Finite Group Databasebeta

← #11866278

Subgroups — #11866278

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5526C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic
5#10592698C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590363C214yesmaximal, complemented
9#10590348C214yesmaximal, complemented
10#83405—31nomaximal
11#82544—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#897—22no—
20C3×#893—22no—
21C3×#886—22no—
22C3×D3×C22⋊C4—22no—
23C3×#875C2212yescomplemented
24C3×C4×D12C2214yes—
25C3×#869C2212yescomplemented
26C2×#3715—24no—
27C2×#3715C2214yes—
28C2×#3715C2212yes—
29#63823—24no—
30C2×#3713C2212yes—
31C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
32#63565C2212yescomplemented
33#63565C2214yescomplemented
34#63562C2212yescomplemented
35C3×#536—31no—
36C3×#518—31no—
37C2×#949—31no—
38C22×#215—31no—
39C22×#214—31no—
40C2×#932—31no—
41#5526D311yescharacteristic, complemented
42#5521D311yescharacteristic, complemented
43#5233—31no—
44#5225—31no—
45#5083—34no—
46#5057—34no—
47#5019—34no—
48#5016—34no—
49#5004—31no—
50#5002—31no—
51#4999—31no—
52#4999—31no—
53#4999—61no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C22×C3×Dic3—21no—
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12D414yes—
63C2×C3×D12C2311yescharacteristic
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—21no—
66C2×C3×C4×D3—24no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C32×C4⋊C4D412yes—
73C32×C22⋊C4D412yes—
74C32×C42C2312yes—
75#3748—22no—
76C2×C3⋊(C3⋊C8)—22no—
77C2×C3⋊(C3⋊C8)C2312yes—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×#217—21no—
80C3×(C2×D3)⋊C4—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—24no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—21no—
85#3715—24no—
86#3715—28no—
87#3713—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C22×C3×D4—31no—
92C2×#235C2×D311yescharacteristic
93C22×D12C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C3×C4⋊Q8—32no—
96C3×#124—32no—
97C3×#123—62no—
98C3×C22⋊Q8—62no—
99C3×C4×D4—34no—
100C3×C4×D4—62no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117C2×D311yescharacteristic
104C3×#117C2×D311yescharacteristic
105C2×C3×C22⋊C4—62no—
106#949—64no—
107C2×#215—34no—
108C2×#215—32no—
109C2×#215—64no—
110C2×#214—34no—
111C2×#214—32no—
112C2×#214—64no—
113#932—64no—
114C2×#213—32no—
115C2×#213—32no—
116#926C2×D311yescharacteristic
117C2×#208—31no—
118C2×#208—31no—
119C2×#208—61no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123#897—22no—
124#893—22no—
125#886—22no—
126D3×C22⋊C4—22no—
127#875C2×D312yescomplemented
128C4×D12C2×D314yes—
129#869C2×D312yescomplemented
130#835—34no—
131#835—32no—
132#832—32no—
133#810—32no—
134#810—34no—
135#809—32no—
136C4⋊(C3⋊C8)—34no—
137C4⋊(C3⋊C8)—34no—
138C4⋊(C3⋊C8)—64no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—21no—
143C22×C3×D3—82no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D414yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C3×#67—42no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—42no—
154C3×D12—24no—
155C3×D12—21no—
156C3×D12—22no—
157C3×D12—21no—
158C3×D12C2×D414yes—
159C3×C4×D3—42no—
160C3×C4×D3—84no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—22no—
164C3×Dic6—21no—
165C3×Dic6—42no—
166C3⋊(C3⋊C8)—22no—
