Finite Group Databasebeta

← #29837010

Subgroups — #29837010

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#21458164C211yesmaximal, characteristic, complemented
2#21457560C211yesmaximal, characteristic, complemented
3#21448057C211yesmaximal, characteristic, complemented
4#21448020C211yesmaximal, characteristic, complemented
5#21447999C211yesmaximal, characteristic, complemented
6#21447969C211yesmaximal, characteristic, complemented
7#21447935C211yesmaximal, characteristic, complemented
8#21447905C211yesmaximal, characteristic, complemented
9#21447877C211yesmaximal, characteristic, complemented
10#21447745C211yesmaximal, characteristic, complemented
11#21447736C211yesmaximal, characteristic, complemented
12#21447686C211yesmaximal, characteristic, complemented
13#21447644C211yesmaximal, characteristic, complemented
14#21447530C211yesmaximal, characteristic, complemented
15C2×C61×#358C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17#16840423—21no—
18#16840413—21no—
19C2×#14519720C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21C2×D976C2211yescharacteristic
22C2×#14519716C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840147C2211yescharacteristic
25#16840077—21no—
26#16840075—21no—
27#16840041—21no—
28#16840000C2211yescharacteristic
29#16839999C2211yescharacteristic
30#16839998C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839986—21no—
33#16839923—21no—
34#16839901—21no—
35Q16×Dic61C2211yescharacteristic
36#16839844C2211yescharacteristic
37C8×C22⋊D61C2211yescharacteristic
38#107×D61C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839537C2211yescharacteristic
52C22×Q16×C61C2211yescharacteristic
53C22×C16×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C61×#358C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×#11758226—21no—
60C2×#11758222—41no—
61#14519800—22no—
62#14519800—41no—
63C2×#11758201—21no—
64C2×#11758201—21no—
65C2×D488C2311yescharacteristic
66C2×D488C2311yescharacteristic
67C2×C8×D61C2311yescharacteristic
68#14519776—21no—
69#14519766—21no—
70#14519766—41no—
71#14519762—41no—
72#14519760—41no—
73#14519755—41no—
74#14519753—21no—
75#14519753—41no—
76#14519752—21no—
77#14519751—21no—
78#14519751—21no—
79#14519751—41no—
80Q8×Dic61—21no—
81#14519739—21no—
82C4×C22⋊D61—41no—
83C4×C22⋊D61D411yescharacteristic
84C4⋊C4×D61—21no—
85#14519720—22no—
86#14519720—41no—
87D976—41no—
88#14519716—41no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519706D411yescharacteristic
96#14519701—21no—
97#14519701—21no—
98#14519699—21no—
99#14519699—21no—
100#14519697—21no—
101#14519697—21no—
102C22⋊#92418D411yescharacteristic
103#14519689D411yescharacteristic
104C8×Dic61C2311yescharacteristic
105C22×Q8×C61—21no—
106C2×Q16×C61—22no—
107C2×Q16×C61—21no—
108C2×Q16×C61—41no—
109C2×Q16×C61C2311yescharacteristic
110C2×Q16×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C4⋊C4×C61—21no—
113C2×C16×C61—41no—
114C2×C16×C61C2311yescharacteristic
115C2×C16×C61C2311yescharacteristic
116#107×C61—21no—
117#107×C61C2311yescharacteristic
118#107×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61—42no—
122C2×Q8×C61—41no—
123C2×Q8×C61—81no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C2×C22⋊D61D811yescharacteristic
130#11758226—42no—
131#11758226—81no—
132#11758222—84no—
133C2×D244—21no—
134C2×D244—21no—
135C2×D244—41no—
136C2×D244—41no—
137C2×C4×D61—41no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61C2×D411yescharacteristic
141C2×Dic122—41no—
142Q16×C61—21no—
143Q16×C61—21no—
144Q16×C61—21no—
145Q16×C61—42no—
146Q16×C61#4112yescomplemented
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61C2×D411yescharacteristic
150C2×C8×C61C2411yescharacteristic
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—41no—
154C22⋊Dic61D811yescharacteristic
155#11758201—42no—
156#11758201—81no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198—41no—
162#11758198—41no—
163#11758198—41no—
164#11758198D811yescharacteristic
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61—41no—
168#11758196—41no—
169#11758196—41no—
170#11758196—41no—
171#11758196D811yescharacteristic
172C4×Dic61—41no—
173C4×Dic61C2×D411yescharacteristic
174C2×#92418C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176D488—21no—
177D488—21no—
178D488—21no—
179D488—21no—
180C8×D61—21no—
181C8×D61—21no—
182C16×C61—21no—
183C16×C61—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61C2×D811yescharacteristic
187C22×D61—41no—
188C22×D61—41no—
189C22×D61C2×D811yescharacteristic
190Q8×C61—22no—
191Q8×C61—41no—
192Q8×C61—41no—
193Q8×C61—41no—
194Q8×C61—82no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—82no—
202C2×C4×C61—82no—
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C22⋊D61—22no—
206C22⋊D61—82no—
207C22⋊D61—82no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61C2×D811yescharacteristic
211C2×Dic61C2×D811yescharacteristic
212C2×Dic61C2×D811yescharacteristic
213D244—41no—
214D244—41no—
215D244—41no—
216D244—41no—
217D244—82no—
218D244—82no—
219C4×D61—21no—
220C4×D61—21no—
221C4×D61—82no—
222C4×D61—82no—
223C4×D61—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—21no—
