Finite Group Databasebeta

← #11876938

Subgroups — #11876938

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594965C212yesmaximal, complemented
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#5137C211yesmaximal, characteristic, complemented
4C3×#5135C211yesmaximal, characteristic
5#10591180C212yesmaximal, complemented
6#10590874C211yesmaximal, characteristic, complemented
7#10590869C211yesmaximal, characteristic, complemented
8#10590868C212yesmaximal, complemented
9#10590819C211yesmaximal, characteristic, complemented
10#10590781C211yesmaximal, characteristic, complemented
11#10590743C212yesmaximal, complemented
12#80892—31nomaximal
13#80852—31nomaximal
14C2×C32×M16C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#930C2212yes—
18C3×#924C2212yes—
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21#67⋊Dic3—22no—
22#63962—22no—
23#63898C2212yes—
24#63878—22no—
25#63872C2212yes—
26#63863C2212yes—
27#63862—22no—
28#63843C2212yes—
29C2×#3715C2212yes—
30#63642C2211yescharacteristic
31#63642C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C3×#821C2212yes—
35C3×#817C2211yescharacteristic
36C3×#817C2211yescharacteristic
37C3×#816C2212yes—
38#63576C2212yes—
39#63565C2212yes—
40#63562C2212yes—
41#5624—32no—
42#5600—32no—
43C3×#470—31no—
44C3×#469—31no—
45#5191—31no—
46#5184—31no—
47#5155—31no—
48#5152—31no—
49#5137D311yescharacteristic, complemented
50#5135D311yescharacteristic
51Dic3×M16—31no—
52Dic3×M16—31no—
53Dic3×M16—61no—
54#5049—32no—
55#5042—32no—
56#4869—31no—
57#4858—31no—
58#4858—31no—
59#4853—31no—
60#4817—32no—
61#4800—32no—
62#4768—32no—
63#4757—32no—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3D412yes—
66C2×C3×#67—22no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6C2312yes—
69C2×D3×Dic3—22no—
70C32×M16—22no—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2311yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76#3748—22no—
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C3×#217—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×C4⋊Dic3C2312yes—
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×Dic12—22no—
85C3×D24—22no—
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32—22no—
93#3715—24no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×D8—31no—
97C2×C3×M16—21no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C2×D311yescharacteristic
100C3×C22⋊Q8—32no—
101C3×#121—32no—
102#947—32no—
103Q8×Dic3—32no—
104C2×#215—32no—
105#936—32no—
106#935—62no—
107D4×Dic3—32no—
108D4×Dic3—62no—
109C2×#214—32no—
110#930C2×D312yes—
111#924C2×D312yes—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C2×#208—31no—
116C2×#208—31no—
117C2×#208—61no—
118C2×Dic12C2×D311yescharacteristic
119C2×D24C2×D311yescharacteristic
120#898—62no—
121#893—32no—
122#892—62no—
123#890—32no—
124#890—32no—
125#887—32no—
126#886—62no—
127#67⋊C4—62no—
128#879—62no—
129#877—62no—
130C3×#106—31no—
131C3×#106—31no—
132C3×#103—32no—
133C3×#102—32no—
134#835—32no—
135#832—32no—
136#821C2×D312yes—
137#817C2×D311yescharacteristic
138#817C2×D311yescharacteristic
139#816C2×D312yes—
140#815—31no—
141#815—31no—
142#815—31no—
143#815—31no—
144#815—61no—
145#815—61no—
146C8×Dic3—31no—
147C8×Dic3—31no—
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—61no—
151C8×Dic3—61no—
152#810—32no—
153#809—32no—
154#807—32no—
155#807—32no—
156C23×C32C2×D411yescharacteristic
157C22×C3×D3—22no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2411yescharacteristic
162C2×C3⋊Dic3—42no—
163C2×C3⋊Dic3C2×D412yes—
164C2×C3⋊Dic3C2×D412yes—
165C3×#67—44no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C3×D12—22no—
170C3×D12—22no—
171C3×Dic6—22no—
172C3×Dic6—22no—
173D3×Dic3—44no—
174C32×C8—21no—
175C32×C8#4112yes—
176C3⋊(C3⋊C8)—21no—
177C3⋊(C3⋊C8)#4112yes—
178#529—92no—
179#499—91no—
180#495—91no—
181#488—92no—
182#470—31no—
183#469—31no—
184#468—92no—
185#442—91no—
186#441—91no—
187#440—92no—
188C4×M16—91no—
189C2×C3×Q8—32no—
190C2×C3×D4—32no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—22no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200C2×D12C22×D312yes—
201C2×C4×D3—62no—
202C2×Dic6C22×D312yes—
203C3×Q16—62no—
204C3×D8—62no—
205C3×M16—24no—
206C3×M16—22no—
207C3×M16—22no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C2×C3×C8C22×D311yescharacteristic
214C3×C4⋊C4—32no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C22⋊C4—62no—
219#217—22no—
220#217—62no—
221#217—62no—
222#217—62no—
223#215—64no—
224#214—64no—
225(C2×D3)⋊C4—22no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3C22×D312yes—
233C4⋊Dic3C22×D312yes—
