Finite Group Databasebeta

← #29837031

Subgroups — #29837031

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#21458222C211yesmaximal, characteristic, complemented
2#21457579C211yesmaximal, characteristic, complemented
3#21448061C211yesmaximal, characteristic, complemented
4#21448011C211yesmaximal, characteristic, complemented
5#21448000C211yesmaximal, characteristic, complemented
6#21447984C211yesmaximal, characteristic, complemented
7#21447922C211yesmaximal, characteristic, complemented
8#21447905C211yesmaximal, characteristic, complemented
9#21447855C211yesmaximal, characteristic, complemented
10#21447744C211yesmaximal, characteristic, complemented
11#21447744C211yesmaximal, characteristic, complemented
12#21447685C211yesmaximal, characteristic, complemented
13#21447532C211yesmaximal, characteristic, complemented
14#21447527C211yesmaximal, characteristic, complemented
15C61×#2168C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18#16840458—21no—
19#16840433—21no—
20C2×#14519722C2211yescharacteristic
21C2×D976C2211yescharacteristic
22C2×D976C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840139C2211yescharacteristic
25#16840087—21no—
26#16840081—21no—
27#16840063—21no—
28#16839998C2211yescharacteristic
29#16839998C2211yescharacteristic
30#16839998C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839963—21no—
33#16839909—21no—
34#16839909—21no—
35C4×Dic244C2211yescharacteristic
36C4×D488C2211yescharacteristic
37#16839800C2211yescharacteristic
38C2×#14519711C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C2×M32×C61C2211yescharacteristic
53C22×C16×C61C2211yescharacteristic
54C8×D4×C61C2211yescharacteristic
55C61×C4⋊C16C2211yescharacteristic
56C61×C22⋊C16C2211yescharacteristic
57C61×C22⋊C16C2211yescharacteristic
58C61×#346C2211yescharacteristic
59C2×#11758222—21no—
60C2×#11758222—21no—
61#14519799—22no—
62#14519799—22no—
63#14519799—41no—
64#14519799—41no—
65C2×Dic244C2311yescharacteristic
66C2×#11758190—21no—
67C2×#11758190—21no—
68C2×D488—21no—
69C2×D488C2311yescharacteristic
70C2×D488C2311yescharacteristic
71C2×D488C2311yescharacteristic
72#14519774—21no—
73#14519773—41no—
74#14519772—41no—
75#14519769—21no—
76#14519759—41no—
77#14519751—21no—
78#14519751—21no—
79#14519751—21no—
80#14519751—21no—
81#14519750—41no—
82#14519750—41no—
83#14519749—41no—
84C4×Dic122—21no—
85C4×D244—21no—
86#14519739—41no—
87#14519737—41no—
88#14519736—21no—
89C2×C4⋊Dic61—21no—
90#14519722—22no—
91D976—41no—
92D976—41no—
93#14519711—21no—
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519711C2311yescharacteristic
97#14519711C2311yescharacteristic
98#14519709—21no—
99#14519709—21no—
100#14519702—21no—
101#14519699—21no—
102#14519699—21no—
103#14519699—21no—
104#14519699—21no—
105#14519699—21no—
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C4×D4×C61D411yescharacteristic
109M32×C61—41no—
110C2×C16×C61—41no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114C2×C16×C61C2311yescharacteristic
115C4⋊C8×C61D411yescharacteristic
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C2×D4×C61D811yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C22×Dic61—41no—
129#11758222—42no—
130#11758222—42no—
131#11758222—81no—
132#11758222—81no—
133C2×D244—21no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—41no—
137C2×D244—41no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61—41no—
141C2×Dic122—21no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2×D411yescharacteristic
