Finite Group Databasebeta

← #11860769

Subgroups — #11860769

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic
4#10592830C211yesmaximal, characteristic
5C3×#5122C211yesmaximal, characteristic, complemented
6C3×#5120C211yesmaximal, characteristic, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10590795C214yesmaximal, complemented
9#10590792C214yesmaximal, complemented
10#78947—31nomaximal
11#78572—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64135C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19#63974—22no—
20#63955—22no—
21#63894—22no—
22#63894C2214yes—
23#63843—22no—
24Dic3×Dic6C2214yescomplemented
25C2×#3717C418yescomplemented
26C2×#3717C2212yes—
27C2×#3717C2212yes—
28#63648C2214yes—
29C3×#816C2214yescomplemented
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32#63575C2212yescomplemented
33#63573C2212yescomplemented
34#5812—31no—
35C22×#215—31no—
36C22×#204—31no—
37#5521—31no—
38#5521—31no—
39#5516—31no—
40C3×#419—31no—
41C3×#405—31no—
42#5131—31no—
43#5131—31no—
44#5131—61no—
45#5122D311yescharacteristic, complemented
46#5120D311yescharacteristic, complemented
47#5106—31no—
48#4998—31no—
49#4817—34no—
50#4788—34no—
51#4710—34no—
52C4×#204—34no—
53C23×C3⋊D3—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)C2×C414yes—
58C2×C4⋊(C3⋊D3)C2312yes—
59C22×C3×Dic3—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×#624—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
79Dic3⋊Dic3—24no—
80#3722—24no—
81Dic32—24no—
82#3717C2×C418yescomplemented
83#3717C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×Dic6C2×D311yescharacteristic
90C2×C3×M16—21no—
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×M16C2×D311yescharacteristic
93C22×C3×C8—31no—
94C3×#117—31no—
95C3×#117—31no—
96Q8×Dic3—34no—
97Q8×Dic3—62no—
98C2×#215—38no—
99C2×#215—32no—
100C2×#215—32no—
101#926—31no—
102#926—31no—
103#926—61no—
104#926—62no—
105#926C2×D311yescharacteristic
106#926C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×#204—38no—
109C2×#204—32no—
110C2×#204—32no—
111#893—34no—
112#893—62no—
113#887—62no—
114D3×C22⋊C4—62no—
115D3×C22⋊C4—62no—
116#877—62no—
117C4×D12—34no—
118C4×D12—62no—
119C4×Dic6—34no—
120C3×#103—34no—
121C3×#97—32no—
122C3×C4×C8—32no—
123#821—34no—
124#821—34no—
125#821—64no—
126#818—32no—
127#817—32no—
128#816C2×D314yescomplemented
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—22no—
142C4⋊(C3⋊D3)—24no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)C22×C414yes—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3C2×D414yes—
149C3×Dic6—24no—
150C3×Dic6—22no—
151C3×Dic6C22×C414yes—
152#624—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—31no—
163#418—91no—
164#405—31no—
165C23×D3—61no—
166C23×D3—61no—
167C23×D3—121no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—62no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—21no—
177C2×D12—34no—
178C2×D12—34no—
179C2×D12—32no—
180C2×D12—32no—
181C2×D12—62no—
182C2×D12—64no—
183C2×D12—61no—
184C2×D12—62no—
185C2×D12—61no—
186C2×D12—62no—
187C2×D12—121no—
188C2×D12—122no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×Dic6—21no—
192C2×Dic6—22no—
193C2×Dic6C4×D314yescomplemented
194C2×Dic6C22×D312yes—
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—121no—
214#217D1212yes—
215#215—38no—
216#215—38no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—32no—
220C4⋊Dic3—32no—
221C4⋊Dic3—62no—
222C4⋊Dic3—64no—
223C4⋊Dic3D1212yes—
224C4⋊Dic3C22×D312yes—
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—42no—
248C3×Dic3—24no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8—31no—
252C22×D4—91no—
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—34no—
270#102—94no—
271#97—32no—
272C4×C8—32no—
273C23×C3—21no—
274C23×C3C2×D1211yescharacteristic
275C23×C3D3×D411yescharacteristic
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—64no—
279C22×D3—64no—
280C22×D3—122no—
281C22×D3—124no—
282C22×D3—242no—
283C22×D3—242no—
284C22×D3—244no—
285C3×Q8—34no—
286C3×Q8—64no—
287C3×Q8—62no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—34no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4C2×C4×D312yes—
