Finite Group Databasebeta

← #29836925

Subgroups — #29836925

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458222C211yesmaximal, characteristic, complemented
2#21448050C211yesmaximal, characteristic, complemented
3#21448024C211yesmaximal, characteristic, complemented
4#21448002C211yesmaximal, characteristic, complemented
5#21447983C211yesmaximal, characteristic, complemented
6#21447917C211yesmaximal, characteristic, complemented
7#21447903C211yesmaximal, characteristic, complemented
8#21447871C211yesmaximal, characteristic, complemented
9#21447742C211yesmaximal, characteristic, complemented
10#21447736C211yesmaximal, characteristic, complemented
11C4×#14519720C211yesmaximal, characteristic, complemented
12D4×#11758185C211yesmaximal, characteristic, complemented
13#21447526C211yesmaximal, characteristic, complemented
14C2×#16839566C211yesmaximal, characteristic, complemented
15C61×#3285C211yesmaximal, characteristic, complemented
16#16840458—21no—
17C2×#14519720C2211yescharacteristic
18C2×#14519720C2211yescharacteristic
19C2×#14519718C2211yescharacteristic
20C22×#11758185C2211yescharacteristic
21C22×#11758185C2211yescharacteristic
22#16840164C2211yescharacteristic
23#16840087—21no—
24#16840081—21no—
25#16840063—21no—
26#16839998C2211yescharacteristic
27#16839998C2211yescharacteristic
28C4×D488C2211yescharacteristic
29#16839800C2211yescharacteristic
30C2×#14519711C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839587C2211yescharacteristic
34C4⋊#11758185C2211yescharacteristic
35#16839566C2211yescharacteristic
36#16839566C2211yescharacteristic
37#16839566C2211yescharacteristic
38#16839566C2211yescharacteristic
39#16839566C2211yescharacteristic
40#16839566C2211yescharacteristic
41#16839563C2211yescharacteristic
42#16839563C2211yescharacteristic
43#16839563C2211yescharacteristic
44#16839562C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C2×#135×C61C2211yescharacteristic
49C22×Q16×C61C2211yescharacteristic
50C61×#548—21no—
51C61×#495C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C61×#466C2211yescharacteristic
54C61×#464—21no—
55C61×#452—21no—
56C61×#448—21no—
57C4×Q16×C61C2211yescharacteristic
58C8×D4×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#14519720—41no—
72#14519718—41no—
73C2×#11758185—41no—
74C2×#11758185—41no—
75C2×#11758185C2311yescharacteristic
76C2×#11758185C2311yescharacteristic
77C2×#11758185C2311yescharacteristic
78C2×#11758185C2311yescharacteristic
79#14519711—21no—
80#14519711C2311yescharacteristic
81#14519711C2311yescharacteristic
82#14519711C2311yescharacteristic
83#14519709—21no—
84#14519709—21no—
85#14519699—21no—
86#14519699—21no—
87#14519699—21no—
88C2×#41×C61—21no—
89C22×Q8×C61—21no—
90#135×C61—22no—
91#135×C61—41no—
92C2×Q16×C61—22no—
93C2×Q16×C61—21no—
94C2×Q16×C61—41no—
95C2×Q16×C61C2311yescharacteristic
96C2×Q16×C61C2311yescharacteristic
97C2×SD16×C61—21no—
98C2×SD16×C61—21no—
99C2×D8×C61C2311yescharacteristic
100C22×C8×C61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102#124×C61—21no—
103#124×C61—41no—
104C22⋊Q8×C61—21no—
105C22⋊Q8×C61—41no—
106#121×C61—21no—
107#121×C61—41no—
108C4×Q8×C61—21no—
109C4×D4×C61—41no—
110C4×D4×C61D411yescharacteristic
111#107×C61C2311yescharacteristic
112C4⋊C8×C61D411yescharacteristic
113#103×C61—21no—
114#103×C61—21no—
115#102×C61—21no—
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119#41×C61—42no—
120#41×C61—81no—
121C2×Q8×C61—21no—
122C2×Q8×C61—21no—
123C2×Q8×C61—42no—
124C2×Q8×C61—41no—
125C2×Q8×C61—81no—
126C2×D4×C61—21no—
127C2×D4×C61—41no—
128C2×D4×C61—41no—
129C2×D4×C61D811yescharacteristic
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C2×C22⋊D61—41no—
135C2×C22⋊D61—41no—
136C22×Dic61—41no—
137C2×D244—21no—
138C2×C4×D61—41no—
139Q16×C61—21no—
140Q16×C61—21no—
141Q16×C61—21no—
142Q16×C61—42no—
