Finite Group Databasebeta

← #29837585

Subgroups — #29837585

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#21458188C211yesmaximal, characteristic, complemented
3#21448098C211yesmaximal, characteristic, complemented
4#21448028C211yesmaximal, characteristic, complemented
5#21448017C211yesmaximal, characteristic, complemented
6#21448011C211yesmaximal, characteristic, complemented
7#21448005C211yesmaximal, characteristic, complemented
8#21447984C211yesmaximal, characteristic, complemented
9#21447977C211yesmaximal, characteristic, complemented
10#21447932C211yesmaximal, characteristic, complemented
11#21447932C211yesmaximal, characteristic, complemented
12C4×#14519722C211yesmaximal, characteristic, complemented
13#21447607C211yesmaximal, characteristic, complemented
14#21447607C211yesmaximal, characteristic, complemented
15C61×#2169C211yesmaximal, characteristic, complemented
16#16840458—21no—
17#16840452—21no—
18C2×#14519722C2211yescharacteristic
19#16840164C2211yescharacteristic
20#16840164C2211yescharacteristic
21#16840104—21no—
22#16840093—21no—
23#16840087—21no—
24#16840081—21no—
25#16840070—21no—
26#16840063—21no—
27#16840003C2211yescharacteristic
28#16840003C2211yescharacteristic
29#16839998C2211yescharacteristic
30#16839998C2211yescharacteristic
31C4×Dic244C2211yescharacteristic
32C4×D488C2211yescharacteristic
33#16839800C2211yescharacteristic
34#16839800C2211yescharacteristic
35C2×#14519711C2211yescharacteristic
36C2×#14519711C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839590C2211yescharacteristic
41#16839590C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839588C2211yescharacteristic
44#16839588C2211yescharacteristic
45#16839588C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839567C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C2×M32×C61C2211yescharacteristic
53C2×M32×C61C2211yescharacteristic
54C8×D4×C61C2211yescharacteristic
55C61×C4⋊C16C2211yescharacteristic
56C61×C22⋊C16C2211yescharacteristic
57C61×C22⋊C16C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×D488C2311yescharacteristic
61#14519772—41no—
62#14519770—41no—
63#14519769—21no—
64#14519769—21no—
65#14519767—41no—
66#14519759—41no—
67#14519758—41no—
68#14519756—21no—
69#14519756—21no—
70#14519751—21no—
71#14519751—21no—
72#14519749—41no—
73C4×Dic122—21no—
74C4×D244—21no—
75#14519737—41no—
76#14519736—21no—
77#14519736—21no—
78#14519733—41no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81#14519722—22no—
82#14519711—21no—
83#14519711—21no—
84#14519711C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519709—21no—
91#14519709—21no—
92#14519709—21no—
93#14519709—21no—
94#14519702—21no—
95#14519702—21no—
96#14519702—21no—
97#14519699—21no—
98#14519699—21no—
99#14519699—21no—
100C22×C8×C61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102C4×D4×C61D411yescharacteristic
103M32×C61—22no—
104M32×C61—22no—
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108C2×C16×C61C2311yescharacteristic
109C4⋊C8×C61D411yescharacteristic
110C22⋊C8×C61D411yescharacteristic
111C22⋊C8×C61D411yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×D4×C61D811yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C2×D244—21no—
121C2×C4×D61—41no—
122C2×Dic122—21no—
123C2×C8×C61—21no—
124C2×C8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61—21no—
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2411yescharacteristic
131C4⋊C4×C61D811yescharacteristic
132C22⋊C4×C61D811yescharacteristic
133C22⋊C4×C61D811yescharacteristic
134C42×C61C2×D411yescharacteristic
135C22⋊Dic61—41no—
136C22⋊Dic61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198—41no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160Dic244—21no—
161Dic244—21no—
162D488—21no—
163D488—21no—
164C16×C61—21no—
165C16×C61—21no—
166C16×C61—21no—
167C16×C61#4112yes—
168C23×C61C2×D811yescharacteristic
169C23×C61C2×D811yescharacteristic
170C22×D61—41no—
171D4×C61—41no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61C2×D811yescharacteristic
177C2×C4×C61C2×D811yescharacteristic
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C22⋊D61—82no—
182C22⋊D61—161no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—82no—
191C2×Dic61—161no—
192D244—41no—
193D244—41no—
194C4×D61—161no—
195Dic122—41no—
196Dic122—41no—
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#54711yescharacteristic
218C4×C61#57811yescharacteristic
219Dic61—81no—
220Dic61—81no—
221Dic61—81no—
222Dic61—81no—
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226#3339—611no—
227#3336—611no—
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#2169D6111yescharacteristic, complemented