297C2×C3×C4C2×C4×D312yes—
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4#23512yes—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23712yes—
302C2×C3×C4C23×D311yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×Dic3—24no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—122no—
310C2×Dic3C2×D1214yes—
311D12—34no—
312D12—34no—
313D12—64no—
314D12—64no—
315D12—64no—
316D12—62no—
317D12—62no—
318D12—122no—
319D12—124no—
320C4×D3—244no—
321C4×D3—244no—
322Dic6—24no—
323Dic6—22no—
324Dic6C2×C4×D314yes—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8—32no—
328C3×C8—32no—
329C3×C8—42no—
330C3⋊C8C2×C4×D312yes—
331C3⋊C8C2×C4×D312yes—
332C2×C32—22no—
333C2×C32C2×C4×D411yescharacteristic
334C2×C32#57712yes—
335C3⋊D3—44no—
336C24—181no—
337C2×Q8—32no—
338C2×Q8—34no—
339C2×Q8—61no—
340C2×Q8—62no—
341C2×D4—92no—
342C2×D4—94no—
343C2×D4—181no—
344C2×D4—182no—
345C22×C4—61no—
346C22×C4—184no—
347C22×C4C2×D3211yescharacteristic
348SD16—98no—
349SD16—98no—
350M16—22no—
351C2×C8—31no—
352C2×C8—31no—
353C2×C8—34no—
354C2×C8C2×D3212yes—
355C4⋊C4—32no—
356C4⋊C4—32no—
357C4⋊C4—92no—
358C4⋊C4—184no—
359C22⋊C4—32no—
360C22⋊C4—61no—
361C22⋊C4—184no—
362C22⋊C4—181no—
363C42—32no—
364C42—61no—
365C42—184no—
366C42—181no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—42no—
372C22×C3C4×D1212yes—
373C22×C3#67⋊C412yes—
374C22×C3C22×D1211yescharacteristic
375C22×C3C2×D3×D411yescharacteristic
376C2×D3—64no—
377C2×D3—64no—
378C2×D3—124no—
379C2×D3—124no—
380C2×D3—124no—
381C2×D3—244no—
382C2×D3—244no—
383C2×D3—244no—
384C2×D3—248no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—22no—
388C3×C4—64no—
389C3×C4—64no—
390C3×C4—122no—
391C3×C4C4×D1212yes—
392C3×C4#67⋊C412yes—
393C3×C4C22×C4×D311yescharacteristic
394C3×C4C22×C4×D311yescharacteristic
395C3×C4C2×#23511yescharacteristic
396C3×C4C2×#23711yescharacteristic
397Dic3—24no—
398Dic3—24no—
399Dic3—42no—
400Dic3—122no—
401Dic3—122no—
402Dic3—242no—
403C32#294911yescharacteristic, complemented, Sylow
404C23—182no—
405C23—184no—
406C23—722no—
407C23D3×D1211yescharacteristic
408Q8—34no—
409Q8—62no—
410Q8—64no—
411D4—94no—
412D4—182no—
413D4—184no—
414C2×C4—34no—
415C2×C4—62no—
416C2×C4—64no—
417C2×C4—62no—
418C2×C4—182no—
419C2×C4—724no—
420C2×C4C4×D3212yes—
421C2×C4D3×D1211yescharacteristic
422C2×C4#380412yes—
423C2×C4C22×D3211yescharacteristic
424C8—22no—
425C8—32no—
426C8—32no—
427C2×C3—22no—
428C2×C3—22no—
429C2×C3—21no—
430C2×C3—22no—
431C2×C3—42no—
432C2×C3C2×C4×D1211yescharacteristic
433C2×C3C2×#67⋊C411yescharacteristic
434C2×C3#575112yes—
435C2×C3#577812yes—
436D3—124no—
437D3—124no—
438D3—244no—
439C22—22no—
440C22—184no—
441C22—364no—
442C22—724no—
443C22#6388012yes—
444C22C2×D3×D1211yescharacteristic
445C4—64no—
446C4—64no—
447C4—122no—
448C4—362no—
449C4#6388012yes—
450C4C2×C4×D3211yescharacteristic
451C4C2×#380411yescharacteristic
452C3—21no—
453C3#7857211yescharacteristic, complemented
454C3#7894711yescharacteristic, complemented
455C2—22no—
456C2—364no—
457C2#1059471512yes—
458C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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. #10594818C2semidirect
5. C3×#5122C2semidirect
6. C3×#5120C2semidirect
7. #10591122C2semidirect
8. #10590795C2semidirect
9. #10590792C2semidirect
24. Dic3×Dic6C22semidirect
25. C2×#3717C4semidirect
29. C3×#816C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. #63575C22semidirect
33. #63573C22semidirect
45. #5122D3semidirect
46. #5120D3semidirect
62. C2×C3×Dic6C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
82. #3717C2×C4semidirect
83. #3717C2×C4semidirect
128. #816C2×D3semidirect
129. #815C2×D3semidirect
130. C8×Dic3C2×D3semidirect
193. C2×Dic6C4×D3semidirect
233. C2×C3⋊C8C4×D3semidirect
403. C32#2949semidirect
453. C3#78572semidirect
454. C3#78947semidirect

Maximal subgroups

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

subgroupindex
#105949962
#105948182
C22×#37172
#105928302
C3×#51222
C3×#51202
#105911222
#105907952
#105907922
#789473
#785723