Finite Group Databasebeta

← #11919284

Subgroups — #11919284

Order 1152.

12433 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C3×#5964C212yesmaximal, complemented
3#10596697C2116yesmaximal, complemented
4D3×#1009C2116yesmaximal, complemented
5#10596689C214yesmaximal, complemented
6#10596675C2112yesmaximal, complemented
7#10596669C216yesmaximal, complemented
8C2×#64308C216yesmaximal, complemented
9#87574—32nomaximal
10C2×C32×#41C2211yescharacteristic, complemented
11#64366C22116yescomplemented
12C2×#3832C2212yescomplemented
13C2×D4×C3⋊D3C2216yescomplemented
14C2×#3828C2213yescomplemented
15C22×C4⋊(C3⋊D3)C2213yescomplemented
16C3×#1010C2218yescomplemented
17C3×#1009C2218yescomplemented
18C3×D3×#41C22116yescomplemented
19C3×#1007C2214yescomplemented
20C3×#1004C22112yescomplemented
21C2×C3×#235C22112yescomplemented
22#64330C22124yescomplemented
23C2×#3811C22124yescomplemented
24#64320C22116yescomplemented
25D3×#239C22132yescomplemented
26#64316C22116yescomplemented
27#64314C22196yescomplemented
28#64312C22148yescomplemented
29D32×D4C22148yescomplemented
30#64308C22112yescomplemented
31#64308C22124yescomplemented
32#64308C22148yescomplemented
33#64307C22124yescomplemented
34#64306C22124yescomplemented
35D3×#235C22148yescomplemented
36C2×D3×D12C22124yescomplemented
37C2×#3799C22124yescomplemented
38#64298C2214yescomplemented
39#64297C22124yescomplemented
40C3×#585—32no—
41#5968—316no—
42#5968—38no—
43D3×H(5,𝔽2)—316no—
44D3×H(5,𝔽2)—324no—
45#5964—316no—
46#5964—312no—
47#5964D312yescomplemented
48C2×#1009—32no—
49C2×#1009—316no—
50C2×#1009—312no—
51C2×#1009—61no—
52C23×C3⋊D3C2316yescomplemented
53C22×D32C23124yescomplemented
54C32×#41C2318yescomplemented
55C2×C32×Q8C2311yescharacteristic, complemented
56C2×C32×D4C2313yescomplemented
57C22×C32×C4C2313yescomplemented
58C2×#638C2316yescomplemented
59#3832C23116yescomplemented
60D4×C3⋊D3C23148yescomplemented
61#3828C23124yescomplemented
62C2×C4⋊(C3⋊D3)C23124yescomplemented
63C2×C4⋊(C3⋊D3)C2313yescomplemented
64C2×C4⋊(C3⋊D3)C2316yescomplemented
65C2×C4×C3⋊D3C2316yescomplemented
66C2×#634C2311yescharacteristic, complemented
67C2×C3×#67C23124yescomplemented
68C3×#239C23116yescomplemented
69C3×D3×Q8C23116yescomplemented
70C3×#237C23148yescomplemented
71C3×D3×D4C23148yescomplemented
72C3×#235C23124yescomplemented
73C3×#235C2318yescomplemented
74C3×#235C23124yescomplemented
75C3×#235C23124yescomplemented
76C2×C3×D12C23112yescomplemented
77C2×C3×C4×D3C23124yescomplemented
78C2×C3×Dic6C23112yescomplemented
79#3811C23148yescomplemented
80#3811C23196yescomplemented
81D3×#67C23196yescomplemented
82C2×#626C23148yescomplemented
83C2×#624C23124yescomplemented
84#3805C23116yescomplemented
85#3804C23196yescomplemented
86#3802C23124yescomplemented
87D3×D12C23148yescomplemented
88D3×D12C23196yescomplemented
89C4×D32C23148yescomplemented