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—1221no—
249C2×SD32—611no—
250C2×M32C2×D6111yescharacteristic
251C2×M32C2×D6111yescharacteristic
252#499—611no—
253#499—611no—
254#485—1221no—
255#483—1221no—
256#482—1221no—
257#481—1221no—
258#479—1221no—
259#478—1221no—
260#467—611no—
261#467—611no—
262#466—611no—
263#466—611no—
264C4×Q16—611no—
265C4×D8—611no—
266C8×D4C2×D6111yescharacteristic
267#427—611no—
268#427—611no—
269C2×#107—611no—
270C2×#107—611no—
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⋊C16C2×D6111yescharacteristic
281#358—611no—
282#358—611no—
283#358—611no—
284#357—611no—
285#357—611no—
286#357—611no—
287C22⋊C16C2×D6111yescharacteristic
288C22⋊C16C2×D6111yescharacteristic
289C4×C16C2×D6111yescharacteristic
290C61#3391811yescharacteristic, complemented, Sylow
291C2×Q16—611no—
292C2×D8—611no—
293C22×C8C22×D6111yescharacteristic
294C22×C8C22×D6111yescharacteristic
295#126—2441no—
296#126—2441no—
297#125—1221no—
298#125—1221no—
299#125—2441no—
300#123—2441no—
301#123—2441no—
302C22⋊Q8—1221no—
303C22⋊Q8—1221no—
304#121—1221no—
305#121—1221no—
306#121—2441no—
307C4×Q8—1221no—
308C4×D4—1221no—
309C4×D4—2441no—
310C4×D4D24411yescharacteristic
311#117—1221no—
312#117—1221no—
313#117—2441no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316SD32—1222no—
317M32—22no—
318M32—22no—
319C2×C16C22×D6111yescharacteristic
320C2×C16C22×D6111yescharacteristic
321C2×C16C22×D6111yescharacteristic
322C2×C16C22×D6111yescharacteristic
323#107—611no—
324#107—611no—
325#107—611no—
326#107—611no—
327#107—611no—
328#107—611no—
329#107—1221no—
330#107—1221no—
331#106—1221no—
332#106—1221no—
333#106—1221no—
334#106—1221no—
335C4⋊C8D24411yescharacteristic
336#103—1221no—
337#103—1221no—
338#103—1221no—
339#102—1221no—
340#102—1221no—
341#102—1221no—
342C22⋊C8D24411yescharacteristic
343C22⋊C8D24411yescharacteristic
344C4×C8C22×D6111yescharacteristic
345C2×Q8—1221no—
346C2×D4—1221no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4D48811yescharacteristic
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4C2×D24411yescharacteristic
354C22×C4C2×D24411yescharacteristic
355Q16—1221no—
356Q16—1221no—
357D8—1221no—
358D8—1221no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×D24411yescharacteristic
364C2×C8C2×D24411yescharacteristic
365C2×C8C2×D24411yescharacteristic
366C2×C8C23×D6111yescharacteristic
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4D48811yescharacteristic
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4D48811yescharacteristic
391C22⋊C4D48811yescharacteristic
392C42—2441no—
393C42—2441no—
394C42—2441no—
395C42C2×D24411yescharacteristic
396C16—21no—
397C16—21no—
398C16—21no—
399C16#1175822412yes—
400C23—2441no—
401C23C2×D48811yescharacteristic
402C23C2×D48811yescharacteristic
403Q8—2441no—
404Q8—2441no—
405D4—41no—
406D4—9761no—
407D4—4882no—
408D4—2441no—
409D4—2441no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—9761no—
415C2×C4—9761no—
416C2×C4—4882no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4C2×D48811yescharacteristic
425C2×C4C2×D48811yescharacteristic
426C2×C4C2×D48811yescharacteristic
427C2×C4C2×D48811yescharacteristic
428C2×C4C22×D24411yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×#1175822411yescharacteristic
433C8#1451982411yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—4881no—
441C22—4881no—
442C22—4881no—
443C22C22×D48811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—4881no—
449C4—4881no—
450C4—4881no—
451C4—4881no—
452C4—4881no—
453C4—4881no—
454C4—4881no—
455C4#1684041611yescharacteristic
456C4#1684057911yescharacteristic
457C2—41no—
458C2—41no—
459C2—9761no—
460C2#2145816711yescharacteristic
461C2#2145895511yescharacteristic
462C2#2145896711yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2169C2
socleC22×C61C22×D8
prime radical#21458222C2
hypercenter#2169D61
hypocenterC61#33918
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
2. #21458188C2semidirect
3. #21448098C2semidirect
4. #21448028C2semidirect
5. #21448017C2semidirect
6. #21448011C2semidirect
7. #21448005C2semidirect
8. #21447984C2semidirect
9. #21447977C2semidirect
10. #21447932C2semidirect
11. #21447932C2semidirect
12. C4×#14519722C2semidirect
13. #21447607C2semidirect
14. #21447607C2semidirect
15. C61×#2169C2semidirect
238. #2169D61semidirect
290. C61#33918semidirect

Maximal subgroups

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

subgroupindex
#214582222
#214581882
#214480982
#214480282
#214480172
#214480112
#214480052
#214479842
#214479772
#214479322
C4×#145197222
#214476072
C61×#21692
#3391861