Finite Group Databasebeta

← #11866275

Subgroups — #11866275

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3#10594982C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic
5#10592924C211yesmaximal, characteristic, complemented
6#10591567C214yesmaximal, complemented
7#10591564C214yesmaximal, complemented
8#10591116C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#83848—31nomaximal
11#83405—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#947C2212yescomplemented
18C3×#946—22no—
19C3×#944C2212yescomplemented
20C2×C3×#215—24no—
21C2×C3×#215C2214yes—
22C3×#929—22no—
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898—22no—
27Dic3×D12C2214yes—
28C2×#3715C2212yes—
29#63823—24no—
30C2×#3713C2212yes—
31#63662C2214yescomplemented
32Dic3⋊(C3⋊C8)C2214yescomplemented
33#63566C2212yescomplemented
34#63563C2212yescomplemented
35C22×C3×SD16—31no—
36C3×#536—31no—
37C2×#949—31no—
38#5816D311yescharacteristic, complemented
39C22×#215D311yescharacteristic, complemented
40#5798—31no—
41C2×#932—31no—
42#5521—31no—
43#5233—31no—
44#5225—31no—
45#5225—31no—
46#5225—61no—
47#5165—34no—
48#5162—34no—
49#5113—31no—
50#5102—31no—
51#5083—34no—
52#5057—34no—
53#4999—31no—
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×C3×#67—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12—21no—
65C2×C3×D12—22no—
66C2×C3×D12D414yes—
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×D3×Dic3—24no—
72#3757—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4×C3⋊Dic3—21no—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217D412yes—
78C3×#215—28no—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3D412yes—
81C3×Dic3⋊C4—24no—
82C3×C4×Dic3C2312yes—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85(C2×D3)⋊Dic3—24no—
86#3715—24no—
87#3713—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—21no—
91C22×C3×Q8C2×D311yescharacteristic
92C22×C3×Q8C2×D311yescharacteristic
93C22×C3×D4—31no—
94C2×#235C2×D311yescharacteristic
95C22×D12C2×D311yescharacteristic
96C2×C3×SD16—34no—
97C2×C3×SD16—64no—
98C22×C3×C8—31no—
99C3×C4⋊Q8—32no—
100C3×#124—32no—
101C3×#123—62no—
102C3×C22⋊Q8—62no—
103C3×#117—31no—
104C2×#217—62no—
105#949—64no—
106#947C2×D312yescomplemented
107#946—22no—
108#944C2×D312yescomplemented
109C2×#215—24no—
110C2×#215—32no—
111C2×#215C2×D314yes—
112D4×Dic3—34no—
113D4×Dic3—62no—
114C2×#214—32no—
115#932—64no—
116C2×#213—32no—
117C2×#213—32no—
118#929—22no—
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—34no—
131#835—34no—
132#835—32no—
133#835—64no—
134#832—32no—
135#821—32no—
136#816—32no—
137Dic3⋊C8—34no—
138C4⋊(C3⋊C8)—34no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—21no—
143C22×C3×D3—82no—
144C32×Q8—22no—
145C32×Q8—22no—
146C32×Q8—42no—
147C2×C32×C4—22no—
148C2×C32×C4—42no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D412yes—
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154C3×#67—42no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—24no—
158C3×D12—21no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12C2×D414yes—
162C3×C4×D3—42no—
163C3×Dic6—21no—
164C3×Dic6—21no—
165D3×Dic3—84no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C2×AGL(1,ℤ/8)—91no—
169C22×SD16—31no—
170#536—31no—
171#518—91no—
172#463—94no—
173#461—94no—
174#424—91no—
175#419—91no—
176#416—91no—
177C24×C3—61no—
178C23×D3—21no—
179C3×#41—62no—
180C3×#41—62no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—24no—
184C2×C3×Q8—22no—
185C2×C3×Q8—22no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—31no—
190C2×C3×Q8—41no—
191C2×C3×Q8—42no—
192C2×C3×Q8C22×D312yes—
193C2×C3×Q8C22×D312yes—
194C2×C3×D4—34no—
195C2×C3×D4—32no—
196C2×C3×D4—31no—
197C2×C3×D4—61no—
198C2×C3×D4—62no—
199C2×C3×D4—61no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—41no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C22×Dic3—64no—
209#235—22no—
210#235—22no—
211C2×D12—21no—
212C2×D12—22no—
213C2×D12#6714yes—
214C2×D12C22×D311yescharacteristic
215C2×D12C22×D312yes—
216C2×C4×D3—21no—
217C2×C4×D3—64no—
218C2×Dic6C22×D311yescharacteristic
219C3×SD16—68no—
220C2×C3×C8—32no—
221C2×C3×C8—62no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—64no—
224C3×C22⋊C4—32no—
225C3×C22⋊C4—64no—
226C3×C42—32no—
227#217—61no—
228#217—61no—
229#217—64no—
230#217—121no—
231#217#6712yes—
232#215—28no—
233#215—64no—
234#214—64no—
235#213—64no—
236#213—64no—
237(C2×D3)⋊C4—24no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3#6712yes—
243Dic3⋊C4—24no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—121no—
247C4×Dic3C22×D312yes—
248#208—62no—
249#208—62no—
250#208—122no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8C22×D312yes—
256C22×C32—22no—
257C22×C32#12112yes—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—24no—
260C2×C3×D3—44no—
261C2×C3×D3—41no—
262C2×C3×D3—42no—
263C2×C3×D3—84no—
