Finite Group Databasebeta

← #29837019

Subgroups — #29837019

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#21458168C211yesmaximal, characteristic, complemented
2#21457561C211yesmaximal, characteristic, complemented
3#21448056C211yesmaximal, characteristic, complemented
4#21448023C211yesmaximal, characteristic, complemented
5#21448001C211yesmaximal, characteristic, complemented
6#21447971C211yesmaximal, characteristic, complemented
7#21447931C211yesmaximal, characteristic, complemented
8#21447904C211yesmaximal, characteristic, complemented
9#21447874C211yesmaximal, characteristic, complemented
10#21447741C211yesmaximal, characteristic, complemented
11#21447734C211yesmaximal, characteristic, complemented
12#21447646C211yesmaximal, characteristic, complemented
13#21447530C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C61×#2175C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18#16840424—21no—
19#16840417—21no—
20C2×#14519721C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22C2×#14519716C2211yescharacteristic
23C2×C16×D61C2211yescharacteristic
24#16840167C2211yescharacteristic
25#16840146C2211yescharacteristic
26#16840074—21no—
27#16840074—21no—
28#16840042—21no—
29#16840004C2211yescharacteristic
30#16839999C2211yescharacteristic
31#16839995C2211yescharacteristic
32#16839995C2211yescharacteristic
33#16839984—21no—
34#16839927—21no—
35#16839902—21no—
36C8×D244C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#107×D61C2211yescharacteristic
39#16839587C2211yescharacteristic
40#16839587C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839541C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C4×D8×C61C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#346C2211yescharacteristic
59C2×#11758226—21no—
60C2×#11758222—41no—
61C2×Q8×D61—21no—
62#14519800—22no—
63#14519800—41no—
64C2×Dic244C2311yescharacteristic
65C2×#11758202—21no—
66Q16×D61—22no—
67Q16×D61—41no—
68C2×#11758190—21no—
69C2×#11758201—21no—
70C2×D488C2311yescharacteristic
71C2×C8×D61C2311yescharacteristic
72C2×C8×D61C2311yescharacteristic
73#14519777—21no—
74#14519765—21no—
75#14519765—41no—
76#14519759—41no—
77#14519759—41no—
78#14519757—21no—
79#14519757—41no—
80#14519756—41no—
81#14519752—21no—
82#14519752—41no—
83#14519748—21no—
84#14519748—21no—
85C4×D244—41no—
86C4×D244D411yescharacteristic
87C4⋊C4×D61—21no—
88C4⋊C4×D61—21no—
89#14519721—41no—
90#14519718—41no—
91#14519716—41no—
92C2×#11758185C2311yescharacteristic
93C2×#11758185C2311yescharacteristic
94C16×D61—41no—
95#14519711—21no—
96#14519711C2311yescharacteristic
97#14519711C2311yescharacteristic
98#14519710—21no—
99#14519710—21no—
100C4⋊#92418D411yescharacteristic
101#14519700—21no—
102#14519698—21no—
103#14519698—21no—
104#14519697—21no—
105#14519689D411yescharacteristic
106#14519689D411yescharacteristic
107C2×Q16×C61C2311yescharacteristic
108C2×D8×C61C2311yescharacteristic
109C4×Q8×C61—21no—
110C4×D4×C61—21no—
111SD32×C61—22no—
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#103×C61—21no—
117#102×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×D4×C61—21no—
121C22×C4×C61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124#11758226—42no—
125#11758226—81no—
126Q8×D61—42no—
127Q8×D61—81no—
128#11758222—84no—
129C2×D244—21no—
130C2×D244—41no—
131C2×D244—41no—
132C2×D244D811yescharacteristic
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×D411yescharacteristic
139C2×Dic122—21no—
140C2×Dic122—41no—
141C2×Dic122—41no—
142Q16×C61—21no—
143Q16×C61#4112yescomplemented
