#1175819911yescharacteristic
445C2×C4C2×#1175819911yescharacteristic
446C2×C4C2×#1175819911yescharacteristic
447C2×C4C22×C22⋊D6111yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#1175822211yescharacteristic
452C8C2×#1175822211yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—4881no—
457C22—4881no—
458C22—4881no—
459C22C22×#1175819911yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—4881no—
470C4—4881no—
471C4—4881no—
472C4#1684027311yescharacteristic
473C4#1684056011yescharacteristic
474C2—41no—
475C2—9761no—
476C2#2145581911yescharacteristic
477C2#2145896311yescharacteristic
478C2#2145897011yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2950C2
socleC22×C61C22×D8
prime radical#16839998C22
hypercenter#2950D61
hypocenterC61#33681
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2950

Complements

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

NH ≅ G/Ntype
2. #21448027C2semidirect
4. #21447971C2semidirect
5. #21447961C2semidirect
6. #21447881C2semidirect
7. #21447881C2semidirect
8. #21447753C2semidirect
10. #21447688C2semidirect
11. #21447681C2semidirect
12. C4×#14519723C2semidirect
13. C4×#14519720C2semidirect
14. #21447626C2semidirect
15. C61×#2950C2semidirect
236. #2950D61semidirect
298. C61#33681semidirect

Maximal subgroups

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

subgroupindex
#214564582
#214480272
#214480102
#214479712
#214479612
#214478812
#214477532
#214477362
#214476882
#214476812
C4×#145197232
C4×#145197202
#214476262
C61×#29502
#3368161