Finite Group Databasebeta

← #11866908

Subgroups — #11866908

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63796C211yesmaximal, characteristic, complemented
2C2×#63791C211yesmaximal, characteristic, complemented
3#10594631C211yesmaximal, characteristic, complemented
4#10594612C211yesmaximal, characteristic
5C3⋊D3×#107C211yesmaximal, characteristic, complemented
6C3×#4886C212yesmaximal, complemented
7#10590833C212yesmaximal, complemented
8#10590601C211yesmaximal, characteristic, complemented
9#10590593C211yesmaximal, characteristic, complemented
10#10590515C212yesmaximal, complemented
11#10590503C212yesmaximal, complemented
12D3×#468—32nomaximal
13C2×#3802—21no—
14C2×#3802C2211yescharacteristic
15C2×C4×D32C2211yescharacteristic
16C2×#3797C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C4⋊C4×C3⋊D3C2211yescharacteristic
20C2×C3×#204C2212yescomplemented
21C2×C3×ΓL(1,𝔽25)C2212yescomplemented
22C3×#897C2212yescomplemented
23C3×#895C2212yes—
24#63921—21no—
25#63921—21no—
26#63908C2212yes—
27#63900—21no—
28#63899—22no—
29#63885—22no—
30#63856C2212yescomplemented
31C2×#3715C2212yescomplemented
32C2×#3711C2212yescomplemented
33C2×#3710C2211yescharacteristic
34#63796—24no—
35#63791—24no—
36C32×#107C2211yescharacteristic, complemented
37#63645C2211yescharacteristic, complemented
38#63634C2211yescharacteristic, complemented
39#63634C2211yescharacteristic, complemented
40C3×#810C2212yescomplemented
41C3×#809C2212yescomplemented
42#63566C2212yescomplemented
43#63563C2212yescomplemented
44C2×D3×SD16—32no—
45C2×D3×M16—32no—
46D3×C22⋊Q8—32no—
47D3×#121—32no—
48C3×#468—32no—
49#5174—32no—
50#5134—32no—
51#5049—32no—
52#5042—32no—
53#4886D312yescomplemented
54D3×#107—32no—
55D3×#107—61no—
56#4812—32no—
57D3×#103—32no—
58#4780—32no—
59D3×#102—32no—
60C22×D32—21no—
61C22×D32D411yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3C2312yes—
68C2×C3×Dic6C2312yes—
69C2×#627—21no—
70C2×#625—22no—
71C2×#625—21no—
72C2×#624—21no—
73C2×#624D411yescharacteristic
74C2×D3×Dic3D412yes—
75#3802—22no—
76#3802—22no—
77#3802—44no—
78C4×D32—22no—
79C4×D32—22no—
80#3797—22no—
81#3797—22no—
82C2×C32×C8C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—21no—
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C8×C3⋊D3D414yescomplemented
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3—22no—
94C2×C3×C3⋊C8C2312yes—
95C3×#204—24no—
96C3×ΓL(1,𝔽25)—24no—
97#3724—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3715—24no—
101#3711—24no—
102#3710—22no—
103C2×#468—91noSylow
104C2×D3×Q8—32no—
105C2×D3×D4—32no—
106C2×D3×D4—62no—
107C22×C4×D3—32no—
108C2×C3×SD16—32no—
109C2×C3×M16—32no—
110C3×C22⋊Q8—32no—
111C3×#121—32no—
112#946—32no—
113C2×#215—32no—
114#939—62no—
115#938—32no—
116C2×#214—32no—
117#930—32no—
118#924—32no—
119C2×#208—32no—
120D3×SD16—68no—
121D3×M16—68no—
122C2×#204C2×D312yescomplemented
123C2×ΓL(1,𝔽25)—32no—
124C2×ΓL(1,𝔽25)C2×D312yescomplemented
125C2×D3×C8—32no—
126C2×D3×C8—32no—
127C2×D3×C8—61no—
128#897C2×D312yescomplemented
129#896—62no—
130#895C2×D312yes—
131D3×C4⋊C4—32no—
132D3×C4⋊C4—32no—
133D3×C4⋊C4—61no—
134D3×C4⋊C4—61no—
135D3×C4⋊C4—62no—
136#884—62no—
137D3×C22⋊C4—62no—
138D3×C22⋊C4—62no—
139#878—62no—
140C3×#107—21no—
141C3×#107C2×D312yescomplemented
142C3×#103—32no—
143C3×#102—32no—
144#835—32no—
145#832—32no—
146#821—32no—
147#818—32no—
148#818—61no—
149#816—32no—
150#810C2×D312yescomplemented
151#809C2×D312yescomplemented
152#807—32no—
153#807—32no—
154#807—61no—
155#807—61no—
156C22×C3⋊D3C2×D411yescharacteristic
157C22×C3×D3—22no—
158C22×C3×D3C2×D412yes—
159C2×D32—22no—
160C2×D32—22no—
161C2×D32—22no—
162C2×D32—42no—
163C2×D32—42no—
164C2×D32—42no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3C2×D411yescharacteristic
171C4×C3⋊D3—42no—
172C4×C3⋊D3—42no—
173C4×C3⋊D3C2×D412yes—
174C4×C3⋊D3#4112yes—
175C2×C3×Dic3—22no—
176C2×C3×Dic3C2×D412yes—
