Finite Group Databasebeta

← #11860871

Subgroups — #11860871

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic
2#10595222C212yesmaximal, complemented
3D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×Dic3×D8C211yesmaximal, characteristic, complemented
5#10591446C212yesmaximal, complemented
6#10591440C212yesmaximal, complemented
7#10591414C212yesmaximal, complemented
8#10590818C211yesmaximal, characteristic, complemented
9Dic3×Dic12C211yesmaximal, characteristic, complemented
10#10590692C211yesmaximal, characteristic, complemented
11D3×#818C211yesmaximal, characteristic, complemented
12#83898—31nomaximal
13#79589—31nomaximal
14C2×C3×#237C2212yes—
15C2×C32×D8C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17C3×D4×Dic3C2212yes—
18C2×C3×#214C2212yes—
19C3×#912C418yescomplemented
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22#67⋊Dic3—22no—
23Dic3×#67—22no—
24C2×Dic3⋊Dic3—22no—
25#63955—22no—
26D3×C4⋊Dic3C2212yes—
27#63855C2211yescharacteristic
28#63843C2212yes—
29Dic3×Dic6C2212yes—
30C2×#3711C2211yescharacteristic
31#63659C2212yes—
32#63645C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C3×#832C2212yes—
35C3×#818C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37#63575C2212yes—
38#63566C2212yes—
39#63565C2212yes—
40#63555C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×C3×#135—31no—
43#5827—32no—
44C2×#912D311yescharacteristic
45#5546—32no—
46C3×C4×D8—31no—
47#5232—32no—
48Dic3×Q16—31no—
49Dic3×Q16—31no—
50#5164—32no—
51#5164—32no—
52Dic3×D8—31no—
53Dic3×D8—31no—
54Dic3×D8—61no—
55Dic3×D8D311yescharacteristic, complemented
56C2×#818—31no—
57#5101—31no—
58#5018—32no—
59D3×#107—31no—
60#4873—31no—
61#4771—32no—
62#4757—32no—
63C4×Dic12—31no—
64#4689—31no—
65C2×C32×D4C2312yes—
66C22×C3⋊Dic3—22no—
67C2×C3×#67—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C3×#237—24no—
71C3×#237C2×C418yescomplemented
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×D3×Dic3—22no—
75C32×D8C2×C414yescomplemented
76C2×C32×C8C2311yescharacteristic
77#3757—22no—
78C4⋊(C3⋊Dic3)C2312yes—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×#217—22no—
82C3×#214C2×C418yescomplemented
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×Dic12C2×C414yescomplemented
88C3×D3×C8C2×C414yescomplemented
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3D411yescharacteristic
93Dic3⋊Dic3D411yescharacteristic
94(C2×D3)⋊Dic3D411yescharacteristic
95(C2×D3)⋊Dic3D411yescharacteristic
96Dic32—22no—
97Dic32—22no—
98#3711—22no—
99#2951—91noSylow
100C2×C3×#41—32no—
101C2×#237C2×D312yes—
102C3×#135—38no—
103C2×C3×Q16—31no—
104C2×C3×SD16—32no—
105C2×C3×D8—21no—
106C2×C3×D8C2×D311yescharacteristic
107C2×C3×D8C2×D311yescharacteristic
108C22×C3×C8—31no—
109C3×C4×D4—32no—
110Q8×Dic3—32no—
111Q8×Dic3—32no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—62no—
115D4×Dic3—62no—
116D4×Dic3—62no—
117D4×Dic3C2×D312yes—
118C2×#214C2×D312yes—
119C4×#67—62no—
120#926—31no—
121#926—62no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—62no—
124C2×Dic3⋊C4—62no—
125C2×#208—31no—
126#912Dic318yescomplemented
127C2×Dic12C2×D311yescharacteristic
128C2×ΓL(1,𝔽25)—31no—
129C2×D3×C8C2×D311yescharacteristic
130D3×C4⋊C4—32no—
131#887—32no—
132#67⋊C4—62no—
133#877—62no—
134#872—31no—
135C4×Dic6—32no—
136C3×#107—31no—
137C3×#102—32no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#832—32no—
142#832—32no—
143#832—62no—
144#832C2×D312yes—
145#818—31no—
146#818—31no—
147#818—32no—
148#818—61no—
149#818C2×D311yescharacteristic
150#816—32no—
151#815—31no—
152#815—31no—
153#815—31no—
154C8×Dic3—31no—
155C8×Dic3—31no—
156C8×Dic3—61no—
157C8×Dic3C2×D311yescharacteristic
158#810—32no—
159#807—32no—
160#803—31no—
161C23×C32—22no—
162C22×C3×D3C2×D411yescharacteristic
163C32×D4—22no—
164C32×D4C22×C414yes—
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—82no—
