Finite Group Databasebeta

← #29730386

Subgroups — #29730386

Order 15616.

764 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456212C211yesmaximal, characteristic, complemented
2C2×#16840043C211yesmaximal, characteristic, complemented
3#21455279C211yesmaximal, characteristic
4#21447259C212yesmaximal, complemented
5#21447110C212yesmaximal, complemented
6#21446808C211yesmaximal, characteristic, complemented
7#21446595C211yesmaximal, characteristic, complemented
8#21446327C212yesmaximal, complemented
9#21445883C212yesmaximal, complemented
10C4×#14519693C211yesmaximal, characteristic, complemented
11C61×#2935C211yesmaximal, characteristic, complemented
12C2×#14519802C2212yes—
13C2×#14519777C2211yescharacteristic
14C2×C4×D244C2211yescharacteristic
15#16840121—22no—
16#16840112—21no—
17#16840108—21no—
18#16840043—21no—
19#16840043—22no—
20#16840043—21no—
21#16839974—22no—
22#16839964—21no—
23#16839954—21no—
24C2×#14519713C2212yes—
25C2×#14519711C2212yes—
26#16839786C2211yescharacteristic
27#16839763C2212yes—
28#16839763C2212yes—
29#16839763C2212yes—
30C2×#14519699C2212yes—
31C2×#14519693C2211yescharacteristic
32C2×#14519693C2211yescharacteristic
33C4×#11758194C2211yescharacteristic
34#16839530C2211yescharacteristic
35#16839530C2212yes—
36#16839530C2212yes—
37#16839530C2211yescharacteristic
38#16839527C2212yes—
39C2×#131×C61C2212yes—
40C61×#532C2211yescharacteristic
41C61×#436—21no—
42C61×#435—22no—
43C8×D4×C61—21no—
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#408C2212yes—
46C4×M16×C61C2211yescharacteristic
47C22×Dic122—21no—
48C22×D244C2311yescharacteristic
49C22×C4×D61—21no—
50#14519802—24no—
51#14519802—42no—
52C2×#11758201—22no—
53C2×#11758199—22no—
54C2×#11758194C2311yescharacteristic
55C2×#11758194C2311yescharacteristic
56C2×#11758194C2312yes—
57#14519777—21no—
58#14519777—21no—
59#14519777—21no—
60#14519777—21no—
61C4×D244—21no—
62C4×D244—21no—
63C4×D244—21no—
64C4×D244—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2312yes—
68C2×#11758198—21no—
69#14519713—42no—
70#14519711—22no—
71#14519711—22no—
72C4⋊#92418—21no—
73C4⋊#92418—21no—
74#14519701—22no—
75#14519701—22no—
76#14519701—22no—
77#14519699—22no—
78#14519699—22no—
79#14519698—22no—
80#14519698—22no—
81#14519698—22no—
82#14519693—22no—
83#14519693—22no—
84#14519688—21no—
85C4×#92418—21no—
86C2×#41×C61C2312yes—
87#131×C61—24no—
88#131×C61—42no—
89C2×M16×C61—22no—
90C2×M16×C61C2311yescharacteristic
91C2×M16×C61C2311yescharacteristic
92C22×C8×C61—22no—
93C22×C8×C61C2312yes—
94C4⋊Q8×C61D411yescharacteristic
95#127×C61D411yescharacteristic
96#124×C61D412yes—
97#121×C61—21no—
98#121×C61—21no—
99C4×D4×C61—21no—
100C4×D4×C61—21no—
101C2×C42×C61C2311yescharacteristic
102C4⋊C8×C61D411yescharacteristic
103C4⋊C8×C61D412yes—
104C4⋊C8×C61D411yescharacteristic
105C22⋊C8×C61—22no—
106C22⋊C8×C61—22no—
107#97×C61—21no—
108C4×C8×C61—21no—
109C23×D61—21no—
110#41×C61—22no—
111#41×C61—22no—
112#41×C61—22no—
113#41×C61—22no—
114C2×Q8×C61C2×D412yes—
115C2×D4×C61—22no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61C2×D412yes—
119C22×C4×C61—22no—
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61C2411yescharacteristic
123C22×Dic61—21no—
124C22×Dic61—22no—
125C2×D244—21no—
126C2×D244—21no—
127C2×D244—21no—
128C2×D244—21no—
129C2×D244—21no—
130C2×D244#4112yes—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×C4×D61—82no—
134C2×Dic122—41no—
135C2×Dic122—41no—
136C2×Dic122—82no—
137M16×C61—21no—
138M16×C61—21no—
139M16×C61—21no—
140M16×C61—44no—
141M16×C61#4112yes—
142C2×C8×C61—21no—
143C2×C8×C61—22no—
144C2×C8×C61—22no—
145C2×C8×C61—21no—
146C2×C8×C61—44no—
147C2×C8×C61C2×D412yes—
148C2×C8×C61C2×D412yes—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C22⋊C4×C61—22no—
152C22⋊C4×C61—22no—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157#11758201—44no—
