Finite Group Databasebeta

← #11887025

Subgroups — #11887025

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#625C211yesmaximal, characteristic, complemented
2#10595134C211yesmaximal, characteristic, complemented
3D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5156C212yesmaximal, complemented
5#10591498C212yesmaximal, complemented
6#10591494C211yesmaximal, characteristic, complemented
7#10591486C211yesmaximal, characteristic, complemented
8D3×#832C212yesmaximal, complemented
9#10590885C211yesmaximal, characteristic, complemented
10#10590718C211yesmaximal, characteristic, complemented
11#10590680C212yesmaximal, complemented
12#80014—32nomaximal
13C2×C3×D3×D4C2212yes—
14C22×#625—21no—
15C2×#3805—21no—
16C2×C32×D8C2211yescharacteristic
17D4×C3⋊Dic3C2211yescharacteristic
18D4×C3⋊Dic3C2211yescharacteristic, complemented
19C3×#938C2212yescomplemented
20C2×C3×#213C2212yescomplemented
21#63982—21no—
22#63980—21no—
23#63976—22no—
24#63969—22no—
25#63919C2211yescharacteristic, complemented
26#63914C2211yescharacteristic
27#63908C2212yes—
28C4×#625C2211yescharacteristic
29D3×C4⋊Dic3C2212yescomplemented
30C2×D3×C3⋊C8C2212yescomplemented
31#63659C2211yescharacteristic
32#63659C2211yescharacteristic, complemented
33#63645C2211yescharacteristic, complemented
34C8×C3⋊Dic3C2211yescharacteristic, complemented
35C3×#832C2212yes—
36C3×#821C2212yescomplemented
37C3×(C2×D3)⋊C8C2212yescomplemented
38#63575C2212yescomplemented
39#63572C2211yescharacteristic, complemented
40#63563C2212yescomplemented
41#63562C2212yescomplemented
42D4×#67—32no—
43#5611—32no—
44C3×#447—32no—
45C2×#832—32no—
46#5157—32no—
47#5156D312yescomplemented
48#5150—32no—
49Dic3×D8—32no—
50Dic3×D8—61no—
51#5038—32no—
52#4774—32no—
53D3×#102—32no—
54#4760—32no—
55#4759—32no—
56#4736—32no—
57#67⋊C8—32no—
58C23×C3×D3—22no—
59C2×C32×D4C2311yescharacteristic
60C2×C32×D4C2311yescharacteristic
61C22×C3⋊Dic3—21no—
62C22×C3⋊Dic3—21no—
63C2×C3×#67—22no—
64C2×C3×#67—22no—
65C3×D3×D4—24no—
66C3×D3×D4—42no—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3C2312yes—
69C2×#627—21no—
70C2×#625—22no—
71C2×#625—21no—
72C2×#625—21no—
73C2×#625—44no—
74C2×#625D411yescharacteristic
75#3805—44no—
76C2×D3×Dic3—22no—
77C32×D8—22no—
78C2×C32×C8C2311yescharacteristic
79#3757—21no—
80#3757—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—22no—
86C3×#213—42no—
87C3×C4⋊Dic3C2312yes—
88C2×C3×C3⋊C8C2312yes—
89#3724—21no—
90#3724D411yescharacteristic
91Dic3⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3D412yes—
94D3×C3⋊C8—42no—
95#3294—91noSylow
96C22×C3×D4—32no—
97C22×#67—62no—
98C2×#237—62no—
99C2×D3×D4C2×D312yes—
100C2×C3×D8—21no—
101C2×C3×D8—32no—
102C2×C3×D8C2×D312yes—
103C3×#121—32no—
104#953—62no—
105#940—32no—
106#939—62no—
107#938—32no—
108#938C2×D312yescomplemented
109#937—62no—
110#935—62no—
111D4×Dic3—32no—
112D4×Dic3—32no—
113D4×Dic3—61no—
114D4×Dic3—61no—
115C2×#213C2×D312yescomplemented
116#930—32no—
117C4×#67—32no—
118C2×C4⋊Dic3—32no—
119C22×C3⋊C8—32no—
120C2×D3×C8—32no—
121D3×C4⋊C4—32no—
122#888—32no—
123#883—62no—
124#878—62no—
125C3×#102—32no—
126C3×#102—32no—
127C3×C22⋊C8—32no—
128#832—32no—
129#832—32no—
130#832—32no—
131#832—32no—
132#832—61no—
133#832—61no—
134#832C2×D312yes—
135#821—32no—
136#821C2×D312yescomplemented
137(C2×D3)⋊C8C2×D312yescomplemented
138#818—32no—
139#818—32no—
140#818—61no—
141Dic3⋊C8—32no—
142C8×Dic3—32no—
143C8×Dic3—61no—
144#809—32no—
145#807—32no—
146C23×C32—21no—
147C23×C32—21no—
148C22×C3×D3—22no—
149C22×C3×D3—44no—
150C22×C3×D3—44no—
151C22×C3×D3—82no—
152C22×C3×D3C2×D412yes—
153C32×D4—21no—
154C32×D4—21no—
155C32×D4—21no—
156C32×D4#4112yescomplemented
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—42no—
161C2×C3⋊Dic3—42no—
