Finite Group Databasebeta

← #11860772

Subgroups — #11860772

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4#10592914C211yesmaximal, characteristic
5#10591440C214yesmaximal, complemented
6Dic3×#214C214yesmaximal, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10591099C211yesmaximal, characteristic, complemented
9#10591055C211yesmaximal, characteristic, complemented
10#83843—31nomaximal
11#82543—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#217—22no—
17C3×D4×Dic3—22no—
18C3×D4×Dic3C2214yes—
19C2×C3×#214C418yescomplemented
20C2×C3×#214C2212yes—
21C2×C3×#214C2212yes—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25#63955—22no—
26#63843—22no—
27Dic3×Dic6C2214yescomplemented
28#63659C2214yes—
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63565C2214yescomplemented
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C22×C3×SD16—31no—
35C3×#518—31no—
36#5812—31no—
37#5798D311yescharacteristic
38C22×#214D311yescharacteristic
39#5516—31no—
40#5225—31no—
41#5215—31no—
42#5215—31no—
43#5215—61no—
44#5164—34no—
45Dic3×SD16—34no—
46#5106—31no—
47#5101—31no—
48#5018—34no—
49C4×#214—34no—
50#5004—31no—
51#4998—31no—
52#4997—31no—
53C24×C32—21no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2×C414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3×Dic3—21no—
60C22×C3×Dic3—24no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65#3757—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C4×C3⋊Dic3—21no—
68#3748—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×#217—21no—
71C3×#217—24no—
72C3×#217D412yes—
73C3×#214C2×C418yescomplemented
74C3×#214C2×C418yescomplemented
75C3×C4⋊Dic3D412yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—21no—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8C2×C414yescomplemented
80C2×C3×C3⋊C8C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82Dic3⋊Dic3—24no—
83Dic32—24no—
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C2×C3×SD16—38no—
91C2×C3×SD16—32no—
92C2×C3×SD16—32no—
93C22×C3×C8—31no—
94C3×C4×D4—34no—
95C3×C4×D4—62no—
96C3×#117—31no—
97C3×#117—31no—
98C2×C3×C22⋊C4—62no—
99C2×#217—22no—
100Q8×Dic3—34no—
101Q8×Dic3—62no—
102D4×Dic3—22no—
103D4×Dic3C2×D314yes—
104C2×#214Dic318yescomplemented
105C2×#214C2×D312yes—
106C2×#214C2×D312yes—
107#926—31no—
108#926—31no—
109#926—61no—
110#926—62no—
111#926C2×D311yescharacteristic
112#926C2×D311yescharacteristic
113C2×#208—31no—
114C2×#208—31no—
115C2×#208—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117#887—62no—
118#877—62no—
119C4×Dic6—34no—
120#835—34no—
121#832—34no—
122#832—34no—
123#832—64no—
124#818—32no—
125#817—32no—
126#815—32no—
127C8×Dic3—32no—
128#810—34no—
129#808—32no—
130#807—32no—
131#803—32no—
132C4×C3⋊C8—32no—
133C23×C32—22no—
134C23×C32—24no—
135C23×C32—82no—
136C23×C32C2×D411yescharacteristic
137C32×D4—24no—
138C32×D4—22no—
139C32×D4C22×C414yes—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3—22no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—84no—
149C2×C3×Dic3C2×D414yes—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yes—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8C22×C412yes—
155C3×C3⋊C8C22×C412yes—
156C22×SD16—31no—
157#519—91no—
158#518—31no—
159#440—94no—
160C4×SD16—94no—
161#427—91no—
162#419—91no—
