Finite Group Databasebeta

← #11904334

Subgroups — #11904334

Order 1152.

4481 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#64308C211yesmaximal, characteristic, complemented
3C3×#5791C212yesmaximal, complemented
4#10595527C214yesmaximal, complemented
5#10595080C214yesmaximal, complemented
6#10595074C218yesmaximal, complemented
7#10595045C212yesmaximal, complemented
8#10595018C218yesmaximal, complemented
9#10594996C211yesmaximal, characteristic, complemented
10#86039—32nomaximal
11C24×C3⋊D3C2212yescomplemented
12C23×C32×C4C2211yescharacteristic, complemented
13C22×C4⋊(C3⋊D3)—28no—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2218yescomplemented
16C22×C4⋊(C3⋊D3)C2212yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C2×C3×#235C2212yescomplemented
19C2×#3811C2214yescomplemented
20C2×#3811C2218yescomplemented
21#64308—28no—
22C2×D3×D12C2214yescomplemented
23C2×#3799C2214yescomplemented
24C3×#953C2214yescomplemented
25C3×#930C2214yescomplemented
26C3×#929C2214yescomplemented
27C3×C4×#67C2218yescomplemented
28C3×#926C2212yescomplemented
29C3×#924C2214yescomplemented
30#63981C22116yescomplemented
31#63981C2218yescomplemented
32#63974C2214yescomplemented
33#63974C2218yescomplemented
34#63923C2218yescomplemented
35#63911C2214yescomplemented
36#63910C22116yescomplemented
37#63909C2218yescomplemented
38#63897C2218yescomplemented
39#63894C2218yescomplemented
40#63864C2214yescomplemented
41C2×#1009—32no—
42C23×D12—32no—
43C23×D12—61no—
44C3×#525—32no—
45#5830—32no—
46#5791D312yescomplemented
47#5653—38no—
48#5630—38no—
49#5609—38no—
50D3×#120—38no—
51#5550—38no—
52D4×D12—38no—
53#5525—32no—
54#5521—32no—
55C24×C32C2311yescharacteristic
56C23×C3⋊D3—28no—
57C23×C3⋊D3—48no—
58C23×C3⋊D3C2318yes—
59C23×C3⋊D3C2312yes—
60C23×C3⋊D3C2312yes—
61C22×D32C2314yescomplemented
62C22×C32×C4—24no—
63C22×C32×C4C2314yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C2×C4⋊(C3⋊D3)—28no—
67C2×C4⋊(C3⋊D3)—24no—
68C2×C4⋊(C3⋊D3)—232no—
69C2×C4⋊(C3⋊D3)D418yescomplemented
70C2×C4⋊(C3⋊D3)C2314yes—
71C2×C4⋊(C3⋊D3)C2318yes—
72C2×C4⋊(C3⋊D3)C2314yes—
73C2×C3×#67C2318yes—
74C2×C3×#67C2314yes—
75C3×#235—28no—
76C2×C3×D12C2312yescomplemented
77C2×C3×C4×D3C2314yescomplemented
78C2×C3×Dic6C2312yescomplemented
79#3811—216no—
80#3811—416no—
81C2×#626C2318yescomplemented
82C2×#626C23116yescomplemented
83C2×#624C2314yescomplemented
84C2×#624C2318yescomplemented
85D3×D12—216no—
86#3799—216no—
87C3×#217C2318yes—
88C3×#217C2314yes—
89C3×(C2×D3)⋊C4C2318yescomplemented
90C3×C4⋊Dic3C2314yescomplemented
91C3×Dic3⋊C4C2318yescomplemented
92C3×C4×Dic3C2314yescomplemented
93#3722C23116yescomplemented
94#3722C2318yescomplemented
95#3484—91noSylow