158#11758199—44no—
159#11758198—41no—
160#11758198—41no—
161C4⋊Dic61—21no—
162C4⋊Dic61—22no—
163C4⋊Dic61—22no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166C4⋊Dic61—41no—
167#11758194—21no—
168#11758194—21no—
169#11758194—22no—
170#11758194—21no—
171#11758194—22no—
172#11758194—21no—
173C2×#92418—21no—
174C2×#92418—21no—
175C2×#92418—22no—
176C23×C61—22no—
177C23×C61C2×#4111yescharacteristic
178C22×D61—22no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—81no—
182C22×D61—81no—
183Q8×C61—22no—
184Q8×C61—22no—
185D4×C61—22no—
186D4×C61—22no—
187D4×C61—42no—
188D4×C61—42no—
189D4×C61—42no—
190D4×C61—81no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—41no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61#12111yescharacteristic
198C2×C4×C61#12111yescharacteristic
199C2×C4×C61#12111yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C2×#4111yescharacteristic
203C2×C4×C61C2×#4111yescharacteristic
204C2×C4×C61H(5,𝔽2)11yescharacteristic
205C2×C4×C612−1+411yescharacteristic
206C2×Dic61—42no—
207C2×Dic61—41no—
208C2×Dic61—82no—
209C2×Dic61—81no—
210D244—22no—
211D244—22no—
212D244—41no—
213D244—41no—
214C4×D61—82no—
215C4×D61—82no—
216Dic122—82no—
217Dic122—82no—
218C8×C61—22no—
219C8×C61—22no—
220C8×C61—22no—
221C8×C61—41no—
222#92418—41no—
223#92418—42no—
224#92418—41no—
225#25358—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—42no—
229C22×C61—42no—
230C22×C61—42no—
231C22×C61C2×#12111yescharacteristic
232C22×C61#52911yescharacteristic
233C22×C61#54211yescharacteristic
234C2×D61—42no—
235C2×D61—82no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—82no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—42no—
243C4×C61#47212yes—
244C4×C61#54611yescharacteristic
245C4×C61#54611yescharacteristic
246C4×C61#54711yescharacteristic
247C4×C61#54811yescharacteristic
248Dic61—82no—
249Dic61—81no—
250#3141—611no—
251C2×#474—611no—
252#3036—611no—
253#2935D6111yescharacteristic, complemented
254#2078—612no—
255#2051—612no—
256#1997—611no—
257#1950—611no—
258#1907—612no—
259#1816—612no—
260C4×#100—611no—
261C2×C61—21no—
262C2×C61—21no—
263C2×C61—82no—
264C2×C61#242711yescharacteristic
265C2×C61C2×#47211yescharacteristic
266C2×C61#306911yescharacteristic
267D61—82no—
268C2×AGL(1,ℤ/8)—612no—
269C2×#131C2×D6112yes—
270#532C2×D6111yescharacteristic
271C2×C4⋊Q8—611no—
272C2×C4×D4—611no—
273#489—1222no—
274#487—1221no—
275#486—1221no—
276#474—1221no—
277#474—1222no—
278#474—1221no—
279#463—1222no—
280#461—1221no—
281#459—1221no—
282#436—21no—
283#435—22no—
284C8×D4—21no—
285C2×#108—612no—
286C2×#107—612no—
287#423—611no—
288C2×C4⋊C8C2×D6111yescharacteristic
289#417—612no—
290#417—612no—
291#417—612no—
292C2×#102—612no—
293C2×#100—611no—
294C2×#100—611no—
295#408C2×D6112yes—
296C4×M16—611no—
297C4×M16C2×D6111yescharacteristic
298#343—612no—
299#343—611no—
300#343—612no—
301#343—611no—
302#341—612no—
303C61#2535811yescharacteristic, complemented, Sylow
304C2×#41C22×D6112yes—
305C22×Q8—1221no—
306C22×D4—611no—
307C23×C4—1221no—
308AGL(1,ℤ/8)—1224no—
309AGL(1,ℤ/8)—2442no—
310C2×SD16—1222no—
311C2×D8—1222no—
312#131—24no—
313#131—42no—
314C2×M16—22no—
315C2×M16—612no—
316C2×M16—611no—
317C2×M16—611no—
318C2×M16C22×D6111yescharacteristic
319C2×M16C22×D6111yescharacteristic
320C22×C8—22no—
321C22×C8C22×D6112yes—
322C4⋊Q8—1221no—
323C4⋊Q8—1221no—
324C4⋊Q8—1221no—
325C4⋊Q8—1221no—
326C4⋊Q8D24411yescharacteristic
327#127D24411yescharacteristic
328#124D24412yes—
329#121—21no—
330#121—21no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—1221no—
334C4×D4—1221no—
335C4×D4—1221no—
336C4×D4—1221no—
337C2×C4⋊C4—611no—
338C2×C4⋊C4—612no—
339C2×C4⋊C4—1221no—
340C2×C22⋊C4—1221no—
341C2×C42C22×D6111yescharacteristic
342#108—2442no—
343#107—1222no—
344#107—1222no—
345C4⋊C8—1221no—
346C4⋊C8—1221no—
347C4⋊C8C22⋊D6111yescharacteristic
