Finite Group Databasebeta

← #11876939

Subgroups — #11876939

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594949C212yesmaximal, complemented
2#10592836C211yesmaximal, characteristic, complemented
3C3×#5135C211yesmaximal, characteristic
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5#10591176C212yesmaximal, complemented
6#10590871C211yesmaximal, characteristic, complemented
7#10590864C211yesmaximal, characteristic, complemented
8#10590863C212yesmaximal, complemented
9#10590810C211yesmaximal, characteristic, complemented
10#10590771C211yesmaximal, characteristic, complemented
11#10590747C212yesmaximal, complemented
12#80852—31nomaximal
13#78534—31nomaximal
14C2×C32×M16C2211yescharacteristic
15#64133C2212yes—
16C2×#3746C2211yescharacteristic
17C3×#930C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21Dic3×#67—22no—
22#63961—22no—
23Dic3×D12C2212yes—
24#63877—22no—
25#63869C2212yes—
26#63860C2212yes—
27#63859—22no—
28#63844C2212yes—
29C2×#3716C2212yes—
30#63644C2211yescharacteristic
31#63643C2212yes—
32C3×#821C2212yes—
33C3×#817C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38#63575C2212yes—
39#63567C2212yes—
40#63563C2212yes—
41#5600—32no—
42#5479—32no—
43C3×#469—31no—
44C3×C4×M16—31no—
45#5155—31no—
46#5152—31no—
47#5137—31no—
48#5137—31no—
49#5137—61no—
50#5135D311yescharacteristic
51#5134—32no—
52Dic3×M16D311yescharacteristic, complemented
53#5042—32no—
54#4858—31no—
55#4853—31no—
56#4768—32no—
57#4757—32no—
58#4716—31no—
59#4711—31no—
60#4710—32no—
61#4697—32no—
62#4696—31no—
63#4683—31no—
64C22×C32×C4C2311yescharacteristic
65C2×#634C2312yes—
66C2×C3×#67—22no—
67C22×C3×Dic3D412yes—
68C2×C3×D12C2312yes—
69C2×D3×Dic3—22no—
70C32×M16—22no—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73#3757—22no—
74C4⋊(C3⋊Dic3)C2312yes—
75#3750—22no—
76#3746—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3D412yes—
80C3×C4×Dic3C2311yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C3×#208—22no—
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×D24—22no—
86#3724—22no—
87#3724—22no—
88Dic3⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32—22no—
93#3716—24no—
94#3183—91noSylow
95C2×C3×D8—31no—
96C2×C3×M16—21no—
97C2×C3×M16—31no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C2×D311yescharacteristic
100C3×#121—32no—
101C2×C3×C42—31no—
102#936—32no—
103#935—62no—
104D4×Dic3—32no—
105D4×Dic3—62no—
106C2×#214—32no—
107#930C2×D312yes—
108#929—62no—
109C4×#67—62no—
110#924—32no—
111#924—32no—
112#924—62no—
113C2×C4×Dic3C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115C2×Dic12—31no—
116C2×Dic12—31no—
117C2×Dic12—61no—
118C2×D24C2×D311yescharacteristic
119C2×#204—32no—
120#890—32no—
121#887—32no—
122#879—62no—
123#877—62no—
124#876—62no—
125#875—32no—
126C4×D12—32no—
127#872—62no—
128#870—32no—
129C4×Dic6—32no—
130C3×#106—31no—
131C3×#102—32no—
132C3×#97—31no—
133C3×#97—31no—
134C3×C4×C8—31no—
135C3×C4×C8—31no—
136#832—32no—
137#821—32no—
138#821C2×D312yes—
139#818—32no—
140#817—31no—
141#817—31no—
142#817—61no—
143#817C2×D311yescharacteristic
144#816—32no—
145#816—32no—
146#816—32no—
147#816—62no—
148#815C2×D311yescharacteristic
149#815C2×D311yescharacteristic
150C8×Dic3C2×D311yescharacteristic
151C8×Dic3C2×D311yescharacteristic
152#810—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
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162#634—22no—
163#634—22no—
164C3×#67—44no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—42no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×D12—22no—
170C3×D12—22no—
171D3×Dic3—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—91no—
181#469—31no—
182#468—92no—
183#442—91no—
184#441—91no—
185#440—92no—
186C4×M16—31no—
187C2×C3×D4—32no—
188C2×C3×D4—62no—
189C22×C3×C4—21no—
190C22×C3×C4—32no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—22no—
194C22×Dic3—62no—
195C22×Dic3D1212yes—
196C2×D12C22×D312yes—
197C2×C4×D3—62no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C3×D8—62no—
202C3×M16—22no—
203C3×M16—22no—
204C3×M16—42no—
205C3×M16—62no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—31no—
209C2×C3×C8—31no—
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C2×C3×C8C22×D311yescharacteristic
214C3×C4⋊C4—32no—
215C3×C22⋊C4—62no—
216C3×C42—32no—
217C3×C42—31no—
218C3×C42—31no—
219#217—62no—
220#217—62no—
221#217—62no—
222#217—62no—
223#217—62no—
224#217—122no—
225#214—64no—