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C3×#67—28no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—28no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—82no—
175C2×C3×Dic3C2×D411yescharacteristic
176C2×C3×Dic3C2×D411yescharacteristic
177C2×C3×Dic3C2×D411yescharacteristic
178C3×C4×D3C22×C412yes—
179C3×C4×D3#4112yes—
180C3×Dic6—22no—
181C3×Dic6C22×C414yes—
182D3×Dic3—82no—
183C32×C8C22×C412yes—
184C3⋊(C3⋊C8)—21no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C2×#135—31no—
188#520—92no—
189#440—92no—
190#440—92no—
191C4×Q16—91no—
192C4×Q16—91no—
193C4×D8—31no—
194C4×D8—91no—
195C2×#107—91no—
196#417—92no—
197#405—91no—
198C3×#41—38no—
199C3×#41—64no—
200C2×C3×Q8—32no—
201C2×C3×D4—22no—
202C2×C3×D4—62no—
203C2×C3×D4C22×D312yes—
204C2×C3×D4C22×D312yes—
205C22×C3×C4—31no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C2×#67—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—62no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—122no—
215#237—24no—
216#237C2×Dic318yescomplemented
217C2×C4×D3—62no—
218C2×C4×D3C22×D311yescharacteristic
219C2×Dic6C22×D312yes—
220C3×Q16—34no—
221C3×SD16—38no—
222C3×D8—24no—
223C3×D8C4×D314yescomplemented
224C3×D8C2×Dic314yescomplemented
225C2×C3×C8—21no—
226C2×C3×C8—31no—
227C2×C3×C8—34no—
228C2×C3×C8—31no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C3×C4⋊C4—32no—
232C3×C22⋊C4—62no—
233C3×C42—31no—
234#217—22no—
235#217—31no—
236#217—31no—
237#217—62no—
238#217—62no—
239#217—122no—
240#214C2×Dic318yescomplemented
241(C2×D3)⋊C4—31no—
242(C2×D3)⋊C4—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—31no—
253Dic3⋊C4—31no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257C4×Dic3—31no—
258C4×Dic3—31no—
259C4×Dic3—61no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3C22×D311yescharacteristic
265#208—62no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271Dic12C2×Dic314yescomplemented
272ΓL(1,𝔽25)—62no—
273D3×C8C2×Dic314yescomplemented
274C22×C32—24no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32C22×D411yescharacteristic
278C2×C3×D3—21no—
279C2×C3×D3—21no—
280C2×C3×D3C4×D412yes—
281C32×C4C23×C411yescharacteristic
282C32×C4C2×#4111yescharacteristic
283C3⋊Dic3—21no—
284C3⋊Dic3—21no—
285C3⋊Dic3—42no—
286C3×Dic3—24no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C2×#41—32no—
292#135—38no—
293C2×Q16—31no—
294C2×SD16—32no—
295C2×D8D3211yescharacteristic
296C2×M16—91no—
297C22×C8—31no—
298C4×Q8—92no—
299C4×Q8—92no—
300C4×D4—32no—
301C4×D4—92no—
302C4×D4—182no—
303C4×D4—182no—
304#117—91no—
305#117—182no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—182no—
308#107—31no—
309#107—92no—
310#107—91no—
311#103—92no—
312#103—92no—
313#102—32no—
314#102—92no—
315#97—91no—
316#97—91no—
317C4×C8—31no—
318C4×C8—91no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—31no—
322C23×C3—42no—
323C22×D3D3×D411yescharacteristic
324C3×Q8—34no—
325C3×Q8—62no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—24no—
329C3×D4—42no—
330C3×D4—68no—
331C3×D4C2×C4×D314yes—
332C3×D4C22×Dic314yes—
333C2×C3×C4—21no—
334C2×C3×C4—31no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—31no—
338C2×C3×C4—31no—
339C2×C3×C4—68no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—242no—
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—28no—
346C2×Dic3—22no—
347C2×Dic3—28no—
348C2×Dic3—22no—
349C2×Dic3—31no—
350C2×Dic3—31no—
351C2×Dic3—31no—
352C2×Dic3—31no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—82no—
358C2×Dic3—122no—
359C2×Dic3—242no—
360C2×Dic3—242no—
361C2×Dic3—242no—
362C2×Dic3—244no—
363C2×Dic3D3×D411yescharacteristic
364C2×Dic3D3×D411yescharacteristic
365C2×Dic3D3×D411yescharacteristic
366C4×D3—242no—
367C4×D3#23712yes—
368C4×D3C22×Dic312yes—
369Dic6—22no—
370Dic6C22×Dic314yes—
371C3×C8—22no—
372C3×C8—32no—
373C3×C8—61no—
374C3×C8C2×C4×D312yes—
375C3×C8C22×Dic312yes—
