Finite Group Databasebeta

← #11866200

Subgroups — #11866200

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5805C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3#10594982C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592914C211yesmaximal, characteristic, complemented
6#10591431C214yesmaximal, complemented
7#10591428C214yesmaximal, complemented
8#10591116C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#83826—31nomaximal
11#83384—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#953—22no—
18C3×#940C2212yescomplemented
19C3×#938—22no—
20C3×#936C2212yescomplemented
21C2×C3×#213—24no—
22C2×C3×#213C2214yes—
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898—22no—
27Dic3×D12C2214yescomplemented
28C2×#3715C2212yescomplemented
29#63823—24no—
30C2×#3713C2212yescomplemented
31#63659C2214yescomplemented
32Dic3⋊(C3⋊C8)C2214yescomplemented
33#63566C2212yescomplemented
34#63563C2212yescomplemented
35C22×C3×D8—31no—
36C3×#535—31no—
37C2×#949—31no—
38#5805D311yescharacteristic, complemented
39#5798—31no—
40C2×#932—31no—
41C22×#213D311yescharacteristic, complemented
42#5521—31no—
43#5233—31no—
44#5215—31no—
45#5215—31no—
46#5215—61no—
47#5153—34no—
48#5150—34no—
49#5113—31no—
50#5102—31no—
51#5072—34no—
52#5057—34no—
53#4999—31no—
54C24×C32—21no—
55C23×C3×D3—21no—
56C2×C32×D4—22no—
57C2×C32×D4—21no—
58C2×C32×D4—22no—
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—21no—
62C2×C3×#67—24no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12—21no—
66C2×C3×D12—22no—
67C2×C3×D12D414yescomplemented
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×D3×Dic3—24no—
73#3757—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C4×C3⋊Dic3—21no—
76#3748—22no—
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×#217—24no—
79C3×#217D412yes—
80C3×#213—28no—
81C3×C4⋊Dic3D412yes—
82C3×C4×Dic3C2312yes—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85(C2×D3)⋊Dic3—24no—
86#3715—24no—
87#3713—24no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—21no—
91C22×C3×D4—31no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C2×D311yescharacteristic
94C2×#235C2×D311yescharacteristic
95C22×D12C2×D311yescharacteristic
96C2×C3×D8—34no—
97C2×C3×D8—64no—
98C22×C3×C8—31no—
99C3×#127—32no—
100C3×#124—32no—
101C3×#121—62no—
102C3×#120—62no—
103C3×#117—31no—
104#953—22no—
105C2×#217—62no—
106#949—64no—
107C2×#215—32no—
108#940C2×D312yescomplemented
109#938—22no—
110#936C2×D312yescomplemented
111D4×Dic3—34no—
112D4×Dic3—62no—
113C2×#214—32no—
114#932—64no—
115C2×#213—24no—
116C2×#213—32no—
117C2×#213—32no—
118C2×#213C2×D314yes—
119#926—31no—
120#926—31no—
121#926—61no—
122#926C2×D311yescharacteristic
123C2×#208—31no—
124C2×#208—31no—
125C2×#208—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127#893—62no—
128D3×C22⋊C4—62no—
129C4×D12—34no—
130#835—32no—
131#832—34no—
132#832—34no—
133#832—32no—
134#832—64no—
135#821—32no—
136#816—32no—
137Dic3⋊C8—34no—
138C4⋊(C3⋊C8)—34no—
139C23×C32—22no—
140C23×C32—42no—
141C23×C32—82no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—24no—
145C22×C3×D3—21no—
146C22×C3×D3—82no—
147C32×D4—22no—
148C32×D4—22no—
149C32×D4—42no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C3×#67—42no—
156C3×#67—84no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3C2×D414yes—
159C3×D12—24no—
160C3×D12—21no—
161C3×D12—22no—
162C3×D12—21no—
163C3×D12C2×D414yes—
164C3×C4×D3—42no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167D3×Dic3—84no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170C2×AGL(1,ℤ/8)—91no—