96C24×D3—34no—
97C24×D3—62no—
98C2×C3×#41—32no—
99C23×C3×C4—21no—
100C23×C3×C4C2×D312yescomplemented
101#1009—616no—
102C2×#239—34no—
103C2×D3×D4—38no—
104C2×D3×D4—316no—
105C2×D3×D4—34no—
106C2×#235—34no—
107C2×#235C2×D312yescomplemented
108C22×D12—32no—
109C22×D12—34no—
110C22×D12—32no—
111C22×D12—38no—
112C22×D12—38no—
113C22×D12—34no—
114C22×D12—61no—
115C22×D12—62no—
116C22×D12—61no—
117C22×D12—68no—
118C22×D12—616no—
119C22×D12—616no—
120C3×#123—34no—
121C3×C22⋊Q8—34no—
122C3×#121—34no—
123C3×#120—34no—
124C3×C4×D4—38no—
125C3×#117—32no—
126#953C2×D314yescomplemented
127#947—34no—
128#940—34no—
129#937—38no—
130#937—316no—
131#930—38no—
132#930C2×D314yescomplemented
133#929C2×D314yescomplemented
134C4×#67C2×D318yescomplemented
135#926C2×D312yescomplemented
136#924C2×D314yescomplemented
137#895—38no—
138#895—316no—
139#894—316no—
140#893—38no—
141#884—316no—
142#882—38no—
143#882—316no—
144#882—316no—
145D3×C22⋊C4—38no—
146D3×C22⋊C4—316no—
147#875—34no—
148#874—34no—
149C4×D12—38no—
150C23×C32—22no—
151C23×C32—24no—
152C23×C32C2411yescharacteristic
153C23×C32C2412yes—
154C22×C3⋊D3—24no—
155C22×C3⋊D3—216no—
156C22×C3⋊D3—216no—
157C22×C3⋊D3—44no—
158C22×C3⋊D3—48no—
159C22×C3⋊D3—44no—
160C22×C3⋊D3—432no—
161C22×C3⋊D3C2×D418yescomplemented
162C22×C3⋊D3C2414yes—
163C22×C3⋊D3C2414yes—
164C22×C3×D3C2414yes—
165C2×D32—28no—
166C2×D32—48no—
167C2×C32×C4—22no—
168C2×C32×C4—28no—
169C2×C32×C4C2×D414yescomplemented
170C2×C32×C4C2412yes—
171C2×C32×C4C2412yes—
172C4⋊(C3⋊D3)—216no—
173C4⋊(C3⋊D3)—28no—
174C4⋊(C3⋊D3)C2×D4116yescomplemented
175C3×#67—28no—
176C3×#67—216no—
177C2×C3×Dic3C2418yes—
178C2×C3×Dic3C2414yes—
179C3×D12—24no—
180C3×C4×D3—28no—
181C3×Dic6—24no—
182#626—216no—
183#626—416no—
184#624—28no—
185#624—48no—
186C2×H(5,𝔽2)—91no—
187C23×D4—91no—
188#546—98no—
189D42—98no—
190#535—92no—
191#534—94no—
192#525—32no—
193C2×#120—94no—
194#518—91no—
195C24×C3—21no—
196C24×C3C22×D312yes—
197C23×D3—34no—
198C23×D3—316no—
199C23×D3—34no—
200C23×D3—38no—
201C23×D3—62no—
202C23×D3—68no—
203C23×D3—62no—
204C23×D3—616no—
205C23×D3—616no—
206C23×D3—1216no—
207C23×D3—1216no—
208C3×#41—68no—
209C2×C3×Q8—32no—
210C2×C3×D4—38no—
211C2×C3×D4—34no—
212C2×C3×D4—32no—
213C22×C3×C4—28no—
214C22×C3×C4—28no—
215C22×C3×C4—24no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—34no—
219C22×C3×C4C22×D314yes—
220C22×C3×C4C22×D314yes—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C2×#67—38no—
224C2×#67—316no—
225C2×#67C22×D318yes—
226C2×#67C22×D314yes—
227#239—616no—
228D3×D4—616no—
229D3×D4—632no—
230D3×D4—1232no—
231#235—28no—
232#235—616no—
233C2×D12—316no—
234C2×D12—34no—
235C2×D12—34no—
236C2×D12—38no—
237C2×D12—34no—
