Finite Group Databasebeta

← #11887069

Subgroups — #11887069

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
1#10595134C211yesmaximal, characteristic, complemented
2#10594618C211yesmaximal, characteristic, complemented
3#10592455C211yesmaximal, characteristic, complemented
4C3×#4775C212yesmaximal, complemented
5#10591515C212yesmaximal, complemented
6#10591486C211yesmaximal, characteristic, complemented
7D3×#821C212yesmaximal, complemented
8#10590885C211yesmaximal, characteristic, complemented
9C8×#625C211yesmaximal, characteristic, complemented
10#10590438C212yesmaximal, complemented
11#10590430C211yesmaximal, characteristic, complemented
12#80731—32nomaximal
13C2×#3805—21no—
14C2×#3802—21no—
15C2×D3×D12C2212yes—
16D4×C3⋊Dic3C2211yescharacteristic, complemented
17C2×#3753C2211yescharacteristic
18#64102C2211yescharacteristic
19C3×#938C2212yescomplemented
20C2×C3×#213C2212yescomplemented
21C2×C3×D3×C8C2212yescomplemented
22C3×#895C2212yes—
23#63982—21no—
24#63969—22no—
25#63922—22no—
26#63919C2211yescharacteristic, complemented
27#63914C2211yescharacteristic
28#63912—21no—
29C4×#625C2211yescharacteristic
30D3×C4⋊Dic3C2212yescomplemented
31C32×#102C2211yescharacteristic, complemented
32#63648C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic, complemented
34#63634C2211yescharacteristic, complemented
35C3×#821C2212yescomplemented
36C3×#807C2212yescomplemented
37#63572C2211yescharacteristic, complemented
38#63564C2212yes—
39#63563C2212yescomplemented
40#63562C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yescomplemented
42#5611—32no—
43#5609—32no—
44C3×#466—32no—
45#5156—32no—
46#5150—32no—
47C2×#821—32no—
48C8×#67—32no—
49#5036—32no—
50#5033—32no—
51#4890—32no—
52#4882—32no—
53#4775D312yescomplemented
54D3×#102—32no—
55#4760—32no—
56#4756—32no—
57#4756—61no—
58C22×D32—22no—
59C2×C32×D4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×C4⋊(C3⋊D3)C2311yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×C3×#67—22no—
64C2×C3×D12—22no—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3C2312yes—
67C2×#627—21no—
68C2×#626—22no—
69C2×#625—21no—
70C2×#625—21no—
71C2×#625D411yescharacteristic
72#3805—44no—
73C2×D3×Dic3—22no—
74#3802—44no—
75D3×D12—24no—
76D3×D12—42no—
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79#3757—21no—
80#3753—22no—
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—22no—
86C3×#213—42no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3C2312yes—
89C2×C3×C3⋊C8C2312yes—
90C3×D3×C8—42no—
91#3724—21no—
92#3724D411yescharacteristic
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3D412yes—
95#3294—91noSylow
96C2×#237—62no—
97C2×D3×D4—32no—
98C2×D3×D4—62no—
99C22×D12—32no—
100C2×C3×D8—32no—
101C22×C3×C8—32no—
102C3×#121—32no—
103C3×#121—32no—
104#940—32no—
105#938C2×D312yescomplemented
106#937—62no—
107#935—62no—
108D4×Dic3—32no—
109D4×Dic3—61no—
110C2×#213—32no—
111C2×#213—61no—
112C2×#213C2×D312yescomplemented
113C4×#67—32no—
114C2×C4⋊Dic3—32no—
115C2×D3×C8C2×D312yescomplemented
116#895C2×D312yes—
117#893—32no—
118#893—61no—
119D3×C4⋊C4—32no—
120#888—32no—
121#884—62no—
122#883—62no—
123#882—62no—
124#878—62no—
125C3×#107—32no—
126C3×#102—21no—
127C3×#102—32no—
128C3×#102C2×D312yescomplemented
129#832—32no—
130#832—32no—
131#830—32no—
132#821—32no—
133#821—32no—
134#821—32no—
135#821—61no—
136#821C2×D312yescomplemented
137(C2×D3)⋊C8—32no—
138Dic3⋊C8—32no—
139C8×Dic3—32no—
140C8×Dic3—61no—
141#809—32no—
142#809—32no—
143#807—32no—
144#807—61no—
145#807C2×D312yescomplemented
146C23×C32—21no—
147C22×C3⋊D3—21no—
148C22×C3×D3—22no—
149C22×C3×D3C2×D412yes—
150C2×D32—44no—
151C2×D32—44no—
152C2×D32—82no—
153C32×D4—21no—
154C32×D4—21no—
155C2×C32×C4—21no—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—42no—
