Finite Group Databasebeta

← #11866274

Subgroups — #11866274

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic, complemented
2C3×#5816C211yesmaximal, characteristic, complemented
3#10594996C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591568C214yesmaximal, complemented
7#10591565C214yesmaximal, complemented
8#10591117C211yesmaximal, characteristic, complemented
9#10591083C211yesmaximal, characteristic, complemented
10#83405—31nomaximal
11#78976—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×#3755—24no—
16C2×#3755C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#947C2212yescomplemented
19C3×#946—22no—
20C3×#944C2212yescomplemented
21C3×#929—22no—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63974—22no—
26#63894—22no—
27#63894C2214yes—
28C2×#3717C2212yes—
29#63825—24no—
30C2×#3714C2212yes—
31C3×#835C2214yescomplemented
32Dic3⋊(C3⋊C8)C2214yescomplemented
33#63565C2212yescomplemented
34#63562C2212yescomplemented
35C3×#536—31no—
36C2×#949—31no—
37#5816D311yescharacteristic, complemented
38C22×#215—31no—
39C22×#215—31no—
40C22×#215—61no—
41C2×#908—31no—
42#5521—31no—
43#5521—31no—
44C3×#419—31no—
45#5233—31no—
46#5225D311yescharacteristic, complemented
47#5119—31no—
48#5083—34no—
49#5057—34no—
50#5002—31no—
51#4999—31no—
52#4819—34no—
53#4818—34no—
54C23×C3⋊D3—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—22no—
57C2×C32×Q8—22no—
58C2×C32×Q8C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)D414yes—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C3×#67—21no—
66C3×#235—22no—
67C3×#235—22no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×#624—24no—
72#3755—28no—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#217—21no—
76C3×#217D412yes—
77C3×(C2×D3)⋊C4—24no—
78C3×C4⋊Dic3D412yes—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—24no—
81C3×C4×Dic3—21no—
82C3×C4×Dic3C2312yes—
83C3×#208—22no—
84C2×C3×C3⋊C8C2312yes—
85#3722—24no—
86#3717—24no—
87#3714—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—21no—
91C22×C3×Q8C2×D311yescharacteristic
92C22×C3×Q8C2×D311yescharacteristic
93C2×#235C2×D311yescharacteristic
94C22×D12—31no—
95C22×D12—31no—
96C22×D12—61no—
97C2×C3×M16—31no—
98C3×C4⋊Q8—32no—
99C3×#124—32no—
100C3×#123—62no—
101C3×C22⋊Q8—62no—
102C3×#117—31no—
103C3×#117—31no—
104#949—64no—
105#947C2×D312yescomplemented
106#946—22no—
107#944C2×D312yescomplemented
108C2×#215—34no—
109C2×#215—34no—
110C2×#215—32no—
111C2×#215—64no—
112C2×#215—64no—
113C2×#215—64no—
114C2×#215—68no—
115C2×#213—32no—
116#929—22no—
117#926C2×D311yescharacteristic
118#926C2×D311yescharacteristic
119C2×#208C2×D311yescharacteristic
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123#908—64no—
124C2×D24—32no—
125C2×#204—32no—
126#893—34no—
127#893—62no—
128D3×C22⋊C4—62no—
129D3×C22⋊C4—62no—
130C4×D12—34no—
131C4×D12—62no—
132C3×#103—34no—
133#835—32no—
134#835C2×D314yescomplemented
135#832—32no—
136Dic3⋊C8—34no—
137#810—32no—
138#809—32no—
139C4⋊(C3⋊C8)—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3—82no—
144C22×C3×D3—21no—
145C32×Q8—22no—
146C32×Q8—22no—
147C32×Q8—42no—
148C2×C32×C4—22no—
149C2×C32×C4—42no—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C4⋊(C3⋊D3)—24no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)C2×D414yes—
157C3×#67—42no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3C2×D414yes—
161C3×D12—21no—
162C3×D12—21no—
163C3×C4×D3—42no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166#624—84no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C2×AGL(1,ℤ/8)—91no—