238C2×D12—316no—
239C2×D12—34no—
240C2×D12—316no—
241C2×D12—68no—
242C2×D12—64no—
243C2×D12—68no—
244C2×D12—64no—
245C2×D12—616no—
246C2×D12—632no—
247C2×D12—632no—
248C2×D12—616no—
249C2×D12—664no—
250C2×D12—616no—
251C2×D12—68no—
252C2×D12—68no—
253C2×D12C22×D312yescomplemented
254C2×C4×D3—38no—
255C2×C4×D3—316no—
256C2×C4×D3C22×D314yescomplemented
257C2×Dic6C22×D312yescomplemented
258C3×C4⋊C4—34no—
259C3×C4⋊C4—38no—
260C3×C22⋊C4—34no—
261C3×C22⋊C4—38no—
262C3×C22⋊C4—38no—
263C3×C42—34no—
264#217C22×D318yes—
265#217C22×D314yes—
266(C2×D3)⋊C4—316no—
267(C2×D3)⋊C4—316no—
268(C2×D3)⋊C4—316no—
269(C2×D3)⋊C4C22×D318yescomplemented
270C4⋊Dic3C22×D314yescomplemented
271Dic3⋊C4C22×D318yescomplemented
272C4×Dic3C22×D314yescomplemented
273C22×C32—28no—
274C22×C32—22no—
275C22×C32—22no—
276C22×C32—22no—
277C22×C32C22×D412yes—
278C22×C32H(5,𝔽2)14yescomplemented
279C22×C32C2511yescharacteristic
280C2×C3⋊D3—24no—
281C2×C3⋊D3—28no—
282C2×C3⋊D3—28no—
283C2×C3⋊D3—48no—
284C2×C3⋊D3—432no—
285C2×C3⋊D3—48no—
286C2×C3⋊D3C22×D418yes—
287C2×C3×D3—24no—
288C2×C3×D3—28no—
289D32—88no—
290C32×C4—22no—
291C32×C4C22×D414yes—
292C3×Dic3—24no—
293C3×Dic3—28no—
294C25—92no—
295H(5,𝔽2)—188no—
296C2×#41—32no—
297C2×#41—94no—
298C22×D4—94no—
299C22×D4—94no—
300C22×D4—98no—
301C22×D4—91no—
302C22×D4—92no—
303C22×D4—91no—
304C22×D4—98no—
305C22×D4—188no—
306C23×C4D3211yescharacteristic, complemented
307#127—94no—
308#124—94no—
309#123—34no—
310#123—98no—
311C22⋊Q8—34no—
312#121—34no—
313#121—916no—
314#121—98no—
315#120—34no—
316#120—98no—
317#120—98no—
318#120—916no—
319C4×D4—38no—
320C4×D4—98no—
321#117—32no—
322C2×C22⋊C4—94no—
323C2×C22⋊C4—98no—
324C23×C3—24no—
325C23×C3—28no—
326C23×C3—24no—
327C23×C3—28no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—34no—
331C23×C3C23×D312yes—
332C23×C3C23×D314yes—
333C22×D3—38no—
334C22×D3—316no—
335C22×D3—38no—
336C22×D3—68no—
337C22×D3—64no—
338C22×D3—64no—
339C22×D3—616no—
340C22×D3—632no—
341C22×D3—632no—
342C22×D3—68no—
343C22×D3—68no—
344C22×D3—632no—
345C22×D3—1216no—
346C22×D3—1216no—
347C22×D3—128no—
348C22×D3—1216no—
349C22×D3—128no—
350C22×D3—128no—
351C22×D3—1216no—
352C22×D3—128no—
353C22×D3—1264no—
354C22×D3—1264no—
355C22×D3C23×D314yes—
356C3×Q8—64no—
357C3×D4—68no—
358C3×D4—616no—
359C3×D4—64no—
360C2×C3×C4—24no—
361C2×C3×C4—216no—
362C2×C3×C4—24no—
363C2×C3×C4—28no—
364C2×C3×C4—28no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—24no—
368C2×C3×C4—38no—
369C2×C3×C4—34no—
370C2×C3×C4—68no—
371C2×C3×C4D3×D418yescomplemented
372C2×C3×C4C23×D314yes—
373C2×C3×C4C23×D312yes—
374C2×C3×C4C23×D312yes—
375#67—28no—
376#67—216no—
377#67—616no—
378#67—1216no—
379C2×Dic3C23×D318yes—
