Finite Group Databasebeta

← #11867759

Subgroups — #11867759

Order 1152.

1416 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#131C211yesmaximal, characteristic, complemented
2#10596304C211yesmaximal, characteristic
3#10596296C211yesmaximal, characteristic, complemented
4C2×#64118C211yesmaximal, characteristic, complemented
5#10592836C212yesmaximal, complemented
6#10592833C212yesmaximal, complemented
7#10592820C211yesmaximal, characteristic, complemented
8#10592815C212yesmaximal, complemented
9#10592813C212yesmaximal, complemented
10#10592812C211yesmaximal, characteristic, complemented
11C2×#63643C211yesmaximal, characteristic, complemented
12#83808—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C32×#131—24no—
17C2×C32×M16C2212yes—
18C2×C32×M16C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20C22×C32×C8C2212yes—
21#64155—21no—
22#64153—21no—
23#64148—22no—
24#64147—21no—
25#64145—21no—
26#64144—22no—
27#64139C2212yes—
28#64135C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30#64133C2212yes—
31#64133C2212yes—
32#64133C2212yes—
33#64118—24no—
34C2×#3746C2212yes—
35C2×#3744C2212yes—
36#63648C2211yescharacteristic
37#63648C2211yescharacteristic
38#63645C2212yes—
39#63644C2212yes—
40#63643C2212yes—
41#63643C2212yes—
42#63643C2211yescharacteristic
43#63643C2211yescharacteristic
44C2×C3×#131D314yescomplemented
45#5833—34no—
46#5825—34no—
47C2×#909—34no—
48#5137—38no—
49#5134—38no—
50#5121—34no—
51#5116—38no—
52#5114—38no—
53#5113—34no—
54C2×#816—34no—
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8D411yescharacteristic
58C2×C32×D4D412yes—
59C2×C32×D4D411yescharacteristic
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63C2×#638—22no—
64C22×C3⋊Dic3—21no—
65C22×C3⋊Dic3—21no—
66#3828—22no—
67#3828—22no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634—22no—
71C2×#634—22no—
72C2×#634—21no—
73C2×#634C2312yes—
74C2×#634C2311yescharacteristic
75C32×M16—24no—
76C32×M16D414yescomplemented
77C2×C32×C8—22no—
78C2×C32×C8—24no—
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2312yes—
82#3757—22no—
83#3757—22no—
84#3757—22no—
85#3757—21no—
86#3752—22no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2312yes—
91#3750—22no—
92#3750—22no—
93#3750—22no—
94C4×C3⋊Dic3—21no—
95#3746—24no—
96#3744—24no—
97#3063—91noSylow
98C2×C3×#41C2×D314yes—
99C2×#235—34no—
100C22×Dic6—34no—
101C3×#131—216no—
102C2×C3×M16C2×D318yes—
103C2×C3×M16C2×D314yes—
104C22×C3×C8C2×D314yes—
105C22×C3×C8C2×D318yes—
106#946—64no—
107#944—64no—
108#939—68no—
109#938—64no—
110#936—64no—
111#935—68no—
112#930—38no—
113#926—34no—
114C2×C4⋊Dic3—34no—
115#924—38no—
116#924—38no—
117#924—38no—
118#909—616no—
119C2×Dic12—38no—
120C2×#204—38no—
121#821—34no—
122#821—34no—
123#818—38no—
124#817—38no—
125#816—38no—
126#816—34no—
127#816—38no—
128#816—34no—
129C23×C32C2×D412yes—
130C23×C32C2×D411yescharacteristic
131C22×C3⋊D3—21no—
132C32×Q8—22no—
133C32×D4—24no—
134C32×D4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4C2×D412yes—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142#638—42no—
