Finite Group Databasebeta

← #29835138

Subgroups — #29835138

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456469C211yesmaximal, characteristic, complemented
2#21454696C211yesmaximal, characteristic, complemented
3#21448005C211yesmaximal, characteristic, complemented
4#21448000C211yesmaximal, characteristic, complemented
5#21447984C211yesmaximal, characteristic, complemented
6#21447977C211yesmaximal, characteristic, complemented
7#21447860C211yesmaximal, characteristic, complemented
8#21447855C211yesmaximal, characteristic, complemented
9#21447744C211yesmaximal, characteristic, complemented
10#21447744C211yesmaximal, characteristic, complemented
11#21447696C211yesmaximal, characteristic, complemented
12#21447685C211yesmaximal, characteristic, complemented
13C4×#14519722C211yesmaximal, characteristic, complemented
14C4×D976C211yesmaximal, characteristic, complemented
15C61×#2164C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17#16840367—21no—
18#16840242—21no—
19C2×#14519722C2211yescharacteristic
20C2×#14519722C2211yescharacteristic
21C2×D976C2211yescharacteristic
22C2×D976C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840139C2211yescharacteristic
25#16840127—21no—
26#16840015—21no—
27#16839998C2211yescharacteristic
28#16839998C2211yescharacteristic
29#16839875—21no—
30#16839864—21no—
31#16839864—21no—
32C4×Dic244C2211yescharacteristic
33C4×Dic244C2211yescharacteristic
34C4×D488C2211yescharacteristic
35C4×D488C2211yescharacteristic
36C4×D488C2211yescharacteristic
37C4×D488C2211yescharacteristic
38C2×#14519711C2211yescharacteristic
39#16839764—21no—
40#16839590C2211yescharacteristic
41#16839590C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839588C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C61×#405C2211yescharacteristic
53C61×C4⋊C16C2211yescharacteristic
54C61×C4⋊C16C2211yescharacteristic
55C61×C22⋊C16C2211yescharacteristic
56C61×C22⋊C16C2211yescharacteristic
57C61×#346C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×#11758222—21no—
60#14519799—22no—
61#14519799—22no—
62C2×Dic244C2311yescharacteristic
63C2×#11758190—21no—
64C2×D488—21no—
65C2×D488C2311yescharacteristic
66C2×D488C2311yescharacteristic
67C2×D488C2311yescharacteristic
68#14519774—21no—
69#14519769—21no—
70#14519762—41no—
71#14519762—41no—
72#14519751—21no—
73#14519751—21no—
74#14519750—41no—
75#14519750—41no—
76C4×Dic122—21no—
77C4×Dic122—21no—
78C4×D244—21no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244—21no—
82#14519737—41no—
83#14519737—41no—
84#14519735—41no—
85C2×C4⋊Dic61—21no—
86C4⋊C4×D61—41no—
87#14519722—22no—
88#14519722—22no—
89D976—22no—
90D976—22no—
91#14519711—21no—
92#14519711C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519709—21no—
97#14519702—21no—
98#14519702—21no—
99#14519699—21no—
100#14519699—21no—
101#14519699—21no—
102#14519699—21no—
103#14519699—21no—
104#14519699—21no—
105C2×M16×C61D411yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#117×C61D411yescharacteristic
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C22×Dic61—41no—
121#11758222—24no—
122#11758222—42no—
123C2×D244—21no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244—41no—
127C2×D244—41no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×Dic122—21no—
134M16×C61—41no—
135C2×C8×C61—21no—
136C2×C8×C61—21no—
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2×D411yescharacteristic
140C2×C8×C61C2411yescharacteristic
141C4⋊C4×C61D811yescharacteristic
142C4⋊C4×C61D811yescharacteristic
143C22⋊C4×C61D811yescharacteristic
144C22⋊C4×C61D811yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147#11758198—41no—