380C2×Dic3C23×D314yes—
381D12—24no—
382D12—316no—
383D12—316no—
384D12—616no—
385D12—632no—
386D12—632no—
387D12—616no—
388D12—616no—
389D12—68no—
390D12—68no—
391D12—1216no—
392C4×D3—28no—
393C4×D3—616no—
394C4×D3—1216no—
395Dic6—24no—
396C2×C32—22no—
397C2×C32—24no—
398C2×C32C23×D411yescharacteristic
399C2×C32C2×H(5,𝔽2)12yes—
400C3⋊D3—28no—
401C3⋊D3—44no—
402C3×D3—44no—
403C24—94no—
404C24—92no—
405C24—98no—
406C24—92no—
407C24—188no—
408C24—368no—
409C24C2×D3211yescharacteristic
410#41—68no—
411#41—1816no—
412C2×Q8—32no—
413C2×D4—38no—
414C2×D4—34no—
415C2×D4—32no—
416C2×D4—98no—
417C2×D4—916no—
418C2×D4—94no—
419C2×D4—98no—
420C2×D4—94no—
421C2×D4—98no—
422C2×D4—1832no—
423C2×D4—188no—
424C2×D4—1816no—
425C2×D4—1816no—
426C2×D4—184no—
427C2×D4—3616no—
428C22×C4—24no—
429C22×C4—34no—
430C22×C4—94no—
431C22×C4—98no—
432C22×C4C2×D3214yes—
433C22×C4C2×D3211yescharacteristic
434C22×C4C2×D3211yescharacteristic
435C4⋊C4—34no—
436C4⋊C4—38no—
437C22⋊C4—34no—
438C22⋊C4—38no—
439C22⋊C4—38no—
440C22⋊C4—98no—
441C22⋊C4—916no—
442C42—34no—
443C22×C3—24no—
444C22×C3—216no—
445C22×C3—216no—
446C22×C3—24no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—64no—
455C22×C3—68no—
456C22×C3C2×D3×D414yes—
457C22×C3#100918yescomplemented
458C22×C3C24×D312yes—
459C2×D3—24no—
460C2×D3—28no—
461C2×D3—316no—
462C2×D3—68no—
463C2×D3—616no—
464C2×D3—68no—
465C2×D3—68no—
466C2×D3—616no—
467C2×D3—128no—
468C2×D3—128no—
469C2×D3—1216no—
470C2×D3—1264no—
471C2×D3—1216no—
472C2×D3—1264no—
473C2×D3—1216no—
474C2×D3—1216no—
475C2×D3—2416no—
476C3×C4—24no—
477C3×C4—24no—
478C3×C4—24no—
479C3×C4—64no—
480C3×C4—68no—
481C3×C4C2×D3×D414yes—
482C3×C4C2×D3×D414yes—
483Dic3—24no—
484Dic3—28no—
485C32#348411yescharacteristic, complemented, Sylow
486C23—24no—
487C23—22no—
488C23—34no—
489C23—94no—
490C23—98no—
491C23—94no—
492C23—1816no—
493C23—188no—
494C23—1816no—
495C23—184no—
496C23—364no—
497C23—368no—
498C23—364no—
499C23—3632no—
500C23—368no—
501C23C22×D3212yes—
502C23C22×D3211yescharacteristic
503Q8—64no—
504D4—616no—
505D4—68no—
506D4—64no—
507D4—916no—
508D4—1816no—
509D4—1816no—
510D4—188no—
511D4—3616no—
512C2×C4—22no—
513C2×C4—28no—
514C2×C4—38no—
515C2×C4—34no—
516C2×C4—68no—
517C2×C4—188no—
518C2×C4—368no—
519C2×C4#381114yescomplemented
520C2×C4C22×D3212yes—
521C2×C4C22×D3212yes—
522C2×C3—28no—
523C2×C3—24no—
524C2×C3—24no—
525C2×C3—28no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—124no—
529C2×C3C22×D3×D412yes—
530C2×C3C2×#100914yes—
531D3—44no—
532D3—616no—
533D3—128no—
534D3—128no—
535D3—128no—
536C22—28no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—68no—
541C22—64no—
542C22—98no—
543C22—188no—
544C22—188no—