90#3799C23148yescomplemented
91#3799C23196yescomplemented
92#3798C23148yescomplemented
93#3797C23124yescomplemented
94#3796C23148yescomplemented
95#3795C23116yescomplemented
96D3×Dic6C23116yescomplemented
97H(7,𝔽2)—91noSylow
98C3×2−1+4—38no—
99C3×2−1+4—34no—
100C3×H(5,𝔽2)—38no—
101C3×H(5,𝔽2)—312no—
102C2×C3×#41—21no—
103C2×C3×#41—316no—
104C2×C3×#41—312no—
105C2×C3×#41C2×D312yescomplemented
106#1010—38no—
107#1010—324no—
108#1010C2×D318yescomplemented
109#1009—316no—
110#1009—316no—
111#1009—332no—
112#1009—396no—
113#1009—348no—
114#1009—324no—
115#1009—348no—
116#1009—348no—
117#1009—324no—
118#1009—616no—
119#1009C2×D318yescomplemented
120D3×#41—332no—
121D3×#41—396no—
122D3×#41—348no—
123D3×#41—348no—
124D3×#41C2×D3116yescomplemented
125#1007—332no—
126#1007—324no—
127#1007C2×D314yescomplemented
128C2×#239—34no—
129C2×#239—332no—
130C2×#239—324no—
131C2×#239—62no—
132#1004—348no—
133#1004—396no—
134#1004—324no—
135#1004C2×D3112yescomplemented
136C2×D3×D4—312no—
137C2×D3×D4—348no—
138C2×D3×D4—396no—
139C2×D3×D4—324no—
140C2×D3×D4—66no—
141C2×#235—36no—
142C2×#235—348no—
143C2×#235—324no—
144C2×#235—63no—
145C2×#235C2×D3112yescomplemented
146C22×D12—36no—
147C22×D12—324no—
148C22×D12—63no—
149C23×C32C2413yes—
150C22×C3⋊D3—86no—
151C22×C3⋊D3C24124yes—
152C22×C3⋊D3C2416yes—
153C22×C3×D3C24124yes—
154C2×D32—824no—
155C2×D32C24148yes—
156C32×Q8C2414yes—
157C32×D4C24112yes—
158C2×C32×C4C24112yes—
159C2×C32×C4C2411yescharacteristic
160C2×C32×C4C2413yes—
161#638C24124yes—
162C2×C3⋊Dic3C2412yes—
163C4⋊(C3⋊D3)C24112yes—
164C4⋊(C3⋊D3)C24124yes—
165C4×C3⋊D3C24124yes—
166#634C2414yes—
167C3×#67C24148yes—
168C3×#67C24116yes—
169C2×C3×Dic3C24124yes—
170C3×D12C2418yes—
171C3×D12C24124yes—
172C3×C4×D3C24116yes—
173C3×C4×D3C24148yes—
174C3×Dic6C2418yes—
175C3×Dic6C24124yes—
176#627C24116yes—
177#626C24196yes—
178#625C24116yes—
179#624C24148yes—
180D3×Dic3C24132yes—
181#585—32no—
182#585—96no—
183#585—916no—
184#585—94no—
185C2×H(5,𝔽2)—96no—
186C2×H(5,𝔽2)—916no—
187C2×H(5,𝔽2)—912no—
188C2×H(5,𝔽2)—91no—
189C23×D3—312no—
190C23×D3—348no—
191C23×D3—66no—
192C3×#41—28no—
193C3×#41—316no—
194C3×#41—348no—
195C3×#41—324no—
196C3×#41—324no—
197C3×#41—38no—
198C3×#41—324no—
199C3×#41C22×D318yescomplemented
200C3×#41C22×D318yescomplemented
201C2×C3×Q8—21no—
202C2×C3×Q8—316no—
203C2×C3×Q8—312no—
204C2×C3×Q8C22×D312yescomplemented
205C2×C3×D4—23no—
206C2×C3×D4—324no—
207C2×C3×D4—348no—
208C2×C3×D4—312no—
209C2×C3×D4C22×D316yescomplemented
210C22×C3×C4—23no—
211C22×C3×C4—324no—
212C22×C3×C4C22×D316yescomplemented
213C2×#67—312no—
214C2×#67—396no—
215C2×#67—348no—
216C2×#67—66no—
217C2×#67C22×D3124yescomplemented
218#239—332no—
219#239—348no—
220#239—396no—
221#239—348no—
222#239—616no—
223#239C22×D3116yescomplemented
224D3×Q8—316no—
225D3×Q8—348no—
226D3×Q8C22×D3116yescomplemented