348C4⋊C8C22⋊D6112yes—
349C4⋊C8C22⋊D6111yescharacteristic
350#103—1222no—
351#103—1222no—
352#103—1222no—
353#102—1222no—
354#102—1222no—
355#102—1222no—
356#102—1222no—
357#102—1222no—
358#100—1222no—
359#100—1222no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362#97—21no—
363#97—1221no—
364C4×C8—21no—
365C4×C8—1221no—
366C24—1221no—
367#41—22no—
368#41—22no—
369#41—22no—
370#41—22no—
371C2×Q8—4882no—
372C2×Q8—2441no—
373C2×Q8—2441no—
374C2×Q8C2×D24412yes—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—612no—
379C2×D4—1221no—
380C2×D4—1221no—
381C2×D4—1221no—
382C2×D4—1221no—
383C2×D4—1221no—
384C2×D4C2×D24412yes—
385C22×C4—22no—
386C22×C4—1221no—
387C22×C4—1222no—
388C22×C4—4882no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4#1175822211yescharacteristic
392C22×C4#1175822211yescharacteristic
393C22×C4C23×D6111yescharacteristic
394SD16—2444no—
395D8—2444no—
396M16—21no—
397M16—21no—
398M16—21no—
399M16—44no—
400M16—1221no—
401M16—1222no—
402M16—1221no—
403M16—1221no—
404M16—1222no—
405M16—1221no—
406M16#1175822412yes—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—21no—
411C2×C8—44no—
412C2×C8—1221no—
413C2×C8—1221no—
414C2×C8—1222no—
415C2×C8C2×C22⋊D6112yes—
416C2×C8C2×C22⋊D6112yes—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—1222no—
420C4⋊C4—1221no—
421C4⋊C4—1221no—
422C4⋊C4—1222no—
423C4⋊C4—2441no—
424C4⋊C4—2441no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—2441no—
428C22⋊C4—2441no—
429C42C2×D24411yescharacteristic
430C42C2×D24411yescharacteristic
431C42C2×C22⋊D6111yescharacteristic
432C42C2×C22⋊D6111yescharacteristic
433C23—22no—
434C23—1222no—
435C23—4881no—
436C23—4881no—
437C23—2441no—
438C23—2441no—
439C23C2×#1175822211yescharacteristic
440Q8—22no—
441Q8—22no—
442Q8—4882no—
443Q8—4882no—
444D4—22no—
445D4—22no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—81no—
450D4—1222no—
451D4—1222no—
452D4—2441no—
453D4—2441no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—4882no—
460C2×C4—4882no—
461C2×C4—4881no—
462C2×C4—4882no—
463C2×C4—2441no—
464C2×C4—2442no—
465C2×C4#1451975111yescharacteristic
466C2×C4#1451975111yescharacteristic
467C2×C4#1451975111yescharacteristic
468C2×C4#1451975111yescharacteristic
469C2×C4C22×C22⋊D6111yescharacteristic
470C2×C4C22×D24411yescharacteristic
471C2×C4#41×D6111yescharacteristic
472C2×C4C2×#1175822411yescharacteristic
473C2×C4#1451982211yescharacteristic
474C2×C4#1451982411yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8—41no—
479C8—2441no—
480C8—2442no—
481C8—2441no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—4882no—
488C22—4882no—
489C22—4881no—
490C22—4881no—
491C22—2442no—
492C22C2×#1451975111yescharacteristic
493C22#1684029411yescharacteristic
494C22#1684037711yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—4881no—
500C4—4882no—
501C4#1684003212yes—
502C4#1684040611yescharacteristic
503C4#1684040711yescharacteristic
504C4#1684041611yescharacteristic
505C4#1684041911yescharacteristic
506C2—21no—
507C2—21no—
508C2—82no—
509C2—4882no—
510C2#2144939011yescharacteristic
511C2C2×#1684003211yescharacteristic
512C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2935C2
socleC22×C61C2×#121
prime radical#21455279C2
hypercenter#2935D61
hypocenterC61#25358
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #21456212C2semidirect
2. C2×#16840043C2semidirect
4. #21447259C2semidirect
5. #21447110C2semidirect
6. #21446808C2semidirect
7. #21446595C2semidirect
8. #21446327C2semidirect
9. #21445883C2semidirect
10. C4×#14519693C2semidirect
11. C61×#2935C2semidirect
253. #2935D61semidirect
303. C61#25358semidirect

Maximal subgroups

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

subgroupindex
#214562122
C2×#168400432
#214552792
#214472592
#214471102
#214468082
#214465952
#214463272
#214458832
C4×#145196932
C61×#29352
#2535861