Finite Group Databasebeta

← #11876937

Subgroups — #11876937

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594955C212yesmaximal, complemented
2#10592834C211yesmaximal, characteristic
3C3×#5137C211yesmaximal, characteristic, complemented
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5#10591178C212yesmaximal, complemented
6#10590872C212yesmaximal, complemented
7#10590871C211yesmaximal, characteristic, complemented
8#10590865C211yesmaximal, characteristic, complemented
9#10590812C211yesmaximal, characteristic, complemented
10#10590795C212yesmaximal, complemented
11#10590768C211yesmaximal, characteristic, complemented
12#80892—31nomaximal
13#78534—31nomaximal
14C2×C32×M16C2211yescharacteristic
15#64139C2212yes—
16C2×#3745C2211yescharacteristic
17C3×#924C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×Dic12C2211yescharacteristic
21#63966—22no—
22#63952—22no—
23#63894C2212yes—
24#63869C2212yes—
25#63868—22no—
26#63864C2212yes—
27Dic3×Dic6C2212yes—
28#63836—22no—
29C2×#3717C2212yes—
30#63648C2212yes—
31#63644C2211yescharacteristic
32C3×#817C2211yescharacteristic
33C3×#816C2212yes—
34C3×#815C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38#63575C2212yes—
39#63566C2212yes—
40#63564C2212yes—
41#5624—32no—
42#5479—32no—
43C3×#470—31no—
44C3×C4×M16—31no—
45#5191—31no—
46#5184—31no—
47#5137D311yescharacteristic, complemented
48#5135—31no—
49#5135—31no—
50#5135—61no—
51#5134—32no—
52Dic3×M16D311yescharacteristic, complemented
53#5049—32no—
54#4869—31no—
55#4858—31no—
56#4817—32no—
57#4800—32no—
58#4716—31no—
59#4711—31no—
60#4710—32no—
61#4697—32no—
62#4696—31no—
63#4683—31no—
64C22×C32×C4C2311yescharacteristic
65C2×#638—22no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C22×C3×Dic3D412yes—
68C2×C3×Dic6C2312yes—
69C2×#624—22no—
70C32×M16—22no—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73#3752—22no—
74C4⋊(C3⋊Dic3)C2312yes—
75#3745—22no—
76C3×#217—22no—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×C4×Dic3D412yes—
80C3×C4×Dic3C2311yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C3×#208—22no—
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×Dic12—22no—
86#3724—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89#3722—22no—
90#3722—22no—
91#3722—22no—
92Dic32—22no—
93#3717—24no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×M16—21no—
97C2×C3×M16—31no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C2×D311yescharacteristic
100C3×C22⋊Q8—32no—
101C2×C3×C42—31no—
102#947—32no—
103Q8×Dic3—32no—
104C2×#215—32no—
105#930—32no—
106#930—32no—
107#930—62no—
108#929—62no—
109C4×#67—62no—
110#924C2×D312yes—
111C2×C4×Dic3C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113C2×Dic12C2×D311yescharacteristic
114C2×D24—31no—
115C2×D24—31no—
116C2×D24—61no—
117C2×#204—32no—
118#898—62no—
119#893—32no—
120#892—62no—
121#890—32no—
122#886—62no—
123#67⋊C4—62no—
124#876—62no—
125#875—32no—
126C4×D12—32no—
127#872—62no—
128#870—32no—
129C4×Dic6—32no—
130C3×#106—31no—
131C3×#103—32no—
132C3×#97—31no—
133C3×#97—31no—
134C3×C4×C8—31no—
135C3×C4×C8—31no—
136#835—32no—
137#821—32no—
138#821—32no—
139#821—32no—
140#821—62no—
141#818—32no—
142#817—31no—
143#817—31no—
144#817—61no—
145#817C2×D311yescharacteristic
146#816—32no—
147#816C2×D312yes—
148#815C2×D311yescharacteristic
149#815C2×D311yescharacteristic
150C8×Dic3C2×D311yescharacteristic
151C8×Dic3C2×D311yescharacteristic
152#809—32no—
153#807—32no—
154C23×C32C2×D411yescharacteristic
155C22×C3⋊D3—22no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2411yescharacteristic
160#638—44no—
161C2×C3⋊Dic3—22no—
162C4⋊(C3⋊D3)—22no—
163C4⋊(C3⋊D3)—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—42no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×Dic6—22no—
170C3×Dic6—22no—
171#624—44no—
172C32×C8—21no—
173C32×C8#4112yes—
174C3×C3⋊C8—21no—
175C3×C3⋊C8#4112yes—
176#529—92no—
177#499—91no—
178#495—91no—
179#488—92no—
180#470—31no—
181#469—91no—
182#468—92no—
183#442—91no—
184#441—91no—
185#440—92no—
186C4×M16—31no—
187C2×C3×Q8—32no—
188C22×C3×C4—21no—
189C22×C3×C4—32no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—62no—
193C2×#67—62no—
194C2×#67—122no—
195C22×Dic3D1212yes—
196C2×D12—32no—
197C2×D12—32no—
198C2×D12—62no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×Dic6C22×D312yes—
202C3×Q16—62no—
203C3×M16—22no—
204C3×M16—22no—
205C3×M16—42no—
206C3×M16—62no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—31no—
210C2×C3×C8—31no—
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C2×C3×C8C22×D311yescharacteristic
214C2×C3×C8C22×D311yescharacteristic
215C3×C4⋊C4—32no—
216C3×C4⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C42—32no—
219C3×C42—31no—
220C3×C42—31no—
221#217—22no—
222#215—64no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—122no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—62no—
235C4⋊Dic3—62no—