170C22×SD16—91no—
171#536—31no—
172#518—91no—
173#463—94no—
174#461—94no—
175#424—91no—
176#419—31no—
177#416—91no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3—121no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—24no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—22no—
190C2×C3×Q8—22no—
191C2×C3×Q8—31no—
192C2×C3×Q8—41no—
193C2×C3×Q8—42no—
194C2×C3×Q8C22×D312yes—
195C2×C3×Q8C22×D312yes—
196C2×C3×D4—31no—
197C2×C3×D4—61no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—21no—
206#235—22no—
207#235—22no—
208C2×D12—34no—
209C2×D12—34no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—64no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—61no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—122no—
219C2×D12—121no—
220C2×D12C22×D311yescharacteristic
221C2×C4×D3—21no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×Dic6C22×D311yescharacteristic
225C3×M16—62no—
226C2×C3×C8—32no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—64no—
230C3×C22⋊C4—32no—
231C3×C22⋊C4—64no—
232C3×C22⋊C4—61no—
233C3×C42—32no—
234C3×C42—61no—
235#217—21no—
236#217#6712yes—
237#215—64no—
238#215—68no—
239#215—68no—
240#215—616no—
241#213—64no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3#6712yes—
246C4⋊Dic3C22×D312yes—
247Dic3⋊C4—24no—
248C4×Dic3—21no—
249C4×Dic3C22×D312yes—
250#208—22no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—64no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8C22×D312yes—
258D24—64no—
259#204—64no—
260C22×C32—22no—
261C22×C32#12112yes—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—24no—
264C2×C3⋊D3—44no—
265C2×C3⋊D3—84no—
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C32×C4—42no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3×Dic3—24no—
273C3×Dic3—41no—
274C3×Dic3—42no—
275C2×#41—31no—
276C22×Q8D3211yescharacteristic
277C22×D4—91no—
278AGL(1,ℤ/8)—184no—
279C2×SD16—92no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—92no—
283C2×M16—31no—
284C22×C8—91no—
285C4⋊Q8—32no—
286#124—32no—
287#123—62no—
288C22⋊Q8—62no—
289C4×D4—94no—
290C4×D4—182no—
291#117—31no—
292#117—31no—
293C2×C22⋊C4—182no—
294C4⋊C8—94no—
295#103—34no—
296#103—92no—
297#102—92no—
298C23×C3—21no—
299C23×C3—61no—
300C23×C3D3×D411yescharacteristic
301C23×C3C2×#6711yescharacteristic
302C22×D3—21no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—64no—
306C22×D3—64no—
307C22×D3—122no—
308C22×D3—124no—
309C22×D3—242no—
310C22×D3—242no—
311C22×D3—244no—
312C3×Q8—24no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—42no—
318C3×Q8—44no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—61no—
322C3×Q8—61no—
323C3×D4—61no—
324C3×D4—61no—
325C3×D4—122no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—34no—
333C2×C3×C4—42no—
334C2×C3×C4—44no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—122no—
340C2×C3×C4#23512yes—
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D412yes—
343C2×C3×C4D3×D412yes—
344C2×C3×C4#23712yes—
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—42no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3C2×#6714yes—
352D12—21no—
353D12—21no—
354D12—34no—
355D12—34no—
356D12—64no—
357D12—64no—
358D12—64no—
359D12—62no—
360D12—62no—
361D12—122no—
362D12—124no—
363C4×D3—42no—
364C4×D3—244no—
365C4×D3—244no—
366Dic6—21no—
367Dic6—21no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—64no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C2×C32—22no—
