Finite Group Databasebeta

← #11867134

Subgroups — #11867134

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596299C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×#64104C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6#10592830C211yesmaximal, characteristic, complemented
7#10592663C211yesmaximal, characteristic, complemented
8#10592511C212yesmaximal, complemented
9#10592506C212yesmaximal, complemented
10#10592481C212yesmaximal, complemented
11#10592474C212yesmaximal, complemented
12#78888—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C22×C4⋊(C3⋊D3)—21no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19#64158—24no—
20#64155C2211yescharacteristic, complemented
21#64155C2211yescharacteristic, complemented
22C2×#3755C2212yescomplemented
23#64147C2211yescharacteristic, complemented
24#64147C2211yescharacteristic, complemented
25#64146—21no—
26#64144—21no—
27C2×#3753C2212yescomplemented
28C4×#638—21no—
29C4×#638—21no—
30C2×#3752—21no—
31#64135C2211yescharacteristic
32C2×#3748C2211yescharacteristic
33M16×C3⋊D3—24no—
34C2×#3743C2212yescomplemented
35C2×C8×C3⋊D3C2212yescomplemented
36#64104—21no—
37#64104—21no—
38#64104C2212yes—
39#64104C2212yes—
40C32×#103C2212yescomplemented
41C32×#102C2212yescomplemented
42#63648C2212yescomplemented
43#63648C2212yescomplemented
44#63635C2212yescomplemented
45#63634C2212yescomplemented
46#5828—34no—
47C2×#949—34no—
48C2×D3×M16—34no—
49C2×#895—34no—
50C3×#417D314yescomplemented
51#5131—34no—
52#4964—34no—
53#4812—38no—
54#4807—38no—
55#4782—38no—
56#4775—38no—
57C23×C3⋊D3—21no—
58C23×C3⋊D3D411yescharacteristic
59C32×#41—22no—
60C32×#41—22no—
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68C2×#638—21no—
69C22×C3⋊Dic3D411yescharacteristic
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)—22no—
74C2×C4⋊(C3⋊D3)—21no—
75C2×C4⋊(C3⋊D3)—44no—
76C2×C4⋊(C3⋊D3)C2312yes—
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3—22no—
79C2×C4×C3⋊D3D411yescharacteristic
80C2×C4×C3⋊D3D411yescharacteristic
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C32×M16—22no—
84C2×C32×C8C2312yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2312yes—
87#3757—21no—
88#3757—21no—
89#3757—21no—
90#3755—24no—
91#3753—24no—
92#3752—21no—
93#3752—21no—
94#3752—22no—
95#3752—22no—
96C4⋊(C3⋊Dic3)C2311yescharacteristic
97C4⋊(C3⋊Dic3)C2311yescharacteristic
98#3750—21no—
99#3750—21no—
100C4×C3⋊Dic3—21no—
101#3748D414yescomplemented
102C2×C3⋊(C3⋊C8)C2312yes—
103#3743—24no—
104C8×C3⋊D3—24no—
105#3055—91noSylow
106C2×C3×#41C2×D314yes—
107C22×D12—34no—
108C22×D12—64no—
109C22×C4×D3—34no—
110C2×C3×M16C2×D314yes—
111C2×C3×C4⋊C4C2×D314yes—
112#949—616no—
113#946—34no—
114#946—34no—
115C2×#215—38no—
116#938—34no—
117#938—34no—
118#937—64no—
119#935—64no—
120C2×#213—38no—
121C4×#67—64no—
122C4×#67—64no—
123C2×(C2×D3)⋊C4—64no—
124#926—34no—
125C2×#208—34no—
126D3×M16—616no—
127C2×ΓL(1,𝔽25)—38no—
128C2×D3×C8—38no—
129#895—38no—
130#895—38no—
131#895—64no—
132#895—64no—
133C3×#103C2×D318yescomplemented
134C3×#102C2×D318yescomplemented
135#821—38no—
136#821—38no—
137#808—38no—
138#807—38no—
139C23×C32—21no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—41no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—42no—
147C22×C3⋊D3—42no—
148C22×C3⋊D3C2×D411yescharacteristic
149C22×C3⋊D3C2×D411yescharacteristic
150C32×Q8—21no—
151C32×Q8—21no—
152C32×D4—21no—
153C32×D4—21no—
154C32×D4—42no—
155C2×C32×C4—21no—
156C2×C32×C4—22no—
157C2×C32×C4—42no—
158C2×C32×C4—42no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D412yes—
161C2×C32×C4#4112yes—
162C2×C32×C4C2411yescharacteristic
163#638—42no—
164#638—42no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—44no—