232C22×C61—21no—
233C22×C61#50912yes—
234C22×C61C22×D811yescharacteristic
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C4×C61—21no—
245C4×C61—42no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61—81no—
249C4×C61#54611yescharacteristic
250C4×C61#57711yescharacteristic
251Dic61—21no—
252Dic61—21no—
253Dic61—21no—
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#2168—611no—
269#2139—611no—
270C2×#358D6111yescharacteristic, complemented
271C2×C61—22no—
272C2×C61#329411yescharacteristic
273C2×C61C2×#50911yescharacteristic
274C2×C61#341711yescharacteristic
275D61—41no—
276D61—161no—
277D61—161no—
278C2×#135—611no—
279C22×Q16C2×D6111yescharacteristic
280#548—1221no—
281#547—1221no—
282C2×SD32—611no—
283C2×SD32—611no—
284C2×D16—611no—
285C2×M32—611no—
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×D4—611no—
302C2×#107—611no—
303C2×#107C2×D6111yescharacteristic
304#366—611no—
305#366—611no—
306#366—611no—
307C4⋊C16—611no—
308#358—611no—
309#358—611no—
310#358C2×D6111yescharacteristic
311#358C2×D6111yescharacteristic
312#358C2×D6111yescharacteristic
313#358C2×D6111yescharacteristic
314#357—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318C22⋊C16—611no—
319C22⋊C16—611no—
320#346—611no—
321C61#3387511yescharacteristic, complemented, Sylow
322C2×#41—1221no—
323C2×#41—2441no—
324C22×Q8—21no—
325#135—1222no—
326#135—2441no—
327C2×Q16—22no—
328C2×Q16—21no—
329C2×Q16—41no—
330C2×Q16C22×D6111yescharacteristic
331C2×Q16C22×D6111yescharacteristic
332C2×SD16—1221no—
333C2×SD16—1221no—
334C2×D8—611no—
335C2×D8—611no—
336C22×C8—611no—
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—611no—
352C4×D4—1221no—
353C4×D4—2441no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—1221no—
356SD32—1222no—
357SD32—2441no—
358D16—2441no—
359M32—2441no—
360C2×C16—41no—
361C2×C16—611no—
362C2×C16—611no—
363C2×C16C22×D6111yescharacteristic
364C2×C16C22×D6111yescharacteristic
365#107—21no—
366#107—611no—
367#107—611no—
368#107—1221no—
369#107—1221no—
370#107C22×D6111yescharacteristic
371#107C22×D6111yescharacteristic
372C4⋊C8—611no—
373#103—1221no—
374#103—1221no—
375#102—1221no—
376#102—1221no—
377#102—1221no—
378#102—1221no—
379C22⋊C8—611no—
380C22⋊C8—611no—
381C4×C8—611no—
382#41—4884no—
383#41—4881no—
384#41—2442no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—42no—
388C2×Q8—41no—
389C2×Q8—81no—
390C2×Q8—2441no—
391C2×D4—611no—
392C2×D4—1221no—
393C2×D4—1221no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—611no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4D4×D6111yescharacteristic
405Q16—21no—
406Q16—21no—
407Q16—21no—
408Q16—42no—
409Q16#1175822212yescomplemented
410SD16—4881no—
411SD16—2442no—
412D8—1221no—
413D8—1221no—
414D8—1221no—
415D8—1221no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—611no—
419C2×C8—611no—
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—611no—
435C22⋊C4—611no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C42—611no—
444C42—2441no—
445C16—21no—
446C16—21no—
447C16—1221no—
448C16—1221no—
449C23—611no—
450C23—2441no—
451C23—2441no—
452C23D8×D6111yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—4882no—
459D4—1222no—
460D4—4882no—
461D4—4882no—
462D4—4882no—
463D4—4882no—
464D4—2441no—
465D4—2441no—
466D4—2441no—
467D4—2441no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—611no—
477C2×C4—611no—
478C2×C4—611no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—4882no—
482C2×C4—4882no—
483C2×C4—4882no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4D8×D6111yescharacteristic
487C2×C4C2×D4×D6111yescharacteristic
488C8—21no—
489C8—1221no—
490C8—1221no—
491C8C2×#1175822211yescharacteristic
492C8#1451982211yescharacteristic
493C22—21no—
494C22—21no—
495C22—1221no—
496C22—1221no—
497C22—1221no—
498C22—4881no—
499C22—4881no—
500C22—4881no—
501C22—4881no—
502C22—4881no—
503C22—4881no—
504C22#1684019912yes—
505C22C2×D8×D6111yescharacteristic
506C4—21no—
507C4—42no—
508C4—81no—
509C4—81no—
510C4—81no—
511C4—1221no—
512C4—1221no—
513C4—1221no—
514C4—4881no—
515C4—4881no—
516C4#1684040211yescharacteristic
517C4#1684056811yescharacteristic
518C2—22no—
519C2—9761no—
520C2—9761no—
521C2—2441no—
522C2#2145762811yescharacteristic
523C2C2×#1684019911yescharacteristic
524C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#358C2
socleC22×C61C22×D8
hypercenterC2×#358D61
hypocenterC61#33875
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
1. #21458164C2semidirect
2. #21457560C2semidirect
3. #21448057C2semidirect
4. #21448020C2semidirect
5. #21447999C2semidirect
6. #21447969C2semidirect
7. #21447935C2semidirect
8. #21447905C2semidirect
9. #21447877C2semidirect
10. #21447745C2semidirect
11. #21447736C2semidirect
12. #21447686C2semidirect
13. #21447644C2semidirect
14. #21447530C2semidirect
15. C2×C61×#358C2semidirect
146. Q16×C61#41semidirect
270. C2×#358D61semidirect
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
#214581642
#214575602
#214480572
#214480202
#214479992
#214479692
#214479352
#214479052
#214478772
#214477452
#214477362
#214476862
#214476442
#214475302
C2×C61×#3582
#3387561