Finite Group Databasebeta

← #11788761

Subgroups — #11788761

Order 1152.

735 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5525C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3#10591231C211yesmaximal, characteristic, complemented
4#10591086C211yesmaximal, characteristic, complemented
5#10591085C211yesmaximal, characteristic, complemented
6#10589397C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8#71854—31nomaximal
9#68713—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#895—22no—
18C3×#882—22no—
19C3×#875C412yescomplemented
20C3×#874C412yescomplemented
21#63815—22no—
22#63814—22no—
23D3×#208—22no—
24#63580—22no—
25#63563—22no—
26#63562—22no—
27C3×#535—31no—
28#5819—31no—
29#5745—31no—
30#5525D311yescharacteristic
31#5240—31no—
32#5215—31no—
33#5215—31no—
34#5131—31no—
35#5006—31no—
36#5001—31no—
37C3×H(3,ℤ/4)—31no—
38#4531—31no—
39#4531—31no—
40#4531—61no—
41#4531D311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67D412yes—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—24no—
55C2×C3×D12C2×C412yes—
56C2×C3×D12C2×C411yescharacteristic
57C2×C3×C4×D3D412yes—
58C2×C3×Dic6C2×C411yescharacteristic
59C32×C4⋊C4—21no—
60C32×C22⋊C4—21no—
61C32×C42C2×C412yes—
62#3757—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4×C3⋊Dic3—21no—
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)D412yescomplemented
68C3×#217—21no—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8D412yescomplemented
75#3711—24no—
76D3×C3⋊C8—24no—
77#1910—91noSylow
78C2×C3×#41—31no—
79C22×C3×D4—31no—
80C2×#235C2×D311yescharacteristic
81C22×D12C2×D311yescharacteristic
82C2×C3×M16—31no—
83C3×#127—32no—
84C3×#124—32no—
85C3×#121—62no—
86C3×#120—62no—
87C3×#117—21no—
88C3×#117—31no—
89C3×#117C2×D311yescharacteristic
90C3×#117C2×D311yescharacteristic
91#948—62no—
92#948—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208—62no—
101C2×#208C2×D311yescharacteristic
102#907—62no—
103D3×M16—62no—
104#901—62no—
105#895—22no—
106#882—22no—
107#875Dic312yescomplemented
108#874Dic312yescomplemented
109#834—62no—
110#832—62no—
111#832—62no—
112#821—62no—
113#809—62no—
114#806—62no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—82no—
120C22×C3×D3C22⋊C412yes—
121C2×C32×C4—22no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—41no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3C22⋊C412yes—
133C3×D12—21no—
134C3×D12—21no—
135C3×D12—22no—
136C3×D12—22no—
137C3×D12—41no—
138C3×D12—41no—
139C3×D12—84no—
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142C3×Dic6—21no—
143C3×Dic6—21no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146#568—91no—
147#535—31no—
148#418—91no—
149#418—91no—
150#410—91no—
151H(3,ℤ/4)—31no—
152H(3,ℤ/4)—91no—
153C24×C3—61no—
154C23×D3—21no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—32no—
161C2×C3×D4—31no—
162C2×C3×D4—32no—
163C2×C3×D4—64no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—32no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67#6712yes—
174#235—21no—
175#235—21no—
176#235—21no—
177#235—21no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—24no—
184C2×D12C2×Dic312yes—
185C2×D12C2×Dic311yescharacteristic
186C2×C4×D3#6712yes—
187C2×Dic6C2×Dic311yescharacteristic
188C3×M16—61no—
189C3×M16—61no—
190C2×C3×C8—32no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—41no—
194C3×C4⋊C4—61no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—41no—
198C3×C22⋊C4—64no—
199C3×C22⋊C4—61no—
200C3×C42—22no—
201C3×C42—61no—
202C3×C42C4×D312yes—
203C3×C42C2×Dic312yes—
204#217—21no—
205#217—61no—
206#217—61no—
207#217—121no—
208(C2×D3)⋊C4—24no—
209C4⋊Dic3—21no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4×Dic3—21no—
214C4×Dic3—62no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217#208—21no—
218#208—21no—
219#208—64no—
220#208—61no—
221#208—61no—
222#208—61no—
223#208—61no—
224#208—121no—
225#208—121no—
226C2×C3⋊C8—32no—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—64no—
230C2×C3⋊C8D1212yescomplemented
231ΓL(1,𝔽25)—64no—
232D3×C8—64no—
233C22×C32—41no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32#12111yescharacteristic
236C22×C32#12111yescharacteristic
237C2×C3×D3—22no—
238C2×C3×D3—42no—
239C2×C3×D3—44no—
240C2×C3×D3—42no—
241C2×C3×D3—82no—
242C2×C3×D3—82no—
243C32×C4—42no—
244C32×C4C4×D411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C32×C4#12011yescharacteristic
247C32×C4#12311yescharacteristic
248C3⋊Dic3—81no—
249C3×Dic3—22no—
250C3×Dic3—81no—
251C2×#41—31no—
252C22×D4—31no—
253#131—182no—
254#131—182no—
255C2×M16—31no—
256C2×M16—91no—
257C2×M16—182no—
258#127—32no—
259#124—32no—
260#121—62no—
261#120—62no—
262#117—31no—
263#117—91no—
264#117D3211yescharacteristic
265#102—182no—
266#102—182no—
267#99—182no—
268C23×C3—21no—