143#638—82no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C2×C3⋊Dic3—81no—
151C4⋊(C3⋊D3)—21no—
152C4⋊(C3⋊D3)—21no—
153C4×C3⋊D3—42no—
154#634—22no—
155#634—21no—
156#634—22no—
157#634—21no—
158#634—42no—
159C32×C8—21no—
160C32×C8—21no—
161C32×C8C2×D414yes—
162C2×#137—91no—
163C2×#131C3⋊D311yescharacteristic, complemented
164#537—91no—
165#536—91no—
166#470—92no—
167#468—92no—
168#467—92no—
169#465—92no—
170#428—91no—
171#416—91no—
172C2×#103—91no—
173C3×#41—28no—
174C3×#41—28no—
175C2×C3×Q8D1214yes—
176C2×C3×D4D1218yes—
177C2×C3×D4D1214yes—
178C22×C3×C4C22×D318yes—
179C22×C3×C4C22×D314yes—
180C2×#67—64no—
181C2×#67—68no—
182C22×Dic3—64no—
183C22×Dic3—64no—
184#235—68no—
185#235—68no—
186C2×D12—34no—
187C2×C4×D3—64no—
188C2×Dic6—38no—
189C2×Dic6—34no—
190C2×Dic6—68no—
191C2×Dic6—68no—
192C2×Dic6—64no—
193C3×M16—216no—
194C3×M16#67116yescomplemented
195C2×C3×C8—28no—
196C2×C3×C8—216no—
197C2×C3×C8C22×D314yes—
198C2×C3×C8C22×D314yes—
199C2×C3×C8C22×D318yes—
200#217—68no—
201#217—68no—
202#217—68no—
203#217—64no—
204(C2×D3)⋊C4—68no—
205C4⋊Dic3—38no—
206C4⋊Dic3—34no—
207C4⋊Dic3—34no—
208C4⋊Dic3—64no—
209Dic3⋊C4—68no—
210Dic3⋊C4—68no—
211Dic3⋊C4—68no—
212C4×Dic3—64no—
213Dic12—616no—
214#204—616no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32—22no—
218C22×C32—22no—
219C22×C32—22no—
220C22×C32#12112yes—
221C22×C32C22×D411yescharacteristic
222C2×C3⋊D3—41no—
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C32×C4—22no—
226C32×C4#12112yes—
227C32×C4C22×D411yescharacteristic
228C32×C4C2×#4111yescharacteristic
229C3⋊Dic3—42no—
230C3⋊Dic3—41no—
231C3⋊Dic3—41no—
232C3⋊Dic3—42no—
233C3⋊Dic3—41no—
234C2×#41—91no—
235C2×#41C2×C3⋊D311yescharacteristic
236C22×Q8—91no—
237#137—184no—
238C2×Q16—92no—
239C2×SD16—92no—
240#131—24no—
241C2×M16C2×C3⋊D312yes—
242C2×M16C2×C3⋊D311yescharacteristic
243C22×C8C2×C3⋊D311yescharacteristic
244C22×C8C2×C3⋊D312yes—
245C4⋊Q8—181no—
246#124—181no—
247#123—182no—
248C22⋊Q8—92no—
249C22⋊Q8—92no—
250C22⋊Q8—92no—
251C22⋊Q8—181no—
252#121—92no—
253#121—181no—
254#121—182no—
255#117—91no—
256C2×C4⋊C4—91no—
257#107—92no—
258#106—92no—
259#103—92no—
260#103—92no—
261#103—91no—
262#103—91no—
263#102—91no—
264#102—91no—
265C23×C3C2×D1218yes—
266C23×C3C2×D1214yes—
267C22×D3—64no—
268C3×Q8—28no—
269C3×D4—216no—
270C3×D4—28no—
271C2×C3×C4—28no—
272C2×C3×C4—28no—
273C2×C3×C4C2×D1218yes—
274C2×C3×C4C2×D1214yes—
275C2×C3×C4#23518yes—
276C2×C3×C4C2×#6718yes—
277C2×C3×C4C23×D314yes—
278#67—128no—
279#67—248no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—68no—
283C2×Dic3—64no—
284C2×Dic3—68no—
285C2×Dic3—128no—
286C2×Dic3—244no—
287D12—64no—
288D12—64no—
289C4×D3—128no—
290Dic6—68no—
291Dic6—64no—
292Dic6—68no—
293Dic6—64no—
294Dic6—128no—
295C3×C8—24no—
296C3×C8—24no—
297C3×C8C2×#67116yes—
298C2×C32—22no—
299C2×C32—42no—
300C2×C32C2×#12111yescharacteristic
301C2×C32#57711yescharacteristic
302C2×C32#57811yescharacteristic
303C3⋊D3—81no—
304#41—22no—
305#41—22no—
306#41—182no—
307#41—182no—
308C2×Q8—92no—
309C2×Q8—91no—