163#418—91no—
164#405—91no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—41no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—62no—
171C2×C3×Q8—61no—
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—22no—
175C2×C3×D4—21no—
176C2×C3×D4—24no—
177C2×C3×D4—22no—
178C2×C3×D4—42no—
179C2×C3×D4—41no—
180C2×C3×D4C4×D314yes—
181C2×C3×D4C2×Dic314yes—
182C2×C3×D4C22×D312yes—
183C2×C3×D4C22×D312yes—
184C22×C3×C4—21no—
185C22×C3×C4—64no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—24no—
191C2×Dic6—21no—
192C2×Dic6—22no—
193C2×Dic6C2×Dic314yescomplemented
194C2×Dic6C22×D312yes—
195C3×SD16—38no—
196C3×SD16—38no—
197C2×C3×C8—34no—
198C2×C3×C8—31no—
199C2×C3×C8—31no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—32no—
202C3×C22⋊C4—32no—
203C3×C22⋊C4—64no—
204C3×C22⋊C4—61no—
205C3×C42—32no—
206C3×C42—61no—
207#217—21no—
208#217—24no—
209#217—61no—
210#217—61no—
211#217—121no—
212#217#6712yes—
213#214C2×Dic318yescomplemented
214#214C2×Dic318yescomplemented
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—64no—
219C4⋊Dic3#6712yes—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—64no—
222C4×Dic3—21no—
223C4×Dic3—64no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3—64no—
227C4×Dic3—121no—
228C4×Dic3C22×D312yes—
229#208—62no—
230#208—62no—
231#208—122no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8C2×Dic314yescomplemented
236C2×C3⋊C8C22×D311yescharacteristic
237C2×C3⋊C8C22×D311yescharacteristic
238C22×C32—22no—
239C22×C32—24no—
240C22×C32—44no—
241C22×C32—84no—
242C22×C32C4×D412yes—
243C22×C32C22×D411yescharacteristic
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—42no—
248C3×Dic3—24no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8—31no—
252C22×D4D3211yescharacteristic
253C2×SD16—38no—
254C2×SD16—32no—
255C2×SD16—32no—
256C2×M16—91no—
257C22×C8—31no—
258C4×Q8—94no—
259C4×Q8—182no—
260C4×D4—34no—
261C4×D4—62no—
262#117—31no—
263#117—31no—
264#117—91no—
265#117—182no—
266C2×C22⋊C4—62no—
267#107—92no—
268#106—92no—
269#103—94no—
270#102—94no—
271#97—92no—
272C4×C8—92no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—24no—
276C23×C3—24no—
277C23×C3—21no—
278C23×C3—42no—
279C23×C3—44no—
280C23×C3—82no—
281C23×C3—82no—
282C23×C3—84no—
283C23×C3D3×D411yescharacteristic
284C23×C3C2×#6711yescharacteristic
285C3×Q8—34no—
286C3×Q8—64no—
287C3×Q8—62no—
288C3×D4—24no—
289C3×D4—24no—
290C3×D4—22no—
291C3×D4—22no—
292C3×D4—24no—
293C3×D4—42no—
294C3×D4—44no—
295C3×D4C2×C4×D314yes—
296C3×D4C22×Dic314yes—
297C2×C3×C4—21no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—34no—
302C2×C3×C4—64no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—244no—
306C2×C3×C4C2×C4×D312yes—
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23712yes—
310C2×C3×C4C22×Dic312yes—
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C23×D311yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×Dic3—24no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—84no—
320C2×Dic3—122no—
321C2×Dic3C2×#6714yes—
322Dic6—24no—
323Dic6—22no—
324Dic6C22×Dic314yes—
325C3×C8—32no—
326C3×C8—32no—
327C3⋊C8—62no—
328C3⋊C8—62no—
329C3⋊C8—122no—
330C3⋊C8C22×Dic312yes—
331C3⋊C8C22×Dic312yes—
332C2×C32—22no—
333C2×C32—44no—
334C2×C32C2×C4×D411yescharacteristic
335C2×C32#57712yes—