173C4⋊(C3⋊D3)—44no—
174C4⋊(C3⋊D3)—42no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3—21no—
178C4×C3⋊D3—21no—
179C4×C3⋊D3—21no—
180C4×C3⋊D3—21no—
181C32×C8—22no—
182C3⋊(C3⋊C8)C2×D414yescomplemented
183C2×AGL(1,ℤ/8)—91no—
184C22×M16—91no—
185#525—91no—
186C2×#121—91no—
187#469—92no—
188#468—92no—
189#466—92no—
190#465—92no—
191#428—91no—
192#418—91no—
193#417C3⋊D311yescharacteristic, complemented
194C23×D3—34no—
195C23×D3—64no—
196C3×#41—28no—
197C3×#41—28no—
198C2×C3×Q8C22×D314yes—
199C2×C3×D4—24no—
200C2×C3×D4C22×D314yes—
201C22×C3×C4—24no—
202C22×C3×C4—24no—
203C22×C3×C4C22×D314yes—
204C2×#67—64no—
205C2×#67—64no—
206C22×Dic3—34no—
207C2×D12—38no—
208C2×D12—68no—
209C2×D12—68no—
210C2×D12—68no—
211C2×D12—68no—
212C2×D12—64no—
213C2×D12—1216no—
214C2×C4×D3—34no—
215C2×C4×D3—34no—
216C2×C4×D3—34no—
217C2×C4×D3—34no—
218C2×C4×D3—68no—
219C2×C4×D3—68no—
220C3×M16—28no—
221C2×C3×C8C22×D318yes—
222C3×C4⋊C4—24no—
223C3×C4⋊C4C22×D318yes—
224#217—64no—
225#217—64no—
226#217—64no—
227#215—616no—
228#213—616no—
229(C2×D3)⋊C4—68no—
230(C2×D3)⋊C4—68no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—34no—
234C4⋊Dic3—34no—
235Dic3⋊C4—64no—
236Dic3⋊C4—64no—
237C4×Dic3—64no—
238#208—316no—
239C2×C3⋊C8—38no—
240ΓL(1,𝔽25)—616no—
241D3×C8—616no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32—41no—
247C22×C32#12112yes—
248C22×C32C22×D411yescharacteristic
249C2×C3⋊D3—21no—
250C2×C3⋊D3—21no—
251C2×C3⋊D3—21no—
252C2×C3⋊D3—21no—
253C2×C3⋊D3—21no—
254C2×C3⋊D3—44no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—84no—
259C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
260C32×C4—41no—
261C32×C4—42no—
262C32×C4#12112yes—
263C32×C4C22×D411yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—21no—
266C3⋊Dic3—21no—
267C3⋊Dic3—41no—
268C3⋊Dic3—41no—
269C2×#41C2×C3⋊D311yescharacteristic
270C22×D4—91no—
271C22×D4—181no—
272C23×C4—91no—
273AGL(1,ℤ/8)—184no—
274C2×SD16—92no—
275C2×D8—92no—
276C2×M16—91no—
277C2×M16—92no—
278C2×M16—184no—
279C2×M16C2×C3⋊D311yescharacteristic
280C22×C8—92no—
281#123—181no—
282C22⋊Q8—91no—
283C22⋊Q8—91no—
284#121—91no—
285#121—91no—
286#121—92no—
287#121—92no—
288#121—181no—
289#121—181no—
290#120—181no—
291C4×D4—181no—
292C4×D4—181no—
293#117—91no—
294C2×C4⋊C4C2×C3⋊D311yescharacteristic
295C2×C22⋊C4—181no—
296#107—92no—
297#106—92no—
298#103C2×C3⋊D312yescomplemented
299#102—92no—
300#102—92no—
301#102C2×C3⋊D312yescomplemented
302C23×C3—24no—
303C23×C3D3×D414yes—
304C22×D3—34no—
305C22×D3—34no—
306C22×D3—68no—
307C22×D3—68no—
308C22×D3—68no—
309C22×D3—124no—
310C22×D3—128no—
311C22×D3—128no—
312C22×D3—128no—
313C3×Q8—24no—
314C3×Q8—24no—
315C3×D4—24no—
316C3×D4—24no—
317C3×D4—48no—
318C2×C3×C4—24no—
319C2×C3×C4—28no—
320C2×C3×C4—48no—
321C2×C3×C4—48no—
322C2×C3×C4#23518yes—
323C2×C3×C4D3×D414yes—
324C2×C3×C4D3×D418yes—
325C2×C3×C4C23×D314yes—
326#67—128no—
327#67—128no—
328C2×Dic3—34no—
329C2×Dic3—34no—
330C2×Dic3—68no—
331C2×Dic3—64no—
332C2×Dic3—64no—
333D12—68no—
334D12—68no—
335D12—1216no—
336D12—1216no—
337D12—128no—
338C4×D3—68no—
339C4×D3—68no—
340C4×D3—64no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—64no—
344C3×C8—28no—
345C3⋊C8—316no—
346C2×C32—22no—
347C2×C32—81no—
348C2×C32C2×#12111yescharacteristic
349C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
350C2×C32#57511yescharacteristic
351C3⋊D3—22no—
352C3⋊D3—41no—
353C3⋊D3—82no—
354C24—91no—
355C24—181no—
356#41—22no—
357#41—22no—
358C2×Q8C22×C3⋊D311yescharacteristic
359C2×D4—21no—
360C2×D4—92no—
361C2×D4—182no—
362C2×D4—182no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—182no—
366C2×D4—182no—
367C2×D4—181no—
368C2×D4—364no—