236C4⋊Dic3—62no—
237C4⋊Dic3C22×D312yes—
238Dic3⋊C4—22no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3D1212yes—
246C4×Dic3C22×D311yescharacteristic
247C4×Dic3C22×D311yescharacteristic
248#208—22no—
249C2×C3⋊C8C22×D311yescharacteristic
250C2×C3⋊C8C22×D311yescharacteristic
251Dic12—22no—
252D24—62no—
253D24—62no—
254D24—122no—
255#204—64no—
256C22×C32—21no—
257C22×C32—22no—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C32×C4—21no—
263C32×C4C2×#4111yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—42no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C2×Q16—31no—
271C2×SD16—92no—
272C2×D8—91no—
273C2×M16—31no—
274C2×M16D3211yescharacteristic
275#126—182no—
276#125—92no—
277#124—92no—
278#123—182no—
279C22⋊Q8—32no—
280#121—92no—
281C4×Q8—92no—
282C4×D4—92no—
283C4×D4—182no—
284#117—182no—
285C2×C42—31no—
286#107—92no—
287#106—31no—
288#106—91no—
289#103—32no—
290#103—92no—
291#102—92no—
292#102—92no—
293#97—31no—
294#97—31no—
295C4×C8—31no—
296C4×C8—31no—
297C23×C3—21no—
298C23×C3C2×D1211yescharacteristic
299C23×C3D3×D411yescharacteristic
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—122no—
303C3×Q8—62no—
304C3×Q8—62no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—32no—
312C2×C3×C4—32no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—122no—
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322#67—124no—
323#67—124no—
324#67—244no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—42no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—122no—
331C2×Dic3C2×D1212yes—
332C2×Dic3C2×D1212yes—
333D12—62no—
334D12—62no—
335D12—62no—
336D12—62no—
337D12—122no—
338D12—122no—
339C4×D3—124no—
340C4×D3—124no—
341Dic6—22no—
342Dic6—22no—
343C3×C8—21no—
344C3×C8—21no—
345C3×C8—22no—
346C3×C8—32no—
347C3×C8—41no—
348C3×C8—61no—
349C3×C8#23512yes—
350C3×C8#23712yes—
351C3⋊C8—21no—
352C3⋊C8#23512yes—
353C2×C32—41no—
354C2×C32#53211yescharacteristic
355C2×C32#57512yes—
356C3⋊D3—82no—
357C2×Q8—32no—
358C2×D4—92no—
359C2×D4—182no—
360C22×C4—32no—
361C22×C4—182no—
362C22×C4C2×D3211yescharacteristic
363Q16—62no—
364SD16—184no—
365D8—182no—
366M16—22no—
367M16—62no—
368C2×C8—31no—
369C2×C8—31no—
370C2×C8C2×D3211yescharacteristic
371C2×C8C2×D3211yescharacteristic
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—92no—
375C4⋊C4—182no—
376C4⋊C4—182no—
377C4⋊C4—182no—
378C22⋊C4—62no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C22⋊C4—182no—
383C42—31no—
384C42—31no—
385C42—32no—
386C42—182no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—42no—
393C22×C3—41no—
394C22×C3C22×D1211yescharacteristic
395C22×C3C2×D3×D411yescharacteristic
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—122no—
402C2×D3—242no—
403C2×D3—242no—
404C2×D3—242no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—62no—
411C3×C4—62no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23511yescharacteristic
416C3×C4C2×#23711yescharacteristic
417C3×C4D3×#4111yescharacteristic
418Dic3—22no—
419Dic3—22no—
420Dic3—42no—
421Dic3—42no—
422Dic3—122no—
423Dic3—122no—
424Dic3—242no—
425C32#318311yescharacteristic, complemented, Sylow
426C23—182no—
427C23D3×D1211yescharacteristic
428Q8—62no—
429Q8—62no—
430D4—182no—
431D4—182no—
432D4—364no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—32no—
436C2×C4—32no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—122no—
440C2×C4—182no—
441C2×C4—364no—
442C2×C4D3×D1211yescharacteristic
443C2×C4C22×D3211yescharacteristic
444C8—21no—
445C8—32no—
446C8—61no—
447C8#380412yes—
448C2×C3—21no—
449C2×C3—22no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—81no—
453C2×C3#547711yescharacteristic
454C2×C3#559611yescharacteristic
455C2×C3#574812yes—
456C2×C3#577712yes—
457D3—242no—
458D3—242no—
459D3—482no—
460C22—21no—
461C22—22no—
462C22—362no—
463C22—362no—
464C22—362no—
465C22C2×D3×D1211yescharacteristic
466C4—21no—
467C4—62no—
468C4—62no—
469C4—122no—
470C4—122no—
471C4—362no—
472C4D3×#23511yescharacteristic
473C4C2×#380411yescharacteristic
474C3—21no—
475C3#7853411yescharacteristic, complemented
476C3#8089211yescharacteristic, complemented
477C2—41no—
478C2—722no—
479C2#1059471112yes—
480C2#1059491011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10592834C2
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. #10594955C2semidirect
3. C3×#5137C2semidirect
4. C3×Dic3×M16C2semidirect
5. #10591178C2semidirect
6. #10590872C2semidirect
7. #10590871C2semidirect
8. #10590865C2semidirect
9. #10590812C2semidirect
10. #10590795C2semidirect
11. #10590768C2semidirect
47. #5137D3semidirect
52. Dic3×M16D3semidirect
425. C32#3183semidirect
475. C3#78534semidirect
476. C3#80892semidirect

Maximal subgroups

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

subgroupindex
#105949552
#105928342
C3×#51372
C3×Dic3×M162
#105911782
#105908722
#105908712
#105908652
#105908122
#105907952
#105907682
#808923
#785343