149C2×C8×C61C2411yescharacteristic
150C4⋊C4×C61D811yescharacteristic
151C22⋊C4×C61D811yescharacteristic
152C22⋊C4×C61D811yescharacteristic
153C42×C61C2×D411yescharacteristic
154C22⋊Dic61—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61—41no—
165#11758196—41no—
166#11758196—41no—
167#11758196—41no—
168C4×Dic61—41no—
169C4×Dic61—41no—
170Dic244—21no—
171Dic244#4112yes—
172D488—21no—
173D488—21no—
174D488—21no—
175D488—21no—
176D488—21no—
177D488—21no—
178D488—81no—
179#11758190—42no—
180#11758190—42no—
181C16×C61—21no—
182C16×C61—21no—
183C16×C61—21no—
184C16×C61—21no—
185C23×C61C2×D811yescharacteristic
186C23×C61C2×D811yescharacteristic
187C22×D61—41no—
188C22×D61—41no—
189C22×D61—41no—
190D4×C61—41no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C22⋊D61—82no—
201C22⋊D61—82no—
202C22⋊D61—82no—
203C22⋊D61—161no—
204C22⋊D61—161no—
205C22⋊D61—161no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—161no—
212D244—41no—
213D244—41no—
214D244—41no—
215D244—41no—
216D244—41no—
217D244—41no—
218D244—82no—
219D244—161no—
220C4×D61—82no—
221C4×D61—82no—
222C4×D61—161no—
223Dic122—22no—
224Dic122—41no—
225C8×C61—21no—
226C8×C61—21no—
227C8×C61—21no—
228C8×C61C2×#4111yescharacteristic
229C8×C61H(5,𝔽2)11yescharacteristic
230#33876—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61C22×D811yescharacteristic
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61#54611yescharacteristic
252C4×C61#57711yescharacteristic
253Dic61—42no—
254Dic61—81no—
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#2186—611no—
269#2175—611no—
270#2168D6111yescharacteristic, complemented
271#2139—611no—
272#2138—611no—
273C2×C61—41no—
274C2×C61—41no—
275C2×C61#329411yescharacteristic
276C2×C61#341411yescharacteristic
277C2×C61#341511yescharacteristic
278D61—161no—
279D61—161no—
280D61—161no—
281C2×#135—611no—
282C2×#135—611no—
283#553—1221no—
284#550—1221no—
285C2×SD32—611no—
286C2×D16—611no—
287C2×D16—611no—
288C2×M32C2×D6111yescharacteristic
289C22×C16C2×D6111yescharacteristic
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#466—611no—
299#460—1221no—
300#449—1221no—
301#449—1221no—
302C4×Q16—611no—
303C4×D8—611no—
304C8×D4C2×D6111yescharacteristic
305#427—611no—
306C2×#107—611no—
307#367—611no—
308#366—611no—
309#366—611no—
310C4⋊C16C2×D6111yescharacteristic
311#358—611no—
312#358—611no—
313#358—611no—
314#357—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321C22⋊C16C2×D6111yescharacteristic
322C22⋊C16C2×D6111yescharacteristic
323#346C2×D6111yescharacteristic
324C61#3387611yescharacteristic, complemented, Sylow
325C2×#41—1221no—
326C2×#41—1221no—
327#135—1222no—
328#135—1222no—
329#135—2441no—
330#135—2441no—
331C2×Q16—611no—
332C2×SD16—1221no—
333C2×SD16—1221no—
334C2×D8—611no—
335C2×D8—611no—
336C2×D8—611no—
337C2×D8—1221no—
338C22×C8C22×D6111yescharacteristic
339C22×C8C22×D6111yescharacteristic
340#127—1221no—
341#127—2441no—
342#126—2441no—
343#125—1221no—
344#123—2441no—
345#121—1221no—
346#121—1221no—
347#121—1221no—
348#121—1221no—
349#121—2441no—
350#121—2441no—
351#121—2441no—
352C4×Q8—1221no—
353C4×D4—1221no—
354C4×D4—2441no—
355C4×D4—2441no—
356C4×D4D24411yescharacteristic
357#117—1221no—
358C2×C4⋊C4—1221no—
359SD32—1222no—
360D16—2441no—
361D16—2441no—
362M32—41no—
363C2×C16—41no—
364C2×C16C22×D6111yescharacteristic
365C2×C16C22×D6111yescharacteristic
366C2×C16C22×D6111yescharacteristic
367C2×C16C22×D6111yescharacteristic
368#107—611no—
369#107—611no—
370#107—611no—
371#107—611no—