171C22×D8—31no—
172#535—31no—
173#518—91no—
174#463—94no—
175#459—94no—
176#424—91no—
177#418—91no—
178#416—91no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—41no—
182C24×C3—61no—
183C23×D3—21no—
184C3×#41—62no—
185C3×#41—62no—
186C2×C3×Q8—31no—
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—34no—
196C2×C3×D4—32no—
197C2×C3×D4—31no—
198C2×C3×D4—42no—
199C2×C3×D4—41no—
200C2×C3×D4—64no—
201C2×C3×D4—61no—
202C2×C3×D4—62no—
203C2×C3×D4—61no—
204C2×C3×D4C22×D312yes—
205C2×C3×D4C22×D312yes—
206C22×C3×C4—21no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—21no—
211C2×#67—24no—
212C22×Dic3—64no—
213#235—22no—
214#235—22no—
215C2×D12—21no—
216C2×D12—22no—
217C2×D12#6714yescomplemented
218C2×D12C22×D311yescharacteristic
219C2×D12C22×D312yes—
220C2×C4×D3—21no—
221C2×C4×D3—64no—
222C2×Dic6C22×D311yescharacteristic
223C3×D8—68no—
224C2×C3×C8—32no—
225C2×C3×C8—62no—
226C3×C4⋊C4—32no—
227C3×C22⋊C4—32no—
228C3×C22⋊C4—64no—
229C3×C42—32no—
230#217—24no—
231#217—61no—
232#217—61no—
233#217—64no—
234#217—121no—
235#217#6712yes—
236#215—64no—
237#214—64no—
238#213—28no—
239#213—64no—
240#213—64no—
241(C2×D3)⋊C4—64no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245C4⋊Dic3#6712yes—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3C22×D312yes—
250#208—62no—
251#208—62no—
252#208—122no—
253C2×C3⋊C8—22no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8C22×D312yes—
258C22×C32—22no—
259C22×C32—42no—
260C22×C32—44no—
261C22×C32—84no—
262C22×C32#12112yes—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—24no—
265C2×C3×D3—44no—
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C2×C3×D3—84no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—42no—
273C3×Dic3—24no—
274C3×Dic3—41no—
275C2×#41—31no—
276C22×D4—31no—
277C22×D4D3211yescharacteristic
278AGL(1,ℤ/8)—184no—
279C2×SD16—92no—
280C2×D8—34no—
281C2×D8—64no—
282C2×D8—92no—
283C2×M16—91no—
284C22×C8—31no—
285#127—32no—
286#124—32no—
287#121—62no—
288#120—62no—
289C4×D4—94no—
290C4×D4—182no—
291#117—31no—
292#117—91no—
293C2×C22⋊C4—182no—
294C4⋊C8—94no—
295#103—92no—
296#102—92no—
297#102—94no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—42no—
302C23×C3—44no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—62no—
306C23×C3—64no—
307C23×C3—61no—
308C23×C3—82no—
309C23×C3—82no—
310C23×C3—84no—
311C23×C3—242no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×#6711yescharacteristic
314C22×D3—22no—
315C22×D3—24no—
316C22×D3—21no—
317C22×D3—82no—
318C3×Q8—61no—
319C3×Q8—61no—
320C3×D4—24no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—34no—
326C3×D4—42no—
327C3×D4—44no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—64no—
331C3×D4—62no—
332C3×D4—61no—
333C3×D4—61no—
334C3×D4—122no—
335C3×D4—244no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—34no—
341C2×C3×C4—61no—
342C2×C3×C4—122no—
343C2×C3×C4D3×D412yes—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4#23712yes—
346C2×C3×C4#23712yes—
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6712yes—
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351#67—42no—
352#67—84no—
353C2×Dic3—21no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357C2×Dic3—244no—
358C2×Dic3C2×#6714yes—
359D12—24no—
360D12—21no—
361D12—22no—
362D12—21no—
363D12C2×#6714yes—
364C4×D3—42no—
365C4×D3—244no—
366Dic6—21no—
367Dic6—21no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C2×C32—22no—
374C2×C32—82no—
375C2×C32C2×#12111yescharacteristic
376C2×C32#57612yes—
377C3×D3—44no—
378C3×D3—81no—