310C2×Q8—181no—
311C2×Q8—182no—
312C2×Q8—182no—
313C2×Q8C4⋊(C3⋊D3)11yescharacteristic
314C2×D4—91no—
315C2×D4—181no—
316C2×D4—182no—
317C2×D4C4⋊(C3⋊D3)12yes—
318C2×D4C4⋊(C3⋊D3)11yescharacteristic
319C22×C4—181no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4C22×C3⋊D312yes—
323C22×C4C22×C3⋊D311yescharacteristic
324Q16—184no—
325SD16—184no—
326M16—24no—
327M16#63814yescomplemented
328C2×C8—22no—
329C2×C8—24no—
330C2×C8C22×C3⋊D311yescharacteristic
331C2×C8C22×C3⋊D311yescharacteristic
332C2×C8C22×C3⋊D312yes—
333C4⋊C4—91no—
334C4⋊C4—91no—
335C4⋊C4—92no—
336C4⋊C4—181no—
337C4⋊C4—182no—
338C4⋊C4—182no—
339C4⋊C4—182no—
340C22⋊C4—181no—
341C22⋊C4—182no—
342C22⋊C4—182no—
343C22⋊C4—182no—
344C22⋊C4—182no—
345C42—181no—
346C22×C3—24no—
347C22×C3—24no—
348C22×C3—28no—
349C22×C3—28no—
350C22×C3—28no—
351C22×C3#93018yes—
352C22×C3C22×D1214yes—
353C2×D3—124no—
354C2×D3—124no—
355C2×D3—124no—
356C3×C4—28no—
357C3×C4#93018yes—
358C3×C4C2×#23514yes—
359C3×C4C22×#6714yes—
360Dic3—128no—
361Dic3—124no—
362Dic3—124no—
363Dic3—128no—
364Dic3—124no—
365C32#306311yescharacteristic, complemented, Sylow
366C23—181no—
367C23C2×C4⋊(C3⋊D3)12yes—
368C23C2×C4⋊(C3⋊D3)11yescharacteristic
369Q8—22no—
370Q8—182no—
371Q8—181no—
372Q8—182no—
373Q8—181no—
374Q8—362no—
375D4—24no—
376D4—22no—
377D4—181no—
378D4—181no—
379D4—362no—
380D4—722no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4—182no—
386C2×C4—181no—
387C2×C4—182no—
388C2×C4—362no—
389C2×C4—362no—
390C2×C4—721no—
391C2×C4C2×C4⋊(C3⋊D3)12yes—
392C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
393C2×C4#382812yes—
394C2×C4C2×#63812yes—
395C2×C4C23×C3⋊D311yescharacteristic
396C8—21no—
397C8—21no—
398C8C2×#63814yes—
399C2×C3—28no—
400C2×C3—48no—
401C2×C3#575114yes—
402C2×C3#575314yes—
403C2×C3C2×#93014yes—
404D3—244no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—361no—
411C22—361no—
412C22—361no—
413C22#6413912yes—
414C22C22×C4⋊(C3⋊D3)11yescharacteristic
415C4—22no—
416C4—362no—
417C4—361no—
418C4—361no—
419C4—361no—
420C4—362no—
421C4#6413912yes—
422C4C2×#382811yescharacteristic
423C4C22×#63811yescharacteristic
424C3#8380814yescomplemented
425C2—22no—
426C2—42no—
427C2—721no—
428C2#1059622211yescharacteristic
429C2#1059622411yescharacteristic
430C2C2×#6413911yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#131C2
socleC22×C32C22×D4
prime radical#10596304C2
hypercenterC2×#131C3⋊D3
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×C32×#131C2semidirect
3. #10596296C2semidirect
4. C2×#64118C2semidirect
5. #10592836C2semidirect
6. #10592833C2semidirect
7. #10592820C2semidirect
8. #10592815C2semidirect
9. #10592813C2semidirect
10. #10592812C2semidirect
11. C2×#63643C2semidirect
44. C2×C3×#131D3semidirect
76. C32×M16D4semidirect
163. C2×#131C3⋊D3semidirect
194. C3×M16#67semidirect
327. M16#638semidirect
365. C32#3063semidirect
424. C3#83808semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1312
#105963042
#105962962
C2×#641182
#105928362
#105928332
#105928202
#105928152
#105928132
#105928122
C2×#636432
#838083