226(C2×D3)⋊C4—22no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3C22×D312yes—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—122no—
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—62no—
252Dic12—62no—
253Dic12—122no—
254D24—22no—
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—42no—
267C3×Dic3—22no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C2×Q16—91no—
271C2×SD16—92no—
272C2×D8—31no—
273C2×M16—31no—
274C2×M16D3211yescharacteristic
275#126—182no—
276#125—92no—
277#124—92no—
278#123—182no—
279C22⋊Q8—92no—
280#121—32no—
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—92no—
290#103—92no—
291#102—32no—
292#102—92no—
293#97—31no—
294#97—31no—
295C4×C8—31no—
296C4×C8—31no—
297C23×C3—21no—
298C23×C3—62no—
299C23×C3C2×D1211yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—22no—
302C3×D4—62no—
303C3×D4—62no—
304C3×D4—124no—
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—122no—
317C2×C3×C4C2×D1211yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321#67—44no—
322C2×Dic3—22no—
323C2×Dic3—42no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C2×Dic3—124no—
331C2×Dic3C2×D1212yes—
332C2×Dic3C2×D1212yes—
333D12—22no—
334D12—22no—
335C4×D3—124no—
336Dic6—62no—
337Dic6—62no—
338Dic6—62no—
339Dic6—62no—
340Dic6—122no—
341Dic6—122no—
342C3×C8—21no—
343C3×C8—21no—
344C3×C8—22no—
345C3×C8—32no—
346C3×C8—41no—
347C3×C8—61no—
348C3×C8#23512yes—
349C3×C8#23712yes—
350C3⋊C8—21no—
351C3⋊C8#23512yes—
352C2×C32—41no—
353C2×C32#53211yescharacteristic
354C2×C32#57512yes—
355C3×D3—82no—
356C2×Q8—92no—
357C2×D4—32no—
358C2×D4—62no—
359C22×C4—32no—
360C22×C4—182no—
361C22×C4C2×D3211yescharacteristic
362Q16—182no—
363SD16—184no—
364D8—62no—
365M16—22no—
366M16—62no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8C2×D3211yescharacteristic
370C2×C8C2×D3211yescharacteristic
371C4⋊C4—32no—
372C4⋊C4—92no—
373C4⋊C4—182no—
374C4⋊C4—182no—
375C4⋊C4—182no—
376C4⋊C4—182no—
377C22⋊C4—62no—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C42—31no—
383C42—31no—
384C42—32no—
385C42—182no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—42no—
393C22×C3—122no—
394C22×C3—122no—
395C22×C3—122no—
396C22×C3C22×D1211yescharacteristic
397C22×C3C2×D3×D411yescharacteristic
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—42no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—41no—
406C3×C4—62no—
407C3×C4—62no—
408C3×C4—122no—
409C3×C4C2×#23511yescharacteristic
410C3×C4C2×#23511yescharacteristic
411C3×C4C2×#23711yescharacteristic
412C3×C4D3×#4111yescharacteristic
413Dic3—22no—
414Dic3—22no—
415Dic3—42no—
416Dic3—122no—
417Dic3—122no—
418Dic3—122no—
419Dic3—122no—
420Dic3—242no—
421Dic3—242no—
422C32#318311yescharacteristic, complemented, Sylow
423C23—62no—
424C23D3×D1211yescharacteristic
425Q8—182no—
426Q8—182no—
427D4—62no—
428D4—62no—
429D4—124no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—32no—
433C2×C4—32no—
434C2×C4—62no—
435C2×C4—122no—
436C2×C4—182no—
437C2×C4—182no—
438C2×C4—364no—
439C2×C4D3×D1211yescharacteristic
440C2×C4C22×D3211yescharacteristic
441C8—21no—
442C8—32no—
443C8—61no—
444C8#380412yes—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—41no—
448C2×C3—41no—
449C2×C3—81no—
450C2×C3—242no—
451C2×C3#547711yescharacteristic
452C2×C3#559611yescharacteristic
453C2×C3#574812yes—
454C2×C3#577312yes—
455D3—82no—
456C22—21no—
457C22—22no—
458C22—122no—
459C22—122no—
460C22—122no—
461C22C2×D3×D1211yescharacteristic
462C4—21no—
463C4—62no—
464C4—62no—
465C4—122no—
466C4—362no—
467C4—362no—
468C4D3×#23511yescharacteristic
469C4C2×#380411yescharacteristic
470C3—21no—
471C3#7853411yescharacteristic, complemented
472C3#8085211yescharacteristic, complemented
473C2—41no—
474C2—242no—
475C2#1059471212yes—
476C2#1059491011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. #10594949C2semidirect
2. #10592836C2semidirect
4. C3×Dic3×M16C2semidirect
5. #10591176C2semidirect
6. #10590871C2semidirect
7. #10590864C2semidirect
8. #10590863C2semidirect
9. #10590810C2semidirect
10. #10590771C2semidirect
11. #10590747C2semidirect
52. Dic3×M16D3semidirect
422. C32#3183semidirect
471. C3#78534semidirect
472. C3#80852semidirect

Maximal subgroups

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

subgroupindex
#105949492
#105928362
C3×#51352
C3×Dic3×M162
#105911762
#105908712
#105908642
#105908632
#105908102
#105907712
#105907472
#808523
#785343