234Dic3⋊C4—22no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238C4×Dic3—32no—
239C4×Dic3—32no—
240C4×Dic3—31no—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249#208—62no—
250#208—62no—
251#208—64no—
252C2×C3⋊C8—31no—
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258Dic12—22no—
259D24—22no—
260C22×C32—21no—
261C22×C32—22no—
262C22×C32C22×D411yescharacteristic
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C32×C4—21no—
267C32×C4C2×#4111yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—22no—
270C3⋊Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C2×Q16—31no—
275C2×SD16—92no—
276C2×D8—31no—
277C2×M16—91no—
278C2×M16D3211yescharacteristic
279#126—182no—
280#125—92no—
281#124—92no—
282#123—182no—
283C22⋊Q8—32no—
284#121—32no—
285C4×Q8—92no—
286C4×D4—92no—
287C4×D4—182no—
288#117—182no—
289C2×C42—91no—
290#107—92no—
291#106—31no—
292#106—31no—
293#103—32no—
294#103—92no—
295#102—32no—
296#102—92no—
297#97—91no—
298#97—91no—
299C4×C8—91no—
300C4×C8—91no—
301C23×C3—21no—
302C23×C3—62no—
303C23×C3D3×D411yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—22no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×D4—62no—
309C3×D4—62no—
310C3×D4—124no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326#67—44no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—124no—
337C2×Dic3—122no—
338C2×Dic3—122no—
339C2×Dic3—124no—
340D12—22no—
341D12—22no—
342C4×D3—124no—
343Dic6—22no—
344Dic6—22no—
345C3×C8—22no—
346C3×C8—21no—
347C3×C8—21no—
348C3×C8—22no—
349C3×C8#23712yes—
350C3×C8#23712yes—
351C3⋊C8—32no—
352C3⋊C8—32no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—61no—
356C3⋊C8—61no—
357C2×C32—41no—
358C2×C32#53211yescharacteristic
359C2×C32#57512yes—
360C3×D3—82no—
361C2×Q8—32no—
362C2×D4—32no—
363C2×D4—62no—
364C22×C4—92no—
365C22×C4—182no—
366C22×C4C2×D3211yescharacteristic
367Q16—62no—
368SD16—184no—
369D8—62no—
370M16—22no—
371M16—182no—
372C2×C8—91no—
373C2×C8—91no—
374C2×C8C2×D3211yescharacteristic
375C2×C8C2×D3211yescharacteristic
376C4⋊C4—32no—
377C4⋊C4—32no—
378C4⋊C4—62no—
379C4⋊C4—182no—
380C4⋊C4—182no—
381C4⋊C4—182no—
382C22⋊C4—62no—
383C22⋊C4—62no—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C22⋊C4—182no—
387C42—91no—
388C42—91no—
389C42—92no—
390C42—182no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—42no—
398C22×C3—122no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3C2×D3×D411yescharacteristic
402C22×C3C2×D3×D411yescharacteristic
403C2×D3—42no—
404C2×D3—42no—
405C2×D3—42no—
406C3×C4—22no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—122no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4C2×#23711yescharacteristic
415C3×C4C2×#23711yescharacteristic
416C3×C4D3×#4111yescharacteristic
417C3×C4D3×#4111yescharacteristic
418Dic3—42no—
419Dic3—42no—
420Dic3—42no—
421Dic3—64no—
422Dic3—62no—
423Dic3—62no—
424Dic3—62no—
425Dic3—62no—
426Dic3—122no—
427C32#318311yescharacteristic, complemented, Sylow
428C23—62no—
429C23#380211yescharacteristic
430Q8—62no—
431Q8—62no—
432D4—62no—
433D4—62no—
434D4—124no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—92no—
441C2×C4—92no—
442C2×C4—364no—
443C2×C4—362no—
444C2×C4#380211yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—21no—
447C8—92no—
448C8—181no—
449C8#380512yes—
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—42no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3—242no—
456C2×C3#559611yescharacteristic
457C2×C3#559611yescharacteristic
458C2×C3#577312yes—
459C2×C3#577712yes—
460D3—82no—
461C22—21no—
462C22—22no—
463C22—122no—
464C22—122no—
465C22—122no—
466C22C2×#380211yescharacteristic
467C4—21no—
468C4—122no—
469C4—122no—
470C4—122no—
471C4—182no—
472C4—182no—
473C4#6430611yescharacteristic
474C4C2×#380511yescharacteristic
475C3—21no—
476C3#8085211yescharacteristic, complemented
477C3#8089211yescharacteristic, complemented
478C2—41no—
479C2—242no—
480C2#1059471812yes—
481C2#1059492911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC3×#5135C2
hypercenterC2×M16D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594965C2semidirect
2. M16×C3⋊Dic3C2semidirect
3. C3×#5137C2semidirect
5. #10591180C2semidirect
6. #10590874C2semidirect
7. #10590869C2semidirect
8. #10590868C2semidirect
9. #10590819C2semidirect
10. #10590781C2semidirect
11. #10590743C2semidirect
49. #5137D3semidirect
427. C32#3183semidirect
476. C3#80852semidirect
477. C3#80892semidirect

Maximal subgroups

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

subgroupindex
#105949652
M16×C3⋊Dic32
C3×#51372
C3×#51352
#105911802
#105908742
#105908692
#105908682
#105908192
#105907812
#105907432
#808923
#808523