227#237—332no—
228#237—396no—
229#237—316no—
230#237—348no—
231#237C22×D3148yescomplemented
232D3×D4—396no—
233D3×D4—396no—
234D3×D4—3192no—
235D3×D4—396no—
236D3×D4—348no—
237D3×D4—396no—
238D3×D4—348no—
239D3×D4—648no—
240D3×D4C22×D3148yescomplemented
241#235—324no—
242#235—324no—
243#235—396no—
244#235—316no—
245#235—396no—
246#235—348no—
247#235—396no—
248#235—624no—
249#235C22×D3124yescomplemented
250#235C22×D318yescomplemented
251#235C22×D3124yescomplemented
252#235C22×D3124yescomplemented
253C2×D12—348no—
254C2×D12—36no—
255C2×D12—324no—
256C2×D12—312no—
257C2×D12—324no—
258C2×D12—348no—
259C2×D12—396no—
260C2×D12—63no—
261C2×D12—66no—
262C2×D12—624no—
263C2×D12C22×D3112yescomplemented
264C2×C4×D3—312no—
265C2×C4×D3—348no—
266C2×C4×D3—396no—
267C2×C4×D3—66no—
268C2×C4×D3C22×D3124yescomplemented
269C2×Dic6—32no—
270C2×Dic6—316no—
271C2×Dic6—61no—
272C2×Dic6C22×D3112yescomplemented
273C22×C32—43no—
274C22×C32C2516yes—
275C22×C32C2511yescharacteristic
276C2×C3⋊D3—46no—
277C2×C3⋊D3—424no—
278C2×C3⋊D3C25112yes—
279C2×C3×D3—424no—
280C2×C3×D3C25116yes—
281D32—448no—
282C32×C4C2512yes—
283C32×C4C2516yes—
284C3⋊Dic3C2514yes—
285C3×Dic3C25116yes—
2862−1+4—38no—
2872−1+4—34no—
2882−1+4—916no—
2892−1+4—924no—
2902−1+4—94no—
291H(5,𝔽2)—38no—
292H(5,𝔽2)—312no—
293H(5,𝔽2)—924no—
294H(5,𝔽2)—996no—
295H(5,𝔽2)—924no—
296H(5,𝔽2)—916no—
297H(5,𝔽2)—912no—
298H(5,𝔽2)—948no—
299H(5,𝔽2)—924no—
300H(5,𝔽2)—916no—
301C2×#41—316no—
302C2×#41—312no—
303C2×#41—924no—
304C2×#41—948no—
305C2×#41—932no—
306C2×#41—948no—
307C2×#41—924no—
308C2×#41—92no—
309C2×#41—93no—
310C2×#41D3211yescharacteristic, complemented
311C22×D4—924no—
312C22×D4—924no—
313C22×D4—948no—
314C22×D4—96no—
315C22×D4—93no—
316C23×C3—23no—
317C23×C3—324no—
318C23×C3C23×D316yes—
319C22×D3—312no—
320C22×D3—348no—
321C22×D3—396no—
322C22×D3—66no—
323C22×D3—624no—
324C22×D3—2448no—
325C22×D3—2412no—
326C22×D3—2412no—
327C22×D3C23×D3124yes—
328C3×Q8—24no—
329C3×Q8—38no—
330C3×Q8—324no—
331C3×Q8C23×D318yes—
332C3×D4—212no—
333C3×D4—316no—
334C3×D4—348no—
335C3×D4—38no—
336C3×D4—324no—
337C3×D4C23×D3124yes—
338C2×C3×C4—21no—
339C2×C3×C4—23no—
340C2×C3×C4—212no—
341C2×C3×C4—324no—
342C2×C3×C4—316no—
343C2×C3×C4—348no—
344C2×C3×C4C23×D312yes—
345C2×C3×C4C23×D3112yes—
346C2×C3×C4C23×D316yes—
347C2×C3×C4C23×D3112yes—
348#67—348no—
349#67—332no—
350#67—396no—
351#67—624no—
352#67C23×D3148yes—
353#67C23×D3116yes—
354C2×Dic3—34no—
355C2×Dic3—332no—
356C2×Dic3—62no—
357C2×Dic3C23×D3124yes—
358D12—396no—
359D12—312no—
360D12—312no—
361D12—348no—
362D12—612no—
363D12—624no—
364D12C23×D318yes—
365D12C23×D3124yes—
366C4×D3—332no—
367C4×D3—348no—
368C4×D3—396no—
369C4×D3—624no—
370C4×D3C23×D3148yes—
371C4×D3C23×D3116yes—
372Dic6—34no—
373Dic6—34no—
374Dic6—332no—
375Dic6—64no—
376Dic6C23×D318yes—
377Dic6C23×D3124yes—
378C2×C32—21no—