369C2×D4C22×C3⋊D311yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—182no—
378C22×C4—182no—
379C22×C4C22×C3⋊D311yescharacteristic
380SD16—184no—
381D8—184no—
382M16—22no—
383M16—94no—
384M16—184no—
385C2×C8—92no—
386C2×C8—184no—
387C2×C8C22×C3⋊D312yes—
388C4⋊C4—21no—
389C4⋊C4—91no—
390C4⋊C4—91no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4C22×C3⋊D312yes—
394C22⋊C4—182no—
395C22⋊C4—182no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C42—181no—
402C22×C3—24no—
403C22×C3—24no—
404C22×C3—44no—
405C22×C3—44no—
406C22×C3—44no—
407C22×C3#88418yes—
408C22×C3C2×D3×D414yes—
409C2×D3—38no—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—64no—
413C2×D3—64no—
414C2×D3—64no—
415C2×D3—1216no—
416C2×D3—128no—
417C2×D3—128no—
418C2×D3—128no—
419C2×D3—2416no—
420C3×C4—44no—
421C3×C4—48no—
422C3×C4#88418yes—
423C3×C4C2×#23514yes—
424C3×C4C2×D3×D414yes—
425Dic3—64no—
426Dic3—64no—
427Dic3—124no—
428Dic3—124no—
429C32#305511yescharacteristic, complemented, Sylow
430C23—21no—
431C23—91no—
432C23—91no—
433C23—182no—
434C23—182no—
435C23—182no—
436C23—361no—
437C23—362no—
438C23—362no—
439C23—362no—
440C23D4×C3⋊D311yescharacteristic
441Q8—21no—
442Q8—21no—
443D4—21no—
444D4—21no—
445D4—42no—
446D4—182no—
447D4—182no—
448D4—364no—
449D4—364no—
450D4—362no—
451D4—362no—
452D4—362no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—91no—
458C2×C4—91no—
459C2×C4—182no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4#382812yes—
469C2×C4D4×C3⋊D311yescharacteristic
470C2×C4D4×C3⋊D312yes—
471C2×C4C23×C3⋊D311yescharacteristic
472C8—22no—
473C8—94no—
474C2×C3—28no—
475C2×C3—84no—
476C2×C3C2×#88414yes—
477C2×C3D3×AGL(1,ℤ/8)14yes—
478C2×C3#577714yes—
479D3—68no—
480D3—124no—
481D3—248no—
482C22—21no—
483C22—21no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—92no—
488C22—181no—
489C22—181no—
490C22—181no—
491C22—181no—
492C22—181no—
493C22—364no—
494C22—362no—
495C22—362no—
496C22—362no—
497C22—724no—
498C22#6409312yes—
499C22C2×D4×C3⋊D311yescharacteristic
500C4—41no—
501C4—42no—
502C4—181no—
503C4—181no—
504C4—361no—
505C4—361no—
506C4#6409312yes—
507C4C2×#382811yescharacteristic
508C4C2×D4×C3⋊D311yescharacteristic
509C3#7888814yescomplemented
510C2—22no—
511C2—81no—
512C2—182no—
513C2—361no—
514C2—722no—
515C2C2×#6409311yescharacteristic
516C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
517C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#417C2
socleC22×C32C22×D4
hypercenter#417C3⋊D3
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #10596299C2semidirect
2. C2×#64158C2semidirect
3. C2×M16×C3⋊D3C2semidirect
4. C2×#64104C2semidirect
5. C32×#417C2semidirect
6. #10592830C2semidirect
7. #10592663C2semidirect
8. #10592511C2semidirect
9. #10592506C2semidirect
10. #10592481C2semidirect
11. #10592474C2semidirect
20. #64155C22semidirect
21. #64155C22semidirect
22. C2×#3755C22semidirect
23. #64147C22semidirect
24. #64147C22semidirect
27. C2×#3753C22semidirect
34. C2×#3743C22semidirect
35. C2×C8×C3⋊D3C22semidirect
40. C32×#103C22semidirect
41. C32×#102C22semidirect
42. #63648C22semidirect
43. #63648C22semidirect
44. #63635C22semidirect
45. #63634C22semidirect
50. C3×#417D3semidirect
101. #3748D4semidirect
133. C3×#103C2×D3semidirect
134. C3×#102C2×D3semidirect
182. C3⋊(C3⋊C8)C2×D4semidirect
193. #417C3⋊D3semidirect
259. C2×C3⋊D3AGL(1,ℤ/8)semidirect
298. #103C2×C3⋊D3semidirect
301. #102C2×C3⋊D3semidirect
429. C32#3055semidirect
509. C3#78888semidirect

Maximal subgroups

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

subgroupindex
#105962992
C2×#641582
C2×M16×C3⋊D32
C2×#641042
C32×#4172
#105928302
#105926632
#105925112
#105925062
#105924812
#105924742
#788883