143Q16×C61#4112yes—
144SD16×C61—42no—
145SD16×C61—81no—
146D8×C61—21no—
147D8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61C2×D411yescharacteristic
153C2×C8×C61C2×D411yescharacteristic
154C2×C8×C61C2×D411yescharacteristic
155C2×C8×C61C2411yescharacteristic
156C4⋊C4×C61—21no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61D811yescharacteristic
160C22⋊C4×C61—41no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61—41no—
164C22⋊C4×C61D811yescharacteristic
165C22⋊C4×C61D811yescharacteristic
166C42×C61—41no—
167C42×C61C2×D411yescharacteristic
168C22⋊Dic61—41no—
169#11758198—41no—
170#11758198—41no—
171#11758198—41no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—41no—
176#11758196—41no—
177#11758196—41no—
178C4×Dic61—41no—
179D488—21no—
180D488—21no—
181#11758185—21no—
182#11758185—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61C2×D811yescharacteristic
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189Q8×C61—22no—
190Q8×C61—41no—
191Q8×C61—41no—
192Q8×C61—41no—
193Q8×C61—82no—
194D4×C61—22no—
195D4×C61—41no—
196D4×C61—41no—
197D4×C61—82no—
198D4×C61—82no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—82no—
207C2×C4×C61—82no—
208C2×C4×C61C2×D811yescharacteristic
209C2×C4×C61C2×D811yescharacteristic
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C2×D811yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C22⋊D61—82no—
214C22⋊D61—161no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—161no—
219D244—41no—
220D244—41no—
221C4×D61—161no—
222C8×C61—21no—
223C8×C61—21no—
224C8×C61—21no—
225C8×C61C2×#4111yescharacteristic
226C8×C61H(5,𝔽2)11yescharacteristic
227#33868—611nomaximal, Sylow
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61#50812yes—
237C22×C61C22×D811yescharacteristic
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—42no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61#54611yescharacteristic
249C4×C61#57711yescharacteristic
250Dic61—81no—
251Dic61—81no—
252Dic61—81no—
253#3339—611no—
254#3285D6111yescharacteristic, complemented
255#2242—611no—
256#2237—611no—
257#2233—611no—
258#2229—611no—
259#2217—611no—
260#2215—611no—
261#2210—611no—
262#2186—611no—
263#2185—611no—
264C4×SD32—611no—
265D4×C16—611no—
266#2138—611no—
267C2×#358—611no—
268C2×C61—22no—
269C2×C61—41no—
270C2×C61—161no—
271C2×C61#329411yescharacteristic
272C2×C61C2×#50811yescharacteristic
273C2×C61#341611yescharacteristic
274D61—161no—
275C2×#135C2×D6111yescharacteristic
276C22×Q16C2×D6111yescharacteristic
277#553—1221no—
278#548—21no—
279C2×SD32—611no—
280C2×SD32—611no—
281C2×D16—611no—
282C22×C16—611no—
283C22×C16—611no—
284#499—611no—
285#495C2×D6111yescharacteristic
286#482—1221no—
287#481—1221no—
288#478—1221no—
289#467C2×D6111yescharacteristic
290#466—611no—
291#466—611no—
292#466C2×D6111yescharacteristic
293#464—21no—
294#452—21no—
295#448—21no—
296C4×Q16C2×D6111yescharacteristic
297C4×D8—611no—
298C8×D4C2×D6111yescharacteristic
299#427—611no—
300C2×#107—611no—
301#367—611no—
302#367—611no—
303#366—611no—
304C4⋊C16—611no—
305#358—611no—
306#358—611no—
307#358—611no—
308#358—611no—
309#358—611no—
310#358—611no—
311#357—611no—
312#357—611no—
313#357—611no—
314#357—611no—
315C22⋊C16—611no—
316C22⋊C16—611no—
317C4×C16—611no—
318C61#3386811yescharacteristic, complemented, Sylow
319C2×#41—21no—
320C22×Q8—21no—
321#135—22no—
322#135—41no—
323C2×Q16—22no—
324C2×Q16—21no—
325C2×Q16—41no—
326C2×Q16C22×D6111yescharacteristic
327C2×Q16C22×D6111yescharacteristic
328C2×SD16—21no—
329C2×SD16—21no—
330C2×D8—611no—
331C2×D8C22×D6111yescharacteristic
332C22×C8C22×D6111yescharacteristic
333C22×C8C22×D6111yescharacteristic
334#126—2441no—
335#125—1221no—
336#124—21no—
337#124—41no—
338#123—2441no—
339C22⋊Q8—21no—
340C22⋊Q8—41no—
341#121—21no—
342#121—41no—
343#121—1221no—
344#121—1221no—
345#121—2441no—
