Finite Group Databasebeta

← #29837022

Subgroups — #29837022

Order 15616.

564 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458224C211yesmaximal, characteristic, complemented
2#21457573C211yesmaximal, characteristic, complemented
3#21448059C211yesmaximal, characteristic, complemented
4#21448008C211yesmaximal, characteristic, complemented
5#21448000C211yesmaximal, characteristic, complemented
6#21447985C211yesmaximal, characteristic, complemented
7#21447920C211yesmaximal, characteristic, complemented
8#21447902C211yesmaximal, characteristic, complemented
9#21447852C211yesmaximal, characteristic, complemented
10#21447741C211yesmaximal, characteristic, complemented
11#21447684C211yesmaximal, characteristic, complemented
12#21447647C211yesmaximal, characteristic, complemented
13#21447531C211yesmaximal, characteristic, complemented
14#21447525C211yesmaximal, characteristic, complemented
15C61×#2186C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17#16840464—21no—
18#16840431—21no—
19C2×#14519718C2211yescharacteristic
20C2×#14519717C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840137C2211yescharacteristic
24#16840084—21no—
25#16840078—21no—
26#16840060—21no—
27#16839998C2211yescharacteristic
28#16839995C2211yescharacteristic
29#16839995C2211yescharacteristic
30#16839960—21no—
31#16839907—21no—
32#16839906—21no—
33Q16×Dic61C2211yescharacteristic
34D8×Dic61C2211yescharacteristic
35C8×C22⋊D61C2211yescharacteristic
36#16839799C2211yescharacteristic
37C2×#14519711C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839566C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839564C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839537C2211yescharacteristic
52C2×#135×C61C2211yescharacteristic
53C2×SD32×C61C2211yescharacteristic
54C2×D16×C61C2211yescharacteristic
55C61×#466C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758226—21no—
60#14519800—22no—
61#14519800—41no—
62C2×#11758201—21no—
63C2×D488C2311yescharacteristic
64C2×#11758199—21no—
65C2×C8×D61C2311yescharacteristic
66#14519773—21no—
67#14519773—41no—
68#14519770—41no—
69#14519768—21no—
70#14519761—41no—
71#14519751—21no—
72#14519751—41no—
73#14519749—41no—
74#14519748—21no—
75#14519748—21no—
76#14519748—41no—
77Q8×Dic61—21no—
78D4×Dic61—21no—
79D4×Dic61—41no—
80C4×C22⋊D61—41no—
81C4×C22⋊D61D411yescharacteristic
82#14519735—21no—
83C2×C4⋊Dic61—21no—
84#14519718—41no—
85#14519717—41no—
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88C16×D61—41no—
89#14519711—21no—
90#14519711C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519708—21no—
94#14519708—21no—
95#14519706D411yescharacteristic
96#14519701—21no—
97#14519699—21no—
98#14519698—21no—
99#14519698—21no—
100#14519698—21no—
101C22⋊#92418D411yescharacteristic
102#14519689D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×#41×C61—21no—
105#135×C61—22no—
106#135×C61—41no—
107C2×Q16×C61C2311yescharacteristic
108C2×SD16×C61—21no—
109C2×D8×C61C2311yescharacteristic
110C2×D8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#121×C61—21no—
113SD32×C61—22no—
114D16×C61—41no—
115C2×C16×C61C2311yescharacteristic
116C2×C16×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#102×C61—21no—
119#41×C61—42no—
120#41×C61—81no—
121C2×Q8×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—41no—
125C2×D4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61C2×D411yescharacteristic
128C2×C22⋊D61—41no—
129C2×C22⋊D61—41no—
130C2×C22⋊D61—41no—
131C2×C22⋊D61—41no—
132C2×C22⋊D61—41no—
133C2×C22⋊D61D811yescharacteristic
134C22×Dic61—41no—
135C22×Dic61—41no—
136#11758226—42no—
137#11758226—81no—
138C2×D244—21no—
139C2×D244—41no—
140C2×C4×D61—41no—
141C2×C4×D61C2×D411yescharacteristic
142Q16×C61—21no—
143Q16×C61#4112yes—
144SD16×C61—42no—