148#11758198—41no—
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152#11758198—41no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162C4×Dic61—41no—
163C4×Dic61—41no—
164Dic244—21no—
165Dic244#4112yes—
166D488—21no—
167D488—21no—
168D488—21no—
169D488—21no—
170D488—21no—
171D488—42no—
172D488#4112yes—
173#11758190—24no—
174C16×C61—21no—
175C16×C61—21no—
176C16×C61—21no—
177C16×C61—21no—
178C23×C61C2×D811yescharacteristic
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—41no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C22⋊D61—44no—
191C22⋊D61—161no—
192C22⋊D61—161no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—161no—
199D244—22no—
200D244—41no—
201D244—41no—
202D244—41no—
203D244—41no—
204D244—41no—
205D244—161no—
206D244—161no—
207C4×D61—44no—
208C4×D61—161no—
209C4×D61—161no—
210C4×D61—161no—
211C4×D61—161no—
212Dic122—22no—
213Dic122—41no—
214C8×C61—21no—
215C8×C61—21no—
216C8×C61—21no—
217C8×C61C2×#4111yescharacteristic
218C8×C61C2×#4111yescharacteristic
219#33679—611nomaximal, Sylow
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61C22×D811yescharacteristic
224C2×D61—42no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61—81no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61#52511yescharacteristic
239C4×C61#57511yescharacteristic
240Dic61—42no—
241Dic61—81no—
242Dic61—81no—
243Dic61—81no—
244Dic61—81no—
245#3176—611no—
246#2951—611no—
247#2233—611no—
248#2232—611no—
249#2229—611no—
250#2228—611no—
251#2207—611no—
252#2206—611no—
253#2186—611no—
254#2186—611no—
255#2177—611no—
256#2175—611no—
257C4×SD32—611no—
258C4×D16—611no—
259#2164D6111yescharacteristic, complemented
260C2×C61—41no—
261C2×C61#310011yescharacteristic
262C2×C61#341511yescharacteristic
263C2×C61#341611yescharacteristic
264D61—82no—
265D61—161no—
266D61—161no—
267C2×#135—611no—
268#540—1221no—
269#520—1221no—
270C2×SD32—611no—
271C2×SD32—611no—
272C2×D16—611no—
273C2×D16—611no—
274#499—611no—
275#493—611no—
276#490—1221no—
277#469—1221no—
278#466—611no—
279#466—611no—
280#442—1221no—
281#440—1221no—
282#440—1221no—
283C4×Q16—611no—
284C4×Q16—611no—
285C4×D8—611no—
286C4×D8—611no—
287C4×D8—611no—
288C4×D8—611no—
289C2×#107—611no—
290#417—1221no—
291#405C2×D6111yescharacteristic
292#367—611no—
293#367—611no—
294#366—611no—
295#366—611no—
296C4⋊C16C2×D6111yescharacteristic
297C4⋊C16C2×D6111yescharacteristic
298#358—611no—
299#358—611no—
300#357—611no—
301#357—611no—
302#357—611no—
303#357—611no—
304#357—611no—
305#357—611no—
306C22⋊C16C2×D6111yescharacteristic
307C22⋊C16C2×D6111yescharacteristic
308#346C2×D6111yescharacteristic
309C4×C16C2×D6111yescharacteristic
310C61#3367911yescharacteristic, complemented, Sylow
311C2×#41—1221no—
312#135—1222no—
313#135—1222no—
314C2×Q16—611no—
315C2×SD16—1221no—
316C2×D8—611no—
317C2×D8—611no—
318C2×D8—611no—
319C2×D8—1221no—
320C2×M16D24411yescharacteristic
321C22×C8C22×D6111yescharacteristic
322#127—1221no—
323#125—1221no—
324#123—2441no—
325#123—2441no—
326#121—1221no—
327#121—1221no—
328#121—2441no—
329#121—2441no—
330C4×Q8—1221no—
331C4×Q8—1221no—
332C4×D4—1221no—
333C4×D4—1221no—
334C4×D4—1221no—
335C4×D4—1221no—
336C4×D4—2441no—
337C4×D4—2441no—
338#117—2441no—
339#117D24411yescharacteristic
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—2441no—
342SD32—1222no—
343SD32—1222no—
344D16—1222no—
345D16—1222no—
346C2×C16C22×D6111yescharacteristic
347C2×C16C22×D6111yescharacteristic
348C2×C16C22×D6111yescharacteristic
349C2×C16C22×D6111yescharacteristic
350#107—611no—
351#107—611no—
352#107—611no—