346C4×Q8—21no—
347C4×D4—41no—
348C4×D4—1221no—
349C4×D4—2441no—
350C4×D4C22⋊D6111yescharacteristic
351#117—1221no—
352C2×C4⋊C4—1221no—
353SD32—1222no—
354SD32—2441no—
355D16—2441no—
356C2×C16—611no—
357C2×C16—611no—
358C2×C16—611no—
359C2×C16—611no—
360C2×C16—2441no—
361C2×C16—2441no—
362#107—611no—
363#107—611no—
364#107—611no—
365#107—1221no—
366#107C22×D6111yescharacteristic
367#106—1221no—
368#106—1221no—
369C4⋊C8C22⋊D6111yescharacteristic
370#103—21no—
371#103—21no—
372#102—21no—
373#102—1221no—
374#102—1221no—
375#102—1221no—
376C22⋊C8C22⋊D6111yescharacteristic
377C22⋊C8C22⋊D6111yescharacteristic
378C4×C8C22×D6111yescharacteristic
379#41—42no—
380#41—81no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—42no—
384C2×Q8—41no—
385C2×Q8—81no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—1221no—
390C2×D4—2441no—
391C2×D4—2441no—
392C2×D4#1175819911yescharacteristic
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4C2×C22⋊D6111yescharacteristic
398C22×C4C2×C22⋊D6111yescharacteristic
399Q16—21no—
400Q16—21no—
401Q16—21no—
402Q16—42no—
403Q16#1175822412yes—
404SD16—42no—
405SD16—81no—
406D8—21no—
407D8—21no—
408D8—1221no—
409D8—1221no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8C2×C22⋊D6111yescharacteristic
415C2×C8C2×C22⋊D6111yescharacteristic
416C2×C8C2×C22⋊D6111yescharacteristic
417C2×C8C23×D6111yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—1221no—
422C4⋊C4—1221no—
423C4⋊C4—1221no—
424C4⋊C4—2441no—
425C4⋊C4—2441no—
426C4⋊C4—2441no—
427C4⋊C4#1175819911yescharacteristic
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4#1175819911yescharacteristic
437C22⋊C4#1175819911yescharacteristic
438C42—41no—
439C42—2441no—
440C42C2×C22⋊D6111yescharacteristic
441C16—1221no—
442C16—1221no—
443C16—1221no—
444C16—1221no—
445C23—41no—
446C23—2441no—
447C23C2×#1175819911yescharacteristic
448C23C2×#1175819911yescharacteristic
449Q8—22no—
450Q8—41no—
451Q8—41no—
452Q8—41no—
453Q8—82no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—82no—
458D4—82no—
459D4—9761no—
460D4—4882no—
461D4—2441no—
462D4—2441no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—9761no—
473C2×C4—9761no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4C2×#1175819911yescharacteristic
478C2×C4C2×#1175819911yescharacteristic
479C2×C4C2×#1175819911yescharacteristic
480C2×C4C2×#1175819911yescharacteristic
481C2×C4C22×C22⋊D6111yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8C2×#1175822411yescharacteristic
486C8#1451982211yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—4881no—
496C22—4881no—
497C22—4881no—
498C22#1684019212yes—
499C22C22×#1175819911yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—4881no—
508C4—4881no—
509C4—4881no—
510C4#1684040611yescharacteristic
511C4#1684057311yescharacteristic
512C2—22no—
513C2—41no—
514C2—161no—
515C2—9761no—
516C2#2145763211yescharacteristic
517C2C2×#1684019211yescharacteristic
518C2#2145896311yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3285C2
socleC22×C61C22×D8
hypercenter#3285D61
hypocenterC61#33868
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #21458222C2semidirect
2. #21448050C2semidirect
3. #21448024C2semidirect
4. #21448002C2semidirect
5. #21447983C2semidirect
6. #21447917C2semidirect
7. #21447903C2semidirect
8. #21447871C2semidirect
9. #21447742C2semidirect
10. #21447736C2semidirect
11. C4×#14519720C2semidirect
12. D4×#11758185C2semidirect
13. #21447526C2semidirect
14. C2×#16839566C2semidirect
15. C61×#3285C2semidirect
254. #3285D61semidirect
318. C61#33868semidirect

Maximal subgroups

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

subgroupindex
#214582222
#214480502
#214480242
#214480022
#214479832
#214479172
#214479032
#214478712
#214477422
#214477362
C4×#145197202
D4×#117581852
#214475262
C2×#168395662
C61×#32852
#3386861