379C24—21no—
380C24—61no—
381#41—62no—
382#41—62no—
383C2×Q8—31no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—32no—
388C2×D4—31no—
389C2×D4—34no—
390C2×D4—64no—
391C2×D4—61no—
392C2×D4—62no—
393C2×D4—61no—
394C2×D4C2×D3212yes—
395C22×C4—61no—
396C22×C4—184no—
397C22×C4C2×D3211yescharacteristic
398SD16—184no—
399D8—68no—
400D8—184no—
401M16—182no—
402C2×C8—32no—
403C2×C8—62no—
404C2×C8—92no—
405C4⋊C4—32no—
406C4⋊C4—92no—
407C22⋊C4—32no—
408C22⋊C4—64no—
409C22⋊C4—184no—
410C22⋊C4—181no—
411C42—32no—
412C42—181no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—42no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—44no—
423C22×C3—64no—
424C22×C3—84no—
425C22×C3—84no—
426C22×C3—84no—
427C22×C3—88no—
428C22×C3—124no—
429C22×C3—122no—
430C22×C3—121no—
431C22×C3—244no—
432C22×C3#93812yes—
433C22×C3#93912yes—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×#6711yescharacteristic
436C2×D3—24no—
437C2×D3—44no—
438C2×D3—41no—
439C2×D3—42no—
440C2×D3—84no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—64no—
445C3×C4—121no—
446C3×C4#93812yes—
447C3×C4#93912yes—
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C2×#23711yescharacteristic
450C3×C4C2×#23711yescharacteristic
451C3×C4C22×#6711yescharacteristic
452Dic3—24no—
453Dic3—41no—
454Dic3—122no—
455Dic3—122no—
456Dic3—242no—
457C32#304111yescharacteristic, complemented, Sylow
458C23—22no—
459C23—42no—
460C23—62no—
461C23—64no—
462C23—61no—
463C23—82no—
464C23—242no—
465C23D3×#6711yescharacteristic
466Q8—61no—
467Q8—61no—
468D4—22no—
469D4—22no—
470D4—34no—
471D4—42no—
472D4—62no—
473D4—61no—
474D4—61no—
475D4—64no—
476D4—122no—
477D4—244no—
478C2×C4—34no—
479C2×C4—61no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—724no—
483C2×C4#380512yes—
484C2×C4D3×#6712yes—
485C2×C4D3×#6711yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—62no—
488C8—182no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—42no—
494C2×C3—84no—
495C2×C3—82no—
496C2×C3—82no—
497C2×C3—124no—
498C2×C3—241no—
499C2×C3#575712yes—
500C2×C3C2×#93811yescharacteristic
501C2×C3C2×#93911yescharacteristic
502C2×C3#583512yes—
503D3—44no—
504D3—81no—
505C22—22no—
506C22—44no—
507C22—42no—
508C22—64no—
509C22—84no—
510C22—124no—
511C22—122no—
512C22—121no—
513C22—244no—
514C22#6397012yes—
515C22C2×D3×#6711yescharacteristic
516C4—64no—
517C4—121no—
518C4—362no—
519C4#6397012yes—
520C4C2×#380511yescharacteristic
521C4C2×D3×#6711yescharacteristic
522C3—21no—
523C3#8338411yescharacteristic, complemented
524C3#8382611yescharacteristic, complemented
525C2—22no—
526C2—82no—
527C2—124no—
528C2—241no—
529C2#1059509612yes—
530C2C2×#6397011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5805C2semidirect
2. C22×C3×#213C2semidirect
3. #10594982C2semidirect
4. C2×#63823C2semidirect
5. #10592914C2semidirect
6. #10591431C2semidirect
7. #10591428C2semidirect
8. #10591116C2semidirect
9. #10591084C2semidirect
18. C3×#940C22semidirect
20. C3×#936C22semidirect
27. Dic3×D12C22semidirect
28. C2×#3715C22semidirect
30. C2×#3713C22semidirect
31. #63659C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
38. #5805D3semidirect
41. C22×#213D3semidirect
67. C2×C3×D12D4semidirect
108. #940C2×D3semidirect
110. #936C2×D3semidirect
217. C2×D12#67semidirect
457. C32#3041semidirect
523. C3#83384semidirect
524. C3#83826semidirect

Maximal subgroups

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

subgroupindex
C3×#58052
C22×C3×#2132
#105949822
C2×#638232
#105929142
#105914312
#105914282
#105911162
#105910842
#838263
#833843