144D8×C61—21no—
145D8×C61—21no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2411yescharacteristic
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C42×C61—41no—
153C42×C61C2×D411yescharacteristic
154C22⋊Dic61—41no—
155C22⋊Dic61—41no—
156#11758202—42no—
157#11758201—42no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198—41no—
162#11758198D811yescharacteristic
163#11758198D811yescharacteristic
164C4⋊Dic61—21no—
165C4⋊Dic61—21no—
166C4⋊Dic61—41no—
167C4⋊Dic61—41no—
168C4⋊Dic61D811yescharacteristic
169#11758196—41no—
170#11758196—41no—
171C2×#92418C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173Dic244—21no—
174Dic244—21no—
175D488—21no—
176D488—21no—
177#11758190—81no—
178C8×D61—21no—
179C8×D61—21no—
180C8×D61—21no—
181C8×D61—21no—
182C16×C61—21no—
183C16×C61—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61—41no—
187C22×D61—41no—
188C22×D61C2×D811yescharacteristic
189C22×D61C2×D811yescharacteristic
190Q8×C61—22no—
191Q8×C61—41no—
192D4×C61—41no—
193D4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—82no—
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C22⋊D61—82no—
202C22⋊D61—82no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61C2×D811yescharacteristic
207C2×Dic61C2×D811yescharacteristic
208D244—22no—
209D244—41no—
210D244—41no—
211D244—82no—
212D244—82no—
213C4×D61—21no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—82no—
218C4×D61—82no—
219C4×D61—82no—
220C4×D61—82no—
221Dic122—41no—
222Dic122—41no—
223Dic122—82no—
224Dic122—82no—
225C8×C61—21no—
226C8×C61C2×#4111yescharacteristic
227C8×C61H(5,𝔽2)11yescharacteristic
228#92418—21no—
229#92418—21no—
230#33875—611nomaximal, Sylow
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61C22×D811yescharacteristic
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—81no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61#50912yes—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—42no—
247C4×C61—81no—
248C4×C61—81no—
249C4×C61#54611yescharacteristic
250C4×C61#57711yescharacteristic
251Dic61—21no—
252Dic61—21no—
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#2175D6111yescharacteristic, complemented
268#2168—611no—
269#2139—611no—
270C2×#358—611no—
271C2×C61—161no—
272C2×C61#329411yescharacteristic
273C2×C61C2×#50911yescharacteristic
274C2×C61#341711yescharacteristic
275D61—22no—
276D61—41no—
277D61—161no—
278C2×#135—611no—
279C22×Q16—611no—
280#548—1221no—
281#547—1221no—
282C2×SD32—611no—
283C2×SD32C2×D6111yescharacteristic
284C2×D16—611no—
285C2×M32—611no—
286C22×C16—611no—
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×Q16C2×D6111yescharacteristic
300C4×D8C2×D6111yescharacteristic
301C8×D4—611no—
302C2×#107—611no—
303C2×#107—611no—
304#366—611no—
305#366—611no—
306#366C2×D6111yescharacteristic
307C4⋊C16—611no—
308#358—611no—
309#358—611no—
310#358—611no—
311#358—611no—
312#358—611no—
313#358C2×D6111yescharacteristic
314#357—611no—
315#357—611no—
316#357—611no—
317#357C2×D6111yescharacteristic
318C22⋊C16—611no—
319C22⋊C16—611no—
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—1221no—
329C2×Q16—1222no—
330C2×Q16—2441no—
331C2×Q16C22×D6111yescharacteristic
332C2×SD16—1221no—
333C2×SD16—1221no—
334C2×D8—611no—
335C2×D8C22×D6111yescharacteristic
336C22×C8—611no—
337C22×C8—611no—
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—21no—
351C4×D4—21no—
352C4×D4—611no—
353C4×D4—2441no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356SD32—22no—
357SD32—2441no—
358D16—2441no—
359M32—2441no—
360C2×C16—611no—
