Finite Group Databasebeta

← #11878773

Subgroups — #11878773

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593897C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592380C211yesmaximal, characteristic, complemented
4C3×#4695C211yesmaximal, characteristic, complemented
5C3×#4685C211yesmaximal, characteristic, complemented
6#10590962C214yesmaximal, complemented
7#10590755C214yesmaximal, complemented
8#10590369C211yesmaximal, characteristic, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#81786—31nomaximal
11#79304—31nomaximal
12C2×#3795—21no—
13C2×#3795C2212yes—
14#64078C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×D24C2214yes—
17C3×#874C2211yescharacteristic
18C3×#874C2211yescharacteristic
19C3×C42×D3C2211yescharacteristic
20#63908—21no—
21#63908—21no—
22#63908—21no—
23#63908C2212yes—
24Dic3×D12—21no—
25Dic3×D12—21no—
26Dic3×D12—21no—
27Dic3×D12C2212yes—
28#63860—21no—
29#63860C2212yes—
30C2×#3716C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63643C2214yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63563C2214yes—
37#5716—31no—
38#5716—31no—
39#5477—31no—
40#5477—31no—
41C3×#493—31no—
42C3×#431—31no—
43#5158—34no—
44#5153—34no—
45#5076—31no—
46#5070—31no—
47#4844—34no—
48#4734—34no—
49#4695D311yescharacteristic, complemented
50#4694—31no—
51#4693—31no—
52#4685D311yescharacteristic, complemented
53#4681—31no—
54#4681—31no—
55#4681—61no—
56C2×#634—21no—
57C2×#634C2312yes—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3C2311yescharacteristic
67C2×#625—22no—
68C2×#625—22no—
69C2×D3×Dic3—22no—
70C2×D3×Dic3—22no—
71#3795—44no—
72#3795—44no—
73C2×C32×C8C2312yes—
74C32×C42C2311yescharacteristic
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C3×C4×Dic3D411yescharacteristic
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2312yes—
83C3×D24—44no—
84(C2×D3)⋊Dic3—22no—
85(C2×D3)⋊Dic3—22no—
86(C2×D3)⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88#3716—44no—
89#3207—91noSylow
90C2×#237—32no—
91C2×#237—61no—
92C2×#235—32no—
93C2×#235—61no—
94C2×C3×D8—34no—
95C3×#127—31no—
96C3×#127—31no—
97C2×C3×C42—31no—
98#938—32no—
99#938—61no—
100#938—61no—
101#938—61no—
102#936—32no—
103#936—61no—
104D4×Dic3—32no—
105D4×Dic3—61no—
106D4×Dic3—61no—
107D4×Dic3—61no—
108C2×#214—34no—
109#930—32no—
110#930—61no—
111#930—61no—
112#930—61no—
113C2×D24C2×D314yes—
114C2×#204—34no—
115#875—32no—
116#875—61no—
117#874C2×D311yescharacteristic
118#874C2×D311yescharacteristic
119C4×D12—32no—
120C4×D12—61no—
121C4×D12—61no—
122C4×D12—61no—
123C42×D3C2×D311yescharacteristic
124#869—31no—
125#869—31no—
126#869—31no—
127#869—31no—
128#869—61no—
129#869—61no—
130C3×C4⋊C8—32no—
131C3×C22⋊C8—32no—
132C3×C4×C8—21no—
133C3×C4×C8—31no—
134C3×C4×C8C2×D311yescharacteristic
135C3×C4×C8C2×D311yescharacteristic
136#832—34no—
137#821—34no—
138(C2×D3)⋊C8C2×D312yes—
139#816—34no—
140#816—34no—
141#816—64no—
142Dic3⋊C8C2×D312yes—
143C4×C3⋊C8C2×D311yescharacteristic
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2411yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152#634—24no—
153#634—42no—
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C2×C3×Dic3C2×D411yescharacteristic
157C3×D12—24no—
158C3×D12—24no—