379C2×C32—26no—
380C2×C32C2611yescharacteristic
381C3⋊D3—212no—
382C3×D3—216no—
383C24—924no—
384C24—96no—
385#41—316no—
386#41—348no—
387#41—324no—
388#41—38no—
389#41—324no—
390#41—324no—
391#41—948no—
392#41—996no—
393#41—916no—
394#41—948no—
395#41—996no—
396#41—916no—
397#41—948no—
398#41—916no—
399#41—924no—
400#41C2×D3218yescomplemented
401C2×Q8—316no—
402C2×Q8—312no—
403C2×Q8—916no—
404C2×Q8—924no—
405C2×Q8—91no—
406C2×Q8C2×D3211yescharacteristic, complemented
407C2×D4—324no—
408C2×D4—348no—
409C2×D4—312no—
410C2×D4—948no—
411C2×D4—996no—
412C2×D4—948no—
413C2×D4—948no—
414C2×D4—996no—
415C2×D4—924no—
416C2×D4—996no—
417C2×D4—96no—
418C2×D4—948no—
419C2×D4—924no—
420C2×D4—96no—
421C2×D4—93no—
422C2×D4C2×D3213yescomplemented
423C22×C4—324no—
424C22×C4—924no—
425C22×C4—948no—
426C22×C4—96no—
427C22×C4C2×D3213yescomplemented
428C22×C3—21no—
429C22×C3—26no—
430C22×C3—316no—
431C22×C3—46no—
432C22×C3—46no—
433C22×C3—1224no—
434C22×C3C24×D312yes—
435C22×C3C24×D3112yes—
436C2×D3—324no—
437C2×D3—424no—
438C2×D3—612no—
439C2×D3—1296no—
440C2×D3—1212no—
441C2×D3—1248no—
442C2×D3—1212no—
443C2×D3—2424no—
444C2×D3C24×D3116yes—
445C3×C4—22no—
446C3×C4—26no—
447C3×C4—316no—
448C3×C4C24×D312yes—
449C3×C4C24×D312yes—
450C3×C4C24×D3112yes—
451Dic3—38no—
452Dic3—64no—
453Dic3C24×D3116yes—
454C32H(7,𝔽2)11yescharacteristic, complemented, Sylow
455C23—324no—
456C23—948no—
457C23—96no—
458C23—924no—
459C23—726no—
460C23—7224no—
461C23C22×D3213yes—
462Q8—324no—
463Q8—38no—
464Q8—916no—
465Q8—94no—
466Q8C22×D3214yes—
467D4—348no—
468D4—316no—
469D4—324no—
470D4—38no—
471D4—996no—
472D4—916no—
473D4—924no—
474D4—924no—
475D4—912no—
476D4C22×D32112yes—
477C2×C4—324no—
478C2×C4—316no—
479C2×C4—348no—
480C2×C4—948no—
481C2×C4—932no—
482C2×C4—92no—
483C2×C4—924no—
484C2×C4C22×D32112yes—
485C2×C4C22×D3213yes—
486C2×C4C22×D3211yescharacteristic
487C2×C3—22no—
488C2×C3—212no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—46no—
492C2×C3—616no—
493C2×C3C25×D312yes—
494D3—216no—
495D3—624no—
496D3—1212no—
497C22—316no—
498C22—43no—
499C22—912no—
500C22—1224no—
501C22—366no—
502C22—3624no—
503C22—3648no—
504C22C23×D3216yes—
505C22C23×D3211yescharacteristic
506C4—316no—
507C4—94no—
508C4C23×D3216yes—
509C4C23×D3212yes—
510C3—21no—
511C3#8757412yescomplemented
512C2—21no—
513C2—26no—
514C2—616no—
515C2—1812no—
516C2C24×D3211yescharacteristic
subgroupG/H
center, FrattiniC2C24×D32
commutator, socle, cosocleC2×C32C26
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32H(7,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C3×#5964C2semidirect
3. #10596697C2semidirect
4. D3×#1009C2semidirect
5. #10596689C2semidirect
6. #10596675C2semidirect
7. #10596669C2semidirect
8. C2×#64308C2semidirect
10. C2×C32×#41C22semidirect
11. #64366C22semidirect
12. C2×#3832C22semidirect