162C2×C3⋊Dic3C2×D411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164C3×#67—44no—
165C3×#67—44no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3C2×D412yes—
168C3×D12—22no—
169C3×D12—22no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172#627—42no—
173#625—44no—
174#625—42no—
175#625—81no—
176#625D814yescomplemented
177D3×Dic3—44no—
178C32×C8—21no—
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8—22no—
181#547—91no—
182D42—91no—
183#486—91no—
184#480—92no—
185#474—91no—
186#466—92no—
187#459—91no—
188#447—32no—
189C4×D8—91no—
190C8×D4—91no—
191C2×#102—92no—
192C24×C3—62no—
193C23×D3—22no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—32no—
197C2×C3×D4—62no—
198C2×C3×D4—64no—
199C2×C3×D4—62no—
200C2×C3×D4—122no—
201C2×C3×D4C22×D312yes—
202C2×C3×D4C22×D312yes—
203C22×C3×C4—32no—
204C2×#67—22no—
205C2×#67—22no—
206C2×#67—32no—
207C2×#67—62no—
208C2×#67—62no—
209C2×#67—62no—
210C2×#67—62no—
211C2×#67—128no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—62no—
215C22×Dic3—121no—
216C22×Dic3—121no—
217#237—128no—
218D3×D4—24no—
219D3×D4—42no—
220C2×D12C22×D312yes—
221C2×C4×D3—62no—
222C2×C4×D3C22×D312yes—
223C2×Dic6—62no—
224C3×D8—24no—
225C3×D8—24no—
226C3×D8—122no—
227C2×C3×C8—21no—
228C2×C3×C8—32no—
229C2×C3×C8C22×D312yes—
230C3×C4⋊C4—32no—
231C3×C22⋊C4—62no—
232#217—22no—
233#217—32no—
234#217—62no—
235#217—62no—
236#217—62no—
237#217—121no—
238#217—121no—
239#213—42no—
240(C2×D3)⋊C4—32no—
241(C2×D3)⋊C4—62no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—32no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251C4×Dic3—32no—
252C4×Dic3—61no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—122no—
256C2×C3⋊C8C22×D312yes—
257D3×C8—122no—
258C22×C32—22no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32C22×D411yescharacteristic
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—88no—
271C2×C3×D3C2×D814yes—
272C32×C4C2×#4111yescharacteristic
273C32×C4H(5,𝔽2)11yescharacteristic
274C3⋊Dic3—21no—
275C3⋊Dic3—41no—
276C3⋊Dic3—41no—
277C3⋊Dic3C2×D812yes—
278C3×Dic3—22no—
279C3×Dic3—42no—
280C2×#41—181no—
281C22×D4—32no—
282C22×D4—181no—
283C2×D8—32no—
284C2×D8D3211yescharacteristic
285C22×C8—92no—
286C4⋊Q8—91no—
287#127—91no—
288#123—182no—
289C22⋊Q8—181no—
290#121—32no—
291#121—92no—
292#121—181no—
293#120—182no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—91no—
297C2×C4⋊C4—92no—
298#107—92no—
299#107—91no—
300C4⋊C8—91no—
301#102—32no—
302#102—32no—
303#102—92no—
304#102—92no—
305#102—91no—
306#102—91no—
307C22⋊C8—32no—
308C4×C8—91no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—32no—
312C23×C3—41no—
313C23×C3—41no—
314C23×C3—62no—
315C23×C3—124no—
316C23×C3—124no—
317C23×C3—242no—
318C22×D3—22no—
319C22×D3—44no—
320C22×D3—44no—
321C22×D3—82no—
322C22×D3D3×D412yes—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—41no—
329C3×D4—41no—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—124no—
333C3×D4—124no—
334C3×D4#23714yescomplemented
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4C23×D312yes—
341#67—38no—
342#67—44no—
343#67—44no—
344#67—124no—
345#67—124no—
346#67—124no—
347#67—242no—
348C2×Dic3—22no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—124no—
358C2×Dic3—124no—
359C2×Dic3—124no—
360C2×Dic3—242no—
361C2×Dic3—242no—
362C2×Dic3D3×D412yes—
363D12—22no—
364D12—22no—
365C4×D3—22no—
366C4×D3—22no—
367C4×D3—124no—
368Dic6—124no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—62no—
372C3⋊C8—22no—
373C3⋊C8—62no—
374C3⋊C8—121no—
375C2×C32—42no—
376C2×C32—81no—
377C2×C32#54611yescharacteristic
378C2×C32C22×D811yescharacteristic
379C2×C32#57711yescharacteristic
380C3×D3—24no—
381C3×D3—82no—
382C24—62no—
383#41—364no—