159C3×D12—42no—
160C3×D12—42no—
161C3×D12—42no—
162C3×D12—42no—
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166#625—44no—
167#625—44no—
168D3×Dic3—44no—
169D3×Dic3—44no—
170C32×C8—22no—
171C3×C3⋊C8—22no—
172#532—91no—
173#532—91no—
174#493—31no—
175#492—91no—
176#487—91no—
177#486—91no—
178#463—94no—
179#449—94no—
180#431—31no—
181C2×C3×D4—32no—
182C2×C3×D4—32no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C2×#67—62no—
191C2×#67—62no—
192C2×#67—62no—
193C2×#67—62no—
194C22×Dic3—62no—
195C22×Dic3—62no—
196#237—124no—
197#237—124no—
198#235—124no—
199#235—124no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12C22×D312yes—
205C2×D12C22×D312yes—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3D1211yescharacteristic
209C2×C4×D3D1211yescharacteristic
210C2×C4×D3C22×D311yescharacteristic
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—62no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—121no—
217C3×D8—124no—
218C2×C3×C8—22no—
219C2×C3×C8—32no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C22×D312yes—
222C3×C42—21no—
223C3×C42—31no—
224C3×C42—31no—
225C3×C42—31no—
226C3×C42C22×D311yescharacteristic
227C3×C42C22×D311yescharacteristic
228#217—62no—
229#217—62no—
230#217—62no—
231#217—62no—
232#214—124no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237C4⋊Dic3—32no—
238C4⋊Dic3—32no—
239C4⋊Dic3—62no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247C4⋊Dic3—121no—
248C4⋊Dic3—121no—
249C4×Dic3D1211yescharacteristic
250C4×Dic3D1211yescharacteristic
251C4×Dic3C22×D311yescharacteristic
252C2×C3⋊C8C22×D312yes—
253D24—44no—
254#204—124no—
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—21no—
257C2×C3×D3—21no—
258C2×C3×D3—21no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C32×C4#13512yes—
266C32×C4AGL(1,ℤ/8)12yes—
267C32×C4H(5,𝔽2)12yes—
268C3⋊Dic3—42no—
269C3⋊Dic3—42no—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—21no—
273C2×#41—92no—
274C2×#41—181no—
275C2×SD16—94no—
276C2×D8—34no—
277C4⋊Q8—91no—
278C4⋊Q8—91no—
279#127—31no—
280#127—31no—
281#124—92no—
282#124—181no—
283#121—92no—
284#121—181no—
285#121—181no—
286#121—181no—
287C4×D4—92no—
288C4×D4—181no—
289C4×D4—181no—
290C4×D4—181no—
291C2×C42—31no—
292C4⋊C8—32no—
293#103—94no—
294#102—94no—
295C22⋊C8—32no—
296C4×C8—31no—
297C4×C8D3211yescharacteristic
298C23×C3—31no—
299C23×C3—62no—
300C23×C3—62no—
301C22×D3—22no—
302C22×D3—22no—
303C22×D3C2×D1211yescharacteristic
304C3×D4—64no—
305C3×D4—64no—
306C3×D4—122no—
307C3×D4—122no—
308C3×D4—122no—
309C3×D4—122no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—31no—
314C2×C3×C4—31no—
315C2×C3×C4—31no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325#67—124no—
326#67—124no—
327#67—124no—
328#67—124no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—124no—
336C2×Dic3—124no—
337C2×Dic3C2×D1211yescharacteristic
338C2×Dic3C2×D1211yescharacteristic
339C2×Dic3C2×D1211yescharacteristic
340D12—24no—
341D12—24no—
342D12—42no—
343D12—42no—
344D12—42no—
345D12—42no—
346C4×D3—22no—
347C4×D3—22no—
348C4×D3—22no—
349C4×D3—124no—
350C4×D3—124no—
351Dic6—64no—
352Dic6—64no—
353Dic6—124no—
354Dic6—122no—
355Dic6—122no—
356Dic6—242no—
357C3×C8—22no—
358C3×C8—22no—