13. C2×D4×C3⋊D3C22semidirect
14. C2×#3828C22semidirect
15. C22×C4⋊(C3⋊D3)C22semidirect
16. C3×#1010C22semidirect
17. C3×#1009C22semidirect
18. C3×D3×#41C22semidirect
19. C3×#1007C22semidirect
20. C3×#1004C22semidirect
21. C2×C3×#235C22semidirect
22. #64330C22semidirect
23. C2×#3811C22semidirect
24. #64320C22semidirect
25. D3×#239C22semidirect
26. #64316C22semidirect
27. #64314C22semidirect
28. #64312C22semidirect
29. D32×D4C22semidirect
30. #64308C22semidirect
31. #64308C22semidirect
32. #64308C22semidirect
33. #64307C22semidirect
34. #64306C22semidirect
35. D3×#235C22semidirect
36. C2×D3×D12C22semidirect
37. C2×#3799C22semidirect
38. #64298C22semidirect
39. #64297C22semidirect
47. #5964D3semidirect
52. C23×C3⋊D3C23semidirect
53. C22×D32C23semidirect
54. C32×#41C23semidirect
55. C2×C32×Q8C23semidirect
56. C2×C32×D4C23semidirect
57. C22×C32×C4C23semidirect
58. C2×#638C23semidirect
59. #3832C23semidirect
60. D4×C3⋊D3C23semidirect
61. #3828C23semidirect
62. C2×C4⋊(C3⋊D3)C23semidirect
63. C2×C4⋊(C3⋊D3)C23semidirect
64. C2×C4⋊(C3⋊D3)C23semidirect
65. C2×C4×C3⋊D3C23semidirect
66. C2×#634C23semidirect
67. C2×C3×#67C23semidirect
68. C3×#239C23semidirect
69. C3×D3×Q8C23semidirect
70. C3×#237C23semidirect
71. C3×D3×D4C23semidirect
72. C3×#235C23semidirect
73. C3×#235C23semidirect
74. C3×#235C23semidirect
75. C3×#235C23semidirect
76. C2×C3×D12C23semidirect
77. C2×C3×C4×D3C23semidirect
78. C2×C3×Dic6C23semidirect
79. #3811C23semidirect
80. #3811C23semidirect
81. D3×#67C23semidirect
82. C2×#626C23semidirect
83. C2×#624C23semidirect
84. #3805C23semidirect
85. #3804C23semidirect
86. #3802C23semidirect
87. D3×D12C23semidirect
88. D3×D12C23semidirect
89. C4×D32C23semidirect
90. #3799C23semidirect
91. #3799C23semidirect
92. #3798C23semidirect
93. #3797C23semidirect
94. #3796C23semidirect
95. #3795C23semidirect
96. D3×Dic6C23semidirect
105. C2×C3×#41C2×D3semidirect
108. #1010C2×D3semidirect
119. #1009C2×D3semidirect
124. D3×#41C2×D3semidirect
127. #1007C2×D3semidirect
135. #1004C2×D3semidirect
145. C2×#235C2×D3semidirect
199. C3×#41C22×D3semidirect
200. C3×#41C22×D3semidirect
204. C2×C3×Q8C22×D3semidirect
209. C2×C3×D4C22×D3semidirect
212. C22×C3×C4C22×D3semidirect
217. C2×#67C22×D3semidirect
223. #239C22×D3semidirect
226. D3×Q8C22×D3semidirect
231. #237C22×D3semidirect
240. D3×D4C22×D3semidirect
249. #235C22×D3semidirect
250. #235C22×D3semidirect
251. #235C22×D3semidirect
252. #235C22×D3semidirect
263. C2×D12C22×D3semidirect
268. C2×C4×D3C22×D3semidirect
272. C2×Dic6C22×D3semidirect
310. C2×#41D32semidirect
400. #41C2×D32semidirect
406. C2×Q8C2×D32semidirect
422. C2×D4C2×D32semidirect
427. C22×C4C2×D32semidirect
454. C32H(7,𝔽2)semidirect
511. C3#87574semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C3×#59642
#105966972
D3×#10092
#105966892
#105966752
#105966692
C2×#643082
#875743