269C23×C3—32no—
270C23×C3—62no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3—242no—
274C23×C3D3×D411yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C22×D3—22no—
277C22×D3—41no—
278C22×D3—41no—
279C22×D3—82no—
280C22×D3#21712yes—
281C3×Q8—61no—
282C3×Q8—61no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—61no—
286C3×D4—62no—
287C3×D4—61no—
288C3×D4—62no—
289C3×D4—121no—
290C3×D4—121no—
291C3×D4—244no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—32no—
301C2×C3×C4—42no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—121no—
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4#23911yescharacteristic
315C2×C3×C4C22×Dic311yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317#67—22no—
318#67—22no—
319C2×Dic3—41no—
320C2×Dic3—122no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3#21712yes—
324D12—21no—
325D12—21no—
326D12—22no—
327D12—22no—
328D12—41no—
329D12—41no—
330D12—84no—
331C4×D3—22no—
332C4×D3—22no—
333Dic6—21no—
334Dic6—21no—
335C3×C8—62no—
336C3⋊C8—22no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C3⋊C8—122no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32#38611yescharacteristic
344C3×D3—42no—
345C3×D3—82no—
346C24—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—31no—
352C2×D4—32no—
353C2×D4—31no—
354C2×D4—32no—
355C2×D4—64no—
356C2×D4—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C22×C4—32no—
362C22×C4C2×D3211yescharacteristic
363M16—61no—
364M16—61no—
365M16—184no—
366M16—181no—
367M16—181no—
368C2×C8—32no—
369C2×C8—92no—
370C2×C8—184no—
371C4⋊C4—21no—
372C4⋊C4—61no—
373C4⋊C4—181no—
374C22⋊C4—21no—
375C22⋊C4—64no—
376C22⋊C4—61no—
377C22⋊C4—181no—
378C42—61no—
379C42—181no—
380C42D3×Dic312yes—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—62no—
387C22×C3—81no—
388C22×C3—122no—
389C22×C3—124no—
390C22×C3—122no—
391C22×C3—242no—
392C22×C3—242no—
393C22×C3D3×C22⋊C411yescharacteristic
394C22×C3#88411yescharacteristic
395C22×C3#89511yescharacteristic
396C22×C3#93911yescharacteristic
397C22×C3#93911yescharacteristic
398C22×C3C2×#21711yescharacteristic
399C2×D3—22no—
400C2×D3—42no—
401C2×D3—44no—
402C2×D3—42no—
403C2×D3—82no—
404C2×D3—82no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—62no—
412C3×C4—82no—
413C3×C4—241no—
414C3×C4C4×D1211yescharacteristic
415C3×C4#88211yescharacteristic
416C3×C4#89311yescharacteristic
417C3×C4#89411yescharacteristic
418C3×C4D4×Dic311yescharacteristic
419C3×C4D4×Dic311yescharacteristic
420C3×C4#93511yescharacteristic
421C3×C4#93711yescharacteristic
422Dic3—22no—
423Dic3—81no—
424Dic3—241no—
425Dic3—241no—
426Dic3—242no—
427C32#191011yescharacteristic, complemented, Sylow
428C23—32no—
429C23—62no—
430C23—121no—
431C23—121no—
432C23—242no—
433C23D3×#6711yescharacteristic
434Q8—61no—
435Q8—61no—
436D4—62no—
437D4—62no—
438D4—61no—
439D4—62no—
440D4—61no—
441D4—62no—
442D4—121no—
443D4—121no—
444D4—244no—
445C2×C4—22no—
446C2×C4—32no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—121no—
450C2×C4—361no—
451C2×C4#379511yescharacteristic
452C2×C4#379611yescharacteristic
453C2×C4D3×D1211yescharacteristic
454C2×C4#380211yescharacteristic
455C2×C4C2×D3×Dic311yescharacteristic
456C2×C4D3×#6711yescharacteristic
457C8—62no—
458C8—182no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—122no—
470C2×C3—242no—
471C2×C3#466511yescharacteristic
472C2×C3#522011yescharacteristic
473D3—42no—
474D3—82no—
475C22—41no—
476C22—62no—
477C22—122no—
478C22—124no—
479C22—122no—
480C22—242no—
481C22—242no—
482C22#6388511yescharacteristic
483C22#6388611yescharacteristic
484C22D3×#21711yescharacteristic
485C4—42no—
486C4—62no—
487C4—241no—
488C4—721no—
489C4#6388411yescharacteristic
490C4Dic3×D1211yescharacteristic
491C4#6389811yescharacteristic
492C4#6392211yescharacteristic
493C3—21no—
494C3#6871311yescharacteristic, complemented
495C3#7185411yescharacteristic, complemented
496C2—21no—
497C2—21no—
498C2—21no—
499C2—122no—
500C2—242no—
501C2#1059137611yescharacteristic
subgroupG/H
centerC2#10591376
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radicalC3×#5525C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1910
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. #10591231C2semidirect
4. #10591086C2semidirect
5. #10591085C2semidirect
6. #10589397C2semidirect
7. C3×#4531C2semidirect
19. C3×#875C4semidirect
20. C3×#874C4semidirect
41. #4531D3semidirect
67. C2×C3⋊(C3⋊C8)D4semidirect
74. C2×C3×C3⋊C8D4semidirect
107. #875Dic3semidirect
108. #874Dic3semidirect
230. C2×C3⋊C8D12semidirect
427. C32#1910semidirect
494. C3#68713semidirect
495. C3#71854semidirect

Maximal subgroups

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

subgroupindex
C3×#55252
#105947762
#105912312
#105910862
#105910852
#105893972
C3×#45312
#718543
#687133