Finite Group Databasebeta

← #29837016

Subgroups — #29837016

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458167C211yesmaximal, characteristic, complemented
2#21457562C211yesmaximal, characteristic, complemented
3#21448056C211yesmaximal, characteristic, complemented
4#21448022C211yesmaximal, characteristic, complemented
5#21448000C211yesmaximal, characteristic, complemented
6#21447972C211yesmaximal, characteristic, complemented
7#21447932C211yesmaximal, characteristic, complemented
8#21447905C211yesmaximal, characteristic, complemented
9#21447875C211yesmaximal, characteristic, complemented
10#21447744C211yesmaximal, characteristic, complemented
11#21447738C211yesmaximal, characteristic, complemented
12#21447685C211yesmaximal, characteristic, complemented
13#21447532C211yesmaximal, characteristic, complemented
14C2×#16839567C211yesmaximal, characteristic, complemented
15C61×#2168C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18#16840421—21no—
19#16840416—21no—
20C2×#14519722C2211yescharacteristic
21C2×#14519722C2211yescharacteristic
22C2×D976C2211yescharacteristic
23#16840167C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840076—21no—
26#16840076—21no—
27#16840043—21no—
28#16840003C2211yescharacteristic
29#16839998C2211yescharacteristic
30#16839998C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839985—21no—
33#16839926—21no—
34#16839903—21no—
35C4×Dic244C2211yescharacteristic
36C4×D488C2211yescharacteristic
37C2×#14519711C2211yescharacteristic
38C2×#14519711C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
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×#11758224—41no—
61C22×Dic122—21no—
62#14519799—22no—
63#14519799—41no—
64C2×Dic244—22no—
65C2×Dic244—21no—
66C2×Dic244—41no—
67C2×Dic244C2311yescharacteristic
68C2×Dic244C2311yescharacteristic
69C2×#11758190—21no—
70C2×#11758190—21no—
71C2×D488C2311yescharacteristic
72C2×D488C2311yescharacteristic
73#14519777—21no—
74#14519765—21no—
75#14519763—41no—
76#14519761—41no—
77#14519761—41no—
78#14519757—41no—
79#14519756—21no—
80#14519755—41no—
81#14519751—21no—
82#14519751—21no—
83#14519751—21no—
84#14519749—41no—
85C4×Dic122—21no—
86C4×D244—21no—
87#14519737—41no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90#14519722—22no—
91#14519722—41no—
92D976—41no—
93#14519711—21no—
94#14519711—21no—
95#14519711—21no—
96#14519711C2311yescharacteristic
97#14519711C2311yescharacteristic
98#14519711C2311yescharacteristic
99#14519711C2311yescharacteristic
100#14519702—21no—
101#14519702—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—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129#11758224—84no—
130#11758222—42no—
131#11758222—81no—
132C2×D244—21no—
133C2×D244—21no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×Dic122—21no—
137C2×Dic122—21no—
138C2×Dic122—42no—
139C2×Dic122—41no—
140C2×Dic122—41no—
141C2×Dic122—81no—
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—
160#11758198—41no—
161C4⋊Dic61—21no—
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166C4⋊Dic61—41no—
167C4⋊Dic61—41no—
168#11758196—41no—
169#11758196—41no—
170C4×Dic61—41no—
171Dic244—21no—
172Dic244—21no—
173Dic244—21no—
174Dic244—42no—
175Dic244#4112yescomplemented
176D488—21no—
177D488—21no—
178D488—21no—
179D488—21no—
180#11758190—42no—
181#11758190—81no—
182C16×C61—21no—
183C16×C61—21no—
184C16×C61—21no—