336C24—21no—
337C2×Q8—32no—
338C2×Q8—34no—
339C2×Q8—62no—
340C2×Q8—61no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4D3×Dic314yes—
344C2×D4C2×D3212yes—
345C22×C4—64no—
346C22×C4—61no—
347C22×C4C2×D3211yescharacteristic
348SD16—38no—
349SD16—38no—
350M16—182no—
351C2×C8—31no—
352C2×C8—31no—
353C2×C8—34no—
354C2×C8—92no—
355C4⋊C4—32no—
356C4⋊C4—32no—
357C4⋊C4—92no—
358C4⋊C4—184no—
359C22⋊C4—32no—
360C22⋊C4—64no—
361C22⋊C4—61no—
362C22⋊C4—181no—
363C42—32no—
364C42—61no—
365C42—184no—
366C42—181no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—24no—
370C22×C3—24no—
371C22×C3—21no—
372C22×C3—22no—
373C22×C3—42no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—44no—
377C22×C3—84no—
378C22×C3—84no—
379C22×C3—84no—
380C22×C3—88no—
381C22×C3C4×#6712yes—
382C22×C3D4×Dic312yes—
383C22×C3C2×D3×D411yescharacteristic
384C22×C3C22×#6711yescharacteristic
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—22no—
388C3×C4—64no—
389C3×C4—64no—
390C3×C4—122no—
391C3×C4C4×#6712yes—
392C3×C4D4×Dic312yes—
393C3×C4C22×C4×D311yescharacteristic
394C3×C4C2×#23511yescharacteristic
395C3×C4C2×#23711yescharacteristic
396C3×C4C23×Dic311yescharacteristic
397Dic3—24no—
398Dic3—24no—
399Dic3—42no—
400Dic3—122no—
401Dic3—122no—
402Dic3—242no—
403C32#294911yescharacteristic, complemented, Sylow
404C23—22no—
405C23—24no—
406C23—82no—
407C23D3×#6711yescharacteristic
408Q8—34no—
409Q8—62no—
410Q8—64no—
411D4—22no—
412D4—24no—
413D4C2×D3×Dic314yes—
414C2×C4—34no—
415C2×C4—62no—
416C2×C4—64no—
417C2×C4—62no—
418C2×C4—182no—
419C2×C4—244no—
420C2×C4C2×D3×Dic312yes—
421C2×C4#380412yes—
422C2×C4D3×#6711yescharacteristic
423C2×C4C22×D3211yescharacteristic
424C8—32no—
425C8—32no—
426C8—182no—
427C2×C3—22no—
428C2×C3—22no—
429C2×C3—22no—
430C2×C3—21no—
431C2×C3—42no—
432C2×C3—44no—
433C2×C3—44no—
434C2×C3—84no—
435C2×C3#576212yes—
436C2×C3C2×C4×#6711yescharacteristic
437C2×C3C2×D4×Dic311yescharacteristic
438C2×C3#583612yes—
439C22—22no—
440C22—24no—
441C22—44no—
442C22—84no—
443C22Dic3×#6712yes—
444C22C2×D3×#6711yescharacteristic
445C4—64no—
446C4—64no—
447C4—122no—
448C4—362no—
449C4Dic3×#6712yes—
450C4C22×D3×Dic311yescharacteristic
451C4C2×#380411yescharacteristic
452C3—21no—
453C3#8254311yescharacteristic, complemented
454C3#8384311yescharacteristic, complemented
455C2—22no—
456C2—44no—
457C2#1059510512yes—
458C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32#2949
LCSG ▷ 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
3. #10594818C2semidirect
5. #10591440C2semidirect
6. Dic3×#214C2semidirect
7. #10591122C2semidirect
8. #10591099C2semidirect
9. #10591055C2semidirect
19. C2×C3×#214C4semidirect
27. Dic3×Dic6C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
31. #63565C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
63. C2×C3×Dic6C2×C4semidirect
73. C3×#214C2×C4semidirect
74. C3×#214C2×C4semidirect
79. C2×C3×C3⋊C8C2×C4semidirect
104. C2×#214Dic3semidirect
193. C2×Dic6C2×Dic3semidirect
213. #214C2×Dic3semidirect
214. #214C2×Dic3semidirect
235. C2×C3⋊C8C2×Dic3semidirect
403. C32#2949semidirect
453. C3#82543semidirect
454. C3#83843semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C22×C3×#2142
#105948182
#105929142
#105914402
Dic3×#2142
#105911222
#105910992
#105910552
#838433
#825433