145D8×C61—21no—
146D8×C61—21no—
147D8×C61—21no—
148D8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61C2×D411yescharacteristic
152C2×C8×C61C2411yescharacteristic
153C4⋊C4×C61—21no—
154C22⋊C4×C61—41no—
155C22⋊Dic61—41no—
156C22⋊Dic61—41no—
157C22⋊Dic61—41no—
158C22⋊Dic61D811yescharacteristic
159#11758201—42no—
160#11758199—81no—
161#11758198—41no—
162#11758198—41no—
163#11758198D811yescharacteristic
164C4⋊Dic61—21no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61—41no—
168C4⋊Dic61—41no—
169C4⋊Dic61—41no—
170#11758196—41no—
171#11758196D811yescharacteristic
172C4×Dic61—41no—
173C4×Dic61—41no—
174C4×Dic61C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176C2×#92418C2×D411yescharacteristic
177D488—21no—
178D488—21no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189C22×D61C2×D811yescharacteristic
190Q8×C61—22no—
191Q8×C61—41no—
192D4×C61—41no—
193D4×C61—41no—
194D4×C61—41no—
195D4×C61—41no—
196D4×C61—82no—
197D4×C61—82no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—82no—
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C22⋊D61—41no—
206C22⋊D61—82no—
207C22⋊D61—161no—
208C22⋊D61—161no—
209C22⋊D61—161no—
210C22⋊D61—161no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—161no—
215C2×Dic61—161no—
216C2×Dic61C2×D811yescharacteristic
217C2×Dic61C2×D811yescharacteristic
218C2×Dic61C2×D811yescharacteristic
219D244—41no—
220D244—41no—
221D244—82no—
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—82no—
225C8×C61—21no—
226C8×C61C2×#4111yescharacteristic
227C8×C61H(5,𝔽2)11yescharacteristic
228#92418—21no—
229#92418—21no—
230#33876—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61C22×D811yescharacteristic
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C4×C61—21no—
248C4×C61—42no—
249C4×C61—81no—
250C4×C61#54611yescharacteristic
251C4×C61#57711yescharacteristic
252Dic61—21no—
253Dic61—21no—
254Dic61—21no—
255Dic61—81no—
256Dic61—81no—
257Dic61—81no—
258#3339—611no—
259#3287—611no—
260#2244—611no—
261#2234—611no—
262#2232—611no—
263#2229—611no—
264#2218—611no—
265#2215—611no—
266#2206—611no—
267#2186—611no—
268#2186D6111yescharacteristic, complemented
269#2175—611no—
270#2168—611no—
271#2139—611no—
272#2138—611no—
273C2×C61—41no—
274C2×C61—161no—
275C2×C61—161no—
276C2×C61#329411yescharacteristic
277C2×C61#341411yescharacteristic
278C2×C61#341511yescharacteristic
279D61—41no—
280D61—161no—
281C2×#135—611no—
282C2×#135C2×D6111yescharacteristic
283#553—1221no—
284#550—1221no—
285C2×SD32C2×D6111yescharacteristic
286C2×D16—611no—
287C2×D16C2×D6111yescharacteristic
288C2×M32—611no—
289C22×C16—611no—
290#499—611no—
291#493—611no—
292#482—1221no—
293#481—1221no—
294#478—1221no—
295#466—611no—
296#466—611no—
297#466—611no—
298#466C2×D6111yescharacteristic
299#460—1221no—
300#449—1221no—
301#449—1221no—
302C4×Q16—611no—
303C4×D8—611no—
304C8×D4—611no—
305#427—611no—
306C2×#107—611no—
307#367—611no—
308#366—611no—
309#366—611no—
310C4⋊C16—611no—
311#358—611no—
312#358—611no—
313#358C2×D6111yescharacteristic
314#357—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357C2×D6111yescharacteristic
321C22⋊C16—611no—
322C22⋊C16C2×D6111yescharacteristic
323#346—611no—
324C61#3387611yescharacteristic, complemented, Sylow
325C2×#41—21no—
326C2×#41—1221no—
327#135—22no—
328#135—41no—
329#135—1222no—
330#135—2441no—
331C2×Q16C22×D6111yescharacteristic
332C2×SD16—21no—
333C2×SD16—1221no—
334C2×D8—611no—
335C2×D8—1221no—
336C2×D8C22×D6111yescharacteristic
337C2×D8C22×D6111yescharacteristic
338C22×C8—611no—
339C22×C8C22×D6111yescharacteristic
340#127—1221no—
341#127—2441no—
342#126—2441no—
343#125—1221no—
344#123—2441no—
345#121—21no—
346#121—1221no—
347#121—1221no—
348#121—1221no—
349#121—2441no—
350#121—2441no—
351#121—2441no—
352C4×Q8—1221no—
353C4×D4—611no—