372#107—1221no—
373#106—1221no—
374#106—1221no—
375C4⋊C8D24411yescharacteristic
376#103—1221no—
377#102—1221no—
378#102—1221no—
379#102—1221no—
380#102—1221no—
381#102—1221no—
382C22⋊C8D24411yescharacteristic
383C22⋊C8D24411yescharacteristic
384C4×C8C22×D6111yescharacteristic
385#41—4881no—
386#41—4881no—
387#41—2442no—
388#41—2442no—
389C2×Q8—1221no—
390C2×D4—1221no—
391C2×D4—1221no—
392C2×D4—1221no—
393C2×D4—2441no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4D48811yescharacteristic
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4C2×D24411yescharacteristic
407C22×C4C2×D24411yescharacteristic
408Q16—612no—
409Q16—1221no—
410SD16—2442no—
411SD16—2442no—
412D8—1221no—
413D8—1221no—
414D8—1221no—
415D8—1221no—
416D8—1221no—
417D8—1221no—
418D8—4881no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8C2×D24411yescharacteristic
424C2×C8C2×D24411yescharacteristic
425C2×C8C2×D24411yescharacteristic
426C2×C8C23×D6111yescharacteristic
427C4⋊C4—1221no—
428C4⋊C4—1221no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C4⋊C4—2441no—
435C4⋊C4D48811yescharacteristic
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4D48811yescharacteristic
443C22⋊C4D48811yescharacteristic
444C42—2441no—
445C42—2441no—
446C42C2×D24411yescharacteristic
447C16—21no—
448C16—21no—
449C16—21no—
450C16—21no—
451C23—2441no—
452C23—2441no—
453C23—2441no—
454C23C2×D48811yescharacteristic
455C23C2×D48811yescharacteristic
456Q8—1222no—
457Q8—2441no—
458D4—41no—
459D4—9761no—
460D4—9761no—
461D4—9761no—
462D4—9761no—
463D4—4882no—
464D4—4882no—
465D4—4882no—
466D4—4882no—
467D4—2441no—
468D4—2441no—
469D4—2441no—
470D4—2441no—
471D4—2441no—
472D4—2441no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—9761no—
478C2×C4—9761no—
479C2×C4—4882no—
480C2×C4—4882no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4C2×D48811yescharacteristic
487C2×C4C2×D48811yescharacteristic
488C2×C4C2×D48811yescharacteristic
489C2×C4C2×D48811yescharacteristic
490C2×C4C22×D24411yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8#41×D6111yescharacteristic
495C8#1451982211yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—4881no—
503C22—4881no—
504C22—4881no—
505C22—4881no—
506C22—4881no—
507C22—4881no—
508C22—4881no—
509C22—4881no—
510C22—4881no—
511C22C22×D48811yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—4881no—
517C4—4881no—
518C4—4881no—
519C4—4881no—
520C4—2442no—
521C4#1684040711yescharacteristic
522C4#1684057411yescharacteristic
523C2—41no—
524C2—41no—
525C2—9761no—
526C2—9761no—
527C2—9761no—
528C2#2145763311yescharacteristic
529C2#2145895511yescharacteristic
530C2#2145896011yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2168C2
socleC22×C61C22×D8
hypercenter#2168D61
hypocenterC61#33876
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #21458222C2semidirect
2. #21457579C2semidirect
3. #21448061C2semidirect
4. #21448011C2semidirect
5. #21448000C2semidirect
6. #21447984C2semidirect
7. #21447922C2semidirect
8. #21447905C2semidirect
9. #21447855C2semidirect
10. #21447744C2semidirect
11. #21447744C2semidirect
12. #21447685C2semidirect
13. #21447532C2semidirect
14. #21447527C2semidirect
15. C61×#2168C2semidirect
270. #2168D61semidirect
324. C61#33876semidirect

Maximal subgroups

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

subgroupindex
#214582222
#214575792
#214480612
#214480112
#214480002
#214479842
#214479222
#214479052
#214478552
#214477442
#214476852
#214475322
#214475272
C61×#21682
#3387661