167C3⋊(C3⋊C8)—22no—
168C2×AGL(1,ℤ/8)—91no—
169C22×SD16—91no—
170#536—31no—
171#518—31no—
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—32no—
182C2×C3×Q8—31no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×D4—34no—
187C2×C3×D4—32no—
188C2×C3×D4—31no—
189C2×C3×D4—61no—
190C2×C3×D4—62no—
191C2×C3×D4—61no—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4—64no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—21no—
199C22×Dic3—21no—
200#235—22no—
201#235—22no—
202C2×D12—22no—
203C2×D12—21no—
204C2×D12D1214yes—
205C2×D12C22×D311yescharacteristic
206C2×D12C22×D312yes—
207C2×C4×D3—21no—
208C2×C4×D3—24no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6C22×D311yescharacteristic
213C2×Dic6C22×D312yes—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—64no—
217C3×C4⋊C4#6712yes—
218C3×C4⋊C4#6712yes—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—64no—
222C3×C22⋊C4—64no—
223C3×C22⋊C4#6712yes—
224C3×C22⋊C4#6712yes—
225C3×C42—22no—
226C3×C42—61no—
227C3×C42C22×D312yes—
228C3×C42C22×D312yes—
229#217—21no—
230#215—68no—
231#215—64no—
232#214—64no—
233#214—68no—
234#213—64no—
235#213—64no—
236(C2×D3)⋊C4—24no—
237(C2×D3)⋊C4—24no—
238C4⋊Dic3—24no—
239C4⋊Dic3C22×D312yes—
240C4×Dic3—21no—
241#208—62no—
242#208—62no—
243#208—122no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—122no—
253C22×C32—22no—
254C22×C32#12112yes—
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—24no—
257C2×C3×D3—44no—
258C2×C3×D3—41no—
259C2×C3×D3—42no—
260C2×C3×D3—84no—
261C32×C4—24no—
262C32×C4#12112yes—
263C32×C4C22×D411yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3×Dic3—42no—
266C3×Dic3—41no—
267C3×Dic3—42no—
268C2×#41—31no—
269C22×Q8—31no—
270C22×D4—31no—
271AGL(1,ℤ/8)—184no—
272C2×SD16—94no—
273C2×SD16—92no—
274C2×SD16—184no—
275C2×D8—92no—
276C2×M16—91no—
277C22×C8—91no—
278C4⋊Q8—32no—
279#124—32no—
280#123—62no—
281C22⋊Q8—62no—
282C4×D4—34no—
283C4×D4—62no—
284#117—31no—
285#117D3211yescharacteristic
286C2×C22⋊C4—62no—
287C4⋊C8—94no—
288#103—92no—
289#103—94no—
290#102—92no—
291C23×C3—21no—
292C23×C3—62no—
293C23×C3—64no—
294C23×C3—61no—
295C23×C3—242no—
296C23×C3C2×#6711yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—22no—
299C22×D3—24no—
300C22×D3—21no—
301C22×D3—82no—
302C3×Q8—62no—
303C3×Q8—61no—
304C3×Q8—62no—
305C3×Q8—61no—
306C3×Q8—122no—
307C3×D4—34no—
308C3×D4—64no—
309C3×D4—61no—
310C3×D4—61no—
311C3×D4—62no—
312C3×D4—122no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—24no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—122no—
322C2×C3×C4—122no—
323C2×C3×C4—244no—
324C2×C3×C4C2×D1212yes—
325C2×C3×C4#23512yes—
326C2×C3×C4D3×D412yes—
327C2×C3×C4#23712yes—
328C2×C3×C4C2×#6714yes—
329C2×C3×C4C2×#6714yes—
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334#67—42no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—42no—
339D12—24no—
340D12—22no—
341D12—21no—
342D12—21no—
343D12C2×D1214yes—
344C4×D3—42no—
345C4×D3—84no—
346Dic6—22no—
347Dic6—21no—
348Dic6—22no—
349Dic6—21no—
350Dic6—42no—
351C3⋊C8—62no—
352C3⋊C8—62no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—122no—
356C3⋊C8—122no—
357C2×C32—22no—
358C2×C32C2×#12111yescharacteristic
359C2×C32#57712yes—
360C3×D3—44no—
361C3×D3—81no—
362C24—61no—
363#41—62no—
364#41—62no—
365C2×Q8—32no—