545C22—184no—
546C22—368no—
547C22—3632no—
548C22—368no—
549C22—728no—
550C22#6430814yescomplemented
551C22C2×#381112yes—
552C22C23×D3211yescharacteristic
553C4—22no—
554C4—68no—
555C4—64no—
556C4C2×#381114yes—
557C3—21no—
558C3#8603912yescomplemented
559C2—24no—
560C2—22no—
561C2—124no—
562C2—188no—
563C2—364no—
564C2C2×#6430812yes—
565C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3484
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊(C3⋊D3)C2semidirect
2. C2×#64308C2semidirect
3. C3×#5791C2semidirect
4. #10595527C2semidirect
5. #10595080C2semidirect
6. #10595074C2semidirect
7. #10595045C2semidirect
8. #10595018C2semidirect
9. #10594996C2semidirect
11. C24×C3⋊D3C22semidirect
12. C23×C32×C4C22semidirect
15. C22×C4⋊(C3⋊D3)C22semidirect
16. C22×C4⋊(C3⋊D3)C22semidirect
17. C22×C4⋊(C3⋊D3)C22semidirect
18. C2×C3×#235C22semidirect
19. C2×#3811C22semidirect
20. C2×#3811C22semidirect
22. C2×D3×D12C22semidirect
23. C2×#3799C22semidirect
24. C3×#953C22semidirect
25. C3×#930C22semidirect
26. C3×#929C22semidirect
27. C3×C4×#67C22semidirect
28. C3×#926C22semidirect
29. C3×#924C22semidirect
30. #63981C22semidirect
31. #63981C22semidirect
32. #63974C22semidirect
33. #63974C22semidirect
34. #63923C22semidirect
35. #63911C22semidirect
36. #63910C22semidirect
37. #63909C22semidirect
38. #63897C22semidirect
39. #63894C22semidirect
40. #63864C22semidirect
46. #5791D3semidirect
61. C22×D32C23semidirect
69. C2×C4⋊(C3⋊D3)D4semidirect
76. C2×C3×D12C23semidirect
77. C2×C3×C4×D3C23semidirect
78. C2×C3×Dic6C23semidirect
81. C2×#626C23semidirect
82. C2×#626C23semidirect
83. C2×#624C23semidirect
84. C2×#624C23semidirect
89. C3×(C2×D3)⋊C4C23semidirect
90. C3×C4⋊Dic3C23semidirect
91. C3×Dic3⋊C4C23semidirect
92. C3×C4×Dic3C23semidirect
93. #3722C23semidirect
94. #3722C23semidirect
100. C23×C3×C4C2×D3semidirect
107. C2×#235C2×D3semidirect
126. #953C2×D3semidirect
132. #930C2×D3semidirect
133. #929C2×D3semidirect
134. C4×#67C2×D3semidirect
135. #926C2×D3semidirect
136. #924C2×D3semidirect
161. C22×C3⋊D3C2×D4semidirect
169. C2×C32×C4C2×D4semidirect
174. C4⋊(C3⋊D3)C2×D4semidirect
253. C2×D12C22×D3semidirect
256. C2×C4×D3C22×D3semidirect
257. C2×Dic6C22×D3semidirect
269. (C2×D3)⋊C4C22×D3semidirect
270. C4⋊Dic3C22×D3semidirect
271. Dic3⋊C4C22×D3semidirect
272. C4×Dic3C22×D3semidirect
278. C22×C32H(5,𝔽2)semidirect
306. C23×C4D32semidirect
371. C2×C3×C4D3×D4semidirect
457. C22×C3#1009semidirect
485. C32#3484semidirect
519. C2×C4#3811semidirect
550. C22#64308semidirect
558. C3#86039semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊(C3⋊D3)2
C2×#643082
C3×#57912
#105955272
#105950802
#105950742
#105950452
#105950182
#105949962
#860393