374C2×C32C2×#12111yescharacteristic
375C2×C32#57712yes—
376C3⋊D3—44no—
377C3×D3—81no—
378C24—181no—
379#41—62no—
380#41—62no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—31no—
385C2×Q8C2×D3212yes—
386C2×D4—31no—
387C2×D4—61no—
388C2×D4—92no—
389C2×D4—94no—
390C2×D4—182no—
391C2×D4—181no—
392C22×C4—21no—
393C22×C4—61no—
394C22×C4—184no—
395C22×C4C2×D3211yescharacteristic
396SD16—184no—
397SD16—188no—
398D8—184no—
399M16—62no—
400C2×C8—32no—
401C2×C8—92no—
402C2×C8—182no—
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—64no—
406C22⋊C4—32no—
407C22⋊C4—64no—
408C22⋊C4—61no—
409C22⋊C4—184no—
410C42—32no—
411C42—61no—
412C22×C3—24no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—121no—
418C22×C3—122no—
419C22×C3#88412yes—
420C22×C3#93812yes—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C22×#6711yescharacteristic
423C2×D3—41no—
424C2×D3—42no—
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—124no—
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—244no—
431C2×D3—244no—
432C2×D3—244no—
433C2×D3—248no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—44no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—64no—
441C3×C4—121no—
442C3×C4—122no—
443C3×C4#88412yes—
444C3×C4#93812yes—
445C3×C4C2×#23511yescharacteristic
446C3×C4C2×D3×D411yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C2×#23711yescharacteristic
449Dic3—24no—
450Dic3—42no—
451Dic3—41no—
452C32#304211yescharacteristic, complemented, Sylow
453C23—61no—
454C23—182no—
455C23—184no—
456C23—722no—
457C23D3×#6711yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—42no—
461Q8—61no—
462Q8—61no—
463D4—61no—
464D4—61no—
465D4—94no—
466D4—122no—
467D4—182no—
468D4—184no—
469C2×C4—22no—
470C2×C4—34no—
471C2×C4—42no—
472C2×C4—62no—
473C2×C4—61no—
474C2×C4—122no—
475C2×C4—724no—
476C2×C4#380412yes—
477C2×C4D3×#6711yescharacteristic
478C2×C4#381112yes—
479C2×C4C22×D3211yescharacteristic
480C8—62no—
481C8—182no—
482C2×C3—24no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—22no—
487C2×C3—241no—
488C2×C3C2×#88411yescharacteristic
489C2×C3#577812yes—
490C2×C3C2×#93811yescharacteristic
491C2×C3#583712yes—
492D3—81no—
493D3—124no—
494D3—124no—
495D3—244no—
496C22—22no—
497C22—121no—
498C22—122no—
499C22—184no—
500C22—364no—
501C22—724no—
502C22#6395812yes—
503C22C2×D3×#6711yescharacteristic
504C4—42no—
505C4—64no—
506C4—121no—
507C4—122no—
508C4#6395812yes—
509C4C2×#380411yescharacteristic
510C4C2×#381111yescharacteristic
511C3—21no—
512C3#7897611yescharacteristic, complemented
513C3#8340511yescharacteristic, complemented
514C2—22no—
515C2—241no—
516C2—364no—
517C2#1059531912yes—
518C2C2×#6395811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63825C2
hypercenterC22×Q8D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3755C2semidirect
2. C3×#5816C2semidirect
3. #10594996C2semidirect
5. C3×#5225C2semidirect
6. #10591568C2semidirect
7. #10591565C2semidirect
8. #10591117C2semidirect
9. #10591083C2semidirect
18. C3×#947C22semidirect
20. C3×#944C22semidirect
31. C3×#835C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
33. #63565C22semidirect
34. #63562C22semidirect
37. #5816D3semidirect
46. #5225D3semidirect
105. #947C2×D3semidirect
107. #944C2×D3semidirect
134. #835C2×D3semidirect
452. C32#3042semidirect
512. C3#78976semidirect
513. C3#83405semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C3×#58162
#105949962
C2×#638252
C3×#52252
#105915682
#105915652
#105911172
#105910832
#834053
#789763