159C2×C3⋊Dic3C2×D411yescharacteristic
160C2×C3⋊Dic3C2×D411yescharacteristic
161C4⋊(C3⋊D3)—21no—
162C4⋊(C3⋊D3)#4112yescomplemented
163C4×C3⋊D3—42no—
164C3×#67—44no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×D12—22no—
169C3×D12—44no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172#627—42no—
173#626—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—32no—
187#459—91no—
188#447—92no—
189C4×D8—91no—
190C8×D4—91no—
191C2×#102—92no—
192C23×D3—62no—
193C23×D3—62no—
194C2×C3×D4—21no—
195C2×C3×D4—32no—
196C2×C3×D4—62no—
197C2×C3×D4—62no—
198C2×C3×D4C22×D312yes—
199C22×C3×C4—32no—
200C2×#67—22no—
201C2×#67—32no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—62no—
205C22×Dic3—62no—
206C22×Dic3—62no—
207C22×Dic3—121no—
208#237—128no—
209D3×D4—64no—
210D3×D4—122no—
211D3×D4—128no—
212C2×D12—22no—
213C2×D12—32no—
214C2×D12—61no—
215C2×D12—64no—
216C2×D12—62no—
217C2×D12—122no—
218C2×D12C22×D312yes—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—121no—
222C2×C4×D3C22×D312yes—
223C2×Dic6—62no—
224C3×D8—122no—
225C2×C3×C8—21no—
226C2×C3×C8—32no—
227C2×C3×C8—122no—
228C2×C3×C8C22×D312yes—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4C22×D312yes—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—62no—
234#217—22no—
235#217—32no—
236#217—62no—
237#217—121no—
238#213—42no—
239#213—64no—
240#213—64no—
241(C2×D3)⋊C4—22no—
242(C2×D3)⋊C4—32no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—121no—
245C4⋊Dic3—32no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—32no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252C4×Dic3—32no—
253C4×Dic3—61no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8C22×D312yes—
257D3×C8—42no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32C22×D411yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3C2×D814yes—
271D32—88no—
272C32×C4—41no—
273C32×C4C2×#4111yescharacteristic
274C32×C4H(5,𝔽2)11yescharacteristic
275C3⋊Dic3—21no—
276C3⋊Dic3—41no—
277C3⋊Dic3C2×D812yes—
278C3×Dic3—22no—
279C3×Dic3—42no—
280C2×#41—181no—
281C22×D4—92no—
282C22×D4—181no—
283C2×D8—32no—
284C2×D8—91no—
285C22×C8—32no—
286C4⋊Q8—91no—
287#127—91no—
288#123—182no—
289C22⋊Q8—181no—
290#121—32no—
291#121—32no—
292#121—181no—
293#120—182no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—91no—
297C2×C4⋊C4—92no—
298#107—32no—
299#107—91no—
300C4⋊C8—91no—
301#102—32no—
302#102—92no—
303#102—92no—
304#102—92no—
305#102—91no—
306#102D3211yescharacteristic, complemented
307C22⋊C8—92no—
308C4×C8—91no—
309C23×C3—22no—
310C23×C3—32no—
311C23×C3—41no—
312C23×C3—62no—
313C22×D3—22no—
314C22×D3—62no—
315C22×D3—121no—
316C22×D3—124no—
317C22×D3—124no—
318C22×D3—124no—
319C22×D3—124no—
320C22×D3—242no—
321C22×D3—242no—
322C22×D3D3×D412yes—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—41no—
327C3×D4—62no—
328C3×D4—62no—
329C3×D4—124no—
330C3×D4—124no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—32no—
334C2×C3×C4—41no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4C23×D312yes—
339#67—38no—
340#67—44no—
341#67—124no—
342#67—124no—
343#67—242no—
344C2×Dic3—22no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—62no—
350C2×Dic3—121no—
351C2×Dic3—124no—
352C2×Dic3—124no—
353C2×Dic3—242no—
354C2×Dic3D3×D412yes—
355D12—22no—
356D12—22no—
357D12—34no—
358D12—44no—
359D12—62no—
360D12—62no—
361D12—121no—
362D12—124no—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—124no—
366C4×D3—124no—
367C4×D3—242no—
368Dic6—124no—
369C3×C8—22no—
370C3×C8—41no—
371C3×C8—62no—
372C3⋊C8—22no—
373C3⋊C8—62no—
374C3⋊C8—62no—
375C2×C32—81no—
376C2×C32#54611yescharacteristic
377C2×C32C22×D811yescharacteristic
378C2×C32#57711yescharacteristic
379C3⋊D3—42no—
380C3×D3—24no—
381C3×D3—82no—
382C24—182no—
