Finite Group Databasebeta

← #11860767

Subgroups — #11860767

Order 1152.

1059 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594982C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic
4#10592819C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic
6C3×#5122C211yesmaximal, characteristic, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10590747C214yesmaximal, complemented
9#10590744C214yesmaximal, complemented
10#78916—31nomaximal
11#78572—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64135C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19D3×#217—22no—
20#63957—22no—
21#63898—22no—
22Dic3×D12C2214yes—
23#63844—22no—
24#63844C2214yescomplemented
25C2×#3716C418yescomplemented
26C2×#3716C2212yes—
27C2×#3716C2212yes—
28#63643C2214yescomplemented
29C3×#821C2214yes—
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32#63575C2212yescomplemented
33#63573C2212yescomplemented
34#5798—31no—
35C22×#214—31no—
36C22×#204—31no—
37#5521—31no—
38#5516—31no—
39#5516—31no—
40C3×#418—31no—
41C3×#405—31no—
42#5131D311yescharacteristic
43#5122D311yescharacteristic, complemented
44#5120—31no—
45#5120—31no—
46#5120—61no—
47#5106—31no—
48#4998—31no—
49#4758—34no—
50#4757—34no—
51#4710—34no—
52C4×#204—34no—
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634C2×C414yescomplemented
59C2×#634C2312yes—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×D3×Dic3—24no—
65C32×M16—22no—
66C2×C32×C8C2312yes—
67#3757—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C4×C3⋊Dic3—21no—
70C3×#217—21no—
71C3×#217D412yes—
72C3×C4⋊Dic3D412yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3—21no—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8C2×C414yescomplemented
77C2×C3×C3⋊C8C2311yescharacteristic
78C2×C3×C3⋊C8C2311yescharacteristic
79#3724—24no—
80(C2×D3)⋊Dic3—24no—
81Dic32—24no—
82#3716C2×C418yescomplemented
83#3716C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C2×C3×M16—21no—
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×M16C2×D311yescharacteristic
93C22×C3×C8—31no—
94C3×#117—31no—
95C3×#117—31no—
96C2×#217—62no—
97D4×Dic3—34no—
98D4×Dic3—62no—
99C2×#214—38no—
100C2×#214—32no—
101C2×#214—32no—
102#926—31no—
103#926—31no—
104#926—61no—
105#926C2×D311yescharacteristic
106#926C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×#204—38no—
109C2×#204—32no—
110C2×#204—32no—
111#893—62no—
112#887—34no—
113#887—62no—
114D3×C22⋊C4—62no—
115#877—62no—
116#877—62no—
117C4×D12—34no—
118C4×Dic6—34no—
119C4×Dic6—62no—
120C3×#102—34no—
121C3×#97—32no—
122C3×C4×C8—32no—
123#821C2×D314yes—
124#818—32no—
125#817—32no—
126#816—34no—
127#816—34no—
128#816—64no—
129#815C2×D312yescomplemented
130C8×Dic3C2×D312yescomplemented
131#808—32no—
132#807—32no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—24no—
136C22×C3×D3—82no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—24no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144#634—24no—
145#634—22no—
146#634C22×C414yes—
147C2×C3×Dic3—22no—
148C2×C3×Dic3C2×D414yes—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12C22×C414yes—
152D3×Dic3—84no—
153C32×C8—22no—
154C3×C3⋊C8C22×C412yes—
155C3×C3⋊C8C22×C412yes—