185C16×C61—21no—
186C23×C61C2×D811yescharacteristic
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189C22×D61—41no—
190D4×C61—22no—
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—82no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—82no—
211C2×Dic61—82no—
212C2×Dic61—82no—
213D244—41no—
214D244—41no—
215D244—41no—
216D244—41no—
217C4×D61—82no—
218C4×D61—82no—
219Dic122—22no—
220Dic122—41no—
221Dic122—41no—
222Dic122—41no—
223Dic122—82no—
224Dic122—82no—
225C8×C61—21no—
226C8×C61—21no—
227C8×C61—21no—
228C8×C61C2×#4111yescharacteristic
229C8×C61H(5,𝔽2)11yescharacteristic
230#33875—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61#50912yes—
237C22×C61C22×D811yescharacteristic
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61#54611yescharacteristic
249C4×C61#57711yescharacteristic
250Dic61—42no—
251Dic61—81no—
252Dic61—81no—
253Dic61—81no—
254Dic61—81no—
255Dic61—81no—
256#3334—611no—
257#3285—611no—
258#2243—611no—
259#2236—611no—
260#2232—611no—
261#2227—611no—
262#2220—611no—
263#2215—611no—
264#2210—611no—
265#2186—611no—
266#2185—611no—
267#2175—611no—
268#2168D6111yescharacteristic, complemented
269#2139—611no—
270C2×#358—611no—
271C2×C61—22no—
272C2×C61—41no—
273C2×C61#329411yescharacteristic
274C2×C61C2×#50911yescharacteristic
275C2×C61#341711yescharacteristic
276D61—161no—
277D61—161no—
278C2×#135—611no—
279C22×Q16—611no—
280#548—1221no—
281#547—1221no—
282C2×SD32—611no—
283C2×SD32—611no—
284C2×D16—611no—
285C2×M32C2×D6111yescharacteristic
286C22×C16C2×D6111yescharacteristic
287#500—611no—
288#495—611no—
289#480—1221no—
290#480—1221no—
291#474—1221no—
292#467—611no—
293#466—611no—
294#466—611no—
295#466—611no—
296#464—1221no—
297#452—1221no—
298#448—1221no—
299C4×Q16—611no—
300C4×D8—611no—
301C8×D4C2×D6111yescharacteristic
302C2×#107—611no—
303C2×#107—611no—
304#366—611no—
305#366—611no—
306#366—611no—
307C4⋊C16C2×D6111yescharacteristic
308#358—611no—
309#358—611no—
310#358—611no—
311#358—611no—
312#358—611no—
313#358—611no—
314#357—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318C22⋊C16C2×D6111yescharacteristic
319C22⋊C16C2×D6111yescharacteristic
320#346C2×D6111yescharacteristic
321C61#3387511yescharacteristic, complemented, Sylow
322C2×#41—1221no—
323C2×#41—2441no—
324C22×Q8—1221no—
325#135—1222no—
326#135—2441no—
327C2×Q16—611no—
328C2×Q16—611no—
329C2×Q16—1222no—
330C2×Q16—1221no—
331C2×Q16—2441no—
332C2×SD16—1221no—
333C2×SD16—1221no—
334C2×D8—611no—
335C2×D8—611no—
336C22×C8C22×D6111yescharacteristic
337C22×C8C22×D6111yescharacteristic
338C4⋊Q8—1221no—
339#124—1221no—
340#124—2441no—
341#123—2441no—
342#123—2441no—
343C22⋊Q8—1221no—
344C22⋊Q8—2441no—
345C22⋊Q8—2441no—
346#121—1221no—
347#121—1221no—
348#121—1221no—
349#121—2441no—
350C4×Q8—1221no—
351C4×D4—1221no—
352C4×D4—2441no—
353C4×D4D24411yescharacteristic
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356SD32—1222no—
357SD32—2441no—
358D16—2441no—
359M32—41no—
360C2×C16—41no—
361C2×C16C22×D6111yescharacteristic
362C2×C16C22×D6111yescharacteristic
363C2×C16C22×D6111yescharacteristic
364C2×C16C22×D6111yescharacteristic
365#107—611no—
366#107—611no—
367#107—611no—
368#107—611no—
369#107—1221no—
370#107—1221no—
371#107—1221no—
372C4⋊C8D24411yescharacteristic
373#103—1221no—
374#103—1221no—
375#102—1221no—
376#102—1221no—
377#102—1221no—
378#102—1221no—
379C22⋊C8D24411yescharacteristic