359C3×C8—42no—
360C3×C8—62no—
361C3⋊C8—22no—
362C2×C32#53511yescharacteristic
363C2×C32C2×#13511yescharacteristic
364C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
365C3×D3—41no—
366C3×D3—82no—
367C3×D3—82no—
368#41—364no—
369#41—364no—
370C2×Q8—92no—
371C2×Q8—181no—
372C2×D4—32no—
373C2×D4—32no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—182no—
379C2×D4—182no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—182no—
384C22×C4—182no—
385SD16—364no—
386D8—124no—
387C2×C8—32no—
388C2×C8C2×D3212yes—
389C4⋊C4—92no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C22⋊C4—182no—
394C22⋊C4—182no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C42—31no—
398C42—31no—
399C42—31no—
400C42C2×D3211yescharacteristic
401C22×C3—21no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C22×D1211yescharacteristic
412C22×C3C2×D3×D411yescharacteristic
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3—42no—
421C2×D3—42no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—22no—
425C3×C4—61no—
426C3×C4—61no—
427C3×C4—61no—
428C3×C4#90412yes—
429C3×C4#90812yes—
430C3×C4#91112yes—
431C3×C4#91212yes—
432C3×C4#100412yes—
433C3×C4#100912yes—
434Dic3—21no—
435Dic3—21no—
436Dic3—21no—
437Dic3—122no—
438Dic3—122no—
439Dic3—122no—
440Dic3—122no—
441Dic3—242no—
442Dic3—242no—
443C32#320711yescharacteristic, complemented, Sylow
444C23—31no—
445C23—62no—
446C23—62no—
447Q8—184no—
448Q8—362no—
449D4—64no—
450D4—64no—
451D4—122no—
452D4—122no—
453D4—122no—
454D4—122no—
455D4—364no—
456D4—364no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—364no—
466C2×C4—364no—
467C2×C4D3×D1211yescharacteristic
468C2×C4D3×D1211yescharacteristic
469C2×C4C22×D3211yescharacteristic
470C8—22no—
471C8—62no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—121no—
476C2×C3—242no—
477C2×C3—242no—
478C2×C3#552511yescharacteristic
479C2×C3#571511yescharacteristic
480C2×C3C2×#90411yescharacteristic
481C2×C3C2×#90811yescharacteristic
482C2×C3C2×#91111yescharacteristic
483C2×C3C2×#91211yescharacteristic
484D3—41no—
485D3—82no—
486D3—82no—
487C22—61no—
488C22—61no—
489C22—61no—
490C22—122no—
491C22—122no—
492C22—122no—
493C22—122no—
494C22—122no—
495C22—122no—
496C22C2×D3×D1211yescharacteristic
497C4—61no—
498C4—61no—
499C4—61no—
500C4—362no—
501C4—362no—
502C4#6379512yes—
503C4#6380712yes—
504C4#6430712yes—
505C3—21no—
506C3#7930411yescharacteristic, complemented
507C3#8178611yescharacteristic, complemented
508C2—121no—
509C2—242no—
510C2—242no—
511C2#1059400011yescharacteristic
512C2C2×#6379511yescharacteristic
513C2C2×#6380711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3207
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593897C2semidirect
2. #10593897C2semidirect
3. #10592380C2semidirect
4. C3×#4695C2semidirect
5. C3×#4685C2semidirect
6. #10590962C2semidirect
7. #10590755C2semidirect
8. #10590369C2semidirect
9. #10590273C2semidirect
49. #4695D3semidirect
52. #4685D3semidirect
443. C32#3207semidirect
506. C3#79304semidirect
507. C3#81786semidirect

Maximal subgroups

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

subgroupindex
#105938972
#105923802
C3×#46952
C3×#46852
#105909622
#105907552
#105903692
#105902732
#817863
#793043