Finite Group Databasebeta

← #11877004

Subgroups — #11877004

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5716C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5073C211yesmaximal, characteristic, complemented
5#10591451C214yesmaximal, complemented
6#10591430C214yesmaximal, complemented
7C4×#3711C211yesmaximal, characteristic, complemented
8#10590303C211yesmaximal, characteristic, complemented
9#10590277C211yesmaximal, characteristic, complemented
10#83295—31nomaximal
11#81777—31nomaximal
12C2×C3×#237—21no—
13C2×#3795—21no—
14C32×#127C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#938—21no—
17C3×#938C2212yes—
18C3×#936—21no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3C2212yes—
21C2×C3×#213C2214yes—
22C3×#874C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63908—21no—
26#63908C2212yes—
27Dic3×D12—21no—
28Dic3×D12C2212yes—
29#63860—21no—
30C2×#3711C2212yes—
31#63659C2214yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34#63573C2214yes—
35#63562C2214yes—
36#63554C2212yes—
37C3×#532—31no—
38#5716—31no—
39#5716D311yescharacteristic, complemented
40#5477—31no—
41C3×#493—31no—
42#5159—34no—
43#5152—34no—
44#5088—31no—
45#5080—31no—
46#5073D311yescharacteristic, complemented
47#5070—31no—
48#5070—31no—
49#5070—31no—
50#5070—61no—
51#5039—34no—
52#5014—34no—
53C4×#208—31no—
54C4×ΓL(1,𝔽25)—31no—
55#4680—31no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×#634—21no—
60C2×C3×#67—22no—
61C22×C3×Dic3—22no—
62C3×#237—44no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6—21no—
70C2×#625—22no—
71C2×D3×Dic3—22no—
72#3795—44no—
73C32×C42C2311yescharacteristic
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217—22no—
78C3×#217—22no—
79C3×#213—28no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86(C2×D3)⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88#3711—24no—
89#3184—91noSylow
90C2×C3×#41—61no—
91C2×#237—21no—
92C2×#237—61no—
93C2×#235—61no—
94C2×C3×D8—34no—
95C3×C4⋊Q8—31no—
96C3×#127—21no—
97C3×#127—31no—
98C3×#127C2×D311yescharacteristic
99C3×#127C2×D311yescharacteristic
100C3×#124—61no—
101C3×#121—32no—
102C3×#121—61no—
103C3×C4×D4—32no—
104C3×C4×D4—61no—
105C2×C3×C42—31no—
106#938—21no—
107#938—32no—
108#938—61no—
109#938C2×D312yes—
110#936—21no—
111#936—61no—
112D4×Dic3—21no—
113D4×Dic3—32no—
114D4×Dic3—61no—
115D4×Dic3C2×D312yes—
116C2×#213C2×D314yes—
117#930—32no—
118#930—61no—
119C2×#208—32no—
120C2×ΓL(1,𝔽25)—32no—
121#875—61no—
122#874C2×D311yescharacteristic
123C4×D12—32no—
124C4×D12—61no—
125C42×D3C2×D311yescharacteristic
126#869—31no—
127#869—31no—
128#869—61no—
129#869C2×D311yescharacteristic
130C3×C4×C8—31no—
131#832—34no—
132#832—34no—
133#832—34no—
134#832—64no—
135#817—34no—
136#815—32no—
137#809—34no—
138#808—34no—
139#803—32no—
140C4×C3⋊C8—31no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—61no—
143C4×C3⋊C8C2×D311yescharacteristic
144C23×C32—22no—
145C22×C3×D3—22no—
146C22×C3×D3C2×D411yescharacteristic
147C32×D4—24no—
148C32×D4—42no—
149C32×D4—42no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154#634—42no—
155C3×#67—44no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—44no—
158C2×C3×Dic3C2×D411yescharacteristic
159C2×C3×Dic3C2×D411yescharacteristic
160C2×C3×Dic3C2×D411yescharacteristic
161C3×D12—24no—
162C3×D12—42no—
163C3×D12—42no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167C3×Dic6—42no—
168#625—44no—
169D3×Dic3—44no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8#4114yescomplemented
172#532—31no—
173#532—91no—
174#498—91no—
175#493—31no—
176#486—91no—
177#486—91no—
178#469—94no—
179#442—94no—
180C4×M16—91no—
181C3×#41—124no—
182C2×C3×Q8—61no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—32no—
189C2×C3×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4—62no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4C22×D312yes—
195C2×C3×D4C22×D312yes—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—62no—
200C2×#67—22no—
201C2×#67—62no—
202C2×#67—62no—
203C22×Dic3—22no—
204C22×Dic3—62no—
205#237—44no—
206#237—124no—
207#235—124no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12C22×D312yes—
211C2×C4×D3—62no—
212C2×C4×D3#6711yescharacteristic
213C2×C4×D3#6711yescharacteristic
214C2×C4×D3C22×D311yescharacteristic
215C2×Dic6—21no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—121no—
219C3×D8—68no—
220C2×C3×C8—32no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—62no—
224C3×C22⋊C4—62no—
225C3×C42—21no—
226C3×C42—31no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231#217—22no—
232#217—22no—
233#217—62no—
234#217—62no—
235#213—28no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238C4⋊Dic3—21no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—121no—
245C4⋊Dic3C22×D312yes—
246C4×Dic3#6711yescharacteristic
247C4×Dic3#6711yescharacteristic
248C4×Dic3C22×D311yescharacteristic