380C22⋊C8D24411yescharacteristic
381C4×C8C22×D6111yescharacteristic
382#41—4881no—
383#41—4884no—
384#41—2442no—
385C2×Q8—1221no—
386C2×Q8—1221no—
387C2×Q8—4881no—
388C2×Q8—2442no—
389C2×Q8—2441no—
390C2×Q8—2441no—
391C2×D4—1221no—
392C2×D4—1221no—
393C2×D4—2441no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4D48811yescharacteristic
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4C2×D24411yescharacteristic
404C22×C4C2×D24411yescharacteristic
405Q16—612no—
406Q16—1221no—
407Q16—1221no—
408Q16—1221no—
409Q16—2442no—
410SD16—4881no—
411SD16—2442no—
412D8—1221no—
413D8—1221no—
414D8—1221no—
415D8—1221no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8C2×D24411yescharacteristic
421C2×C8C2×D24411yescharacteristic
422C2×C8C2×D24411yescharacteristic
423C2×C8C23×D6111yescharacteristic
424C4⋊C4—1221no—
425C4⋊C4—1221no—
426C4⋊C4—1221no—
427C4⋊C4—1221no—
428C4⋊C4—2441no—
429C4⋊C4—2441no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C4⋊C4D48811yescharacteristic
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4D48811yescharacteristic
442C22⋊C4D48811yescharacteristic
443C42—2441no—
444C42C2×D24411yescharacteristic
445C16—21no—
446C16—21no—
447C16—21no—
448C16—21no—
449C23—2441no—
450C23—2441no—
451C23C2×D48811yescharacteristic
452C23C2×D48811yescharacteristic
453Q8—1222no—
454Q8—4882no—
455Q8—4882no—
456Q8—2441no—
457Q8—2441no—
458Q8—2441no—
459D4—22no—
460D4—4882no—
461D4—4882no—
462D4—4882no—
463D4—4882no—
464D4—2441no—
465D4—2441no—
466D4—2441no—
467D4—2441no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—4882no—
473C2×C4—4882no—
474C2×C4—4882no—
475C2×C4—4882no—
476C2×C4—4882no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4C2×D48811yescharacteristic
484C2×C4C2×D48811yescharacteristic
485C2×C4C2×D48811yescharacteristic
486C2×C4C2×D48811yescharacteristic
487C2×C4C22×D24411yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8#41×D6111yescharacteristic
492C8#1451982211yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—4881no—
499C22—4881no—
500C22—4881no—
501C22—4881no—
502C22—4881no—
503C22—4881no—
504C22#1684020012yes—
505C22C22×D48811yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—4881no—
511C4—4881no—
512C4—4881no—
513C4—4881no—
514C4—4881no—
515C4—2442no—
516C4#1684040711yescharacteristic
517C4#1684057411yescharacteristic
518C2—22no—
519C2—41no—
520C2—9761no—
521C2—9761no—
522C2#2145763311yescharacteristic
523C2C2×#1684020011yescharacteristic
524C2#2145897211yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2168C2
socleC22×C61C22×D8
hypercenter#2168D61
hypocenterC61#33875
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. #21458167C2semidirect
2. #21457562C2semidirect
3. #21448056C2semidirect
4. #21448022C2semidirect
5. #21448000C2semidirect
6. #21447972C2semidirect
7. #21447932C2semidirect
8. #21447905C2semidirect
9. #21447875C2semidirect
10. #21447744C2semidirect
11. #21447738C2semidirect
12. #21447685C2semidirect
13. #21447532C2semidirect
14. C2×#16839567C2semidirect
15. C61×#2168C2semidirect
175. Dic244#41semidirect
268. #2168D61semidirect
321. C61#33875semidirect

Maximal subgroups

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

subgroupindex
#214581672
#214575622
#214480562
#214480222
#214480002
#214479722
#214479322
#214479052
#214478752
#214477442
#214477382
#214476852
#214475322
C2×#168395672
C61×#21682
#3387561