Finite Group Databasebeta

← #29837583

Subgroups — #29837583

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458222C211yesmaximal, characteristic
2#21448095C211yesmaximal, characteristic, complemented
3#21448024C211yesmaximal, characteristic, complemented
4#21448014C211yesmaximal, characteristic, complemented
5#21448010C211yesmaximal, characteristic, complemented
6#21448004C211yesmaximal, characteristic, complemented
7#21447983C211yesmaximal, characteristic, complemented
8#21447973C211yesmaximal, characteristic, complemented
9#21447934C211yesmaximal, characteristic, complemented
10#21447934C211yesmaximal, characteristic, complemented
11C4×#14519720C211yesmaximal, characteristic, complemented
12#21447651C211yesmaximal, characteristic, complemented
13#21447608C211yesmaximal, characteristic, complemented
14#21447605C211yesmaximal, characteristic, complemented
15C61×#3336C211yesmaximal, characteristic, complemented
16#16840458—21no—
17C2×#14519720C2211yescharacteristic
18C2×#14519717C2211yescharacteristic
19C2×#14519717C2211yescharacteristic
20#16840164C2211yescharacteristic
21#16840087—21no—
22#16840081—21no—
23#16840063—21no—
24#16839998C2211yescharacteristic
25#16839998C2211yescharacteristic
26C4×D488C2211yescharacteristic
27#16839800C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29#16839589C2211yescharacteristic
30#16839589C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839589C2211yescharacteristic
34#16839587C2211yescharacteristic
35#16839587C2211yescharacteristic
36#16839587C2211yescharacteristic
37#16839587C2211yescharacteristic
38C4⋊#11758185C2211yescharacteristic
39#16839566C2211yescharacteristic
40#16839566C2211yescharacteristic
41#16839566C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44#16839562C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C61×#552—21no—
49C61×#499C2211yescharacteristic
50C61×#485—21no—
51C61×#483—21no—
52C61×#479—21no—
53C61×#467C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C4×Q16×C61C2211yescharacteristic
56C8×D4×C61C2211yescharacteristic
57C61×#427C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×D488C2311yescharacteristic
60#14519772—41no—
61#14519769—21no—
62#14519759—41no—
63#14519751—21no—
64#14519751—21no—
65#14519749—41no—
66C4×D244—21no—
67#14519737—41no—
68#14519736—21no—
69C2×C4⋊Dic61—21no—
70#14519720—22no—
71#14519717—22no—
72#14519717—22no—
73C2×#11758185C2311yescharacteristic
74C2×#11758185C2311yescharacteristic
75C2×#11758185C2311yescharacteristic
76C2×#11758185C2311yescharacteristic
77#14519711—21no—
78#14519711C2311yescharacteristic
79#14519711C2311yescharacteristic
80#14519711C2311yescharacteristic
81#14519709—21no—
82#14519709—21no—
83#14519699—21no—
84#14519699—21no—
85#14519699—21no—
86C2×Q16×C61C2311yescharacteristic
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89#126×C61—41no—
90#125×C61—21no—
91#125×C61—41no—
92#123×C61—41no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×D4×C61D411yescharacteristic
97#117×C61—21no—
98#117×C61—41no—
99C2×C4⋊C4×C61—21no—
100#107×C61—21no—
101#107×C61C2311yescharacteristic
102#107×C61C2311yescharacteristic
103#107×C61C2311yescharacteristic
104#106×C61—21no—
105#106×C61—21no—
106C4⋊C8×C61D411yescharacteristic
107#103×C61—21no—
108#103×C61—21no—
109#103×C61—21no—
110C22⋊C8×C61D411yescharacteristic
111C22⋊C8×C61D411yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×D4×C61D811yescharacteristic
115C22×C4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C22×Dic61—41no—
121C2×D244—21no—
122C2×C4×D61—41no—
123Q16×C61—21no—
124Q16×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61—21no—
127C2×C8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2411yescharacteristic
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61D811yescharacteristic
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61D811yescharacteristic
147C22⋊C4×C61D811yescharacteristic
148C42×C61—41no—
149C42×C61—41no—
150C42×C61C2×D411yescharacteristic
151C22⋊Dic61—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—21no—
158C4⋊Dic61—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162D488—21no—
163D488—21no—
164#11758185—21no—
165#11758185—21no—
166#11758185—21no—
167#11758185#4112yes—
168C23×C61C2×D811yescharacteristic
169C23×C61C2×D811yescharacteristic
170C22×D61—41no—
171Q8×C61—41no—
172Q8×C61—41no—
173D4×C61—41no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—82no—
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C22⋊D61—82no—
189C22⋊D61—161no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—161no—
194D244—41no—
195D244—41no—
196C4×D61—161no—
197C8×C61—21no—
198C8×C61—21no—
199C8×C61—21no—
200C8×C61C2×#4111yescharacteristic
201C8×C612−1+411yescharacteristic
202#33918—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61C22×D811yescharacteristic
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61—81no—
221C4×C61#54711yescharacteristic
222C4×C61#57811yescharacteristic
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226#3339—611no—
227#3336D6111yescharacteristic, complemented
228#2253—611no—