366C2×Q8—31no—
367C2×Q8—61no—
368C2×Q8—62no—
369C2×Q8—62no—
370C2×D4—32no—
371C2×D4—31no—
372C2×D4—34no—
373C2×D4—61no—
374C2×D4—62no—
375C2×D4—61no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—64no—
379C22×C4C2×D3211yescharacteristic
380SD16—188no—
381SD16—184no—
382D8—184no—
383M16—182no—
384C2×C8—92no—
385C2×C8—92no—
386C2×C8—182no—
387C4⋊C4—32no—
388C4⋊C4—64no—
389C4⋊C4#62512yes—
390C22⋊C4—61no—
391C22⋊C4—64no—
392C22⋊C4—64no—
393C22⋊C4#62512yes—
394C42—61no—
395C42C2×D3212yes—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—42no—
401C22×C3—64no—
402C22×C3—124no—
403C22×C3—121no—
404C22×C3—122no—
405C22×C3—244no—
406C22×C3#93012yes—
407C22×C3#93812yes—
408C22×C3C22×#6711yescharacteristic
409C22×C3C22×#6711yescharacteristic
410C2×D3—24no—
411C2×D3—44no—
412C2×D3—41no—
413C2×D3—42no—
414C2×D3—84no—
415C3×C4—24no—
416C3×C4—24no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—44no—
421C3×C4—121no—
422C3×C4—122no—
423C3×C4—122no—
424C3×C4#93012yes—
425C3×C4#93812yes—
426C3×C4C22×D1211yescharacteristic
427C3×C4C2×#23511yescharacteristic
428C3×C4C2×D3×D411yescharacteristic
429C3×C4C2×#23711yescharacteristic
430Dic3—42no—
431Dic3—41no—
432Dic3—42no—
433C32#304211yescharacteristic, complemented, Sylow
434C23—62no—
435C23—64no—
436C23—61no—
437C23—242no—
438C23C2×#62511yescharacteristic
439Q8—62no—
440Q8—61no—
441Q8—62no—
442Q8—61no—
443Q8—122no—
444D4—34no—
445D4—62no—
446D4—61no—
447D4—61no—
448D4—64no—
449D4—122no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—122no—
454C2×C4—122no—
455C2×C4—244no—
456C2×C4#379512yes—
457C2×C4D3×D1212yes—
458C2×C4C2×#62514yes—
459C2×C4C2×#62511yescharacteristic
460C2×C4C22×D3211yescharacteristic
461C8—182no—
462C8—182no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—21no—
467C2×C3—42no—
468C2×C3—124no—
469C2×C3—241no—
470C2×C3C2×#93011yescharacteristic
471C2×C3C2×#93811yescharacteristic
472C2×C3#583612yes—
473C2×C3#583712yes—
474D3—44no—
475D3—81no—
476C22—22no—
477C22—64no—
478C22—124no—
479C22—122no—
480C22—121no—
481C22—244no—
482C22#6390812yes—
483C22C22×#62511yescharacteristic
484C4—24no—
485C4—122no—
486C4—121no—
487C4—122no—
488C4#6390812yes—
489C4C2×#379511yescharacteristic
490C4C2×D3×D1211yescharacteristic
491C3—21no—
492C3#8254411yescharacteristic, complemented
493C3#8340511yescharacteristic, complemented
494C2—22no—
495C2—124no—
496C2—241no—
497C2C2×#6390811yescharacteristic
498C2#1059544612yes—
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63823C2
hypercenter#117D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5526C2semidirect
2. C3×#5521C2semidirect
3. C22×#3715C2semidirect
5. #10592698C2semidirect
6. #10591099C2semidirect
7. #10591083C2semidirect
8. #10590363C2semidirect
9. #10590348C2semidirect
23. C3×#875C22semidirect
25. C3×#869C22semidirect
31. C4⋊(C3⋊(C3⋊C8))C22semidirect
32. #63565C22semidirect
33. #63565C22semidirect
34. #63562C22semidirect
41. #5526D3semidirect
42. #5521D3semidirect
127. #875C2×D3semidirect
129. #869C2×D3semidirect
433. C32#3042semidirect
492. C3#82544semidirect
493. C3#83405semidirect

Maximal subgroups

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

subgroupindex
C3×#55262
C3×#55212
C22×#37152
C2×#638232
#105926982
#105910992
#105910832
#105903632
#105903482
#834053
#825443