156C22×SD16—91no—
157#519—91no—
158#518—91no—
159#440—94no—
160C4×SD16—94no—
161#427—91no—
162#419—91no—
163#418—31no—
164#405—31no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×D4—34no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—62no—
171C22×C3×C4—21no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—64no—
177C22×Dic3—121no—
178C2×D12—21no—
179C2×D12—22no—
180C2×D12C4×D314yes—
181C2×D12C22×D312yes—
182C2×C4×D3—64no—
183C2×Dic6—34no—
184C2×Dic6—34no—
185C2×Dic6—32no—
186C2×Dic6—32no—
187C2×Dic6—62no—
188C2×Dic6—64no—
189C2×Dic6—61no—
190C2×Dic6—62no—
191C2×Dic6—61no—
192C2×Dic6—62no—
193C2×Dic6—121no—
194C2×Dic6—122no—
195C3×M16—22no—
196C3×M16—22no—
197C3×M16—42no—
198C2×C3×C8—22no—
199C2×C3×C8—34no—
200C2×C3×C8—31no—
201C2×C3×C8—31no—
202C2×C3×C8C22×D312yes—
203C2×C3×C8C22×D312yes—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—32no—
206C3×C22⋊C4—32no—
207C3×C22⋊C4—61no—
208C3×C42—32no—
209C3×C42—61no—
210#217—21no—
211#217—61no—
212#217—61no—
213#217—64no—
214#217—121no—
215#217D1212yes—
216#214—38no—
217#214—38no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—32no—
220C4⋊Dic3—32no—
221C4⋊Dic3—62no—
222C4⋊Dic3D1212yes—
223C4⋊Dic3C22×D312yes—
224Dic3⋊C4—64no—
225Dic3⋊C4—64no—
226C4×Dic3—21no—
227C4×Dic3—64no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C4×Dic3—64no—
231C4×Dic3—121no—
232C4×Dic3C22×D312yes—
233C2×C3⋊C8C4×D314yescomplemented
234C2×C3⋊C8C22×D311yescharacteristic
235C2×C3⋊C8C22×D311yescharacteristic
236#204—38no—
237#204—38no—
238C22×C32—22no—
239C22×C32C4×D412yes—
240C22×C32C22×D411yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—24no—
248C3⋊Dic3—42no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8—91no—
252C22×D4—31no—
253C2×SD16—98no—
254C2×SD16—92no—
255C2×SD16—92no—
256C2×M16D3211yescharacteristic
257C22×C8—31no—
258C4×Q8—94no—
259C4×Q8—182no—
260C4×D4—94no—
261C4×D4—182no—
262#117—31no—
263#117—31no—
264#117—91no—
265#117—182no—
266C2×C22⋊C4—182no—
267#107—92no—
268#106—92no—
269#103—94no—
270#102—34no—
271#97—32no—
272C4×C8—32no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—64no—
276C23×C3—242no—
277C23×C3C2×D1211yescharacteristic
278C23×C3D3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—24no—
281C22×D3—82no—
282C3×D4—34no—
283C3×D4—64no—
284C3×D4—62no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—34no—
290C2×C3×C4—62no—
291C2×C3×C4C2×C4×D312yes—
292C2×C3×C4C2×C4×D312yes—
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4#23512yes—
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23712yes—
297C2×C3×C4C23×D311yescharacteristic
298C2×C3×C4C23×D311yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—122no—
307C2×Dic3—124no—
308C2×Dic3—122no—
309C2×Dic3—244no—
310C2×Dic3C2×D1214yes—
311D12—24no—
312D12—22no—
313D12C2×C4×D314yes—
314C4×D3—244no—
315Dic6—34no—
316Dic6—34no—
317Dic6—64no—
318Dic6—64no—
319Dic6—64no—
320Dic6—62no—
321Dic6—62no—
322Dic6—122no—
323Dic6—124no—
324C3×C8—22no—
325C3×C8—22no—
326C3×C8—32no—
327C3×C8—32no—
328C3×C8—42no—
329C3⋊C8C2×C4×D312yes—
330C3⋊C8C2×C4×D312yes—
331C2×C32—22no—
332C2×C32C2×C4×D411yescharacteristic
333C2×C32#57712yes—