361C2×C16—611no—
362C2×C16—2441no—
363C2×C16C22×D6111yescharacteristic
364C2×C16C22×D6111yescharacteristic
365#107—611no—
366#107—611no—
367#107—1221no—
368#107—1221no—
369#107—1221no—
370#107C22×D6111yescharacteristic
371#107C22×D6111yescharacteristic
372C4⋊C8—611no—
373#103—21no—
374#103—1221no—
375#102—21no—
376#102—1221no—
377#102—1221no—
378#102—1221no—
379C22⋊C8—611no—
380C22⋊C8—611no—
381C4×C8C22×D6111yescharacteristic
382#41—4884no—
383#41—4881no—
384#41—2442no—
385C2×Q8—21no—
386C2×Q8—1221no—
387C2×Q8—4881no—
388C2×Q8—2441no—
389C2×Q8—2442no—
390C2×Q8—2441no—
391C2×D4—21no—
392C2×D4—611no—
393C2×D4—1221no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C22×C4—41no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405Q16—21no—
406Q16—1221no—
407Q16—1221no—
408Q16—2442no—
409Q16#1175822212yescomplemented
410SD16—4881no—
411SD16—2442no—
412D8—21no—
413D8—21no—
414D8—1221no—
415D8—1221no—
416C2×C8—611no—
417C2×C8—611no—
418C2×C8—1221no—
419C2×C8—1221no—
420C2×C8—1221no—
421C2×C8—1221no—
422C2×C8D4×D6111yescharacteristic
423C2×C8C23×D6111yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—611no—
428C4⋊C4—1221no—
429C4⋊C4—1221no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C22⋊C4—41no—
435C22⋊C4—611no—
436C22⋊C4—611no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C42—41no—
444C42D4×D6111yescharacteristic
445C16—21no—
446C16—21no—
447C16—1221no—
448C16—1221no—
449C23—41no—
450C23—611no—
451C23—611no—
452C23—2441no—
453Q8—22no—
454Q8—41no—
455Q8—4882no—
456Q8—4882no—
457Q8—2441no—
458Q8—2441no—
459D4—41no—
460D4—41no—
461D4—1222no—
462D4—4882no—
463D4—4882no—
464D4—4882no—
465D4—4882no—
466D4—2441no—
467D4—2441no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—4882no—
479C2×C4—4882no—
480C2×C4—4882no—
481C2×C4—4882no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4D8×D6111yescharacteristic
486C2×C4D8×D6111yescharacteristic
487C2×C4C2×D4×D6111yescharacteristic
488C8—21no—
489C8—1221no—
490C8—1221no—
491C8C2×#1175822211yescharacteristic
492C8#1451982311yescharacteristic
493C22—81no—
494C22—81no—
495C22—81no—
496C22—612no—
497C22—1221no—
498C22—1221no—
499C22—1221no—
500C22—1221no—
501C22—1221no—
502C22—4881no—
503C22—4881no—
504C22—4881no—
505C22C2×D8×D6111yescharacteristic
506C4—21no—
507C4—21no—
508C4—42no—
509C4—81no—
510C4—81no—
511C4—1221no—
512C4—1221no—
513C4—4881no—
514C4—4881no—
515C4—4881no—
516C4#1684040811yescharacteristic
517C4#1684056911yescharacteristic
518C2—161no—
519C2—1222no—
520C2—9761no—
521C2—2441no—
522C2#2145763411yescharacteristic
523C2#509×D6111yescharacteristic
524C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2175C2
socleC22×C61C22×D8
hypercenter#2175D61
hypocenterC61#33875
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #21458168C2semidirect
2. #21457561C2semidirect
3. #21448056C2semidirect
4. #21448023C2semidirect
5. #21448001C2semidirect
6. #21447971C2semidirect
7. #21447931C2semidirect
8. #21447904C2semidirect
9. #21447874C2semidirect
10. #21447741C2semidirect
11. #21447734C2semidirect
12. #21447646C2semidirect
13. #21447530C2semidirect
14. #358×D61C2semidirect
15. C61×#2175C2semidirect
143. Q16×C61#41semidirect
267. #2175D61semidirect
321. C61#33875semidirect
409. Q16#11758222semidirect

Maximal subgroups

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

subgroupindex
#214581682
#214575612
#214480562
#214480232
#214480012
#214479712
#214479312
#214479042
#214478742
#214477412
#214477342
#214476462
#214475302
#358×D612
C61×#21752
#3387561