249#208—64no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8C22×D312yes—
254ΓL(1,𝔽25)—64no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—21no—
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C32×C4AGL(1,ℤ/8)12yes—
266C32×C4AGL(1,ℤ/8)12yes—
267C32×C4C2×#4112yes—
268C3⋊Dic3—42no—
269C3×Dic3—21no—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—42no—
273C2×#41—61no—
274C2×#41—181no—
275C2×D8—34no—
276C2×M16—92no—
277C4⋊Q8—31no—
278C4⋊Q8—91no—
279#127—31no—
280#127D3211yescharacteristic
281#124—61no—
282#124—181no—
283#121—32no—
284#121—61no—
285#121—92no—
286#121—181no—
287C4×D4—32no—
288C4×D4—61no—
289C4×D4—92no—
290C4×D4—181no—
291C2×C42—31no—
292#106—94no—
293#102—94no—
294#102—94no—
295#97—92no—
296C4×C8—31no—
297C4×C8—91no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—31no—
301C23×C3—42no—
302C23×C3—62no—
303C22×D3—22no—
304C22×D3C2×#6711yescharacteristic
305C3×Q8—122no—
306C3×D4—24no—
307C3×D4—24no—
308C3×D4—44no—
309C3×D4—42no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—42no—
313C3×D4—64no—
314C3×D4—82no—
315C3×D4—82no—
316C3×D4—124no—
317C3×D4—122no—
318C3×D4—122no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—124no—
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336#67—44no—
337#67—124no—
338#67—124no—
339C2×Dic3—22no—
340C2×Dic3—44no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—122no—
344C2×Dic3—124no—
345C2×Dic3C2×#6711yescharacteristic
346C2×Dic3C2×#6711yescharacteristic
347C2×Dic3C2×#6711yescharacteristic
348D12—24no—
349D12—42no—
350D12—42no—
351C4×D3—22no—
352C4×D3—22no—
353C4×D3—22no—
354C4×D3—124no—
355Dic6—42no—
356Dic6—122no—
357Dic6—122no—
358Dic6—242no—
359C3×C8—34no—
360C3⋊C8—62no—
361C3⋊C8—62no—
362C3⋊C8—122no—
363C3⋊C8#23714yescomplemented
364C2×C32—82no—
365C2×C32#53211yescharacteristic
366C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
367C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
368C3×D3—41no—
369C3×D3—82no—
370#41—124no—
371#41—364no—
372C2×Q8—61no—
373C2×Q8—181no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—32no—
377C2×D4—62no—
378C2×D4—61no—
379C2×D4—61no—
380C2×D4—182no—
381C2×D4C2×D3212yes—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—62no—
386C22×C4—182no—
387D8—68no—
388M16—184no—
389C2×C8—32no—
390C2×C8—92no—
391C4⋊C4—32no—
392C4⋊C4—61no—
393C4⋊C4—92no—
394C4⋊C4—181no—
395C22⋊C4—62no—
396C22⋊C4—62no—
397C22⋊C4—182no—
398C22⋊C4—182no—
399C42—31no—
400C42—31no—
401C42—31no—
402C42C2×D3211yescharacteristic
403C22×C3—21no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—61no—
411C22×C3—61no—
412C22×C3—61no—
413C22×C3—82no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—21no—
422C2×D3—21no—
423C2×D3—21no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—61no—
431C3×C4—61no—
432C3×C4—61no—
433C3×C4—122no—
434C3×C4#91112yes—
435C3×C4#91112yes—
436C3×C4#93212yes—
437C3×C4#94912yes—
438C3×C4C2×#23712yes—
439C3×C4D3×#4112yes—
440Dic3—21no—
441Dic3—21no—
442Dic3—21no—
443Dic3—42no—
444Dic3—122no—
445Dic3—122no—
446Dic3—242no—
447C32#318411yescharacteristic, complemented, Sylow
448C23—22no—
449C23—31no—
450C23—62no—
451Q8—122no—
452Q8—362no—
453D4—24no—
454D4—42no—
455D4—42no—
456D4—64no—
457D4—124no—
458D4—122no—
459D4—122no—
460D4—364no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—124no—
469C2×C4—182no—
470C2×C4—364no—
471C2×C4D3×#6711yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C2×C4C22×D3211yescharacteristic
474C8—34no—
475C8—182no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—82no—
480C2×C3—82no—
481C2×C3—121no—
482C2×C3—162no—
483C2×C3—242no—
484C2×C3#571611yescharacteristic
485C2×C3C2×#91111yescharacteristic
486C2×C3C2×#91111yescharacteristic
487C2×C3C2×#93211yescharacteristic
488C2×C3C2×#94911yescharacteristic
489C2×C3#583211yescharacteristic
490D3—41no—
491D3—82no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—122no—
499C22—122no—
500C22—122no—
501C22C2×D3×#6711yescharacteristic
502C4—61no—
503C4—61no—
504C4—61no—
505C4—122no—
506C4—362no—
507C4#6392512yes—
508C4#6393212yes—
509C4D3×#23712yes—
510C3—21no—
511C3#8177711yescharacteristic, complemented
512C3#8329511yescharacteristic, complemented
513C2—82no—
514C2—121no—
515C2—242no—
516C2C2×#6392511yescharacteristic
517C2C2×#6393211yescharacteristic
518C2#1059515211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5716C2semidirect
2. #10593897C2semidirect
3. #10592769C2semidirect
4. C3×#5073C2semidirect
5. #10591451C2semidirect
6. #10591430C2semidirect
7. C4×#3711C2semidirect
8. #10590303C2semidirect
9. #10590277C2semidirect
39. #5716D3semidirect
46. #5073D3semidirect
171. C3×C3⋊C8#41semidirect
363. C3⋊C8#237semidirect
447. C32#3184semidirect
511. C3#81777semidirect
512. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
#105938972
#105927692
C3×#50732
#105914512
#105914302
C4×#37112
#105903032
#105902772
#832953
#817773