384C2×Q8—181no—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—64no—
388C2×D4—62no—
389C2×D4—91no—
390C2×D4—122no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—182no—
394C2×D4—364no—
395C2×D4C2×D3211yescharacteristic
396C2×D4C2×D3211yescharacteristic
397C22×C4—32no—
398C22×C4—182no—
399C22×C4—181no—
400C22×C4—181no—
401D8—22no—
402D8—122no—
403C2×C8—32no—
404C2×C8—91no—
405C2×C8—362no—
406C2×C8C2×D3211yescharacteristic
407C4⋊C4—32no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—91no—
411C4⋊C4—182no—
412C4⋊C4—181no—
413C22⋊C4—62no—
414C22⋊C4—92no—
415C22⋊C4—182no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C42—91no—
419C22×C3—24no—
420C22×C3—21no—
421C22×C3—34no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—62no—
430C22×C3—62no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—248no—
439C22×C3C2×D3×D412yes—
440C2×D3—22no—
441C2×D3—22no—
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—88no—
446C2×D3D3×D814yes—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—62no—
450C3×C4—122no—
451C3×C4C2×#23712yes—
452C3×C4#100412yes—
453Dic3—22no—
454Dic3—34no—
455Dic3—42no—
456Dic3—62no—
457Dic3—62no—
458Dic3—121no—
459Dic3—122no—
460Dic3—122no—
461Dic3—241no—
462Dic3—241no—
463C32#329411yescharacteristic, complemented, Sylow
464C23—21no—
465C23—21no—
466C23—32no—
467C23—62no—
468C23—124no—
469C23—124no—
470C23—242no—
471Q8—362no—
472D4—21no—
473D4—21no—
474D4—21no—
475D4—62no—
476D4—62no—
477D4—94no—
478D4—124no—
479D4—124no—
480D4—362no—
481D4—364no—
482D4—721no—
483D4#380512yescomplemented
484C2×C4—32no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—91no—
489C2×C4—91no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4—364no—
495C2×C4C22×D3211yescharacteristic
496C8—21no—
497C8—62no—
498C8—181no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—44no—
503C2×C3—64no—
504C2×C3—82no—
505C2×C3—82no—
506C2×C3—82no—
507C2×C3—242no—
508C2×C3#559112yes—
509C2×C3C2×D3×D812yes—
510C2×C3#577512yes—
511D3—24no—
512D3—82no—
513C22—22no—
514C22—34no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—62no—
521C22—62no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22—248no—
526C22D32×D411yescharacteristic
527C4—62no—
528C4—92no—
529C4—122no—
530C4—181no—
531C4—361no—
532C4—361no—
533C4#6431311yescharacteristic
534C4C2×#380511yescharacteristic
535C3—21no—
536C3#8001412yescomplemented
537C2—42no—
538C2—64no—
539C2—81no—
540C2—242no—
541C2D32×D811yescharacteristic
542C2#1059473311yescharacteristic
543C2#1059522511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D4×#625C2semidirect
2. #10595134C2semidirect
3. D8×C3⋊Dic3C2semidirect
4. C3×#5156C2semidirect
5. #10591498C2semidirect
6. #10591494C2semidirect
7. #10591486C2semidirect
8. D3×#832C2semidirect
9. #10590885C2semidirect
10. #10590718C2semidirect
11. #10590680C2semidirect
18. D4×C3⋊Dic3C22semidirect
19. C3×#938C22semidirect
20. C2×C3×#213C22semidirect
25. #63919C22semidirect
29. D3×C4⋊Dic3C22semidirect
30. C2×D3×C3⋊C8C22semidirect
32. #63659C22semidirect
33. #63645C22semidirect
34. C8×C3⋊Dic3C22semidirect
36. C3×#821C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. #63575C22semidirect
39. #63572C22semidirect
40. #63563C22semidirect
41. #63562C22semidirect
47. #5156D3semidirect
108. #938C2×D3semidirect
115. C2×#213C2×D3semidirect
136. #821C2×D3semidirect
137. (C2×D3)⋊C8C2×D3semidirect
156. C32×D4#41semidirect
176. #625D8semidirect
334. C3×D4#237semidirect
463. C32#3294semidirect
483. D4#3805semidirect
536. C3#80014semidirect

Maximal subgroups

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

subgroupindex
D4×#6252
#105951342
D8×C3⋊Dic32
C3×#51562
#105914982
#105914942
#105914862
D3×#8322
#105908852
#105907182
#105906802
#800143