383#41—364no—
384C2×Q8—181no—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—62no—
388C2×D4—91no—
389C2×D4—91no—
390C2×D4—182no—
391C2×D4—184no—
392C2×D4—181no—
393C2×D4—181no—
394C2×D4—362no—
395C2×D4—364no—
396C2×D4C2×D3211yescharacteristic
397C22×C4—32no—
398C22×C4—181no—
399C22×C4—182no—
400C22×C4—181no—
401D8—122no—
402D8—182no—
403C2×C8—32no—
404C2×C8—91no—
405C2×C8—122no—
406C2×C8C2×D3211yescharacteristic
407C4⋊C4—32no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—182no—
411C4⋊C4—181no—
412C4⋊C4C2×D3211yescharacteristic
413C22⋊C4—62no—
414C22⋊C4—62no—
415C22⋊C4—92no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C42—91no—
419C22×C3—21no—
420C22×C3—34no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—62no—
426C22×C3—62no—
427C22×C3—81no—
428C22×C3—81no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3C2×D3×D412yes—
433C2×D3—22no—
434C2×D3—22no—
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—64no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—241no—
443C2×D3—241no—
444C2×D3—248no—
445C2×D3—248no—
446C2×D3D3×D814yes—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—42no—
450C3×C4—62no—
451C3×C4—81no—
452C3×C4—122no—
453C3×C4#100412yes—
454C3×C4D3×#4112yes—
455Dic3—22no—
456Dic3—34no—
457Dic3—42no—
458Dic3—62no—
459Dic3—62no—
460Dic3—121no—
461Dic3—122no—
462Dic3—241no—
463C32#329411yescharacteristic, complemented, Sylow
464C23—21no—
465C23—32no—
466C23—62no—
467C23—181no—
468C23—364no—
469C23—364no—
470C23—722no—
471Q8—362no—
472D4—21no—
473D4—21no—
474D4—62no—
475D4—62no—
476D4—94no—
477D4—92no—
478D4—124no—
479D4—124no—
480D4—181no—
481D4—364no—
482D4—362no—
483D4—721no—
484C2×C4—21no—
485C2×C4—32no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—91no—
490C2×C4—91no—
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—64no—
503C2×C3—82no—
504C2×C3—82no—
505C2×C3—242no—
506C2×C3#561012yes—
507C2×C3C2×D3×D812yes—
508C2×C3#577012yes—
509D3—24no—
510D3—82no—
511D3—124no—
512D3—242no—
513C22—34no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—62no—
518C22—62no—
519C22—122no—
520C22—122no—
521C22—122no—
522C22—182no—
523C22—361no—
524C22—361no—
525C22—728no—
526C22D32×D411yescharacteristic
527C4—41no—
528C4—62no—
529C4—92no—
530C4—122no—
531C4—181no—
532C4—361no—
533C4#6430611yescharacteristic
534C4#6431311yescharacteristic
535C3—21no—
536C3#8073112yescomplemented
537C2—64no—
538C2—81no—
539C2—242no—
540C2—362no—
541C2#1059427611yescharacteristic
542C2D32×D811yescharacteristic
543C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595134C2semidirect
2. #10594618C2semidirect
3. #10592455C2semidirect
4. C3×#4775C2semidirect
5. #10591515C2semidirect
6. #10591486C2semidirect
7. D3×#821C2semidirect
8. #10590885C2semidirect
9. C8×#625C2semidirect
10. #10590438C2semidirect
11. #10590430C2semidirect
16. D4×C3⋊Dic3C22semidirect
19. C3×#938C22semidirect
20. C2×C3×#213C22semidirect
21. C2×C3×D3×C8C22semidirect
26. #63919C22semidirect
30. D3×C4⋊Dic3C22semidirect
31. C32×#102C22semidirect
33. C8×C3⋊Dic3C22semidirect
34. #63634C22semidirect
35. C3×#821C22semidirect
36. C3×#807C22semidirect
37. #63572C22semidirect
39. #63563C22semidirect
40. #63562C22semidirect
41. (C2×D3)⋊(C3⋊C8)C22semidirect
53. #4775D3semidirect
105. #938C2×D3semidirect
112. C2×#213C2×D3semidirect
115. C2×D3×C8C2×D3semidirect
128. C3×#102C2×D3semidirect
136. #821C2×D3semidirect
145. #807C2×D3semidirect
162. C4⋊(C3⋊D3)#41semidirect
176. #625D8semidirect
306. #102D32semidirect
463. C32#3294semidirect
536. C3#80731semidirect

Maximal subgroups

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

subgroupindex
#105951342
#105946182
#105924552
C3×#47752
#105915152
#105914862
D3×#8212
#105908852
C8×#6252
#105904382
#105904302
#807313