229#2237—611no—
230#2235—611no—
231#2234—611no—
232#2233—611no—
233#2229—611no—
234#2228—611no—
235#2220—611no—
236#2220—611no—
237C4×SD32—611no—
238#2169—611no—
239#2159—611no—
240#2159—611no—
241C2×C61—41no—
242C2×C61—41no—
243C2×C61#333411yescharacteristic
244C2×C61#341411yescharacteristic
245C2×C61#341611yescharacteristic
246D61—161no—
247#553—1221no—
248#552—21no—
249C2×SD32—611no—
250C2×M32—611no—
251C2×M32—611no—
252#499—611no—
253#499C2×D6111yescharacteristic
254#485—21no—
255#483—21no—
256#482—1221no—
257#481—1221no—
258#479—21no—
259#478—1221no—
260#467C2×D6111yescharacteristic
261#467C2×D6111yescharacteristic
262#466—611no—
263#466—611no—
264C4×Q16C2×D6111yescharacteristic
265C4×D8—611no—
266C8×D4C2×D6111yescharacteristic
267#427—611no—
268#427C2×D6111yescharacteristic
269C2×#107—611no—
270C2×#107C2×D6111yescharacteristic
271#367—611no—
272#367—611no—
273#367—611no—
274#367—611no—
275#367—611no—
276#366—611no—
277#366—611no—
278#366—611no—
279#366—611no—
280C4⋊C16—611no—
281#358—611no—
282#358—611no—
283#358—611no—
284#357—611no—
285#357—611no—
286#357—611no—
287C22⋊C16—611no—
288C22⋊C16—611no—
289C4×C16—611no—
290C61#3391811yescharacteristic, complemented, Sylow
291C2×Q16C22×D6111yescharacteristic
292C2×D8—611no—
293C22×C8C22×D6111yescharacteristic
294C22×C8C22×D6111yescharacteristic
295#126—41no—
296#126—2441no—
297#125—21no—
298#125—41no—
299#125—1221no—
300#123—41no—
301#123—2441no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304#121—1221no—
305#121—1221no—
306#121—2441no—
307C4×Q8—21no—
308C4×D4—1221no—
309C4×D4—2441no—
310C4×D4C22⋊D6111yescharacteristic
311#117—21no—
312#117—41no—
313#117—1221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—1221no—
316SD32—1222no—
317M32—1222no—
318M32—1222no—
319C2×C16—611no—
320C2×C16—611no—
321C2×C16—611no—
322C2×C16—611no—
323#107—21no—
324#107—611no—
325#107—611no—
326#107—611no—
327#107—1221no—
328#107C22×D6111yescharacteristic
329#107C22×D6111yescharacteristic
330#107C22×D6111yescharacteristic
331#106—21no—
332#106—21no—
333#106—1221no—
334#106—1221no—
335C4⋊C8C22⋊D6111yescharacteristic
336#103—21no—
337#103—21no—
338#103—21no—
339#102—1221no—
340#102—1221no—
341#102—1221no—
342C22⋊C8C22⋊D6111yescharacteristic
343C22⋊C8C22⋊D6111yescharacteristic
344C4×C8C22×D6111yescharacteristic
345C2×Q8—21no—
346C2×D4—1221no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4#1175819911yescharacteristic
350C22×C4—41no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4C2×C22⋊D6111yescharacteristic
354C22×C4C2×C22⋊D6111yescharacteristic
355Q16—21no—
356Q16—21no—
357D8—1221no—
358D8—1221no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×C22⋊D6111yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C2×C8C2×C22⋊D6111yescharacteristic
366C2×C8C23×D6111yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4#1175819911yescharacteristic
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4#1175819911yescharacteristic
391C22⋊C4#1175819911yescharacteristic
392C42—41no—
393C42—41no—
394C42—2441no—
395C42C2×C22⋊D6111yescharacteristic
396C16—612no—
397C16—1221no—
398C16—1221no—
399C16—1221no—
400C23—2441no—
401C23C2×#1175819911yescharacteristic
402C23C2×#1175819911yescharacteristic
403Q8—41no—
404Q8—41no—
405D4—41no—
406D4—9761no—
407D4—4882no—
408D4—2441no—
409D4—2441no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4—9761no—
420C2×C4—9761no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4C2×#1175819911yescharacteristic
425C2×C4C2×#1175819911yescharacteristic
426C2×C4C2×#1175819911yescharacteristic
427C2×C4C2×#1175819911yescharacteristic
428C2×C4C22×C22⋊D6111yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8#41×D6111yescharacteristic
433C8#1451982411yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—4881no—
441C22—4881no—
442C22—4881no—
443C22C22×#1175819911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—4881no—
453C4—4881no—
454C4—4881no—
455C4#1684041111yescharacteristic
456C4#1684057711yescharacteristic
457C2—41no—
458C2—41no—
459C2—9761no—
460C2#2145816211yescharacteristic
461C2#2145895311yescharacteristic
462C2#2145896311yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3336C2
socleC22×C61C22×D8
prime radical#21458222C2
hypercenter#3336D61
hypocenterC61#33918
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3336

Complements

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

NH ≅ G/Ntype
2. #21448095C2semidirect
3. #21448024C2semidirect
4. #21448014C2semidirect
5. #21448010C2semidirect
6. #21448004C2semidirect
7. #21447983C2semidirect
8. #21447973C2semidirect
9. #21447934C2semidirect
10. #21447934C2semidirect
11. C4×#14519720C2semidirect
12. #21447651C2semidirect
13. #21447608C2semidirect
14. #21447605C2semidirect
15. C61×#3336C2semidirect
227. #3336D61semidirect
290. C61#33918semidirect

Maximal subgroups

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

subgroupindex
#214582222
#214480952
#214480242
#214480142
#214480102
#214480042
#214479832
#214479732
#214479342
C4×#145197202
#214476512
#214476082
#214476052
C61×#33362
#3391861