334C3×D3—44no—
335C24—61no—
336C2×Q8—92no—
337C2×Q8—94no—
338C2×Q8—181no—
339C2×Q8—182no—
340C2×D4—32no—
341C2×D4—34no—
342C2×D4—61no—
343C2×D4—62no—
344C22×C4—184no—
345C22×C4—181no—
346C22×C4C2×D3211yescharacteristic
347SD16—98no—
348SD16—98no—
349M16—22no—
350C2×C8—31no—
351C2×C8—31no—
352C2×C8—34no—
353C2×C8C2×D3212yes—
354C4⋊C4—32no—
355C4⋊C4—32no—
356C4⋊C4—92no—
357C4⋊C4—184no—
358C22⋊C4—32no—
359C22⋊C4—61no—
360C22⋊C4—184no—
361C22⋊C4—181no—
362C42—32no—
363C42—61no—
364C42—184no—
365C42—181no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—42no—
371C22×C3—64no—
372C22×C3—124no—
373C22×C3—244no—
374C22×C3C4×D1212yes—
375C22×C3#67⋊C412yes—
376C22×C3C22×D1211yescharacteristic
377C22×C3C2×D3×D411yescharacteristic
378C2×D3—24no—
379C2×D3—44no—
380C2×D3—84no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—22no—
384C3×C4—64no—
385C3×C4—122no—
386C3×C4C4×D1212yes—
387C3×C4#67⋊C412yes—
388C3×C4C22×C4×D311yescharacteristic
389C3×C4C22×C4×D311yescharacteristic
390C3×C4C2×#23511yescharacteristic
391C3×C4C2×#23711yescharacteristic
392Dic3—24no—
393Dic3—42no—
394Dic3—64no—
395Dic3—64no—
396Dic3—124no—
397Dic3—122no—
398Dic3—122no—
399Dic3—242no—
400C32#294911yescharacteristic, complemented, Sylow
401C23—62no—
402C23—64no—
403C23—242no—
404C23D3×D1211yescharacteristic
405Q8—94no—
406Q8—182no—
407Q8—184no—
408D4—34no—
409D4—62no—
410D4—64no—
411C2×C4—34no—
412C2×C4—62no—
413C2×C4—182no—
414C2×C4—184no—
415C2×C4—182no—
416C2×C4—724no—
417C2×C4C4×D3212yes—
418C2×C4D3×D1211yescharacteristic
419C2×C4#380412yes—
420C2×C4C22×D3211yescharacteristic
421C8—22no—
422C8—32no—
423C8—32no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—22no—
428C2×C3—42no—
429C2×C3—124no—
430C2×C3C2×C4×D1211yescharacteristic
431C2×C3C2×#67⋊C411yescharacteristic
432C2×C3#575112yes—
433C2×C3#577512yes—
434D3—44no—
435C22—22no—
436C22—64no—
437C22—124no—
438C22—244no—
439C22#6388012yes—
440C22C2×D3×D1211yescharacteristic
441C4—64no—
442C4—122no—
443C4—184no—
444C4—362no—
445C4#6388012yes—
446C4C2×C4×D3211yescharacteristic
447C4C2×#380411yescharacteristic
448C3—21no—
449C3#7857211yescharacteristic, complemented
450C3#7891611yescharacteristic, complemented
451C2—22no—
452C2—124no—
453C2#1059471312yes—
454C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2949
LCSG ▷ 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
2. #10594828C2semidirect
4. #10592819C2semidirect
6. C3×#5122C2semidirect
7. #10591122C2semidirect
8. #10590747C2semidirect
9. #10590744C2semidirect
24. #63844C22semidirect
25. C2×#3716C4semidirect
28. #63643C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. #63575C22semidirect
33. #63573C22semidirect
43. #5122D3semidirect
58. C2×#634C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
82. #3716C2×C4semidirect
83. #3716C2×C4semidirect
129. #815C2×D3semidirect
130. C8×Dic3C2×D3semidirect
233. C2×C3⋊C8C4×D3semidirect
400. C32#2949semidirect
449. C3#78572semidirect
450. C3#78916semidirect

Maximal subgroups

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

subgroupindex
#105949822
#105948282
C22×#37162
#105928192
C3×#51312
C3×#51222
#105911222
#105907472
#105907442
#789163
#785723