177C3×D12—22no—
178C3×D12—22no—
179C3×D12—44no—
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184#627—42no—
185#625—44no—
186#625—42no—
187#624—22no—
188#624—42no—
189D3×Dic3—24no—
190C32×C8C2×D412yescomplemented
191C3⋊(C3⋊C8)C2×D412yescomplemented
192C3×C3⋊C8—22no—
193C22×SD16—91no—
194C22×M16—91no—
195C2×C22⋊Q8—91no—
196C2×#121—91no—
197#468—32no—
198#468—92no—
199#468—92no—
200#468—92no—
201C2×#107—91no—
202C2×#103—91no—
203C2×#102—91no—
204C23×D3—32no—
205C23×D3—62no—
206C2×C3×Q8—32no—
207C2×C3×D4—32no—
208C2×C3×D4—62no—
209C22×C3×C4—32no—
210C2×#67—62no—
211C2×#67—62no—
212C2×#67—62no—
213C22×Dic3—32no—
214D3×Q8—64no—
215D3×Q8—64no—
216D3×D4—64no—
217D3×D4—64no—
218D3×D4—128no—
219C2×D12—22no—
220C2×D12C22×D312yes—
221C2×C4×D3—32no—
222C2×C4×D3—32no—
223C2×C4×D3—32no—
224C2×C4×D3—61no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—121no—
231C2×C4×D3—121no—
232C2×C4×D3C22×D312yes—
233C2×Dic6—62no—
234C2×Dic6C22×D312yes—
235C3×SD16—64no—
236C3×M16—64no—
237C2×C3×C8—21no—
238C2×C3×C8—32no—
239C2×C3×C8C22×D312yes—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4C22×D312yes—
244C3×C4⋊C4C22×D312yes—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—62no—
247#217—62no—
248#217—62no—
249#215—64no—
250#214—64no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—22no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—121no—
265Dic3⋊C4—121no—
266#208—64no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8C22×D312yes—
270#204—24no—
271ΓL(1,𝔽25)—24no—
272ΓL(1,𝔽25)—64no—
273D3×C8—38no—
274D3×C8—64no—
275D3×C8—64no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3#12112yes—
278C2×C3⋊D3AGL(1,ℤ/8)12yes—
279C2×C3⋊D3#13712yes—
280C2×C3×D3—22no—
281C2×C3×D3—22no—
282C2×C3×D3—22no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286D32—44no—
287D32—84no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C22×D411yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3⋊Dic3#12112yes—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C22×Q8—91no—
298C22×D4—91no—
299C22×D4—181no—
300C23×C4—91no—
301C2×SD16—32no—
302C2×SD16—92no—
303C2×SD16—184no—
304C2×M16—32no—
305C2×M16—92no—
306C2×M16—184no—
307C22×C8—91no—
308C22×C8—91no—
309C22⋊Q8—32no—
310C22⋊Q8—92no—
311C22⋊Q8—182no—
312#121—32no—
313#121—92no—
314#121—182no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4—181no—
318C2×C22⋊C4—181no—
319C2×C22⋊C4—181no—
320#107—91no—
321#107—91no—
322#107—91no—
323#107D3211yescharacteristic, complemented
324#103—32no—
325#103—92no—
326#102—32no—
327#102—92no—
328C23×C3—32no—
329C23×C3—62no—
330C22×D3—22no—
331C22×D3—32no—
332C22×D3—61no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—124no—
337C22×D3—124no—
338C22×D3—124no—
339C22×D3D3×D412yes—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—124no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4C23×D312yes—
355#67—124no—
356#67—124no—
357#67—124no—
358C2×Dic3—22no—
359C2×Dic3—32no—
360C2×Dic3—61no—
361C2×Dic3—64no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3D3×D412yes—
367D12—22no—
368D12—22no—
369D12—44no—
370C4×D3—22no—
371C4×D3—22no—
372C4×D3—34no—
373C4×D3—34no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—64no—
377C4×D3—64no—
378C4×D3—124no—
379C4×D3—124no—
380C4×D3—124no—
381C4×D3—242no—
382C4×D3—242no—
383Dic6—22no—
384Dic6—22no—
385Dic6—124no—
386C3×C8—22no—
387C3×C8—62no—
388C3×C8D3×D414yescomplemented
389C3⋊C8—22no—
390C3⋊C8—34no—
391C3⋊C8—62no—
392C2×C32C2×#12111yescharacteristic
393C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
394C2×C32C2×#13711yescharacteristic
395C3⋊D3#46814yescomplemented
396C3×D3—42no—
397C3×D3—82no—
398C24—91no—
399C24—181no—
400C2×Q8—32no—
401C2×Q8—181no—
402C2×Q8—182no—
403C2×Q8—182no—
404C2×D4—32no—
405C2×D4—62no—
406C2×D4—182no—
407C2×D4—182no—
408C2×D4—181no—
409C2×D4—182no—
410C2×D4—364no—
411C22×C4—32no—
412C22×C4—91no—