353#107—611no—
354#107—1221no—
355#106—1221no—
356#103—1221no—
357#103—1221no—
358#102—1221no—
359#102—1221no—
360#102—1221no—
361#102—1221no—
362#102—1221no—
363#102—1221no—
364#97D24411yescharacteristic
365#97D24411yescharacteristic
366C4×C8C22×D6111yescharacteristic
367C4×C8C22×D6111yescharacteristic
368#41—1224no—
369#41—2442no—
370C2×Q8—1221no—
371C2×D4—1221no—
372C2×D4—1221no—
373C2×D4—1221no—
374C2×D4—2441no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C22×C4—2441no—
380C22×C4—2441no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4C2×D24411yescharacteristic
386Q16—612no—
387Q16—1221no—
388SD16—1224no—
389D8—612no—
390D8—1221no—
391D8—1221no—
392D8—1221no—
393D8—1221no—
394D8—1221no—
395D8—2442no—
396M16—41no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×D24411yescharacteristic
400C2×C8C2×D24411yescharacteristic
401C2×C8C2×D24411yescharacteristic
402C2×C8C23×D6111yescharacteristic
403C4⋊C4—1221no—
404C4⋊C4—1221no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—2441no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4D48811yescharacteristic
413C4⋊C4D48811yescharacteristic
414C22⋊C4—2441no—
415C22⋊C4—2441no—
416C22⋊C4—2441no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4D48811yescharacteristic
421C22⋊C4D48811yescharacteristic
422C42—2441no—
423C42—2441no—
424C42C2×D24411yescharacteristic
425C42C2×D24411yescharacteristic
426C16—21no—
427C16—21no—
428C16—21no—
429C16—21no—
430C23—2441no—
431C23—2441no—
432C23—2441no—
433C23C2×D48811yescharacteristic
434Q8—1222no—
435Q8—2441no—
436D4—1222no—
437D4—9761no—
438D4—9761no—
439D4—9761no—
440D4—9761no—
441D4—2444no—
442D4—2441no—
443D4—2441no—
444D4—2441no—
445D4—2441no—
446D4—2441no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—9761no—
450C2×C4—9761no—
451C2×C4—9761no—
452C2×C4—9761no—
453C2×C4—9761no—
454C2×C4—2444no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4C2×D48811yescharacteristic
461C2×C4C2×D48811yescharacteristic
462C2×C4C2×D48811yescharacteristic
463C2×C4C2×D48811yescharacteristic
464C2×C4C2×D48811yescharacteristic
465C2×C4C22×D24411yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8#41×D6111yescharacteristic
470C8#41×D6111yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—4881no—
475C22—4881no—
476C22—4881no—
477C22—4881no—
478C22—4881no—
479C22—4881no—
480C22—4881no—
481C22—4881no—
482C22—2442no—
483C22C22×D48811yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—4881no—
490C4—4881no—
491C4—4881no—
492C4—4881no—
493C4—2442no—
494C4#1684027411yescharacteristic
495C4#1684056211yescharacteristic
496C2—41no—
497C2—9761no—
498C2—9761no—
499C2—4882no—
500C2#2145582011yescharacteristic
501C2#2145896011yescharacteristic
502C2#2145896711yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2164C2
socleC22×C61C22×D8
hypercenter#2164D61
hypocenterC61#33679
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
1. #21456469C2semidirect
2. #21454696C2semidirect
3. #21448005C2semidirect
4. #21448000C2semidirect
5. #21447984C2semidirect
6. #21447977C2semidirect
7. #21447860C2semidirect
8. #21447855C2semidirect
9. #21447744C2semidirect
10. #21447744C2semidirect
11. #21447696C2semidirect
12. #21447685C2semidirect
13. C4×#14519722C2semidirect
14. C4×D976C2semidirect
15. C61×#2164C2semidirect
259. #2164D61semidirect
310. C61#33679semidirect

Maximal subgroups

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

subgroupindex
#214564692
#214546962
#214480052
#214480002
#214479842
#214479772
#214478602
#214478552
#214477442
#214476962
#214476852
C4×#145197222
C4×D9762
C61×#21642
#3367961