376C3⋊C8—21no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—121no—
380C3⋊C8C22×Dic312yes—
381C2×C32—44no—
382C2×C32C2×C4×D411yescharacteristic
383C2×C32#57611yescharacteristic
384C2×C32#57811yescharacteristic
385C3×D3—22no—
386#41—38no—
387#41—64no—
388C2×Q8—32no—
389C2×D4—62no—
390C2×D4C2×D3212yes—
391C22×C4—31no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—182no—
395C22×C4—182no—
396Q16—34no—
397SD16—38no—
398D8D3×Dic314yescomplemented
399M16—182no—
400C2×C8—31no—
401C2×C8—34no—
402C2×C8—31no—
403C2×C8—91no—
404C2×C8C2×D3211yescharacteristic
405C4⋊C4—32no—
406C4⋊C4—91no—
407C4⋊C4—91no—
408C4⋊C4—92no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C22⋊C4—62no—
413C22⋊C4—91no—
414C22⋊C4—91no—
415C22⋊C4—182no—
416C42—31no—
417C42—91no—
418C42—182no—
419C42—182no—
420C22×C3—24no—
421C22×C3—24no—
422C22×C3—21no—
423C22×C3—32no—
424C22×C3—44no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—61no—
430C22×C3—61no—
431C22×C3—82no—
432C22×C3—82no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C2×D3×D411yescharacteristic
435C2×D3—21no—
436C2×D3—21no—
437C2×D3D4×Dic312yes—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—32no—
441C3×C4—61no—
442C3×C4—61no—
443C3×C4—64no—
444C3×C4—122no—
445C3×C4C22×C4×D311yescharacteristic
446C3×C4C2×#23711yescharacteristic
447C3×C4D3×#4111yescharacteristic
448C3×C4C23×Dic311yescharacteristic
449Dic3—21no—
450Dic3—21no—
451Dic3—24no—
452Dic3—42no—
453Dic3—62no—
454Dic3—61no—
455Dic3—61no—
456Dic3—61no—
457Dic3—61no—
458Dic3—121no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462Dic3D4×Dic312yes—
463C32#295111yescharacteristic, complemented, Sylow
464C23—22no—
465C23—31no—
466Q8—34no—
467Q8—62no—
468D4—22no—
469D4—68no—
470D4C2×D3×Dic314yes—
471C2×C4—31no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—68no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—91no—
480C2×C4—91no—
481C2×C4—182no—
482C2×C4—242no—
483C2×C4—722no—
484C2×C4—722no—
485C2×C4C22×D3211yescharacteristic
486C8—32no—
487C8—61no—
488C8—181no—
489C8C2×D3×Dic312yes—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—44no—
494C2×C3—44no—
495C2×C3—62no—
496C2×C3—84no—
497C2×C3C4×D3×D411yescharacteristic
498C2×C3#575711yescharacteristic
499C2×C3#576911yescharacteristic
500C2×C3#577111yescharacteristic
501C2×C3#577111yescharacteristic
502C2×C3C2×D4×Dic311yescharacteristic
503D3—22no—
504C22—24no—
505C22—32no—
506C22—42no—
507C22—42no—
508C22—61no—
509C22—61no—
510C22D32×D411yescharacteristic
511C4—32no—
512C4—64no—
513C4—61no—
514C4—61no—
515C4—122no—
516C4—181no—
517C4—181no—
518C4—362no—
519C4D3×#23711yescharacteristic
520C4C22×D3×Dic311yescharacteristic
521C3—21no—
522C3#7958911yescharacteristic, complemented
523C3#8389811yescharacteristic, complemented
524C2—44no—
525C2—62no—
526C2#1059473411yescharacteristic
527C2#1059473711yescharacteristic
528C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×C3×#912C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10595222C2semidirect
3. D8×C3⋊Dic3C2semidirect
4. C3×Dic3×D8C2semidirect
5. #10591446C2semidirect
6. #10591440C2semidirect
7. #10591414C2semidirect
8. #10590818C2semidirect
9. Dic3×Dic12C2semidirect
10. #10590692C2semidirect
11. D3×#818C2semidirect
19. C3×#912C4semidirect
55. Dic3×D8D3semidirect
71. C3×#237C2×C4semidirect
75. C32×D8C2×C4semidirect
82. C3×#214C2×C4semidirect
87. C3×Dic12C2×C4semidirect
88. C3×D3×C8C2×C4semidirect
126. #912Dic3semidirect
216. #237C2×Dic3semidirect
223. C3×D8C4×D3semidirect
224. C3×D8C2×Dic3semidirect
240. #214C2×Dic3semidirect
271. Dic12C2×Dic3semidirect
273. D3×C8C2×Dic3semidirect
398. D8D3×Dic3semidirect
463. C32#2951semidirect
522. C3#79589semidirect
523. C3#83898semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
#105952222
D8×C3⋊Dic32
C3×Dic3×D82
#105914462
#105914402
#105914142
#105908182
Dic3×Dic122
#105906922
D3×#8182
#838983
#795893