413C22×C4—92no—
414C22×C4—91no—
415C22×C4—181no—
416C22×C4—181no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—181no—
420SD16—64no—
421SD16—184no—
422M16—64no—
423M16—184no—
424C2×C8—32no—
425C2×C8—91no—
426C2×C8—94no—
427C2×C8—182no—
428C2×C8C2×D3211yescharacteristic
429C4⋊C4—62no—
430C4⋊C4—91no—
431C4⋊C4—91no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4—182no—
435C4⋊C4C2×D3211yescharacteristic
436C4⋊C4C2×D3211yescharacteristic
437C22⋊C4—62no—
438C22⋊C4—62no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C22×C3—21no—
442C22×C3—62no—
443C22×C3—62no—
444C22×C3—62no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3C2×D3×D412yes—
449C2×D3—22no—
450C2×D3—22no—
451C2×D3—22no—
452C2×D3—34no—
453C2×D3—34no—
454C2×D3—34no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—62no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—128no—
462C2×D3—248no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—62no—
468C3×C4—81no—
469C3×C4—81no—
470C3×C4—122no—
471C3×C4C2×D3×D412yes—
472C3×C4D3×#4112yes—
473Dic3—22no—
474Dic3—34no—
475Dic3—42no—
476Dic3—62no—
477Dic3—122no—
478Dic3—122no—
479Dic3—241no—
480Dic3—241no—
481C32C2×#46811yescharacteristic, complemented, Sylow
482C23—32no—
483C23—62no—
484C23—91no—
485C23—182no—
486C23—182no—
487C23—182no—
488C23—362no—
489C23—362no—
490C23—362no—
491Q8—62no—
492Q8—62no—
493Q8—362no—
494D4—62no—
495D4—62no—
496D4—124no—
497D4—362no—
498D4—364no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—32no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—91no—
506C2×C4—92no—
507C2×C4—92no—
508C2×C4—182no—
509C2×C4—184no—
510C2×C4—181no—
511C2×C4—181no—
512C2×C4—362no—
513C2×C4—362no—
514C2×C4—362no—
515C2×C4C22×D3211yescharacteristic
516C8—62no—
517C8—92no—
518C8#380212yescomplemented
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—122no—
523C2×C3—242no—
524C2×C3D3×#12112yes—
525C2×C3D3×AGL(1,ℤ/8)12yes—
526C2×C3D3×#13712yes—
527D3—38no—
528D3—42no—
529D3—64no—
530D3—82no—
531C22—62no—
532C22—62no—
533C22—62no—
534C22—92no—
535C22—92no—
536C22—92no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22—364no—
541C22—724no—
542C22D32×D411yescharacteristic
543C4—41no—
544C4—41no—
545C4—62no—
546C4—92no—
547C4—122no—
548C4—361no—
549C4—361no—
550C4C2×#380211yescharacteristic
551C4#6431911yescharacteristic
552C3—21no—
553C3D3×#46812yescomplemented
554C2—94no—
555C2—122no—
556C2—242no—
557C2#1059461211yescharacteristic
558C2#1059472611yescharacteristic
559C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594612C2
hypercenter#107D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#63796C2semidirect
2. C2×#63791C2semidirect
3. #10594631C2semidirect
5. C3⋊D3×#107C2semidirect
6. C3×#4886C2semidirect
7. #10590833C2semidirect
8. #10590601C2semidirect
9. #10590593C2semidirect
10. #10590515C2semidirect
11. #10590503C2semidirect
20. C2×C3×#204C22semidirect
21. C2×C3×ΓL(1,𝔽25)C22semidirect
22. C3×#897C22semidirect
30. #63856C22semidirect
31. C2×#3715C22semidirect
32. C2×#3711C22semidirect
36. C32×#107C22semidirect
37. #63645C22semidirect
38. #63634C22semidirect
39. #63634C22semidirect
40. C3×#810C22semidirect
41. C3×#809C22semidirect
42. #63566C22semidirect
43. #63563C22semidirect
53. #4886D3semidirect
90. C8×C3⋊D3D4semidirect
122. C2×#204C2×D3semidirect
124. C2×ΓL(1,𝔽25)C2×D3semidirect
128. #897C2×D3semidirect
141. C3×#107C2×D3semidirect
150. #810C2×D3semidirect
151. #809C2×D3semidirect
190. C32×C8C2×D4semidirect
191. C3⋊(C3⋊C8)C2×D4semidirect
323. #107D32semidirect
388. C3×C8D3×D4semidirect
395. C3⋊D3#468semidirect
481. C32C2×#468semidirect
518. C8#3802semidirect
553. C3D3×#468semidirect

Maximal subgroups

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

subgroupindex
C2×#637962
C2×#637912
#105946312
#105946122
C3⋊D3×#1072
C3×#48862
#105908332
#105906012
#105905932
#105905152
#105905032
D3×#4683