264C32×C4—42no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8D3211yescharacteristic
273C22×D4—31no—
274AGL(1,ℤ/8)—184no—
275C2×SD16—34no—
276C2×SD16—64no—
277C2×SD16—92no—
278C2×D8—92no—
279C2×M16—91no—
280C22×C8—31no—
281C4⋊Q8—32no—
282#124—32no—
283#123—62no—
284C22⋊Q8—62no—
285C4×D4—94no—
286C4×D4—182no—
287#117—31no—
288#117—91no—
289C2×C22⋊C4—182no—
290C4⋊C8—94no—
291#103—92no—
292#103—94no—
293#102—92no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—64no—
297C23×C3—61no—
298C23×C3—242no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—22no—
302C22×D3—24no—
303C22×D3—21no—
304C22×D3—82no—
305C3×Q8—24no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—22no—
310C3×Q8—42no—
311C3×Q8—44no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—61no—
315C3×Q8—61no—
316C3×D4—34no—
317C3×D4—64no—
318C3×D4—62no—
319C3×D4—61no—
320C3×D4—61no—
321C3×D4—122no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—34no—
329C2×C3×C4—42no—
330C2×C3×C4—44no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—61no—
334C2×C3×C4—122no—
335C2×C3×C4D3×D412yes—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23712yes—
338C2×C3×C4#23712yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6712yes—
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343#67—42no—
344C2×Dic3—21no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—244no—
349C2×Dic3C2×#6714yes—
350D12—24no—
351D12—21no—
352D12—22no—
353D12—21no—
354D12C2×#6714yes—
355C4×D3—42no—
356C4×D3—244no—
357Dic6—21no—
358Dic6—21no—
359C3×C8—62no—
360C3⋊C8—22no—
361C3⋊C8—62no—
362C3⋊C8—62no—
363C3⋊C8—122no—
364C2×C32—22no—
365C2×C32C2×#12111yescharacteristic
366C2×C32#57712yes—
367C3×D3—44no—
368C3×D3—81no—
369C24—61no—
370#41—62no—
371#41—62no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—31no—
376C2×Q8C2×D3212yes—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—34no—
380C2×D4—61no—
381C2×D4—62no—
382C2×D4—61no—
383C22×C4—21no—
384C22×C4—61no—
385C22×C4—184no—
386C22×C4C2×D3211yescharacteristic
387SD16—68no—
388SD16—184no—
389D8—184no—
390M16—182no—
391C2×C8—32no—
392C2×C8—62no—
393C2×C8—92no—
394C4⋊C4—32no—
395C4⋊C4—64no—
396C4⋊C4—92no—
397C22⋊C4—32no—
398C22⋊C4—64no—
399C22⋊C4—184no—
400C22⋊C4—181no—
401C42—32no—
402C42—181no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—42no—
408C22×C3—64no—
409C22×C3—124no—
410C22×C3—122no—
411C22×C3—121no—
412C22×C3—244no—
413C22×C3#93812yes—
414C22×C3#93912yes—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C2×D3—24no—
418C2×D3—44no—
419C2×D3—41no—
420C2×D3—42no—
421C2×D3—84no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—44no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—64no—
429C3×C4—121no—
430C3×C4#93812yes—
431C3×C4#93912yes—
432C3×C4C2×D3×D411yescharacteristic
433C3×C4C2×#23711yescharacteristic
434C3×C4C2×#23711yescharacteristic
435C3×C4C22×#6711yescharacteristic
436Dic3—24no—
437Dic3—41no—
438Dic3—122no—
439Dic3—122no—
440Dic3—242no—
441C32#304211yescharacteristic, complemented, Sylow
442C23—62no—
443C23—64no—
444C23—61no—
445C23—242no—
446C23D3×#6711yescharacteristic
447Q8—22no—
448Q8—22no—
449Q8—42no—
450Q8—61no—
451Q8—61no—
452D4—34no—
453D4—62no—
454D4—61no—
455D4—61no—
456D4—64no—
457D4—122no—
458C2×C4—22no—
459C2×C4—34no—
460C2×C4—42no—
461C2×C4—61no—
462C2×C4—122no—
463C2×C4—182no—
464C2×C4—724no—
465C2×C4#380512yes—
466C2×C4D3×#6712yes—
467C2×C4D3×#6711yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—62no—
470C8—182no—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—42no—
476C2×C3—124no—
477C2×C3—241no—
478C2×C3#576212yes—
479C2×C3C2×#93811yescharacteristic
480C2×C3C2×#93911yescharacteristic
481C2×C3#583712yes—
482D3—44no—
483D3—81no—
484C22—22no—
485C22—64no—
486C22—124no—
487C22—121no—
488C22—122no—
489C22—244no—
490C22#6397012yes—
491C22C2×D3×#6711yescharacteristic
492C4—42no—
493C4—64no—
494C4—121no—
495C4—362no—
496C4#6397012yes—
497C4C2×#380511yescharacteristic
498C4C2×D3×#6711yescharacteristic
499C3—21no—
500C3#8340511yescharacteristic, complemented
501C3#8384811yescharacteristic, complemented
502C2—22no—
503C2—124no—
504C2—241no—
505C2#1059531812yes—
506C2C2×#6397011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63823C2
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. C3×#5816C2semidirect
2. C22×C3×#215C2semidirect
3. #10594982C2semidirect
5. #10592924C2semidirect
6. #10591567C2semidirect
7. #10591564C2semidirect
8. #10591116C2semidirect
9. #10591084C2semidirect
17. C3×#947C22semidirect
19. C3×#944C22semidirect
31. #63662C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
38. #5816D3semidirect
39. C22×#215D3semidirect
106. #947C2×D3semidirect
108. #944C2×D3semidirect
441. C32#3042semidirect
500. C3#83405semidirect
501. C3#83848semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C22×C3×#2152
#105949822
C2×#638232
#105929242
#105915672
#105915642
#105911162
#105910842
#838483
#834053