354C4×D4—1221no—
355C4×D4—2441no—
356C4×D4—2441no—
357#117—1221no—
358C2×C4⋊C4—1221no—
359SD32—22no—
360D16—41no—
361D16—2441no—
362M32—2441no—
363C2×C16—611no—
364C2×C16—611no—
365C2×C16—2441no—
366C2×C16C22×D6111yescharacteristic
367C2×C16C22×D6111yescharacteristic
368#107—611no—
369#107—611no—
370#107—611no—
371#107—1221no—
372#107C22×D6111yescharacteristic
373#106—1221no—
374#106—1221no—
375C4⋊C8—611no—
376#103—1221no—
377#102—21no—
378#102—1221no—
379#102—1221no—
380#102—1221no—
381#102—1221no—
382C22⋊C8—611no—
383C22⋊C8—611no—
384C4×C8—611no—
385#41—42no—
386#41—81no—
387#41—4881no—
388#41—2442no—
389C2×Q8—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—611no—
395C2×D4—1221no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4—2441no—
402C22×C4—41no—
403C22×C4—611no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407C22×C4D4×D6111yescharacteristic
408Q16—21no—
409Q16#1175822412yes—
410SD16—42no—
411SD16—2442no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—1221no—
417D8—1221no—
418D8—4881no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—611no—
422C2×C8—611no—
423C2×C8—1221no—
424C2×C8—1221no—
425C2×C8D4×D6111yescharacteristic
426C2×C8C23×D6111yescharacteristic
427C4⋊C4—21no—
428C4⋊C4—611no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—1221no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C4⋊C4—2441no—
435C4⋊C4—2441no—
436C22⋊C4—41no—
437C22⋊C4—611no—
438C22⋊C4—611no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C22⋊C4—2441no—
444C42—611no—
445C42—2441no—
446C42—2441no—
447C16—21no—
448C16—21no—
449C16—1221no—
450C16—1221no—
451C23—41no—
452C23—41no—
453C23—611no—
454C23—2441no—
455C23D8×D6111yescharacteristic
456Q8—22no—
457Q8—41no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—82no—
463D4—82no—
464D4—9761no—
465D4—9761no—
466D4—9761no—
467D4—9761no—
468D4—4882no—
469D4—4882no—
470D4—2441no—
471D4—2441no—
472D4—2441no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—82no—
478C2×C4—611no—
479C2×C4—611no—
480C2×C4—611no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—9761no—
484C2×C4—9761no—
485C2×C4—4882no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4D8×D6111yescharacteristic
490C2×C4C2×D4×D6111yescharacteristic
491C8—21no—
492C8—1221no—
493C8—1221no—
494C8C2×#1175822411yescharacteristic
495C8#1451982211yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—4881no—
509C22—4881no—
510C22—4881no—
511C22C2×D8×D6111yescharacteristic
512C4—21no—
513C4—42no—
514C4—81no—
515C4—1221no—
516C4—1221no—
517C4—1221no—
518C4—4881no—
519C4—4881no—
520C4—4881no—
521C4#1684039911yescharacteristic
522C4#1684057211yescharacteristic
523C2—41no—
524C2—161no—
525C2—161no—
526C2—9761no—
527C2—2441no—
528C2#2145762511yescharacteristic
529C2#2145895111yescharacteristic
530C2#2145895711yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2186C2
socleC22×C61C22×D8
hypercenter#2186D61
hypocenterC61#33876
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2186

Complements

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

NH ≅ G/Ntype
1. #21458224C2semidirect
2. #21457573C2semidirect
3. #21448059C2semidirect
4. #21448008C2semidirect
5. #21448000C2semidirect
6. #21447985C2semidirect
7. #21447920C2semidirect
8. #21447902C2semidirect
9. #21447852C2semidirect
10. #21447741C2semidirect
11. #21447684C2semidirect
12. #21447647C2semidirect
13. #21447531C2semidirect
14. #21447525C2semidirect
15. C61×#2186C2semidirect
268. #2186D61semidirect
324. C61#33876semidirect

Maximal subgroups

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

subgroupindex
#214582242
#214575732
#214480592
#214480082
#214480002
#214479852
#214479202
#214479022
#214478522
#214477412
#214476842
#214476472
#214475312
#214475252
C61×#21862
#3387661